# VLASS tidal disruption events with optical flares I: the sample and a
comparison to optically-selected TDEs

Jean J. Somalwar<EMAIL_ADDRESS>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.  Dillon Z. Dong
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  Gregg Hallinan
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Casey Law Cahill Center for Astronomy
and Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA
91125, USA.  Jessie Miller  Cahill Center for Astronomy and Astrophysics, MC
249-17 California Institute of Technology, Pasadena CA 91125, USA.  Steven T.
Myers  National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801,
USA  Yuhan Yao Cahill Center for Astronomy and Astrophysics, MC 249-17
California Institute of Technology, Pasadena CA 91125, USA.  Richard Dekany
Caltech Optical Observatories, California Institute of Technology, Pasadena,
CA 91125  Matthew Graham  Cahill Center for Astronomy and Astrophysics, MC
249-17 California Institute of Technology, Pasadena CA 91125, USA.  Steven L.
Groom IPAC, California Institute of Technology, 1200 E. California Blvd,
Pasadena, CA 91125, USA  Josiah Purdum  Cahill Center for Astronomy and
Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA 91125,
USA.  Avery Wold IPAC, California Institute of Technology, 1200 E. California
Blvd, Pasadena, CA 91125, USA

###### Abstract

In this work, we use the Jansky VLA Sky Survey (VLASS) to compile the first
sample of six radio-selected tidal disruption events (TDEs) with transient
optical counterparts. While we still lack the statistics to do detailed
population studies of radio-selected TDEs, we use these events to suggest
trends in host galaxy and optical light curve properties that may correlate
with the presence of radio emission, and hence can inform optically-selected
TDE radio follow-up campaigns. We find that radio-selected TDEs tend to have
faint and cool optical flares, as well as host galaxies with low SMBH masses.
Our radio-selected TDEs also tend to have more energetic, larger radio
emitting regions than radio-detected, optically-selected TDEs. We consider
possible explanations for these trends, including by invoking super-Eddington
accretion and enhanced circumnuclear media. Finally, we constrain the radio-
emitting TDE rate to be $\gtrsim 10$ Gpc-3 yr-1.

##  1 Introduction

Extragalactic radio-synchrotron transients open a novel window onto some of
the most extreme activity in the universe. These transients are typically
associated with dramatic accretion events and stellar explosions, among a
multitude of other possibilities. Until recently, it was impossible to obtain
a uniform census of the transient radio sky due to the difficulty of
performing a multi-epoch, full sky radio survey. The advent of surveys like
the Caltech-NRAO Stripe 82 Survey (CNSS; Mooley et al., 2016), the Jansky Very
Large Array Sky Survey (VLASS; Lacy et al., 2020), the Australian Square
Kilometre Array Pathfinder Variables and Slow Transients (ASKAP VAST; Murphy
et al., 2013) survey have transformed our understanding by enabling the
compilation of samples of radio transients that are assembled with a known
selection function.

Despite this progress, many open questions remain. In particular, the
relationship between radio transients and higher wavelength flares remains
poorly understood, despite providing significant insight on the underlying
physical processes. Tidal disruption events (TDEs) provide a quintessential
example of this. TDEs occur when a star strays within the tidal radius111The
tidal radius $R_{T}$ where the tidal forces from a SMBH overpower the internal
gravity of a star is given by $R_{T}\approx R_{*}(M_{\rm BH}/M_{*})^{-1/3}$
for a non-spinning black hole of mass $M_{\rm BH}$ and a star of mass $M_{*}$
and radius $R_{*}$. of a supermassive black hole (SMBH) (e.g. Evans &
Kochanek, 1989; Rees, 1988; Phinney, 1989). TDEs were originally theorized to
produce X-ray emission, so many of the early searches for these events focused
on this waveband using the ROSAT All Sky Survey (RASS; e.g., Saxton et al.,
2012). Soon, UV and optical searches using GALEX and SDSS began producing TDE
candidates (e.g. Gezari et al., 2008).

Throughout this effort, the question of radio emission from TDEs remained
unconstrained. Giannios & Metzger (2011) first suggested that a radio
transient could be produced if TDEs can launch relativistic, highly collimated
jets, and the first detection of a candidate jetted TDE followed shortly
(Bloom et al., 2011a). Efforts to follow-up TDEs in the radio followed, but
these tended to involve one or a few observations shortly after the higher
wavelength flare and few detections resulted (see Alexander et al., 2020, for
a review). Recently, the detection rate has increased through long-timescale
follow-up of optically-selected TDEs (e.g. Horesh et al., 2021; Cendes et al.,
2022, 2023). Still, without a better understanding of the mechanisms that
produce TDE radio emission and how they may be related to the multiwavelength
properties of the events, it is difficult the identify the optimal candidates
for follow-up, the optimal follow-up cadence, and the optimal follow-up
sensitivity.

Moreover, even if radio instruments could be used to comprehensively follow up
all TDEs, the resulting radio-detected samples will be biased. Any radio-
emitting TDEs discovered through follow-up of, e.g., optically-selected
events, will be biased towards those TDEs that produce optical emission, and
it has already been established that not all TDEs do so (e.g. Somalwar et al.,
2021; Sazonov et al., 2021). This renders it near impossible to compile a view
of the complete landscape of radio emission through follow-up of known TDEs:
if there is a correlation between optical emission and radio emission,
selecting on optically-emitting TDEs will bias the expected types of radio
emission.

Table 1: Properties of our TDE sample

Name | AT Name | R.A. | Dec. |  $\Delta d$ [$\arcsec$] | $z$ | $f_{\nu,\rm E2}$ [mJy]
---|---|---|---|---|---|---
VT J08131,2,3 | AT 2019azh | $08^{\mathrm{h}}13^{\mathrm{m}}17.0^{\mathrm{s}}$ | $+22^{\circ}38{}^{\prime}54.0{}^{\prime\prime}$ | 0.0 | 0.022 | 1.0
VT J10084,5,6 | AT 2020vdq | $10^{\mathrm{h}}08^{\mathrm{m}}53.4^{\mathrm{s}}$ | $+42^{\circ}43{}^{\prime}00.2{}^{\prime\prime}$ | 0.18 | 0.045 | 1.5
VT J1356 |  | $13^{\mathrm{h}}56^{\mathrm{m}}12.1^{\mathrm{s}}$ | $-26^{\circ}58{}^{\prime}50.7{}^{\prime\prime}$ | 0.54 | 0.018 | 2.5
VT J17524,6 | AT 2019baf | $17^{\mathrm{h}}52^{\mathrm{m}}00.1^{\mathrm{s}}$ | $+65^{\circ}37{}^{\prime}36.0{}^{\prime\prime}$ | 0.13 | 0.089 | 1.4
VT J2012 |  | $20^{\mathrm{h}}12^{\mathrm{m}}29.9^{\mathrm{s}}$ | $-17^{\circ}05{}^{\prime}56.3{}^{\prime\prime}$ | 0.2 | 0.053 | 1.1
VT J2030 |  | $20^{\mathrm{h}}30^{\mathrm{m}}47.3^{\mathrm{s}}$ | $+04^{\circ}13{}^{\prime}31.0{}^{\prime\prime}$ | 0.19 | 0.061 | 1.4

Note. — Redshifts are measured from our follow-up optical spectroscopy as
described in Appendix B. References: 1van Velzen et al., 2021b,2Goodwin et
al., 2022, 3Sfaradi et al., 2022,4Yao et al., 2023,5Somalwar et al.,
2023a,6Somalwar & Ravi,2023

A radio-selected TDE sample is key to constraining these many unknowns, and
the 3 GHz Jansky Very Large Array Sky Survey (VLASS; Lacy et al., 2020) is
ideal for such an effort: predictions have estimated that ${\sim}100$ TDEs
could be detectable using that survey (Anderson et al., 2020). The first
candidates detected in this survey have already been published (Ravi et al.,
2021; Somalwar et al., 2021, 2023b), and compilation of the first VLASS-
selected TDE sample, regardless of multiwavelength counterpart, is underway
(Somalwar et al., in prep.).

With this VLASS TDE sample, we can begin answering some of the questions posed
earlier about the range of radio emission and the emission mechanisms, as well
as the relationship between the radio emission and multiwavelength emission.
In this paper, we focus on the latter questions: we present the first sample
of radio-selected, optically-detected TDEs.

For clarity, we have divided our analysis into three papers. In this paper
(Paper I), we present our full radio-selected, optically-detected TDE sample
and perform observational comparisons between radio-selected, optically-
detected TDEs and optically-selected TDEs, with the aim of identifying those
factors that distinguish between radio-emitting TDEs and radio-quiet TDEs. We
also discuss the rate of radio-bright, optically-bright TDEs. We will briefly
speculate on the physical mechanisms at play. We defer detailed discussion of
both the multiwavelength properties and physical interpretations of each event
to the companion papers. Somalwar & Ravi (2023) discusses late-time,
transient, optical spectral features detected from two of the events. Somalwar
et al. (in prep.) discusses evidence for and implications of jet launching
from three of the events.

##  2 Sample Selection

We compile our radio-selected TDE sample using data from the Very Large Array
Sky Survey (VLASS; Lacy et al., 2020). VLASS is an ongoing effort to observe
the entire sky with $\delta>-40^{\circ}$ at 3 GHz for three epochs with a
cadence of ${\sim}2$ years. VLASS has a $1\sigma$ sensitivity of ${\sim}0.13$
mJy/beam and a spatial resolution of ${\sim}2.5\arcsec$. Each epoch is divided
into two halves. The first half of epoch one, which we denote E1.1, was
observed in 2017. The second half of epoch one (E1.2) was observed 2018. E2.1
was observed in 2020, and E2.2 was observed from 2021. E3.1 is ongoing (Jan
2023-present).

We identified TDE candidates using the transient catalog of Dong et al., in
prep., who identified all sources that were detected at $>7\sigma$ in E2 but
not significantly detected ($<3\sigma$) in E1; i.e., this catalog contains all
transients that are rising between E1 and E2. Details about the transient
detection algorithm are described in Somalwar et al. (2021) and Dong et al.,
in prep. We select TDE candidates from this catalog using the following
criteria:

  1. 1.

the transient is within $1\arcsec$ of the position of a source in the
PanSTARRS catalog (Chambers et al., 2016; Flewelling et al., 2020);

  2. 2.

the associated source is a galaxy; i.e., it is inconsistent with being a star
using all public catalogs, including GAIA (to remove all objects with
significant parallax; Gaia Collaboration et al., 2022, 2016) and the PanSTARRS
star-galaxy classifier (Beck et al., 2021);

  3. 3.

the host galaxy must show no evidence for strong AGN activity. Among the
criteria used to identify AGN, we consider: the position of the source on the
WISE W1-W2 and W2-W3 color diagram (Stern et al., 2012); any evidence for past
optical, X-ray, or radio variability/detections that could indicate AGN
activity; and any public optical spectra with broad or narrow line emission
that indicate strong AGN activity. We have found that this criteria rules out
strong AGN, but some weak AGN remain. In this paper, we include these objects
and will discuss the implications of their AGN activity primarily in Somalwar
et al. (in prep.);

  4. 4.

the host galaxy must have a PanSTARRS photometric redshift $z_{\rm phot}<0.25$
(Beck et al., 2021). When PanSTARRS photometric redshifts are unavailable, we
inspect catalog data for the galaxy to identify the redshift. If no redshift
information is available, we measure a redshift using an SED fit to the galaxy
photometry, following the procedure discussed in Appendix B. We include this
redshift cut to ensure that we can obtain multiwavelength follow-up to detect
counterparts and classify the host galaxies with reasonable exposure times.
This redshift cut will bias us against rare TDEs; e.g., we are not sensitive
to most on-axis jetted TDEs, which are generally found at $z\gtrsim 0.3$.
Future work will consider the higher-redshift transients.

In summary, this selection criteria will identify nuclear radio flares in
nearby non- or weakly-active galaxies. We obtained optical spectroscopy for
all events to measure spectroscopic redshifts, and do not consider any source
with $z_{\rm spec}>0.25$. The resulting sample has ${\sim}100$ objects. We
will perform a detailed analysis of the completeness of this selection in
future work, when we present the full VLASS TDE sample.

In this paper, we only consider transients with associated optical flares. We
obtained forced-photometry at the position of each transient from the Zwicky
Transient Facility (ZTF; $gri$ bands; Bellm et al., 2019) and the Asteroid
Terrestrial-impact Last Alert System (ATLAS; $co$ bands; Tonry et al., 2018)
using recommended procedures. Our sample includes every transient with an
optical lightcurve with at least three $5\sigma$ detections and at least one
$10\sigma$ in any bands. We chose this criteria to ensure that the flare is
significantly detected, and thus amenable to quantitative analysis of the
flare evolution. Note that we have already ruled out events with long-term,
AGN-like variability in our TDE candidate selection. While we do not do a
detailed search of optical lightcurves from the All-Sky Automated Survey for
Supernovae (ASASSN; Kochanek et al., 2017) because of limited optical color
information and sensitivity, our final sample includes one source that has an
ASASSN flare with simultaneous MIR observations, and thus more constraints on
the physical properties of the optical flare (Appendix A).

The resulting sample has six objects, the properties of which are summarized
in Table 1. These sources are named using our VLASS transient naming
convention: VT J081316.97+223853.99 (henceforth VT J0813), VT
J100853.44+424300.22 (VT J1008), VT J135612.14-265850.71 (VT J1356), VT
J175200.13+653736.04 (J1752), VT J201229.90-170556.32 (VT J2012), and VT
J203057.34+041330.97 (VT J2030). We refer to the host galaxies of these
objects using the coordinates prefixed with HG (host galaxy; e.g., HG J1356,
HG J1008, etc.). In plots, we often label the individual transients or host
galaxies without the prefixes (e.g., J1356, J1008), except when the prefixes
are necessary for clarity.

###  2.1 The optically-selected TDE sample

A key aspect of this paper is our comparison of radio-selected and optically-
selected TDEs; hence, here we present our chosen optically-selected comparison
samples. We consider two different samples: the Yao et al. (2023) and
Hammerstein et al. (2023) samples. The Hammerstein et al. (2023) sample
includes all classified TDEs discovered in the first ${\sim}3$ years of ZTF.
Yao et al. (2023) presents a complete sample of TDEs with peak $g$-band mag
$\lesssim 19$ during the first three years of ZTF.

We largely compare to the Yao et al. (2023) sample. However, when considering
host galaxy stellar masses, colors, or star-formation rates, or Baldwin,
Phillips & Terlevich (BPT;Baldwin et al., 1981) classifications, we adopt the
Hammerstein et al. (2023) sample, because our methods better align with
theirs.

In both cases, we restrict our comparison to events at redshifts $z<0.1$. We
apply this cut to ensure that redshift evolution doesn’t bias our results: the
highest redshift object in our sample is at $z=0.089$, whereas the optically-
selected TDEs range to much larger redshifts.

##  3 Observations and Data Reduction

We have performed an extensive multi-wavelength follow-up campaign for all of
our TDE candidates. We present a relevant subset of that data here; the full
dataset for each TDE candidate is presented in the corresponding companion
paper. In this section, we describe our observations and data reduction
procedures.

###  3.1 Radio observations

Table 2: Summary of VLA follow-up

Name | MJD | Configuration | Freq. range [GHz] | Program (PI)
---|---|---|---|---
VT J1008 | 59612 | B$\rightarrow$BnA | $1{-}12$ | 21B-322 (G. Hallinan)
VT J1356 | 59626 | BnA | $1{-}12$ | 21B-322 (G. Hallinan)
VT J1752 | 59273 | A | $1{-}12$ | 20B-393 (D. Dong)
| 59632 | BnA | $1{-}12$ | 21B-322 (G. Hallinan)
VT J2012 | 59257 | A | $1{-}12$ | 20B-393 (D. Dong)
| 59271 | A | $1{-}12$ | 20B-393 (D. Dong)
VT J2030 | 58881 | C | $1{-}18$ | 19A-013 (PI: K. Alexander)
| 59130 | C | $1{-}18$ | 20A-372 (PI: K. Alexander)
| 59257 | C | $1{-}12$ | 20B-393 (PI: D. Dong)

Each TDE candidate has one or more multi-frequency radio observations from the
Jansky Very Large Array. We summarize the observations for all sources except
J0813 in Table 2. The reduced VLA SEDs for J0813 were published in Goodwin et
al. (2022), so we adopt the spectra tabulated in that work. We reduced all
other observations using the VLA Calibration Pipeline 2022.2.0.64 and CASA
version 6.4.1 (CASA Team et al., 2022). We imaged the data using standard CASA
recipes, and measured the flux density of each source as the flux density of
the peak pixel in a $50\times 50$ pixel box centered on the source location.

###  3.2 Optical transient photometry

We retrieve forced, difference photometry from the Asteroid Terrestrial-impact
Last Alert System (ATLAS; Tonry et al., 2018) and Zwicky Transient Facility
(ZTF; Bellm et al., 2019; Graham et al., 2019; Dekany et al., 2020; Masci et
al., 2019) using the recommended procedures and automated pipelines for each
survey. We use public data from the ATLAS survey, and both public and
partnership data from ZTF. We load the data from both surveys using the Hybrid
Analytic Flux FittEr (HAFFET; Yang et al., 2021) code, and then bin each
lightcurve with a binsize of one day. The ATLAS photometry of J0813 use
different baselines for MJD $>58895$, leading to zeropoint offsets for this
MJD range. We correct for the zeropoint offset by estimating the median non-
transient flux in each filter from those data points at MJD $>59200$ in each
and subtract that median flux from the lightcurve for MJD $>58895$. Similarly,
the ZTF host reference image of J2030 was taken while the transient was
active, so it overestimates the baseline flux, and we correct for this by
calculating the median flux in each band for MJD$>58500$ and subtracting this
flux from the entire lightcurve.

We treat J1356 separately because it is the oldest transient and is not
detected by ATLAS or ZTF. It is, however, detected by the All-Sky Automated
Survey for Supernovae (ASASSN; Kochanek et al., 2017). We retrieved and
processed the lightcurve using the recommended ASASSN tools (Jayasinghe et
al., 2019; Shappee et al., 2014). Like for the other events, we binned the
lightcurve in one day bins.

###  3.3 Host photometry

We retrieve host photometry for each TDE using the same methods as Hammerstein
et al. (2023), to enable a like-to-like comparison with the results from that
work. We refer the reader to Hammerstein et al. (2023) for a detailed
description of the adopted methods. In brief, we retrieve SDSS or PanSTARRS,
where SDSS is unavailable, Kron magnitudes. We also retrieve GALEX NUV and FUV
photometry using recommended methods.

###  3.4 Optical spectroscopy

HG J0813 was previously observed as part of the Sloan Digital Sky Survey
(SDSS; Abdurro’uf et al., 2022) Spectroscopic survey (Strauss et al., 2002) on
MJD 52943. We retrieved the spectrum of this source from the SDSS DR17
website.

We obtained optical spectra for the all our TDE candidates except VT J0813
using the Low Resolution Imaging Spectrometer (LRIS) on the Keck I telescope.
In all cases, we centered the observation on the galactic nucleus using a
parallactic angle. We used the 400/3400 grism, the 400/8500 grating with
central wavelength 7830, and the 560 dichroic. The resulting wavelength range
was ${\sim}1300{-}10000\,{\rm\AA}$ and the resolution $R{\sim}700$. We
observed VT J1008 on MJD 59676 for 20 min using the $1\arcsec$ slit with the
standard star Feige 34. We observed VT J1356 on MJD 59616 for 10 min using the
$1\arcsec$ slit with the standard star Feige 34. We observed VT J1752 on MJD
59260 for 10 min using the $1\farcs 5$ slit with the standard star Feige 34.
We observed VT J2012 on MJD 59464 for 10 min using the $1\farcs 5$ slit with
the standard star BD+28. We observed VT J2030 on MJD 59464 for 10 min using
the $1\farcs 5$ slit with the standard star Feige 34. We reduced the
observations using the lpipe code with standard settings (Perley, 2019).

We obtained high-resolution optical spectra for a subset of the TDE candidates
using the Echellette Spectrograph and Imager (ESI) on the Keck II telescope.
We used the Echelle mode for all observations. We observed VT J0813 on MJD
59874 for 20 minutes using the $0\farcs 5$ arcsec slit. We observed VT J1008
on MJD 59908 for 22.5 min using the $0\farcs 3$ slit. We observed VT J2012 on
MJD 59876 for 20 min using the $0\farcs 5$ arcsec slit. We observed VT J2030
on MJD 59874 for 20 min using the $0\farcs 5$ arcsec slit. The $0\farcs 5$
($0\farcs 3$) slit leads to an instrumental broadening of $\sigma_{\rm
inst}=15.8(9.5)$ km s-1. We reduced the spectra using the makee software
following the default, recommended procedures for ESI data reduction.

##  4 Summary of detailed transient properties

In this paper, we focus on the properties of the radio-selected, optically-
bright TDE population, rather than the individual characteristics of each
source. Hence, we will primarily discuss observations that are available for
our full sample and for comparison optical TDE samples; namely, the optical
lightcurves and spectra, host galaxy observations from public survey data, and
the radio observations. Context about the individual transients is, however,
useful for interpreting the results of this paper. Thus, we begin our paper
with a brief review of the properties of each transient detailed in papers
II/III and other sources.

VT J0813 (Somalwar et al., in prep.; van Velzen et al., 2021b; Goodwin et al.,
2022; Sfaradi et al., 2022): VT J0813 (otherwise known as ASASSN-19dj or
AT2019azh) was first discovered as an optical transient by the ASASSN survey
on Feb. 22 2019 (Hinkle et al., 2021). It was also detected by the ZTF and
ATLAS surveys. The optical lightcurve is typical of TDEs. Transient Balmer and
Helium lines were detected in follow-up optical spectra, leading to the
classification of this source as a TDE-H+He (van Velzen et al., 2021b;
Hammerstein et al., 2023). In addition to the optical flare, this source was
detected as an X-ray transient with peak luminosity $L_{X}=10^{43}$ erg s-1
that brightened ${\sim}7$ months after the optical peak (van Velzen et al.,
2021b). The host galaxy shows a disturbed morphology, characteristic of a
recent merger or interaction (Somalwar et al., in prep.).

This source was first detected as a GHz radio transient by Perez-Torres et al.
(2019) with the e-MERLIN telescope and was then observed by numerous radio
telescopes, notably by Goodwin et al. (2022), who obtained multi-epoch radio
SEDs and argued that the radio-emitting outflow was non-relativistic and had a
very optically-thin spectral index. Sfaradi et al. (2022) further observed
this source with a high cadence and argued that the radio variability was
correlated with the X-ray spectral variability and luminosity in a manner
similar to that observed from X-ray binaries. They used this to argue for the
presence of a jet subject to the accretion state changes in the accretion
disk.

VT J1008 (Somalwar & Ravi, 2023; Yao et al., 2023; Somalwar et al., 2023a): VT
J1008 (AT 2020vdq) was first detected as an optical transient by ZTF on Oct. 4
2020. There is no prompt follow-up for this source, so the early time radio
and X-ray behavior is unknown. It was not reported as an X-ray transient in
any public X-ray surveys. Late-time (${\sim}2$ years post-optical peak) Neil
Gehrels Swift Observatory X-ray Telescope (Swift/XRT; Burrows et al., 2005)
follow-up ${\sim}2$ years post-TDE did not detect any significant X-ray
emission ($3\sigma$ upper limit $<10^{41.8}$ erg s-1). In an optical spectrum
${\sim}2$ years post-optical-peak, transient Balmer lines and He II lines are
detected with widths ${\sim}1000$ km s-1 and luminosities ${\sim}10^{40}$ erg
s-1. These lines are commonly detected from TDEs, but they are typically much
broader (${\sim}10^{4}$ km s-1) and fade within a year. The origin of these
lines is considered in detail by Somalwar & Ravi (2023). Roughly three years
after the initial optical flare, this source re-brightened in the optical.
Somalwar et al. (2023a) constrain the origin of the rebrightening and suggest
that this event is a repeating, partial tidal disruption event. No new radio
emission was detected post-rebrightening.

VT J1356 (Appendix A): VT J1356 is detected as a transient in ASASSN forced
photometry. It is simultaneously detected as a NIR transient in NEOWISE
photometry. It is the oldest of our TDE sample, with the ASASSN detections
occuring ${\sim}8$ years ago. The NIR flare is double peaked, with an initial,
hot ($T\sim 10^{4}$ K) flare followed by a $\gtrsim 5$ year cool flare ($T\sim
10^{3}$ K), consistent with blackbody emission from dust at ${\sim}0.5$ pc
that has been heated by the high energy emission produced during the
transient. This source is not discussed in either of the companion papers, so
we describe its properties in detail in Appendix A.

VT J1752 (Somalwar et al., in prep., simultaneously reported by Yao et al.
(2023)): VT J1752 (AT2019baf) was first reported as a transient by ZTF on Jan.
9 2019. The optical lightcurve showed an unusual double peaked structure.
There was no prompt multiwavelength follow-up for this source, so the early
time radio and X-ray behavior is unknown. It was not reported as an X-ray
transient in any public X-ray surveys. Late-time (${\sim}2$ years post-optical
peak) Swift/XRT follow-up detected an X-ray source with $L_{X}=10^{42.4}$ erg
s-1. No transient optical spectral features were detected in follow-up optical
spectra. The host galaxy shows a disturbed morphology, characteristic of a
recent merger or interaction. The radio SED is best-fit by a multi-component
synchrotron model, suggesting the presence of multiple outflows or a
structured outflow. The outflows have high luminosities and energies,
suggestive of the presence of a jet.

VT J2012 (Somalwar & Ravi, 2023): VT J2012 was first detected as a transient
by the ATLAS survey on 58772. It has multiwavelength properties identical to
those of VT J1008. The only major differences between these two events is that
no transient Helium lines are detected from VT J2012, and the transient Balmer
lines are redshifted by ${\sim}700$ km s-1. There is no blueshifted component.

VT J2030 (Somalwar et al., in prep.): VT J2030 was first detected as transient
by the XMM-Newton Slew Survey team, who undertook an X-ray and radio follow-up
campaign. The X-ray emission from this source has an peak luminosity
${\sim}10^{43.8}$ erg s-1, but with strong variability of a factor of a few on
${\sim}$week timescales. The radio emission also shows non-monotonic
evolution. Both of these properties are consistent with the presence of a
young jet.

VT J2030 was detected as an optical transient by the ZTF survey. However, the
transient occurred during the start of ZTF, so it was present in the reference
images and the transient appeared as a negative flux in the ZTF photometry. VT
J2030 was also detected as a transient by the ATLAS survey. In this survey, it
appeared like a typical TDE, with a positive rise and then decay.

##  5 Host galaxies

Table 3: Host Galaxy

Name | $z$ | $\log\frac{M_{*}}{M_{\odot}}$ | $\log\frac{\sigma_{*}}{{\rm kms}^{-1}}$ | $\log\frac{M_{\rm BH}(M_{*})}{M_{\odot}}$ | $\log\frac{M_{\rm BH}(\sigma_{*})}{M_{\odot}}$ | BPT | $\log\frac{\rm SFR_{SED}}{(M_{\odot}\/{\rm yr})}$ | $A_{V}$ | $(u-r)_{0}$
---|---|---|---|---|---|---|---|---|---
J0813 | 0.022 | $9.79_{0.00}^{0.00}$ | $68\pm 2$ | $6.99^{+0.19}_{-0.21}$ | $6.44\pm 0.29$ | Sey. | $0.27_{0.04}^{0.04}$ | $0.12^{+0.08}_{-0.10}$ | $1.77_{0.00}^{0.01}$
J1008 | 0.045 | $9.16_{0.10}^{0.30}$ | $44\pm 3$ | $4.81^{+0.40}_{-0.32}$ | $5.59\pm 0.29$ | Q? | $0.07_{0.06}^{0.03}$ | $0.18^{+0.14}_{-0.13}$ | $1.86_{0.11}^{0.15}$
J1356 | 0.018 | $8.94_{0.09}^{0.39}$ | $-$ | $5.08^{+0.28}_{-0.30}$ | $-$ | SF | $0.08_{0.08}^{0.07}$ | $0.08^{+0.05}_{-0.23}$ | $1.63_{0.24}^{0.25}$
J1752 | 0.089 | $10.07_{0.07}^{0.32}$ | $-$ | $6.91^{+0.28}_{-0.31}$ | $-$ | Sey. | $2.41_{0.78}^{3.70}$ | $1.10^{+0.35}_{-0.30}$ | $1.93_{0.15}^{0.15}$
J2012 | 0.053 | $9.90_{0.09}^{0.32}$ | $59\pm 2$ | $6.55^{+0.24}_{-0.32}$ | $6.17\pm 0.31$ | Q? | $0.00_{0.00}^{0.06}$ | $0.32^{+0.23}_{-0.28}$ | $2.34_{0.10}^{0.08}$
J2030 | 0.061 | $9.79_{0.01}^{0.26}$ | $62\pm 5$ | $6.37^{+0.22}_{-0.23}$ | $6.25\pm 0.31$ | SF | $0.50_{0.07}^{0.10}$ | $0.14^{+0.09}_{-0.13}$ | $1.84_{0.07}^{0.09}$

Note. — The host galaxy properties of our radio-selected TDE sample. The
methods of measuring these properties are described in Section 5.

Figure 1: The optical spectra for the radio-selected TDEs in our sample. The
observed spectra are shown in black and the best-fit stellar continuum in red
(Appendix B). The Balmer, He II, and [Fe X] features observed from J1008 and
J2012 are associated with the transient and are discussed in (Somalwar & Ravi,
2023).

In the rest of this paper, our primary goal is to constrain the physical
properties that distinguish between radio-selected, optically-bright and
optically-selected TDEs. This will rely on observations that are uniformly
available for both the radio and optically selected samples; namely, host
galaxy photometry and spectroscopy and optical light curves.

We begin by considering the properties of the host galaxies. The properties of
host galaxy directly affect the environment in which the transient occurs and
the properties of the astrophysical objects that produced the transient; for
example, the presence of long-lived ionized emission lines in the optical
spectra can suggest the presence of an AGN, or the morphology and color of the
host can suggest that the galaxy recently underwent a merger or interaction.
The differences in the host galaxies of these radio-selected, optically-
detected transients will inform our understanding of the parameters that
control radio emission from TDEs.

Each of the following sections considers one or a subset of the host galaxy
properties. We begin by describing the relevance of each property, then
discuss our methodology for constraining it, and finally compare the radio-
selected host properties to those of the optically-selected sample. The host
galaxy properties of our sample, constrained as described in the following
sections, are summarized in Table 3.

###  5.1 Black hole and stellar mass

SMBHs are central to TDEs and the TDE evolution is certainly affected by the
black hole mass. For SMBH masses $M_{\rm BH}\gtrsim 10^{8}M_{\odot}$ the tidal
radius $R_{T}\sim R_{*}(M_{\rm BH}/M_{*})^{2/3}$ is smaller than the
Schwarzchild radius $R_{s}\sim 2GM_{\rm BH}/c^{2}$, so any star on an orbit
that reaches $R<R_{T}$ is swallowed whole rather than disrupted. This analysis
assumes a non-spinning SMBH: if the SMBH has a high spin, the event horizon is
smaller and thus TDEs can occur. SMBH mass may also affect the efficiency with
which the TDE accretion disk forms. In some models of TDE evolution, an
accretion disk forms when the stellar tidal stream precesses due to
Lense–Thirring precession and collides with itself, dissipating energy
(Guillochon & Ramirez-Ruiz, 2015). The rate of Lense-Thirring precession is
$\dot{\Omega}\sim M_{\rm BH}^{2}$, so these collisions will occur less
frequently, if at all, for TDEs by low mass SMBHs (Lu & Bonnerot, 2020). This
might reduce the high energy (X-ray, UV) emission, if that emission is partly
produced during these shocks. Lower precession could also reduce optical
emission, if optical emission is produced when outflowing material that
becomes unbound during the shocks reprocesses the higher energy emission (Lu &
Bonnerot, 2020). Radio emission may also be affected; for example, if radio
emission is produced from accretion disk winds, as delayed accretion disk
formation could produce delayed winds.

We constrain the SMBH mass using two methods. First, the SMBH mass is tightly
connected to the stellar mass (Kormendy & Ho, 2013). Thus, we begin by simply
considering the stellar mass distributions of our galaxies as compared to that
of the optically-selected sample. We measure the stellar masses using fits to
the UV/optical/IR spectral energy distributions with the prospector SED
fitting code (Johnson et al., 2021), following the exact methods of
Hammerstein et al. (2023). The SMBH mass is also tightly connected to the
stellar velocity dispersion, which we measure from our high resolution ESI
spectra following the same methodology used by Somalwar et al. (2021).

We can then measure SMBH mass distribution in two ways: (1) using SMBH masses
from the host galaxy stellar mass-black hole mass relation from Yao et al.
(2023):

$\displaystyle{\rm log}$ $\displaystyle M_{\rm BH,9}=-(1.83\pm 0.15)+(1.64\pm
0.27)\times$ $\displaystyle{\rm log}\left(\frac{M_{\ast}}{3\times
10^{10}\,M_{\odot}}\right);\;{\rm intrinsic\;scatter=0.18},$ (1)

where $M_{\rm BH,9}$ is the SMBH mass in units of $10^{9}\,M_{\odot}$; (2) for
those sources with high-resolution optical spectra, we use SMBH masses
measured using the stellar velocity dispersion-black hole mass relation. We
adopt the $M_{\rm BH}-\sigma_{*}$ relation from Kormendy & Ho (2013), to match
that used by Yao et al. (2023):

$\displaystyle\log\frac{M_{\rm BH}}{10^{9}\,M_{\odot}}=-(0.509\pm 0.049)$
$\displaystyle+(4.384\pm 0.287)\times\log\big{(}\frac{\sigma_{*}}{200\,{\rm
km\,s}^{-1}}\big{)}.$ (2)

The intrinsic scatter in this relation is $0.29$ dex.

Figure 2: Left panel: Stellar mass distributions for the radio-selected TDE
hosts in this work (red line) as compared to the optically-selected TDE hosts
from Hammerstein et al. (2023) (dashed black line). The radio-selected TDEs
tentatively prefer lower mass galaxies. Middle panel: Stellar velocity
dispersion distributions for the radio-selected TDE hosts in this work (red
line) as compared to the optically-selected TDE hosts from Yao et al. (2023)
(dotted black line). The radio-selected TDEs tentatively prefer lower velocity
dispersion galaxies. Right panel: SMBH mass distributions for the radio-
selected TDE hosts in this work (red line) as compared to the optically-
selected TDE hosts from Yao et al. (2023) (dotted black line).

We consider the relative black hole masses of the optically-selected and
radio-selected samples using three different methods. First, we compare the
stellar mass distributions of the two samples, with the caveat that
differences in stellar mass can suggest different SMBH masses, or the same
SMBH mass but different galactic formation pathways. Then, we compare the
stellar velocity dispersion for those objects with stellar velocity
measurements, which is a more direct probe of SMBH mass, but is limited by
statistics. Finally, we compare the SMBH mass distributions directly, where
the masses are inferred from the stellar velocity dispersions and stellar
masses.

In Figure 2, we show histograms of each of these quantities for the radio-
selected sample and the optically-selected sample. In the leftmost panel, we
show the stellar mass distribution. In the middle panel, we show the stellar
velocity dispersion distribution. In the rightmost panel, we show the black
hole mass distribution. In all cases, we have chosen the bin size to be larger
than the typical measurement uncertainty. While we do not have the statistics
to make any definitive claims from these distributions, we can hypothesize
possible trends. In both the stellar mass and velocity dispersion panels, the
radio-selected TDEs appear to prefer lower values than those of the optically-
selected TDEs. This suggests that radio-emitting TDEs tend to occur when the
SMBH has a lower mass. Alternatively, there may be differences in the star-
formation histories and galactic evolution that lead to radio-emitting TDEs
from SMBHs with lower mass and velocity dispersion; such differences will also
be considered in Section 5.3 and Section 8.

This trend towards lower SMBH masses is not present in the rightmost panel of
Figure 2; however, we urge caution in interpreting this result. While our
velocity dispersion measurements agree with Yao et al. (2023), to which work
we are comparing in this figure, our stellar mass measurements follow the
methods of Hammerstein et al. (2023) and are consistently larger than those of
Yao et al. (2023) (see Figure 24 of Yao et al., 2023), which biases our SMBH
mass distribution towards higher values. Hence, despite the apparent
agreement, we believe there is a tentative trend towards lower SMBH masses for
radio-selected TDEs.

###  5.2 SMBH activity

Figure 3: Baldwin, Phillips & Terlevich (BPT) and WHα versus [N II]/${\rm
H\alpha}$ (WHAM) diagrams (Baldwin et al., 1981; Kewley et al., 2006; Cid
Fernandes et al., 2011) for those radio- and optically-selected TDEs with
detected nebular emission lines. The radio-selected TDEs are shown as colored
markers with different shapes, while the optically-selected TDEs are shown as
black, thin markers. Note that VT J0813 and VT J1752 are also in the
optically-selected sample. The optically-selected TDE hosts with nebular
emission appear to favor composite galaxies, whereas the radio-selected TDE
hosts favor Seyfert hosts.

TDEs by SMBHs that were actively accreting in the years prior to the event may
have substantially altered local environments compared to disruptions by non-
accreting SMBHs. AGN tend to have more dust and gas in the nuclei, which will
obscure optical emission but can enhance radio and infrared emission.
Moreover, a pre-existing accretion disk will alter the properties of the TDE
accretion disk; for example, a fossil disk can provide a seed magnetic field
that may enable jet launching. While our selection criteria excludes strong
AGN, weak Seyferts or retired AGN are included in our sample.

We constrain the SMBH activity in each host using Baldwin, Phillips &
Terlevich (BPT) and WHα versus [N II]/${\rm H\alpha}$ (WHAM) diagrams (Baldwin
et al., 1981; Kewley et al., 2006; Cid Fernandes et al., 2011). We place the
host galaxies on BPT and WHAM diagrams using fits to the narrow emission lines
in stellar-continuum-subtracted optical spectra. We use the lower resolution
LRIS and SDSS spectra for this fit; these are shown in Figure 1. We model the
spectral continua and emission lines as described in Appendix B. The stellar
continuum model is shown in red in Figure 1.

The resulting emission line ratios are shown on the BPT and WHAM diagrams in
Figure 3. In the top left panel, we have overlaid the BPT classifications of
the subset of optically-selected TDEs with host galaxy spectral information
(Hammerstein et al., 2021). Seven of the nineteen ($(37\pm 13)\%$, adopting
hereafter Poisson frequentist-confidence uncertainties, Maxwell, 2011)
optically-selected TDEs considered in that work show strong nebular emission
lines, and can thus be placed on a BPT diagram. In contrast, four out of our
six events ($(67\pm 25)\%$) have nebular emission lines. These fractions are
consistent within statistical uncertainties, although they may suggest that
active/star-forming galaxies tend to host radio-loud AGN.

A larger fraction of our sample lies in the AGN region than found for the
optically-selected events: 2/19 ($(11\pm 9)\%$) of the optically-selected
events are classified as AGN, whereas 3/6 ($(50\pm 26)\%$) of the radio-
selected events are classified as AGN, where we have identified AGN as those
host galaxies that are classified as an AGN or Seyfert in the BPT diagrams. We
note that VT J0813 is classified as a retired galaxy in the WHAM diagram,
suggesting that some of the emission line flux is contributed by an old
stellar population. However, the classification of this object as a Seyfert in
the BPT diagrams, rather than a LINER, suggests that there may be some
emission component resulting from AGN activity: AGN-free, retired galaxies are
typically BPT liners (Cid Fernandes et al., 2011). 4/19 ($(21\pm 12)\%$) of
the optically-selected events are classified as composite, whereas none of the
radio-selected events are classified as such. Finally, 1/19 ($(5\pm 8)\%$) of
the optically-selected events are classified as star-forming, whereas 1/6
($(17\pm 21)\%$) of the radio-selected events are classified as such. These
results suggest that radio-selected TDEs may prefer galaxies with more recent
or stronger AGN activity, and they may prefer star-forming hosts more than
optically-selected TDEs. These trends are not statistically significant,
however.

Note that if this AGN activity trend is real (as we do not have the statistics
to determine), it may be induced by different selection criteria between the
samples – while both samples exclude strong AGN, the treatment of weak AGN,
like those discussed here, is ambiguous. We include those sources that may
have had a recent AGN, but are not necessarily still active. The optical
selection may be different, leading to some of these trends. The trend with
star-forming hosts should be more robust to selection effects.

The presence of recent AGN activity in the hosts of VT J1752, J2030, and
likely J0813 may call into question their TDE classification. Low luminosity
AGN can produce flares through mechanisms other than stellar disruption, such
as accretion disk instabilities, and distinguishing between TDEs and AGN
flares is notoriously difficult (e.g. Somalwar et al., 2021). We cannot rule
out that these three events are caused by AGN variability. However, in this
paper, we have empirically classified these events as TDEs for consistency
with the optical selection: all of these events would pass the typical optical
TDE selection cuts (such as those used in Yao et al., 2023), and both VT J0813
and VT J1752 are, in fact, included in optical TDE samples. We consider these
events to be TDEs for the rest of this work given the consistency with typical
optically-selected events and the fact that the AGN are very low luminosity,
if on at all. We urge further research on distinguishing between AGN flares
and TDEs.

###  5.3 Stellar population and star-formation

Figure 4: Left panel: The rest-frame $u-r$ color (${}^{0.0}u-r$) of the TDE
host galaxies vs the host galaxy stellar mass. The radio-selected sample is
shown as colored markers, and the optically-selected sample is shown as light
blue squares. The region of this plot occupied by galaxies in the green valley
is shown as a green shaded region (Schawinski et al., 2014). Right panel: The
H$\alpha$ equivalent width versus the Lick H$\delta_{A}$ absorption for the
TDE host galaxies. The different TDEs are formatted the same way as in the
left panel, except upper limits are shown as arrows.

Galactic star-formation histories, and thus stellar populations, are tightly
connected to the galaxy evolution. They may reflect processes that can drive
stars to the galactic nucleus; for example, mergers can trigger starbursts and
may enhance the TDE rate, so recent bursts of star-formation and young
($\lesssim 1$ Gyr) stellar populations may correlate TDE rate. Optically-
selected TDE hosts also tend to reside in the green valley, which includes the
population of galaxies transitioning from the starforming state (blue cloud)
to a non-starforming (red-and-dead) state or vice versa (e.g. Martin et al.,
2007). They are well established to predominantly reside in E+A galaxies
(French et al., 2020; Hammerstein et al., 2021), which are galaxies that have
undergone a recent ($\lesssim 1$ Gyr) starburst.

Because indicators of the presence of an E+A and/or green valley galaxy have
been studied in detail for optically-selected TDEs, we focus on those same
indicators for our galaxies (Hammerstein et al., 2021). We discuss the star
formation histories of the individual VLASS transients in more detail in the
companion papers and Appendix A.

We determine whether a galaxy is in the green valley by comparing its MW
extinction and redshift-corrected $u-r$ color, which we denote ${}^{0.0}u-r$,
and stellar mass to those for green valley galaxies, as shown in the left
panel of Figure 4. We adopt the same definition of green valley as Hammerstein
et al. (2023) and overplot the ${}^{0.0}u-r$ colors and stellar masses for
their optically-selected sample as blue squares. Qualitatively, all the radio-
selected TDE hosts are towards the edges of or outside the green valley, with
a preference towards bluer hosts, whereas the optically-selected TDE hosts
span it. Quantitatively, two of the six ($(33\pm 25)\%$) radio-selected TDEs
fall within the green valley, which is consistent with the eight of the
seventeen ($(47\pm 14)\%$) optically-selected TDEs in the same region.

We also constrain the stellar populations using the optical spectra. In
particular, we identify E+A galaxies using the Lick H$\delta_{A}$ absorption
index and H$\alpha$ equivalent width, as shown in the right panel of Figure 4.
The E+A region is shown in black solid lines. We have adopted the same E+A
galaxy definition as Hammerstein et al. (2023). We also show the quiescent
balmer strong (QBS) region is dashed black lines. Up to 2/6 ($(33\pm 25\%$) of
the VLASS TDE hosts are consistent with E+A galaxies, although a quiescent
H$\alpha$ luminosity for J1008 is required to confirm that result. This
fraction is consistent with the $2/12$ ($(16\pm 14\%$) of the optically-
selected TDEs that satisfy the E+A definition.

###  5.4 Summary

Our host galaxy analysis can be summarized as follows:

  1. 1.

Radio-selected, optically-bright TDEs tend to lie at lower stellar masses and
SMBH masses than optically-selected TDEs

  2. 2.

Radio-selected TDEs occur at a slightly higher rate in galaxies with
detectable nebular emission relative to optically-selected TDEs. A larger
fraction of these radio-selected events with nebular emission lie in AGN
hosts, whereas optically-selected events tend to prefer composite hosts,
although this trend may be in part due to different treatments of transients
in AGN between the samples.

  3. 3.

Radio-selected, optically-bright TDEs occupy green valley galaxies and E+A
galaxies at approximately the same rate as the optically-selected TDEs.

Future studies with larger radio-selected TDE samples will test whether these
correlations are real, or statistical flukes.

##  6 Optical transient broadband emission analysis

Informed by the discussion of the host emission from the last section, we
begin our analysis of the multiwavelength transient emission. We first
consider the optical broadband emission for two reasons: (1) the optical
emission from TDEs probes the evolution of the TDE debris and the accretion
flow at early times (${\sim}$months). Later, we will consider the radio
emission, which can be delayed and long-lived. (2) A key datum is the MJD on
which the TDE began; VLASS alone is not sufficiently high-cadence to constrain
this date. The optical light curves set the strongest constraints because they
have long baselines and high cadences. In this section, we present the optical
light-curves of our events (Figure 5) and perform a basic analysis of their
evolution.

###  6.1 Methodology

Table 4: Optical light curve parameters

Name | $L_{\rm bb}$ | $T_{\rm bb}$ | $R_{\rm bb}$ | $t_{1/2,{\rm decay}}$ | $t_{1/2,{\rm rise}}$ | Ref.
---|---|---|---|---|---|---
VT J0813 | 44.30 | 4.46 | 14.80 | $45.4^{+1.0}_{-0.9}$ | $24.1^{+1.1}_{-0.9}$ | Yao et al.,2023
VT J1008 | 42.98 | 4.15 | 14.76 | $23.1^{+1.8}_{-1.2}$ | $11.8^{+1.5}_{-1.3}$ | Yao et al.,2023
VT J1356 | 42.64 | 3.73 | 15.44 | $21.2^{+2.7}_{-2.2}$ | $2.6^{+1.4}_{-0.7}$ | This work
VT J1752 | 43.81 | 4.10 | 15.28 | $27.4^{+0.7}_{-0.7}$ | $23.1^{+0.9}_{-0.9}$ | Yao et al.,2023
VT J2012 | 43.07 | 3.93 | 15.26 | $26.2^{+5.4}_{-5.1}$ | $10.2^{+1.5}_{-1.1}$ | This work
VT J2030 | 43.09 | 3.88 | 15.36 | $66.6^{+2.0}_{-4.4}$ | $15^{+14}_{-10}$ | This work

Figure 5: The optical lightcurves for our TDE candidates. Each band is shown
in a different color.

TDE optical lightcurves are typically modelled as evolving blackbodies. We aim
to constrain four basic parameters of our lightcurves: the peak luminosity
$L_{\rm bb}$, the blackbody temperature at the time of the peak luminosity
Tbb, the rise time from half-max-luminosity to max-luminosity $t_{1/2,\rm
rise}$, and the decay time from max-luminosity to half-max luminosity
$t_{1/2,\rm decay}$. These parameters have already been constrained for J0813,
J1008, and J1752 by Yao et al. (2023) and we refer the reader to that work for
details.

Figure 6: The transient optical-IR SED for VT J1356 near optical peak. The
observations are shown as black scatter points. The black line and band shows
the best-fit blackbody and $\pm 1\sigma$. The best-fit parameters are shown in
the figure.

In the case of J1356 (described in detail in Appendix A), we only have one
band in the optical, so we do not have enough information to simultaneously
fit the blackbody temperature and luminosity from that data alone.
Fortuitously, J1356 was observed near the optical peak in the IR, and the
resulting IR and optical SED is shown in Figure 6. We fit this SED to a
blackbody and found a best-fit temperature of $\log T/{\rm
K}=3.73^{+0.01}_{-0.01}$. Errors are statistical. We then fit the optical
lightcurve to a Gaussian rise and exponential decay model, which is commonly
adopted for TDEs. We used the dynesty dynamic nested sampling software.

In the case of J2012, the sparse optical observations preclude any detailed
constraints on the optical evolution. We fit the optical lightcurve at $t<1$
year to a Gaussian rise and exponential decay model with a fixed temperature,
but urge caution in interpreting the results.

For J2030, there are no optical observations during the rise or peak of the
source, so we can only set a limit on the blackbody temperature and
luminosity, and we have no constraints on the rise time. We fit the decay to a
exponential model with a fixed blackbody temperature and set a lower limit on
the peak luminosity based on the luminosity during the first detection of the
source.

The adopted optical lightcurve parameters for each source are summarized in
Table 4.

###  6.2 Results

Figure 7: Left panel: The peak blackbody luminosity vs the blackbody
temperature at peak luminosity for the radio-selected TDEs and the optically-
selected TDEs, in the same format as other figures. Radio-selected TDEs may
have optical lightcurves with lower temperatures and luminosities than those
of the typical optically-selected event. Right panel: The rise versus decay
times for the optically- and radio-selected events, in the same format as the
left panel. No obvious trends are present.

In the rest of this section, we compare the optical lightcurve parameters for
our radio-selected, optically-detected TDEs to those for the optically-
selected TDE sample from Yao et al. (2023).

In Figure 7, we show the distribution of blackbody temperature and luminosity
in the left panel and $t_{1/2,{\rm rise}}$ vs $t_{1/2,{\rm decay}}$ in the
right panel. We see no obvious correlations in the rise/decay times of the
lightcurves. Radio-selected TDE hosts seem to lie towards lower temperature
and luminosities than the optically-selected sample, although the bulk of
those events at extreme temperatures/luminosities are those without well-
sampled data, suggesting this correlation may be an artifact of our analysis
methods or data quality. Ignoring those sources (J1356, J2012, J2030), two out
of three of the remaining events do lie at low temperatures and luminosities.

##  7 Radio emission properties and mechanism

Figure 8: Representative radio SEDs for each VLASS TDE candidate. The
observations are shown as scatter points, and the best-fit synchrotron $\pm
1\sigma$ models shown as transparent colored bands. The color of the scatter
points and fit bands correspond to the time since optical peak of each radio
observation. Note that VT J1752 is an example of a source that is very poorly
fit by a simple synchrotron model; we adopt this model despite the
inconsistent fit for uniformity.

Next, we consider the radio emission mechanisms for our sample and compare to
published radio follow-up of optically-selected TDEs. A small but growing
sample of TDEs have radio detections; the brightest four of which comprise the
on-axis, jetted TDE population (Andreoni et al., 2022; Bloom et al., 2011b;
Brown et al., 2015; Burrows et al., 2011; Cenko et al., 2012; Mattila et al.,
2018; Pasham et al., 2023; Zauderer et al., 2011; Ravi et al., 2022; Somalwar
et al., 2023b). Most TDEs with radio detections have non-relativistic, wide-
angle outflows. The non-relativistic TDEs were largely selected in the optical
and followed up in the radio, with a few exceptions. In the following
sections, we first consider the radio lightcurves of our events in the context
of published TDE radio lightcurves. Then, we constrain the physical parameters
of the emitting region and compare these to those of optically-selected,
radio-detected TDEs.

Figure 9: GHz radio lightcurves for a representative sample of radio-detected
TDEs. The solid, blue lines show example jetted TDEs and the dashed, cyan
lines show the non-relativistic TDE sample. The thick lines correspond to
objects that were found in untargeted radio searches, whereas the thin lines
correspond to objects that were selected in other bands (see Somalwar et al.,
2023b, and references therein).

###  7.1 The radio lightcurves of TDEs

First, we show the radio lightcurves for our TDEs and representative sub-
sample of all radio-detected TDEs in Figure 9. The jetted and non-jetted TDEs
are denoted with different line styles and colors. The radio-selected TDEs all
have thicker lines than those selected in other bands. The TDEs presented in
this paper are demarcated with unique colors and markers.

There are a number of key takeaways from this plot. From the non-radio-
selected TDEs alone, there was an apparent bifurcation of the events into
those with luminosities $\gtrsim 10^{31}$ erg s-1 Hz-1 and those with
luminosities $\lesssim 10^{29}$ erg s-1 Hz-1. This split approximately mapped
onto the type of outflow: relativistic, collimated jet, or non-relativistic,
wide-angle outflow. With the radio-selected TDEs, we have begun spanning the
gap between these two outflow classes. For example, we see evidence for jetted
sources at luminosities $\lesssim 10^{30}$ erg s-1 Hz-1, like J1533 from Ravi
et al. (2021) and J2030 from this work. The radio-selected TDEs alone span a
luminosity range $10^{28-31}$ erg s-1 Hz-1, with no clear division into
separate classes.

The fact that the radio-selected sample has more luminous emission may be a
selection effect - radio surveys are biased towards brighter radio sources.
The fact that optical surveys do not see these bright sources results from the
trends discussed in previous sections; in particular, it arises naturally from
the optical faintness of radio-selected TDEs.

We also see a wide range of lightcurve shapes. Until recently, TDE radio
lightcurves were expected to follow gamma-ray burst models, with a power law
rise and decay. This paradigm shifted with the discovery of $\gtrsim 5$-year-
old radio-selected TDEs (e.g. Ravi et al., 2021; Somalwar et al., 2023b) and
the discovery of radio rebrightening and other late-time radio emission from
optically-selected TDEs (e.g. Horesh et al., 2021). The radio TDEs presented
in this work extend the range of radio lightcurves. We see a wide range of
light curve shapes, including multiple examples that show late-time rise or
rebrightenings. Some of the rises and rebrightenings occur remarkably long
after the initial TDE. VT J2030 declines and then brightens ${\sim}3$ years
post-optical flare, while VT J1752 is still rising at that time. VT J1356 is
still rising after ${\sim}8$ years, making this one of the oldest known radio-
emitting TDEs, and the first known in a non-active galaxy. We also see
examples like VT J1008 and VT J2012, which show similar multiwavelength
properties and are at similar epochs post-TDE, but the 3 GHz luminosities are
rising at significantly different rates.

Of course, these single frequency lightcurves cannot provide a complete view
of the physical properties of the radio-emitting outflows. Instead, we require
multi-frequency radio SEDs (i.e., near-simultaneous observations at multiple
frequencies, spanning a few GHz range) spanning multiple epochs, which we can
fit to radio outflow models. Hence, for the rest of this section, we analyze
the radio SEDs of our events and briefly compare them to published results for
optically-selected, radio-detected TDEs.

###  7.2 Analysis of the TDE radio spectral energy distributions

We modelled the SED of each of the TDEs presented in this work uniformly. A
detailed model description is provided in Appendix C, which we briefly
summarize here. We assume all TDE radio emission is produced by the
synchrotron mechanism. We model each radio SED as a spherical outflow of
radius $R$ expanding into a medium with uniform density and magnetic field
$B$. We assume a single power-law electron population with density $N_{0}$,
minimum Lorentz factor $\gamma=\gamma_{\rm min}$ and spectral index $p$:

$N(\gamma)\propto\gamma^{-p},\gamma_{\rm min}<\gamma.$ (3)

With these definitions, the synchrotron flux density can be calculated as a
function of frequency, with free parameters $R$, $B$, $n$, $N_{0}$, and
$\gamma_{\rm min}$. We assume equipartition with $\epsilon_{\rm e}=0.1$ and
$\epsilon_{\rm B}=0.1$, as is standard in TDE modelling. This assumption
allows us to eliminate one parameter from our fit. We fit the synchrotron flux
density to each radio SED independently (i.e., assuming no model for time
evolution) using the dynesty dynamic nested sampler.

In the case of J1752, the radio emission model required with two components.
Our methodology was otherwise identical to that used when modelling the rest
of the sample.

The best-fit synchrotron parameters for each source at each epoch are
summarized in Table 5. We additionally include the total energy in the outflow
$E$, the equivalent ejecta mass $M_{\rm ej}=2E/c^{2}$, and the average $\beta$
factor of the ejecta ($\beta=v/c$, for velocity $v$) assuming the first
optical detection is the launch date of the outflow. For illustration, we show
a representative sample of the radio SEDs for the six TDEs published in this
paper in Figure 8, with the fits overlaid.

###  7.3 Comparison to optically-selected, radio-detected TDEs

In the rest of this section, we discuss the radio emission observed from both
our sample and place it in the context of the general radio-detected TDE
population. As a comparison, we primarily rely on Cendes et al. (2023), who
presented radio follow-up of 23 optically-selected TDEs, although without a
well-defined selection function. Radio emission was detected from $15$ of the
sources, although the transient nature of the emission could only be confirmed
for $9$ sources. Thus at least $40\%$ of the optically-selected TDEs that were
considered were radio emitting.

Cendes et al. (2023) obtained multi-frequency SEDs for their sample and
constrained the radii, magnetic field, and energies using methods similar to
ours although using a broken power-law fit to measure the peak flux/frequency
of the radio SEDs; we refer the reader to that work for details. In the rest
of this section we will compare these physical parameters between our sample
and that in Cendes et al. (2023), while keeping in mind that the differences
is SED fitting methods may result in small offsets in the measured outflow
physical parameters,

Figure 10: The evolution of the equipartition energies (top), radii (middle,
and magnetic fields (bottom for the TDEs in our sample (colored markers)
compared to those in the Cendes et al. (2023) sample (blue circles and
limits). The objects from the Cendes et al. (2023) with unconstrained peak
flux densities/frequencies are shown as limits. Our events tend to occupy a
higher energy, lower magnetic field, large radius state than the objects in
the Cendes et al. (2023) sample.

In Figure 10, we show the radius, energy, and magnetic field evolution as a
function of time. We do not adopt the energies reported in Cendes et al.
(2023), but instead adopt $E=\frac{B^{2}}{8\pi\epsilon_{B}}4\pi R^{3}f_{V}$,
where $f_{V}$ is the volume filling factor. The clearest discrepancy between
our sources and the sources from Cendes et al. (2023) is that the latter turn
on in the radio later than our sources. Our sources also tend to reside at the
upper end of the energy and radius range observed by Cendes et al. (2023), and
the lower end of the magnetic field range.

These differences between our sample and the Cendes et al. (2023) sample show
that radio and optical searches for TDEs are currently finding fundamentally
different events, even when only considering those TDEs that emit in both
bands. Our selection criteria, combined with the flux-limited nature of VLASS
and the timeline between the start of ZTF and VLASS E1/2 will tend to produce
events that brighten within ${\sim}3$ years post-optical flare and that are
intrinsically luminous. As we have argued, these sources tend to have faint
optical flares, so they will not be as dominant in the Cendes et al. (2023),
which is based on optically-discovered TDEs and so will be biased towards
objects with brighter optical flares. The Cendes et al. (2023) is also based
on deep radio follow-up, and thus is sensitive to events with fainter radio
emission than is detectable by VLASS.

##  8 Discussion

In the following sections, we briefly comment on physical explanations for the
tentative trends observed in this work and we constrain the rate of radio-
emitting, optically-bright TDEs. First, we recapitulate the results of the
following sections.

  * •

The radio-selected TDEs show a tentative preference for lower stellar mass and
velocity dispersion galaxies, suggesting that radio-selected TDEs may prefer
low SMBH masses.

  * •

Radio-selected TDEs are more likely to occur in galaxies with nebular emission
lines than optically-selected TDEs. The radio-selected TDE hosts with nebular
emission lines are predominantly Seyferts, whereas the optically-selected TDE
hosts with nebular emission lines are predominantly composite galaxies.

  * •

Radio-selected TDE hosts occupy E+A galaxies and green valley galaxies at a
consistent rate to that of optically-selected TDE hosts.

  * •

The optical light-curves for the radio-selected TDEs tend to peak at lower
blackbody temperatures and luminosities than those of the optically-selected
TDEs, although this difference could be caused by the difference in available
optical datasets for these sources.

  * •

TDEs show a wide-range of radio emission. In our sample, alone, we have TDEs
that, at ${\sim}3$-years post-first-detection, are both rising and fading at 3
GHz. We have TDEs with strongly non-monotonic evolution, and some with
brightening 3 GHz emission almost a decade post-event. The radio luminosities
of the radio-selected TDEs alone span the range $10^{28-31}$ erg s-1 Hz-1,
with no obvious division into subclasses.

  * •

Our radio-selected TDEs tend to have emitting regions with larger energies and
radii and smaller magnetic fields than optically-selected/radio-detected TDEs,
despite the fact that the radio-selected TDE radio emission turns on at
earlier times.

###  8.1 Physical explanations for the observed differences between radio- and
optically-selected TDEs

With these observations in mind, we briefly hypothesize physical explanations
for the observed trends. A comprehensive review of possible models is beyond
the scope of this paper.

If we adopt the model for TDE evolution where radio emission from TDEs may be
produced when a wind or jet launched from near an accretion disk, it is
possible to unify the observed trends. First, we consider the low SMBH masses.
TDEs with lower black hole masses spend more time in a near- to super-
Eddington state (Wu et al., 2018). Super-Eddington accretion disks have a
puffy structure, with significant unbound material, that may be conducive to
launching winds and/or aiding in collimating jets (Curd et al., 2023). Hence,
one might expect that radio emitting TDEs tend to occur when the SMBH mass is
lower because of the puffier accretion disk structure.

Of course, the wind and/or jet cannot necessarily be detected unless it shocks
against the circumnuclear material (CNM). Then, events with more material in
the vicinity of the SMBH will be more likely to produce detectable radio
emission. It is well established that AGN tend to have a significant CNM
relative to completely quiescent galaxies (Jiang et al., 2021), so a TDE in a
galaxy with a weak or retired AGN may be more likely to produce synchrotron-
emitting shocks. This would then explain the prevalence of galaxies with
strong nebular emission in our sample.

The faint and cool optical flares may also be explained by the enhanced
circumnuclear material, combined with the low black hole masses. Lower black
hole masses produce fainter optical flares (Mummery et al., 2023). Moreover,
the presence of enhanced circumnuclear material will tend to obscure emission
from the nucleus. Then, before correcting for this obscuration, any detected
optical flare will appear fainter and cooler. If we had higher quality optical
observations, it is plausible that we could constrain the amount of extinction
caused by the CNM, although this is not possible with the current data.
Another possible method of constraining increased CNM in radio-selected TDE
hosts is through MIR studies: we would have direct evidence for the presence
of enhanced circumnuclear dust if radio-selected TDEs are more likely than
optically-selected events to have a MIR flare, which in TDEs is associated
with thermally-emitting dust in the vicinity of the SMBH.

Thus, by invoking super-Eddington accretion around low mass SMBHs and enhanced
circumnuclear material, we can reconcile most of our observations. Future
samples of radio-selected TDEs with larger statistics and improved
multiwavelength coverage will be able to probe these possibilities.

###  8.2 The rate of radio-emitting, optically-bright TDEs

One of the key benefits of performing a untargeted search for optically- and
radio-detected TDEs is that we can set limits on the rate of such events.
Hence, we conclude our discussion by considering the rate of GHz-emitting,
optically-bright TDEs on ${\sim}3$ year timescales.

Because the GHz lightcurve evolution of TDEs is poorly understood, we cannot
robustly estimate the incompleteness of VLASS to radio-emitting, optically-
detected TDEs. Instead, we simply set an lower limit, which acknowledges that
fact that there may be some optically-detected, radio-bright TDEs that did not
make it into our sample because of, e.g., the cadence of sensitivity of VLASS.
Of the thirty-three ZTF TDEs presented in Yao et al. (2023), three are in our
sample. Hence, with $90\%$ confidence, $>3\%$ of optically-selected TDEs are
radio-emitting. The integrated volumetric TDE rate from Yao et al. (2023) is
$2.9^{+0.6}_{-1.3}\times 10^{-7}$ Mpc-3 yr-1, leading to a volumetric radio-
emitting, optically-bright TDE rate of $\gtrsim 10$ Gpc-3 yr-1.

We defer discussion of the luminosity function of radio-selected TDEs, as well
as predictions for future surveys, to future work on the full VLASS-selected
TDE sample.

##  9 Conclusions

We have presented the first sample of radio-selected TDEs. We selected six
radio transients in the VLASS with multiwavelength emission consistent with
TDEs; in particular, we require the detection of an optical counterpart. We
have compared the properties of these events to optically-selected TDE
samples. We tentatively suggest that radio-selected, optically-bright TDEs
occur at a higher rate in galaxies with low stellar/black hole masses. They
also tend to have cooler and fainter optical emission that optically-selected
TDEs. We compare to the results of radio follow-up campaigns of optical TDE
samples and find slightly larger energies and radii in our sample, as well as
earlier outflow launch times relative to the initial TDE. We constrain the
rate of radio-emitting, optically-bright TDEs to be $>3\%$ of the optical TDE
rate, or $\gtrsim 10$ Gpc-3 yr-1.

In future work, we will use VLASS to extend this sample to include those
events without multiwavelength counterparts. VLASS, of course, is limited by
the observation cadence: it will only be able to identify TDEs with radio
emission that lasts for ${\sim}3$ years. By combining VLASS with past radio
surveys like FIRST or NVSS, we can probe long timescales. Current and planned
radio surveys and instruments, including ASKAP (Hotan et al., 2021), the ngVLA
(Murphy et al., 2018) and the DSA 2000 (Hallinan et al., 2019), will probe
different timescales. The combined radio TDE samples from these surveys will
revolutionize our understanding of the landscape of TDE radio emission.

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. The Legacy Surveys consist of three individual and complementary
projects: the Dark Energy Camera Legacy Survey (DECaLS; Proposal ID
#2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky
Survey (BASS; NOAO Prop. ID #2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and
the Mayall z-band Legacy Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey).
DECaLS, BASS and MzLS together include data obtained, respectively, at the
Blanco telescope, Cerro Tololo Inter-American Observatory, NSF’s NOIRLab; the
Bok telescope, Steward Observatory, University of Arizona; and the Mayall
telescope, Kitt Peak National Observatory, NOIRLab. Pipeline processing and
analyses of the data were supported by NOIRLab and the Lawrence Berkeley
National Laboratory (LBNL). The Legacy Surveys project is honored to be
permitted to conduct astronomical research on Iolkam Du’ag (Kitt Peak), a
mountain with particular significance to the Tohono O’odham Nation. NOIRLab is
operated by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation. LBNL is
managed by the Regents of the University of California under contract to the
U.S. Department of Energy. This project used data obtained with the Dark
Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES)
collaboration. Funding for the DES Projects has been provided by the U.S.
Department of Energy, the U.S. National Science Foundation, the Ministry of
Science and Education of Spain, the Science and Technology Facilities Council
of the United Kingdom, the Higher Education Funding Council for England, the
National Center for Supercomputing Applications at the University of Illinois
at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the
University of Chicago, Center for Cosmology and Astro-Particle Physics at the
Ohio State University, the Mitchell Institute for Fundamental Physics and
Astronomy at Texas A&M University, Financiadora de Estudos e Projetos,
Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos,
Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro,
Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the
Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche
Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy
Survey. The Collaborating Institutions are Argonne National Laboratory, the
University of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH)
Zurich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the
Institut de Fisica d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig Maximilians Universitat Munchen and the associated Excellence
Cluster Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, the Ohio State University, the University of Pennsylvania, the
University of Portsmouth, SLAC National Accelerator Laboratory, Stanford
University, the University of Sussex, and Texas A&M University. BASS is a key
project of the Telescope Access Program (TAP), which has been funded by the
National Astronomical Observatories of China, the Chinese Academy of Sciences
(the Strategic Priority Research Program “The Emergence of Cosmological
Structures” Grant # XDB09000000), and the Special Fund for Astronomy from the
Ministry of Finance. The BASS is also supported by the External Cooperation
Program of Chinese Academy of Sciences (Grant # 114A11KYSB20160057), and
Chinese National Natural Science Foundation (Grant # 12120101003, # 11433005).
The Legacy Survey team makes use of data products from the Near-Earth Object
Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet
Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by
the National Aeronautics and Space Administration. The Legacy Surveys imaging
of the DESI footprint is supported by the Director, Office of Science, Office
of High Energy Physics of the U.S. Department of Energy under Contract No. DE-
AC02-05CH1123, by the National Energy Research Scientific Computing Center, a
DOE Office of Science User Facility under the same contract; and by the U.S.
National Science Foundation, Division of Astronomical Sciences under Contract
No. AST-0950945 to NOAO.

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##  Appendix A The multi-wavelength properties of VT J1356

Figure 11: Summary of the properties of VT J1356. The bottom left panel shows
a PANSTARRS image of the host galaxy before the flare. The top left panel
shows a Legacy survey (Dey et al., 2019) image of the host galaxy and
transient during the flare. The transient is visible as a blue nucleus in the
galaxy. The right panels summarize the transient emission associated with the
event. The top right panel shows the 3 GHz and 887.5 MHz radio lightcurves.
Example power law fits to the 3 GHz lightcurve are overlaid in black. The
middle right panel shows the ASASSN lightcurve of this source. The bottom
right panel shows the WISE infrared lightcurve of this source (Wright et al.,
2010).

In this appendix, we discuss the multiwavelength properties of VT J1356 in
detail because this source is not discussed in either of the companion papers.

###  A.1 Discovery and host galaxy

We first identified VT J1356 as a radio flare with an unusual MIR counterpart
in data from the WISE survey, shown in the right panel of Figure 11. The IR
flare showed a double peaked structure, with an initial, blue peak, and then a
secondary, long-lived, red flare. We obtained optical lightcurves from public,
high cadence optical surveys, including ZTF, ASASSN, and ATLAS, and found an
optical transient detected in ASASSN data ${\sim}8$ years before the VLASS
detection. This transient coincided with the first IR transient peak.

The host galaxy of this transient is shown in the left panel of Figure 11.
Note that this image was taken during the transient, so the bright nucleus is
the optical emission associated with the TDE. We obtained an optical spectrum
of the host galaxy, which is described in Section 3.4. The spectrum is that of
a star-forming galaxy. There are no obvious transient spectral features. There
is no optical spectrum available at times closer to the optical peak.

###  A.2 Optical and IR analysis

We analyzed the optical flare as described in Section 6. We fit the combined
optical-IR SED at the peak of the IR flare to a blackbody and found a
temperature ${\sim}10^{4}$ K (Figure 6), consistent with an optically-flaring
TDE. The shape of the optical flare is also consistent with TDE observations
(see Section 6).

The secondary IR peak is reminiscent of the “dust echoes” occasionally seen
from TDEs (van Velzen et al., 2021a). Dust echoes are produced by thermally
emitting dust in the vicinity of the SMBH, which is heated by UV emission from
the TDE. The temperature of the emission is generally ${\sim}1000$ K, i.e.,
close to but below the sublimation temperature of the dust. To test this
hypothesis and constrain the physical properties of the transient, we perform
a detailed analysis of this secondary IR flare. We began by fitting blackbody
models to each epoch of the secondary flare with $>3\sigma$ detections in both
the W1 and W2 bands.

If this flare is a dust echo, the luminosity and timescale of the IR flare is
set by the UV lightcurve and the geometry of the dust. Applying simple
assumptions, we can set constraints on the dust structure. The secondary IR
flare from VT J1356 rose to a peak ${\sim}1200$ days post-optical peak.
Assuming the UV flare traces the optical flare and that the dust is in a
spherical or torus-like geometry with radius $R_{\rm dust}$, this then
constrains $R_{\rm dust}$: the rise time $t_{\rm IR,rise}$ is given by $t_{\rm
IR,rise}\sim 2R_{\rm dust}/c$. Then, we have $R_{\rm dust}\sim 0.5$ pc, which
is comparable to values found for similar sources (e.g. Somalwar et al.,
2021).

###  A.3 Radio and X-ray observations and analysis

We searched for archival X-ray flares using the ESA high energy lightcurve
tool. We obtained X-ray follow-up of this source ${\sim}3000$ days post-peak
using the Swift/XRT telescope. We reduced the observations using the online
Swift/XRT data analysis tool. No emission was detected ($L_{X}\lesssim 6\times
10^{41}$ erg s-1).

In addition to the VLASS observations of this source, we crossmatched against
the Rapid ASKAP Continuum Survey (RACS) catalog (Hale et al., 2021). The
source was detected on MJD 58600 with a 887.5 MHz flux density of $3.5\pm 0.9$
mJy. We also obtained a follow-up radio SED, as described in Section 3.1. We
fit it to a synchrotron emission model as described in Appendix C.

We begin by discussing the radio lightcurve. We combined the VLASS, RACS, and
follow-up data to construct 887.5 MHz and 3 GHz radio lightcurves, as shown in
the top left panel of Figure 11.

###  A.4 The origin of VT J1356

In this section, we constrain the origin of VT J1356: is it in fact a TDE? We
consider three plausible origins to explain these observations: (1) an AGN
flare, (2) a supernova (SN), or (3) a TDE. While exotic models may be able to
replicate the data, constraining them is beyond the scope of this work.

We immediately exclude the possibility that we are observing an AGN flare. HG
J1356 shows no evidence for AGN activity, either in the form of AGN-like
infrared colors nor strong forbidden line emission. If we are observing an AGN
flare, it is from an extraordinarily weak AGN, so we consider this scenario
unlikely.

Next, we consider a supernova origin. HG J1356 is an actively star forming
galaxy, so this possibility is more feasible. Our main evidence against a SN
origin comes from the MIR emission. Yang et al. (2019) analyzed NEOWISE
lightcurves (Mainzer et al., 2014) for 2812 SNe from the Open Catalogue of
Supernovae (Guillochon & Ramirez-Ruiz, 2015) and found that (1) the MIR
variability typically occured on a ${\sim}6$ month timescale and (2) SNe MIR
lightcurves tend to show a bluer-when-brighter behavior. Our source is
variable on many year timescales, and the MIR color becomes redder when the
flare is more luminous. As in the AGN flare case, if this event is an SN, it
is a very unusual example of such, so we do not prefer this possibility.

We are left with a TDE origin for VT J1356. The optical flare, IR flare, and
energetics are consistent with a TDE.

##  Appendix B Optical spectrum fitting methods

We fit the stellar continua of the spectra using the ppxf code (Cappellari &
Emsellem, 2004; Cappellari, 2017) with the MILES templates (Vazdekis et al.,
2010) following the method detailed in Appendix B of Somalwar et al. (2021).
The best fit stellar continua are overlaid on Figure 1. We then subtracted the
stellar continuum from each spectrum and fit the individual emission lines to
measure the fluxes. We jointly model lines that are closer together than a few
times the instrument resolution to ensure reliable fits, such as the [N
II]+H$\alpha$ complex. We assumed each line could be modelled by a Gaussian.
We allowed the amplitude, width, and centroid of each line to float, although
when simultaneously modelling multiple lines, we assumed the widths were the
same for every line. We included a linear component to account for any
residual continuum. For each line or line complex, we ran emcee for $2000$
steps with $200$ walkers and discarded the first $1000$ steps as burn-in.

##  Appendix C Synchrotron analysis methodology

We consider an electron in a homogeneous region at redshift $z$ and luminosity
distance $d_{L}$. The rest-frame frequency $\nu$ is related to the observed
frequency as $\nu=(1+z)\nu_{\rm obs}$. We will perform most calculations using
rest-frame frequency, and transform to observer frequency before comparing to
observations. The magnetic field is given by $B$. Consider a single electron
with Lorentz factor (LF) $\gamma$. The pitch angle, or the angle between the
electron’s velocity and the magnetic field, is $\theta$. The rest-frame
synchrotron frequency is

$\nu_{s}=\frac{eB\gamma^{2}}{2\pi mc}.$ (C1)

The synchrotron power for a single electron at rest-frame frequency $\nu$ is
given by

$P_{s}(\nu\mid
B,\gamma,\theta)=\frac{\sqrt{3}e^{2}B\sin\theta}{m_{e}c^{2}}F(\nu/\nu_{c}),\nu_{c}=\frac{3}{2}\nu_{s}\sin\theta.$
(C2)

The function $F(\nu/\nu_{c})$ encapsulates the frequency dependence of the
spectrum. It is defined as

$F(x)=x\int_{x}^{\infty}K_{5/3}(y)dy.$ (C3)

$K_{5/3}(y)$ is the modified Bessel function of order $5/3$.

At low and high frequencies, $F(x)$ is well approximated by

$\displaystyle F(x)\longrightarrow
F_{1}(x)=\frac{4\pi}{\sqrt{3}\Gamma(1/3)}\bigg{(}\frac{x}{2}\bigg{)}^{1/3},x\rightarrow
0;$ (C4) $\displaystyle F(x)\rightarrow
F_{2}(x)=\sqrt{\frac{\pi}{2}}x^{1/2}e^{-x},x\rightarrow\infty.$ (C5)

Here, $\Gamma$ is the Gamma function, rather than bulk Lorentz factor. For all
equations hereafter, an expression of the form $\Gamma(x)$ refers to the Gamma
function, an expression of the form $\Gamma(s,x)$ refers to the upper
incomplete Gamma function, and the character $\Gamma$ with no argument refers
to the bulk Lorentz factor. For $x\leq 10^{-5}$ and $x\geq 10^{3}$, these
formulae give relative errors $<0.1\%$. For the regime $10^{-5}<x<10^{3}$,
$F(x)$ is well approximated (relative error $<0.8\%$) as

$\displaystyle F(x)\approx
F^{(1)}(x)=F_{1}(x)\frac{\sum_{i=0}^{14}n_{1i}e^{-\alpha_{1i}x}}{\sum_{i=0}^{14}n_{1i}}+F_{2}(x)\bigg{(}1-\frac{\sum_{i=0}^{14}n_{2i}e^{-\alpha_{2i}x}}{\sum_{i=0}^{14}n_{1i}}\bigg{)}$
(C6)

Note that the factor $\sum_{i=0}^{14}n_{1i}$ is the denominator of the final
term is not a typo. Because we use the sum over $n_{1i}$ in the denominator,
$F^{(1)}(x)$ does not approach $F(x)$ exactly as $x$ goes to infinity.
However, as we will show, the difference does not affect our results: for all
upcoming calculations, this error will prove insignificant.

The single electron synchrotron spectrum, Equation C2, is only valid when the
emitting energy during a single orbit is smaller than the energy of the
particle, in which regime quantum effects are negligible. The condition
corresponds to

$B<\frac{e/\sigma_{\rm T}}{\gamma^{2}\sin^{2}\theta}\sim\frac{7.22\times
10^{14}}{\gamma^{2}\sin^{2}\theta}\,{\rm G},$ (C7)

where $\sigma_{\rm T}$ is the Thomson cross section.

To compute the synchrotron spectrum for a population of electrons, we must
assume an electron energy distribution. We adopt the standard assumption that
the electron lorentz factors are drawn from a cut-off power-law with index
$-p$

$\displaystyle N(\gamma)d\gamma=N_{0}\gamma^{-p}d\gamma\,\,(\gamma_{\rm
min}<\gamma<\gamma_{\rm max})$ (C8) $\displaystyle=N_{\rm
tot}\frac{1-p}{\gamma_{\rm max}^{1-p}-\gamma_{\rm
min}^{1-p}}\gamma^{-p}d\gamma\,\,(\gamma_{\rm min}<\gamma<\gamma_{\rm max})$
(C9) $\displaystyle=E_{\rm e}\frac{2-p}{\gamma_{\rm max}^{2-p}-\gamma_{\rm
min}^{2-p}}\gamma^{-p}d\gamma\,\,(\gamma_{\rm min}<\gamma<\gamma_{\rm max}).$
(C10)

$\gamma_{\rm min(max)}$ is the minimum (maximum) electron Lorentz factor. A
common assumption is $\gamma_{\rm max}=\infty$. Throughout the rest of this
work, we assume $\gamma_{\rm max}=10^{9}$, which is roughly equivalent to
$\gamma_{\rm max}=\infty$, although all derivations are generalized to
arbitrary $\gamma_{\rm max}$. $N_{0}$ is the normalization of the electron
distribution, and is related to both the total number of electrons $N_{\rm
tot}=\int_{\gamma_{\rm min}}^{\gamma_{\rm max}}N(\gamma)d\gamma$ and the total
energy stored in the electrons $E_{e}=\int_{\gamma_{\rm min}}^{\gamma_{\rm
max}}\gamma m_{e}c^{2}N(\gamma)d\gamma$.

Using this energy distribution, the synchrotron emissivity (cgs units erg s-1
cm-3 sterad-1) is given by

$\displaystyle\epsilon_{s}(\nu)=\frac{1}{4\pi}\int_{\gamma_{\rm
min}}^{\gamma_{\rm max}}d\gamma N(\gamma)P(\nu\mid B,\gamma,\theta)$ (C11)
$\displaystyle=\frac{\sqrt{3}}{8\pi}\frac{e^{3}N_{0}B\sin\theta}{m_{e}c^{2}}\bigg{(}\frac{\nu}{\nu_{0}}\bigg{)}^{\frac{1-p}{2}}\int_{x_{\rm
max}}^{x_{\rm min}}x^{(3-p)/2}F(x)dx.$ (C12)

Here, we have defined the variable $\nu_{0}=\frac{3eB\sin\theta\Gamma}{4\pi
m_{e}c(1+z)}$, so that $\nu_{c}=\gamma^{2}\nu_{0}$. We have also defined
$x_{\rm min}=\nu/(\nu_{0}\gamma_{\rm min}^{2})$ and $x_{\rm
max}=\nu/(\nu_{0}\gamma_{\rm max}^{2})$; note that, despite the subscripts,
$x_{\rm min}>x_{\rm max}$. In the limit $x_{\rm min}\rightarrow\infty$ and
$x_{\rm max}\rightarrow 0$, we find the expected frequency dependence
$\epsilon_{s}(\nu)\propto(\nu/\nu_{0})^{(1-p)/2}$.

The approximation for $F(x)$ described above allows this integral to be
analytically evaluated. We find

$\displaystyle\epsilon^{(2)}_{s}(\nu)=\frac{\sqrt{3}}{8\pi}\frac{e^{3}N_{0}B\sin\theta}{m_{e}c^{2}}\bigg{(}\frac{\nu}{\nu_{0}}\bigg{)}^{\frac{1-p}{2}}\Bigg{\\{}F_{1}\frac{\sum_{i=0}^{14}n_{1i}\alpha_{1i}^{-z_{1}}\big{(}\Gamma(z_{1},\alpha_{1i}x_{\rm
min})-\Gamma(z_{1},\alpha_{1i}x_{\rm max})\big{)}}{\sum_{i=0}^{14}n_{1i}}+$
$\displaystyle F_{2}\bigg{[}\big{(}\Gamma(z_{2},x_{\rm
min})-\Gamma(z_{2},x_{\rm
max})\big{)}-\frac{\sum_{i=0}^{14}n_{2i}(\alpha_{2i}+1)^{-z_{2}}\big{(}\Gamma(z_{2},(\alpha_{2i}+1)x_{\rm
min})-\Gamma(z_{2},(\alpha_{2i}+1)x_{\rm
max})\big{)}}{\sum_{i=0}^{14}n_{1i}}\bigg{]}\Bigg{\\}};$ (C13) $\displaystyle
z_{1}=\frac{3-p}{2}+\frac{1}{3}+1,z_{2}=\frac{3-p}{2}+\frac{1}{2}+1.$

The relative error of this expression is $<0.1\%$ across the full parameter
range.

With these expressions for the emissivity, we can readily calculate the
synchrotron spectrum for any optically thin emission region. In many cases,
however, we must consider absorption processes. First, we consider synchrotron
self-absorption. The synchrotron self-absorption coefficient is given by

$\displaystyle\alpha_{\nu}=\frac{1}{8\pi m_{e}\nu^{2}}\int_{\gamma_{\rm
min}}^{\gamma_{\rm max}}d\gamma
P_{s}(\nu)\gamma^{2}\frac{\partial}{\partial\gamma}\bigg{[}\frac{N(\gamma)}{\gamma^{2}}\bigg{]}=\frac{1}{8\pi
m_{e}\nu^{2}}\int_{\gamma_{\rm min}}^{\gamma_{\rm
max}}d\gamma\frac{N(\gamma)}{\gamma^{2}}\frac{\partial}{\partial\gamma}\bigg{[}\gamma^{2}P_{s}(\nu,\theta)\bigg{]},$
(C14)

where the second expression uses the fact that $N(\gamma_{\rm
min})=N(\gamma_{\rm max})=0$, and is particularly relevant in cases where the
derivative of $N(\gamma)$ is not well-defined. Using our power-law expression
for $N(\gamma)$, we find

$\displaystyle\alpha_{\nu}=\frac{(p+2)\sqrt{3}e^{3}N_{0}B\sin\theta}{16\pi\nu^{2}m_{e}^{2}c^{2}}\bigg{(}\frac{\nu}{\nu_{0}}\bigg{)}^{-\frac{p}{2}}\int_{x_{\rm
min}}^{x_{\rm max}}dx\,x^{p/2-1}F(x)$ (C15)

In the limit $x_{\rm min}\rightarrow\infty$ and $x_{\rm max}\rightarrow 0$, we
find $\alpha_{\nu}\propto\nu^{-(p+4)/2}$, as expected.

As before, we can analytically evaluate this expression using our
approximations. Evaluating for $F^{(1)}(x)$, we find

$\displaystyle\alpha^{(1)}_{\nu}=\frac{(p+2)\sqrt{3}e^{3}N_{0}B\sin\theta}{16\pi\nu^{2}m_{e}^{2}c^{2}}\bigg{(}\frac{\nu}{\nu_{0}}\bigg{)}^{-\frac{p}{2}}\Bigg{\\{}F_{1}\frac{\sum_{i=0}^{14}n_{1i}\alpha_{1i}^{-z_{1}}\big{(}\Gamma(z_{1},\alpha_{1i}x_{\rm
min})-\Gamma(z_{1},\alpha_{1i}x_{\rm max})\big{)}}{\sum_{i=0}^{14}n_{1i}}+$
$\displaystyle F_{2}\bigg{[}\big{(}\Gamma(z_{2},x_{\rm
min})-\Gamma(z_{2},x_{\rm
max})\big{)}-\frac{\sum_{i=0}^{14}n_{2i}(\alpha_{2i}+1)^{-z_{2}}\big{(}\Gamma(z_{2},(\alpha_{2i}+1)x_{\rm
min})-\Gamma(z_{2},(\alpha_{2i}+1)x_{\rm
max})\big{)}}{\sum_{i=0}^{14}n_{1i}}\bigg{]}\Bigg{\\}};$ (C16) $\displaystyle
z_{3}=\frac{2-p}{2}+\frac{1}{3}+1,z_{4}=\frac{2-p}{2}+\frac{1}{2}+1.$

The relative error in this expression is $<0.1\%$ across the full parameter
space.

We are now in a position to solve the radiative transfer equation to calculate
the observed spectrum for an arbitrary source. For reference, we restate the
radiative transfer equation here:

$\frac{dI_{\nu}}{ds}=\alpha_{\nu}I_{\nu}+\epsilon_{s}.$ (C17)

Here, $I_{\nu}$ is the specific intensity [erg cm-2 s-1 Hz-1 sterad-1] and $s$
is the path length. $\alpha_{\nu}$ and $\epsilon_{s}$ are still, respectively,
the absorption coefficient [cm-1] and emissivity [erg cm-3 s-1 sterad-1]. For
a sphere with radius $R$ ($A=\pi R^{2}$, $s=2R$), the flux density is given by

$F_{\nu,{\rm
sphere}}=\frac{f_{A}A}{d_{L}^{2}}\frac{\epsilon_{s}(\nu)}{\alpha_{\nu}(\nu)}\Bigg{[}1-\frac{2}{\tau_{\nu}^{2}}\bigg{(}1-(1+\tau_{\nu})e^{-\tau_{\nu}}\bigg{)}\Bigg{]};\,\,\,\tau_{\rm
sa}(\nu)=s\alpha_{\nu}(\nu).$ (C18)

We adopt this approximation for the synchrotron SED for all the analysis in
this work.

Table 5: TDEs with published radio SEDs

Name | $t_{\rm obs}-t_{\rm opt.peak}$ | $\log R/{\rm cm}$ | $\log B/{\rm G}$ | $\log N_{0}/{\rm cm^{-3}}$ | $p$ | $\beta$ | $\log E$ | $\log M_{\rm ej}/M_{\odot}$ | SED Source
---|---|---|---|---|---|---|---|---|---
VT J0813 | 17 | $18.2_{-0.9}^{+0.8}$ | $-2.0_{-0.7}^{+0.8}$ | $-2_{-1}^{+1}$ | $1.69_{-0.05}^{+0.06}$ | $-0.03_{-0.16}^{+0.03}$ | $50.4_{-1.0}^{+1.0}$ | $-3.5_{-1.0}^{+1.0}$ |
| 45 | $17.2_{-0.7}^{+1.2}$ | $-1.4_{-1.0}^{+0.6}$ | $1_{-2}^{+2}$ | $2.08_{-0.08}^{+0.13}$ | $-0.4_{-0.5}^{+0.3}$ | $48.4_{-1.0}^{+1.6}$ | $-5.5_{-1.0}^{+1.6}$ |
| 53 | $17.7_{-0.8}^{+0.9}$ | $-1.8_{-0.8}^{+0.6}$ | $0_{-2}^{+1}$ | $2.06_{-0.10}^{+0.11}$ | $-0.2_{-0.4}^{+0.1}$ | $49_{-1}^{+1}$ | $-5_{-1}^{+1}$ |
| 83 | $18.1_{-0.6}^{+0.7}$ | $-2.2_{-0.6}^{+0.5}$ | $-0_{-1}^{+1}$ | $2.20_{-0.03}^{+0.03}$ | $-0.09_{-0.22}^{+0.07}$ | $49.6_{-0.8}^{+0.9}$ | $-4.3_{-0.8}^{+0.9}$ |
| 134 | $17.05_{-0.01}^{+0.01}$ | $-1.17_{-0.02}^{+0.02}$ | $2.35_{-0.06}^{+0.06}$ | $2.55_{-0.03}^{+0.03}$ | $-0.68_{-0.01}^{+0.01}$ | $48.49_{-0.02}^{+0.03}$ | $-5.46_{-0.02}^{+0.03}$ |
| 205 | $17.169_{-0.006}^{+0.007}$ | $-1.15_{-0.01}^{+0.01}$ | $2.56_{-0.04}^{+0.03}$ | $2.81_{-0.03}^{+0.02}$ | $-0.712_{-0.005}^{+0.006}$ | $48.88_{-0.02}^{+0.02}$ | $-5.07_{-0.02}^{+0.02}$ |
| 247 | $17.2_{-0.2}^{+1.4}$ | $-1.3_{-1.1}^{+0.3}$ | $2.2_{-2.3}^{+0.6}$ | $2.57_{-0.09}^{+0.16}$ | $-0.7_{-0.2}^{+0.7}$ | $48.8_{-0.2}^{+1.9}$ | $-5.1_{-0.2}^{+1.9}$ |
| 302 | $17.00_{-0.05}^{+0.11}$ | $-1.10_{-0.11}^{+0.06}$ | $2.3_{-0.3}^{+0.2}$ | $2.38_{-0.10}^{+0.08}$ | $-0.98_{-0.04}^{+0.10}$ | $48.48_{-0.04}^{+0.10}$ | $-5.47_{-0.04}^{+0.10}$ |
| 410 | $17.25_{-0.01}^{+0.02}$ | $-0.86_{-0.02}^{+0.02}$ | $3.42_{-0.05}^{+0.05}$ | $3.51_{-0.03}^{+0.03}$ | $-0.86_{-0.01}^{+0.01}$ | $49.73_{-0.02}^{+0.02}$ | $-4.23_{-0.02}^{+0.02}$ |
| 618 | $17.341_{-0.005}^{+0.005}$ | $-1.237_{-0.008}^{+0.008}$ | $2.29_{-0.02}^{+0.02}$ | $2.65_{-0.01}^{+0.01}$ | $-0.933_{-0.005}^{+0.005}$ | $49.221_{-0.008}^{+0.008}$ | $-4.730_{-0.008}^{+0.008}$ |
| 701 | $17.43_{-0.01}^{+0.01}$ | $-1.11_{-0.02}^{+0.01}$ | $2.80_{-0.04}^{+0.03}$ | $3.19_{-0.02}^{+0.02}$ | $-0.90_{-0.01}^{+0.01}$ | $49.74_{-0.01}^{+0.01}$ | $-4.21_{-0.01}^{+0.01}$ |
| 800 | $17.23_{-0.02}^{+0.02}$ | $-1.15_{-0.04}^{+0.04}$ | $2.6_{-0.1}^{+0.1}$ | $2.85_{-0.06}^{+0.07}$ | $-1.13_{-0.02}^{+0.02}$ | $49.08_{-0.04}^{+0.05}$ | $-4.87_{-0.04}^{+0.05}$ |
VT J1008 | 507 | $17.06_{-0.01}^{+0.01}$ | $-0.73_{-0.04}^{+0.05}$ | $3.5_{-0.1}^{+0.2}$ | $3.0_{-0.1}^{+0.1}$ | $-1.37_{-0.01}^{+0.01}$ | $49.4_{-0.1}^{+0.1}$ | $-4.5_{-0.1}^{+0.1}$ |
VT J1356 | 2581 | $17.40_{-0.04}^{+0.04}$ | $-1.12_{-0.03}^{+0.03}$ | $0.2_{-0.2}^{+0.2}$ | $1.80_{-0.04}^{+0.04}$ | $-1.73_{-0.04}^{+0.04}$ | $49.7_{-0.1}^{+0.1}$ | $-4.3_{-0.1}^{+0.1}$ |
VT J1752 | 756 | $17.814_{-0.004}^{+0.003}$ | $0.629_{-0.013}^{+0.007}$ | $-2.75_{-0.02}^{+0.03}$ | $1.004_{-0.003}^{+0.007}$ | $-0.819_{-0.003}^{+0.003}$ | $54.38_{-0.04}^{+0.02}$ | $0.43_{-0.04}^{+0.02}$ |
| 1115 | $17.99_{-0.02}^{+0.02}$ | $-0.87_{-0.05}^{+0.05}$ | $-0.5_{-0.2}^{+0.2}$ | $1.64_{-0.04}^{+0.04}$ | $-0.75_{-0.02}^{+0.02}$ | $51.9_{-0.1}^{+0.1}$ | $-2.0_{-0.1}^{+0.1}$ |
VT J2012 | 469 | $17.225_{-0.006}^{+0.006}$ | $-0.83_{-0.02}^{+0.02}$ | $3.27_{-0.08}^{+0.08}$ | $2.95_{-0.06}^{+0.07}$ | $-1.178_{-0.006}^{+0.006}$ | $49.69_{-0.05}^{+0.05}$ | $-4.26_{-0.05}^{+0.05}$ |
VT J2030 | 675 | $17.44_{-0.01}^{+0.01}$ | $-0.94_{-0.02}^{+0.02}$ | $3.09_{-0.06}^{+0.06}$ | $3.03_{-0.04}^{+0.04}$ | $-1.122_{-0.010}^{+0.011}$ | $50.11_{-0.03}^{+0.03}$ | $-3.84_{-0.03}^{+0.03}$ |
| 934 | $17.622_{-0.009}^{+0.009}$ | $-1.02_{-0.02}^{+0.02}$ | $3.04_{-0.04}^{+0.04}$ | $3.31_{-0.03}^{+0.03}$ | $-1.021_{-0.008}^{+0.008}$ | $50.51_{-0.03}^{+0.03}$ | $-3.44_{-0.03}^{+0.03}$ |
| 1051 | $17.51_{-0.01}^{+0.01}$ | $-1.05_{-0.03}^{+0.03}$ | $2.89_{-0.07}^{+0.08}$ | $3.07_{-0.06}^{+0.06}$ | $-1.15_{-0.01}^{+0.01}$ | $50.11_{-0.04}^{+0.04}$ | $-3.84_{-0.04}^{+0.04}$ |

Note. — The physical parameters of the radio emission regions for our TDE
candidates.