# Lightcurve Evolution of the nearest Tidal Disruption Event: A late-time,
radio-only flare

Eric S. Perlman  Department of Physics and Space Sciences, Florida Institute
of Technology, 150 W. University Blvd., Melbourne, FL 32901, USA  Eileen T.
Meyer  Department of Physics, University of Maryland – Baltimore County, 1000
Hilltop Circle, Baltimore, MD 21250, USA  Q. Daniel Wang  Department of
Astronomy, University of Massachusetts, LGRT-B 619E, 710 North Pleasant
Street, Amherst, MA 01003-9305, USA  Qiang Yuan  Key Laboratory of Dark Matter
and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
10 Yuanhua Road, Nanjing 210023, China  School of Astronomy and Space Science,
University of Science and Technology of China, Hefei 230026, China  Richard
Henriksen, Judith Irwin  Department of Physics, Engineering Physics &
Astronomy, Queens University, Kingston, Ontario, K7L 3N6, Canada  Jiangtao Li
Department of Astronomy, University of Michigan, 311 West Hall, 1085 South
University Avenue, Ann Arbor, Michigan, 48109, USA  Theresa Wiegert
Department of Physics, Engineering Physics & Astronomy, Queens University,
Kingston, Ontario, K7L 3N6, Canada  Haochuan Li  Department of Physics,
Engineering Physics & Astronomy, Queens University, Kingston, Ontario, K7L
3N6, Canada  Yang Yang  School of Astronomy and Space Science, Nanjing
University, Nanjing 210093, China

###### Abstract

Tidal disruption events (TDEs) occur when a star passes close enough to a
galaxy’s supermassive black hole to be disrupted by tidal forces. We discuss
new observations of IGRJ12580+0134, a TDE observed in NGC 4845 ($d=17$ Mpc) in
November 2010, with the Karl G. Jansky Very Large Array (VLA111The National
Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.).We also
discuss a reanalysis of 2010-2011 Swift and XMM-Newton observations, as well
as new, late-time Swift observations. Our JVLA observations show a decay of
the nuclear radio flux until 2015, when a plateau was seen, and then a
significant ($\sim$factor 3) radio flare during 2016. The 2016 radio flare was
also accompanied by radio spectral changes, but was not seen in the X-rays. We
model the flare as resulting from the interaction of the nuclear jet with a
cloud in the interstellar medium. This is distinct from late-time X-ray flares
in a few other TDEs where changes in the accretion state and/or a fallback
event were suggested, neither of which appears possible in this case. Our
reanalysis of the Swift and XMM-Newton data from 2011 shows significant
evidence for thermal emission from a disk, as well as a very soft power-law.
This, in addition to the extreme X-ray flux increase seen in 2010 (a factor of
$>$100) bolsters the identification of IGRJ12580+0134 as a TDE, not an unusual
AGN variability event.

galaxies: active; galaxies: individual (NGC 4845); galaxies: nuclei; radio
continuum: galaxies

††software: CASA (v5.6.2-3; McMullin et al. 2007), SAS (Gabriel et al. 2021),
Sherpa Freeman, Doe & Siemiginowka (2001); Doe, Nguyen & Stawarz (2007)

##  1 Introduction

Tidal disruption events (TDEs) are expected to occur every $10^{3}-10^{5}$
years for a typical galaxy (Magorrian & Tremaine, 1999; Wang & Merritt, 2004;
Van Velzen & Farrar, 2014; Holoien et al., 2016). They occur when a star or
sub-stellar object passes close enough by the galaxy’s central supermassive
black hole (SMBH) to be tidally disrupted. The debris of the disrupted object
gets accreted onto the black hole, producing flaring emission at X-ray,
ultraviolet, and optical wavelengths. Jets can also be launched by the SMBH
after a TDE. When they interact with the circum-nuclear medium (CNM) high
energy particle acceleration could occur. Sw J1644+57 ($z=0.3534$; Bloom et
al., 2011; Burrows et al., 2011; Levan et al., 2011; Zauderer et al., 2011,
2013) and Sw J2058+05 ($z=1.1853$; Cenko et al., 2012) are examples of TDEs
that have associated jets, exhibiting super-Eddington X-ray emission and a
long lasting radio emission expected to arise from the jet-CNM interaction.
Detailed modeling of both Sw J1644+57 and Sw J2058+05 suggests that the jets
were strongly relativistically beamed. A recent review by Alexander et al.
(2020) discusses the history of radio-loud TDE to date. It is natural to
expect that there should be more events with off-axis jets, even though
detection of these would be less likely, with statistics similar to the
detection of off-axis blazars in a high flux limit survey (e.g., Urry &
Shafer, 1984).

IGR J12580+0134 is a TDE that occurred in 2010 in the nucleus of NGC 4845 – a
galaxy located in the Virgo cluster. Its distance of just $\sim 17$ Mpc, gave
us a rare chance to scrutinize a TDE and its aftermath with the highest
possible resolution. The source was initially detected in 2010 November by
Integral (Walter et al., 2011). Follow-up X-ray observations with XMM-Newton,
Swift and MAXI, together with Integral data, suggest that the source probably
resulted from a tidal disruption of a super-Jupiter by the galaxy’s central
SMBH (i.e., a sub-stellar TDE; Nikolajuk & Walter, 2013). The source is
underluminous compared to many TDEs (sub-Eddington as compared to super-
Eddington). The radio counterpart of the TDE was detected serendipitously in
2011 December by the VLA in a nearby galaxy survey (CHANG-ES; Irwin et al.,
2015) where the core was a factor of more than 10 brighter than seen in FIRST
observations conducted between 1993-2004. A search of archival Planck data
showed bright flaring emissions in January 2011 in the millimeter wavelengths
(Yuan et al., 2016).

The radio spectrum, peaking at GHz frequencies, and its evolution through 2015
suggest self-absorbed synchrotron emission with changing optical thickness.
VLBA and VLA observations of IGRJ1258+0134 in 2015 detected both a bright core
on arcsecond scales and resolved, milliarcsecond-scale emission (Perlman et
al., 2017). The resolved milli-arcsecond core emission was believed to be due
to the expansion of the radio jet. A model for the radio jet (Irwin et al.,
2015; Perlman et al., 2017) shows the data to be consistent with an initial
Lorentz factor $\Gamma_{i}\sim 10$ and a viewing angle of $40^{\circ}$ (Lei et
al., 2016).

Here we discuss new observations of IGRJ1258+0134 obtained with the VLA, the
Neil Gehrels Swift X-ray Telescope and XMM-Newton. The 2015-2016 VLA data
(Table 1) shows a flare in the radio that is not accompanied by a similar
increase in the X-ray light curve. A reanalysis of archival data from Swift
and XMM-Newton reveals significant evidence for thermal emission from a disk
for a TDE.

This paper is laid out as follows. In §2 we discuss our observations and data
reduction procedures. In §3 we discuss the results, while in §4 we present a
discussion of the overall implications of these findings.

##  2 Observations and Data Reduction

Table 1: VLA Observations

Datea |  Projectb |  $\Delta$ Tc |  Configd |  Freqe (Band) |  $\Delta$ Bf |  Beamg |  RMSh |  Nuclear Fluxi |  |
---|---|---|---|---|---|---|---|---|---|---
|  | (days) |  | (GHz) | (MHz) |  ($\prime\prime$, $\prime\prime$, $\circ$) | (mJy/beam) | Density (mJy) |  |
1995-Feb-27 |  NVSSj | -6150 | D | 1.4 (L) | 50 | 45, 45, 0 | 0.45 |  26$\,\pm\,4$ |  |
1998-Jul-26 |  AB0879k | -4905 | B | 1.4 (L) | 100 | 5.1, 4.2, 24.0 | 1.0 |  34$\pm\,2$ |  |
2011-Dec-19 |  10C-119l |  $-$11 | D | 6.0 (C) | 2048 | 11.0, 9.1, -1.4 | 0.015 |  425$\,\pm\,3$ |  |
2011-Dec-30 (T1) |  10C-119l | 0 | D | 1.6 (L) | 500 | 38.6, 34.3, -5.22 | 0.040 |  211$\,\pm\,3$ |  |
2012-Feb-24 |  10C-119l | 56 | C | 6.0 (C) | 2048 | 3.1, 2.8, -11.7 | 0.0039 |  355$\,\pm\,2$ |  |
2012-Mar-30 |  10C-119l | 91 | C | 1.6 (L) | 500 | 12.2, 11.1, -41.8 | 0.045 |  241$\,\pm\,3$ |  |
2012-Jun-11 |  10C-119l | 164 | B | 1.6 (L) | 500 | 3.5, 3.3, 22.7 | 0.018 |  219$\,\pm\,4$ |  |
2015-Jun-22 |  15A-357m | 1270 | A | 1.5 (L) | 1000 | 1.73, 1.06, 43.2 | 0.12 |  115$\,\pm$2 |  |
2015-Jun-22 |  15A-357m | 1270 | A | 5.5 (C) | 1000 | 0.47, 0.33, 46.2 | 0.013 |  36.3$\,\pm\,0.3$ |  |
2015-Jul-06 |  15A-400n | 1284 | A | 9 (X) | 2048 | 0.21, 0.2, 20 | 0.010 | $22.7\pm 0.3$ |  |
2015-Jul-14 |  15A-400n | 1292 | A | 9 (X) | 2048 | 0.27, 0.16, 43 | 0.020 | $17.1\pm 0.2$ |  |
2015-Jul-28 |  15A-400n | 1306 | A | 6 (C) | 2048 | 0.37, 0.28, 48.5 | 0.015 | $33.6\pm 0.2$ |  |
2016-Mar-16 |  16A-420o | 1538 | C | 6.0 (C) | 2048 | 3.5, 3.0, -52.5 | 0.012 |  27$\,\pm\,2$ |  |
2016-Mar-16 |  16A-420o | 1538 | C | 3.0 (S) | 2048 | 6.4, 5.2, -18.4 | 0.032 | $60\,\pm\,3$ |  |
2016-Mar-16 |  16A-420o | 1538 | C | 1.5 (L) | 1024 | 12.9, 9.9, -21.0 | 0.48 |  171$\,\pm\,5$ |  |
2016-May-21 |  16A-420o | 1604 | B | 6.0 (C) | 2048 | 0.98, 0.86, -23.5 | 0.034 | $61\,\pm\,2$ |  |
2016-May-21 |  16A-420o | 1604 | B | 3.0 (S) | 2048 | 1.8, 1.7, -20.0 | 0.058 | $167\,\pm\,2$ |  |
2016-May-21 |  16A-420o | 1604 | B | 1.5 (L) | 1024 | 3.6, 3.1, -20.7 | 0.50 |  261$\,\pm\,5$ |  |
2019-Apr-21 |  VLASSp | 2669 | B | 3.0 (S) | 2048 | 2.9, 2.1, 31.1 | 0.169 |  21$\,\pm\,2$ |  |
2019-Jun-24 |  19A-425q | 2733 | B | 1.5 (L) | 64 | 4.9, 3.3, -13.8 | 0.170 |  50$\,\pm\,5$ |  |

a Date of observation.
b Project name or code.
c Elapsed time since T1 = Dec 30, 2011.
d VLA array configuration.
e Central frequency of the band followed by the name of the band in
parentheses.
f Total bandwidth.
g Synthesized beam major axis, minor axis, and position angle.
h Measured rms map noise (primary beam corrected, near source).
i Flux of nucleus after correction for surrounding disk emission for low
resolution images (see text) or directly from Gaussian fitting for high
resolution data.
j Downloaded and measured from the NRAO VLA Sky Survey (NVSS) (Condon et al.,
1998).
kThis work. Imaged from the VLA archive.
l Irwin et al. (2015).
m Data from Perlman et al. (2017).
n This work.
o This work. At S-band, the correction for disk emission has been interpolated
between known C-band and L-band values.
p This work. Measured from VLASS (VLA Sky Survey) data (VLASS; Lacy et al.,
2019), downloaded from http://cutouts.cirada.ca/ on April 1, 2021.
q This work. Imaged from VLA archive. The uncertainty includes a primary beam
error of 5% for this source (Bhatnagar et al., 2013), which is 18.2 arcmin
from the field center.

###  2.1 VLA Observations

We present a number of VLA observations of NGC 4845 (Table 1), collected here
for the first time. Some are new data that we have obtained, some are re-
imaged from previous data in the VLA archive, and some are reduced images from
previous surveys. Together with previously known values, we now have 20 data
points from 15 separate dates. This fairly extensive lightcurve is one of the
most extensive and long-lasting of any TDE. The only one with similar numbers
of long-term points, extending for several years is that of Sw J1644+57, which
has more data points but does not extend for quite as many years (Alexander et
al., 2020).

In Table 1, the first two rows correspond to historical observations of which
we include here as a check on the pre-TDE flux level. Following these in the
table are the first four epochs of data for NGC 4845 corresponding to the
actual TDE event (including epoch T1). These observations were taken in 2011
and 2012 as a part of the CHANG-ES project (CHANG-ES, observation ID: 10C-119,
PI: J. Irwin; Irwin et al., 2012). These include L-band and C-band (centering
at 1.6 and 6.0 GHz respectively) data in three array configurations, B, C and
D. The data reductions are described in Irwin et al. (2015). In 2015, the
source was observed in L and C band as part of VLA project 15A-357 (PI: E.
Meyer). These data were previously described and published in Perlman et al.
(2017).

The remaining entries in the table correspond to additional subsequent
observations of NGC 4845, observed in multiple array configurations and bands
(L, S, C and X). The separate observations all share a number of steps in
reduction procedure, which we describe here. We have attempted to measure each
new data point in a consistent manner; however an unusual number of co-authors
were involved in individually reducing different data sets. Minor differences
in e.g., settings during de-convolution imaging and the co-author responsible
for the analysis are noted below and are not expected to impact any of the
results.

####  2.1.1 General VLA data processing

All newly presented observations were reduced using the Common Astronomy
Software Applications package (CASA; McMullin et al., 2007) and standard
calibration procedures, see e.g. Irwin et al. (2013) and Wiegert et al.
(2015). In short, the data were Hanning-smoothed in order to reduce the
effects of strong radio-frequency interference and flagged. We used the
primary 3C286 and secondary calibrators (the latter differs between datasets)
to correct the antenna baselines, the gain curve, and the antenna based
delays. This was followed by additional flagging and gain and bandpass
calibrations. The flux density scale was set for each channel in the band
using the most recent model for Stokes I (Perley & Butler, 2013). Gain
calibrations were performed in two steps, first phase-only calibration,
followed by the amplitude calibration. All calibrations were performed twice,
with additional flags applied after the first run.

Imaging deconvolution was done using the CASA task clean where we used the
multi-scale multifrequency synthesis mode (ms-mfs; Rau & Cornwell, 2011) to
better represent faint emission, with a Briggs robust parameter of 0 (or in
some cases 0.5). In general we performed one to two self-calibration rounds
for each data set.

In general, the somewhat different parameters and other details adopted in the
various data reduction procedures described here should have essentially no
impact on the reported flux values. The Briggs parameter, which is mentioned
in particular, determines the weights of the visibilities when imaging
deconvolution is performed. The range of values is from -2 (‘uniform’
weighting) and +2 (’natural’ weighting). The difference between these is
basically a tradeoff between better RMS (i.e., sensitivity to faint point
sources) versus preserving a higher angular resolution. Natural weighting
preserves sensitivity at the expense of resolution, while uniform weighting
(which gives more weight to longer baselines) will enhance/preserve angular
resolution at the expense of a noisier image. Values of 0 or 0.5 are extremely
common choices representing a compromise between these extremes. Since the
flux of our object is well above the noise level, the differences induced by
the choice of Briggs parameter is negligible.

The CASA widebandpbcor task was used to carry out wide-band primary beam
corrections. Flux measurements were made from the primary beam-corrected
images in all cases but one. The exception is the the July 2015 data
(15A-400), but with the source in the field center (as is the case here),
there should be no difference.

The low-resolution 2016 March and May fluxes at L and C bands, as well as the
NVSS measurement, have been corrected for the disk emission of NGC 4845 as
discussed in Irwin et al. (2015), subtracting a disk flux of $19\pm 4$ mJy at
L band and $7\pm 1$ mJy at C band. These disk values were interpolated for
S-band. Note that there is no need to do this for the 2015 July C-band data or
any of the X-band data due to their higher angular resolution. At high
resolution, the fluxes were measured by a Gaussian fit to the central point
source using the Gaussian fit tool in CASA. In cases in which some blending
occurred between the central strong peak and the surrounding disk emission,
the Gaussian fit was carried out within a region approximately twice the full-
width-half-maximum (FWHM) of the synthesized beam.

####  2.1.2 2015 high-resolution observations (ID: 15A-400)

We observed the nuclear region of NGC 4845 with the VLA in A-configuration, in
three epochs (2015 July 6, 14, and 28) with a dual-polarization setup. The
first two epochs were observed at X-band (centered at 9 GHz), and the third at
C-band (centered at 6 GHz). We used J1229+0203 as the secondary calibrator and
version 4.5 of CASA for the reductions. For the final imaging we used only one
combined amplitude and phase self-calibration.

####  2.1.3 2016 Swift-concurrent observations (ID: 16A-420)

These observations were taken simultaneously with Swift observations on March
16 and May 21, 2016, as a spin-off project of CHANG-ES. The data were observed
at L-band, S-band and C-band (centering at 1.5 GHz, 3 GHz and 6 GHz
respectively). We processed the data using version 5.4.0 of CASA and used
J1224+0330 as the secondary calibrator in all three bands.

In addition to manually processing the March observations, we fed them through
the VLA pipeline and found the results to be comparable. The May observations
were output entirely from the pipeline and double checked before imaging.
During imaging, we performed two self calibrations for each data set; in
C-band two phase-only calibrations (no improvements could be made after that)
and in S-band and L-band one phase-only followed by one amplitude and phase
calibration.

####  2.1.4 2019 June L-band Observation (ID: 19A-425)

NGC 4845 was observed serendipitously in 2019 June during observations of
field J125912+013051 for project 19A-425. NGC 4845 is clearly detected though
the source is 18′ from the primary beam center, so sensitivity is reduced and
the error on the flux is accordingly higher. The data were reduced using the
VLA pipeline in CASA (version 5.6.2-3), where J1254+1141 served as the initial
phase calibrator. No additional flagging of the data was required and self-
calibration was used after initial imaging, with one round of phase-only
followed by a final round of amplitude and phase calibration. During imaging,
we used a Briggs weighting with robust parameter of 0.5.

####  2.1.5 Archival Data from project AB0879

To verify the pre-TDE flux level, we re-analyzed observations of NGC 4845 from
1998 July originally taken for the FIRST 1.4 GHz survey. We imaged field
12585+01310 in which NGC 4845 is 8’ from the primary beam center (at this
distance the sensitivity for the pre-upgrade VLA is reduced approximately
12%). The uvfits data were imported to a CASA measurement set using the task
importvla and otherwise standard calibration was applied, with 1354-021 as
initial phase calibrator, though the field was ultimately self-calibrated. The
final image was made with Briggs robust parameter of 0.5.

###  2.2 X-ray Observations

The X-ray data comes from the Neil Gehrels Swift Observatory (Swift hereafter)
and XMM-Newton telescopes with detailed information in Table 2. Some early
XMM-Newton and Swift observations were published in Nikolajuk & Walter (2013)
but are reanalyzed here. The 2016 March and 2016 May observations were meant
to coincide closely with two of our VLA observations. Before calibration, we
combined any two Swift/XRT observations that are only minutes or hours apart
because sudden gamma-ray bursts can divide a pre-planned Swift observation
into two. For XMM, we only keep data from EPIC because it is the only
instrument onboard XMM-Newton covering soft X-rays with 2D imaging. Then, we
use the xrtpipeline command for Swift and the emchain/epchain command in SAS
(Science Analysis System) respectively for MOS/PN CCD data of XMM/EPIC to
conduct necessary calibrations including calibrating bias, removing bad
pixels, removing flares, etc.

Table 2: X-ray Observations Telescope | OBSID | Start Date/ Time | Total exposure time/s | Annotation | Phase
---|---|---|---|---|---
Swift/XRT | 31911001 | 2011-01-13 00:03:18.8 | 74.92 | Combined | Bright
|  | 2011-01-13 00:05:49.5 | 1440.93 |  |
|  | 2011-01-13 01:48:20.9 | 1528.33 |  |
| 31911002 | 2011-01-13 03:29:18.9 | 1053.85 |  |
|  | 2011-01-13 05:10:16.7 | 1056.35 |  |
| 31911003 | 2012-06-29 07:59:53.3 | 1675.68 | Combined | Faint
|  | 2012-06-29 11:07:39.4 | 1690.66 |  |
|  | 2012-06-29 12:44:31.2 | 1638.21 |  |
| 31911004 | 2016-03-16 05:11:55.2 | 177.31 | Combined | Faint
|  | 2016-03-16 07:02:04.8 | 169.82 |  |
|  | 2016-03-16 07:02:04.8 | 177.31 |  |
| 31911005 | 2016-03-16 05:15:15.6 | 1293.59 |  |
|  | 2016-03-16 07:05:16.2 | 1233.66 |  |
|  | 2016-03-16 08:26:16.0 | 1293.59 |  |
| 31911006 | 2016-05-21 03:32:31.0 | 202.28 | Combined | Faint
|  | 2016-05-21 05:09:10.2 | 162.32 |  |
0 |  | 2016-05-21 06:48:06.6 | 167.32 |  |
| 31911007 | 2016-05-21 03:36:15.8 | 1113.79 |  |
|  | 2016-05-21 05:12:16.3 | 1473.4 |  |
|  | 2016-05-21 06:51:15.6 | 1233.66 |  |
| 31911008 | 2017-11-12 00:08:34.7 | 1333.55 | Combined | Faint
|  | 2017-11-12 01:53:17.4 | 991.42 |  |
XMM-Newton | 658400501 | 2011-01-22 13:42:32 | 8529 | EPIC data | Bright
|  |  |  | not included |
|  |  | MOS1:15165.5 |  |
| 658400601 | 2011-01-22 16:23:28 | MOS2:16632.0 |  | Bright
|  |  | PN:9645.6 |  |

With Swift and XMM-Newton event files that were cleaned of background flares,
we choose source and background radii according to the central PSFs of the
telescopes, and extracted source and background counts using typical
procedures222For XMM-Newton details, see Weaver et al. (2018), while for
Swift, see https://swift.gsfc.nasa.gov/analysis/. We generated Swift response
files by selecting the correct RMFs in its calibration database based on their
observation times and calculate ARFs by “xrtmkarf” command. For XMM-Newton,
the “rmfgen” and “arfgen” commands in SAS are used to produce all response
files. We use absorbed power law plus absorbed APEC models, according to the
expression ${\rm{TBabs_{G}(APEC+TBabs(powerlaw))}}$, where ${\rm TBabs_{G}}$
is the Galactic absorption, 333The APEC model is discussed in detail at the
website http://www.atomdb.org. The atomic database AtomDB includes the
Astrophysical Plasma Emission Database (APED) and the spectral models output
from the Astrophysical Plasma Emission Code (APEC). The APED files contain
information such as wavelengths, radiative transition rates, and electron
collisional excitation rate coefficients. APEC uses these data to calculate
plasma model spectra. The APEC output models in AtomDB are for optically-thin
plasmas in collisional ionization equilibrium. for the two bright-phase
observations in Table 3, accounting for both the nucleus and the surrounding
hot gas. We considered the source to be extincted by the Galactic column of
$N_{\rm H}^{\rm Gal}=1.67\times 10^{20}~{}{\rm cm^{-2}}$ (Dickey & Lockman,
1990; Stark et al., 1992), and absorption from the host galaxy was allowed to
vary freely. The default version of the solar abundances were assumed for all
APEC models. All spectra are regrouped to contain at least 30 counts per bin,
which should be sufficient for using a simple $\chi^{2}$ minimization.
Although the C-statistic is statistically more accurate, we have not used it
because its use would involve complication and uncertainty in having to model
the background spectral contribution.

##  3 Results

In this section we discuss the results of those observations as well as those
in the X-rays. Table 1 contains the radio data and Table 2 contains the x-ray
data.

Figure 1: Nuclear flux density from Table 1 as a function of time, measured
from T1 (T = 0). Error bars are plotted but typically have sizes that are
smaller than the icons. Two very early points at L-band have been omitted for
ease of viewing. The X-ray outburst (denoted as T0$=-342$ days=2011-01-22, as
consistent with Irwin et al. (2015) and other papers

) is marked at far left. The first and second radio peaks are marked. L-band
is shown in blue, S-band in red, C-band in green, and X-band in black.

###  3.1 Continued evolution of the Nuclear radio flux

Consistent with Irwin et al. (2015), we define 2011 Dec 30 as time T1 ($t=0$
on the plot), and plot the other data given here and in Perlman et al. (2017)
in Figure 1. As can be seen in Figure 1, the nuclear radio flux declined
monotonically from the radio peak until approximately 2015. In 2015, we saw a
plateau in the radio flux, with 20% temporal variability in the X-band between
2015 July 06 and 2015 July 14 (the apparent C-band variability seen in June-
July 2015 is more likely a result of the two slightly different radio
frequencies). Then, in 2016 (day 1538), a sharp increase began in the radio
flux. By day 1604 the flux in C, S and L band had increased by a factor of
2.5-3. This defines the epoch of our new ‘flare’. Unfortunately there is
almost no information on the radio variability of the nuclear source of NGC
4845 previous to the TDE, although we note that the two L-band fluxes in 1995
and 1998 are consistent with one another at the 2 $\sigma$ level.

###  3.2 Results from the reanalysis of Swift and XMM-Newton data

Power-law fits to both XMM-Newton and Swift data (Nikolajuk & Walter 2013)
found a steep ($\Gamma\approx 2.35$) X-ray spectrum with a column density
$N_{H}\approx 7\times 10^{22}~{}{\rm cm^{-2}}$. Our reanalysis confirms that
result, but we find that an APEC model is a better fit to the data, with the
main improvement being an improved fitting of the soft excess. A simultaneous
fit of all three 2011 datasets yielded a power-law $\Gamma=2.316\pm 0.042$,
$kT=0.238_{-0.052}^{+0.149}$ keV for the thermal component, and absorbing
column $N_{H}=8.8\pm 0.2\times 10^{21}~{}{\rm cm^{-2}}$. The decrease in the
$\chi^{2}_{\nu}$ was highly significant – from 0.973 to 0.410 for the Swift
data and from 1.291 to 0.710 for the XMM-Newton observations. The soft X-ray
component is also noted by Nikolajuk & Walter (2013), but those authors
suggest it is unrelated to the nuclear emission associated with the TDE based
on a fit to a blackbody component with temperature $kT=0.33\pm 0.04$ keV that
is extincted only by the Milky Way’s column, which they claim (their section
3.2) is consistent with diffuse emission from galaxies (Bogdán & Gilfanov
2011; Jia et al. 2012). They do not provide any statistics on that fit;
however, it would be one additional degree of freedom beyond our model, which
as noted shows a large improvement over a power-law. We suggest that the
evidence for a smaller column for the thermal component is not persuasive, and
moreover we point out that diffuse emission from a galaxy at only 17 Mpc
distance would easily be resolved with XMM-Newton. Moreover, the 0.5-7.0 keV
flux from the thermal component, $4.3\times
10^{-13}{\rm~{}erg~{}cm^{-2}~{}s^{-1}}$, differs by more than 3$\sigma$ from
the value observed in 20160-2017 (Table 3). We therefore assess that the soft
component is more likely to be nuclear in origin.

Table 3 presents the X-ray source and background region information, as well
as counts and fluxes associated with each observation. The fluxes for the 2011
XMM-Newton and Swift observations come from the procedure discussed above. For
the 2012-2017 Swift observations, the count rates are far too small to allow
for any spectral fitting. We thus use the above best-fit spectral model to
convert the count rates to the corresponding energy fluxes for comparison. For
the two bright phase (2011) observations plus the 2012 Swift  observation, we
were able to extract background information from the individual observations.
However, for the 2016-2017 Swift observations, where this was not possible
with the individual observations, the background levels were taken from the
combined 2016-2017 observations. Figure 3 shows the 0.5-7 keV X-ray fluxes in
the 0.5-7 keV band (with no absorption correction, thus allowing us to include
the INTEGRAL observation) as a function of time. In addition, we show in
Figure 3 the X-ray fluxes from Nikolajuk & Walter (2013), extrapolated down to
the 0.5-7 keV band using the joint INTEGRAL \+ XMM-Newton best-fit model in
that paper, namely a hard X-ray spectral index of $\Gamma=2.22\pm 0.03$,
slightly different from what we find here.

Three things are clear from Figure 3. First, IGRJ12580+0134 represented a much
larger departure from the “quiescent” level of X-ray flux than was previously
realized. Based on the INTEGRAL lightcurve of Nikolajuk & Walter (2013) one
could only say that the event was an increase in X-ray flux of at most a
factor 10. Figure 3 makes it clear that IGRJ12580+0134 represented a much
larger increase in NGC 4845’s X-ray flux – more than two orders of magnitude.
Second, as also found by Nikolajuk & Walter (2013), there is no evidence for
spectral curvature between 7 keV and the 17.3-80 keV band of INTEGRAL. Not
only are the power-law components of the INTEGRAL spectral fit and our XMM-
Newton + Swift fit roughly consistent within the errors (they differ by less
than 2 $\sigma$), but in addition, the 2011 Swift/XRT  and XMM-Newton fluxes
fit smoothly on the curve described by the INTEGRAL points, without any
evidence of error due to extrapolation. Finally, there is no evidence that the
2016 radio flare described in §3.1 (Figure 1) was accompanied by an X-ray
flare. While the two 2016 data points are not detections (and for them as well
as the 2017 Swift observation we show 2$\sigma$ upper limits), we see that
when the three 2016-2017 observations are added together a significant
detection is seen and the detected flux is within $1\sigma$ of the 2012 data
point. If indeed there had been an X-ray component to the 2016 flare, the two
2016 Swift observations would dominate that point, and we see no evidence of
that.

Table 3: X-ray Source and Background Details Observation(s) | PSF | Center | Source | Background | Source | Background | 0.5-7.0 keV Flux
---|---|---|---|---|---|---|---
|  |  | Radius | Radius | Counts | Counts | ${\rm(erg~{}cm^{-2}~{}s^{-1}})$
00031911001 + 00031911002 |  |  |  |  | 2026 | 283 | $2.60\pm 0.06\times 10^{-11}$
00031911003 |  | DEC= |  |  | 9 | 4 | $2.4^{+1.3}_{-0.9}\times 10^{-13}$
00031911004 + 00031911005 | 18$\farcs$ | +1d34m33s, | 30$\farcs$ | 30$\farcs$-60$\farcs$ | 6 | 1 | $<3.75\times 10^{-13}$
00031911006 + 00031911007 |  |  |  |  | 6 | 2 | $<3.75\times 10^{-13}$
00031911008 |  |  |  |  | 6 | 3 | $<7.35\times 10^{-13}$
00031911004-00031911008 |  | RA= |  |  | 18 | 6 | $1.8^{+0.7}_{-0.5}\times 10^{-13}$
|  | 12h58m1s.3 |  |  | MOS1: 14091 | MOS 1: 9439 |
0658400601 | 6$\farcs$ |  | 10$\farcs$ | 10$\farcs$-30$\farcs$ | MOS2:14930 | MOS2: 9902 | $2.87^{+0.08}_{-0.03}\times 10^{-11}$
|  |  |  |  | PN: 28475 | PN: 16216 |

Figure 2: X-ray data for IGRJ12580+0134, with Swift data shown at top and XMM-
Newton data shown at bottom. The residuals shown in each panel are for the
spectral models discussed in §3.2. Figure 3: X-ray fluxes for IGRJ12580+0134
plotted as a function of time. Two curves are overplotted: In black, an
exponential + a constant background level, and in green, a $t^{-5/3}$ power
law plus exponential. See §3.2 for details.

##  4 Discussion

###  4.1 Classification & X-ray Spectrum of IGRJ12580+0134

Recently, Auchettl et al. (2017) have questioned the classification of IGR
J12580+0134 as a TDE, based on the fact that the host galaxy, NGC 4845, is a
Sey 2/LINER (Ho et al., 1995). They claimed that IGRJ12580+0134 could be
explained by AGN processes444The source is listed in the “TDE Graveyard”
section of the Open TDE Catalog, https://tde.space, presumably for similar
reasons.. The nucleus likely has some X-ray variability, so we definitely
agree with the general cautions regarding AGN variability expressed by those
authors. But we contend that IGR J12580+0134 is still likely to be a TDE, for
several reasons.

First, the large X-ray and radio flux increases observed (now seen to be at
least two orders of magnitude in X-rays, much larger than could be justified
based on the INTEGRAL data in Nikolajuk & Walter, 2013) are well beyond what
is usual for AGN, with less than 1% of AGN having flares of that magnitude
(Auchettl et al., 2017). The flares that tend to be similarly extreme are in
blazars (e.g., the 1998 flare of PKS 2005-489; Perlman et al., 1999) and
narrow-line Sey 1 galaxies (e.g., 1ES 1927+654; Trakhtenbrot et al., 2019a, b;
Boller et al., 2003), and NGC 4845 displays no properties in common with such
sources. Also, the nuclear luminosity in quiescence would be $\leq 6.2\times
10^{39}{\rm~{}erg~{}s^{-1}}$, as observed in the 2016-2017 Swift observations
(of which some could be due to stellar or gas processes), much more in line
with a quiescent galaxy nucleus or low-luminosity AGN (e.g., Ptak et al.
1999).

Second, Nikolajuk & Walter (2013) pointed out that the hard X-ray (17.3-80
keV) flux evolution after the peak was consistent with a $t^{-5/3}$ law based
upon INTEGRAL data. Arguments consistent with Kepler’s second law predict that
the mass infall rate should approach $t^{-5/3}$ at late times for all types of
disrupted stars (Phinney, 1989; Lodato et al., 2009, note that the evolution
close to the peak can depend on the stellar structure). However, if a
thermally emitting disk forms, the evolution can be very different, $\propto
t^{-5/12}$ if emission sits in the Rayleigh-Jeans tail of a thermal component.
Indeed, at much later times a $t^{-5/3}$ evolution is not fully consistent
with the X-ray lightcurve. (Figure 3). Alternative fits are also possible,
including an exponential fit and/or power law at earlier time with an
exponential decline at later times. Exponential behavior in the X-ray/optical
has been observed in some TDEs, including e.g., iPTF16fnl (Onori, Cannizzaro,
Jonker et al., 2019), another faint TDE. Such behavior is not unexpected in
TDE, as Lodato & Rossi (2011) point out, the $t^{-5/3}$ behavior is expected
to continue for only a few months before steepening to become essentially
exponential in the X-ray band, where the X-ray emission at later times would
be dominated by an outflow.

Figure 3 makes clear that the 2012 Swift flux fits neatly on that same power-
law as the early INTEGRAL data. Thus the $t^{-5/3}$ behavior continued for
nearly 500 days. In addition, the quickness of the decline is not consistent
with an extinguishing event, which should take place over much longer
timescales ($\sim 10^{4}$ years, Shen 2021).

The X-ray spectrum of IGRJ12580+0134 also has several properties that are more
in common with TDEs. Its spectral index, $\Gamma=2.316\pm 0.042$, is rare
among AGN (which are dominated by objects with $\Gamma\approx 1.8$; Auchettl
et al., 2018; Ricci et al., 2017) but common among TDEs (Auchettl et al.,
2018). While the X-ray power-law emission of IGRJ12580+0134 continues to 80
keV (Nikolajuk & Walter, 2013), unlike any other TDE, the power-law component
of at least one other jetted TDE, Swift J1644+57, continues up to at least
$\sim 30$ keV (Bloom et al., 2011; Kara et al., 2016), as evidenced by its
Swift/BAT detection. X-ray spectral indices over 2 are seen in HSP BL Lac
objects (e.g., Perlman et al., 2005; Paliya et al., 2019), where the X-ray
spectrum is dominated by the tail of synchrotron emission, but IGRJ12580+0134
shows no evidence for beaming. A thermal excess is almost universally found in
TDEs, but the temperature, $kT=0.24_{-0.05}^{+0.15}$ keV, is somewhat higher
than seen in most TDEs (typically $\sim 50$ eV, although comparably high
temperatures are seen in $\sim 10\%$ of cases; Auchettl et al., 2018) and AGN
(typically $\sim 100$ eV but a with a handful over 200 eV; Ricci et al.,
2017). As discussed in §3.2, this thermal component is very likely to be of
nuclear origin. Finally, the absorbing column is reasonable both for AGN and
TDEs (Auchettl et al., 2018) and is similar to that seen in the jetted TDE
Swift J1644+57.

This re-assessment confirms that IGR J12580+0134 was a TDE in at most a low-
luminosity AGN. Two very recent reviews make the point that TDE and TDE-like
events should be common in AGN (Gezari, 2021; Saxton et al., 2021). Saxton et
al. (2021) specifically discusses IGR J12580+0134 and mentions this
possibility. As Saxton et al. note, at least a few other possible TDEs fall
into this category. One particularly interesting case could even be a recent
event in OJ287 where the X-ray lightcurve shows a clear, $t^{-5/3}$ decay
after the event (Huang et al., 2021). A much more doubtful case is Arp 299,
where Mattila et al. (2018) suggested the presence of a TDE, attributing the
lack of signatures in other bands to a large obscuration. However, that event
was more than an order of magnitude smaller in amplitude than IGR J12580 and
lacked the characteristic lightcurve variability. A recent paper by Zabludoff
et al. (2021) discussed a more sophisticated way to discriminate TDEs from
interloper events, which will be critical for future surveys such as the LSST.

The clarification of IGR J12580+0134’s nature as a TDE also allows us to
discuss other aspects of its X-ray spectral behavior. The flow of matter into
the near vicinity of an active black hole might make TDEs more common in AGN
than in quiescent galaxies, although this hypothesis needs to be tested by
LSST observations. Stolc & Karas (2019) have pointed out that in such systems
one might expect an evolving, relativistic Fe K$\alpha$ line. Our X-ray
spectral data do not show such a line, but the signal to noise at 6.4 keV is
low.

###  4.2 Continuing Radio Flux and Spectrum Variability

As discussed in §3, the radio flux of IGR12580+0134 has continued to evolve,
as shown in Figure 1. Up to and including 2015, VLA data show descent to a
plateau in the radio flux. During that plateau, $\sim 20\%$ variability was
seen in the X-band, which is common in radio-loud AGN and also more quiescent
galaxies. For an example of the latter, see the lightcurve of Sgr A* shown in
Subroweit, Garcia-Marin, Eckart et al. (2017). Very little data exist on the
long-term radio lightcurves of TDE (Alexander et al., 2020), so it is
difficult to comment on the frequency of such small scale radio variability in
that population. The plateau in the radio emission seen in 2015 is reminiscent
of events seen in the X-ray lightcurve of ASASSN-14li, 1-2 years after the TDE
(Bright et al., 2018). In that object, Pasham & van Velzen (2018) have
detected a time-lag between the soft X-ray and radio emission, and interpreted
it as linear disk-jet coupling. Unfortunately, we do not have sufficient radio
or X-ray data in IGR J12580+0134 to perform such a test. In addition, we have
found a major radio flare in 2016. Our sole radio point after 2016, taken in
2019, shows a large decline in radio flux, however due to the lack of
monitoring between 2016-2019 we cannot speculate on the speed of the decline.

Figure 4: AGN flux density from Table 1 as a function of frequency for the
time period 2015-2019. Spectra from the time periods 2015 June, 2015 July and
2019 Mar-May are not truly simultaneous and combine all observations from the
noted time period. Both axes are logarithmic, and error bars are shown (Table
1). See §4.2 for discussion.

It is interesting to look at the evolution of the radio spectrum during these
events, shown in Figure 4. In that plot, two of the spectra are truly
simultaneous (March 2016 and May 2016), while the others simply show all data
during the indicated periods. In 2015, we saw a C-L band spectral index of
$\alpha_{CL}=0.89$, while the X-C band spectral index in July 2015 was
$\alpha_{XC}=1.67$ (the slightly different June and July 2015 C-band flux
points is clearly a result of observing at two different central frequencies,
as Figure 4 makes clear). The spectral index at lower frequencies (L and S
bands) was at its flattest during the flare’s brightest stage, in May 2016,
when a value of $\alpha_{SL}=0.64~{}(F_{\nu}\propto\nu^{-\alpha})$ was seen,
as compared to a value of $\alpha_{SL}=1.51$ in March 2016 when the flare was
in an earlier stage. However,in May 2016, the higher frequency (C to S band)
spectral index was significantly steeper ($\alpha_{CS}=1.45$) than it was in
March 2016 ($\alpha_{CS}=1.15$). Thus the radio spectrum in March 2016
steepened moderately as one went to lower frequencies, while in May 2016 it
flattened drastically as one went to lower frequencies. The new flare has not
been monitored sufficiently to show the decline behaviour between 2016-2019.
However, in 2019, the radio spectrum between S and L bands was
$\alpha_{SL}=1.25$.

IGR J12580+0134 joins ASASSN-15oi (Horesh, Cenko & Arcavi, 2021) as one of
only two TDEs with late-time radio flares observed. Comparing the two,
ASASSN-15oi during the peak of its late-time radio flare was two orders of
magnitude fainter in flux than IGRJ12580+0134, but due to its much greater
distance (216 Mpc) its peak luminosity was a factor of a few higher, actually
higher than its radio peak during the primary TDE event. The increase in radio
luminosity observed in ASASSN-15oi was actually larger than that observed in
IGRJ12580+0134 – a full order of magnitude, as compared to a factor 3 here.
The two occur at similarly late times after the TDE (4 years after the TDE in
ASASSN-15oi as compared to 5.5 years after the TDE in IGRJ1258+0134). However,
apparently no radio monitoring of ASASSN-15oi exists after the late-time rise
in 2019, at least up until the publication this year of Horesh et al. (2021).

There are to our knowledge four other TDE that show late-time X-ray flares.
These are PS10adi (Jiang et al., 2019), OGLE16aaa (Kajava et al., 2020),
ASASSN-15oi (at the same time as its radio flare, Gezari et al. (2017);
Holoien et al. (2018)), ASASSN-18jd (Neustadt et al., 2020), and AT2019azh
(Liu et al., 2019). All four have been modeled as possibly due to a second
fallback event due to circularization of the orbits of accreting material (van
Velzen et al., 2019; Gezari, 2021) or a sub-relativistic shockwave (Alexander
et al., 2020; Yalinewich et al., 2019). As discussed below, the radio-only
flare in IGR J12580+0134 cannot be explained in this context, similar to
ASASSN-15oi where a similar conclusion was reached (Horesh et al. 2021).

###  4.3 Radio flare from a jet-cloud encounter

The 2016 radio flare seems more likely to be the result of the jet
intercepting a circumnuclear cloud and accelerating particles to relativistic
energies. Following the modeling of an off-axis jet propagating in the CNM
employed to explain the multi-wavelength evolution of radio emission from IGR
J12580+0134 (Lei et al., 2016; Perlman et al., 2017), we fit the fluxes
assuming that a denser gas cloud exists in the path of the propagating jet.
The jet dynamics is described by a set of hydrodynamical equations, including
the evolution of the radius and Lorentz factor of the jet, and the swept mass
(Huang et al., 2000; Liu et al., 2020). The magnetic field and accelerated
electron population share parts of the thermal energy of the downstream medium
of the shock, with fractions $\epsilon_{B}$ and $\epsilon_{e}$, respectively.
Electrons were accelerated to form a power-law spectrum with an index of $-p$.
Synchrotron radiation was then calculated given the magnetic field and
electron distribution at each time.

Figure 5: Model fitting of the radio light curves (upper sub-panel) of IGR
J12580+0134 in a scenario with a jet propagating in the CNM. The radio flare
is explained by the encounter with a gas cloud as indicated by the density
profile in the bottom sub-panel.

Figure 5 shows the light curves from the model calculation, compared with the
data. The main model parameters include: the total kinetic energy of the
ejecta $E_{k}=2.5\times 10^{52}$ erg, the initial ejecta Lorentz factor
$\Gamma_{i}=8.5$, $\epsilon_{e}=0.27$, $\epsilon_{B}=0.09$, the jet opening
angle $\theta_{j}=5.4^{\circ}$, the viewing angle $\theta_{\rm
obs}=36^{\circ}$, the electron spectral index $p=2.80$, and the background
medium density $n=5.2$ cm-3. A gas cloud with an average density of $n_{\rm
cl}=10.3$ cm-3 spanning from 0.95 to 0.97 pc from the central black hole, as
indicated by the bottom panel of Figure 5, is found to be able to fit the
radio flare. The cloud mass swept by the jet (with opening angle of
$\theta_{j}$) is estimated to be about $1.8\times 10^{-4}$ M⊙, and the jet
velocity is about $0.17c$ when it hits the cloud. Given the soft spectrum of
electrons and the cooling effect, we estimate that the flux in the X-ray band
(at 1 keV) during the radio flare time is about $3.4\times 10^{-17}$ erg cm-2
s-1 keV-1, which is several orders of magnitude lower than the upper limits
shown in Fig. 3.

Note that there is degeneracy among the model parameters, and the above
parameters are one example of those with reasonable values. Nevertheless, some
of these parameters can be constrained by the data. While the CNM density
degenerates with the total kinetic energy as well as the energy partition
fractions, the density contrast between the gas cloud and the CNM background
can be constrained relatively well (about 2, although the exact value is
affected somehow by the thickness of the shell). The swept mass, derived by
the gas density and cloud thickness, is constrained by the declining profile
and post-flare fluxes.

This simplified model fits the observational data, including the radio flare,
fairly well. The flattening of the radio spectral index at the brightest phase
of the late-time radio flare (Figure 4) is consistent with this model, as such
an interaction would cause a shock in the jet. The rapid steepening of the
radio spectral index in the later 2016 epoch is consistent with a small size
for the cloud. The late-time L-band flux in 2019 is a little bit higher than
the model expected flux. The X-band fluxes also show a quick decrease which
was not observed in other bands. Further refinement of the model may improve
the match between the model and data. If this scenario is correct, the radio
monitoring of jetted TDE could allow us to probe the surrounding medium of the
galactic nuclei. The density profile of the background CNM can in principle be
probed with the light curves (Berger et al., 2012). It is, however, difficult
for IGR J12580+0134 given the sparse data points during and immediately after
the flare, since as can be seen additional observations would have been
helpful.

Horesh et al. (2021) reached a similar conclusion regarding the nature of the
late-time radio flare of ASASSN-15oi. They modeled it as due to the collision
of the radio jet with a circumstellar shell of material, after rejecting
fallback events and shocks within a structured jet due to the steepness of the
radio rise. We cannot distinguish that possibility from the model we propose
in this paper, and in fact such a shell would be consistent with the
possibility we model, although resulting in a considerably greater mass for
the disturbance.

##  5 Conclusions

TDEs are some of the most energetic events that occur in a galaxy nucleus.
Recent works have shown the similarities of TDEs to AGNs. Both are associated
with accretion events to the nuclear supermassive black hole – relatively
long-lived in the case of AGN, and temporary and short-lived in the case of
TDE. The short-lived nature of TDE may, in fact, be one reason for the
differences between AGN and TDE X-ray spectra. The latter are often blackbody
in nature, and can be explained as material that at any time is orbiting at a
small range of radii. By comparison, the power-law nature of AGN X-ray spectra
require matter orbiting at a large range of radii (Perlman, 2013), both within
the accretion disk and its corona. This necessarily requires a long-lasting,
stable accretion structure with a more continuous accretion stream rather than
a discrete event. In this respect, a late-time radio flares associated with
the interaction of the outflow with an ISM cloud, should not be regarded as a
surprising – in fact, radio-only flares in AGN are commonly modeled in such a
fashion (e.g., Hervet et al. (2017) and references therein).

Other possibilities must be considered for such a radio flare. The first is
the ejection of a new component within the jet very close to the origin of the
outflow near the supermassive black hole. This would be similar to what occurs
in blazars and other AGN during large radio flares (e.g., Larionov et al.
(2020); Blandford, Meier & Readhead (2019)). However, such flares usually are
associated with multiwavelength events, making such an event unlikely. In
addition, a component would become visible at a later epoch, a possibility we
discuss in a future paper (Perlman et al., in prep). A second possibility is
shockwaves in a structured jet, also often invoked for blazar variability but
rejected by Horesh et al. (2021) due to the lightcurve shape. A third
possibility is a delayed ejection of an outflow, perhaps triggered by a change
in accretion state or second, fallback event. This was suggested for the late-
time X-ray-optical flares of PS10adi, OGLE16aaa and AT2019azh, which did not
have an associated radio flare. We do not feel such a model is appropriate for
IGRJ12580+0134 for two reasons. First, in IGRJ12580+0134, the radio outflow
began at early times (Perlman et al., 2017; Irwin et al., 2015). And second,
no flare was seen in other bands for IGRJ12580+0134, as discussed above,
whereas the late-time radio flare of ASSASN-15oi, was associated with an X-ray
and optical flare (Horesh, Cenko & Arcavi, 2021; Gezari et al., 2017; Holoien
et al., 2018). Additionally, given that the original event was associated with
the accretion of a substellar object (e.g., a brown dwarf or super-jupiter
Nikolajuk & Walter (2013)), it is unlikely that adequate mass would be left
over from the addditional event.

It is quite likely that as more TDEs are discovered, an increasing diversity
of ejection and flare events will be seen both in their X-ray, optical-UV and
radio flux, as well as in their radio structure. The events discussed in this
paper are very likely just a preview of some of the things that will be found
in the future. Already in its first year, eROSITA has produced an impressive
diversity of properties in the thirteen TDEs it discovered (Sazonov, Gilfanov,
Medvedev et al., 2021). This is particularly enticing with the advent of
surveys such as the Rubin Observatory LSST and Roman Space Telescope coming in
the near future. Late-time radio flares, such as those found in IGRJ12580+0134
or ASASSN-15oi could be unique probes of the circumnuclear environment,
particularly its density and potentially magnetic field structure (Yuan et al.
2016, Horesh et al. 2021).

The National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. This paper was based partly on observations obtained with XMM-Newton, an
ESA science mission with instruments and contributions directly funded by ESA
Member States and NASA. We acknowledge the use of public data from the Swift
data archive. QY thanks Liang-Duan Liu and He Gao for helpful discussion of
the modeling.
The National Radio Astronomy Observatory is a function of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. The VLA datasets were reduced by different members of the team. EM
processed the data from program 19A-425 as well as the archival data from
AB0879. TW processed the Swift-concurrent observations of 16A-420, and YY
reduced the 2015 high-resolution observations of 15A-400.

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##  Appendix A Modeling of the jet-CNM interaction

The jet dynamics when propagating in the CNM is described by the following
equations (Huang et al., 2000)

$\displaystyle\frac{dR}{dt}$ $\displaystyle=$ $\displaystyle\beta
c\Gamma\left(\Gamma+\sqrt{\Gamma^{2}-1}\right),$ (A1)
$\displaystyle\frac{dM}{dR}$ $\displaystyle=$ $\displaystyle 2\pi
R^{2}\left(1-\cos\theta_{j}\right)nm_{p},$ (A2)
$\displaystyle\frac{d\Gamma}{dM}$ $\displaystyle=$
$\displaystyle-\frac{\Gamma^{2}-1}{M_{\rm ej}+\epsilon M+2(1-\epsilon)\Gamma
M},$ (A3)

where $R$ is the radius of the propagating jet, $\beta$ is the jet velocity in
unit of light speed $c$, $\Gamma=1/\sqrt{1-\beta^{2}}$ is the Lorentz factor
of the jet, $M$ is the swept mass of the CNM by the jet, $\theta_{j}$ is the
jet opening angle, $n$ is the CNM density, $m_{p}$ is proton mass, $M_{\rm
ej}$ is the ejecta mass, and $\epsilon$ describes the radiation efficiency
which is assumed to be $\ll 1$. Note that we neglect the sideway expansion of
the jet and thus $\theta_{j}$ keeps to be constant during the jet propagation.
The ejecta mass can be obtained as

$M_{\rm ej}=\frac{E_{k}}{(\Gamma_{i}-1)c^{2}}\frac{1-\cos\theta_{j}}{2},$ (A4)

where $E_{k}$ is the (isotropic) kinetic energy of the ejecta and $\Gamma_{i}$
is the initial Lorentz factor. The jet is assumed to propagate in a uniform
CNM, and then encounter a gas cloud with finite size and a constant density
(see the parameters in the main text). Eqs. (A1)-(A3) are solved numerically,
taking into account the assumed gas cloud.

After obtaining the jet dynamics, the synchrotron radiation is calculated
following the standard afterglow emission model of gamma-ray bursts (Gao et
al., 2013). For the observations at relatively low frequencies and late time
which correspond to our case, the synchrotron cooling is not important, and we
have $\nu_{c}\gg\nu_{m}$, $\nu_{c}\gg\nu_{a}$, where $\nu_{c}$, $\nu_{m}$, and
$\nu_{a}$ are the characteristic cooling frequency, minimum injection
frequency, and self-absorption frequency, respectively. The radiation flux
density can be calculated as

$\displaystyle F$ $\displaystyle=$ $\displaystyle F_{\rm
max}\left(\frac{\nu_{a}}{\nu_{m}}\right)^{1/3}\left(\frac{\nu}{\nu_{a}}\right)^{2},~{}~{}~{}~{}~{}~{}~{}\nu<\nu_{a}<\nu_{m},$
$\displaystyle F$ $\displaystyle=$ $\displaystyle F_{\rm
max}\left(\frac{\nu}{\nu_{m}}\right)^{1/3},~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\nu_{a}<\nu<\nu_{m},$
(A5) $\displaystyle F$ $\displaystyle=$ $\displaystyle F_{\rm
max}\left(\frac{\nu}{\nu_{m}}\right)^{-(p-1)/2},~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\nu_{m}<\nu,$

and

$\displaystyle F$ $\displaystyle=$ $\displaystyle F_{\rm
max}\left(\frac{\nu_{m}}{\nu_{a}}\right)^{(p+4)/2}\left(\frac{\nu}{\nu_{m}}\right)^{2},~{}~{}~{}~{}~{}\nu<\nu_{m}<\nu_{a},$
$\displaystyle F$ $\displaystyle=$ $\displaystyle F_{\rm
max}\left(\frac{\nu_{a}}{\nu_{m}}\right)^{-(p-1)/2}\left(\frac{\nu}{\nu_{a}}\right)^{5/2},~{}~{}\nu_{m}<\nu<\nu_{a},$
(A6) $\displaystyle F$ $\displaystyle=$ $\displaystyle F_{\rm
max}\left(\frac{\nu}{\nu_{m}}\right)^{-(p-1)/2},~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\nu_{a}<\nu,$

where $p$ is the spectral index of accelerated electrons, $F_{\rm
max}=(m_{e}c^{2}\sigma_{T}\Gamma BM)/(12\pi ed^{2}m_{p})$ is the maximum flux
over all frequencies, with $m_{e}$ being the electron mass, $\sigma_{T}$ being
the Thomson cross section, $B$ being the magnetic field, $e$ being the
electron charge, and $d$ being the distance of NGC 4845.

The TDE of IGR J12580+0134 is expected to be viewed from an off-axis direction
of the jet (Lei et al., 2016). Some corrections of the viewing angle effect
need to be applied, including $\nu^{\rm off}=a_{\rm off}\nu^{\rm on}$, $t^{\rm
off}=t^{\rm on}/a_{\rm off}$, $F_{\nu}^{\rm off}(t)=a_{\rm
off}^{3}F_{\nu/a_{\rm off}}^{\rm on}(a_{\rm off}\,t)$, where $a_{\rm
off}=(1-\beta)/(1-\beta\cos\theta_{\rm obs})$ (Granot et al., 2002). These
corrections are important at early time before the jet decelerates to the non-
relativistic regime.