# The first systematically identified repeating partial tidal disruption event

Jean J. Somalwar Cahill Center for Astronomy and Astrophysics, MC 249-17
California Institute of Technology, Pasadena CA 91125, USA.  Vikram Ravi
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Yuhan Yao Miller Institute for Basic
Research in Science, 468 Donner Lab, Berkeley, CA 94720, USA  Department of
Astronomy, University of California, Berkeley, CA 94720, USA  Muryel Guolo
Bloomberg Center for Physics and Astronomy, Johns Hopkins University, 3400 N.
Charles St., Baltimore, MD 21218, USA  Matthew Graham  Cahill Center for
Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  Erica Hammerstein Department of Astronomy, University
of Maryland, College Park, MD 20742, USA  Wenbin Lu Department of Astronomy
and Theoretical Astrophysics Center, University of California, Berkeley, CA
94720, USA  Matt Nicholl Astrophysics Research Centre, School of Mathematics
and Physics, Queens University Belfast, Belfast BT7 1NN, UK  Yashvi Sharma
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Robert Stein  Cahill Center for
Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  Sjoert van Velzen Leiden Observatory, Leiden
University, Postbus 9513, 2300 RA, Leiden, The Netherlands  Eric C. Bellm
DIRAC Institute, Department of Astronomy, University of Washington, 3910 15th
Avenue NE, Seattle, WA 98195, USA  Michael W. Coughlin School of Physics and
Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA  Steven
L. Groom IPAC, California Institute of Technology, 1200 E. California Blvd,
Pasadena, CA 91125, USA  Frank J. Masci IPAC, California Institute of
Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA  Reed Riddle
Caltech Optical Observatories, California Institute of Technology, Pasadena,
CA 91125, USA

###### Abstract

Tidal disruption events (TDEs) occur when a star enters the tidal radius of a
supermassive black hole (SMBH). If the star only grazes the tidal radius, a
fraction of the stellar mass will be accreted in a partial TDE (pTDE). The
remainder can continue orbiting and may re-disrupted at pericenter, causing a
repeating pTDE. pTDEs may be as or more common than full TDEs (fTDEs), yet few
are known. In this work, we present the discovery of the first repeating pTDE
from a systematically-selected sample, AT 2020vdq. AT 2020vdq was originally
identified as an optically- and radio-flaring TDE. Around $3$ years after its
discovery, it rebrightened dramatically and rapidly in the optical. The
optical flare was remarkably fast and luminous compared to previous TDEs. It
was accompanied by extremely broad (${\sim}0.1c$) optical/UV spectral features
and faint X-ray emission ($L_{X}\sim 3\times 10^{41}$ erg s-1), but no new
radio-emitting component. Based on the transient optical/UV spectral features
and the broadband light curve, we show that AT 2020vdq is a repeating pTDE. We
then use it to constrain TDE models; in particular, we favor a star originally
in a very tight binary system that is tidally broken apart by the Hills
mechanism. We also constrain the repeating pTDE rate to be $10^{-6}$ to
$10^{-5}$ yr-1 galaxy-1, with uncertainties dominated by the unknown
distribution of pTDE repeat timescales. In the Hills framework, this means the
binary fraction in the galactic nucleus is of the order few percent.

##  1 Introduction

Much about supermassive black holes (SMBHs) remains enigmatic, including their
formation pathways, typical growth histories, and effects on their hosts (e.g.
Kormendy & Ho, 2013a). Much of the reason for our lack of knowledge about
SMBHs is their inherent faintness: if the SMBH is not actively accreting as an
active galactic nucleus (AGN), it can only be detected if it is in a very
nearby galaxy. Even if it is accreting, the accretion process is poorly
understood, so inferring physical properties of the SMBH and its environment
from the observed emission is nontrivial.

In the last few decades, tidal disruption events (TDEs) have become key probes
of SMBH physics (see Gezari, 2021, for a review). TDEs occur when a star
ventures within the tidal radius of an SMBH: $R_{T}\approx R_{*}(M_{\rm
BH}/M_{*})^{1/3}$ , where $R_{T}$ is the tidal radius, $M_{\rm BH}$ is the
SMBH mass, $R_{*}$ is the stellar radius, and $M_{*}$ is the stellar mass
(Evans & Kochanek, 1989; Rees, 1988; Phinney, 1989). Tidal forces shred the
star and, eventually, the stellar debris is accreted, producing a bright
multiwavelength flare. The development of high cadence, wide field optical,
radio, and X-ray surveys has enabled the discovery of ${\gtrsim}100$ candidate
events (e.g. Sazonov et al., 2021; Yao et al., 2023).

To produce a TDE, a star must enter into a plunging orbit with a pericenter
that is within the tidal radius of the SMBH but outside the Schwarzschild
radius. This occurs only once every ${\sim}10^{4-5}$ years in galaxies with
$M_{\rm BH}\lesssim 10^{8}\,M_{\odot}$ (van Velzen & Farrar, 2014; Stone et
al., 2020; Yao et al., 2023). In contrast, if the star is on a grazing orbit,
but still reaches the vicinity of the tidal radius, it can be partially
disrupted, and only a fraction of the stellar mass will be deposited on the
SMBH (Guillochon & Ramirez-Ruiz, 2013; Coughlin & Nixon, 2019). These partial
TDEs (pTDEs) may occur only once if the star is on a parabolic orbit, or they
can repeat if the star is on an elliptical orbit. Theoretical work has
suggested that the pTDE rate could be orders of magnitude higher than the full
TDE (fTDE) rate and may contribute significantly to the growth of SMBHs
(Bortolas et al., 2023). They also provide a unique avenue to test/improve our
TDE theory: the only things that may change between disruptions are the
structure of the star (as it is tidally perturbed during each partial
disruption), the amount of mass joining the accretion flow, and the
circumnuclear medium (CNM; if the previous disruptions launched outflows). Any
differences between subsequent pTDE flares can thus be used to rule out models
that invoke any of the static aspects of the system. Moreover, an accretion
disk may form after the first disruptions, so subsequent disruptions can be
used to assess the role that the disk plays in the TDE behavior.

Few candidate pTDEs are confidently identified, despite the high rate
estimates. Given our insufficient understanding of TDE physics, one of the
best ways to confirm a candidate pTDE is if it repeats; i.e. if the star is on
a bound orbit. If the orbital period is $P\simeq
10^{5}\mathrm{\,yr}\,(a/\mathrm{pc})^{3/2}(M/10^{6}M_{\odot})^{-1/2}$ ($a$
being the orbital semi-major axis and $M$ being the SMBH mass), as expected
for isolated stars in a nuclear star cluster slowly migrating onto grazing
orbits due to orbital relaxation, we will not detect a repeat. It is possible
that some or most of the known TDEs are this type of pTDE, but we require a
better understanding of pTDE and fTDE physics to be able to accurately
classify such sources.

Indeed, the pTDE candidates that are known were discovered because they
repeated within ${\sim}0.3-3$ years (ASASSN 14ko Payne et al., 2021; Liu et
al., 2023; Wevers et al., 2023; eRASSt J045650.3-203750 Liu et al., 2023; AT
2018fyk Wevers et al., 2019, 2023; RX J133157.6-324319.7 Hampel et al., 2022;
Malyali et al., 2023). Such tightly bound stars are difficult to reproduce
with orbital relaxation alone (Alexander, 2017). The most likely mechanism for
such objects invokes Hills break-up of a tight binary, resulting in one bound
object and one ejected object. If the binary is tight enough (inner semi-major
axis ${\lesssim}0.01$ AU, with dependence on the SMBH mass), dynamical
arguments predict that the bound star will have a period from
$\mathcal{O}(10^{2})$ days to a few years (Lu & Quataert, 2023). The binary
fraction in galactic nuclei is not well known, but could be sufficiently high
to explain the rate of these events.

These pTDE candidates are an inhomogeneous group, however, with some selected
in the X-ray, some in the optical, and none as part of a uniform search.
Hence, the pTDE rate and the differences in their multiwavelength properties
relative to fTDEs are still unconstrained. Fortunately, over the last few
years, the Zwicky Transient Facility (ZTF; Bellm et al., 2019; Graham et al.,
2019; Dekany et al., 2020; Masci et al., 2019) has enabled systematic searches
for optically-flaring TDEs. It has produced the first uniformly-selected
samples of TDEs (van Velzen et al., 2021a; Hammerstein et al., 2023; Yao et
al., 2023). In May 2023, one of the ZTF TDEs, AT 2020vdq, rebrightened
(Charalampopoulos et al., 2023a). We commenced follow-up efforts and
classified it as a repeating pTDE.

In this work, we will present observations and analysis of AT 2020vdq. We
describe the detection and properties of the first flare from AT 2020vdq in
Section 2 and we detail the second flare in Section 3. We constrain past
flares from this source in Section 4. In Section 5, we summarize key results,
show that AT 2020vdq is consistent with being a pTDE, compare it to published
observations of pTDEs, and use our observations to constrain both TDE and pTDE
models. In particular, we constrain key aspects of TDE radio, optical, and
spectral line emission, and we constrain the pTDE rate and typical number of
repetitions. We also discuss possible contributions of pTDEs to solving the
missing energy problem. Finally, we conclude in Section 6.

Table 1:

Parameter | AT 2020vqd
---|---
R.A. | $10^{\rm h}08^{\rm m}53.50^{\rm s}$
Dec. | $+42^{\rm d}43^{\rm m}00.40^{\rm s}$
Redshift | 0.045
$d_{L}$ [Mpc] | 206

Note. — Basic properties of the host galaxy of AT 2020vdq.

##  2 Observation of the initial flare

Figure 1: The optical and UV lightcurves for the first (top) and second
(bottom) flares from AT 2020vdq. Observations are shown as scattered points.
The best-fit parameteric, evolving black body models, as described in Section
3.1 are shown as solid lines.

We begin by describing the multiwavelength properties of the first flare from
AT 2020vdq. These properties are described in detail by Somalwar et al.
(2023); Somalwar & Ravi (2023); Yao et al. (2023).

AT 2020vdq was first detected as an optical transient by the Zwicky Transient
Facility (ZTF) on Oct. 4 2020 (MJD 59126) using the selection described in Yao
et al. (2023) implemented using the AMPEL filter (Nordin et al., 2019). It was
located at the nucleus of a dwarf galaxy at $z=0.045$ with $\log
M_{*}/M_{\odot}=9.25$. The stellar velocity dispersion of the nucleus host
galaxy was measured to be $\sigma_{*}=44\pm 3$ km s-1 from a high resolution
spectrum obtained with ESI on the Keck II telescope (Yao et al., 2023). This
dispersion corresponds to a black hole mass of $\log M_{\rm
BH,\sigma_{*}}/M_{\odot}=5.59\pm 0.37$ using the $M_{\rm BH}-\sigma_{*}$
relation from Kormendy & Ho (2013b). We refer the reader to Yao et al. (2023);
Somalwar et al. (2023); Somalwar & Ravi (2023) for more details of the host
observations and analysis.

The first optical flare from AT2020vdq is shown in the top panel of Figure 1.
The optical flare peaked in the $r$-band near Sept. 23 2020 (MJD 59115). This
peak was fit to a blackbody by Yao et al. (2023), who found that the peak is
consistent with a blackbody with temperature $\log T_{\rm bb}/{\rm K}=4.16$
and luminosity $\log L_{\rm bb}/({\rm erg\,s}^{-1})=42.99$. Note that this
measurement is based on observations in only the $g$ and $r$ bands, so unknown
systematic errors render the results uncertain. Stronger constraints are not
possible because no UV observations were obtained at peak. This luminosity
makes AT 2020vdq the lowest luminosity TDE in the Yao et al. (2023) sample,
even relative to events with lower black hole masses. The flare temperature is
also in the coolest 20% quantile of the sample.

Figure 2: The radio evolution of AT 2020vdq. The black scatter points show a
VLA observation from 500 days after the initial flare, or equivalently 470
days before the second flare. The red scatter points show a VLA observations
from eight days after the rebrightening. The green upper limit shows a NOEMA
observation from two weeks after the rebrightening. Both SEDs can be fit with
spherical, non-relativistic synchrotron models. No young emitting component is
required in the SED from shortly after the rebrightening.

AT 2020vdq was detected as a radio source in 3 GHz observations from the VLA
Sky Survey (VLASS; Lacy et al., 2020) on Oct. 9 2021 (MJD 59496), or ${\sim}1$
year after the first optical peak. It had a flux of $f_{\nu,{\rm
3\,GHz}}=1.48\pm 0.14\,$mJy or $\nu L_{\nu}=(2.3\pm 0.2)\times 10^{38}\,{\rm
erg}\,{\rm s}^{-1}$. The transient location had been previously observed by
VLASS on May 25, 2019 (MJD 58628), or ${\sim}1.3$ years before the optical
peak. No emission was detected, with a $3\sigma$ upper limit $f_{\nu,{\rm
3\,GHz}}<0.7\,$mJy or $\nu L_{\nu}<10^{38}\,{\rm erg}\,{\rm s}^{-1}$. We
obtained follow-up radio observations with the VLA on Feb. 2, 2022 (MJD
59612), or $1.4$ years after the optical peak. The radio SED, shown in Figure
2 was consistent with a non-relativistic, spherical synchrotron source with
equipartition radius $\log R_{\rm eq}/{\rm cm}=17.07^{+0.01}_{-0.01}$ and
magnetic field $\log B_{\rm eq}/{\rm G}=-0.59^{+0.05}_{-0.04}$. Assuming the
radio-emitting outflow was launched near optical peak, this radius corresponds
to an average velocity $v\approx 2.7\times 10^{4}\,$km s-1, or
$\beta=v/c\approx 0.09$. The energy in the outflow is $\log E_{\rm eq}/{\rm
erg}=49.7^{+0.01}_{-0.01}$. The power-law index of the electron energy
distribution was consistent with $p=3.4^{+0.1}_{-0.1}$. We refer the reader to
Somalwar et al. (2023); Somalwar & Ravi (2023) for more details of the radio
modeling and observations.

AT 2020vdq was not detected as an X-ray transient in observations with the
Swift/XRT telescope on Feb. 28, 2022; the $3\sigma$ upper limit on the
$0.2-10$ keV flux was $L_{X}\lesssim 3\times 10^{42}$ erg s-1. No significant
transient UV emission was detected by Swift/UVOT on the same date.

We obtained optical spectra of AT 2020vdq on Feb. 6 and Apr. 7, 2022 (MJDs
59616, 59676), or 1.4/1.5 years post-optical peak using the LRIS spectrograph
on the Keck I telescope (for reference, the source repeated after $2.7$
years). The observation and reduction details are described in Somalwar et al.
(2023); Somalwar & Ravi (2023). The spectra are shown and discussed in detail
in Somalwar & Ravi (2023). Multiple transient spectral features are visible,
as described in detail in Somalwar & Ravi (2023): intermediate width Balmer,
He II$\lambda 4685$, He I$\lambda 5875$, and [Fe X]$\lambda 6374$ features.
The Balmer features have asymmetric profiles with a slightly redshifted peak
and a blue tail with average FWHM${\sim}900$ km s-1. The Balmer emission is
consistent with being produced by dense $n_{e}\gtrsim 10^{5}$ cm-3, compact
$R\lesssim 10^{17}$ cm gas. The Balmer decrement of these lines is high:
H${\rm\alpha}$/H${\rm\beta}=9$, suggesting that the emission is heavily
extincted or produced by a non-standard ionization mechanism. The Balmer
features brightened between the two spectra. The other transient features have
narrower, symmetric profiles with FWHM${\sim}300$ km s-1.

##  3 Observations of the rebrightening

###  3.1 Broadband transient optical/UV emission

Table 2:

| $t_{\rm peak}$ | $\log\frac{L_{\rm bb}}{{\rm erg\,s}^{-1}}$ | $\lambda_{\rm Edd.}$ | $\log T_{\rm bb}/{\rm K}$ | $\frac{dT}{dt}$ | $t_{\rm 1/2,rise}$ | $t_{\rm 1/2,decay}$ | $\log\frac{E_{\rm bb}}{{\rm erg}}$ | $\log\frac{M_{\rm bb}}{{\rm M_{\odot}}}$
---|---|---|---|---|---|---|---|---|---
|  |  |  |  | [K/day] | [day] | [day] |  |
Flare I | $59113.1\pm 0.8$ | $42.78\pm 0.06$ | $0.12\pm 0.02$ | $4.02\pm 0.04$ | $66\pm 19$ | $7.8\pm 5.6$ | $48\pm 16$ | $49.8$ | $-4.1$
Flare II | $60082.60\pm 0.07$ | $44.00\pm 0.01$ | $1.99\pm 0.05$ | $4.317\pm 0.004$ | $-249\pm 16$ | $4.67\pm 0.06$ | $6.4\pm 0.1$ | $51.3$ | $-2.7$

Note. — Best-fit evolving blackbody parameters for the optical flares from AT
2020vdq.

The rebrightening of AT 2020vdq was first detected by optical surveys: ZTF
detected the rebrightening on May 9, 2023 (MJD 60073), 2.6 years after the
first optical peak. This optical flare is shown in the bottom panel of Figure
1. UV observations with Swift/UVOT were triggered shortly after (PIs: Lin,
Leloudas, Guolo). We processed this data using the same methods as van Velzen
et al. (2021b); Hammerstein et al. (2023); i.e., we reduced the Swift/UVOT
data using recommended procedures, measured the source flux using aperture
photometry, and subtracted the host contribution using the results from
spectral energy distribution fits to the host galaxy from Somalwar et al.
(2023). The UV lightcurve is overlaid on Figure 1. Optical ($ugri$)
observations with the Liverpool telescope observations were also triggered
(PI: Nicholl). The observations were reduced using standard methods and the
host component was subtracted using SDSS photometry. The resulting difference
photometry is overlaid on Figure 1. The evolution of this optical/UV
rebrightening is notably different from that of the first flare. The emission
peaks at a $g$-band luminosity a factor ${\sim}5$ higher than that of the
original flare. Both the rise and decay times of the rebrightening are
significantly faster than those of the original flare. The rebrightening also
cools significantly within ${\sim}10$ days post-peak. Similar cooling is not
obviously visible during the first flare.

We quantify these differences by modelling the optical/UV emission with two
methods. First, we fit the UV/optical lightcurves with a parametric model,
following Yao et al. (2023). We assume the lightcurve can be modeled as an
evolving blackbody. The blackbody luminosity rises as a Gaussian and decays as
a power law and the temperature is constant pre-peak and evolves linearly
post-peak:

$\displaystyle L_{\rm bb}=L_{\rm
peak}\begin{cases}e^{-\frac{1}{2}\big{(}\frac{t-t_{\rm peak}}{\sigma_{\rm
rise}}\big{)}^{2}},&t<t_{\rm peak}\\\ \big{(}\frac{t-t_{\rm
peak+t_{0}}}{t_{0}}\big{)}^{p},&\text{otherwise.}\end{cases}$ (1)
$\displaystyle T_{\rm bb}=T_{0}+\begin{cases}0,&t<t_{\rm peak}\\\
\frac{dT}{dt}\times(t-t_{\rm peak}),&\text{otherwise.}\end{cases}$ (2)

The time of luminosity peak is given by $t_{\rm peak}$, $t_{0}$ and $p$
control the luminosity decay shape, $\sigma_{\rm rise}$ controls the rate of
the rise, and $\frac{dT}{dt}$ controls the rate at which the temperature
evolves. We fit both the initial and second flares using this model so that we
can compare the temperature evolution. The resulting best-fit parameters are
shown in Table 2. Rather than report $t_{0}$, $p$, and $\sigma_{\rm rise}$, we
show the rise time from half-peak to peak luminosity, $t_{\rm 1/2,rise}$, and
the corresponding value for the decay ($t_{\rm 1/2,decay}$). The peak
luminosity of the rebrightening is $1.2$ dex brighter than that of the initial
flare. The optical/UV Eddington ratio $\lambda=L_{\rm peak}/L_{\rm Edd}$ is
correspondingly higher, such that the rebrightening corresponds to super-
Eddington emission. The blackbody temperature of the rebrightening is $0.3$
dex higher than that of the first flare, although we caution that the lack of
UV observations of the first flare render this measurement uncertain. The
rebrightening shows significant cooling, whereas the first flare shows little
temperature evolution. Both the rise and fade times of the rebrightening are
also significantly faster than those of the first flare.

Figure 3: A comparison of the parametric, evolving, blackbody fit parameters
for AT 2020vdq (black) to those of the TDEs from Yao et al. (2023) (blue). The
initial flare from AT 2020vdq is denoted with open markers while the
rebrightening is denoted with filled markers. The pTDE has a lightcurve that
is generally consistent with the broader TDE population, although the
rebrightening is luminous and fast evolving.

We compare these best-fit parameters to the ZTF-selected TDEs from Yao et al.
(2023) in Figure 3. In the top left panel, we show the evolution of the pTDE
in blackbody luminosity/temperature space. The initial flare is remarkably
faint and cool, whereas the rebrightening is relatively typical. In the top
middle panel, we show the evolution of the rise/decay times. Both the initial
and second flares have short rise times relative to the ZTF TDE sample,
although the uncertainties on the rise time of the initial flare are large.
The second flare, in contrast, is the fastest rising TDE observed by ZTF and
it has one of the fastest decay times. In the top right panel, we show the
evolution of the flare Eddington ratio. The peak Eddington ratio of the first
flare is significantly lower than that of the ZTF TDEs at similar black hole
masses. The second flare, on the other hand, is at the upper end of the
Eddington ratio distribution. In the bottom left panel, we show the rise time
versus peak luminosity. In this parameter space, it is clear that AT 2020vdq
is both fast-rising and the rebrightening is very luminous for this fast rise.
Likewise, the bottom right panel shows that the TDE is fast-decaying and
luminous.

Figure 4: The total emitted optical/UV energy inferred from the pTDE
optical/UV flares, in the same format as Figure 3. The left axis shows the
emitted energy while the right axis shows the equivalent stellar mass,
assuming an accretion efficiency of $10\%$.

We integrate this bolometric luminosity to $200$ days post-flare to calculate
the total energy stored in the outflow. The second flare from AT 2020vdq was
only detected to ${\sim}50$ days, so extrapolating to many hundreds of days
would require significant assumptions about the flare shape. It is thus likely
that our energy is slightly underestimated. The resulting bolometric energies
emitted during the first and second flares are shown in Figure 4 and tabulated
in Table 2. We also compute the equivalent stellar mass assuming an accretion
efficiency of 10%. We computed that bolometric energies for the Yao et al.
(2023) following the same procedures. Intriguingly, the energy released during
both flares of AT 2020vdq is comparable to that from the Yao et al. (2023),
despite that fact that partial disruptions only involve a fraction of the
stellar mass. In fact, the second flare from AT 2020vdq was among the most
energetic TDE optical/UV flares. We will discuss the implications of this
result in Section 5.

Figure 5: Non-parametric temperature, radius, and luminosity evolution for
those TDEs and pTDEs that have available multi-epoch UV and optical data. Data
from the rebrightening of AT 2020vdq is shown as black circles. The required
multi-epoch UV data is not available for the initial flare, so only the
rebrightening is shown. The candidate pTDEs AT 2018fyk and ASASSN-14ko are
shown as colored stars, while normal TDEs are shown as open black circles. The
data is retrieved from Holoien et al. (2014); Charalampopoulos et al. (2023b);
Nicholl et al. (2020); Blagorodnova et al. (2017, 2019); Holoien et al.
(2016); Payne et al. (2021). AT 2020vdq shows a significant initial cooling
and a rapid luminosity evolution. Otherwise, this pTDE is generally consistent
with the normal TDEs.

We can improve upon the parametric model fits, which do not provide a good fit
near the peak of the rebrightening, by fitting independent blackbodies to the
observations at multiple epochs. This is possible because we have multiple
epochs of UV observations for the rebrightening, so we can tightly constrain
the blackbody parameters for those epochs without relying on a parametric
model. We first interpolate the optical lightcurves to the UV observation
epochs using a Gaussian process model with a Matern kernel, as implemented in
the sklearn package. We then fit the UV+optical for each epoch with a
blackbody curve. The resulting temperature, radius, and luminosity evolution
is shown in Figure 5. As expected given the poor fit near peak from the
parametric model, the peak luminosity and temperature from these single-epochs
fits are significantly altered. The peak luminosity is $\log L_{\rm bb}/({\rm
erg\,s}^{-1})=44.2\pm 0.06$, corresponding to an Eddington ratio
$\lambda=3.5\pm 0.5$. The temperature at peak is $\log T_{\rm bb}/{\rm
K}=4.4\pm 0.03$. The temperature cools dramatically at ${\sim}-2300$ K/day in
the first few days of the flare, and then stabilizes to ${\sim}-200$ K/day.

We overlay the results from similar analyses of other fTDEs and pTDEs in
Figure 5. Candidate pTDEs are distinguished by star markers, while fTDEs are
circle markers. Best-fit values at peak are shown for all ZTF TDEs, although
we note that these values are measured using parametric fits that do not all
include UV observations. The initial temperature evolution of AT 2020vdq is
significantly faster than that of all other TDEs, although this trend is
entirely governed by a single data point. Many other TDEs do, however, show
some initial cooling within the first ${\sim}20$ days post-peak. The typical
cooling rate in these ${\sim}20$ days is comparable to that of AT 2020vdq if
we ignore the first observation. In particular, the temperature evolution from
days ${\sim}5-15$ resembles that of AT 2020wey. The temperature is
significantly hotter than that observed from the partial TDE ASASSN-14ko. The
radius evolution is generally similar to other TDEs. The luminosity evolution,
however, is remarkably rapid. This luminosity fades on a timescale comparable
to the “fast and faint” TDEs AT2020wey and iPTF16fnl despite being an order of
magnitude brighter than these events.

We conclude by briefly considering the flux level between the two flares. We
calculated the average flux between ${\sim}300$ days after the first flare to
${\sim}100$ days before the second flare. We found a quiescent $g$-band
luminosity $L_{g}\approx 4\times 10^{37}$ erg s-1 ($14.5\sigma$ significance)
and an $r$-band luminosity $L_{r}\approx 2\times 10^{37}$ erg s-1 ($7\sigma$
significance). Such emission may be expected if an accretion disk survives
between the partial disruptions.

###  3.2 Transient spectral optical emission

Figure 6: Summary of post-rebrightening UV/optical spectra of AT 2020vdq. Red
regions are contaminated by sky background, telluric lines, or reduction
issues. In all spectra, a variety of strong broad, intermediate width, and
narrow features are visible on top of a blue continuum.

We obtained optical spectra of AT 2020vdq with the LRIS/Keck I telescope using
the same settings as Somalwar & Ravi (2023). These spectra were observed 3 and
27 days post-optical peak (May 21 and Jun. 14 2023; MJDs 60085, 60109). These
LRIS spectra are shown in Figure 6 along with a UV spectrum that will be
discussed in the next section. All spectra were reduced following standard
procedures.

In both LRIS spectra, the host galaxy features, a blue continuum, and
transient spectral features are significantly detected. In particular, we see
clear evidence for a broad He II$\lambda 4686$/H$\beta$ blend, broad He
I$\lambda 5876$, and both broad and intermediate-width H$\alpha$.
Unfortunately, measuring the broad line fluxes in the spectra is complicated
by strong degeneracies between the broad lines and the continuum. We attempt
to model the spectra as the sum of broad Gaussian components near the expected
wavelengths of He II$\lambda 4686$, H$\beta$, He I$\lambda 5876$, and
H$\alpha$ with a fifth degree Legendre polynomial. We also require an
intermediate width H${\rm\alpha}$ component, although we postpone detailed
discussion of that line to later in this section, and a Gaussian absorption
line near the H$\beta$ wavelength.

Table 3:  Broad line properties and evolution

Param. |  | $\Delta t_{\rm ii}=+2$ | $\Delta t_{\rm ii}=+26$
---|---|---|---
|  | (MJD 60085) | (MJD 60109)
${\rm FWHM}_{\rm b}$ | km s-1 | $25227\pm 112$ | $20038\pm 112$
$\frac{{\rm FWHM}_{\rm b}}{c}$ |  | $0.084\pm 0.0$ | $0.067\pm 0.0$
$\Delta v$ | km s-1 | $-256\pm 52$ | $-1225\pm 51$
$L_{\rm H{\rm\alpha}}$ |  $10^{40}$ erg s-1 | $9.3\pm 0.1$ | $5.8\pm 0.1$
$L_{\rm H{\rm\beta}}$ |  $10^{40}$ erg s-1 | $4.5\pm 0.1$ | $2.5\pm 0.1$
$L_{\rm He\,II\lambda 4686}$ |  $10^{40}$ erg s-1 | $3.1\pm 0.1$ | $7.1\pm 0.1$
$L_{\rm He\,I\lambda 5876}$ |  $10^{40}$ erg s-1 | $7.8\pm 0.1$ | $1.4\pm 0.1$

Note. — Broad line fit parameters. We caution against directly interpreting
the reported luminosities as our fit makes many simplified assumptions and
does not fully account for the strong degeneracies between the line fluxes and
the continuum level/shape.

In Figure 7, we show the continuum subtracted spectra with the best-fit lines
overlaid. The best-fit optical broad line parameters are shown in Table 3.
Unfortunately, the continuum level, which is the sum of galactic emission and
the TDE continuum emission, is highly degenerate with the line fluxes (and, to
a lesser extent, the line widths) and rendered uncertain by imperfections in
the flux calibration. Moreover, we have fixed the FWHM and velocity offsets of
all the broad lines to a single value to remove degeneracies between the broad
He II and H$\beta$ emission; however, these assumptions are not physically
motivated and likely cause erroneous flux measurements. Hence, we caution
against detailed interpretation of the line luminosities. The FWHM measurement
is likely more reliable, although it is still subject to significant
degeneracies. Given the aforementioned uncertainties, we will not discuss and
interpret the line fluxes in detail, other than to note that the Balmer
decrement may be tantalizingly flat (H${\rm\alpha}/$H${\rm\beta}\approx 2$),
as has been observed for previous TDEs (Short et al., 2020).

The line FWHM are nearly ${\sim}0.1c$ with small blueshifts. The line width
narrows slightly with time, while the blueshift increases. The H${\rm\alpha}$,
H${\rm\beta}$ and He I lines evolve similarly: they begin bright and broad,
but fade by the second observation. The He II line, in contrast, appears to
brighten between the two observations, suggesting an alternate origin of the
line. Similar behavior has been reported from the TDE candidate AT 2018hyz
(Short et al., 2020).

If we assume that the line widths correspond to the velocity of outflows
launched during the pTDE, that the optical broadband emission is produced by
the same outflowing gas, and that the electron scattering optical depth is
$\tau_{\rm es}\approx 1$, we can calculate the amount of material launched in
outflows. The mass in the outflow $M_{\rm outflow}$ is given by

$M_{\rm outflow}=\dot{M}\Delta t=4\pi\rho vR^{2}\Delta t.$ (3)

Here, $\rho$ is the density of the outflow, $v$ is the velocity of the
outflow, $R$ is the radius at which the optical emission is produced, and
$\Delta t$ is the duration of the outflow. Given the rapid drop in the optical
emission after ${\sim}15$ days, we expect that most of the outflows were
launched early in the flare and we adopt $\Delta t\approx 15$ days. The
average radius in this period is $R\sim 10^{14.8}$ cm. Assuming a fully
ionized Hydrogen and Helium plasma, for $\tau_{\rm es}=1$ we have $\rho
R=\kappa_{\rm es}=0.34$ g cm-2. Then, we find $M_{\rm outflow}\approx
0.05\,M_{\odot}$.

Figure 7: Best-fit models of the broad emission lines from the post-
rebrightening, AT 2020vdq optical spectra. The observed spectra are shown in
black. The best-fit models are shown in blue and the best-fit model
subcomponents are shown in red. Regions highlighted in gray are excluded from
the fit. Broad Balmer, intermediate width Balmer, and Helium lines are
detected. The Balmer lines fade slightly between the two spectra while the He
II line brightens and the He I line fades dramatically, suggesting that these
lines all originate from different locations in the source.

If the electron scattering optical depth is large, line broadening in TDEs may
instead be dominated by electron scattering (Roth & Kasen, 2018a). For a
moderate optical depth, a narrow line is produced by the unscattered photons
and a broad base is visible due to the scatter photons. While we do observe
both broad and narrow line emission in our spectra, it seems unlikely that the
narrow line emission is the unscattered component of the emission: He I and
H$\alpha$ are at similar wavelength and have similar broad line fluxes in the
early spectrum, yet H$\alpha$ shows a strong narrow line and no detectable
narrow He I line is present. Unless the He I emission region has a
substantially higher optical depth than the H$\alpha$ emitting region, the
narrow lines cannot be produced by the same mechanism as the broad lines.
Hence, we assume that no significant unscattered component is detectable, so
the emitting regions all have large electron scattering optical depths. It is
beyond the scope of this work to calculate the exact optical depth required to
produce the line widths observed, although we note that none of the line
profiles presented by Roth & Kasen (2018b) are as broad as the lines observed
here. We urge attempts to reproduce the spectrum observed with this source
with electron scattering models to determine if it is possible to match our
observations. Based on Figure 3 of Roth & Kasen (2018b), symmetric broad lines
similar if not as broad as those produced by AT 2020vdq are emitted by static
or near-static gas with $\tau_{\rm es}\gtrsim 8$. Adopting $R\sim 10^{14.8}$
cm as before, this corresponds to a gas density $\rho\gtrsim 4\times 10^{-15}$
g cm-3 or a number density $n\gtrsim 10^{9}$ cm-3. The total mass in this
outflowing gas is thus $0.002\,M_{\odot}$.

Figure 8: The evolution of the intermediate Balmer lines observed from AT
2020vdq. H$\beta$ is shown in the left panel while H$\alpha$ is shown in the
right. Data is shown as lines with errorbars while Gaussian model fits are
shown as lines. The Balmer lines were brightening ${\sim}2$ years after the
first flare, but faded and became slightly blueshiftedby the rebrightening. A
few weeks post-rebrightening, the Balmer lines began brightening while
remaining blueshifted.

Table 4:  Intermediate Balmer line properties and evolution

Parameter | Unit |  $\Delta t_{\rm ii}=-466$ days |  $\Delta t_{\rm ii}=-406$ days |  $\Delta t_{\rm ii}=+2$ days |  $\Delta t_{\rm ii}=+26$ days
---|---|---|---|---|---
|  | (MJD 59616) | (MJD 59676) | (MJD 60085) | (MJD 60109)
$L_{\alpha}$ |  $10^{40}\,$erg s-1 | $1.231\pm 0.013$ | $1.452\pm 0.011$ | $0.874\pm 0.022$ | $1.69\pm 0.05$
${\rm FWHM}_{\alpha}$ | km s-1 | $855\pm 18$ | $892\pm 12$ | $1077\pm 18$ | $1152\pm 10$
$\Delta v_{\alpha}$ | km s-1 | $128\pm 6$ | $128\pm 5$ | $-94\pm 6$ | $-26\pm 2$
$L_{\beta}$ |  $10^{40}\,$erg s-1 | $0.128\pm 0.009$ | $0.171\pm 0.008$ | $0.025\pm 0.005$ | $0.323\pm 0.004$
${\rm FWHM}_{\beta}$ | km s-1 | $807\pm 57$ | $932\pm 47$ | $464\pm 99$ | $1145\pm 14$
$\Delta v_{\beta}$ | km s-1 | $-104\pm 22$ | $-70\pm 19$ | $630\pm 42$ | $42\pm 6$
${\rm L_{\alpha}}/{\rm L_{\beta}}$ |  | $9.6\pm 0.7$ | $8.5\pm 0.4$ | $35\pm 8$ | $5.22\pm 0.17$

Note. — Best-fit Gaussian model parameters to the intermediate width Balmer
lines, as described in Section 3.2.

In addition to these broad lines, we observe strong intermediate-width
H$\alpha$ emission, similar to that observed following the first flare. These
lines are treated in detail in Somalwar & Ravi (2023), so we only briefly
discuss the properties and interpretation here. The evolution of these
intermediate width lines from before to after the rebrightening is shown in
Figure 8. We have removed the stellar continuum using a fit with the ppxf
software. Following Somalwar & Ravi (2023), we found that the H$\alpha$ lines
could be well modeled as the sum of two Gaussians. The H$\beta$ lines are
well-modeled as single Gaussians. Those fits are overlaid in Figure 8 and the
best-fit parameters are summarized in Table 4.

Before the rebrightening, the emission lines were peaked near the host
redshift and were brightening. They began fading at some point in the
${\sim}400$ days before the source rebrightened. In the earliest spectrum
post-rebrightening, the lines were slightly blueshifted relative to the host.
They had brightened by the next spectrum, ${\sim}24$ later or $27$ days post-
peak, suggesting that the emitting material is located ${\lesssim}7\times
10^{16}$ cm from the SMBH. Assuming the emission is produced via recombination
and using this distance upper limit as an upper limit on the size of the
emitting region, we find that the gas density is $\gtrsim 10^{5}$ cm-3. Such a
high density suggests that we are seeing emission from very compact clumps of
outflowing gas.

###  3.3 UV spectrum

Figure 9: Fit to the Ly$\alpha$ region and a continuum region of the HST
spectrum, in the same format as Figure 7. The spectrum is well-modelled as two
broad lines (Ly$\alpha$ and an ambiguous line near Si IV$\lambda 1394$), one
intermediate line (Ly$\alpha$), two narrow emission lines (Ly$\alpha$ and N
V), and one narrow absorption line (Ly$\alpha$). The broad Ly$\alpha$ line is
redshifted by ${\sim}2\times 10^{4}$ km s-1 relative to the host rest-frame,
which is in strong contrast to the optical broad spectral features.

We obtained a UV spectrum on June 14, 2023 (MJD 60109) using the Space
Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST). We
observed AT 2020vdq with the G140L grating and the FUV-MAMA detector for 3560
seconds and with the G230L grating and the NUV-MAMA detector for 1082 seconds,
for a total of two orbits. All observations used the $52\times 0.2\arcsec$
aperture. The resulting UV spectrum is shown in Figure 6.

We begin with a qualitative description of the spectrum. Strong, hot blackbody
emission is detected in the continuum of the UV spectrum. On top of this
continuum, a number of emission lines are detected. First, an extremely broad
Ly${\rm\alpha}$ emission line is present, which is slightly redshifted and may
have a flat top. Superposed on this broad line is an intermediate width
Ly$\alpha$ emission line with a narrow absorption component. There are other
broad features near the wavelengths of Si IV$\lambda 1394$, N IV$]\lambda
1486$, and C IV$\lambda\lambda 1548,1551$. Near but blueshifted relative to
the wavelength of C IV, two narrow absorption lines are present. A number of
narrow emission lines are also detection: N IV$]\lambda 1486$ and Mg
II]$\lambda\lambda 2796,2803$ are the most significant and He II$\lambda
1640$, N III]$\lambda\lambda 1747,1749$, and N II]$\lambda 2143$ are likely
detected. These lines are often detected in galaxies, so we assume they are
associated with the host. We do not have sufficient signal-to-noise to perform
a detailed analysis of the line emitting regions, so we do not discuss these
lines further.

In the rest of this section, we attempt to quantitatively analyze and
interpret these features. We focus on the broad Ly$\alpha$. While the other
broad emission lines may be present, our spectrum is not of sufficiently high
signal-to-noise to characterize them.

Table 5:  UV spectral features

Name | Lum. | FWHM | $\Delta v$
---|---|---|---
|  $10^{40}$ erg s-1 | km s-1 | km s-1
Ly$\alpha_{1}$ | $95\pm 5$ | $18747\pm 646$ | $7556\pm 344$
Ly$\alpha_{2}$ | $16\pm 3$ | $7290\pm 650$ | $-2883\pm 252$
SiIV | $3\pm 1$ | $7830\pm 2086$ | $-1401\pm 758$

We begin with the broad Ly$\alpha$ line. We fit this line by modelling the
region from $1200{-}1400\,{\rm\AA}$ as the sum of Gaussians and a blackbody.
We also include the continuum-dominated region from $1800{-}2100\,{\rm\AA}$ in
the fit to help constrain the blackbody parameters. While redder regions of
the spectra also are continuum-dominated, we exclude them because the galaxy
contribution is expected to be larger and potentially dominant. Seven
Gaussians are required for a reasonable fit: (1) a Ly$\alpha$ broad component,
(2) an intermediate-width Ly$\alpha$ component, (3) a broad component near
$1400\,{\rm\AA}$ (possible Si IV$\lambda 1394$) (4) a narrow Ly$\alpha$
absorption line, and (5-6) two narrow Ly$\alpha$ and N V$\lambda 1239$
emission components. We generally adopt broad bounds for the parameters in
this fit, including for the blackbody temperature and radius. The best fit
with subcomponents is shown in Figure 9 and the best-fit broad/intermediate
line parameters are tabulated in Table 5.

Like the fit to the broad optical lines, this fit is subject to strong
degeneracies between the continuum and line parameters, so we do not attempt
detailed interpretation. We focus on the intermediate-broad Ly$\alpha$
parameters. The broad L$\alpha$ is well-modelled as a Gaussian redshifted by
${\sim}7600$ km s-1 and with a FWHM ${\sim}19000$ km s${}^{-1}=0.06c$. This
FWHM is consistent with those of the optical broad lines; however, the optical
lines are slightly blueshifted whereas the Ly$\alpha$ line is redshifted. It
is possible that a Gaussian is not the correct parameterization for this line,
which could affect the velocity offset. If this line is, e.g., flat-topped or
has multiple components (both of which can be produced by accretion disks and
have been observed from past TDEs; Short et al., 2020), the redshift may be
lessened. However, regardless of the model, it is clear from inspection that
this broad line will always be at least somewhat redshifted, so we expect that
it is coming from a different outflow component from the optical broad line
emission. Based on the line width, all the broad lines may be produced at a
similar distances from the black hole.

We require a second, intermediate component in our Ly$\alpha$ model that has a
FWHM${\sim}7000$ km s-1 and a blueshift of $\Delta v\sim 3000$ km s-1. This
line is broader than the intermediate width components observed in the
optical. However, the measured width should be interpreted with caution
because there is a strong sky line near the rest-frame Ly$\alpha$ and changing
the parameterization of the broad Ly$\alpha$ line would likely significantly
affect the parameters of this line. Hence, we cautiously regard this as a
analogous to the intermediate width lines in the optical, despite the FWHM
differences.

A few past TDEs (both fTDEs and pTDEs) have UV spectroscopy; a good summary of
observations is provided by Figure 11 of Payne et al. (2023a). Broad
Ly$\alpha$ lines, like that observed here, are detected in most near-peak TDE
UV spectra (Payne et al., 2023a; Brown et al., 2018; Cenko et al., 2016; Hung
et al., 2019, 2021), although the emission from AT 2020vdq appears
significantly broader than typically observed (note that few authors provide
fits to the broad emission, so a quantitative comparison is not possible).
iPTF 15af shows a similarly broad line, although with strong absorption
features superimposed that we do not see here (Blagorodnova et al., 2019). The
broad Si IV and C IV are also frequently observed (e.g. Payne et al., 2023a).
Intermediate width emission from Ly$\alpha$ has not been reported before, to
our knowledge. Thus, other than the intermediate width components and the
extreme width of the broad emission, the UV spectrum of AT 2020vdq resembles
those of past TDEs.

###  3.4 Radio emission

We obtained radio follow-up shortly after the rebrightening of AT 2020vdq
using the VLA telescope (${\sim}1-20$ GHz; Proposal AS1800, PI Somalwar) and
the NOEMA telescope (mm; proposal E22AH, PI Somalwar). All observations used
standard configurations. We observed AT 2020vdq with the VLA in the S, C, X,
K, and Ku bands on May 26, 2023 (MJD 60090), or $7$ days after the peak of the
optical/UV rebrightening. The VLA observations were reduced using the most
recent CASA VLA pipeline (2022.2.0.64). The source was detected in all bands
and was sufficiently bright in S, C, and X to image individual spectral
windows. The signal-to-noise was lower in the K and Ku bands, so we imaged all
spectral windows together.

We observed AT 2020vdq at 95.7 GHz with the NOEMA telescope on June 1, 2023
(MJD 60096), or $14$ days after the rebrightening peak. The observations were
reduced using recommended pipeline procedures. The source was not detected.

The resulting fluxes and upper limits are shown in Figure 2. The fluxes can be
well-modeled as a single power-law: there is no new outflow component
detected.

Table 6:  Swift/XRT $5\sigma$ upper limits

MJD | AT 2020vdq
---|---
| [$10^{40}$ erg s-1]
59638.2 | ${<}34.6$
60081.2 | ${<}6.2$
60084.8 | ${<}11.4$
60087.3 | ${<}96.5$
60090.5 | ${<}90.8$
60093.8 | ${<}90.8$
60099.8 | ${<}4.4$
60102.2 | ${<}147.6$
60105.5 | ${<}170.3$
60108.1 | ${<}4.0$

Figure 10: XMM-Newton spectrum of AT 2020vdq, observed $+2$ days post the peak
of the rebrightening. The data is shown as black points while the best-fit
TBabs$\times$zashift$\times$(simpl$\otimes$diskbb) model is shown as as a blue
line.

###  3.5 X-ray emission

We (among other groups) obtained X-ray follow-up of AT 2020vdq during the
rebrightening using Swift/XRT (PIs: Lin, Leloudas, Guolo) and XMM-Newton (PI
Somalwar). The Swift/XRT observations were performed in photon counting mode
and reduced using standard heasoft procedures. We used the sosta function to
perform forced photometry at the location of the source using default
parameters. The source was not detected in any single Swift/XRT epoch; upper
limits on shown in Table 6.

AT 2020vdq was observed and detected by XMM-Newton in ${\sim}10$ ks on MJD
60085 ($+2$ days post peak; May 21, 2023). The observation data files (ODFs)
were reduced using the XMM-Newton Standard Analysis Software (SAS; Gabriel et
al., 2004), and the detailed reduction processes as described in Guolo et al.
(2023) were followed. The source spectrum, shown in Figure 10, is detected
above the background up to $\sim$ 3.0 keV. The following spectral fitting
procedures were done using the python version of xspec (Arnaud, 1996),
pyxspec111https://heasarc.gsfc.nasa.gov/xanadu/xspec/python. For all spectral
models described below, we included the Galactic absorption using the TBabs
model (Wilms et al., 2000), with the hydrogen-equivalent neutral column
density $N_{H}$ fixed at the galactic value $N_{\rm H}=1.38\times 10^{20}$
cm-2. We shifted the TDE emission using the convolution model zashift. We
start by trying to model the spectrum with a phenomenological powerlaw
(TBabs$\times$zashift$\times$powerflaw), as expected Guolo et al. (2023), the
powerlaw model is an inadequate model for TDE X-ray emission, the resulting
$\chi^{2}$/degrees of freedom ($dof$) $=20/12$. Alternatively, we also employ
a purely thermal model (TBabs$\times$zashift$\times$diskbb)), which also
results in a poor fit $\chi^{2}/dof=30/12$, from a strong residual at energies
higher than 1.0 keV.

Finally, based on Guolo et al. (2023), we combined the thermal model with a
convolution model (simpl, Steiner et al., 2009) that emulates the
comptonization process to create a powerlaw. With two free parameters: $f_{\rm
sc}$, the fraction of comptonized photons, and $\Gamma$, the resulting
powerlaw photon index. Our final model
TBabs$\times$zashift$\times$(simpl$\otimes$diskbb), results in a great fit
$\chi^{2}/dof=10.3/10$, the best-fitted parameters are shown Table 7. The
unabsorbed $0.3{-}10$ keV flux was $\log f_{X}/({\rm erg\,cm}^{-2}\,{\rm
s}^{-1})=-12.95\pm 0.05$, or $\log L_{X}/({\rm erg\,s}^{-1})=41.4\pm 0.05$
($L_{X}=0.005L_{\rm edd.}$)

This X-ray emission is consistent with both observations of X-ray faint TDEs
shortly post-peak (Saxton et al., 2021; Guolo et al., 2023) and late-time
X-ray observations of TDEs (Jonker et al., 2020; Guolo et al., 2023), so it
could be associated with the new flare or it could be relic emission from the
accretion disk created during the first flare. The temperature of the thermal
component is consistent with other optically selected TDEs Guolo et al.
(2023), and the faint powerlaw emission ($f_{\rm sc}=0.03^{+0.01}_{-0.01}$),
could originate both from the reprocessing layer that produces the bright
UV/optical, or a nascent corona (Thomsen et al., 2022; Guolo et al., 2023),
late time observations may be able to distinguish them.

Table 7: Best-fitted parameters XMM-Newton spectrum.

Model | Component | Value
---|---|---
TBabs | $N_{\rm H}$ |  $1.38\times 10^{20}$ cm-2 (fixed)
zashift | $z$ | 0.044 (fixed)
simpl | $f_{\rm sc}$ | $0.03^{+0.01}_{-0.01}$
$\Gamma$ | $1.35^{+0.31}_{-0.25}$
diskbb | $T_{in}$ |  $60^{+6}_{-4}$ eV
norm | $820^{+770}_{-250}$

##  4 Constraints on previous flares from AT 2020vdq

Figure 11: Historical lightcurves for AT 2020vdq. The lightcurves for each
survey/band have been binned in $3$ days bins. For clarity, we distinguish
data from different surveys with different colors, but do not show different
colors for each band (e.g., the ZTF lightcurve includes $gri$ observations).
We find no evidence for earlier flares in any of the data. ATLAS data rule out
similar-brightness flares in the last ${\sim}10$ years.

In this section, we search for past flares from AT 2020vdq. We retrieve
photometry of this source from the ZTF, the Catalina Real Time Transient
Survey (CRTS; Drake et al., 2009), and Asteroid Terrestrial-impact Last Alert
System (ATLAS; Tonry et al., 2018). As shown in Figure 11, no significant
flare is detected by any survey. In both cases, ATLAS coverage is sufficient
to rule out previous flares as bright or brighter than the detected flares. We
cannot, however, rule out previous flares that had peak magnitudes that were
fainter by ${\sim}1$ mag.

##  5 Discussion

We have presented the ZTF-discovered partial TDE candidate AT 2020vdq. Key
properties of this event is summarized in Table 8.

Table 8:  Summary of observations of AT 2020vdq

Parameter | Flare I | Flare II
---|---|---
Host galaxy | post-starburst, green-valley; $M_{\rm BH}=10^{5.6}\,M_{\odot}$
Optical/UV flare |  $L_{\rm bb}{=}10^{42.8}\,{\rm erg\,s}^{-1}{=}0.1L_{\rm edd}$
$T_{\rm bb}=10^{4}$ K
rose over ${\sim}8$ days
decayed over ${\sim}60$ days |  $L_{\rm bb}=10^{44}\,{\rm erg\,s}^{-1}{=}2L_{\rm edd}$
$T_{\rm bb}=10^{4.3}$ K
rose over ${\sim}5$ days
decayed over ${\sim}6$ days
(one of the fastest evolving TDE flares)
Broad lines |  no early time spectra |  extremely broad (${\sim}0.1c$), mildly blueshifted Balmer, He I, He II, and Ly$\alpha$ lines (H+He TDE)
Narrow lines |  ${\sim}1000$ km s-1, slightly redshifted (${\sim}100$ km s-1) Balmer (with large Balmer decrement), He I, He II, and Fe X detected |  ${\sim}1000$ km s-1 lines detected that brightened over the first few weeks, high but variable Balmer decrement
X-ray |  No early-time X-ray observations, $L_{X}\lesssim 3\times 10^{41}$ erg s-1 ${\sim}1.4$ years post-flare |  $L_{X}{\sim}$ within $2$ weeks post-peak
Radio |  Detected as a $L_{R}\approx 10^{38}$ erg s-1 radio transient ${\sim}1.4$ years after the initial flare. The radio-emitting region was consistent with a non-relativistic ($\beta\sim 0.1$), wide-angle outflow. |  No new radio-emitting region was detected in the ${\sim}$month post-rebrightening

In this section, we will first argue that AT 2020vdq is caused by a pTDE
rather than a different type of activity. Then, we will discuss AT 2020vdq in
the context of other pTDEs and we will use it to constrain both TDE and pTDE
models.

###  5.1 The cause of AT 2020vdq

We first argue that AT 2020vdq is a pTDE. We consider four possible origins of
this event (1) a TDE followed by a supernova, (2) AGN variability, (3) a TDE
by a SMBH binary, (4) two independent TDEs, or (5) a repeating partial TDE.

The first scenario is disfavored by many pieces of evidence. First, the
intermediate width Balmer lines were initially caused by a TDE. They began
evolving after the second flare, which would not be expected if the second
flare is caused by a SN rather than an event directly in the vicinity of the
SMBH. In addition, the broad optical spectral features are well-modelled as a
TDE, but are less typical for SN. In the case of a Type II SN, the lack of
star-formation provides additional evidence against a SN flare origin. Hence,
we do not believe that the second flare from AT 2020vdq could be caused by a
SN.

Instead, it is possible that both flares from AT 2020vdq are related to a
flaring AGN. As we argue in Somalwar & Ravi (2023), the lack of any signatures
of AGN activity from this source render this hypothesis unlikely: the WISE
W1-W2 color is $0.088$ mag, which is outside of the AGN regime, and we do not
see significant infrared variability pre-flaring. We do not see evidence for
strong narrow Balmer on top of the intermediate width transient lines and only
weak, narrow [O III] is detected. There are also no archival radio nor X-ray
detections. AT 2020vdq could, at most, be an extremely low luminosity AGN. A
single optical flare like those from AT 2020vdq from such an AGN, let alone
two, is unprecedented.

A TDE by a SMBH in a binary is expected to have an accretion rate that
initially follows standard predictions for TDE evolution. The accretion rate
will then cut off after a fraction of the period of the SMBH binary, but it
eventually may increase again (Liu et al., 2009; Ricarte et al., 2016). In no
model of such events, however, is the accretion rate expected to be increase
after the first flare. Hence, we would not expect a flare such as that
observed from AT 2020vdq, which is more energetic during the rebrightening.

We next consider the possibility that AT 2020vdq is two independent TDEs in a
single galaxy. The TDE rate has been measured to be ${\sim}3.2\times 10^{-5}$
yr-1 galaxy-1 using $33$ ZTF TDEs. After monitoring these TDEs for ${\sim}3$
years post-discovery, we would expect to detect a mean of ${\sim}3.2\times
10^{-5}$ yr-1 Galaxy${}^{-1}\times 33$ Galaxies$\times 3$ years$=0.003$
additional TDEs. Thus, the probability of observing one or more additional,
independent TDE from these $33$ TDE hosts is $0.3\%$. While this probability
is not negligible, it suggests that it is unlikely that we have observed two
independent TDEs. However, we urge careful consideration of this possibility
in future repeating pTDE analyses, as the probability of observing two
independent events in a single galaxy will only increase with time and as TDE
samples grow.

Considering that post-starburst galaxies have elevated TDE rates (by a factor
of 10 to 100) as compared to other types of galaxies, the time interval
between two independent TDEs may be as short as a few hundred years (Arcavi et
al., 2014; French et al., 2016; Law-Smith et al., 2017; Hammerstein et al.,
2021). For an extreme case of an average rate of $3\times
10^{-3}\rm\,yr^{-1}\,galaxy^{-1}$, the probability of detecting two
independent TDEs from $33$ TDE hosts in 3 years is as large as $30\%$. This
possibility can be tested by future monitoring of AT 2020vdq; (not) detecting
another flare from AT 2020vdq in the near future will rule out (or support)
this possibility.

We conclude that AT 2020vdq is most likely a pTDE.

###  5.2 AT 2020vdq in the context of published repeating pTDE candidates

There are a handful of published partial TDE candidates. We only consider
those that flared at least twice. There have been optical/UV pTDE candidates
identified based on their low-luminosity and/or fast-evolving flares (e.g.
Gomez et al., 2020); however, non-repeating pTDEs are very difficult to
confirm as it may be possible to generate low-luminosity/fast flares through
additional mechanisms. The repeating pTDEs that we consider to be reliable
candidates are summarized as follows.

ASASSN-14ko (Payne et al., 2021, 2022, 2023a, 2023b):  ASASSN-14ko is one of
the most well-studied pTDE candidates discovered to date. It is a nuclear
transient in an AGN that was discovered by the ASASSN survey. It flared
seventeen times between 2014 and 2020 in the optical, with a period of $114.2$
days. The optical flaring was accompanied by UV flaring and the best-fit flare
blackbody parameters and evolution are consistent with typical TDEs (grey
stars in Figure 5). At least a subset of the optical flares are accompanied by
X-ray variability. The optical spectra for this source show possible evidence
for broad Balmer features.

eRASSt J045650.3–203750 (Liu et al., 2023): eRASSt J045650.3–203750 (J0456)
was first discovered as a repeating, nuclear, X-ray transient by eROSITA. The
X-ray lightcurve is characterized by a rise followed by a ${\sim}$months-long
plateau that rapidly fades. This flare profile repeats every ${\sim}223$ days
and has repeated three times. The host galaxy has no detectable optical broad
or narrow spectral features, suggesting that it is quiescent in all senses. UV
follow-up detected moderate variability, but no optical variability is
detected. Radio emission was detected during the X-ray plateau.

AT 2018fyk (Wevers et al., 2019, 2023): AT 2018fyk was first detected as a
nuclear optical transient by the ASASSN survey. Optical spectra taken post-
flare detected broad He, He, and Bowen lines, along with narrow Fe II
features. AT 2018fyk was detected as both a UV and X-ray transient in follow-
up ($L_{X}\approx 10^{43}$ erg s-1, $L_{\rm UV,peak}=10^{44}$ erg s-1) and the
UV/X-ray emission remained bright for ${\sim}600$ days. After this period, the
UV and X-ray emission plummeted, although remained detectable (plausibly due
to a disk state change). ${\sim}1200$ days after the first flare, the UV and
X-ray rebrightened, with $L_{X}\approx 8\times 10^{42}$ erg s-1 and $L_{\rm
UV}\approx 10^{43}$ erg s-1. The host galaxy is classified as a retired galaxy
based on its narrow optical emission lines. There is no evidence for AGN
activity from infrared observations. It has a massive blackhole, with $M_{\rm
BH}\approx 10^{7.7}\,M_{\odot}$.

RX J133157.6–324319.7 (Hampel et al., 2022; Malyali et al., 2023): RX
J133157.6–324319.7 (RX J1331) was detected as an ultra-soft X-ray transient
with $L_{X}\approx 10^{43}$ erg s-1 by ROSAT in 1993 (Hampel et al., 2022).
The transient evolved rapidly, with a factor of eight luminosity increase
within ${\sim}8$ days. The host galaxy is non-active and non-star forming. It
was not detected in sparse, survey observations until ${\sim}30$ years later,
when it flared back to ${\sim}10^{43}$ erg s-1 during eROSITA observations.
The X-ray spectrum during this flare was ultra-soft, like the first flare. It
was not detected in follow-up observations ${\sim}20{-}100$ days post-peak.

Table 9: Summary of published repeating pTDEs

Name | Band | Period [years] | $\log M_{\rm BH}/M_{\odot}$ | N. flares
---|---|---|---|---
ASASSN-14ko1,2,3 | Optical/UV/X-ray | 0.3 | 7.9 | ${\gtrsim}20$
eRASSt J045650.3–2037504 | X-ray/UV | 0.61 | 7.0 | 3
AT 2020vdq5 | Optical/UV | 2.7 | 6.1 | 2
AT 2018fyk6,7 | UV/X-ray | 3.3 | 7.7 | 2
RX J133157.6–324319.78,9 | X-ray | ${\lesssim}30$ | 6.5 | 2

Note. — Summary of published repeating pTDE candidates, sorted by flare
period. The bands listed are those in which the rebrightening was detected.
1Payne et al. (2021), 2Payne et al. (2022), 3Payne et al., 2023b, 4Liu et al.,
2023, 5This work, 6Wevers et al., 2019, 7Wevers et al., 2023, 8Hampel et al.,
2022, 9Malyali et al.,2023

In Table 9, we tabulate the bands in which these TDEs were detected, their
periods, and their black hole masses. There are a number of key facts to note
about this sample:

Number of flares: ASASSN-14ko is the only source that has been detected more
than $2{-}3$ times; in fact, it has flared ${\sim}20$ times. It is the oldest
source, which may partly explain the large number of detected flares. However,
ZTF is sensitive to ASASSN-14ko-like objects out to $z\sim 0.1$ and has been
active long enough to detect ten flares from such an object, yet none have
been reported. This may be a selection effect: the ZTF TDE selection requires
that the transient not be present during the reference image, whereas an
ASASSN-14ko-like source is on a larger fraction of the time than repeating
pTDEs with longer periods. Moreover, the ZTF TDE selection will not include
sources that repeated many times in the early months of the survey, so such
events would not be included in the Yao et al. (2023) sample. Regardless,
ASASSN-14ko is clearly distinct from the other pTDE candidates. The lack of
detections of more such events may suggest that most pTDEs do not flare more
than a few times. Alternatively, it may be a selection effect.

Black hole masses: Of the optically-detected pTDEs (AT 2020vdq, ASASSN-14ko,
AT 2018fyk), all but AT 2020vdq have black hole masses $\log M_{\rm
BH}/M_{\odot}>7$. The BH mass function of TDEs in ZTF begins to drop off
around $\log M_{\rm BH}/M_{\odot}\sim 7.4$, and peaks towards masses lower
than $\log M_{\rm BH}/M_{\odot}\sim 7$ (Yao et al., 2023). In contrast, AT
2020vdq has a black hole mass that is relatively typical for optically-
selected TDEs. The host galaxies of ASASSN-14ko and AT 2018fyk are also very
different from typical TDE host galaxies: ASASSN-14ko is a Seyfert, while AT
2018fyk is a retired galaxy with evidence for an old stellar population. In
contrast, AT 2020vdq shows strong Balmer absorption suggestive of ${\sim}$Gyr
old stellar populations. This may suggest that types of stars (or binaries)
being disrupted is different for ASASSN-14ko/AT 2018fyk and AT 2020vdq.

Flare periods: The flare period distribution (excluding RX J1331 due to a lack
of constraints) appears to be bimodal, with one peak at ${\sim}100$s of days
and one peak near ${\sim}2{-}3$ years. As has been detailed in other work
(e.g. Cufari et al., 2022), placing stars on such short period orbits requires
Hills capture of a binary. In this scenario, a binary is destroyed by the SMBH
tidal forces, leading to one object being captured into a tight orbit around
the SMBH and the other ejected. The typical binaries that will undergo this
process will be on tight orbits themselves, as is required for them to survive
the high velocity dispersion environment near the SMBH. These orbits are
sufficiently tight as to require either two low mass stars or one star and one
compact object. We will discuss the consequences of this fact further in
Section 5.4.

Multiwavelength properties: The multiwavelength properties of the known pTDEs
are very inhomogeneous. RX J1331 and J0456 are both primarily detected in the
X-rays, with possible UV variability in the case of J0456. AT 2020vdq, in
contrast, shows little X-ray emission. Even when only comparing the optical/UV
properties of ASASSN-14ko, AT 2020vdq, and AT 2018fyk, we see a wide range of
evolution and blackbody fit parameters, as is highlighted in Figure 5. One
possible common thread is that some, though not all, of the pTDE flares evolve
more rapidly than typical TDEs.

###  5.3 Constraints on TDE models from AT 2020vdq

Partial TDEs provide a unique opportunity to constrain both pTDE, but also
fTDE models: the only aspects of the system we expect to change between
disruptions are the stellar structure and, possibly, the CNM. With this in
mind, we use the changes in the emission between flares from AT 2020vdq to
constrain both pTDE and fTDE models. There are four key takeaways from the
observations of AT 2020vdq:

1\. Launching a radio-emitting outflow may require a sub-Eddington state
AT 2020vdq launched a radio outflow in the ${\sim}2$ years following its
initial flare. Launching such an outflow requires an accretion disk. AT
2020vdq thus likely had a pre-existing accretion disk during its
rebrightening, and that this disk was, at one point, capable of launching
radio-emitting outflows. Despite this, no new radio component was detected in
the weeks following the rebrightening, when the event was in a relatively high
accretion rate state (we are pursuing continued monitoring). There are three
possible explanations for the lack of radio emission: (1) AT 2020vdq-like TDEs
cannot launch radio-emitting outflows except in a sub-Eddington state; (2)
radio emitting TDEs can clear out the circumnuclear region in a region around
the SMBH, so no material was present during AT 2020vdq’s rebrightening against
which the outflow could shock; (3) the change in stellar structure affected
the disk’s ability to launch an outflow.

2\. Bright and fast rebrightening
The rebrightening of AT 2020vdq was rapidly evolving relative to most TDEs. It
has the fastest rise time and one of the fastest decay times of all TDEs. When
controlling for rise time, it is also luminous. pTDE models predict that these
events should evolve more rapidly than fTDEs: the fallback rate of stellar
debris from fTDE decays is expected to follow a ${\sim}t^{-5/3}$ power-law,
whereas pTDE decays are expected to follow a ${\sim}t^{-9/4}$ power-law due to
the gravitational pull of the surviving stellar core. Intriguingly, however,
the first flare from AT 2020vdq was less extreme: the decay time was among the
longest for the Yao et al. (2023) sample. This suggests that while pTDEs can
be fast, they need not produce fast flares. It is possible that the fast
evolution of the rebrightening is tied to the change in the stellar structure,
rather than the pTDE nature of the event. However, Lodato et al. (2009)
simulated the fallback rate for stellar disruptions with a range of polytropic
indices and did not predict any early time fallback rates that were
significantly steeper than the standard ${\sim}t^{-5/3}$. Instead, maybe the
rapid evolution is due to a pre-existing accretion disk: the first pTDE
episode likely created a disk with a size ${\sim}R_{T}$, and the interaction
between a disk and stellar debris can cause rapid circularization and
accretion (Chan et al., 2019).

3\. Initial cooling of the optical flare
The temperature evolution of AT 2020vdq, while not unusual, deserves note.
TDEs are often assumed to not cool. However, multiple TDEs show initial
cooling near-peak, followed by ${\sim}10$s of days in a ${\sim}$constant
temperature state. This has been noted by previous authors (e.g. Nicholl et
al., 2020; Angus et al., 2022), although models do not exist to explain the
evolution to our knowledge. This evolution is particularly apparent from AT
2020vdq: Near-peak, the temperature cools dramatically. It then hovers near a
zero-cooling state.

4\. Otherwise, AT 2020vdq is a fairly normal event
The final point worth noting about AT 2020vdq is that it is a relatively
normal TDE. While it shows some unusual features (fast evolution, broad
emission lines), it is not massively outside the typical TDE parameter space
in any case. Both flares from this source would pass the “normal” TDE cuts
used in Yao et al. (2023). This suggests that some of the known TDEs could
well be pTDEs.

###  5.4 Partial TDE rates and the missing energy problem

We conclude by discussing the rate of partial TDEs. We then apply this
discussion to the enigmatic missing energy problem of TDEs.

We first consider the rate of pTDEs, where each pTDE, regardless of the number
of flares, is counted as a single event. Because AT 2020vdq was drawn from the
Yao et al. (2023) sample, we begin with the TDE rate measured in that work and
scale it to estimate the pTDE rate. We first searched that sample for other
pTDEs. One other transient, AT 2021mhg, showed a rebrightening. However, as we
show in Appendix A, this source is a TDE followed by a Type Ia supernova, so
we do not consider it further. AT 2020vdq is the only definitive pTDE in the
Yao et al. (2023) sample.

Yao et al. (2023) measured a TDE rate of ${\sim}3.2\times 10^{-5}$ yr-1
galaxy-1 using $33$ ZTF TDEs. Note that this rate is an average over the
population, but the rate depends on luminosity and increases for lower
luminosities. Assuming that none of the other TDEs in this sample will
rebrighten, the rate of partial TDEs on ${\sim}3$ year timescales is
${\approx}1/33\times{\sim}3.2\times 10^{-5}$ yr-1 Galaxy${}^{-1}\approx
10^{-6}$ yr-1 galaxy-1. This is a lower limit on the rate, as more
rebrightening TDEs will increase the value, as will accounting for the
luminosity dependence of the ZTF TDE rate and the ASASSN-14ko-like events that
would not make it into the Yao et al. (2023) sample.

Instead of assuming that no more TDEs are hidden pTDEs, we now constrain the
fraction of the Yao et al. (2023) that could be pTDEs. We assume that the pTDE
flare period distribution is a uniform distribution ranging from $0.3{-}2.7$
years (i.e., all flares periods are between that of ASASSN-14ko and AT
2020vdq). This flare period distribution was chosen arbitrarily and could
affect our results: further theoretical studies are needed to motivate the
correct form of this distribution. Assume the fraction of pTDEs in the Yao et
al. (2023) sample is $f_{\rm pTDE}$. We assign each TDE in the Yao et al.
(2023) sample to be a pTDE or fTDE according to this fraction. For those
assigned as pTDEs, we randomly generate a flare period and count the number of
pTDEs that would be observed to repeat before June 2023 (approximately when we
last searched for ZTF pTDEs). We repeat this process $10^{6}$ times and
calculate the fraction of trials where one or fewer objects are observed to
repeat, which we call $P(N_{\rm pTDE}\leq 1)$. We find that $P(N_{\rm
pTDE}\leq 1)<10^{-3}$ for $f_{\rm pTDE}{\gtrsim}0.3$; i.e., we have
constrained the fraction of pTDEs in the Yao et al. (2023) to be
${\lesssim}30\%$ at the $3\sigma$ level. Thus, we can once more constrain the
repeating pTDE rate for ${\sim}0.3-2.7$ year timescales to be ${\lesssim}30\%$
of the TDE rate, or ${\lesssim}10^{-5}$ yr-1 galaxy-1. Combining this result
with the lower limit on the rate computed by assuming that AT 2020vdq is the
only pTDE in the Yao et al. (2023) sample, we find that the repeating pTDE
rate for ${\sim}0.3-2.7$ year timescales is in the range $10^{-(5-6)}$ yr-1
galaxy-1.

Note that this result is strongly dependent on the assumed flare period
distribution. Decreasing the lower limit on this distribution or having it
peak towards smaller values tightens our constraints. However, if maximum
allowed flare period is larger, a larger pTDE fraction is allowed. For
example, if we assume the flare periods are drawn from a uniform distribution
ranging from $0.3{-}5$ years, we can only say that is the pTDE fraction
${\lesssim}40\%$ at the $3\sigma$ level. One way to constrain the potential
for longer timescale pTDEs is to look at older TDE samples, although no
uniformly selected such sample exists. Regardless, we checked all the older
optical/UV TDEs listed in Gezari (2021) for rebrightenings in ZTF or ATLAS
data and do not find any detections. This suggests that TDEs do not frequently
brighten on longer timescales, although this sample is small and
inhomogeneous, so we do not attempt to set any detailed constraints on the
longest allowed flare periods. We suggest, however, that at least some of the
known TDEs are true, full TDEs rather than pTDEs.

In the theoretical frame work of Hills mechanism (Lu & Quataert, 2023), the
rate of repeating pTDEs depends on the rate at which stars migrate into deeply
penetrating orbits and the binary fraction of stars in the galactic nucleus.
From the above discussion, we can conclude that the ratio of the number of
Hills-captured, partially disrupted stars to tidally disrupted single stars is
${\sim}6\%$. This fraction is much less than unity mainly because few binaries
can survive in galactic nuclei with semi-major axes that would produce a
${\sim}$year period pTDE. Simulations of this process assuming different
binary fractions and semi-major axis distributions would provide valuable
information for interpreting the observed rate.

This measured rate, which suggests that pTDEs may not dominate the TDE rate,
as well as the discussion in the previous parts of this work, have intriguing
implications for the long-standing “missing energy problem” of TDEs: the total
energy observed to be emitted during TDEs is always ${\sim}2$ orders of
magnitude lower than expected from the accretion of a ${\sim}$solar mass star.
A number of possible explanations abound; for example, the bolometric
corrections adopted to convert the observed luminosity into the total
luminosity may be hugely overestimated (e.g. Lu & Kumar, 2018; Mummery, 2021;
Mummery et al., 2023; Saxton et al., 2020; Guolo et al., 2023), more energy
may be input into winds and/or jets than is currently expected (e.g. Lu &
Kumar, 2018; Dai et al., 2018), or the energy may be trapped in a disk with
high optical depth (Curd & Narayan, 2019). Alternatively, if all or most of
the known TDEs are in fact pTDEs, the low detected energies would be expected
because only a small fraction of the star need be accreted during each
disruption. Our suggestion above that at least some of the known TDEs are true
full TDEs refutes this hypothesis. Of course, if longer period
(${\sim}$decade) pTDEs are common, it is still possible that pTDEs can aid the
missing energy problems. Intriguingly, this pTDE hypothesis is supported by
the fact that the original flare from AT 2020vdq was originally identified as
relatively typical TDEs, with no extremely unusual features that could have
hinted at the fact that they would rebrighten, supports this possibility: the
multiwavelength properties of the known pTDEs are so similar to the known TDEs
that we can not rule out that any given event is instead a partial disruption.
Future work on the long-term lightcurves of known TDEs will thus be critical
for constraining the contribution of pTDEs to the missing energy problem.

##  6 Conclusions

In this work, we have presented observations and analysis of the partial tidal
disruption event, AT 2020vdq. AT 2020vdq is the first pTDE identified from a
well-characterized TDE sample, allowing us to constrain the pTDE rate to
${\approx}10^{-(5-6)}$ galaxy-1 yr-1, subject to uncertainties in the flare
rate of pTDEs. We have used the properties of AT 2020vdq to constrain TDE and
pTDE models. Of note, the lack of a launch of a radio-emitting outflow shortly
after the second disruption despite the launch of such an outflow after the
first disruption may suggest that some TDEs must be in a low accretion state
to launch such outflows.

Intriguingly, and unlike previous pTDEs, the multiwavelength properties of AT
2020vdq are generally characteristic of “typical” TDEs; for example, it has a
low black hole mass and its optical flares are not hugely divergent from those
observed from other TDEs (it was first identified as part of a standard TDE
sample). This suggests that some of the known TDEs may in fact be pTDEs in
disguise, so we urge careful monitoring of all events. However, we also urge
caution when classifying repeating nuclear transients. As in the case of AT
2021mhg (Appendix A), large TDE samples combined with many-year monitoring
campaigns leads to a high probability of chance detections of multiple,
independent transients in a single host.

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 project. ZTF is supported by the National Science
Foundation under Grants No. AST-1440341 and AST-2034437 and a collaboration
including current partners Caltech, IPAC, the Weizmann Institute of Science,
the Oskar Klein Center at Stockholm University, the University of Maryland,
Deutsches Elektronen-Synchrotron and Humboldt 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, Northwestern University and former partners the University
of Washington, Los Alamos National Laboratories, and Lawrence Berkeley
National Laboratories. Operations are conducted by COO, IPAC, and UW. The ZTF
forced-photometry service was funded under the Heising-Simons Foundation grant
#12540303 (PI: Graham). Some of the data presented herein were obtained at the
W. M. Keck Observatory, which is operated as a scientific partnership among
the California Institute of Technology, the University of California and the
National Aeronautics and Space Administration. The Observatory was made
possible by the generous financial support of the W. M. Keck Foundation. The
authors wish to recognize and acknowledge the very significant cultural role
and reverence that the summit of Maunakea has always had within the indigenous
Hawaiian community. We are most fortunate to have the opportunity to conduct
observations from this mountain. This material is based upon work supported by
the National Science Foundation Graduate Research Fellowship under Grant No.
DGE‐1745301. MWC acknowledge support from the National Science Foundation with
grant numbers PHY-2010970 and OAC-2117997. MN is supported by the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No. 948381) and by UK Space Agency Grant
No. ST/Y000692/1. This research is based on observations made with the
NASA/ESA Hubble Space Telescope obtained from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5–26555. These observations are
associated with program(s) 17314.

##  Appendix A The second repeating ZTF transient, AT 2021mhg: a TDE and SN Ia
in the same galaxy

Figure 12: Optical/UV lightcurve of AT 2021mhg, in the same format as Figure
1.

After the discovery of AT 2020vdq, we performed forced photometry for all ZTF
TDEs to search for any other rebrightenings on ${\sim}$year timescales.
Coincidentally, AT 2021mhg had rebrightened in the $r$-band shortly before AT
2020vdq (Munoz-Arancibia et al., 2023). Upon discovery, we and other groups
triggered multiwavelength follow-up. In this section, we present observations
of this source and constrain its origin. We conclude that this source is a TDE
followed by a Type Ia supernova at the same location.

###  A.1 Host galaxy

AT 2021mhg is hosted by a Balmer-strong, blue galaxy with a black hole mass
$\log M_{\rm BH}/M_{\odot}=6.1\pm 0.37$. No narrow emission lines are detected
in the host spectra, although no host galaxy spectra without any transient
emission are available. Strong host absorption lines are detected, in
contrast. We tentatively identify this galaxy as quiescent, both in terms of
star formation and AGN activity.

Table 10:

| $t_{\rm peak}$ | $\log\frac{L_{\rm bb}}{{\rm erg\,s}^{-1}}$ | $\lambda_{\rm Edd.}$ | $\log T_{\rm bb}/{\rm K}$ | $t_{\rm 1/2,rise}$ | $t_{\rm 1/2,decay}$
---|---|---|---|---|---|---
|  |  |  |  | [day] | [day]
Flare I | $59366.6\pm 0.7$ | $43.65\pm 0.05$ | $0.28\pm 0.03$ | $4.21\pm 0.03$ | $9.7\pm 0.4$ | $26\pm 2$
Flare II |  $60072.5$ (fixed) | $43.00\pm 0.02$ | $0.063\pm 0.002$ | $3.82\pm 0.02$ |  $10$ (fixed) | $18.8\pm 1.1$

Note. — Best-fit evolving blackbody parameters for the optical flares from AT
2021mhg.

###  A.2 Optical/UV broadband emission

The optical/UV emission associated with the initial and secondary flares are
shown in Figure 12. The secondary flare was only observed with ZTF/$r$, but we
have additional Swift/UVOT photometry (PIs Somalwar, Huang). In strong
contrast with the rebrightening of AT 2020vdq, the second flare from AT
2021mhg is significantly redder than the first flare. The rebrightening also
has a slightly lower luminosity. Like AT 2020vdq, the second flare fades
faster than does the first, but the contrast is not as extreme as that of AT
2020vdq.

We model the optical/UV flares following the same methods as used for AT
2020vdq, with small modifications. First, we find that no temperature
evolution is required for either flare, so we fix the time derivative of the
temperature to zero. Second, the rise of the rebrightening was not observed by
any telescopes. Hence, we fix the peak MJD to the date of the first detection
and we arbitrarily fix the rise time to $10$ days (this choice of rise time
does not affect our results). The resulting best-fit lightcurve parameters are
tabulated in Table 10, and the best-fit models are shown in Figure 12. As
expected, the second flare is $0.4$ dex cooler than the first flare; in fact,
AT 2021mhg’s rebrightening would be the reddest known optical TDE flare. It
also has a very low luminosity, with an Eddington ratio $<0.1$.

Figure 13: Spectral evolution of AT 2021mhg. The grey spectrum was observed
$60$ days after the first flare and the black spectrum was observed $36$ days
after the second flare.

We also performed a non-parameteric fit to those epochs with UV data and
confirm the result that the rebrightening was extremely cool: no previously
known TDE with non-parametric modelling was cooler.

###  A.3 Optical Spectral Features

We next consider the optical spectra of AT 2020vdq. In Figure 13, we show one
spectrum of AT 2020vdq observed with P200/DBSP (PI: Kulkarni; (Yao et al.,
2023)) ${\sim}70$ days after the first flare (grey) and one spectrum observed
${\sim}35$ days after the rebrightening with Keck I/LRIS (black). These
spectra look markedly different. Broad Balmer, He II, and N III are detected
after the first flare. Note that the line near $4100\,{\rm\AA}$ is assumed to
be N III$\lambda 4100$ rather than H$\delta$; it would be theoretically
difficult to produce such bright H$\delta$ relative to H$\beta$ and H$\alpha$,
but the detection of N III is fully consistent with TDE models. The detection
of these lines places AT 2021mhg in the H$+$He TDE class. The presence of N
III places AT 2021mhg in the class of Bowen TDEs, which show Bowen
fluorescence lines. The detected lines do not show significant velocity
offsets and have widths ${\sim}8000$ km s${}^{-1}=0.03c$. These line widths
are typical for H$+$He TDEs that are observed ${\sim}50$ days post-peak.

The post-rebrightening spectrum is extremely unusual for a TDE. We detect the
typical broad lines He II$\lambda 4686$, possible H$\beta$ and He I$\lambda
5876$, and H$\alpha$. However, there are also broad features near $5000\,\AA$
and $5500\,\AA$ that, to our knowledge, have not been seen from a TDE before
and that we cannot identify. N III$\lambda 4100$ is not obviously present. The
detected lines are broader than those in the previous spectrum, with
FWHM$\approx 11000$ km s${}^{-1}\approx 0.04c$. This line width is comparable
to that measured for other of non-Bowen TDEs (i.e., those with no detectable N
III lines). They are also significantly blueshifted by $\Delta v\approx 3000$
km s-1.

###  A.4 Radio and X-ray limits

Table 11:  Swift/XRT $5\sigma$ upper limits

MJD | AT 2021mhg
---|---
| [$10^{40}$ erg s-1]
59417.7 | ${<}100.4$
59490.2 | ${<}3.2$
59501.1 | ${<}4.9$
59572.3 | ${<}58.7$
60083.8 | ${<}3.9$
60088.2 | ${<}3.8$
60095.1 | ${<}37.8$
60102.1 | ${<}3.7$

Neither radio nor X-ray detections have been reported for either brightening
of AT 2021mhg. X-ray upper limits from the Swift X-ray telescope are reported
in Table 11.

AT 2021mhg was observed at 15 GHz $70$ days after the initial flare and an
upper limit of $3\times 10^{37}$ erg s-1 was reported Alexander et al. (2021).
It was observed by the VLA Sky Survey at 3 GHz $130$ days after the initial
flare and an upper limit of $3\times 10^{38}$ erg s-1 was reported. No post-
rebrightening radio observations have been reported; we are pursuing follow-
up.

###  A.5 The cause of AT 2021mhg

While the first flare from AT 2021mhg is a typical TDE, the second flare is
highly unusual. In particular, it has a remarkably red color corresponding to
a blackbody temperature that would be significantly cooler than all known
optical TDEs. We also see broad features in the post-rebrightening optical
spectrum that have never been detected from a TDE. Due to these features, we
consider non-TDE origins for the rebrightening of AT 2021mhg. We do not see
any evidence for AGN activity from AT 2021mhg (e.g., no narrow lines are
detected in the optical spectrum); hence, if this source is not a pTDE, it is
most likely a supernova. We use the Supernova Identification (snid) tool to
model the post-rebrightening optical spectrum from this source. The spectrum
is well-modeled ($87\%$ match) as a type Ia supernova observed ${\sim}30$ days
post-peak. The mysterious broad features near $5000\,{\rm\AA}$ are perfectly
modeled in this scenario. If this second flare is indeed a Type Ia SN, the
red, fast-evolving lightcurve is expected.

Thus, the second flare from AT 2021mhg would be extremely unusual if it were
caused by a TDE, but it is fully consistent with originating from a Type Ia
SN. In this case, we have observed a galaxy where a TDE occured, followed by a
Type Ia SN after ${\sim}2$ years. The probability of observing a scenario like
this is non-neglible, and must be considered in future searches for pTDEs. A
Type Ia SN in a ${\sim}$Milky Way-like galaxy once every ${\sim}500$ years.
Assuming this rate is uniform throughout the galaxy, the typical TDE host has
a radius of ${\sim}3\arcsec$and we define the nucleus as the central
${\sim}1\arcsec$, a Type Ia SN will occur in a galaxy nucleus every $2\times
10^{4}$ years.

We have searched a sample of $33$ galaxies (i.e., the Yao et al., 2023 sample)
for flares over a period of ${\sim}3$ years (i.e., the time since the first
TDE flares in each). Thus, the probability of detecting a Type Ia SN from one
of these galaxies in this time period is $33\times 3\,{\rm years}/2\times
10^{4}\,{\rm years}=0.02$. The probability of detecting one or more events
given that this expected probability is ${\sim}2\%$. In other words, the
detection of AT 2021mhg source is only a ${\sim}2\sigma$ fluctuation.

As we continue monitoring TDEs for rebrightenings, the probability of
detecting both a TDE and another transient in the same galaxy will continue
increasing. We strongly urge the careful consideration of this scenario when
future pTDE candidates are detected.

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