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![4.4.5. XRT Analysis
The temporal coverage of each time-averaged XRT spectrum
(generated in Section 2.4.1) is shown as “s1,” “s2,” ..., “s9” in
the lower panel of Figure 8. We fitted the 0.3–10 keV spectra
using a simple model of tbabs*
zashift*
(diskbb
+powerlaw). We did not include the ztbabs component,
as host galaxy absorption was found to be negligible or much
smaller than the Galactic absorption in all previous spectral
analyses (see Tables 4, 5, 6, and 1). The adopted continuum
model does not give realistic model parameters. For example,
the disk radii will be underestimated when the source spectrum
is hard (see a detailed discussion in Steiner et al. 2009). The
main goal of this fitting is to compute the multiplicative factor
to convert the 0.3–10 keV XRT net count rate to X-ray fluxes,
including (i) the observed 0.3–10 keV flux fX(0.3–10 keV), (ii)
the Galactic absorption corrected 0.3–10 keV flux fX, 0
(0.3–10 keV), (iii) the Galactic absorption corrected
0.5–10 keV flux fX, 0 (0.5–10 keV), and (iv) the Galactic
absorption corrected flux density at the rest-frame energies of
0.5 keV and 2 keV (i.e., fν(0.5 keV) and fν(2 keV)). All data
were fitted using C-statistics.
The best-fit models are shown in Figure 15. Scaling factors to
convert 0.3–10 keV net count rate to X-ray fluxes can be computed
using values provided in Table 11 (Appendix A.2). The observed
isotropic equivalent 0.3–10 keV X-ray luminosity, LX, is shown in
the upper panel of Figure 16. Note that for the initial four XRT
nondetections, we assume a spectral shape similar to “s1.”
4.4.6. NICER Analysis
We started with the obsID-binned NICER spectra generated
in Section 2.5. We only performed spectral fitting on obsIDs
with more than 500 total net counts in 0.3–4 keV. Following
Section 4.4.5, we fitted a tbabs*
zashift*
(diskbb
+powerlaw) model to the 0.3–4 keV spectra and inferred
fX from the best-fit models. All data were fitted using
χ2
-statistics. The best-fit models provided a cr
2
close to 1 in
most cases. The LX evolution inferred from NICER spectral
fitting is also shown in the upper panel of Figure 16.
4.5. Spectral Indices αOX and αOSX
To assist comparison with TDEs from the literature, we
computed the UV to X-ray spectral index αOX (Tananbaum
et al. 1979; Ruan et al. 2019; Wevers et al. 2021) and αOSX
(Gezari 2021), which are commonly used in AGN and TDE
literature to characterize the ratio of UV to X-ray fluxes.32
Here
a
n n
º n n
L L
log 2500 Å 2 keV
log 2500 Å 2 keV
, 3
OX
[ ( ) ( )]
[ ( ) ( )]
( )
a
n n
º n n
L L
log 2500 Å 0.5 keV
log 2500 Å 0.5 keV
, 4
OSX
[ ( ) ( )]
[ ( ) ( )]
( )
where Lν is the luminosity at a certain frequency (corrected for
NH and EB−V,MW). We use the Swiftuvw1 host-subtracted
luminosities (rest-frame effective wavelength at 2459 Å for
Teff = 3 × 104
K) as a proxy for Lν(2500 Å). We measure
fν(0.5 keV) and fν(2 keV) by converting the XRT net count
rates to flux densities using the scaling factors derived in
Section 4.4.5. We note that fν(2 keV) mainly traces the
evolution of the nonthermal X-ray component, while
fν(0.5 keV) traces both the thermal and nonthermal compo-
nents. The results are shown in the lower panel of Figure 16.
Based on Figure 16, we divide the evolution of AT2021ehb
into five phases. In phase A (δt 0 days), the UV/optical
luminosity brightens, while X-rays are not detected
Figure 14. SRG/eROSITA spectra of AT2021ehb.
Table 7
Modeling of Two SRG/eROSITA Observations
Component Parameter eRASS4 eRASS5
ztbabs NH (1020
cm−2
) -
+
0.21 0.20
2.19
<3.41
diskbb Tin (eV) -
+
89 13
7
-
+
96 22
32
Rin
* (104
km) -
+
210 38
179
-
+
73 21
243
simpl Γ -
+
4.15 0.73
0.82
2.92 (frozen)
fsc -
+
0.14 0.08
0.12
-
+
0.21 0.09
0.06
L cstat/dof 126.43/140 76.45/85
Figure 15. XRT time-averaged spectra of AT2021ehb. See the lower panel of
Figure 8 for the time span of each spectrum.
32
Note that some papers use these indices with a minus sign in front of our
definitions.
14
The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.](https://image.slidesharecdn.com/yao2022apj9378-221221021109-4f182974/75/The-Tidal-Disruption-Event-AT2021ehb-Evidence-of-Relativistic-Disk-Reflection-and-Rapid-Evolution-of-the-Disk-Corona-System-14-2048.jpg)
![the hardness–intensity diagram (HID; see Figure 22), the
evolution of AT2021ehb is neither similar to the “turtlehead”
pattern observed in XRBs (Fender et al. 2004; Munoz-Darias
et al. 2013; Tetarenko et al. 2016), nor similar to the “brighter
when softer” trend observed in X-ray bright AGNs (Auchettl
et al. 2018). On the Lbol–αOX diagram (Figure 19), its evolution
is also different from that observed in CLAGNs (Ruan et al.
2019). Second, in the canonical hard state (i.e., sub-Eddington
accretion rates), there is a correlation among radio luminosity,
X-ray luminosity, and MBH, which applies to both XRBs and
hard-state AGNs (Merloni et al. 2003; Falcke et al. 2004). A
recent fit to this “fundamental plane of black hole activity” was
provided by Gültekin et al. (2019):
= - -
- - -
+
R M
X
1.09 0.10 log 1 0.55 0.22
0.59 , 8
7
0.15
0.16
( ) ( ) ( )
( ) ( )
where º -
R L
log 10 erg s
5 GHz
38 1
[ ( )] and º -
X L
log 2 10 keV
[
-
10 erg s
40 1
( )]. In the hard state of AT2021ehb, the 2–10 keV
luminosity in the Swift/XRT “s6” spectrum gives X =
2.96 ± 0.02. Using Equation (8), the expected 5 GHz
radio luminosity on the fundamental plane is L
log 5 GHz
[
= + =
- R
erg s 38 38.21 0.59
1
( )] . The uncertainty of R
is calculated from the distribution of 105
MC trials. Using our
radio limit at δt = 228 days (Table 2) and assuming a flat radio
spectrum of fν ∝ ν0
, we find a 5 GHz equivalent radio upper
limit of <
-
L
log erg s 35.76
5 GHz
1
[ ( )] . According to Gültekin
et al. (2019), the scatter on the fundamental plane correlation is
a factor of ∼7.6 in the L5 GHz direction (or ∼10 in the MBH
direction), which is not enough to solve the discrepancy. This
again argues that AT2021ehb is not in a canonical hard state
where we would expect a radio jet to be launched.
The radio behavior of BH binaries at the Eddington accretion
rates might be more relevant to AT2021ehb (at least in phases
B–D). A few XRBs get above the Eddington limit for brief
periods, when they are seen to undergo a sequence of bright
radio flares for a short period of time. Examples include the
2015 outburst of V404 Cygni (Tetarenko et al. 2017, 2019) and
the ultraluminous X-ray source in M31 (Middleton et al. 2013).
In AT2021ehb, the slow cadence of our radio follow-up
observations does not allow us to rule out the existence of such
radio flares, which last for hours to weeks, not months.
Finally, we note that the evolution of the X-ray properties of
AT2021ehb are different from a few other TDEs. For example,
Wevers et al. (2021) constructed the logλEdd–αOX diagram for
AT2018fyk, finding that the 2 keV (corona) emission is
stronger when λEdd is lower. Figure 19 shows that this is
clearly not the case for AT2021ehb. Separately, Hinkle et al.
(2021) studied the evolution of AT2019azh on the canonical
HID, showing that when the X-ray luminosity is higher, the
X-ray spectrum is softer. Figure 22 shows that AT2021ehb
does not follow this trend either. It remains to be seen whether
AT2021ehb is peculiar among the sample of optically selected
TDEs with significant X-ray spectral evolution. To this end,
constructing a systematically selected sample and analyzing the
multiwavelength data in a homogeneous fashion is the key.
6. Conclusion
We have presented an extensive multiwavelength study of
the TDE AT2021ehb. Its peak 0.3–10 keV flux of∼1 mCrab is
brighter than any other non-jetted TDE in the literature,
allowing us to obtain a series of high-quality X-ray spectra,
including the first hard X-ray spectrum of a non-jetted TDE up
to 30 keV. The detection of hard X-ray photons favors a highly
aspherical geometry (Section 5.2), and detailed modeling of the
NICER +NuSTAR spectrum shows evidence of relativistic
disk reflection (Section 4.4.2).
The emission from the self-crossing shock itself might
contribute to the early-time UV/optical emission, while the
post-peak (phase C–E) emission is either dominated by
reprocessing of X-ray photons by the outflow launched from
the shock, or by thermal emission in the outer regions of an
accretion flow (Section 5.4.2). More detailed hydrodynamic
and radiative transfer calculations (e.g., Roth et al. 2016) are
needed to test if such scenarios can reproduce the observed
UV/optical plateau and the featureless optical spectra.
We observed a soft → hard → soft spectral transition in the
X-ray. The initial soft-to-hard transition happened gradually
over ∼170 days. A possible explanation is that magnetic fields
grow with time due to differential rotation, resulting in the
formation of a magnetically dominated hot corona
(Section 5.3.1). The bolometric luminosity of AT2021ehb is
the highest when the X-ray spectrum is the hardest—a property
that is different from XRBs, X-ray bright AGNs, and many
other TDEs (Section 5.5). The latter hard-to-soft transition
happened drastically within 3 days at δt≈272 days, and might
be due to thermal–viscous instability in the inner disk
(Section 5.3.2). Such an instability typically occurs when
Lbol∼0.3LEdd (Tchekhovskoy et al. 2014). This requires that
most of the luminosity of AT2021ehb is emitted in the EUV
band that is not observed.
Systems similar to AT2021ehb are excellent targets for
X-ray telescopes to study the real-time formation of the
accretion disk and corona around MBHs. The detection of
relativistic disk reflection features demonstrates the possibility
of constraining the spin of normally quiescent MBHs via
reflection spectroscopy—an opportunity enabled by combining
modern time-domain surveys with systematic multiwavelength
follow-up observations.
Figure 22. Galactic extinction-corrected 0.3–10 keV X-ray luminosity (LX, 0)
as a function of hardness ratio for Swift/XRT detections only.
19
The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.](https://image.slidesharecdn.com/yao2022apj9378-221221021109-4f182974/75/The-Tidal-Disruption-Event-AT2021ehb-Evidence-of-Relativistic-Disk-Reflection-and-Rapid-Evolution-of-the-Disk-Corona-System-19-2048.jpg)
![4.4.5. XRT Analysis
The temporal coverage of each time-averaged XRT spectrum
(generated in Section 2.4.1) is shown as “s1,” “s2,” ..., “s9” in
the lower panel of Figure 8. We fitted the 0.3–10 keV spectra
using a simple model of tbabs*
zashift*
(diskbb
+powerlaw). We did not include the ztbabs component,
as host galaxy absorption was found to be negligible or much
smaller than the Galactic absorption in all previous spectral
analyses (see Tables 4, 5, 6, and 1). The adopted continuum
model does not give realistic model parameters. For example,
the disk radii will be underestimated when the source spectrum
is hard (see a detailed discussion in Steiner et al. 2009). The
main goal of this fitting is to compute the multiplicative factor
to convert the 0.3–10 keV XRT net count rate to X-ray fluxes,
including (i) the observed 0.3–10 keV flux fX(0.3–10 keV), (ii)
the Galactic absorption corrected 0.3–10 keV flux fX, 0
(0.3–10 keV), (iii) the Galactic absorption corrected
0.5–10 keV flux fX, 0 (0.5–10 keV), and (iv) the Galactic
absorption corrected flux density at the rest-frame energies of
0.5 keV and 2 keV (i.e., fν(0.5 keV) and fν(2 keV)). All data
were fitted using C-statistics.
The best-fit models are shown in Figure 15. Scaling factors to
convert 0.3–10 keV net count rate to X-ray fluxes can be computed
using values provided in Table 11 (Appendix A.2). The observed
isotropic equivalent 0.3–10 keV X-ray luminosity, LX, is shown in
the upper panel of Figure 16. Note that for the initial four XRT
nondetections, we assume a spectral shape similar to “s1.”
4.4.6. NICER Analysis
We started with the obsID-binned NICER spectra generated
in Section 2.5. We only performed spectral fitting on obsIDs
with more than 500 total net counts in 0.3–4 keV. Following
Section 4.4.5, we fitted a tbabs*
zashift*
(diskbb
+powerlaw) model to the 0.3–4 keV spectra and inferred
fX from the best-fit models. All data were fitted using
χ2
-statistics. The best-fit models provided a cr
2
close to 1 in
most cases. The LX evolution inferred from NICER spectral
fitting is also shown in the upper panel of Figure 16.
4.5. Spectral Indices αOX and αOSX
To assist comparison with TDEs from the literature, we
computed the UV to X-ray spectral index αOX (Tananbaum
et al. 1979; Ruan et al. 2019; Wevers et al. 2021) and αOSX
(Gezari 2021), which are commonly used in AGN and TDE
literature to characterize the ratio of UV to X-ray fluxes.32
Here
a
n n
º n n
L L
log 2500 Å 2 keV
log 2500 Å 2 keV
, 3
OX
[ ( ) ( )]
[ ( ) ( )]
( )
a
n n
º n n
L L
log 2500 Å 0.5 keV
log 2500 Å 0.5 keV
, 4
OSX
[ ( ) ( )]
[ ( ) ( )]
( )
where Lν is the luminosity at a certain frequency (corrected for
NH and EB−V,MW). We use the Swiftuvw1 host-subtracted
luminosities (rest-frame effective wavelength at 2459 Å for
Teff = 3 × 104
K) as a proxy for Lν(2500 Å). We measure
fν(0.5 keV) and fν(2 keV) by converting the XRT net count
rates to flux densities using the scaling factors derived in
Section 4.4.5. We note that fν(2 keV) mainly traces the
evolution of the nonthermal X-ray component, while
fν(0.5 keV) traces both the thermal and nonthermal compo-
nents. The results are shown in the lower panel of Figure 16.
Based on Figure 16, we divide the evolution of AT2021ehb
into five phases. In phase A (δt 0 days), the UV/optical
luminosity brightens, while X-rays are not detected
Figure 14. SRG/eROSITA spectra of AT2021ehb.
Table 7
Modeling of Two SRG/eROSITA Observations
Component Parameter eRASS4 eRASS5
ztbabs NH (1020
cm−2
) -
+
0.21 0.20
2.19
<3.41
diskbb Tin (eV) -
+
89 13
7
-
+
96 22
32
Rin
* (104
km) -
+
210 38
179
-
+
73 21
243
simpl Γ -
+
4.15 0.73
0.82
2.92 (frozen)
fsc -
+
0.14 0.08
0.12
-
+
0.21 0.09
0.06
L cstat/dof 126.43/140 76.45/85
Figure 15. XRT time-averaged spectra of AT2021ehb. See the lower panel of
Figure 8 for the time span of each spectrum.
32
Note that some papers use these indices with a minus sign in front of our
definitions.
14
The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.](https://crownmelresort.com/image.slidesharecdn.com/yao2022apj9378-221221021109-4f182974/75/The-Tidal-Disruption-Event-AT2021ehb-Evidence-of-Relativistic-Disk-Reflection-and-Rapid-Evolution-of-the-Disk-Corona-System-14-2048.jpg)
![the hardness–intensity diagram (HID; see Figure 22), the
evolution of AT2021ehb is neither similar to the “turtlehead”
pattern observed in XRBs (Fender et al. 2004; Munoz-Darias
et al. 2013; Tetarenko et al. 2016), nor similar to the “brighter
when softer” trend observed in X-ray bright AGNs (Auchettl
et al. 2018). On the Lbol–αOX diagram (Figure 19), its evolution
is also different from that observed in CLAGNs (Ruan et al.
2019). Second, in the canonical hard state (i.e., sub-Eddington
accretion rates), there is a correlation among radio luminosity,
X-ray luminosity, and MBH, which applies to both XRBs and
hard-state AGNs (Merloni et al. 2003; Falcke et al. 2004). A
recent fit to this “fundamental plane of black hole activity” was
provided by Gültekin et al. (2019):
= - -
- - -
+
R M
X
1.09 0.10 log 1 0.55 0.22
0.59 , 8
7
0.15
0.16
( ) ( ) ( )
( ) ( )
where º -
R L
log 10 erg s
5 GHz
38 1
[ ( )] and º -
X L
log 2 10 keV
[
-
10 erg s
40 1
( )]. In the hard state of AT2021ehb, the 2–10 keV
luminosity in the Swift/XRT “s6” spectrum gives X =
2.96 ± 0.02. Using Equation (8), the expected 5 GHz
radio luminosity on the fundamental plane is L
log 5 GHz
[
= + =
- R
erg s 38 38.21 0.59
1
( )] . The uncertainty of R
is calculated from the distribution of 105
MC trials. Using our
radio limit at δt = 228 days (Table 2) and assuming a flat radio
spectrum of fν ∝ ν0
, we find a 5 GHz equivalent radio upper
limit of <
-
L
log erg s 35.76
5 GHz
1
[ ( )] . According to Gültekin
et al. (2019), the scatter on the fundamental plane correlation is
a factor of ∼7.6 in the L5 GHz direction (or ∼10 in the MBH
direction), which is not enough to solve the discrepancy. This
again argues that AT2021ehb is not in a canonical hard state
where we would expect a radio jet to be launched.
The radio behavior of BH binaries at the Eddington accretion
rates might be more relevant to AT2021ehb (at least in phases
B–D). A few XRBs get above the Eddington limit for brief
periods, when they are seen to undergo a sequence of bright
radio flares for a short period of time. Examples include the
2015 outburst of V404 Cygni (Tetarenko et al. 2017, 2019) and
the ultraluminous X-ray source in M31 (Middleton et al. 2013).
In AT2021ehb, the slow cadence of our radio follow-up
observations does not allow us to rule out the existence of such
radio flares, which last for hours to weeks, not months.
Finally, we note that the evolution of the X-ray properties of
AT2021ehb are different from a few other TDEs. For example,
Wevers et al. (2021) constructed the logλEdd–αOX diagram for
AT2018fyk, finding that the 2 keV (corona) emission is
stronger when λEdd is lower. Figure 19 shows that this is
clearly not the case for AT2021ehb. Separately, Hinkle et al.
(2021) studied the evolution of AT2019azh on the canonical
HID, showing that when the X-ray luminosity is higher, the
X-ray spectrum is softer. Figure 22 shows that AT2021ehb
does not follow this trend either. It remains to be seen whether
AT2021ehb is peculiar among the sample of optically selected
TDEs with significant X-ray spectral evolution. To this end,
constructing a systematically selected sample and analyzing the
multiwavelength data in a homogeneous fashion is the key.
6. Conclusion
We have presented an extensive multiwavelength study of
the TDE AT2021ehb. Its peak 0.3–10 keV flux of∼1 mCrab is
brighter than any other non-jetted TDE in the literature,
allowing us to obtain a series of high-quality X-ray spectra,
including the first hard X-ray spectrum of a non-jetted TDE up
to 30 keV. The detection of hard X-ray photons favors a highly
aspherical geometry (Section 5.2), and detailed modeling of the
NICER +NuSTAR spectrum shows evidence of relativistic
disk reflection (Section 4.4.2).
The emission from the self-crossing shock itself might
contribute to the early-time UV/optical emission, while the
post-peak (phase C–E) emission is either dominated by
reprocessing of X-ray photons by the outflow launched from
the shock, or by thermal emission in the outer regions of an
accretion flow (Section 5.4.2). More detailed hydrodynamic
and radiative transfer calculations (e.g., Roth et al. 2016) are
needed to test if such scenarios can reproduce the observed
UV/optical plateau and the featureless optical spectra.
We observed a soft → hard → soft spectral transition in the
X-ray. The initial soft-to-hard transition happened gradually
over ∼170 days. A possible explanation is that magnetic fields
grow with time due to differential rotation, resulting in the
formation of a magnetically dominated hot corona
(Section 5.3.1). The bolometric luminosity of AT2021ehb is
the highest when the X-ray spectrum is the hardest—a property
that is different from XRBs, X-ray bright AGNs, and many
other TDEs (Section 5.5). The latter hard-to-soft transition
happened drastically within 3 days at δt≈272 days, and might
be due to thermal–viscous instability in the inner disk
(Section 5.3.2). Such an instability typically occurs when
Lbol∼0.3LEdd (Tchekhovskoy et al. 2014). This requires that
most of the luminosity of AT2021ehb is emitted in the EUV
band that is not observed.
Systems similar to AT2021ehb are excellent targets for
X-ray telescopes to study the real-time formation of the
accretion disk and corona around MBHs. The detection of
relativistic disk reflection features demonstrates the possibility
of constraining the spin of normally quiescent MBHs via
reflection spectroscopy—an opportunity enabled by combining
modern time-domain surveys with systematic multiwavelength
follow-up observations.
Figure 22. Galactic extinction-corrected 0.3–10 keV X-ray luminosity (LX, 0)
as a function of hardness ratio for Swift/XRT detections only.
19
The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.](https://crownmelresort.com/image.slidesharecdn.com/yao2022apj9378-221221021109-4f182974/75/The-Tidal-Disruption-Event-AT2021ehb-Evidence-of-Relativistic-Disk-Reflection-and-Rapid-Evolution-of-the-Disk-Corona-System-19-2048.jpg)
Uploaded bySérgio Sacani
The Tidal Disruption Event AT2021ehb: Evidence of Relativistic Disk Reflection, and Rapid Evolution of the Disk–Corona System
The document discusses the tidal disruption event AT2021ehb, focusing on its X-ray, UV, optical, and radio observations over 430 days. The research provides insights into the evolution of the disk-corona system, revealing significant changes in spectral states and a prominent nonthermal component in the X-ray spectrum. It also proposes interpretations for the observed transitions and variations in luminosity, contributing to the understanding of accretion dynamics around supermassive black holes.
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The Tidal Disruption Event AT2021ehb: Evidence of Relativistic Disk Reflection, and Rapid Evolution of the Disk–Corona System
- 1. The Tidal DisruptionEvent AT2021ehb: Evidence of Relativistic Disk Reflection, and Rapid Evolution of the Disk–Corona System Yuhan Yao1 , Wenbin Lu2,3 , Muryel Guolo4 , Dheeraj R. Pasham5 , Suvi Gezari6 , Marat Gilfanov7,8 , Keith C. Gendreau9 , Fiona Harrison1 , S. Bradley Cenko9 , S. R. Kulkarni1 , Jon M. Miller10 , Dominic J. Walton11,12 , Javier A. García1,13 , Sjoert van Velzen14 , Kate D. Alexander15 , James C. A. Miller-Jones16 , Matt Nicholl17 , Erica Hammerstein18 , Pavel Medvedev7 , Daniel Stern19 , Vikram Ravi1 , R. Sunyaev7,8 , Joshua S. Bloom3,20 , Matthew J. Graham1 , Erik C. Kool21 , Ashish A. Mahabal1,22 , Frank J. Masci23 , Josiah Purdum24 , Ben Rusholme23 , Yashvi Sharma1 , Roger Smith24 , and Jesper Sollerman21 1 Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA; yyao@astro.caltech.edu 2 Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton, NJ 08544, USA 3 Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA 4 Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA 5 Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 6 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 7 Space Research Institute, Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow, 117997, Russia 8 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany 9 Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 10 Department of Astronomy, The University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48103, USA 11 Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK 12 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 13 Dr. Karl Remeis-Observatory and Erlangen Centre for Astroparticle Physics, Sternwartstr. 7, D-96049 Bamberg, Germany 14 Leiden Observatory, Leiden University, Postbus 9513, 2300 RA, Leiden, The Netherlands 15 Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA 16 International Centre for Radio Astronomy Research, Curtin University, GPO Box U1987, Perth, WA 6845, Australia 17 Birmingham Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK 18 Department of Astronomy, University of Maryland, College Park, MD 20742, USA 19 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA 20 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50B-4206, Berkeley, CA 94720, USA 21 The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, SE-10691, Stockholm, Sweden 22 Center for Data Driven Discovery, California Institute of Technology, Pasadena, CA 91125, USA 23 IPAC, California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA 91125, USA 24 Caltech Optical Observatories, California Institute of Technology, Pasadena, CA 91125, USA Received 2022 June 25; revised 2022 August 11; accepted 2022 August 11; published 2022 September 15 Abstract We present X-ray, UV, optical, and radio observations of the nearby (≈78 Mpc) tidal disruption event AT2021ehb/ZTF21aanxhjv during its first 430 days of evolution. AT2021ehb occurs in the nucleus of a galaxy hosting a≈107 Me black hole (MBH inferred from host galaxy scaling relations). High-cadence Swift and Neutron Star Interior Composition Explorer (NICER) monitoring reveals a delayed X-ray brightening. The spectrum first undergoes a gradual soft → hard transition and then suddenly turns soft again within 3 days at δt≈272 days during which the X-ray flux drops by a factor of 10. In the joint NICER+NuSTAR observation (δt = 264 days, harder state), we observe a prominent nonthermal component up to 30 keV and an extremely broad emission line in the iron K band. The bolometric luminosity of AT2021ehb reaches a maximum of - + L 6.0 % 3.8 10.4 Edd when the X-ray spectrum is the hardest. During the dramatic X-ray evolution, no radio emission is detected, the UV/optical luminosity stays relatively constant, and the optical spectra are featureless. We propose the following interpretations: (i) the soft → hard transition may be caused by the gradual formation of a magnetically dominated corona; (ii) hard X-ray photons escape from the system along solid angles with low scattering optical depth (∼a few) whereas the UV/optical emission is likely generated by reprocessing materials with much larger column density—the system is highly aspherical; and (iii) the abrupt X-ray flux drop may be triggered by the thermal–viscous instability in the inner accretion flow, leading to a much thinner disk. Unified Astronomy Thesaurus concepts: Tidal disruption (1696); X-ray transient sources (1852); Supermassive black holes (1663); Time domain astronomy (2109); High energy astrophysics (739); Accretion (14) Supporting material: machine-readable table 1. Introduction A star getting too close to a massive black hole (MBH) can get disrupted by the tidal forces in a tidal disruption event (TDE; see recent review by Gezari 2021). The first observa- tional evidence for TDEs came from the detection of X-ray The Astrophysical Journal, 937:8 (25pp), 2022 September 20 https://doi.org/10.3847/1538-4357/ac898a © 2022. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1
- 2. flares from thecenters of quiescent galaxies during the ROSAT (0.1–2.4 keV) all-sky survey (RASS) in 1990–1991 (Donley et al. 2002). The flares exhibit soft spectra that are consistent with blackbody radiation with temperatures Tbb ∼ 106 K and radii Rbb ∼ few × 1011 cm (Saxton et al. 2020). Since 2020, the Spektrum–Roentgen–Gamma (SRG) mission (Sunyaev et al. 2021), with its sensitive eROSITA telescope (0.2–8 keV; Predehl et al. 2021) and 6 month cadenced all-sky surveys, has become the most prolific discoverer of TDEs in X-rays. The majority of X-ray-selected TDEs are faint in the optical (Sazonov et al. 2021). In the UV and optical sky, TDEs have been identified as blue nuclear transients in surveys such as the Galaxy Evolution Explorer (Martin et al. 2005), the Panoramic Survey Telescope and Rapid Response System DR1 (Pan-STARRS, PS1; Flewelling et al. 2020; Waters et al. 2020), the Sloan Digital Sky Survey (SDSS, Alam et al. 2015), the All-Sky Automated Survey for SuperNovae (ASAS-SN; Shappee et al. 2014), the Palomar Transient Factory (PTF; Law et al. 2009; Rau et al. 2009), the intermediate PTF (iPTF), the Asteroid Terrestrial- impact Last Alert System (Tonry et al. 2018), and the Zwicky Transient Facility (ZTF; Bellm et al. 2019; Graham et al. 2019). In most cases, the UV/optical spectral energy distribu- tion (SED) can be described by blackbody radiation with larger radii (Rbb ∼ few × 1014 cm) and lower temperatures (Tbb ∼ few × 104 K) than those of the X-ray discovered events. The origin of this blackbody component has been attributed to reprocessing of disk emission by an optically thick gas layer (Metzger & Stone 2016; Roth et al. 2016; Lu & Bon- nerot 2020), stream self-intersecting shocks formed as a result of general relativistic apsidal precession (Piran et al. 2015; Jiang et al. 2016), or intrinsic thermal emission from the viscously heated accretion disk (Wevers et al. 2021). Among the UV/optically selected TDEs with simultaneous X-ray observations, about two dozen events have been detected in the X-rays (e.g., Auchettl et al. 2017; Wevers 2020). Their X-ray light curves show a wide range of properties. For example, the X-ray emission of ASASSN-14li lags behind its UV/optical emission by 1 month (Pasham et al. 2017); ASASSN-15oi, AT2018fyk, and AT2019azh exhibit a gradual X-ray brightening long after the UV/optical peak (Gezari et al. 2017; Wevers et al. 2021; Hinkle et al. 2021); AT2019ehz and OGLE16aaa show extreme X-ray flares on a timescale of a few days (van Velzen et al. 2021; Kajava et al. 2020; Shu et al. 2020); and the probable neutrino emitter AT2019dsg has a rapid X-ray decline (Stein et al. 2021). Understanding the coevolution between the X-ray and UV/optical emission may hold the key in deciphering the origin of these two components. The majority of TDEs are not associated with on-axis relativistic jets (hereafter non-jetted TDEs; Alexander et al. 2020). The sample of jetted TDEs includes four objects: Sw J1644+57 (Bloom et al. 2011; Burrows et al. 2011; Zauderer et al. 2011), Sw J2058+05 (Cenko et al. 2012; Pasham et al. 2015), and Sw J1112−82 (Brown et al. 2015) were discovered by the hard X-ray Burst Alert Telescope on board Swift, whereas AT2022cmc was discovered by ZTF in the optical (Andreoni et al. 2022; Yao et al. 2022a; Pasham et al. 2022). Among them, Sw J1644+57 is the most well studied. Its fast X-ray variability and extremely high isotropic equivalent X-ray luminosity (∼1047 erg s−1 ) suggest that the early-time X-rays are powered by internal dissipation within a jet. A sudden X-ray flux drop by a factor of ∼102 indicates a jet shut off at rest-frame 370 days after discovery (Zauderer et al. 2013), after which the X-ray emission is consistent with being powered by a forward shock (Eftekhari et al. 2018; Cendes et al. 2021b). During the outburst of a stellar-mass black hole X-ray binary (XRB), as the mass accretion rate (Macc ) varies, the X-ray source transitions between distinct spectral states governed by the global evolution of the disk–corona system (Remillard & McClintock 2006). A major question in accretion physics is whether a similar geometry operates in the environment around MBHs. Recent studies of a sample of changing-look active galactic nuclei (CLAGNs) support a scale-invariant nature of black hole accretion flows (McHardy et al. 2006; Walton et al. 2012; Ruan et al. 2019). However, the preexisting gas and dusty torus sometimes complicate interpretation of the observables in CLAGNs (Guolo et al. 2021). On the other hand, the majority of TDEs are hosted by otherwise quiescent galaxies (French et al. 2020). Therefore, TDEs provide ideal laboratories for studying MBH accretion in different regimes (Ulmer 1999; Strubbe & Quataert 2009). ZTF conducts multiple time-domain surveys using the ZTF mosaic camera (Dekany et al. 2020) on the Palomar Oschin Schmidt 48 inch (P48) telescope. The ZTF team selects TDE candidates by imposing a set of criteria, such as proximity to a galactic nucleus, a lack of pre-flare nuclear activity, and a lack of g–r color change (see detailed descriptions in van Velzen et al. 2019, 2021). The filter is executed by AMPEL (Nordin et al. 2019). We use the Fritz marshal25 to coordinate our follow-up classifications. Thanks to its fast survey speed, ZTF is now reporting ∼15 TDEs per year (van Velzen et al. 2021; Hammerstein et al. 2022). AT2021ehb/ZTF21aanxhjv was first detected by the ZTF public 2 day cadence all-sky survey at a brightness of gZTF = 19.10 ± 0.22 on 2021 March 1. On 2021 March 3, it was reported to the Transient Name Server (TNS) by the ALeRCE broker (Munoz-Arancibia et al. 2021). On 2021 March 25, AT2021ehb passed our TDE selection filter. Swift observations were triggered while the TDE was still on the rise to peak. On 2021 March 26, we classified AT2021ehb as a TDE based on its nuclear location, persistent blue color, and bright UV emission (Gezari et al. 2021; Yao 2021). Four Swift snapshots from 2021 March 26 to April 2 yielded no X-ray detections. From 2021 April 12 to June 16, AT2021ehb was not observed due to occultation by the Sun. On 2021 June 17, ZTF observations resumed. On 2021 July 1, X-rays were detected with Swift (Yao et al. 2021). Its bright X-ray emission (∼1042 erg s−1 ) and the subsequent X-ray brightening moti- vated us to conduct a comprehensive monitoring campaign. At a spectroscopic redshift of z = 0.0180 (see Section 3.1), AT2021ehb is the third closest TDE discovered by optical sky surveys. The previously known lower-redshift events, AT2019qiz (Nicholl et al. 2020) and iPTF16fnl (Blagorodnova et al. 2017), were too faint in the X-ray to be carefully characterized. AT2021ehb, with a peak 0.3–10 keV X-ray flux of 1 mCrab, is the brightest non-jetted TDE in the X-ray sky. We are therefore able to conduct high-cadence monitoring (with Swift and the Neutron Star Interior Composition Explorer, NICER) and obtain high signal-to-noise ratio (S/N) X-ray spectra (with Nuclear Spectroscopic Telescope ARray, NuSTAR; NICER; XMM-Newton; and SRG/eROSITA), 25 https://github.com/fritz-marshal/fritz 2 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 3. which allows forthe search of spectral line features in the X-ray continuum. Unlike the X-ray spectra of most other non-jetted TDEs (Saxton et al. 2020; Sazonov et al. 2021), the X-ray spectrum of AT2021ehb drastically evolves over the X-ray observing campaign of ∼370 days, and at a certain stage, exhibits prominent nonthermal hard emission. Therefore, AT2021ehb is only the second non-jetted TDE, after AT2018fyk (Wevers et al. 2021), which allows us to investigate the rapid evolution between the UV/optical, soft X-ray, and hard X-ray compo- nents. Different from the result presented by Wevers et al. (2021), we find that the disk–corona system of AT2021ehb is dissimilar to XRBs. In this paper, we present an in-depth study of the X-ray, UV, optical, and radio emission of AT2021ehb, using observations obtained from 2021 March 1 to 2022 May 31. We outline the observations in Section 2. We analyze the host galaxy in Section 3, including measurements of the central black hole mass (MBH) and the SED. We study the light curve and spectral evolution of the TDE emission in Section 4. We provide a discussion in Section 5, and conclude in Section 6. UT time is used throughout the paper. We adopt a standard Λ cold dark matter cosmology with matter density ΩM = 0.3, dark energy density ΩΛ = 0.7, and the Hubble constant H0 = 70 km s−1 Mpc−1 , implying a luminosity distance to AT2021ehb of DL = 78.2 Mpc. UV and optical magnitudes are reported in the AB system. We use the extinction law from Cardelli et al. (1989), and adopt a Galactic extinction of EB−V,MW = 0.123 mag (Schlafly & Finkbeiner 2011). Uncer- tainties of X-ray model parameters are reported at the 90% confidence level. Other uncertainties are 68% confidence intervals, and upper limits are reported at 3σ. Coordinates are given in J2000. 2. Observations and Data Reduction 2.1. ZTF Optical Photometry We obtained ZTF26 forced photometry (Masci et al. 2019) in the g and the r bands using the median position of all ZTF alerts up to MJD 59550 (α = 03h 07m 47 82, d = + ¢ 40 18 40. 85). We performed baseline correction follow- ing the procedures outlined in Yao et al. (2019). The peak of the optical light curve probably occurred during Sun occultation and cannot be robustly determined. Therefore, we fitted a five-order polynomial function to the rZTF-band observations, which suggested that the optical maximum light was around MJD≈59321. Hereafter we use δt to denote rest- frame days relative to MJD 59321. The Galactic extinction- corrected ZTF light curves are shown in Figure 1. All ZTF photometry is provided in Appendix A.1 (Table 8). 2.2. SEDM and LT Optical Photometry We obtained additional ugri photometry using the Spectral Energy Distribution Machine (SEDM; Blagorodnova et al. 2018; Rigault et al. 2019) on the robotic Palomar 60 inch telescope (P60; Cenko et al. 2006), and the optical imager on the Liverpool Telescope (LT; Steele et al. 2004). The SEDM photometry was host-subtracted using the automated pipeline FPipe (Fremling et al. 2016). The LT photometry was host- subtracted using SDSS images. We found a mismatch between the SEDM/LT gr photo- metry and the ZTF photometry. This is probably a result of different reference images being used. The ZTF difference photometry is more reliable since the reference images were constructed using P48 observations taken in 2018–2019. The reference images of SEDM/LT come from SDSS images (taken in 2005), and long-term variability of the galactic nucleus will render the difference photometry less robust. Therefore, we present the SEDM and LT photometry in Appendix A.1 (Table 8), but exclude them in the following analysis. 2.3. Optical Spectroscopy We obtained low-resolution optical spectroscopic observa- tions using the Low Resolution Imaging Spectrograph (LRIS; Oke et al. 1995) on the Keck I telescope, the Double Spectrograph (DBSP; Oke & Gunn 1982) on the 200 inch Hale telescope, the integral field unit (R≈100) spectrograph of SEDM, and the De Veny Spectrograph on the Lowell Discovery Telescope (LDT). We also obtained a medium- resolution spectrum using the Echellette Spectrograph and Imager (ESI; Sheinis et al. 2002) on the Keck II telescope. Figure 2 shows the low-resolution spectra. The instrumental details and an observing log can be found in Appendix B. 2.4. Swift AT2021ehb was observed by the X-Ray Telescope (XRT; Burrows et al. 2005) and the Ultra-Violet/Optical Telescope (UVOT; Roming et al. 2005) on board Swift under our GO program 1619088 (as ZTF21aanxhjv; target ID 14217; PI: Gezari) and a series of time-of-opportunity (ToO) requests (PI: Yao). All Swift data were processed with heasoft v6.29 c. Figure 1. Optical and UV light curves of AT2021ehb. The host contribution has been removed using difference photometry (ZTF, Section 2.1) or subtraction of fluxes estimated from the galaxy SED (Ultra-Violet/Optical Telescope, UVOT; Section 2.4.2). Photometry has only been corrected for Galactic extinction. The transparent lines are simple Gaussian process fits in each filter (see Section 4.1), where the width of the lines represent 1σ model uncertainties. For clarity, we only show the model fits in the rZTF, uvw1, and uvw2 bands. Regions where the model uncertainty is greater than 0.3 mag are not shown. The lack of ZTF and UVOT data at 0 δt 50 days is due to Sun occultation; The lack ZTF data at 220 δt 290 days and 310 δt 340 days is due to performance issues with the cooling system for the ZTF Camera (Fremling et al. 2021). The lack of UVOT data at 270 δt 300 days is due to an issue with one of the Swift reaction wheels (Cenko 2022). 26 https://ztfweb.ipac.caltech.edu/cgi-bin/requestForcedPhotometry.cgi 3 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 4. 2.4.1. XRT All XRTobservations were obtained in the photon-counting mode. First, we ran ximage to select snapshots where AT2021ehb was detected above 3σ. For X-ray nondetections, we computed upper limits within a circular region with a radius of 30″, assuming Poisson statistics. For X-ray detections, to calculate the background-subtracted count rates, we filtered the cleaned event files using a source region with rsrc = 30″, and eight background regions with rbkg = 25″ evenly spaced at 80″ from AT2021ehb. A log of XRT observations is given in Appendix A.1 (Table 9). We generated XRT spectra using an automated online tool27 (Evans et al. 2009). To improve the S/N of each spectrum, we stacked consecutive observations with a similar hardness ratio (HR; see details in Section 4.4.5). 2.4.2. UVOT The first four UVOT epochs (obsID 14217001–14217005) were conducted with UBV+All UV filters. Subsequent observations were conducted with U+All UV filters. We measured the UVOT photometry using the uvot- source tool. We used a circular source region with rsrc = 12″, and corrected for the enclosed energy within the aperture.28 We measured the background using two nearby circular source-free regions with rbkg = 15″. Following the procedures outlined in van Velzen et al. (2021), we estimated the host galaxy flux in the UVOT bandpass from the population synthesis models (see Section 3.2). The UVOT light curves are presented in Figure 1 and provided in Appendix A.1 (Table 8). 2.5. NICER AT2021ehb was observed by NICER (Gendreau et al. 2016) under Director’s Discretionary Time (DDT) programs on 2021 March 26, 2021 July 2–7, and from 2021 November 13 to 2022 March 29 (PIs: Yao, Gendreau, Pasham). The NICER data were processed using nicerdas v9 (2021-08-31_V008c). We ran nicerl2 to obtain the cleaned and screened event files. Background was computed using the nibackgen3C50 tool (Remillard et al. 2022). Following the screening criteria Figure 2. Optical spectroscopic evolution of AT2021ehb. The observed spectra have been corrected for Galactic extinction. The vertical lines mark observed strong host absorption lines and spectral features common in TDEs. The vertical gray bands mark atmospheric telluric features, and strong telluric features have been masked. The best-fit galaxy model is shown at the bottom (see Section 3.2). 27 https://www.swift.ac.uk/user_objects 28 A large aperture is chosen to make sure that all of the flux of the host galaxy is captured. 4 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 5. suggested by Remillardet al. (2022), we removed “good time intervals” (GTIs) with hbgcut = 0.05 and s0cut = 2.0. We extracted one spectrum for each obsID, excluding obsIDs with 0.3–1 keV background rate>0.2 count s−1 or 4–12 keV background rate>0.1 count s−1 . Using observations bracketed by the two NuSTAR observations, we also produced two NICER spectra with exposure times of 8.2 ks and 36.6 ks, which we jointly analyzed with the NuSTAR spectra (see Section 4.4.1 and Section 4.4.2). All NICER spectra were binned using the optimal binning scheme (Kaastra & Bleeker 2016), requiring at least 20 counts per bin. Following the NICER calibration memo,29 we added systematic errors of 1.5% with grppha. 2.6. XMM-Newton We obtained two epochs of follow-up observations with XMM-Newton under our Announcement of Opportunity program (PI: Gezari), on 2021 August 4 (obsID 0882590101) and 2022 January 25 (obsID 0882590901). The observations were taken in full-frame mode with the thin filter using the European Photon Imaging Camera (EPIC; Strüder et al. 2001). The observation data files were reduced using the XMM- Newton Standard Analysis Software (Gabriel et al. 2004). The raw data files were then processed using the epproc task. Since the pn instrument generally has better sensitivity than MOS1 and MOS2, we only analyze the pn data. Following the XMM-Newton data analysis guide, to check for background activity and generate GTIs, we manually inspected the background light curves in the 10–12 keV band. Using the evselect task, we only retained patterns that correspond to single and double events (PATTERN< = 4). The source spectra were extracted using a source region of rsrc = 35″ around the peak of the emission. The background spectra were extracted from an rbkg = 108″ region located in the same CCD. The ancillary response files (ARFs) and response matrix files (RMFs) files were created using the arfgen and rmfgen tasks, respectively. We grouped the spectra to have at least 25 counts per bin, and limited the over- sampling of the instrumental resolution to a factor of five. 2.7. SRG/eROSITA The location of AT2021ehb was scanned by eROSITA as part of the planned eight all-sky surveys. Hereafter, eRASSn refers to the nth eROSITA all-sky survey.30 During eRASS4, AT2021ehb was independently identified by SRG as a TDE candidate. A log of SRG observations is given in Table 1. We grouped the eRASS4 and eRASS5 spectra to have at least three counts per bin. 2.8. NuSTAR We obtained NuSTAR (Harrison et al. 2013) observations under a preapproved ToO program (PI: Yao; obsID 80701509002) and a DDT program (PI: Yao; obsID 90801501002). The first epoch was conducted from 2021 November 18.8 to 19.9 with an exposure time of 43.2 ks. The second epoch was conducted from 2022 January 10.4 to 12.1 with an exposure time of 77.5 ks. To generate the first epoch’s spectra for the two photon- counting detector modules (FPMA and FPMB), source photons were extracted from a circular region with a radius of rsrc = 40″ centered on the apparent position of the source in both FPMA and FPMB. The background was extracted from an rbkg = 80″ region located on the same detector. For the second epoch, since the source was brighter, we used a larger source radius of rsrc = 70″, and a smaller background radius of rbkg = 65″. All spectra were binned first with ftgrouppha using the optimal binning scheme developed by Kaastra & Bleeker (2016), and then further binned to have at least 20 counts per bin. 2.9. VLA We began a monitoring program of AT2021ehb using the Very Large Array (VLA; Perley et al. 2011) under program 20B-377 (PI Alexander). All of the data were analyzed following standard radio continuum image analysis procedures in the Common Astronomy Software Applications (CASA; McMullin et al. 2007). The first three observations used a custom data reduction pipeline (pwkit; Williams et al. 2017), while the final observation used the standard NRAO pipeline. AT2021ehb was not detected in any of our observations. All data were imaged using the CASA task clean. We computed 3σ upper limits using the stats command within the imtool package of pwkit. The result of the first epoch was reported in Alexander et al. (2021). The full results are presented in Table 2. In Figure 3, we compare the radio luminosity of AT2021ehb with other UV- and optically selected TDEs. We note that AT2021ehb looks to be significantly (by more than an order of magnitude) radio-underluminous compared to previously observed non-jetted TDEs at similar times post-peak. It has Table 1 Log of SRG Observations of AT2021ehb eRASS MJD δt 0.3–10 keV flux (days) (10−13 erg s−1 cm−2 ) 1 58903.59–58904.59 −409.5 <0.25 2 59083.36–59084.70 −232.8 <0.23 3 59253.16–59254.16 −66.1 <0.23 4 59442.45–59443.62 +119.9 - + 76.8 2.4 2.5 5 59624.53–59625.70 +298.7 - + 30.7 2.3 2.4 Note. Upper limits are computed assuming an absorbed power-law (PL) spectrum with Γ = 2.5 and NH = 9.97 × 1020 cm−2 , and presented at 90% confidence. Table 2 Radio Observations of AT2021ehb Date Δt ν fν νLν (days) (GHz) (μJy) (1036 erg s−1 ) 2021 Mar 28.85 −18.8 15.0 <16 <1.8 2021 Jul 10.53 83.0 10.0 <16 <1.1 2021 Dec 5.09 228.0 10.0 <16 <1.1 2022 May 6.96 378.1 10.0 <14 <1.1 29 See https://heasarc.gsfc.nasa.gov/docs/nicer/data_analysis/nicer_ analysis_tips.html. 30 Here, n runs from 1 to 8. As of April 2022, eRASS1–eRASS4 have been completed, and 38% (sky area) of eRASS5 has been completed. 5 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 6. the deepest limitson any TDE radio emission at>150 days post-discovery. 3. Host Galaxy Analysis Figure 4 shows the pre-TDE optical image centered on AT2021ehb, using data from PS1. The host galaxy appears to be close to edge-on. 3.1. Velocity Dispersion and Black Hole Mass The host galaxy absorption lines are prominent in the optical spectra (see Figure 2). Using our medium-resolution (R = 5350) spectrum taken with Keck II/ESI, we measured the line centers of strong absorption lines, and determined the redshift to be z = 0.0180. Following previous TDE work (Wevers et al. 2017, 2019b; French et al. 2020), we measured the stellar velocity dispersion by fitting the normalized ESI spectrum (see pre-processing procedures in Appendix B) with the penalized pixel-fitting (pPXF) software (Cappellari & Emsellem 2004; Cappel- lari 2017). pPXF fits the absorption line spectrum by convolving a library of stellar spectra with Gauss-Hermite functions. We adopted the ELODIE v3.1 high-resolution (R = 42,000) template library (Prugniel & Soubiran 2001; Prugniel et al. 2007). To robustly measure the velocity dispersion and the associated uncertainties, we performed 1000 Monte Carlo (MC) simulations, following the approach adopted by Wevers et al. (2017). In each fitting routine, we masked wavelength ranges of common galaxy emission lines and hydrogen Balmer lines. The derived velocity dispersion is s = - + - 92.9 km s 5.2 5.3 1 at the 95% confidence interval. According to the MBH–σ relation (Kormendy & Ho 2013), the measured σ corresponds to a black hole mass of log (MBH/Me) = 7.03 ± 0.15(stat) ± 0.29(sys), where 0.29 is the intrinsic scatter of the MBH–σ relation. If adopting the Ferrarese & Ford (2005) MBH–σ relation, then log (MBH/Me) = 6.60 ± 0.20(stat) ± 0.34(sys). Hereafter we adopt the result from the Kormendy & Ho (2013) relation because it includes more low-mass galaxies. We note that although the Kormendy & Ho (2013) relation was originally calibrated mainly at an MBH regime that is too massive to produce a TDE, recent studies show that the same relation holds in the dwarf galaxy regime (Baldassare et al. 2020). 3.2. Host SED Model We constructed the pre-TDE host galaxy SED using photometry from SDSS, the Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006), and the AllWISE catalog (Cutri et al. 2014). The photometry of the host is shown in Table 3. Our SED fitting approach is similar to that described in van Velzen et al. (2021). We used the flexible stellar population synthesis (FSPS) code (Conroy et al. 2009), and adopted a delayed exponentially declining star formation history (SFH) characterized by the e-folding timescale τSFH. The Figure 3. Radio upper limits for AT2021ehb in the context of other UV- and optically discovered TDEs with radio data, including ASASSN-14li (Alexander et al. 2016), ASASSN-15oi (Horesh et al. 2021a), iPTF16fnl (Horesh et al. 2021b), AT2018fyk (Wevers et al. 2019a, 2021), AT2018hyz (Cendes et al. 2022), AT2019azh (Goodwin et al. 2022; Sfaradi et al. 2022), AT2019dsg (Cendes et al. 2021a), and upper limits listed in Table 2 of Alexander et al. (2020). Figure 4. PS1 RGB false-color g/i/z image centered on AT2021ehb. North is up and east to the left. A 10″ scale bar is included. Table 3 Observed Photometry of the Host Galaxy Catalog Band λeff (nm) Magnitude SDSS u 355 17.748 ± 0.019 SDSS g 467 15.814 ± 0.003 SDSS r 616 14.901 ± 0.002 SDSS i 747 14.443 ± 0.003 SDSS z 892 14.094 ± 0.004 2MASS J 1232 13.951 ± 0.025 2MASS H 1642 13.676 ± 0.034 2MASS Ks 2157 13.893 ± 0.043 AllWISE W1 3346 14.816 ± 0.024 AllWISE W2 4595 15.535 ± 0.022 AllWISE W3 11553 16.756 ± 0.229 6 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 7. Prospector package (Johnsonet al. 2021) was utilized to run a Markov Chain Monte Carlo sampler (Foreman-Mackey et al. 2013). We show the best-fit model prediction of the host galaxy optical spectrum at the bottom of Figure 2. From the marginalized posterior probability functions, we obtain the total galaxy stellar mass log = - + M M 10.18 0.02 0.01 ( ) * , the metallicity, = - Z log 0.57 0.04, t = - + 0.19 SFH 0.07 0.18 Gyr, the population age, = - + t 12.1 age 0.6 0.3 Gyr, and negligible host reddening (EB−V,host = 0.01 ± 0.01 mag). The best-fit SED model is shown in Figure 5. Following Gezari (2021), we use the MBH–M* relation from Greene et al. (2020) to obtain a black hole mass of log (MBH/Me) = 7.14 ± (0.10+0.79), where 0.79 is the intrinsic scatter of the scaling relation. This is consistent with the MBH inferred from the MBH–σ relation (Section 3.1). To summarize, the host galaxy of AT2021ehb has a total stellar mass of M*≈1010.18 Me and a BH mass of MBH≈107.03 Me. The measured black hole mass is on the high end of the population of optically selected TDEs (French et al. 2020; Nicholl et al. 2022), and is too massive to disrupt a white dwarf (Rosswog et al. 2009). 4. Analysis of the TDE Emission 4.1. UV/optical Photometric Analysis To capture the general trend of AT2021ehb’s UV/optical photometric evolution, we fit the data in each filter using a combination of five-order polynomial functions and Gaussian process smoothing, following procedures described in Appendix B.4 of Yao et al. (2020). The model fits in rZTF, uvw1, and uvw2 are shown as semitransparent lines in Figure 1. We then define a set of “good epochs” close in time to actual multiband measurements, and fit a Planck function to each set of fluxes to determine the effective temperature Tbb, photo- spheric radius Rbb, and blackbody luminosity of the UV/ optical emitting component Lbb. We initially assume EB−V,host = 0 mag, and then repeat the procedure under different assumptions about the host reddening. We find that the fitting residual monotonically increases as EB−V,host increases from 0 mag to 0.2 mag, suggesting negligible host reddening. Therefore, for the reminder of this discussion, we assume EB−V,host = 0 mag. We also define a set of “ok epochs” where we only have photometric observations in the optical (or only in the UV). Due to a lack of wavelength coverage, Tbb and Rbb can not be simultaneously constrained. As such we fix the Tbb values by interpolating the Tbb evolution of “good epochs,” and fit for Rbb values of “ok epochs.” The physical parameters derived from the blackbody fits are presented in Table 10 (Appendix A.2) and shown in Figure 6, where they are compared with a sample of recent TDEs with multiple X-ray detections. We have measured the blackbody parameters of other TDEs using the same procedures described above. While the temperature of AT2021ehb (Tbb∼2.5 × 104 K) is typical among optical and X-ray bright TDEs, its peak radius (Rbb∼3 × 1014 cm) and luminosity (Lbb∼3 × 1043 erg s−1 ) are at the low end of the distributions. We note that in the ZTF-I sample of 30 TDEs (Hammerstein et al. 2022), only two Figure 5. Host galaxy SED of AT2021ehb. The open squares are the Galactic extinction-corrected host photometry (see Table 3). The green lines are samples from the posterior distribution of host galaxy SED models. The open circles are the synthetic host galaxy magnitudes in the observed bands (shown in blue) and in the UV filters of Swift/UVOT (shown in purple). Figure 6. Evolution of the UV/optical blackbody properties of AT2021ehb compared with a sample of recent X-ray bright TDEs in the literature, including AT2018fyk (Wevers et al. 2019a, 2021), AT2019dsg (Stein et al. 2021), AT2019azh (Hinkle et al. 2021), AT2020ocn, and AT2019ehz (van Velzen et al. 2021). The results of “good epochs” (see definition in the text) are shown in high-opacity colors, whereas results of “ok epochs” are shown in semitransparent. 7 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 8. objects (AT2020ocn andAT2019wey) have peak radii smaller than that of AT2021ehb (see the discussion in Section 5.4.1). 4.2. Optical Spectral Analysis Figure 2 shows that no broad line is evident in the optical spectra of AT2021ehb. To search for weak spectral features from the TDE, we fit the Galactic extinction-corrected long-slit spectra in rest-frame 3600–5400 Å using a combina- tion of blackbody emission and host galaxy contribution: fλ,obs = A1fλ,BB+A2fλ,host. Here p = l l f B T R D BB L , bb bb 2 2 ( )( ), where Tbb and Rbb are obtained by linearly interpolating the blackbody parameters derived in Section 4.1 at the relevant δt. fλ,host is the predicted host galaxy spectrum obtained in Section 3.2 convolved with the instrumental broadening σinst (see Appendix B). A1 and A2 are constants added to account for unknown factors, including the varying amount of host galaxy flux falling within the slit (which depends on the slit width, slit orientation, seeing conditions, and target acquisition), uncer- tainties in the absolute flux calibration, and the adopted blackbody parameters. We note that fλ,host is the predicted spectrum for the whole galaxy, and therefore might not be a perfect description of the bulge spectrum. The fitting results are shown in Figure 7. We mark locations of emission lines commonly seen in TDEs, including Balmer lines, He II, the Bowen fluorescence lines of N III and O III, as well as low-ionization Fe II lines (Blanchard et al. 2017; Wevers et al. 2019a; van Velzen et al. 2021). The observed spectra of AT2021ehb can be well described by a blackbody continuum (dotted lines) plus host galaxy contribution. The spectra at δt>170 days are mostly from the host, and therefore it is not very surprising that no discernible TDE lines were detected. However, at δt< 170 days, the blackbody component contributes 25%–80% of the total flux. As such, it is surprising that no prominent lines from the TDE itself can be identified. We further discuss this result in Section 5.4.1. 4.3. X-Ray Light-curve Analysis The middle panel of Figure 8 shows the XRT and NICER (all binned by obsID) light curves. The lower panel of Figure 8 shows the evolution of the hardness ratio, defined as HR ≡ (H − S)/(H+S), where H is the number of net counts in the hard band, and S is the number of net counts in 0.3–1 keV. For XRT, we take 1–10 keV as the hard band, while for NICER, we take 1–4 keV. X-rays were not detected at δt< 0. Pre-peak X-ray upper limits are provided by Swift/XRT (<1040.9 erg s−1 ; Table 9) and SRG/eROSITA (<1040.2 erg s−1 ; Table 1). X-rays were first detected by XRT at δt = 73.9 days. The exact time of the X-ray onset cannot be accurately constrained. The count rate initially exhibited strong variability from δt = 73.9 days to δt = 82.3 days, and then gradually increased out to δt = 250 days. At the same time, the HR gradually increased. From δt = 250 days to δt = 271 days, both the X-ray flux and the hardness stayed at the maximum values. From δt = 271.0 days to δt = 273.7 days, the NICER net count rate suddenly decreased by a factor of 10 (Yao et al. 2022b). At the same time, the HR significantly decreased. After an X-ray plateau of≈50 days, the XRT net count rate further decreased drastically by a factor of six (from δt = 320.9 days to δt = 327.2 days). 4.4. X-Ray Spectral Analysis In this subsection, we first present a joint spectral analysis of contemporaneous data sets obtained from NICER and NuSTAR, including the first epoch in 2021 November 18–19 (Section 4.4.1) and the second epoch in 2022 January 10–12 (Section 4.4.2). These observations are of high S/N and cover a wide energy range. As such, the fitting results can guide us to choose appropriate spectral models to fit spectra with lower S/ Ns. We then perform analysis on data sets obtained by single telescopes, including XMM-Newton (Section 4.4.3), SRG Figure 7. Long-slit optical spectra of AT2021ehb taken at eight different epochs. The spectrum ( fλ,obs) is plotted in black. The blackbody continuum (A1fλ,BB; dotted lines) plus host galaxy spectrum (A2fλ,host) is plotted in green. No spectral features commonly seen in optically selected TDEs are observed in AT2021ehb. 8 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 9. (Section 4.4.4), Swift/XRT(Section 4.4.5), and NICER (Section 4.4.6). All spectral fitting was performed with xspec (v12.12, Arnaud 1996). We used the vern cross sections (Verner et al. 1996). The wilm abundances (Wilms et al. 2000) were adopted in Sections 4.4.1 and 4.4.2, whereas the Anders & Grevesse (1989) abundances were adopted in Sections 4.4.3, 4.4.4, 4.4.5, and 4.4.6. 4.4.1. NICER+NuSTAR First Epoch, 2021 November We chose energy ranges where the source spectrum dominates over the background. For NICER we used 0.3–4 keV. For NuSTAR/FPMA we used 3–23 keV, and for FPMB we used 3–20 keV.31 All data were fitted using χ2 -statistics. For all spectral models described below, we included the Galactic absorption using the tbabs model (Wilms et al. 2000), with the hydrogen-equivalent column density NH fixed at 9.97 × 1020 cm−2 (HI4PI Collaboration et al. 2016). We shifted the TDE emission using the convolution model zashift, with the redshift z fixed at 0.018. We included possible absorption intrinsic to the source using the ztbabs model. We also included a calibration coefficient (constant; Madsen et al. 2017) between FPMA, FPMB, and NICER, with CFPMA ≡ 1. This term also accounts for the differences in the mean flux between NuSTAR and NICER that results from intrinsic source variability. First, we fitted the spectrum with a power law (PL), and obtained a photon index of Γ≈2.7. The fit is unacceptable, with the reduced χ2 being c = 3.44 r 2 for 144 degrees of freedom (dof). The residuals are most significant between 0.3 and 2 keV, suggesting the existence of a (thermal) soft component. Therefore, we changed the PL to simpl* thermal_model. Here simpl is a Comptonization model that generates the PL component via Compton scattering of a fraction ( fsc) of input seed photons (Steiner et al. 2009). The flag Rup was set to 1 to only include up-scattering. We experimented with three different thermal models: a blackbody (bbody), a multicolor disk (MCD; diskbb; Mitsuda et al. 1984), and a single- temperature thermal plasma (bremss; Kellogg et al. 1975), resulting in c = 1.33 r 2 , 1.15, and 1.35 (for dof = 142), respectively. The fit statistics favors an MCD. The best-fit result with an MCD, defined as model (1a), is shown in Figure 9. We present the best-fit parameters in Table 4. Here, Tin is the inner disk temperature, and º R R i cos in in * is the apparent inner disk radius times the square root of i cos , where i is the system inclination. Rin * is inferred from the normalization parameter of diskbb. Model (1a) gives a good fit with c = = 163 142 1.15 r 2 . 4.4.2. NICER+NuSTAR Second Epoch, 2022 January We chose energy ranges where the source spectrum dominates over the background. For NICER, we used 0.3–7.0 keV; for NuSTAR FPMA and FPMB, we used 3–30 keV. All data were fitted using χ2 -statistics. Unlike in Section 4.4.1, here we use tbfeo to model the Galactic absorption. Compared with tbabs, tbfeo allows the O and Fe abundances (AO, AFe) to be free. We adopted a continuum model of simpl* diskbb, defined as (2a). The result, with c = 2.04 r 2 , is shown in Figure 10 and the upper-left panel of Figure 11. The best-fit parameters are given in Table 5. The residual plot clearly Figure 8. Upper: UV (uvw1UVOT) and optical (rZTF) light curves of AT2021ehb. Middle: XRT and NICER X-ray net count rates of AT2021ehb. Epochs of XMM- Newton, SRG, and NuSTAR observations are marked by the vertical lines. Lower: XRT and NICER hardness ratio (HR) evolution of AT2021ehb. 31 In this NuSTAR observation, FPMB is more affected by a nearby bright source. 9 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 10. indicates the existenceof unmodeled spectral features and a significant offset between NuSTAR and NICER at 6–7 keV. First, we study whether this offset is brought about by a cross-calibration difference between NICER and NuSTAR. To this end, we replaced constant with crabcorr (Ludlam et al. 2022), which multiplies the spectrum by a PL of C · E−ΔΓ . When ΔΓ = 0, crabcorr is equivalent to constant. We fixed ΔΓFPMA = ΔΓFPMB = 0, and allow ΔΓNICER to be free. The best-fit model gives DG = - - + 0.128 NICER 0.023 0.014 , which is too large compared with the value of ΔΓNICER≈− 0.06 found by Ludlam et al. (2022). Therefore, we conclude that a difference in the cross-calibration slope is likely not the primary reason for the 6–7 keV offset. Next, we investigate whether this offset is caused by imperfect NICER calibration at 2–3 keV. NICER effective area changes rapidly in the 2–3 keV band. Calibration issues in that range may cause the model to overestimate the data at 2–3 keV, and to badly underestimate it above 3 keV. As a test, we performed the fit omitting the 2–3 keV region in the NICER data. However, the best-fit result still leaves a significant offset between NICER and NuSTAR at 6–7 keV, similar to that shown in Figure 10. We are left to conclude that the offset is likely caused by either an underestimate of NICER background at the high- energy end or systematic uncertainties in NICER calibration that is not well characterized. This conjecture is based on the fact that NICER uses X-ray concentrators optics, and its 3–7 keV background is>10 times brighter than that of NuSTAR (Figure 10). On the other hand, NuSTAR adopts X-ray focusing optics, which enables more robust background estimation using regions close to the object of interest. In the following, we attempted to improve the fit by three approaches: adding a Gaussian line, adding reflection emission features, and adding absorption features. Modeling with a Gaussian Line Profile—The result with adding a Gaussian line component is shown in the upper- right panel of Figure 11. This model, defined as (2b), provides a much better fit compared with (2a). The best-fit parameters (Table 5) give a very broad emission profile with a central energy at Eline∼5 keV and a line width of σline∼2 keV. If the 3–7 keV spectral feature indeed comes from an emission line, its central energy is different from the emission line at Eline∼8 keV that has been found in the jetted TDE Sw J1644 +57, which has been interpreted as highly ionized iron Kα emission blueshifted by∼0.15c (Kara et al. 2016; Thomsen et al. 2019). Instead, what is shown here indicates the possible existence of a relativistically broadened iron line (either redshifted or with a more distorted red wing). Modeling with Disk Reflection—In this method, we fit the data using a combination of MCD and relativistic reflection from an accretion disk. We utilize the self-consistent relxill model to describe the direct PL component and the reflection part (García et al. 2014; Dauser et al. 2014). In relxill, we fixed the outer disk radius (Rout) at a fiducial value of 400 Rg, since it has little effect on the X-ray spectrum. The redshift parameter in relxill was fixed at 0 since the host redshift was already included by the zashift model. To reduce the complexity of Figure 9. The spectrum of the first joint NICER and NuSTAR observations (2021 November). See Table 4 for best-fit parameters. NuSTAR/FPMB and NICER data have been divided by CFPMB and CNICER, respectively. The data have been rebinned for visual clarity. Table 4 Modeling of the First Joint NICER and NuSTAR Observations, δt = 212 Days Component Parameter (1a) constant CFPMB - + 1.03 0.05 0.06 CNICER - + 0.85 0.05 0.06 ztbabs NH (1020 cm−2 ) <0.75 simpl Γ 2.29 ± 0.05 fsc - + 0.35 0.03 0.02 diskbb Tin (eV) - + 164 9 6 Rin * (104 km) - + 25.5 2.0 4.4 L χ2 /dof 163.17/142 = 1.15 Figure 10. The spectrum of the second joint NICER and NuSTAR observations (2022 January). This figure highlights the flux levels of the source and background spectra. 10 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 11. this model, wefroze the reflection fraction RF (ratio of the reflected to primary emission; Dauser et al. 2016) at 1. The inner and outer emissivity index q were fixed at 3 throughout the accretion disk, making Rbreak obsolete. We assume the inner disk radius is at the innermost stable circular orbit (ISCO), i.e., Rin = RISCO. Other parameters in relxill include the PL index of the incident spectrum Γ, the cutoff energy of the PL Ecut, the black hole spin a, the inclination i, the ionization of the accretion disk ξ, the iron abundance of the accretion disk AFe, and the normalization parameter Normrel. We first fit the data allowing a to be free, finding that the fit is not sensitive to a. Therefore, we performed the fit with a fixed at zero. The best-fit model, hereafter (2c), gives χ2 /dof = 306.65/296 = 1.04 and is shown in the lower-left panel of Figure 11. The best-fit model parameters are given in Table 5. In Figure 12, the solid black line shows the best-fit model; Modifications of the best-fit model are shown as dotted (if a is changed from 0 to 0.998), dashed (if i is changed from 43° .4 to 70°), and dashed–dotted (if logξ is changed from 4.09 to 3.50) lines. The shape and width of the extremely broad iron emission are mainly determined by the high disk ionization state and the moderate inclination. We note that the best-fit ionization of ξ∼104 erg cm s−1 is greater than the typical values observed in Seyfert 1 active galactic nuclei (AGNs; Walton et al. 2013; Ezhikode et al. 2020). Modeling with Absorbers—In this method, we attempt to improve the fit by adding absorption features. First, we added partial covering of a neutral absorber using the pcfabs model. In pcfabs, a fraction fcover of the X-ray source is seen through a neutral absorber with hydrogen-equivalent column density NH, while the rest is assumed to be observed directly. The best-fit model gives χ2 /dof = 386/297 = 1.30. If we add a new free parameter (redshift of the neutral absorber) by replacing pcfabs with zpcfabs, χ2 /dof becomes 370/296 = 1.25. However, both models leave 5–8 keV flux excess in the residual. Therefore, we next allow the absorber to be partially ionized by replacing zpcfabs with a photoionized absorber. This is also motivated by the fact that a good fit to the Chandra LETG Figure 11. The spectrum of the second joint NICER and NuSTAR observations (2022 January). See Table 5 for best-fit parameters. NuSTAR/FPMB and NICER data have been divided by CFPMB and CNICER, respectively. The data have been rebinned for visual clarity. In the lower-left panel, we also show the reflection contribution and the direct PL contribution individually from relxill. In the lower-right panel, we also show the best-fit model (2d) deconvolved with the xstar component. 11 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 12. observation conducted on2021 November 29 was found with such a model by Miller et al. (2022a). This fit utilized the zxipcf model (Reeves et al. 2008), which is a grid of photoionization models computed by the XSTAR code (Kallman & Bautista 2001). However, Reynolds et al. (2012) noted that zxipcf only has a very coarse sampling in ionization space, and so in this work, we use an updated XSTAR grid that is suitable for use with AGNs (computed in Walton et al. 2020). This grid assumes an ionizing continuum of Γ = 2 and a velocity broadening of 100 km s−1 , and allows the ionization parameter, column density, absorber redshift, and both the oxygen and iron abundances to be varied as free parameters (although for simplicity we assume these abun- dances are solar). Fitting the data with the redshift of the absorber fixed at zero yields χ2 /dof = 318.2/296 = 1.08. If the redshift is allowed to be free, we have χ2 /dof = 317.7/295 = 1.08. Since χ2 only reduces by 0.5 for 1 dof, the redshift parameter cannot be well constrained by our data. Therefore, we name the model with the absorber redshift fixed at zero as (2d), and show it in the lower-right panel of Figure 11. The model parameters are given in Table 5. In Figure 12, the solid crimson line shows a high-resolution version of model (2d). Model Comparison and Comments—Between (2b) and (2c), we consider (2c) to be superior since (i) its χ2 is smaller by 24 for only 1 dof, and (ii) it adopts a physically motivated model instead of a mathematical function. To compare (2c) and (2d), we use the Bayesian information criterion (BIC) to assess the goodness of fit. Here = - k N L BIC ln 2 ln 1 · ( ) ( ) c = + + k N ln constant 2 2 · ( ) ( ) where k is the number of free parameters, N is the number of spectral bins, and is the maximum of the likelihood function. Table 5 Modeling of the Second Joint NICER and NuSTAR Observations, δt = 264 Days Component Parameter (2a) (2b) (2c) (2d) constant CFPMB 1.03 1.03 ± 0.01 1.03 ± 0.01 1.03 ± 0.01 CNICER 0.98 1.02 ± 0.01 1.02 ± 0.01 1.03 ± 0.01 tbfeo AO 1.40 - + 1.48 0.08 0.11 1.26 ± 0.13 - + 1.45 0.07 0.10 AFe 1.80 - + 2.07 0.64 0.63 - + 1.99 0.62 0.61 - + 2.37 0.39 0.50 ztbabs NH (1020 cm−2 ) 0.00 <0.12 0.70 ± 0.28 <0.01 diskbb Tin (eV) 187 - + 198 6 8 257 ± 8 - + 180 2 7 Rin * (104 km) 31.7 - + 28.4 1.7 1.2 - + 10.5 0.9 1.0 47.3 ± 2.8 simpl Γ 2.09 2.11 ± 0.01 L 2.26 ± 0.01 fsc 0.52 - + 0.49 0.03 0.02 L 0.61 ± 0.01 Gaussian Eline (keV) L - + 4.92 0.71 0.36 L L σline (keV) L - + 2.18 0.32 0.50 L L Norm (10−4 ph cm−2 s−1 ) L - + 2.52 0.51 1.01 L L relxill q1 = q2 L L 3 (frozen) L a L L 0 (frozen) L i (◦ ) L L - + 43.4 9.6 8.5 L Rin (RISCO) L L 1 (frozen) L Rout (Rg) L L 400 (frozen) L Γ L L 1.86 ± 0.02 L logξ (erg cm s−1 ) L L - + 4.09 0.12 0.20 L AFe L L - + 1.86 0.63 1.46 L Ecut (keV) L L - + 54.0 9.5 13.4 L RF L L 1 (frozen) L Norm (10−5 ) L L - + 6.1 0.40 0.40 L xstar NH (1023 cm−2 ) L L L - + 2.22 0.86 0.49 x log (erg cm s−1 ) L L L - + 1.51 0.32 0.34 fcover L L L 0.31 ± 0.02 Redshift L L L 0 (frozen) L χ2 /dof 609.43/299 = 2.04 330.72/296 = 1.12 306.64/295 = 1.04 318.23/296 = 1.08 Note. Parameter uncertainties of model (2a) cannot be calculated since c > 2 r 2 . Figure 12. Best-fit incident model spectra of (2c) and (2d), as well as modifications of (2c) if one parameter is changed. 12 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 13. Models with lowerBIC values are favored. According to Raftery (1995), a BIC difference between 2 and 6 is positive, a difference between 6 and 10 is strong, and a difference greater than 10 is very strong. Since BIC(2c) − BIC(2d) = − 5.9, model (2c) is slightly favored over (2d). The energy range over which model (2c) performs better than (2d) is ∼8–12 keV. This is because absorption by ionized iron adds a relatively sharp flux decrease at ∼7 keV, while the blue wing of the iron emission in relxill is smoother (see the lower-right panel of Figure 11). We note that the residual below 0.7 keV is strong in all model fits, and is likely caused by underestimated NICER calibration uncertainties at the lowest energies. 4.4.3. XMM-Newton Analysis We chose energy ranges where the source spectrum dominates over the background. For XMM E1, this is 0.2–2.6 keV, while for XMM E2 this is 0.2–7.0 keV. All data were fitted using χ2 -statistics. Following Sections 4.4.1 and 4.4.2, all models described below have been multiplied by tbabs* ztbabs* zashift to include Galactic absorption, host absorption, and host redshift. Although the XMM E1 spectrum is very soft, a single MCD results in a poor fit and leaves a large residual above 1 keV, suggesting the existence of a nonthermal component. A continuum model of simpl* diskbb gives a much better fit with c = 1.35 r 2 . The best-fit model is shown in the upper panel of Figure 13. The XMM E2 spectrum is much harder than that from XMM E1. Fitting with simpl* diskbb gives a good fit with c = 1.19 r 2 (see Figure 13, lower panel). We note that although the cr 2 of our best-fit XMM-Newton models are acceptable, there seems to be some systematic residuals. For example, eight consecutive bins of positive residuals are seen in the 1.7–2.6 keV XMM E1 data. A possible explanation is that there exist spectral features created by absorbing materials in the TDE system, such as the blueshifted absorption lines reported in the TDE ASASSN-14li (Miller 2015; Kara et al. 2018). Seven consecutive bins of positive residuals are seen in the 4.0–7.0 keV XMM E2 data. This might indicate the existence of disk reflection features, such as an iron emission line. We note that 2–4 days after our second XMM-Newton epoch, XMM-Newton/EPIC observa- tions obtained under another program also reveals the existence of interesting features in the iron K band (Miller et al. 2022b). More detailed modeling of the XMM-Newton spectra is beyond the scope of this paper, and is encouraged in future work. 4.4.4. SRG/eROSITA Analysis We chose energy ranges where the source spectrum dominates over the background. For eRASS4 this range is 0.2–3 keV, while for eRASS5 this range is 0.2–2 keV. All data were fitted with the C-statistic (Cash 1979). Following Section 4.4.1 and Section 4.4.3, we fitted the SRG/eROSITA spectra with tbabs* ztbabs* zashift* simpl* diskbb. For the eRASS5 spectrum, since the source is only above background at 0.2–2 keV, the PL index cannot be constrained from the SRG/eROSITA spectrum alone. Therefore, we fixed Γ at the best-fit value of the XMM E2 spectrum (Table 6, Γ = 2.92), and allowed other parameters to be free. This choice is based on the fact that the XMM E2 and eRASS5 observations appear to show the same properties on the light curve and hardness evolution diagrams (Figure 8). The fitting results are shown in Figure 14. The best-fit parameters are shown in Table 7. Figure 13. The XMM-Newton spectra. The data have been rebinned for visual clarity. The dashed lines show the best-fit models. See Table 6 for the best-fit parameters. Table 6 Modeling of Two XMM-Newton Observations Component Parameter XMM E1 XMM E2 ztbabs NH (1020 cm−2 ) - + 1.09 0.45 0.99 <1.22 diskbb Tin (eV) - + 68 4 1 125 ± 8 Rin * (104 km) - + 511 75 144 - + 39 6 10 simpl Γ >4.57 a 2.92 ± 0.15 fsc - + 0.13 0.01 0.03 0.16 ± 0.03 L χ2 /dof 70.26/52 = 1.35 97.49/82 = 1.19 a Upper limit of Γ is at 5. 13 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 14. 4.4.5. XRT Analysis Thetemporal coverage of each time-averaged XRT spectrum (generated in Section 2.4.1) is shown as “s1,” “s2,” ..., “s9” in the lower panel of Figure 8. We fitted the 0.3–10 keV spectra using a simple model of tbabs* zashift* (diskbb +powerlaw). We did not include the ztbabs component, as host galaxy absorption was found to be negligible or much smaller than the Galactic absorption in all previous spectral analyses (see Tables 4, 5, 6, and 1). The adopted continuum model does not give realistic model parameters. For example, the disk radii will be underestimated when the source spectrum is hard (see a detailed discussion in Steiner et al. 2009). The main goal of this fitting is to compute the multiplicative factor to convert the 0.3–10 keV XRT net count rate to X-ray fluxes, including (i) the observed 0.3–10 keV flux fX(0.3–10 keV), (ii) the Galactic absorption corrected 0.3–10 keV flux fX, 0 (0.3–10 keV), (iii) the Galactic absorption corrected 0.5–10 keV flux fX, 0 (0.5–10 keV), and (iv) the Galactic absorption corrected flux density at the rest-frame energies of 0.5 keV and 2 keV (i.e., fν(0.5 keV) and fν(2 keV)). All data were fitted using C-statistics. The best-fit models are shown in Figure 15. Scaling factors to convert 0.3–10 keV net count rate to X-ray fluxes can be computed using values provided in Table 11 (Appendix A.2). The observed isotropic equivalent 0.3–10 keV X-ray luminosity, LX, is shown in the upper panel of Figure 16. Note that for the initial four XRT nondetections, we assume a spectral shape similar to “s1.” 4.4.6. NICER Analysis We started with the obsID-binned NICER spectra generated in Section 2.5. We only performed spectral fitting on obsIDs with more than 500 total net counts in 0.3–4 keV. Following Section 4.4.5, we fitted a tbabs* zashift* (diskbb +powerlaw) model to the 0.3–4 keV spectra and inferred fX from the best-fit models. All data were fitted using χ2 -statistics. The best-fit models provided a cr 2 close to 1 in most cases. The LX evolution inferred from NICER spectral fitting is also shown in the upper panel of Figure 16. 4.5. Spectral Indices αOX and αOSX To assist comparison with TDEs from the literature, we computed the UV to X-ray spectral index αOX (Tananbaum et al. 1979; Ruan et al. 2019; Wevers et al. 2021) and αOSX (Gezari 2021), which are commonly used in AGN and TDE literature to characterize the ratio of UV to X-ray fluxes.32 Here a n n º n n L L log 2500 Å 2 keV log 2500 Å 2 keV , 3 OX [ ( ) ( )] [ ( ) ( )] ( ) a n n º n n L L log 2500 Å 0.5 keV log 2500 Å 0.5 keV , 4 OSX [ ( ) ( )] [ ( ) ( )] ( ) where Lν is the luminosity at a certain frequency (corrected for NH and EB−V,MW). We use the Swiftuvw1 host-subtracted luminosities (rest-frame effective wavelength at 2459 Å for Teff = 3 × 104 K) as a proxy for Lν(2500 Å). We measure fν(0.5 keV) and fν(2 keV) by converting the XRT net count rates to flux densities using the scaling factors derived in Section 4.4.5. We note that fν(2 keV) mainly traces the evolution of the nonthermal X-ray component, while fν(0.5 keV) traces both the thermal and nonthermal compo- nents. The results are shown in the lower panel of Figure 16. Based on Figure 16, we divide the evolution of AT2021ehb into five phases. In phase A (δt 0 days), the UV/optical luminosity brightens, while X-rays are not detected Figure 14. SRG/eROSITA spectra of AT2021ehb. Table 7 Modeling of Two SRG/eROSITA Observations Component Parameter eRASS4 eRASS5 ztbabs NH (1020 cm−2 ) - + 0.21 0.20 2.19 <3.41 diskbb Tin (eV) - + 89 13 7 - + 96 22 32 Rin * (104 km) - + 210 38 179 - + 73 21 243 simpl Γ - + 4.15 0.73 0.82 2.92 (frozen) fsc - + 0.14 0.08 0.12 - + 0.21 0.09 0.06 L cstat/dof 126.43/140 76.45/85 Figure 15. XRT time-averaged spectra of AT2021ehb. See the lower panel of Figure 8 for the time span of each spectrum. 32 Note that some papers use these indices with a minus sign in front of our definitions. 14 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 15. (<1040.9 erg s−1 ). Inphase B (0 δt 100 days), the UV/ optical luminosity declines, and X-rays emerge. Entering into phase C (100 δt 225 days), the X-ray spectrum gradually hardens, while the UV/optical luminosity stays relatively flat. In phase D (225 δt 270 days), the X-ray further brightens two times (indicated by D1 and D2), and the UV/optical plateau persists. In phase E, the X-ray luminosity drops two times (indicated by E1 and E2), while the UV/optical luminosity only slightly declines. Interestingly, the dramatic X-ray evolution in phase D+E does not have much effect on the UV/optical luminosity. Typical SEDs in each phase are shown in Figure 17. 4.6. Bolometric Luminosity Lbol To calculate the bolometric luminosity Lbol at the epochs of the Swift observations, we assume that the bulk of the radiation is between 10,000 Å and 10 keV. We estimate that when the X-ray spectrum is the hardest (i.e., model 2c), the 0.3–10 keV flux still constitutes 72% of the 0.3–100 keV flux. Therefore, this assumption at most underestimates logLbol by 0.14 dex. We compute the 10,000 Å to 10 keV luminosity by adding the luminosities in three energy ranges (see a demonstration in Figure 18). From 10,000 Å to 2500 Å, we integrate below the blackbody model fitted to the UV/optical photometry (Section 4.1). From 2500 Å to 0.5 keV, we assume that the TDE spectrum is continuous and can be approximated by a PL of n µ n a f OSX. Hence, the luminosity is ò ò n n n n n = » n n n n n n a a L L d L d 5 1 1 1 2 1 2 OSX OSX ( ) ( ) n n n n a a n n a = ´ - + ¹ - = - n a a a + + L 1 if 1 ln if 1 6 1 1 2 1 1 1 OSX OSX 2 1 OSX OSX OSX OSX ⎧ ⎨ ⎩ ( ) ( ) ( ) where ν1 = 1015.08 Hz, ν2 = 1017.08 Hz. In this range, we assume that the uncertainty of L is 0.3L. From 0.5 keV to 10 keV, we calculate the luminosity by converting the 0.3–10 keV XRT net count rate to Galactic absorption corrected 0.5–10 keV luminosity using the scaling factors derived in Section 4.4.5. Note that for the first four Swift epochs, since X-rays were not detected, we use the UV/optical blackbody luminosity Lbb as an approximation of Lbol. The evolution of logLbol as a function of αOX is shown in Figure 19. The data points are color coded by their phases (from A to E; see Figure 16). The right y-axis converts Lbol to the Eddington ratio λEdd ≡ Lbol/LEdd. For pure hydrogen, an MBH of 107.03 Me (Section 3.1) implies an Eddington luminosity of LEdd≈1045.13 erg s−1 . We further discuss this figure in Section 5.5. The maximum luminosity was reached at Figure 16. Upper: blackbody luminosity of the UV/optical emission (Lbb; Section 4.1) compared with the observed isotropic equivalent 0.3–10 keV X-ray luminosity (LX) from XRT (Section 4.4.5) and NICER (Section 4.4.6). Lower: the 2500 Å to X-ray spectral slope measured by Swift observations (Equation (3), (4)). Figure 17. Typical SEDs of AT2021ehb in five phases. The data has been corrected for extinction (in UV/optical) and column density absorption (in the X-ray). The solid lines are the blackbody fits to UV/optical data. 15 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 16. δt = 253days, with Lbol = (7.94 ± 0.66) × 1043 erg s−1 and l = - + 6.0 Edd 3.8 10.4 %. As a cautionary note, the relatively low value of λEdd (<16%) does not necessarily imply that the accretion is in the sub-Eddington regime, as the TDE broadband SED may peak in the extreme-UV (EUV) band (Dai et al. 2018; Mummery & Balbus 2020). 5. Discussion Hereafter we define M7 ≡ MBH/(107 Me), º m M M acc Edd , h º M L c Edd Edd 2 ( ) , η−1 ≡ η/10−1 , where Macc is the mass accretion rate and η is the accretion radiative efficiency. With M7≈1, the gravitational radius is Rg = GMBH/c2 ≈1012.20 cm. For a solar-type star, the tidal radius is RT = 1013.19 cm≈10Rg, within which the tidal force exceeds the star’s self-gravity (Rees 1988). 5.1. Origin of the Soft X-Ray Emission The soft X-ray emission of many TDEs has been attributed to the inner regions of an accretion disk (Saxton et al. 2020). Assuming Rin≈6Rg≈1013 cm, the maximum effective temper- ature of an optically thick, geometrically thin accretion disk is » h- T 20 m M eff 1 4 7 1 ( ) eV (Shakura & Sunyaev 1973). With a maximum black hole spin of a → 1, Rin → Rg, and » h- T 78 m M eff 1 4 7 1 ( ) eV. The top panel of Figure 20 shows that in phase D, when the X-ray spectrum is the hardest, the measured Tin is ∼2.5 times greater than the maximum allowed Teff. This high color temperature causes the inferred disk radius = R R i cos d,in in * to be much less than Rg throughout the evolution. The projection factor i cos should not be much less than unity, since for a nearly edge-on viewing angle, the X-rays from the inner disk will be obscured by the gas at larger radii. The relativistic disk reflection model (2c) also suggests = - + i cos 0.85 0.07 0.06 . We note that disk radii much less than Rg have also been inferred in a few other X-ray bright TDEs (see, e.g., Figure 8 of Gezari 2021). This discrepancy may be due to Compton scattering (Shimura & Takahara 1995), which makes the measured temperature greater than the effective inner disk temperature by a factor of fc (Davis & El-Abd 2019), i.e., Tin = fcTeff. The physical reason is that, as the X-ray photons propagate in the vertical direction away from the disk mid-plane, the color temperature is determined by the thermalization depth Figure 18. A snapshot SED of AT2021ehb at δt≈147 days. The data has been corrected for extinction (in UV/optical) and Galactic absorption (in the X-ray). The solid lines are the blackbody fits to UV/optical data (Section 4.1) and the XRT “s3” spectrum best-fit model (Section 4.4.5). The shaded region shows that the Lbol is calculated in three energy ranges (see the text). Figure 19. The bolometric luminosity Lbol as a function of αOX. Lbol is converted to λEdd assuming = M M log 7.03 BH ( ) (Section 3.1). Note that the uncertainty of λEdd should be greater than the uncertainty of Lbol by 0.44 dex (i.e., the uncertainty of MBH), which is not included in the figure. Figure 20. Evolution of best-fit X-ray spectral parameters, including logTin and logRin * in the diskbb component (top two panels), Γ and fsc in the simpl component (third and fourth panels). Note that the uncertainty of log(R R in g * ) is greater than the uncertainty of Rin * by 0.44 dex (i.e., the uncertainty of MBH; Section 3.1), which is not included in the figure. Data are from model (1a) in Table 4, model (2a) in Table 5, Table 6, and Table 7. For parameters in model (2a), we assume an uncertainty of 10%. Fixed values are shown as semitransparent symbols. Background colors follow the scheme shown in Figure 16. 16 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 17. (corresponding to thelast absorption), which could be located at a high scattering optical depth τ ? 1—this causes Tin to be higher than Teff by a factor of∼τ1/4 . As a result of ongoing fallback, the vertical structure of the TDE disk (see Bonnerot et al. 2021) is likely substantially different from the standard thin disk as studied by Davis & El-Abd (2019), who concluded fc 2, so the color correction factor may be different. More detailed radiative transport calculations in the TDE context are needed to provide a reliable fc based on first principles. Another possible reason for the seemingly small disk radii is that a scattering dominated, Compton-thick gas layer can suppress the X-ray flux without causing any significant change to the spectral shape. For a spatially uniform layer, the transmitted flux is exponentially suppressed for a large scattering optical depth ? 1. A more likely configuration is that the layer is like an obscuring wall with small holes where a fraction of the source X-rays can get through, and the rest of the area contributes negligibly to the observed flux. In this scenario, the inferred disk radius is reduced by a factor of the square root of the transmitted over emitted fluxes. 5.2. Implications of the Hard X-Ray Emission Hard X-rays can be generated by Compton up-scattering of soft X-rays from the accretion disk by the hot electrons in the (magnetically dominated) coronal regions above the disk, as is the case in AGNs and XRBs. The physical situation in TDEs is more complicated than in AGNs in that the hard X-rays must make their way out of the complex hydrodynamic structures. An X-ray photon undergoes∼τ2 electron scatterings as it propagates through a gas slab of Thomson optical depth τ. In each scattering, the photon loses a fraction Eγ/mec2 of its energy (where Eγ is the photon energy) as a result of Compton recoil, and hence the cumulative fractional energy loss is∼τ2 Eγ/mec2 . This means that photons above an energy threshold of∼1 keV(τ/20)−2 will be Compton down-scattered by the gas. Our NuSTAR observations clearly detected hard X-ray photons up to 30 keV, which requires that the optical depth along the pathways of these photons from the inner disk ( Rg∼1012.2 cm) to the observer is less than about 4. On the other hand, the UV/optical emission indicates that the reprocessing layer is optically thick up to a radius of the order of Rbb∼1014 cm. Therefore, our observations favor a highly nonspherical system—there are viewing angles that have very large optical depths such that most X-ray photons are absorbed (and reprocessed into the UV/optical bands), and there are other viewing angles with scattering optical depth τ 4 so that hard X-ray photons can escape. 5.3. X-Ray Spectral Evolution 5.3.1. Soft to Hard Transition: Corona Formation The top two panels of Figure 20 show that, during the soft → hard transition, AT2021ehb’s inferred inner disk radius “moves” inward. We find that the main cause of this behavior is that the inner disk temperature increases with time as the spectrum hardens. The gradual hardening is consistent with a picture where it takes ∼102 days to build up the magnetically dominated hot corona region. It is possible that the initially weak magnetic fields in the bound debris are amplified by differential rotation of the disk and the magnetorotational instability (Balbus & Hawley 1991; Miller & Stone 2000). 5.3.2. Hard to Soft Transition: Thermal–Viscous Instability? The rapid X-ray flux drop (D → E) is likely due to a state transition in the innermost regions of the accretion disk. Under the standard α-viscosity prescription where the viscous stress is proportional to the total (radiation + gas) pressure (Shakura & Sunyaev 1973), the disk undergoes a thermal–viscous instability as the accretion rate drops from super- to sub- Eddington regimes (Lightman & Eardley 1974; Shakura & Sunyaev 1976). This instability causes the disk material to suddenly transition from a radiation pressure-dominated to gas pressure-dominated state on a sound-crossing timescale, and the consequence is that the disk becomes much thinner and hence the accretion rate drops. Shen & Matzner (2014) considered the thermal–viscous instability in the TDE context but concluded that the instability should occur within a few months since the disruption and the accretion rate drops by several orders of magnitude—these, taken at face value, are inconsistent with our observations. More detailed work on the disk evolution is needed to draw a firm conclusion. Here, we provide two arguments for the disk state transition explanation. First, TDEs with relativistic jets (e.g., Bloom et al. 2011; Burrows et al. 2011; Cenko et al. 2012; Pasham et al. 2015) also show a sharp drop in X-ray luminosity 200 to 300 days (in the rest frame) after the discovery and that has been interpreted as the thick-to-thin transition of the inner disk (Tchekhovskoy et al. 2014). Second, from the mass fallback rate - M M P t P 3 fb min min 5 3 ( ) * (M* being the stellar mass and P min being the minimum period of the fallback material), one can estimate the time tEdd at which the fallback rate drops below the Eddington accretion rate of∼10LEdd/c2 , and the result is (Lu & Kumar 2018) - + t M M M 309 d , 7 q Edd h,7 2 5 1 3 5 ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ ( ) ( ) * where we have taken the normal mass–radius relation of main- sequence stars R R M M q ( ) * * (q = 0.8 below one solar mass stars and q = 0.57 above one solar mass stars). We expect the inner disk to collapse into a thin state on the timescale tEdd, under the condition that an order-unity fraction of the fallback rate directly reaches near the innermost regions of the disk. We note that the condition is satisfied for a≈107 Me MBH since the tidal radius is only≈10Rg for a solar-type star. If the rapid X-ray flux drop (D → E) is indeed caused by a disk state transition, then after the transition, the disk mass will accumulate over time due to ongoing fallback. This causes the accretion rate to increase, and eventually the disk briefly goes back to a thick state (with a very short viscous time) followed by another transition to the thin state. This is qualitatively consistent with the second rapid X-ray flux decline at δt≈325 days (E1 → E2 in Figure 16). 5.4. Unusual UV/optical Behavior 5.4.1. Featureless Optical Spectrum As shown in Section 4.2, AT2021ehb’s optical spectroscopic properties are dissimilar to the majority of previously known TDEs (i.e., H-rich, He-rich, N-rich, Fe-rich; Leloudas et al. 2019; van Velzen et al. 2021; Wevers et al. 2019a). It is most similar to a few recently reported TDEs with blue and featureless spectra (Brightman et al. 2021; Hammerstein et al. 2022). Hammerstein et al. (2022) found that compared with 17 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 18. TDEs that developbroad emission lines, the UV/optical emission of four featureless events have larger peak Lbb, peak Tbb, and peak Rbb. Figure 21 compares the rest-frame g-band light curve of AT2021ehb with 30 TDEs from phase I of ZTF (Hammerstein et al. 2022). Solid lines are the results of fitting the multiband light curves (δt<100 days) with a Gaussian rise + exponential decay model (see Section 5.1 of van Velzen et al. 2021). We highlight the TDEs lacking line features by plotting the data as colored symbols. Here we have chosen an observing band with good temporal sampling, and converted the observations in this band into ν0 = 6.3 × 1014 Hz by performing a color correction. Our study suggests that not all featureless TDEs are overluminous. In fact, the peak g-band magnitude (Mg,peak) and peak Lbb of AT2021ehb are faint compared with other optically selected TDEs (Figure 6, Figure 21). It is unclear whether Mg,peak of the TDE-featureless class forms a continuous or bimodal distribution between −17 and −22. This question will be addressed in a forthcoming publication (Y. Yao et al. 2022, in preparation). A detailed analysis of Hubble Space Telescope UV spectroscopy (E. Hammerstein et al. 2022, in preparation) will be essential to reveal if AT2021ehb exhibits any spectral lines in the UV. 5.4.2. Origin of the NUV/optical Emission Here we discuss possible origins of AT2021ehbs NUV/ optical emission: stream self-crossing shock, reprocessing, and thermal emission from disk accretion. In the self-crossing shock model, since the radius of the self- crossing shock is determined by the amount of general relativistic apsidal precession as given by the pericenter of the initial stellar orbit (Dai et al. 2015), we expect the power of the self-crossing shock to track the fallback rate and decay with time as∼t−5/3 . This is inconsistent with the flat light curve observed in AT2021ehb in the UV/optical bands (phase C–E), unless there is an additional mechanism that modulates the radiative efficiency of the self-crossing shock such that it roughly cancels the effects of the dropping shock dissipation power. Therefore, the energy dissipated by the stream–stream collision cannot be the primary source of emission during the plateau phase, although it may contribute to the early-time UV/ optical emission. In the reprocessing model, the nature of the reprocessing layer could originate from either a disk wind (Strubbe & Quataert 2009; Miller 2015; Dai et al. 2018; Parkinson et al. 2022; Thomsen et al. 2022) or an outflow from the self- crossing shock (Jiang et al. 2016; Lu & Bonnerot 2020). The outflow scenario is favored for two reasons. First, a radiation pressure-driven disk wind originates from the innermost regions of the disk and the wind density is geometrically diluted as it propagates to a distance of the order of Rbb∼1014 cm, whereas the outflow from the self-crossing shock is expected to be much denser near the self-crossing point and is hence more capable of reprocessing the hard emission from the disk (Bonnerot et al. 2021). Second, as the accretion flow goes from super-Eddington to sub-Eddington (Section 5.3.2), one may expect the reduction in radiation pressure to reduce the strength of the wind outflows. The fact that the UV/optical luminosity only slightly decreases from phase D to phase E suggests that the reprocessing layer is not sensitive to the innermost accretion flow. Finally, if the UV/optical emission is powered by disk accretion, then the outer disk radius must be located at 10RT≈100Rg. Recent simulations show that it is possible that a small fraction of the bound debris circularizes at∼10RT (Bonnerot et al. 2021), but the accretion power at such large radii may be too low to produce the observed UV/optical emission, since the outermost regions of the disk are expected to be geometrically thin (due to efficient radiative cooling) with a very long viscous time. More detailed disk evolution modeling is needed to evaluate this possibility. To summarize, we infer that the early-time UV/optical light may be thermal radiation emitted at the photosphere of a stream–stream collision shock. The late-time UV/optical emission likely comes from reprocessing by the outflow launched from the self-crossing shock, although thermal emission from the outer regions of an accretion flow is not ruled out. 5.5. Comparison to Other Accreting Black Holes In stellar-mass black hole XRB outbursts, some objects are observed to transition between a soft disk-dominated state (SDS) and a hard Comptonized state (HCS). In the SDS of XRBs, the inner radius (Rin, d) of an optically thick, geometrically thin disk stays around the ISCO of RISCO∼a few × Rg. When the outbursts transition to the HCS, Macc decreases, and Rin, d progressively moves outwards to∼few × 100Rg, leaving a radiatively inefficient, advection- dominated accretion flow (Yuan et al. 2005; Yuan & Narayan 2014). At the same time, a region of hot corona is formed close to the BH (Done et al. 2007). For MBH accretors, Seyferts have been proposed as the high-MBH analogs of XRBs in the SDS, whereas low-luminosity AGNs and low-ionization nuclear emission-line regions are considered similar to XRBs in the HCS (Falcke et al. 2004). In Section 5.3.2, we propose that in phases B–D, the accretion flow of AT2021ehb is in a radiation-trapped, super- Eddington regime (see, e.g., Figure 2 of Narayan & Quataert 2005), which is different from the typical sub- Eddington X-ray states observed in AGNs and XRBs. Such a difference is further corroborated by two properties. First, on Figure 21. Rest-frame g-band light curve of AT2021ehb compared with that of the 30 TDEs presented by Hammerstein et al. (2022). The solid lines show the best-fit models (see the text for details). Data points and labeled names are only shown for TDEs with no discernible optical broad lines. 18 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 19. the hardness–intensity diagram(HID; see Figure 22), the evolution of AT2021ehb is neither similar to the “turtlehead” pattern observed in XRBs (Fender et al. 2004; Munoz-Darias et al. 2013; Tetarenko et al. 2016), nor similar to the “brighter when softer” trend observed in X-ray bright AGNs (Auchettl et al. 2018). On the Lbol–αOX diagram (Figure 19), its evolution is also different from that observed in CLAGNs (Ruan et al. 2019). Second, in the canonical hard state (i.e., sub-Eddington accretion rates), there is a correlation among radio luminosity, X-ray luminosity, and MBH, which applies to both XRBs and hard-state AGNs (Merloni et al. 2003; Falcke et al. 2004). A recent fit to this “fundamental plane of black hole activity” was provided by Gültekin et al. (2019): = - - - - - + R M X 1.09 0.10 log 1 0.55 0.22 0.59 , 8 7 0.15 0.16 ( ) ( ) ( ) ( ) ( ) where º - R L log 10 erg s 5 GHz 38 1 [ ( )] and º - X L log 2 10 keV [ - 10 erg s 40 1 ( )]. In the hard state of AT2021ehb, the 2–10 keV luminosity in the Swift/XRT “s6” spectrum gives X = 2.96 ± 0.02. Using Equation (8), the expected 5 GHz radio luminosity on the fundamental plane is L log 5 GHz [ = + = - R erg s 38 38.21 0.59 1 ( )] . The uncertainty of R is calculated from the distribution of 105 MC trials. Using our radio limit at δt = 228 days (Table 2) and assuming a flat radio spectrum of fν ∝ ν0 , we find a 5 GHz equivalent radio upper limit of < - L log erg s 35.76 5 GHz 1 [ ( )] . According to Gültekin et al. (2019), the scatter on the fundamental plane correlation is a factor of ∼7.6 in the L5 GHz direction (or ∼10 in the MBH direction), which is not enough to solve the discrepancy. This again argues that AT2021ehb is not in a canonical hard state where we would expect a radio jet to be launched. The radio behavior of BH binaries at the Eddington accretion rates might be more relevant to AT2021ehb (at least in phases B–D). A few XRBs get above the Eddington limit for brief periods, when they are seen to undergo a sequence of bright radio flares for a short period of time. Examples include the 2015 outburst of V404 Cygni (Tetarenko et al. 2017, 2019) and the ultraluminous X-ray source in M31 (Middleton et al. 2013). In AT2021ehb, the slow cadence of our radio follow-up observations does not allow us to rule out the existence of such radio flares, which last for hours to weeks, not months. Finally, we note that the evolution of the X-ray properties of AT2021ehb are different from a few other TDEs. For example, Wevers et al. (2021) constructed the logλEdd–αOX diagram for AT2018fyk, finding that the 2 keV (corona) emission is stronger when λEdd is lower. Figure 19 shows that this is clearly not the case for AT2021ehb. Separately, Hinkle et al. (2021) studied the evolution of AT2019azh on the canonical HID, showing that when the X-ray luminosity is higher, the X-ray spectrum is softer. Figure 22 shows that AT2021ehb does not follow this trend either. It remains to be seen whether AT2021ehb is peculiar among the sample of optically selected TDEs with significant X-ray spectral evolution. To this end, constructing a systematically selected sample and analyzing the multiwavelength data in a homogeneous fashion is the key. 6. Conclusion We have presented an extensive multiwavelength study of the TDE AT2021ehb. Its peak 0.3–10 keV flux of∼1 mCrab is brighter than any other non-jetted TDE in the literature, allowing us to obtain a series of high-quality X-ray spectra, including the first hard X-ray spectrum of a non-jetted TDE up to 30 keV. The detection of hard X-ray photons favors a highly aspherical geometry (Section 5.2), and detailed modeling of the NICER +NuSTAR spectrum shows evidence of relativistic disk reflection (Section 4.4.2). The emission from the self-crossing shock itself might contribute to the early-time UV/optical emission, while the post-peak (phase C–E) emission is either dominated by reprocessing of X-ray photons by the outflow launched from the shock, or by thermal emission in the outer regions of an accretion flow (Section 5.4.2). More detailed hydrodynamic and radiative transfer calculations (e.g., Roth et al. 2016) are needed to test if such scenarios can reproduce the observed UV/optical plateau and the featureless optical spectra. We observed a soft → hard → soft spectral transition in the X-ray. The initial soft-to-hard transition happened gradually over ∼170 days. A possible explanation is that magnetic fields grow with time due to differential rotation, resulting in the formation of a magnetically dominated hot corona (Section 5.3.1). The bolometric luminosity of AT2021ehb is the highest when the X-ray spectrum is the hardest—a property that is different from XRBs, X-ray bright AGNs, and many other TDEs (Section 5.5). The latter hard-to-soft transition happened drastically within 3 days at δt≈272 days, and might be due to thermal–viscous instability in the inner disk (Section 5.3.2). Such an instability typically occurs when Lbol∼0.3LEdd (Tchekhovskoy et al. 2014). This requires that most of the luminosity of AT2021ehb is emitted in the EUV band that is not observed. Systems similar to AT2021ehb are excellent targets for X-ray telescopes to study the real-time formation of the accretion disk and corona around MBHs. The detection of relativistic disk reflection features demonstrates the possibility of constraining the spin of normally quiescent MBHs via reflection spectroscopy—an opportunity enabled by combining modern time-domain surveys with systematic multiwavelength follow-up observations. Figure 22. Galactic extinction-corrected 0.3–10 keV X-ray luminosity (LX, 0) as a function of hardness ratio for Swift/XRT detections only. 19 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 20. We are gratefulto the NuSTAR, NICER, Swift, XMM- Newton, and VLA teams for making this observing campaign possible. We thank the anonymous referee for constructive comments and suggestions. We thank Julian Krolik for providing comments on an early version of this manuscript. We thank Erin Kara, Renee Ludlam, Guglielmo (Gullo) Mastroserio, and Riley Connors for helpful discussions on the NuSTAR and NICER spectral fitting. We thank Murray Brightman and Hannah Earnshaw for discussions on disk reflection and super-Eddington accretion. Y.Y. acknowledges support from NASA under award No. 80NSSC22K0574. W.L. is supported by the Lyman Spitzer, Jr. Fellowship at Princeton University. This work was supported by the Australian government through the Australian Research Council’s Discovery Projects funding scheme (DP200102471). M.N. is supported by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No. 948381) and by a Fellowship from the Alan Turing Institute. E.C.K. acknowl- edges support from the G.R.E.A.T. research environment funded by Vetenskapsrådet, the Swedish Research Council, under project No. 2016-06012, and support from The Wenner- Gren Foundations. This work has made use of data from the NuSTAR mission, a project led by Caltech, managed by NASA/JPL, and funded by NASA. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS), jointly developed by the ASI Science Data Center (ASDC, Italy) and Caltech (USA). This work is based on observations obtained with the Samuel Oschin Telescope 48 inch and the 60 inch Telescope at the Palomar Observatory as part of the Zwicky Transient Facility (ZTF) project. ZTF is supported by the National Science Foundation under grant No. AST-2034437 and a collaboration including Caltech, IPAC, the Weizmann Institute of Science, the Oskar Klein Center at Stockholm University, the University of Maryland, Deutsches Elektronen-Synchrotron and Hum- boldt University, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee, Trinity College Dublin, Lawrence Livermore National Laboratories, IN2P3, University of Warwick, Ruhr University Bochum, and Northwestern University. Operations are conducted by COO, IPAC, and UW. The ZTF forced-photometry service was funded under the Heising-Simons Foundation grant No. 12540303 (PI: Graham). SED Machine is based upon work supported by the National Science Foundation under grant No. 1106171. This work used observations with the eROSITA telescope on board the SRG observatory. The SRG observatory was built by Roskosmos with the participation of the Deutsches Zentrum fur ̈ Luft- und Raumfahrt (DLR). The SRG/eROSITA X-ray telescope was built by a consortium of German Institutes led by MPE, and supported by DLR. The SRG spacecraft was designed, built, launched, and is operated by the Lavochkin Association and its subcontractors. The eROSITA data used in this work were processed using the eSASS software system developed by the German eROSITA consortium and proprietary data reduction and analysis software developed by the Russian eROSITA Consortium. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Software: astropy (Astropy Collaboration et al. 2013), CASA (McMullin et al. 2007), emcee (Foreman-Mackey et al. 2013), heasoft (Heasarc 2014), LPipe (Perley 2019), matplotlib (Hunter 2007), Prospector (Johnson et al. 2021), pwkit (Williams et al. 2017), python-fsps (Fore- man-Mackey et al. 2014), relxill (García et al. 2014; Dauser et al. 2014), scipy (Virtanen et al. 2020), xspec (Arnaud 1996). Facilities: XMM, NuSTAR, Swift, NICER, SRG, PO:1.2 m, PO:1.5 m, Hale, Keck:I (LRIS), Keck: II (ESI), LDT, VLA. Appendix A Supplementary Tables A.1. Photometry and Observing Logs UV and optical photometry are presented in Table 8. Swift/ XRT observations are summarized in Table 9. Table 8 UV and Optical Photometry of AT2021ehb MJD Instrument Filter fν (μJy) s n f (μJy) 59250.1643 ZTF r −3.31 12.48 59250.2031 ZTF g 2.07 10.91 59299.0783 UVOT uvw1 567.68 27.76 59299.0798 UVOT U 551.85 41.60 59299.0808 UVOT B 487.52 76.95 59299.0831 UVOT uvw2 587.34 22.36 59299.0855 UVOT V 260.66 146.91 59299.0875 UVOT uvm2 528.68 19.49 Note. fν is observed flux density before extinction correction. (This table is available in its entirety in machine-readable form.) 20 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 21. Table 9 Log ofSwift/XRT Observations of AT2021ehb obsID Start Date δt Exp. Net Count Rate fX fX, 0 (days) (s) (count s−1 ) (10−13 erg s−1 cm−2 ) (10−13 erg s−1 cm−2 ) 14217001 2021-03-26.0 −21.6 2669 <0.0019 <0.66 <1.25 14217003 2021-03-28.2 −19.4 1475 <0.0027 <0.96 <1.82 14217004 2021-03-31.0 −16.7 1683 <0.0024 <0.84 <1.59 14217005 2021-04-02.0 −14.7 1336 <0.0030 <1.06 <2.01 14217006 2021-07-01.2 +73.9 4078 0.0339 ± 0.0029 12.01 ± 3.21 22.73 ± 6.08 14217007 2021-07-09.8 +82.3 1366 0.0120 ± 0.0030 4.27 ± 1.52 8.08 ± 2.88 14217008 2021-07-16.1 +88.5 1348 0.0184 ± 0.0037 6.52 ± 2.11 12.34 ± 4.00 14217009 2021-07-23.1 +95.4 1141 0.0343 ± 0.0056 12.13 ± 3.65 22.96 ± 6.90 14217010 2021-07-30.1 +102.3 1366 0.0502 ± 0.0061 16.57 ± 2.23 44.04 ± 5.92 14217011 2021-08-08.1 +111.1 1925 0.0863 ± 0.0067 28.44 ± 2.76 75.62 ± 7.34 14217012 2021-08-15.9 +118.8 1653 0.1635 ± 0.0100 53.90 ± 4.54 143.32 ± 12.08 14217013 2021-08-22.1 +124.8 2065 0.1958 ± 0.0098 64.56 ± 4.94 171.64 ± 13.13 14217014 2021-08-30.9 +133.5 1583 0.2268 ± 0.0120 74.78 ± 5.87 198.82 ± 15.61 14217015 2021-09-05.5 +139.0 1830 0.2548 ± 0.0119 94.07 ± 7.27 200.69 ± 15.51 14217016 2021-09-12.8 +146.2 641 0.2061 ± 0.0180 76.09 ± 8.13 162.34 ± 17.35 14217017 2021-09-15.0 +148.4 1503 0.1281 ± 0.0093 47.29 ± 4.51 100.90 ± 9.63 14217018 2021-09-19.7 +153.0 1580 0.1974 ± 0.0112 72.90 ± 6.12 155.52 ± 13.05 14217019 2021-09-24.2 +157.4 2045 0.1959 ± 0.0098 72.33 ± 5.76 154.31 ± 12.28 14217020 2021-09-30.4 +163.5 1867 0.2675 ± 0.0120 98.74 ± 7.54 210.67 ± 16.09 14217021 2021-10-05.5 +168.5 1595 0.2775 ± 0.0132 104.81 ± 9.01 170.40 ± 14.65 14217022 2021-10-20.2 +182.9 1618 0.2865 ± 0.0134 108.22 ± 9.24 175.94 ± 15.02 14217023 2021-10-27.4 +190.0 1480 0.2698 ± 0.0136 101.93 ± 8.91 165.71 ± 14.48 14217024 2021-11-03.5 +197.0 2010 0.2124 ± 0.0103 80.23 ± 6.94 130.44 ± 11.29 14217025 2021-11-10.7 +204.0 1286 0.3132 ± 0.0157 149.64 ± 15.02 210.15 ± 21.10 14217026 2021-11-17.2 +210.4 1813 0.1251 ± 0.0084 59.75 ± 6.57 83.92 ± 9.23 14217027 2021-11-24.7 +217.7 1957 0.2718 ± 0.0119 129.86 ± 12.64 182.38 ± 17.75 14217028 2021-12-01.5 +224.4 1967 0.2600 ± 0.0116 124.20 ± 12.14 174.42 ± 17.05 14217029 2021-12-08.1 +230.9 2317 0.2596 ± 0.0107 126.84 ± 9.59 168.93 ± 12.77 14217030 2021-12-15.2 +237.9 2010 0.5234 ± 0.0162 255.79 ± 18.06 340.66 ± 24.05 14217031 2021-12-20.3 +242.9 1293 0.5445 ± 0.0206 266.11 ± 19.65 354.40 ± 26.17 14217032 2021-12-25.6 +248.2 1395 0.7108 ± 0.0227 347.35 ± 24.66 462.59 ± 32.84 14217033 2021-12-30.5 +253.0 1371 0.9721 ± 0.0268 551.93 ± 41.79 691.67 ± 52.37 14217034 2022-01-04.5 +257.8 1410 0.9675 ± 0.0263 549.33 ± 41.53 688.41 ± 52.05 14217035 2022-01-09.2 +262.4 1361 0.8629 ± 0.0253 489.92 ± 37.43 613.96 ± 46.91 14217036 2022-01-14.7 +267.9 1423 0.9218 ± 0.0256 523.38 ± 39.68 655.88 ± 49.72 14217041 2022-02-23.1 +306.6 2594 0.0745 ± 0.0054 26.05 ± 3.06 47.73 ± 5.60 14217042 2022-03-02.2 +313.5 3888 0.0706 ± 0.0043 24.72 ± 2.73 45.29 ± 5.01 14217043 2022-03-09.7 +320.9 2766 0.0918 ± 0.0058 32.11 ± 3.59 58.83 ± 6.58 14217044 2022-03-16.1 +327.2 2956 0.0122 ± 0.0022 5.03 ± 1.40 14.35 ± 3.98 14217045 2022-03-23.0 +334.0 3263 0.0197 ± 0.0025 8.08 ± 2.01 23.04 ± 5.73 14217046 2022-03-30.5 +341.3 2354 0.0246 ± 0.0033 10.11 ± 2.55 28.81 ± 7.26 Note. All measurements are given in 0.3–10 keV. fX and fX, 0 are converted using the scaling factors derived in Table 11. 21 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 22. A.2. Model Fits Table10 presents the photospheric parameters derived from fitting a blackbody function to the UV/optical data. Note that the uncertainty of Tbb is only computed for “good” epochs (see details in Section 4.1). The XRT spectral parameters are presented in Table 11. Table 10 UV/optical Blackbody Parameters δt (days) Lbb (1043 erg s−1 ) Rbb (1014 cm) Tbb (103 K) −50.0 0.39 ± 0.15 0.91 ± 0.03 2.85 −45.0 0.67 ± 0.25 1.19 ± 0.01 2.85 −40.0 1.01 ± 0.38 1.46 ± 0.05 2.85 −30.0 2.10 ± 0.78 2.11 ± 0.04 2.85 −25.0 2.62 ± 0.96 2.36 ± 0.03 2.85 −21.5 2.77 ± 1.19 2.42 ± 0.27 2.85 ± 0.26 −19.2 2.92 ± 1.30 2.51 ± 0.29 2.84 ± 0.27 −16.7 3.00 ± 0.89 2.70 ± 0.20 2.75 ± 0.18 −14.7 3.13 ± 0.65 2.80 ± 0.14 2.73 ± 0.13 −10.0 3.31 ± 0.62 2.89 ± 0.02 2.73 70.0 1.33 ± 0.29 1.91 ± 0.02 2.67 74.7 1.12 ± 0.29 1.75 ± 0.12 2.67 ± 0.15 82.4 1.06 ± 0.86 1.45 ± 0.31 2.90 ± 0.50 88.6 1.27 ± 1.46 1.18 ± 0.34 3.36 ± 0.84 95.4 0.79 ± 0.67 1.42 ± 0.33 2.72 ± 0.48 102.3 0.55 ± 0.18 1.79 ± 0.17 2.22 ± 0.15 111.5 0.52 ± 0.12 1.70 ± 0.10 2.24 ± 0.11 119.3 0.60 ± 0.10 1.56 ± 0.07 2.43 ± 0.09 125.1 0.54 ± 0.20 1.67 ± 0.18 2.28 ± 0.18 133.6 0.50 ± 0.18 1.82 ± 0.19 2.14 ± 0.16 139.2 0.52 ± 0.13 1.80 ± 0.12 2.18 ± 0.11 147.0 0.57 ± 0.15 1.65 ± 0.11 2.32 ± 0.13 153.3 0.60 ± 0.25 1.51 ± 0.18 2.47 ± 0.22 157.9 0.57 ± 0.30 1.47 ± 0.21 2.47 ± 0.27 163.6 0.54 ± 0.19 1.50 ± 0.15 2.41 ± 0.18 168.6 0.63 ± 0.25 1.31 ± 0.14 2.68 ± 0.23 178.0 0.42 ± 0.18 1.65 ± 0.18 2.16 ± 0.20 183.1 0.44 ± 0.25 1.51 ± 0.25 2.28 ± 0.26 190.2 0.43 ± 0.22 1.55 ± 0.23 2.24 ± 0.23 197.3 0.37 ± 0.13 1.76 ± 0.17 2.02 ± 0.14 204.1 0.43 ± 0.19 1.53 ± 0.18 2.25 ± 0.20 210.5 0.44 ± 0.25 1.59 ± 0.26 2.22 ± 0.26 217.8 0.44 ± 0.20 1.56 ± 0.05 2.24 224.5 0.42 ± 0.18 1.51 ± 0.07 2.26 231.0 0.40 ± 0.17 1.44 ± 0.05 2.27 238.0 0.42 ± 0.17 1.47 ± 0.04 2.29 242.9 0.42 ± 0.16 1.45 ± 0.05 2.30 248.2 0.42 ± 0.16 1.43 ± 0.05 2.32 253.0 0.43 ± 0.16 1.43 ± 0.04 2.33 257.8 0.43 ± 0.15 1.42 ± 0.03 2.34 262.4 0.42 ± 0.14 1.39 ± 0.03 2.35 267.9 0.41 ± 0.13 1.35 ± 0.03 2.37 276.0 0.39 ± 0.12 1.29 ± 0.04 2.39 296.0 0.42 ± 0.11 1.29 ± 0.03 2.44 302.0 0.38 ± 0.11 1.22 ± 0.08 2.45 ± 0.15 306.7 0.39 ± 0.10 1.22 ± 0.02 2.45 313.7 0.39 ± 0.10 1.23 ± 0.04 2.45 320.9 0.32 ± 0.08 1.11 ± 0.04 2.45 327.5 0.26 ± 0.07 1.01 ± 0.03 2.45 334.3 0.24 ± 0.06 0.97 ± 0.03 2.45 341.4 0.25 ± 0.06 0.98 ± 0.03 2.45 22 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 23. Appendix B Optical SpectroscopyInstrumental/Observational Information A log of optical spectroscopic observation is given in Table 12. For LRIS observations, we used the 560 dichroic, the 400/ 3400 grism on the blue side, the 400/8500 grating on the red side, and the 1″ slit width, which gives σinst≈173 km s−1 on the blue side and σinst≈126 km s−1 on the red side. The LRIS spectra were reduced and extracted using Lpipe (Perley 2019). For DBSP observations, we used the D-55 dichroic filter, the 600/4000 grating on the blue side, and the 316/7500 grating on the red side. With a slit width of 1 5 (2 0), this gives σinst≈106 km s−1 (σinst≈141 km s−1 ) on the blue side and σinst≈143 km s−1 (σinst≈190 km s−1 ) on the red side. The DBSP spectra were reduced using the dbsp_drp pipeline (Roberson et al. 2022), which is based on PypeIt (Prochaska et al. 2020). The ESI observation was performed in the Echellette mode with a 0 75 wide slit, which gives a resolving power of R = 5350 (i.e., σinst = 24 km s−1 ). The ESI spectrum was reduced using the MAKEE pipeline following standard proce- dures. Flux calibration was not performed. We normalized the spectra by fitting third-order cubic splines to the continuum, with prominent emission and absorption lines masked. Observations with DeVeny were performed with the 300/ 4000 grating, with a grating tilt angle of 23° .13 to yield a central wavelength of 5800 Å, the clear rear filter, and a slit width of 1 5. This gives σinst≈169 km s−1 . DeVeny spectra were reduced with PyRAF, including bias correction and flat- fielding. Table 11 X-Ray Fluxes from Modeling of XRT Spectra Observation Net 0.3–10 keV Rate fν(0.5 keV) fν(2 keV) fX (0.3–10 keV) fX, 0 (0.3–10 keV) fX, 0 (0.5–10 keV) (count s−1 ) (μJy) (μJy) (10−13 erg s−1 cm−2 ) (10−13 erg s−1 cm−2 ) (10−13 erg s−1 cm−2 ) s1 0.0276 ± 0.0019 - + 1.133 0.185 0.103 - + 0.030 0.023 0.002 - + 9.76 1.08 1.39 - + 18.47 2.05 2.63 - + 11.34 2.72 0.37 s2 0.1476 ± 0.0041 - + 9.639 0.595 0.178 - + 0.106 0.012 0.008 - + 48.67 1.03 1.79 - + 129.40 2.74 4.76 - + 48.96 2.53 1.34 s3 0.2116 ± 0.0047 - + 10.930 0.694 0.287 - + 0.312 0.018 0.017 - + 78.12 1.95 2.87 - + 166.66 4.15 6.13 - + 86.04 3.95 1.75 s4 0.2584 ± 0.0062 - + 7.565 0.683 0.224 - + 0.544 0.035 0.026 - + 97.63 3.31 3.67 - + 158.72 5.37 5.97 - + 109.87 5.73 2.56 s5 0.2382 ± 0.0058 - + 5.485 0.583 0.211 - + 0.678 0.054 0.029 - + 113.80 4.00 5.90 - + 159.82 5.62 8.29 - + 127.47 7.81 3.50 s6 0.4776 ± 0.0083 - + 8.675 1.257 0.247 - + 1.702 0.063 0.057 - + 233.38 4.48 8.72 - + 310.81 5.97 11.61 - + 256.24 11.39 7.73 s7 0.9314 ± 0.0129 - + 14.647 1.061 0.724 - + 3.575 0.164 0.082 - + 528.81 13.21 20.29 - + 662.69 16.55 25.43 - + 579.24 27.10 11.66 s8 0.0780 ± 0.0029 - + 2.843 0.351 0.121 - + 0.132 0.014 0.010 - + 27.30 0.96 1.56 - + 50.03 1.77 2.85 - + 30.99 2.74 1.06 s9 0.0185 ± 0.0015 - + 1.218 0.741 0.006 - + 0.027 0.005 0.006 - + 7.59 0.52 1.11 - + 21.62 1.48 3.15 - + 6.78 1.38 0.48 Table 12 Log of AT2021ehb Optical Spectroscopy Start Date δt (days) Telescope Instrument Wavelength Range (Å) Slit Width (″) Exp. (s) 2021-03-25.1 −22 P60 SEDM 3770–9223 L 2160 2021-03-27.1 −20 P60 SEDM 3770–9223 L 2160 2021-07-06.6 +79 Keck I LRIS 3200–10250 1.0 300 2021-08-01.4 +104 P200 DBSP 3410–5550, 5750–9995 1.5 900 2021-08-13.6 +116 Keck I LRIS 3200–10250 1.0 300 2021-09-07.6 +141 Keck I LRIS 3200–10250 1.0 300 2021-09-17.4 +150 P60 SEDM 3770–9223 L 2700 2021-10-27.5 +190 LDT DeVeny 35868034 1.5 2400 2021-11-13.3 +206 P60 SEDM 3770–9223 L 2700 2021-12-03.3 +226 P60 SEDM 3770–9223 L 2700 2021-12-28.4 +250 Keck II ESI 4000–10250 0.75 300 2022-01-05.2 +258 P60 SEDM 3770–9223 L 2700 2022-01-12.2 +265 P200 DBSP 3410–5550, 5750–9995 2.0 600 2022-01-20.3 +273 P60 SEDM 3770–9223 L 2700 2022-01-27.3 +280 P60 SEDM 3770–9223 L 2700 2022-02-06.3 +290 Keck I LRIS 3200–10250 1.0 300 2022-03-27.1 +338 P200 DBSP 3410–5550, 5750–9995 1.5 1200 Note. The spectra are available on the TNS page of this source (https://www.wis-tns.org/object/2021ehb). 23 The Astrophysical Journal, 937:8 (25pp), 2022 September 20 Yao et al.
- 24. ORCID iDs Yuhan Yaohttps:/ /orcid.org/0000-0001-6747-8509 Wenbin Lu https:/ /orcid.org/0000-0002-1568-7461 Muryel Guolo https:/ /orcid.org/0000-0002-5063-0751 Dheeraj R. Pasham https:/ /orcid.org/0000-0003-1386-7861 Suvi Gezari https:/ /orcid.org/0000-0003-3703-5154 Keith C. Gendreau https:/ /orcid.org/0000-0001-7115-2819 Fiona Harrison https:/ /orcid.org/0000-0003-2992-8024 S. Bradley Cenko https:/ /orcid.org/0000-0003-1673-970X S. R. Kulkarni https:/ /orcid.org/0000-0001-5390-8563 Jon M. Miller https:/ /orcid.org/0000-0003-2869-7682 Dominic J. Walton https:/ /orcid.org/0000-0001-5819-3552 Javier A. García https:/ /orcid.org/0000-0003-3828-2448 Sjoert van Velzen https:/ /orcid.org/0000-0002-3859-8074 Kate D. Alexander https:/ /orcid.org/0000-0002-8297-2473 James C. A. Miller-Jones https:/ /orcid.org/0000-0003- 3124-2814 Matt Nicholl https:/ /orcid.org/0000-0002-2555-3192 Erica Hammerstein https:/ /orcid.org/0000-0002-5698-8703 Pavel Medvedev https:/ /orcid.org/0000-0002-9380-8708 Daniel Stern https:/ /orcid.org/0000-0003-2686-9241 Vikram Ravi https:/ /orcid.org/0000-0002-7252-5485 Joshua S. Bloom https:/ /orcid.org/0000-0002-7777-216X Matthew J. Graham https:/ /orcid.org/0000-0002-3168-0139 Erik C. Kool https:/ /orcid.org/0000-0002-7252-3877 Ashish A. Mahabal https:/ /orcid.org/0000-0003-2242-0244 Frank J. Masci https:/ /orcid.org/0000-0002-8532-9395 Josiah Purdum https:/ /orcid.org/0000-0003-1227-3738 Ben Rusholme https:/ /orcid.org/0000-0001-7648-4142 Yashvi Sharma https:/ /orcid.org/0000-0003-4531-1745 Roger Smith https:/ /orcid.org/0000-0001-7062-9726 Jesper Sollerman https:/ /orcid.org/0000-0003-1546-6615 References Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12 Alexander, K. 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