Rapid evolution of the recurrence time in the repeating partial tidal disruption event eRASSt J045650.3 − 203750

In this letter, we present the results from subsequent X-ray and UV observations of the nuclear transient eRASSt J045650.3 − 203750 (hereafter, J0456 − 20). We detected ﬁve repeating X-ray and UV ﬂares from J0456 − 20, marking it as one of the most promising repeating partial tidal disruption event ( p TDE) candidates. More importantly, we also found rapid changes in the recurrence time, T recur , of the X-ray ﬂares by modelling the long-term X-ray light curve of J0456 − 20. We found that T recur ﬁrst decreased rapidly from about 300 days to around 230 days. It continued to decrease to around 190 days with an indication of a constant T recur , as evidenced by the latest three cycles. Our hydrodynamic simulations suggest that, in the repeating p TDE scenario, such a rapid evolution of T recur could be reproduced if the original star is a 1M (cid:12) main sequence star near the terminal age, losing nearly 80–90% of its mass during the initial encounter with a supermassive black hole (SMBH) of a mass around 10 5 M (cid:12) . The inferred mass loss of 0.8–0.9 M (cid:12) is higher than the estimated value of around 0.13 M (cid:12) drawn from observations, which could be explained if the radiation e ﬃ ciency is low (i.e. (cid:28) 0 . 1). Our results indicate that repeating p TDEs could be e ﬀ ective tools for exploring the dynamics around SMBHs beyond our own Galaxy.


Introduction
Tidal disruption events (TDEs) are typically considered oneoff events where a star is completely destroyed by a supermassive black hole (SMBH) at the first pericentre passage.However, theoretical calculations and numerical simulations have shown that a partial TDE (pTDE) can also occur (e.g.Guillochon & Ramirez-Ruiz 2013;Ryu et al. 2020).In a pTDE, the star loses only a fraction of its mass and survives its first encounter with the SMBH.If the star is initially in a bound orbit with low eccentricity, it is expected to generate repeating flares (e.g.Hayasaki et al. 2013;Ryu et al. 2020;Nixon & Coughlin 2022;Cufari et al. 2022Cufari et al. , 2023;;Melchor et al. 2024).Because the encounter cross-sections of pTDEs are generally larger than or comparable to those of full TDEs, the rate of pTDEs is expected to be larger or comparable to full TDEs (Krolik et al. 2020;Bortolas et al. 2023).Repeating pTDEs are particularly interesting as they may be effective probes to explore stellar dynamics around SMBHs beyond our own Galaxy and may also serve as ideal laboratories for studying the accretion processes in SMBHs.
Only a few repeating pTDE candidates have been reported so far (e.g.ASASSN-14ko, Payne et al. 2021; HLX-11 , Webb et al. 2023;eRASSt J045650.3−203750, here-after J0456−20, Liu et al. 2023;RX J133157.6−324319.7, Malyali et al. 2023;AT2018fyk, Wevers et al. 2023).Among these, J0456−20 is one of the best-studied repeating nuclear transients discovered in a quiescent galaxy (z = 0.077).Liu et al. (2023) reported the detection of three repeated X-ray and UV flares from J0456−20.In particular, the profiles of the X-ray flares are similar and can be characterised by four distinctive phases: an X-ray rising phase (P X,rise ) leading into an X-ray plateau phase (P X,plat ), which is terminated by a rapid X-ray drop phase (P X,drop ) and followed by an X-ray faint state (P X,faint ).These results provide strong evidence that J0456−20 is a repeating nuclear transient, making J0456−20 one of the most promising pTDE candidates.
Quasi-period eruptions (QPEs) are a class of recurring X-ray flares found in galactic nuclei, with periods of less than one day (Miniutti et al. 2019;Giustini et al. 2020;Arcodia et al. 2021).Their origin remains elusive, though recent studies indicate a potential link to pTDEs (e.g.GSN 069, Miniutti et al. 2023;RX J133157.6−324319.7, Malyali et al. 2023).The discovery of Swift J0230, which exhibits QPE-like behaviours with a period of around 22 days (Evans et al. 2023;Guolo et al. 2024), further strengthens the link between repeating pTDEs and QPEs.It is thus interesting to study the evolution of T recur of the flares for repeating pTDEs.However, any substantial evolution in T recur has only been reported in ASASSN-14ko and HLX-1.A period derivative of −0.0026 ± 0.0006, with a period of 115.2 10 44 L unabs, rest, 0.2 2.0 keV (erg s 1 ) Fig. 1.Long-term X-ray and UV light curves for J0456−20.The coloured regions represent the four phases: the plateau phase (P X,plat , light cyan), the rapid drop phase (P X,drop , light blue), the faint phase (P X,faint , light yellow), and the rising phase (P X,rise , light green).has been reported for ASASSN-14ko (Payne et al. 2022).HLX-1 initially shows quasi-periodic X-ray outbursts spaced by about 1 yr between 2009 and 2012.Then, T recur started to increase until 2018, with no X-ray outbursts detected afterwards (Godet et al. 2014;Webb et al. 2023).Long-term multi-wavelength observations on a larger sample of repeating pTDEs are required to fully understand the evolution of T recur in these objects and potentially provide further evidence to confirm the connection between repeating pTDEs and QPEs.
In this letter, we report the discovery of the rapid evolution of T recur in J0456−20.A detailed analysis of the latest X-ray and UV data has revealed five X-ray and UV flares in J0456−20 (marked as cycle 1-5 in Fig. 1).These results confirm that J0456−20 is indeed a repeating nuclear transient and also suggest an initially rapid decrease in T recur by more than two months between cycles 1 and 2, slowing to around 40 days between cycles 2 and 3. Afterwards, T recur reaches an almost constant value of around 190 days in the latest three cycles.
This paper is structured as follows.In Sect.2, we present the multi-wavelength data reduction.X-ray spectral and light curve modelling are presented in Sect.3. Finally, we discuss and summarise our results in Sects.4 and 5. Throughout this paper, we adopt a flat ΛCDM cosmology with H 0 = 67.7 km s −1 Mpc −1 and Ω m = 0.308 (Planck Collaboration VI 2020).Therefore z = 0.077 corresponds to a luminosity distance of D ld = 360 Mpc.All magnitudes will be reported in the AB system (not corrected for Galactic extinction).All the quoted uncertainties correspond to the 90% confidence level, unless specified otherwise.

Observations and data reduction
In this paper, we analysed all observations after MJD 59720.We refer to Liu et al. (2023) for more details on the data analysis prior to this date.
The Observation Data Files (ODFs) for each observation were reduced using the XMM-Newton Science Analysis System software (Sas, version 19.1, Gabriel et al. 2004), with the latest calibration files.For each observation, the Sas tasks emchain and epchain tasks were used to generate the event lists for the European Photon Imaging Camera (EPIC) MOS (Turner et al. 2001) and pn (Strüder et al. 2001) detectors, respectively.High background flaring periods were identified and filtered from the event lists.For all the EPIC images, a circular region with a radius of 30, 20, 25 was chosen as the source region for X5, X6, and X7, respectively.A source-free annulus region with an inner radius of 50 and an outer radius of 100 was chosen as the background region for all MOS observations.The background for the pn camera was extracted from a circular region with a radius of 60 centred at the same CCD read-out column as the source position for all observations.X-ray events with pattern L13, page 2 of 13 ≤12 for MOS and ≤4 for pn were selected to extract the X-ray spectra.We used the tasks rmfgen and arfgen to generate the response matrix and ancillary files, respectively.The X-ray spectra were rebinned to have at least one count per bin.

Swift observations
The XRT online data analysis tool2 (Evans et al. 2009) was used to check whether the source was detected for each observation.It was also used to generate the X-ray spectra for observations where J0456−20 was detected and to calculate the 3σ count rate upper limits for non-detections.The X-ray spectra were rebinned to have at least one count in each bin.
The Swift/UVOT data were reduced using the UVOT analysis pipeline provided in HEASoft (version 6.31) with UVOT calibration version 20201215.Source counts were extracted from a circular region with a radius of 5 centred at the source position.A 20 radius circle from a source-free region close to the position of J0456−20 was chosen as the background region.The task uvotsource was used to extract the photometry.

NICER observations
The NICER data were analysed using HEASoft with the NICER data analysis software (version 10) and calibration files (version 20221001).The nicerl2 task is used to generate cleaned X-ray events.Events with overshoot higher than 1.5 or undershoot larger than 300 were removed.The nicerl3-spec task was then used to generate the X-ray spectra for each NICER observation.The X-ray spectra were then rebinned to have at least one count per bin.We adopted the Scorpeon model to generate background models for each observation.The nicerarf and nicerrmf tasks were used to generate the response matrix and ancillary file for each observation, respectively.The same procedures were also adopted to re-analyse the NICER observations taken during the first two X-ray rising phases (i.e.observation carried out during MJD 59418-59448 and 59600-59641).

Chandra observations
We requested Chandra DDT observations of J0456−20, which were performed on 2023 Mar. 18, Apr.11, and April 14 with the Advanced CCD Imaging Spectrometer (ACIS).We used the Ciao (Fruscione et al. 2006, version 4.15) software package to reduce the Chandra data with calibration files CALDB version 4.10.4.We reprocessed the Chandra data using the Ciao script chandra_repro.The Ciao task dmextract was used to extract the source and background spectra.We extracted the source spectra using a circular region with a radius of 2 .The background spectra were extracted using an annulus (concentric with the source) region with an inner and outer radius of 6 and 20 , respectively.The response files were generated using the mkacisrmf and mkarf tasks.The position of the X-ray flare measured from Chandra is (RA, Dec) = (04:56:49.81,−20 • 37 47.98 ) with a 2σ uncertainty of 0.54 (Appendix A), consistent with the centre of the host galaxy.

ATCA radio observations
We observed the coordinates of J0456−20 nine times with the Australia Telescope Compact Array (ATCA) between 2022 Aug. and 2023 Mar., in addition to the five observations between 2021 Mar. and 2022 Apr. reported in Liu et al. (2023).We observed the target during the X-ray outburst phase as this was previously when radio emission had been detected and therefore observed the target with the array in various configurations.In each observation, we used the dual 5.5 GHz and 9 GHz receiver, placing the 2×2 GHz of bandwidth split into 2048x1 MHz channels at a central frequency of 5.5 GHz and 9 GHz.Data were reduced in the Common Astronomy Software Application (CASA, version 5.6.3,CASA Team 2022) using standard procedures, including flux and bandpass calibration with PKS 1934-638 and phase calibration with PKS 0454-234.Additionally, we carried out one round of phase-only self-calibration of the target field at both 5.5 and 9 GHz, with a typical solution interval of two minutes, to produce a good quality image due to a bright AGN in the field.Images of the target field were created with the CASA task tclean and in cases where a source was visible at the location of J0456−20, the flux density was extracted with the CASA task imfit by fitting a Gaussian the size of the synthesised beam.

X-ray spectral modelling
The Xspec software (version 12.13.0,Arnaud 1996) was used to fit all X-ray spectra using the Cash statistic (Cash 1979, Cstat in Xspec).As mentioned in Liu et al. (2023), a powerlaw model (i.e.TBabs*zashift*cflux*powerlaw, hereafter M pl ) is preferred for observations taken at relatively high X-ray flux (i.e. the rest-frame unabsorbed 0.2-2.0keV flux, f X,soft , 5 × 10 −13 erg cm −2 s −1 ).We first fit all the new X-ray spectra with the M pl model.The Galactic column density is fixed at 3.3 × 10 20 cm −2 .
For NICER data, we first fit the total X-ray spectra over the 0.25-10.0keV range with the backgrounds model generated using Scorpeon.We then re-fit the data by adding the M pl model.A 3σ upper limit for f X,soft was estimated for observations in which the fit did not improve significantly (i.e.∆C stat < 11.8) after adding the M pl model.A strong oxygen Kα line is presented in some of the NICER data.The niscorpv22_swcxok_norm parameter in the background model was thus left free to properly model the oxygen Kα line in those observations.We fit the background subtracted spectra with the M pl model for the data from the other missions.The Swift/XRT X-ray spectra were fitted over the 0.3-5.0keV energy range, while the 0.5-5.0keV energy band was used for Chandra observations.For XMM-Newton data, we jointly fit the data from the three EPIC cameras over the 0.2-5.0keV energy range for X5 and X7 (0.2-2.0 keV for X6).The best-fit values and the 90% uncertainties were calculated for the f X,soft and photon index parameters.In addition, the 68% uncertainties for the f X,soft were also estimated for observations taken during the P X,rise phase.The 3σ upper limits of f X,soft were calculated for non-detections using either the M pl or a disk model (see below).The details of the fitting results are listed in Table C.2. Liu et al. (2023) noticed that the UV-to-X-ray SEDs of J0456−20 can be described by a multi-colour disk model (TBabs*zashift*cflux*diskbb, hereafter M mcd ) when the X-ray flux is low.Thus, the M mcd model was also used to fit the X-ray spectra at the early stage of the P X,rise phase, namely, observations taken between MJD 59600 and 59620 in cycle 3 and X6 in cycle 5.J0456−20 was detected only on MJD 59619 (NICER, ObsID: 4595020126, hereafter N26) and on MJD 59999 (X6).The best-fitting T in and T recur from P X, rise phases T recur from P X, drop phases Fig. 2. Evolution of the recurrence time.The purple square (blue circle) points represent T recur measured from the P X,rise (P X,drop ) phases.The error bars mark the 1σ uncertainties.The upward arrow indicates the 3σ lower limit.The estimated total mass loss from the star is also marked.
In this work, we used the results from the M mcd model for X6 and N26.The best-fitting T in of N26 is comparable to that obtained from the eRASS2 and Swift observations (in the range of ∼50−100 eV, Liu et al. 2023) at similar f X,soft (i.e.≈4 × 10 −13 erg cm −2 s −1 ), while T in is much higher during the X6 observation when J0456−20 was in a historically low X-ray flux.This suggests a potential change in T in during the P X,rise phase.For this reason, different values of T in (listed in Table C.2) were used to calculate the 3σ flux upper limits for NICER observations before N26 during cycle 3.

Modelling the X-ray rising phase
The P X,rise phases during cycles 2, 3, 4, and 5 were captured by our follow-up observations.We also assumed that J0456−20 is in the P X,rise phase of cycle1 during the eRASS2 observations.This is justified by the duration of the P X,drop phase being much shorter than the P X,rise phase and by the spectral property of eRASS2 (i.e.best described by the M mcd model) being similar to that at the early stage of the P X,rise phase.
We jointly fit the five P X,rise phases with a power-law function f rs,i (t) = A * (t − t i ) β , where i = 1, 2, 3, 4, 5.We assumed that the normalisation, A, and power law index, β, were the same for all the five P X,rise phases.The lmfit package is adopted to fit the data with the least-squares method.To take into account upper limits and to estimate the uncertainties of the parameters in the model, we generated 10 5 realisations of f X,soft in the five P X,rise phases from Gaussian distributions for observations where J0456−20 has been detected as well as uniform distributions with a lower limit of zero (excluded) for non-detections.The best-fitting f X,soft and the 1σ uncertainties obtained from X-ray Notes.Parameters: name of the parameter in the power-law model; Cycles [1,2,5]: results from jointly fitting the P X,rise phases of cycles 1, 2, and 5; All cycles: results by jointly fitting the P X,rise of all the five cycles; T recur and T recur, drop are the recurrence time estimated using the P X,rise and P X,drop phases, respectively.
spectral modelling of each observation are used as the means and standard deviations of the Gaussian distributions, respectively.The 3σ f X,soft upper limits for non-detections are used as the upper limits for the uniform distributions.We obtained 10 5 values for each parameter in the model by fitting the 10 5 datasets using the least squares method.We estimated the best-fitting values using the median values for each parameter and estimated the 1σ confidence intervals using the 16th and 84th percentiles of the fitting results.Similarly, the recurrence time T recur for cycle i and i + 1, and the lower and the upper intervals of the 1σ confidence intervals are estimated using the median, the 16th, and 84th percentiles of a sample calculated using t i+1 − t i .To test whether the results could be affected by the inclusion of flux upper limits, we applied the same procedures to cycles 1, 2, and 5 only (i.e.cycles without upper limits in the P X,rise phases).We found the results to be consistent within 1σ uncertainties (see Table 1).The fitting results and the estimated T recur are listed in Table 1.We also calculated the recurrence time using the P X,drop phase (Appendix B).The estimated values of T recur are also listed in Table 1.It is clear from Fig. 2 that the T recur of the X-ray flares in J0456−20 show rapid changes.The mass loss for each cycle marked in Fig. 2 are calculated using the method outlined in Sect.3.3.

Estimation of the mass loss
Following Liu et al. (2023), a cycle is defined as the time between the start of two consecutive P X,rise phases.The total energy released in each cycle was estimated by where L rs is the bolometric luminosity during the P X,rise phase, which is calculated using the best-fitting power law (see Sect. 3.2), that is, L rs (t) = κ4πD 2 ld f rs (t), where κ = L bol /L X,res0.2−2.0 keV is the bolometric correction factor and D ld is the luminosity distance.Then, L pl and L fa are the average bolometric luminosity during each of the P X,plat and P X,faint phases, respectively, while ∆t fa , ∆t pl , and ∆t rs are the duration of the P X,faint , P X,plat , and P X,rise phases, respectively.The P X,faint phase in cycle 5 was not covered by our follow-up observations.In this work, we assumed ∆t fa = 70 days for cycle 5.Liu et al. (2023) estimated the κ to be in the range of 3−20 during the P X,rise phase, calculated by modelling the UV to X-ray data using either the M mcd (when J0456−20 is X-ray faint) or Comptonized M mcd model.The T in of the M mcd model is around 40−60 eV and does not change significantly (see also Fig. 10 in Liu et al. 2023).Following Liu et al. (2023), we adopted a value of κ = 15 to calculate L rs during the P X,rise phases.The high quality X-ray and UV data taken during the P X,plat phase of cycle 2 (the third XMM-Newton observation, hereafter X3) can be optimally fitted with a multi-coloured disk (with T in around 60 eV) Comptonized by two coronae (XMM-Newton/X3 in Fig. 3; see also Table 3 in Liu et al. 2023 for the best-fitting results for X3).We estimated a value of κ ∼ 3 using this model.Both the X-ray and UV only show mild variability during the P X,plat phases, indicating that κ will not change significantly.We thus calculated L pl assuming κ = 3 for the P X,plat phases.L fa is poorly constrained.We thus estimated L fa using the M mcd model (T in ∼ 45 eV) obtained by modelling the UV and X-ray emission from the first Swift observation in cycle 2 (Swift5 in Fig. 3).This model resulted in a bolometric luminosity of L bol, sw = 9.0 × 10 43 erg s −1 .Considering that the peak UV magnitude in P X,faint phases is 0.6 mag brighter than that during the P X,rise phases, we thus conservatively estimated L fa by multiplying L bol, sw by a factor of 1.8, which leads to a value of 1.6 × 10 44 erg s −1 .The values of the parameters used to calculate E tot for each cycle can be found in Table 2. To calculate the total mass loss in each cycle, we assumed that half of the tidally disrupted debris returns to the SMBH and that the radiation efficiency is 0.1.We estimated a total released energy (mass loss) of 1.12 (0.13), 0.46 (0.05), 0.18 (0.02), 0.15 (0.017), and 0.12×10 52 erg ( 0.014 M ) for cycles 1, 2, 3, 4, and 5, respectively.A lower limit is given for cycle 5 as the P X,plat phase could be longer then the value quoted in Table 2.

Radio variability
J0456−20 was mostly undetected after 2022 Aug., with a detection at 9 GHz on 2022 Oct. 05 and at 5.5 GHz on 2022 Oct. 07 during the P X,plat phase of cycle 4 (see Fig. 1) with a significance of 7 and 9σ, respectively.In order to improve the sensitivity, we additionally stacked the observations from October 2-7 and detected a faint point source at the coordinates of J0456−20.
The radio observations reported here indicate that the transient radio source associated with the X-ray outbursts in 2022 Mar. and Apr. has also been fading, consistent with the decrease in the peak X-ray flux of each cycle (see Fig. 1).A summary of the ATCA radio observations of J0456−20 is given in Table C.

Discussion
We detected five repeating X-ray flares in J0456−20 using the latest data.In addition, repeating transient radio emission has also been detected in J0456−20.These results provide further evidence that J0456−20 is a repeating nuclear transient, making it one of the most promising repeating pTDE candidates.More importantly, our results also revealed rapid evolution of the recurrence time T recur , measured from the P X,rise phases, of the X-ray flares.Specifically, T recur decreased by more than two months between cycles 1 and 2. It continued to decrease by roughly 40 days between cycles 2 and 3.Such a rapid change is likely to have ceased, as suggested by an almost constant T recur (∼190 days) measured from the latest three cycles.Evidence for the evolution of T recur has also been found using the values measured from the P X,drop phases (Appendix B and Table 1).However, the changes in T recur are less dramatic than those measured from the P X,rise phases, which may attributed to the changes in the duration of the other phases (see Table 2).In this work, T recur values derived from the P X,rise phase were used.
The evolution of T recur has been reported only in a few repeating pTDE candidates.For instance, ASASSN-14ko showed a decrease in the periods with a period derivative of around −0.0026 (Payne et al. 2022;Huang et al. 2023), which is much shorter than that found in J0456−20 ( −0.2).The X-ray flares in HLX-1 initially showed a quasi-periodic T recur of around 1 yr.Then, T recur increased by about one month in 2013 (Godet et al. 2014) and continued to increase until 2018, after which no X-ray outbursts were detected (Webb et al. 2023).Unlike the case of HLX-1, we found no evidence for an increase in T recur in J0456−20 as of now.As suggested by Godet et al. (2014), the evolution of T recur can put strong constraints on the initial mass, the mass loss, and the orbital parameters of the star.
L13, page 5 of 13 A repeating pTDE is favoured to explain the long-term multiwavelength light curve of J0456−20 (Liu et al. 2023).We thus performed simulations to test if the changes in T recur , ∆P, can be explained by pTDEs.We made a grid of hydrodynamics simulations, using the moving-mesh code AREPO (Springel 2010;Weinberger et al. 2020;Pakmor et al. 2016), to examine the change in the orbital period of remnants produced in pTDEs of main-sequence stars by BHs with a mass of M BH = 10 5 M .We considered solar-metallicity main sequence stars with masses of M = 1, 2, and 3 M , and a core hydrogen mass fraction of 0.01 (terminal age) and 0.3 (middle age), evolved using the 1D stellar evolution code MESA (Paxton et al. 2013(Paxton et al. , 2015(Paxton et al. , 2019(Paxton et al. , 2011)), imported into AREPO with 0.5M cells3 .We also considered a wide range of the pericentre distance of r p , 0.1 r p /r t 1.2 (tidal radius r t = (M BH /M ) 1/3 R ), encompassing scenarios from the full disruption to no mass loss.We varied the pericentre distance for a given M .Meanwhile, we fixed the orbital period of the original orbit to be 300 days, so that the stellar orbit in each simulation would have a different eccentricity (e 0.99).The initial separation between the black hole and the star is 5 r t .We followed the evolution of the remnant after the first pericentre passage of the original star, using the Helmholtz equation of state (Timmes & Swesty 2000) until the post-disruption orbital parameters do not evolve, which occurred when the separation between the black hole and the remnant is 5r t .We verified that the total energy in all simulations was conserved within a fractional error of 10 −5 .We note that a rapid decrease in T recur requires a BH mass of around 10 5 M in our simulations, which were run with a limited range of parameter space.Our simulations with a higher BH mass of 10 6 M cannot reproduce T recur observed in J0456−20.The required BH mass of 10 5 M is much smaller than the value quoted in Liu et al. (2023), which is around 10 7 M .However, as cautioned in Liu et al. (2023), the values of M BH measured from the M BH − σ relation and the σ 2 rms − M BH relation exhibit notable differences and have large uncertainties.Thus, a M BH on the order of 10 5 M could still be possible for J0456−20.
Figure 4 depicts ∆P as a function of the original stellar mass, M , and the fractional mass loss, ∆M/M .The general trend indicates that ∆P decreases as ∆M/M increases until the fractional mass loss exceeds a critical value ∆m c , roughly ≈0.7−0.8.Above the critical mass loss, ∆P starts to increase with ∆M/M .This trend was observed for parabolic pTDEs in Ryu et al. (2020).However, the values of ∆P strongly depend on the internal structure of the star (i.e.mass and age).For pTDEs of middle age stars, ∆P is negative (positive) when ∆M/M is below (above) ∆m c , meaning the remnants become more (less) bound than that of the original star before the TDE.For this case, ∆P is at most −10 days.However, ∆P is negative across a wider range of ∆M/M and can be as large as −90 days for pTDEs of terminal age stars.Most notably, the large ∆P (i.e.∼−70 days) observed in J0456−20 between cycles 1 and 2 can be reproduced if the original star is a 1 M terminal age star and loses nearly 80-90% of its mass.Although we have not explored the entire parameter space of pTDEs, our simulations suggest that the observed decrease in T recur may be explained by a severe pTDE of a main sequence star near the terminal age.The inferred mass loss (0.8−0.9 M ) is much higher than that estimated for cycle 1 (∼0.13M , Sect.3.3 and Table 2) of J0456−20.We note that this discrepancy can be alleviated if the radiation efficiency in J0456−20 is much lower than the assumed value of 0.1.It is important to also emphasise that our simulation result merely suggests pTDE is a plausible mechanism for generating a transient like J0456−20 and does not rule out other potential mechanisms.For instance, Linial & Quataert (2024) summarized several plausible origins for observed period evolution in repeating nuclear transients.They suggested that the period evolution in ASASSN-14ko is consistent with orbital decay induced by hydrodynamic drag as the star passes through an accretion disk (see also Zhou et al. 2024).The repeating flares in ASASSN-14ko could then be powered primarily through dragging-induced stripping of mass from the star.This scenario, however, is unlikely to be the dominant process in J0456−20, as it requires an accretion disk with mass larger than 10 M (Eq.( 20) in Linial & Quataert 2024, assuming M BH = 10 5 M ) around r p to explain the observed changes in T recur in J0456−20.

Summary
In this letter, we analyse new multi-wavelength observations for the promising repeating pTDE candidate J0456−20.We detected five repeating X-ray flares and repeating transient radio emission from J0456−20, providing additional strong evidence that J0456−20 is a repeating nuclear transient.In addition, the latest X-ray data also reveals changes in the recurrence time, T recur , of the X-ray flare.We found that T recur initially decreased rapidly from ∼300 days to ∼230 days and it continues to decrease by roughly 40 days per cycle, with an indication of constant values of ∼190 days in the latest cycles.Our hydrodynamic simulations show that the large decrease in T recur can be explained in the pTDE scenario, provided that the original star is a 1 M terminal age star with an initial fractional mass loss of around 80-90%.Our results suggest that precise estimations of T recur in repeating pTDEs can provide additional constraints on the initial mass of the disrupted star and mass loss during each passage.They also indicate that repeating pTDEs could be effective tools to probe the stellar and gas dynamics around SMBHs beyond our own Galaxy.
L13, page 6 of 13 Appendix C: Details of the radio and X-ray observations Fig.1.Long-term X-ray and UV light curves for J0456−20.The coloured regions represent the four phases: the plateau phase (P X,plat , light cyan), the rapid drop phase (P X,drop , light blue), the faint phase (P X,faint , light yellow), and the rising phase (P X,rise , light green).Upper panel: red points with error bars are the unabsorbed rest-frame 0.2−2.0keV X-ray light curve from eROSITA (hexagons), Swift/XRT (squares), NICER (circles), XMM-Newton (stars), and Chandra (diamonds).The error bars indicate 90% uncertainties.The points with downward arrows represent the 3σ flux and luminosity upper limits.The points with blue colour are the data used to model the profiles of the P X,rise phase.The green dashed lines show the best-fitting power-law model for the five X-ray rising phases.The grey shaded regions mark the 1σ uncertainty of the model.Bottom panel: UV light curve from Swift/UVOT UVM2 (red squares).The error bars mark the 1σ uncertainties.Squares with downward arrows indicate 3σ upper limits.The vertical lines mark the dates of the ATCA radio observations (black dashed-dotted: non-detections; blue dashed: detections).

Fig. 4 .
Fig. 4. Change in the orbital period ∆P (in days) for remnants in pTDEs of main sequence stars with mass of M = 1, 2, and 3 M in hydrodynamics simulations, as a function of the fractional mass loss ∆M/M .The original stars are Solar metallicity main sequence stars with a core hydrogen mass fraction of X H 0.01 (Terminal age: solid lines) and 0.3 (Middle age: dashed lines).The simulations suggest that ∆P in severe pTDEs of terminal-age main-sequence stars can be compatible with the change in T recur between cycles 1 and 2 ( −70 days, grey horizontal line) of J0456-20.

Fig. C. 1 .
Fig. C.1.Evolution of the radio flux density.The error bars mark the 1σ uncertainties.The downward arrows represent the 3σ upper limits.The black circle shows the flux density at 5.5 GHz measured from the stacked observation from 2023 Mar.The light cyan regions indicate the P X, plat phase in each cycle.

Table 1 .
Results of the X-ray rising phase modelling and estimations of T recur .

Table 2 .
Values of the parameters used to calculate the total release energy (E tot ) and mass loss (∆M) in each cycle.Notes.t s is the start date of the cycle.∆t rs , ∆t pl , and ∆t fa are the duration for the P X,rise , P X,plat , and P X,faint phases, respectively.The estimated values for E tot and ∆M are also listed.
Table C.1 lists the ATCA radio observations for J0456−20.J0456−20was detected only in the P X, plat phase during cycles 3 and 4. The long-term radio variability is shown in Fig. C.1.The details of the X-ray observations and the X-ray spectral fitting results are listed in Table C.2.