A Potential Second Shutoff from AT2018fyk: An updated Orbital Ephemeris of the Surviving Star under the Repeating Partial Tidal Disruption Event Paradigm

Draft version June 27, 2024
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A Potential Second Shutoff from AT2018fyk: An updated Orbital Ephemeris of the Surviving Star
under the Repeating Partial Tidal Disruption Event Paradigm
Dheeraj Pasham,1
E. R. Coughlin,2
M. Guolo,3
T. Wevers,4
C. J. Nixon,5
Jason T. Hinkle,6, ∗
and
A. Bandopadhyay2
1MIT Kavli Institute for Astrophysics and Space Research
Cambridge, MA 02139, USA
2Department of Physics, Syracuse University, Syracuse, NY 13210, USA
3Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles St., Baltimore MD 21218, USA
4Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
5School of Physics and Astronomy, Sir William Henry Bragg Building, Woodhouse Ln., University of Leeds, Leeds LS2 9JT, UK
6Institute for Astronomy, University of Hawai`i at Manoa, 2680 Woodlawn Dr., Honolulu, HI 96822
ABSTRACT
The tidal disruption event (TDE) AT2018fyk showed a rapid dimming event 500 days after discovery,
followed by a re-brightening roughly 700 days later. It has been hypothesized that this behavior results
from a repeating partial TDE (rpTDE), such that prompt dimmings/shutoffs are coincident with the
return of the star to pericenter and rebrightenings generated by the renewed supply of tidally stripped
debris. This model predicted that the emission should shut off again around August of 2023. We report
AT2018fyk’s continued X-ray and UV monitoring, which shows an X-ray (UV) drop in flux by a factor
of 10 (5) over a span of two months, starting 14 Aug 2023. This sudden change can be interpreted
as the second emission shutoff, which 1) strengthens the rpTDE scenario for AT2018fyk, 2) allows
us to constrain the orbital period to a more precise value of 1306±47 days, and 3) establishes that
X-ray and UV/optical emission track the fallback rate onto this SMBH – an often-made assumption
that otherwise lacks observational verification – and therefore the UV/optical lightcurve is powered
predominantly by processes tied to X-rays. The second cutoff implies that another rebrightening
should happen between May-Aug 2025, and if the star survived the second encounter, a third shutoff is
predicted to occur between Jan-July 2027. Finally, low-level accretion from the less bound debris tail
(which is completely unbound/does not contribute to accretion in a non-repeating TDE) can result in
a faint X-ray plateau that could be detectable until the next rebrightening.
Keywords: Galaxies: Optical – Galaxies: X-ray
1. INTRODUCTION
A tidal disruption event (TDE) occurs when a star
approaches a supermassive black hole (SMBH) and is
either completely or partially destroyed (e.g., Rees 1988;
Gezari 2021). TDE candidates were first discovered in
the mid 1990s in the X-rays using the ROSAT soft X-
ray telescope (e.g., Bade et al. 1996; Grupe et al. 1995;
Donley et al. 2002) and more recently with optical sky
surveys like the ASASSN (Shappee et al. 2014), ATLAS
(Tonry et al. 2018), Zwicky Transient Facility (ZTF;
Bellm 2014), and with eROSITA in the X-rays (Sazonov
et al. 2021). With an estimated observed rate of roughly
∗ NASA FINESST FI
one TDE every 104−5
years per galaxy (Yao et al. 2023;
Sazonov et al. 2021), there is huge excitement for Ru-
bin observatory (first light in 2024) which is expected to
identify >100 events every year (van Velzen et al. 2011;
Bricman & Gomboc 2020).
A few dozens of TDEs are known so far and they have
already transformed our understanding of SMBHs and
their immediate surroundings. For example, some TDEs
that were followed up extensively in the X-rays have
shown powerful outflows (e.g., see Wevers et al. 2024;
Kosec et al. 2023; Ajay et al. 2024; Kara et al. 2018).
Some systems have highly relativistic jets (bulk Lorentz
factor ∼ a few tens) akin to blazars and have provided
the best datasets to test models of jet launching (e.g.,
see Pasham et al. 2023; Bloom et al. 2011; Brown et al.
arXiv:2406.18124v1
[astro-ph.HE]
26
Jun
2024

2 Pasham et al.
2015; Pasham et al. 2015; Andreoni et al. 2022; Yao
et al. 2024). In a few systems, radio synchrotron ex-
panding at sub-relativistic speeds has been found which
can be either from internal shocks within a jet (Pasham
& van Velzen 2018) or from external shocks with ambi-
ent medium(Cendes et al. 2023).
In addition to these TDE subclasses, in the last few
years a surprising new sub-class has been uncovered:
those that repeat on timescale of months to years (Payne
et al. 2021, 2022, 2023; Wevers et al. 2023; Liu et al.
2023b; Evans et al. 2023; Guolo et al. 2024; Somalwar
et al. 2023). These events have been postulated to arise
from a star on a bound orbit about an SMBH that is
partially disrupted during each pericenter passage. The
TDE AT2018fyk/ASASSN-18ul (redshift z=0.059, lu-
minosity distance of 264.3 Mpc) is thought to be one
example of this new class, and was discovered by the
ASAS-SN optical survey in 2018, and follow-up mon-
itoring with Swift, NICER, XMM-Newton, and Chan-
dra showed that it remained X-ray and UV bright for
roughly 500 days. Thereafter, it displayed a sudden
and dramatic decrease in the X-ray (by a factor of
>6000) and the UV (by a factor of ≈15; see Fig. 2 and
Wevers et al. 2021). The source also exhibited appar-
ent state transitions similar to outbursting stellar-mass
black hole binaries (soft/UV/accretion disk dominated
state ⇒ hard/X-ray/corona-dominated state ⇒ quies-
cence; see Wevers et al. 2021).
The source was then found to be X-ray and UV-
bright again around day ∼ 12001
, with eROSITA non-
detections interspersed between the last non-detection
at day 600 and the first new detection at day 1200,
showing that AT2018fyk suddenly “turned on” follow-
ing a ∼ 2 year dark period – behavior that is otherwise
unprecedented in observed TDEs. The precipitous drop
in luminosity and the rebrightening can be explained
by the rpTDE scenario2
: Wevers et al. (2023) argued
that if the return of the tidally disrupted debris to the
SMBH is tightly coupled to the accretion rate and the
corresponding luminosity, which is a good approxima-
tion for highly relativistic settings with small viscous
delays, the sudden cessation of accretion coincides with
the return of the star to pericenter, and the time be-
tween the sudden cutoff and the rebrightening equates
to the fallback time of the tidally stripped debris. With
this model, they deduced that the orbital period of the
1 All times in this paper are measured in observer’s frame with
respect to the optical discovery date of MJD 58369.2.
2 The presence of AGN in AT2018fyk was ruled out based on de-
tailed analyses of multi-wavelength data of the host galaxy, see
section 2.4 of Wevers et al. (2023)
star is ∼ 1200 days. They predicted that, if the star was
not destroyed during the second pericenter passage, the
system should display another dimming in August 2023,
analogous to the one observed in 2019.
Here, using continued X-ray monitoring with Swift,
NICER, XMM-Newton and Chandra, we report the find-
ing of this second cutoff at 1830±29 days (14 Aug - 11
Oct 2023). Our data analysis is shown in section 2 while
we discuss the implications and provide specific predic-
tions to further test the rpTDE model in section 3.
2. DATA AND ANALYSIS
We used the following cosmological parameters:
ΛCDM cosmology with parameters H0 = 67.4 km s−1
Mpc−1
, Ωm = 0.315 and ΩΛ = 1 - Ωm = 0.685 (Planck
Collaboration et al. 2020).
2.1. Swift X-Ray Data
Swift (Gehrels et al. 2004) observed AT2018fyk on
210 occasions as of 5 Jan 2024. Out of these, 5 were
corrupted or did not have Photon Counting (PC) data
and were excluded. Observations up to MJD 59809,
i.e., 178 of these observations, were reported in Wev-
ers et al. (2023). Here we present additional monitoring
data since 18 August 2022. For consistency, we reduce
the entire Swift archival data of AT2018fyk here.
We started our analysis by downloading the data
from HEASARC public archive (https://heasarc.gsfc.
nasa.gov/cgi-bin/W3Browse/w3browse.pl) and reduced
the X-Ray Telescope (XRT; Burrows et al. 2005) ob-
servations on a per ObsID basis using the HEASoft
tool xrtpipeline. Then we extracted source and back-
ground count rates in the 0.3-10.0 keV band using the
ftool xrtlccorr. We used a circular aperture of radius
47′′
for source and an annulus of inner and outer radii
of 70′′
and 235′′
, respectively. These values were cho-
sen to ensure there are no contaminating sources within
the chosen boundaries. From these, we obtained a net
(background-subtracted) rate for each ObsID.
AT2018fyk was especially faint with net rates close
to zero in the most recent observing campaign since
MJD 60000 (approved Swift cycle 19 program 1922148;
PI: Pasham). Therefore, we carefully analyzed them
by stacking them into 4 datasets with the following
time boundaries: MJD 60030-60070 (L1), MJD 60070-
60140 (L2), MJD 60140-60200 (L3), and MJD 60200-
60310 (L4). The source was detected in two of these
four stacked datasets. The net 0.3-10.0 keV count
rate/3σ upper limit for L1, L2, L3 and L4 epochs were
(1.5±0.6)×10−3
cps, <4.3×10−3
cps, (2.6±0.7)×10−3
cps, and <2×10−3
cps, respectively. We also visually
inspected the exposure-corrected 0.3-10.0 keV image for

AT2018fyk’s second X-ray shutoff 3
epoch L3 in which a point source is evident (see the mid-
dle panel of Fig. 1). Assuming a spectrum similar to
the one implied by an XMM-Newton observation taken
around that time, the flux conversion factor is 3.1×10−11
erg s−1
cm−2
/counts sec−1
.
2.2. Swift UV Data
UV observations were taken with Swift/UVOT con-
temporaneously with the XRT observations. We used
the uvotsource package to measure the UV photometry,
using an aperture of 5′′
. We subtracted the host galaxy
contribution by modeling archival photometry data with
stellar population synthesis using Prospector (John-
son et al. 2021), following the procedure described in
Wevers et al. (2021) and tabulated in their table 2. We
apply Galactic extinction correction to all bands using
E(B − V ) value of 0.011 from Schlafly & Finkbeiner
(2011).
2.3. XMM-Newton
XMM-Newton observed AT2018fyk on 8 occa-
sions (ObsIDs: 0831790201, 0853980201, 0854591401,
0911790701, 0911790601, 0911791501, 0911791401 and
0921510101). Two observations (0911790701 and
0911791501) did not have any science data and the rest,
except for the latest one (ObsID: 0921510101), have
been published elsewhere (Wevers et al. 2019, 2021,
2023). This latest dataset was part of an approved
XMM-Newton cycle 22 Guest Observer Target Of Op-
portunity (GO ToO program 92151; PI: Pasham) to cap-
ture the second X-ray shutoff of AT2018fyk. While the
main focus in this work will be on this latest dataset we
also reduce all the others here for uniformity.
We started XMM-Newton data analysis by download-
ing the data from the HEASARC public archive (https:
//heasarc.gsfc.nasa.gov/cgi-bin/W3Browse/w3browse.
pl). Then we ran the epproc tool of XMMSAS
software to reduce the European Photon Imaging
Camera (EPIC)’s pn detector. We did not use
MOS data in this work. First, we visually in-
spected the background in all the six ObsIDs follow-
ing the steps outlined in the data analysis thread:
https://www.cosmos.esa.int/web/xmm-newton/
sas-thread-epic-filterbackground-in-python. All obser-
vations were affected by background flares to some
extent and we removed those epochs to obtain a set of
Good Time Intervals (GTIs) per ObsID. Source events
were extracted from a circular aperture with a radius
of 30′′
while background events were extracted from a
nearby circular aperture free of any point sources with
a radius of 50′′
. The source is clearly detected in all but
0854591401 (XMM3 as per Wevers et al. 2023). Conse-
quently, five spectra were extracted following the stan-
dard procedure outlined here: https://www.cosmos.esa.
int/web/xmm-newton/sas-thread-pn-spectrum. The
spectra were grouped using the specgroup task of
XMM-Newton software (XMMSAS) to have minimum
of 1 count per spectral bin. Cash statistic was used for
spectral modeling in XSPEC (Arnaud 1996). For each
spectrum, we only used the bandpass where the source
is above the background (see Table 1).
The most recent dataset is consistent with a simple
powerlaw modified by MilkyWay absorption of 1.2×1020
cm−2
(C-stat/degrees of freedom (dof) of 110/114). Ad-
ditional absorption at the host redshift is not required
by the data in any of the five spectra. The best-fit pow-
erlaw index in the most recent dataset is 1.96+0.86
−0.88 (see
Table 1 for details on flux and luminosity). The spec-
trum did not have enough signal-to-noise to test more
complicated spectral models.
2.4. Chandra
Chandra ’s Advanced CCD Imaging Spectrometer
(ACIS) observed AT2018fyk on three occasions: MJD
59029.22 (29 June 2020), MJD 60227.71 (10 October
2023; ObsID: 28294) and MJD 60228.58 (11 October
2023; ObsID: 28972). All these were carried out in the
ACIS-S array mode and we use the nominal bandpass of
0.5-7.0 keV throughout. The first observation was pub-
lished in Wevers et al. (2021) while the most recent two
datasets were observed as part of an approved Chandra
Cycle 25 guest observer program to catch the source dur-
ing the second shutoff phase predicted by Wevers et al.
(2023) (PI: Pasham; GO proposal number 25700383).
For consistency, we reduce all the three datasets here.
We started our data analysis by reducing the data
with the chandra repro tool of CIAO 4.16 software
using the latest CALDB 4.11.0. First, we extracted
exposure-corrected images in the 0.5-7.0 keV bandpass
using the fluximage task of CIAO and see an excess
at the position of AT2018fyk in both of the most re-
cent observations (IDs: 28294 and 28972). Next, we
extracted the X-ray spectra and relevant response files
for each of the two recent observations separately using
specextract tool of CIAO. These spectra were grouped
to have a minimum of 1 spectral count per bin using
the optmin flag of the HEASoft ftool ftgrouppha. We
modeled them together in XSPEC (Arnaud 1996) with
a powerlaw model modified by MilkyWay neutral ab-
sorption column of 1.2×1020
cm−2
(tbabs*zashift*pow).
With only 25 net (background-corrected) counts the
spectral index is poorly constrained. Therefore, we
fixed it at the best-fit value from the XMM-Newton
data of 1.96. This yields a best-fit C-statistic/dof of

4 Pasham et al.
Figure 1. Left: XMM-Newton/EPIC-pn image of AT2018fyk’s field of view on MJD 60102.76 (XMM ObsID 0921510101).
The circle centered on AT2018fyk has a radius of 30′′
while the arrows pointing North and East are each 30′′
in length. Middle:
Stacked Swift/XRT image of AT2018fyk using data taken between MJDs 60140 and 60200, i.e., the data point around day 1800
between XMM-Newton (pentagon) and Chandra detections (square) in Fig. 2 The statistical significance of the detection is
3.7σ. The circle has a radius of 47′′
while the directional arrows are 90′′
each. Right: Stacked Chandra/ACIS X-ray image
using data from ObsIDs 28294 and 28972. The circle centered on AT2018fyk has a 4′′
radius while the directional arrows are
5′′
each.
38.5/56 and an observed 0.3-10.0 keV flux (luminos-
ity) of (9.0+1.0
−2.0)×10−15
erg s−1
cm−2
(7.0+2.0
−1.0×1040
erg
s−1
). This represents a factor of >7 decrease in flux
since the latest XMM-Newton observation taken roughly
4 months earlier.
2.4.1. Chandra astrometry
We also combined the two observations to esti-
mate an accurate position by following the steps
outlined in https://cxc.cfa.harvard.edu/ciao/threads/
fluxes multiobi/. We computed the offsets between the
two datasets to be 0.18 pixels and 0.42 pixels in the X
and Y directions, respectively. To improve this we per-
formed astrometric correction to obsID 28972 to match
with that of 28294 which has about 60% higher expo-
sure time (33 ks vs 20 ks). Following the steps outlined
in the above Chandra data analysis thread we reduced
the offsets to 0.15 pixels and 0.06 pixels, respectively.
An X-ray (0.5-7.0 keV) image from combining obsIDs
28294 and 28972 is shown in the right panel of Fig. 1.
The source region defined as a circular aperture of 4′′
in radius has 25 net counts. Running wavdetect on
this combined images yields a best-fit X-ray position of
(22:50:16.17,-44:51:53.00) with an uncertainty of 0.12′′
in each direction. This is consistent with the best-fit
Gaia position reported in Wevers et al. (2019) based on
the optical emission during the first outburst in 2018.
2.5. Hubble Space Telescope (HST)
The UV measurement from Hubble Space Telescope’s
F275W filter with an effective wavelength of 2750 Å was
taken from Wen et al. (2024).
2.6. Shutoff and rebrightening times
The first X-ray and UV shutoffs happened between
days 488 and 561 while the second sharp decline oc-
curred sometime during days 1801 and 1859 (see Fig.
2). These values correspond to the observation dates.
Per the model of Wevers et al. (2023), the orbital pe-
riod of the surviving star is the time between shutoffs,
which based on the above values is 1306 ± 47 days3
.
The uncertainty is derived from adding the range in cut-
off times in quadrature. Using this we can formulate a
crude ephemeris to predict the nth
shutoff to be:
tn
shutoff (MJD) = (58893.5 ± 29) + (n − 1)(1306 ± 47)
This equation implies that the next (third) shutoff
should occur sometime between 2 Jan 2027 and 17 July
2027, assuming that the star survived its second en-
counter. Alternatively, if the star was completely de-
stroyed during the second encounter, then there would
be no third cutoff and the luminosity would continue to
smoothly decline.4
The fallback time after the second pericenter passage
of the star is the time between the first shutoff and
the second rebrightening (between 1164 and 1216 days).
The fallback time will differ from one encounter to the
next because mass is stripped from the progenitor and
the star is imparted net rotation (Bandopadhyay et al.
2024a), and hence accurately predicting the next rise is
3 Note that Wevers et al. (2023) estimated the orbital period of
the star by assuming that the fallback time between the first and
second encounters was the same, and while this is likely a fairly
good approximation, observing the successive shutoffs is more
direct. See Section 3 for additional discussion.
4 We note that this possibility may provide a unique opportunity
to explore the differences in emission produced by fallback from
partial and complete disruption events in the same system, i.e.,
comprising the same black hole mass and spin and stellar orbit.

1040
1041
1042
1043
1044
X-ray
Luminosity
[erg
s
−
1
] Swift/XRT
XMM-Newton
Chandra
SRG/eROSITA
0 250 500 750 1000 1250 1500 1750 2000
Time since MJD 58369 (days)
1041
1042
1043
1044
UV
Luminosity
[erg
s
−
1
]
UVOT W1 (2600Å) HST F275W (2750Å)
Figure 2. Top: AT2018fyk’s observed 0.3-10.0 keV X-ray luminosity evolution over the past ∼2000 days. The x-axis is in
observer’s frame. Most recent Chandra and Swift data shows a drop of >10 from 7×1042
to 7×1041
over two months. A similar
change is also evident in the UV light curve (bottom panel). Inverted triangles represent 3σ upper limits. This sudden change
can be interpreted as a shutoff which allows us to refine the orbital period of the star that is repeatedly disrupted to be 1306±47
days. The two shutoff epochs are highlighted with red/vertical bands. The entire X-ray and UV photometry is available at
https://doi.org/10.5281/zenodo.10913475.
not as straightforward as predicting the orbital period.
However, if we assume a similar fallback time, then the
next rise in flux should happen around 2495±54 days,
which corresponds to an MJD 60864±54 (15 May – 31
Aug 2025).
The latest Chandra data point (green square in Fig. 2)
is two orders of magnitude below the peak of the second
outburst and an order of magnitude below a previous
XRT detection roughly two months earlier. However,
it is possible that the latest Chandra data and the cor-
responding UV upper limits may be due to anomalous
source variability. For this reason, we refer to this as
a potential shutoff. This can be confirmed with further
deep X-ray and UV observations between now and the
predicted next rebrightening in 2025.
3. DISCUSSION AND CONCLUSIONS
The rpTDE model proposes that a star is on a highly
eccentric (0.99 ≲ e < 1) orbit about an SMBH, with
the short orbital period and high eccentricity provided
by the Hills mechanism (Cufari et al. 2022; Wevers
et al. 2023). Since the fallback time inferred from
the observations is ∼ 600-700 days, the SMBH pow-
ering the emission from AT2018fyk must be large and
the disruption must be partial, as both of these ef-
fects increase the return time of the debris above the
∼ (30 ± 5) × M•/106
M⊙
1/2
days that is characteris-
tic of complete disruptions, with M• the SMBH mass
(Coughlin Nixon 2022; Bandopadhyay et al. 2024b).
When the SMBH mass is large (as is inferred to be the
case for AT2018fyk; 107.7±0.4
; see Wevers et al. 2023),
the accretion rate should be strongly coupled to the fall-
back rate of debris, because the pericenter distance is
highly relativistic and the accretion timescale is short
relative to the fallback time. This model then predicts
that the accretion rate should shut off when the surviv-
ing core returns to the (partial) tidal disruption radius
(Wevers et al. 2023; see also Liu et al. 2023a), the reason

6 Pasham et al.
being that the Hill sphere that separates material bound
to the black hole and bound to the star grows with time
approximately as ∝ t2/3
, where t is time since pericenter
(Coughlin Nixon 2019). Therefore, when the surviv-
ing core returns to pericenter, there is a sudden drop in
the mass supply to the SMBH and the luminosity plum-
mets. The simultaneous plummeting of the optical/UV
emission alongside the X-ray is also consistent with the
interpretation that the optical/UV emission is tied to
X-ray emission5
that originates from the innermost few
gravitational radii, which in this case may be physically
produced by circularization shocks, accretion, or both
(the former may also give rise to the nonthermal elec-
trons powering the corona; cf. Sironi Tran 2024).
The time between successive cutoffs in emission should
therefore closely track the orbital period of the stellar
core. Because the orbital period is related to the orbital
energy and the orbital energy can at most be reduced
by the binding energy of the star, there is effectively no
change in this recurrence time on a per-orbit basis (Cu-
fari et al. 2023; Bandopadhyay et al. 2024a).6
On the
other hand, the time between the cutoff and the next re-
brightening equals the fallback time of the most-bound
debris that is related to the properties of the star and its
rotation rate, and the latter changes as a consequence of
the tidal interaction with the SMBH (since the imparted
spin is prograde with respect to the orbital angular mo-
mentum, the result is a decrease in the return time of
the debris; Golightly et al. 2019). Wevers et al. (2023)
estimated the orbital time of the star – and thereby pre-
dicted the time of the second cutoff – by assuming that
the fallback time was unchanged between the first and
second encounter: since the first cutoff occurred at ∼
500 days (since first detection) and the second bright-
ening at ∼ 1200 days, the fallback time (for the sec-
ond encounter) was ∼ 700 days and the first pericenter
passage must have occurred ∼ 700 days prior to the
first detection if the fallback times were identical on the
5 This seems inconsistent with the interpretation that the opti-
cal/UV is sourced from a large-scale outflow that is causally dis-
connected from the X-ray emission (e.g., Price et al. 2024).
6 This holds for orbits generated by the Hills disruption of a tight
binary, where by tight we mean that the binding energy of the
binary is comparable to the binding energy of the captured star
(which was one of the members of the original binary). In this
case the binding energy of the captured star’s orbit is larger than
that of the star itself by a factor of (M•/M⋆)1/3 (e.g. Cufari et al.
2022). On the other hand, for a standard TDE in which the bind-
ing energy of the star’s orbit is ∼ 0, the change in the energy of
the core during core reformation (e.g. Nixon et al. 2021; Nixon
Coughlin 2022) or due to a positive-energy kick (e.g. Manukian
et al. 2013; Gafton et al. 2015) can give rise to substantial differ-
ences in the orbital period between successive partial disruptions.
first and second encounter, making the orbital period of
the star ∼ 1200 days. If we now associate the green
datapoint at day ∼ 1850 as the second observed cut-
off (note that this date also coincides with the observed
cutoff in the optical/UV, which is qualitatively in agree-
ment with the behavior observed during the first cutoff),
then this suggests that the true (i.e., from the observed
successive cutoffs) orbital period of the star is between
1250-1350 days. This finding suggests that the fallback
time on the second encounter was shorter than that of
the first by ∼ 50 − 150 days, which is different at the
∼ 10−20% level. This is consistent with the theoretical
results of Golightly et al. (2019) if the imparted spin to
the star was a significant fraction of breakup (which is
expected, given the importance of nonlinear interactions
when the tidal field of the SMBH is comparable to the
self-gravitational field of the star). If the star is spun up
to a closer fraction of the angular velocity at pericenter
on its third encounter, we would expect a reduced fall-
back time in going from the second shutoff to the start of
the third electromagnetic outburst, and the observation
(or lack thereof) of this feature would provide another
test of this model.
A noticeable difference between the first and second
outburst in AT2018fyk’s lightcurve is the peak luminos-
ity, which is reduced by a factor of ∼ 5 − 10 from the
first to second brightening. Under the rpTDE paradigm,
this difference could be due to one or more potential
factors. If, for example, the partially disrupted star was
highly centrally concentrated – which would arise nat-
urally as a consequence of stellar evolution if the star
is sufficiently massive – then it seems plausible that the
stripping of the envelope on the first encounter could
leave the high-density core relatively unperturbed, the
result being that the tidal radius of the surviving core is
smaller. Since the pericenter distance of the star is ef-
fectively unaltered owing to the conservation of angular
momentum, the β (= rt/rp, with rp the pericenter dis-
tance and rt the tidal radius) of the encounter is reduced,
resulting in less mass stripped on subsequent tidal inter-
actions and a reduction in the accretion rate (and the
luminosity).
Bandopadhyay et al. (2024a) recently showed (and in
agreement with the suggestion by Liu et al. 2023a) that
more massive and evolved stars (specifically a 1.3M⊙
and a 3M⊙ star near the end of the main sequence) that
require very deep encounters to be completely destroyed
– and are thus statistically significantly more likely to
be partially disrupted – are capable of producing flares
of nearly equal amplitude after many successive out-
bursts, despite the fact that the amount of mass stripped
from the star declines slightly per pericenter passage (see

their Figures 7, 8, and 11). Contrarily, a sun-like star
closer to the zero-age main sequence, which is signifi-
cantly less centrally concentrated than an evolved star
of the same mass, was shown by the same authors to suf-
fer increasing degrees of mass loss per encounter, even
when the pericenter distance of the encounter was a fac-
tor of ∼ 3 larger than that required to completely de-
stroy the star on the first encounter (see their Figure
13; see also Liu et al. 2024, who came to similar conclu-
sions regarding the fate of a solar-like star after multi-
ple encounters). Similarly, since a star of significantly
lower mass (≲ 0.1 × fewM⊙) cannot evolve substan-
tially over the age of the Universe and is effectively a
5/3-polytrope, the range in radii where such a low-mass
star could be repeatedly stripped of a small amount of
mass (β ≡ rt/rp ≃ 0.5 − 0.6, where rp is the pericenter
distance of the star and rt = R⋆ (M•/M⋆)
1/3
is the tidal
disruption radius with R⋆ and M⋆ the stellar radius and
mass; Guillochon Ramirez-Ruiz 2013; Mainetti et al.
2017; Miles et al. 2020; Cufari et al. 2023) per encounter
is very fine tuned, and the detection of a second cutoff
here suggests that the star must have survived at least
two encounters. Thus, and despite their relative rarity,
a more massive star could be the most promising can-
didate for producing the repeated flares in 2018fyk. A
more massive star would also permit wider initial bi-
naries (while yielding the same period of the captured
star), a less relativistic pericenter distance, and a longer
fallback time of the tidally stripped debris compared to
the more extreme values required for a solar-like star to
fit the observations (see the discussion in Section 4 of
Wevers et al. 2023).
Additionally, if the Hills mechanism is responsible for
placing the star on its tightly bound orbit about the
SMBH, then there will be a difference between the peri-
center distance of the partially disrupted (and captured)
star during its initial hydrodynamical interaction be-
tween the SMBH and the (ultimately ejected) compan-
ion star and subsequent encounters. If it is such that the
∼ conserved pericenter distance of the captured star is
larger than that of the initial interaction, then less mass
will be stripped on the second encounter, resulting in
a relatively smaller accretion luminosity on the second
outburst. Depending on how centrally concentrated the
star is and the β of the encounter, subsequent outbursts
could be progressively more or less luminous with time.
As also discussed in Bandopadhyay et al. (2024a), the
tight binary required to populate the star on its ∼ 1300-
day orbit implies that the rotation rate of the captured
star is a significant fraction of the angular velocity at
pericenter, which will also have a significant impact on
the magnitude of successive flares and the return time
of the debris (Golightly et al. 2019)).
From the rpTDE model, the orbital time of the star is
∼ 1200−1400 days and the fallback time is ∼ 600−800
days (note that such long fallback times require the
event to be a partial disruption; Bandopadhyay et al.
2024a), which predicts that the freshly stripped debris
generated on the third encounter (i.e., the second dim-
ming around the green point in Figure 2) should produce
a third brightening at day ∼ 2500 post-initial-detection
(though, as noted above, the additional imparted spin
to the star near pericenter could yield a time closer to
day ∼ 2400). This third brightening should then oc-
cur in early-2025, which is consistent with the predic-
tions in Wevers et al. (2023), and the future detection
or non-detection thereof would provide strong evidence
in support of or against this model.
An alternative interpretation, as proposed by Wen
et al. (2024), is that the reduction in the luminosity of
AT2018fyk is due to the presence of a companion black
hole, and that the disrupting black hole was of very
low mass compared to the primary. In such extreme-
mass-ratio systems, there could be a dramatic dimming
when the tidally stripped debris nears the Hill sphere
of the secondary (disrupting) black hole after the first
encounter, provided that the orientation of the binary
is favorable (Coughlin Armitage 2018). Wen et al.
(2024) then proposed that the second outburst arose
from accretion onto the primary. However, when the
secondary is the disrupting SMBH and the stream is
relatively confined to the orbital plane of the binary –
which must be the case if accretion onto the primary is
responsible for the second outburst – the distribution of
the debris is highly stochastic (see, e.g., Figures 1 2 of
Coughlin Armitage 2018, or Figures 9 10 of Cough-
lin et al. 2017), and it is difficult to see why this scenario
would produce repeated and dramatic dimmings on this
same timescale.
Finally, the partial TDE results in the production of
two tails of stellar debris. In typical TDEs where the
star is on a parabolic orbit, the second tail is ejected
from the system and yields no observational signature
(with the possible exception of radio emission in the
presence of circumnuclear gas; e.g., Guillochon et al.
2016; Yalinewich et al. 2019). However, and as noted in
Wevers et al. (2023), the bound nature of the stellar or-
bit in this case implies that the second tail may be “less
bound” rather than unbound, with the specific energy
of the second tail a function of the specific energy of the
core and the energy spread imparted by the tidal field.
It could be that deeper X-ray monitoring of AT2018fyk
during the second (current) shutoff phase would reveal

8 Pasham et al.
the presence of low-level emission from this second tail,
and since the energy of the core is constrained from
the observed orbital period, this emission would yield
additional information about the properties of the star
and the SMBH. rpTDEs are thus unique in their ability
to more directly constrain stellar and SMBH properties
in distant galaxies.
D.R.P was supported by NASA XMM-Newton guest ob-
served program, proposal number 92395 (award number
035212-00001), and Chandra program 25700383 (award
number 035385-00001). E.R.C. and A.B. acknowledge
support from NASA through the Neil Gehrels Swift
Guest Investigator Program, proposal number 1922148.
E.R.C. acknowledges additional support from the Na-
tional Science Foundation through grant AST-2006684,
and from NASA through the Astrophysics Theory Pro-
gram, grant 80NSSC24K0897. C.J.N. acknowledges
support from the Science and Technology Facilities
Council (grant No. ST/Y000544/1) and from the Lever-
hulme Trust (grant No. RPG-2021-380). This research
was supported in part by grant NSF PHY-2309135 to
the Kavli Institute for Theoretical Physics (KITP).

Table
1.
Summary
of
XMM-Newton
and
Chandra
X-ray
energy
spectral
modeling.
†
The
net
exposure
after
filtering
for
background
flares.
Total
exposure
before
correcting
for
flares
is
shown
in
brackets.
††
Net
count
rate
(background-corrected)
in
the
bandpass
where
the
source
is
above
the
background.
†††
Bandpass
where
the
source
and
the
background
spectrum
crossover.
This
is
different
for
each
spectrum
and
modeling
was
performed
in
this
custom
band
depending
on
the
observation.
We
repeated
the
entire
analysis
in
a
fixed
0.3-1.5
keV
band
and
the
resulting
values
were
consistent
with
those
reported
in
this
table.
∗
Normalization
of
the
best-fit
disk
black
body.
∗∗
Powerlaw
index.
§
Normalization
value
of
the
powerlaw
model
component.
§§
Observed
flux
and
luminosities
in
the
0.3-10.0
keV
band.
tbabs*zashift(diskbb+pow)
was
used
for
modeling.
In
cases
where
kT
is
indicated
by
“...”
a
disk
component
was
not
necessary.
§§§
Both
the
Chandra
spectra
were
fit
together,
hence
the
same
spectral
parameters.
The
powerlaw
index
was
fixed
at
the
best-fit
XMM-Newton
value
from
ObsID
0921510101.
Telescope
ObsID
MJD
Exposure
†
Count
rate
††
Bandpass
†††
kT
N
kT
∗
Γ
∗∗
N
§
Γ
Flux
§§
×10
−13
Luminosity
§§
C-stat/dof
(ks)
(counts/sec)
(keV)
(keV)
(×10
−5
)
(erg
s
−1
cm
−2
)
(10
42
erg
s
−1
)
XMM
0831790201
58461.72
17.0
(33)
0.403±0.004
0.3-2.5
0.123
+0.005
−0.004
493
+100
−164
3.41
+0.68
−1.38
3.4
+1.4
−1.9
7.7
+0.2
−0.1
7.0
+0.3
−0.1
42.4/48
XMM
0853980201
58783.33
35.0
(55)
0.687±0.004
0.3-9.0
0.146
+0.006
−0.006
170
+32
−25
2.07
+0.06
−0.06
22.6
+1.4
−1.4
15.7
+0.1
−0.2
13.3
+0.1
−0.2
192.0/155
XMM
0911790601
59719.89
8.2
(29)
0.175±0.005
0.3-5.0
0.095
+0.035
−0.032
211
+1700
−173
2.35
+0.19
−0.22
8.6
+0.8
−1.1
3.7
+0.3
−0.3
3.2
+0.3
−0.3
72.1/82
XMM
0911791401
59739.84
3.1
(10.6)
0.130±0.009
0.3-0.8
·
·
·
·
·
·
2.77
+0.54
−0.54
11.1
+4.4
−3.4
4.4
+1.4
−0.6
3.7
+0.8
−0.6
15.0/11
XMM
0921510101
60102.76
8.8
(43.1)
0.011±0.001
0.3-1.0
·
·
·
·
·
·
1.96
+0.86
−0.88
1.1
+0.6
−0.4
0.6
+0.7
−0.2
0.5
+0.3
−0.2
19.1/16
Chandra
§§§
28294
60227.71
32.6
(33)
(3.8±1.2)×10
−4
0.5-7.0
·
·
·
·
·
·
1.96
0.18
+0.08
−0.06
0.09
+0.01
−0.02
0.07
+0.02
−0.01
38.5/56
Chandra
§§§
28972
60228.58
19.8
(20)
(5.0±1.7)×10
−4
0.5-7.0
·
·
·
·
·
·
1.96
0.18
+0.08
−0.06
0.09
+0.01
−0.02
0.07
+0.02
−0.01
”

10 Pasham et al.
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