Delayed and Fast-rising Radio Flares from an Optical and X-Ray-detected Tidal Disruption Event in the Center of a Dwarf Galaxy

AT 2018cqh is a unique tidal disruption event (TDE) discovered in a dwarf galaxy. Both the light-curve fitting and galaxy scaling relationships suggest a central black hole mass in the range of 5.9 < logM BH/M ☉ < 6.4. The r-band peak luminosity is ∼ 1043 erg s−1, making AT 2018cqh relatively faint among known optical TDEs. A delayed X-ray brightening was found around 590 days after the optical discovery but shows an unusually long time rising to peak over at least 558 days, which could be coming from delayed accretion of a newly forming debris disk. We report the discovery of delayed radio flares around 1105 days since its discovery, characterized by an initial steep rise of ≳175 days, a flattening lasting about 544 days, and a phase with another steep rise. The rapid rise in radio flux coupled with the slow decay in the X-ray emission points to a delayed launching of outflow, perhaps due to a transition in the accretion state. However, known accretion models can hardly explain the origins of the secondary radio flare that is rising even more rapidly in comparison with the initial one. If confirmed, AT 2018cqh would be a rare faint TDE in a dwarf galaxy exhibiting optical, X-ray, and radio flares. We call for continued multifrequency radio observations to monitor its spectral and temporal evolution, which may help to reveal new physical processes that are not included in standard TDE models.


INTRODUCTION
It is now widely accepted that most, if not all, massive bulge-dominated galaxies harbor supermassive black holes (SMBH, M BH > ∼ 10 6 M ⊙ ) in their nuclei (e.g., McConnell & Ma 2013).A population of intermediate-mass black holes (IMBHs, M BH ∼ 10 4 − 10 6 M ⊙ ) likely exists, and may live in the centers of dwarf galaxies (M ⋆ < ∼ 10 9 M ⊙ , Greene 2012; Reines et al. 2013).However, identifying BHs in dwarf galaxies and measuring their masses (if present) are not trivial, as they are typically faint and the gravitational influence is expected to be small (e.g., Reines 2022).When a star passes too close to an SMBH, it can be squeezed and torn apart once the tidal force of the SMBH exceeds the star's self-gravity (Stone et al. 2019).Such tidal disruption events (TDEs) can generate luminous flares typically peaking in X-rays and ultraviolet, as a fraction of the disrupted stellar debris falls back and gets accreted by the BH (Rees 1988;Gezari 2021), providing a direct way to probe the SMBHs in otherwise quiescent galaxies (Mockler et al. 2019).
Corresponding author: Xinwen Shu xwshu@ahnu.edu.cn The first TDE candidates were identified as soft X-ray outbursts by the ROSAT all-sky Survey, which are thought to connect with thermal emission from a newly formed accretion disk (e.g., Bade et al. 1996;Saxton et al. 2020).Thanks to the development in wide-field survey capabilities, especially those at optical bands, dozens of TDEs have been identified, making it possible the demographics studies such as correlations between light curve properties, host galaxies, volumetric rates, and luminosity function (van Velzen et al. 2021;Hammerstein et al. 2023;Yao et al. 2023).While most optically-selected TDEs are faint in X-rays within the first few months of discovery, some show the late-time Xray brightening (e.g., Gezari et al. 2017;Shu et al. 2020;Guolo et al. 2023), which can be attributed to the delayed onset of accretion (Piran et al. 2015) or ionization break out of X-ray radiation from the obscuration by optically thick outflows in the early phase (Metzger & Stone 2016).With a flux-limited TDE sample discovered by the Zwicky Transient Facility (ZTF, Bellm et al. 2019) over 3 years, Yao et al. (2023) inferred a flat BH mass function in the regime of 10 5.3 < ∼ (M BH /M⊙) < ∼ 10 7.3 , indicating that IMBHs can be revealed with TDEs.Particularly, the short rise time and fast evolution from TDEs in dwarf galaxies are possibly the signatures of IMBHs (Angus et al. 2022).
While the growing number of TDEs is discovered in widefield optical surveys, rapid follow-up observations have led only a few detections (Alexander et al. 2020).The radio detection rate appears to increase with observations on longer timescale of years since the discovery (Cendes et al. 2023).Several scenarios have been proposed to explain this latetime radio brightening, including a delayed launching of the outflow compared to the time of debris fall-back (Horesh et al. 2021a), decelerating of an off-axis jet launched at the time of disruption (e.g., Giannios & Metzger 2011;Matsumoto & Piran 2023), propagation of the outflow in an inhomogeneous medium (e.g., Nakar & Granot 2007), outflow-cloud interaction (Mou & Wang 2021;Mou et al. 2022), and break out of the choked precessing jets from the accretion disk wind (Lu & Quataert 2023a;Teboul & Metzger 2023).Discriminating between these models will help to determine dependence of jet production on the accretion rate, and/or diagnose the density and its radial structure of circumnuclear medium (CNM).
SRGe J023346.8-010129 was reported as a candidate TDE in a dwarf galaxy (z = 0.048) by SRG/eROSITA (Bykov et al. 2024) on 2019 Nov 13.Prior to the X-ray discovery, the object has also been named as an optical transient by Gaia Alerts Team (Gaia18bod) on 2018 June 16, but was not classified.We will use its TNS ID of AT2018cqh as the transient's name throughout.If the optical transient records the time of tidal disruption, this suggests a delay of X-ray brightening by ∼590 days.Here we report the detection of delayed and rapidly rising radio emission from AT2018cqh, about 1105 days after the optical alert.The observations and data reductions are described in Section 2. In Section 3, we present the detailed analysis of optical light curves, radio flux and SED evolution properties.Discussion on the origins of delayed radio and X-ray emission from AT2018cqh is given in Section 4. We summarize the results in Section 5. We adopt a cosmology of Ω M = 0.3, Ω λ = 0.7, and H 0 = 70 km s −1 Mpc −1 when computing luminosity distance.

Optical photometric and spectral data
As shown in Figure 1, we collected the optical light curves of AT2018cqh obtained by ZTF 1 and Gaia (from its Alerts website2 ).ZTF detects a prominent flare at both its g-, rand i-bands, followed by a fading back to the baseline level in ≈200 days (see also, Bykov et al. 2024).While the rising phase was missed by ZTF observations, it was caught by Gaia observations.The first flux rising epoch (MJD=58285) was set to be the discovery time of optical flare, which is on 2018 June 16.Using this discovery time and the occurrence time of the X-ray brightening from Bykov et al. (2024), we estimated a more precise time delay between the optical and the X-ray flares to be ≈590 days.We measure an offset between the transient position reported in the ZTF observations during the optical flare (RA = 02 h 33 m 46.s 9308 and DEC = -01 • 01 ′ 28.′′ 3009) 3 and the host optical centroid reported by the Gaia DR3 (RA = 02 h 33 m 46.s 9339 and DEC = -01 • 01 ′ 28.′′ 3742, Gaia Collaboration et al. 2021), which is 87.1 milliarcseconds4 .This corresponds to a physical offset of 82.5 pc at the redshift of AT2018cqh, making it consistent with a nuclear origin.We also examined the light curves of AT2018cqh from the Asteroid Terrestrial Impact Last Alert System (ATLAS), which confirm the optical flare but the sampling is sparse.Hence, we do not consider the ATLAS data in the following analysis.
Two optical spectra were acquired for AT2018cqh, including archival one from SDSS DR7 (observed on 2000 Oct 03) and one from our own spectroscopic follow-up with Double Beam Spectrograph (DBSP) on the 200-inch Hale telescope at Palomar Observatory (Oke & Gunn 1982), which was taken on 2023 Oct 6, 1938 days since the optical discovery.We used the D55 dichroic which splits the incoming photons into the 600/4000 (lines/mm) grating for the blue side, and 316/7500 grating for the red side.The grating angles were adjusted to achieve a nearly continuous wavelength coverage from 3300 to 10000 Å .We reduced the P200/DBSP spectrum with the python package Pypeit (Prochaska et al. 2020a,b), which can highly automatically implement the standard reduction procedure for long-slit spectroscopic observations.Figure 2 shows the post-flare P200 spectrum as compared with the pre-flare SDSS spectrum of the host.We modelled the two spectra with the python package BADASS (Sexton et al. 2021) and the best-fitting models are also shown in the figure.No significant change in the spectral features, e.g., continuum and emission lines, is observed before and after the transient event, indicating that either any optical signatures had faded by the time of our follow-up observation, or there is no associated emission-line echo.The latter scenario seems consistent with non-detection of midinfrared echo from the WISE light curve (Bykov et al. 2024).

Radio data
We searched for the radio emission from AT2018cqh using the data from the Very Large Array Sky Survey (VLASS, Lacy et al. 2020).VLASS is an on-going S-band (2-4 GHz) multi-epoch legacy survey aiming at to detect various types  Allison et al. 2022).RACS is a large-area survey in the low frequency at 887.5 MHz covering the entire radio sky south of declination +41 • with typical sensitivities of 0.25-0.3mJy/beam.RACS began observations in 2019 April and is now undertaking its mid-band observations at 1.36 GHz (Duchesne et al. 2023), with a resolution of ∼10 ′′ .By incorporating data from RACS, VAST was designed to detect astronomical phenomena that vary on timescales accessible in the ASKAP imaging mode (from ∼5 s to several years).EMU Pilot Survey covers a total area of 270 square deg and is composed of 10 pointing fields, each  of which was observed for 10 hrs at 943 MHz with an instantaneous 288 MHz bandwidth.The primary goal of EMU is to make a deep (rms noise levels of 10-20 µJy/beam) radio continuum survey of the entire southern sky, extending as far north as +30 • .FLASH is a wide field survey to detect 21-cm absorption lines in the continuum spectra of radio sources at intermediate redshifts, and is planned to cover 80% of the sky at frequencies between 711.5 and 999.5 MHz.We retrieved all the RACS, VAST, EMU, and FLASH survey data currently available through the CASDA archive6 , consisting of 20 individual images observed between 2019 Aug 27 and 2023 Oct 29, with a cadence down to 1 day.While there is no radio emission in the first 11 epochs, a bright radio source was detected after 2021 June 25 whose flux is still rising.This confirms the transient radio brightening of AT2018cqh discovered by VLASS.
To secure the radio detections, we used the IMFIT task in CASA to fit the radio emission component with a twodimensional elliptical Gaussian model to determine the position, integrated and peak flux density.The best-fit radio position from the VLASS epoch III observation is RA = 02 h 33 m 46.s 9361 and DEC = -01 • 01 ′ 28.′′ 3760.In compari-son with the position of optical flare given by ZTF (Section 2.1), we found a positional offset of ∼0.′′ 11.This is a factor of three less than the astrometric accuracy of VLASS observations (∼0.′′ 4, Lacy et al. 2020).Therefore, the optical and radio flares are spatially coincident, indicating that they are physically connected.
For non-detections, we report the 3σ upper limit on the flux, based on the map rms at the offsource position, which is in the range 249.3-616.0µJy/beam.The radio emission at the three bands is unresolved and no extended emission is detected.The compactness of radio emission is confirmed by the ratios of integrated and peak flux density, which are in the range 0.95-1.23,with a median of 1.03.For consistency, only peak flux densities are used in our following analysis.The VLASS and ASKAP observation log and flux density measurements are presented in Table 1.Since the VAST, EMU and FLASH observations have little difference in the central frequency, we will adopt the same frequency of 0.89 GHz in our following analysis.

Optical light curve analysis
To characterize the optical light curve properties, we first fit a power-law model with the form: where L 0 is the peak luminosity measured at the peak time t 0 , t D represents the time of TDE, and τ is the timescale of luminosity decline.Note that only the data collected from the ZTF r-band and Gaia G-band observations are considered, as they have the same central wavelength, and the Gaia data detect an important rise to peak phase.The best-fit model results in a power-law index of p = 2.14 +0.31  −0.24 and a time of disruption t D = −15 +4.7  −8.4 days (relative to MJD 58285).Under this model the implied rise-time-to peak of t rise = t 0 − t D ≈ 37 days.Fixing the decay index at the canonical value of p = 5/3 for TDEs yields consistent results on the rise-time-to peak.
We further explored whether the optical light curves can be fitted with the Monte Carlo software MOSFiT, which has been applied to model the light curves of optical TDEs (Mockler et al. 2019).The TDE model in MOSFiT assumes that emission produced within an elliptical accretion disk of a TDE is partly reprocessed into the UV/optical by an optically thick layer (Guillochon et al. 2018).We run MOSFiT using a variant of the emcee ensemble-based Markov Chain Monte Carlo routine until the fit has converged by reaching a potential scale reduction factor of <1.2 (Mockler et al. 2019).In Figure 1, we show an ensemble of model realizations from MOSFiT.The model is able to reproduce the data quite well, including the stages of the rise to peak, near the peak, and the steady decline at later times.The best-fit model is that of a black hole of 2.5 +0.7 −0.5 ×10 6 M ⊙ disrupting a lowermass star of ∼0.06 ± 0.01 M ⊙ .The stellar mass is similar to that inferred for other TDEs where a disrupted star with mass near 0.1 M ⊙ is preferred (Mockler et al. 2019).Such a slight preference near 0.1 M ⊙ is likely due to the fact that below this mass the radius of the star is assumed constant in the MOSFiT model, which favored for events in which short possible peak times are required (Mockler et al. 2019).
With the best-fit MOSFiT model, we obtained the monochromatic luminosity at the ZTF r-band of νL ν ∼ 10 43 erg s −1 , placing AT2018cqh at the faint end of the luminosity function of optically-selected TDEs (Lin et al. 2022;Yao et al. 2023).The physical mechanisms that make a TDE faint remain poorly understood.Possible scenarios have been proposed including partial disruption, disruption of a lower-mass star (Blagorodnova et al. 2017), or complex outflow dynamics at low BH mass (Charalampopoulos et al. 2023).We note that the penetration parameter obtained from the MOSFiT fittings is β ≡ R t /R p = 2.02 +0.27  −0.20 , where R t refers to the tidal disruption radius and R p is for the pericenter radius.The large β (>1) indicates a deep encounter which is not compatible with a partial-disruption event.Therefore, the low luminosity could be attributed to a lower mass for the disrupted star and/or a lower-mass black hole, though the detailed underlying emission mechanism remains to be explored in future works.

Radio flux and SED evolution
The radio light curves of AT2018cqh at frequencies of 0.89, 1.36 and 3 GHz are shown in Figure 3 (left panel).From the light curve at 0.89 GHz that is relatively wellsampled, we find a rapid rise at t > ∼ 1100 days since the optical discovery.At earlier epochs between 437 and 804 days, AT2018cqh is observed by ASKAP but not detected.Stacking the individual ASKAP images results in a flux limit of < 0.36 mJy/beam (at 3σ level).The flux density rises by at least a factor of 25 from the non-detections at t ∼ 559 days to a peak at ∼ 1961 days.The actual evolution of radio emission is characterized by a rise time of about 175 days, followed by a flattening for about 544 days, and a rebrightening at ∼ 137 days.This suggests a peculiar flux evolution with changing steep power-law (F ν ∝ t α ) from index α > ∼ 6.6, α > ∼ 0.9 to α > ∼ 29.0.Although the data are sparsely sampled, a similarly steep rise is observed at 3 GHz by VLASS from 833 (days) to 1725 (days), corresponding to α > ∼ 4.2.In Figure 3 (right panel) we show the radio luminosity evolution of AT2018cqh, as well as a comparison to previous radio-emitting TDEs, including jetted TDE Swift J1644+57 and those observed to exhibit late-time rise in the radio emission on timescales of hundreds of days.The radio luminosity of AT2018cqh increases from 1.8 × 10 37 erg s −1 at 559 days to 1.7 × 10 39 erg s −1 at 1725 days, making its evolution on a time scale similar to that of the TDE AT2018hyz (Cendes et al. 2022) and secondary rising phase in the TDE ASASSN-15oi.While the radio luminosity of AT2018hyz increases approximately linearly with time, AT2018cqh appears to display three phases in the radio evolution over the same epochs, with a flattening between two rapid rising phases.Due to the gap in the radio observations of AT2018cqh between ∼ 1280 − 1814 days, it is not clear whether the radio emission has declined in these epochs.Note that the overall luminosity evolution for AT2018cqh is different from that of ASASSN-15oi, which had an initial bump in the light curve at ∼ 180 − 550 days.The flux limit of < 0.36 mJy/beam at 0.89 GHz at earlier epochs between 437 and 804 days indicates that AT2018cqh is not as luminous as ASASSN-15oi over the same epochs.On the other hand, the TDE iPTF16nl has also shown a radio re-brightening but at a much earlier epoch of ≈100 days (Horesh et al. 2021b).Given its more gradual rise in luminosity peaking at only ∼10 37 erg s −1 , the origin of radio emission in iPTF16nl might be different from that in AT2018cqh.Finally, it should be noted that the radio luminosity of AT2018cqh is still at least one order of magnitude dimmer than that of Sw J1644+57 at a comparable timescale (≈1100-2000 days), arguing against a process similar to that powering the radio emission in Sw J1644+57.There is a steadily rising in both peak flux density and frequency between the two epochs.
The multi-frequency radio data obtained for AT2018cqh allow to model its spectral energy distribution (SED), which can in principle be used to constrain physical properties of radio-emitting region, such as an outflow expanding into and shocking the CNM (e.g., Giannios & Metzger 2011;Metzger et al. 2012).Figure 4 shows the radio SEDs constructed using the data taking from quasi-simultaneously ASKAP and VLASS observations, at t ∼ 1246 days and t ∼ 1725 days, respectively.Note that we interpolated the flux at 0.89 GHz to t ∼ 1725 days based on the observed radio light curve at between t ∼ 1814 and t ∼ 1846 days, to make it as quasisimultaneous as possible to the flux at 3 GHz observed by VLASS epoch III.It is clear that the SED exhibits a gradual shift to a higher peak flux density and frequency, which is unprecedented in radio observations of TDEs (Cendes et al. 2023).We fit the SED evolution with the synchrotron emission models in the context of an outflow-CNM interaction, following the same approach outlined in (Goodwin et al. 2022).We assume no contribution to the transient radio emission from the host galaxy as it is not detected in pre-event archival FIRST observations (at least a factor of 5 fainter).The synchrotron emission spectrum is characterized by four parameters, namely F 0 , ν m , ν a , and p, where F 0 is the flux normalization at ν m (the synchrotron minimum frequency), ν a is the synchrotron self-absorption frequency, and p is the energy index of the power-law distribution of relativistic electrons.
As in Goodwin et al. (2022), we use a Markov chain Monte Carlo (MCMC) fitting technique (python module emcee, Foreman-Mackey et al. 2013) to marginalize over the synchrotron model parameters to determine the best-fitting parameters and uncertainties.Due to the limited data points especially that at high frequencies (>3 GHz), we fix the synchrotron energy index to p = 3 (e.g.. Alexander et al. 2016;Cendes et al. 2021).In fact, we find that the derived parameters do not deviate significantly within the 1σ uncertainties if adopting other reasonable values, such as p ≈ 2 − 3.In Figure 4, we show the resulting SED models which provide a good fit to the data.From the SED fits we determine the peak flux density and frequency, F ν,p and ν p , respectively.We find that both F ν,p and ν p indeed increase steadily with time, from 2.47 mJy and 1.42 GHz to 10.6 mJy and 2.48 GHz.Using the inferred values of F ν,p and ν p , we can further assume equipartition to derive the radius of the radio emitting region (R eq ) and kinetic energy (E eq ) using the scaling relations outlined in Barniol Duran et al. (2013).Following the procedures described in Goodwin et al. (2022), we provide constraints for two different geometries, a spherical outflow and a mildly collimated conical outflow with a half-opening angle of ϕ = 30 • , in order to account for possible geometric dependence of outflow evolution.
As shown in Figure 5, assuming the spherical outflow, we find that the radius increases slightly from R eq ≈ 2.04 × 10 17 cm to ≈ 2.34 × 10 17 cm between 1246 and 1725 days.The increase in R eq becomes more rapidly for the case of a mildly collimated conical outflow.Under the assumption of free expansion, this corresponds to an outflow velocity (v/c) of 0.024 (spherical) and 0.056 (conical) for the spherical (conical) geometries, with no sign of relativistic motion.Over the same epochs, the outflow kinetic energy increases by a factor of 3.3 (spherical), from E eq ≈ 9.57 × 10 49 erg to 3.19 × 10 50 erg.The kinetic energy is larger than that of other radio-emitting TDEs with non-relativistic outflows (Cendes et al. 2023).However, different from previous TDEs in which the ambient density profile is found approximately proportional to R −2.5 , we find that the inferred ambient density of CNM in AT2018cqh increases with R eq regardless of the outflow geometry.This may suggest that the outflow enters a high-density CNM structure.Because the radio light curve of AT2018cqh is rising, indicating that the blast wave might be still in the expansion phase, continuous multifrequency radio observations with a higher cadence will enable to better constrain the ambient density profile as a function of radius.

A TDE from a candidate IMBH?
The host galaxy of AT2018cqh is blue with an extinctioncorrected rest-frame u − r color ≈1.07.Bulge-disk decomposition of AT2018cqh has been carried out by Simard et al. (2011), which gives the bulge/total surface brightness ratio of 0.65 ± 0.02 at g-band, and a high Sérsic index of 7.64 ± 0.31.The bulge stellar mass is estimated at log(M bulge / M ⊙ ) = 9.14 +0.07 −0.05 , compared to a total stellar mass of log(M stellar / M ⊙ ) = 9.51 +0.16  −0.10 (Mendel et al. 2014).These measurements indicate a high central concentration of stars, which has been seen within other TDE host galaxies (French et al. 2020).With the derived stellar mass, we can estimate the mass of the central BH to be log(M BH / M ⊙ ) ≈ 5.88 using a scaling region for low-mass galaxies (Reines & Volonteri 2015).Spectral analysis suggests that only narrow emission lines are present in the pre-explosion SDSS spectrum after subtracting the host component.The ratios of the narrow lines place AT2018cqh into the Seyfert (II) regime on the the Baldwin-Phillips-Terlevich (BPT) diagram (Figure 2).This may suggest that the multi-band flares of AT2018cqh could be due to the AGN activity.However, this possibility seems unlikely based on the X-ray properties (Bykov et al. 2024).In addition, the rapid (duration of <1 yr) optical flare can also rule out the normal AGN variability as it is rarely seen in the light curves of AGNs (Drake et al. 2011;Kankare et al. 2017;Zhang et al. 2022).The lack of detectable broad permitted lines prevents us from estimating the central BH mass of AT2018cqh using the conventional linewidth-luminosity-mass scaling relation.In the optical spectral fittings, we measure the stellar velocity dispersion with Gaussian σ ⋆ = 62 ± 10 km s −1 after correcting for the instrumental broadening.Using the M BH − σ ⋆ relation for the low-mass end (Xiao et al. 2011), we estimated a BH mass of log(M BH / M ⊙ ) ≈ 5.99.With an intrinsic scatter of 0.5 dex, this is consistent with a relatively low BH mass of M BH ≈ 5.9 derived using the scaling relations between galaxy stellar mass and BH mass.
The properties of the TDE light curve can potentially be used to probe the BH mass (Angus et al. 2022), which could provide a measurement independent of assumptions about the host galaxy.This is because the luminosity of TDE is expected to follow the fallback rate of the stellar debris with a relationship (Rees 1988): where M 6 is the BH mass in 10 6 M ⊙ , r * and m * are the star's radius and mass in R ⊙ and M ⊙ , and β = R T /R p is the penetration factor (Gezari et al. 2017;Bonnerot & Lu 2020).In Section 3.1, we have shown that when fitted the Gaia and ZTF r-band optical light curve of AT2018cqh using the MOSFit code, a BH mass of log(M BH / M ⊙ ) ≈ 6.42 can be obtained.Because of the sparse sampling of the optical light curves during the peak phase, the actual rise to peak time may be even shorter, yielding a smaller BH mass.Combining with the BH masses estimated from the host galaxy properties, we can constrain the BH mass of AT2018cqh in the range of 5.9 < logM BH /M ⊙ < 6.4, placing it at the high mass end of the domain of IMBHs.Note that if the optical emission comes from process of stream-stream collision (Piran et al. 2015), rather than the accretion process hypothesized in MOSFit, the correlation between the rise time of a TDE and the BH mass still holds as BH .Therefore, although AT2018cqh is a rare TDE whose host galaxy is one of only a small number of dwarf galaxies (e.g., Angus et al. 2022), we can not claim the presence of an IMBH with current data.

Origin of the delayed X-ray flare
AT2018cqh is one of few TDEs that has resolved rise-topeak light curves in both X-ray and optical bands (Gezari et al. 2017;Wevers et al. 2019;van Velzen et al. 2020).The Xray emission exhibits a delayed brightening roughly ∼ 590 days with respect to the peak of optical emission which is also unique among optically discovered TDEs (Guolo et al. 2023).Many recent numerical studies have shown that the infalling stellar debris stream will undergo self-intersections as a consequence of relativistic apsidal precession (Shiokawa et al. 2015;Bonnerot et al. 2017;Lu & Bonnerot 2020), where optical/UV emission could be produced because of shock heating.Following the stream self-interactions, the debris spreads inward and gradually circularizes to form an accretion disk on the timescale of ≃ (5 − 10)t 0 (Shiokawa et al. 2015;Bonnerot et al. 2016), where t 0 is the orbital period of the most bound material (equation ( 1)).Within this picture, there will be a time delay between the debris selfcrossing and onset of disk formation, possibly explaining the observed delay of the X-ray emission in AT2018cqh.For a BH mass of ∼10 6 M ⊙ , the circularization timescale can be estimated as t circ ≃ 200 − 400 days, depending on the orbit eccentricity and penetration parameter (Bonnerot et al. 2016).In a more realistic scenario, if the viscous time (t visc ) is not negligible (the time it takes material to accrete) and t visc > ∼ t circ , the flare is prolonged at the expense of reduced peak luminosity (e.g., Guillochon & Ramirez-Ruiz 2015).These predicted accretion properties seem not at odds with the long rise to peak time and relatively low peak luminosity (L 0.3−2keV ∼ 5.5 × 10 42 erg s −1 ) observed with eROSITA (Bykov et al. 2024).The blackbody radius inferred from the eROSITA observations is R bb ∼ 2 × 10 11 cm, comparable to the Schwarzschild radius (R s = 2GM BH /c 2 ) for a black hole mass of ≈ 10 6 M ⊙ .This suggests that the soft X-ray emission indeed originates from a compact accretion disk.
It has been proposed that if the majority of falling-back debris becomes unbound in a dense outflow, the X-ray radiation from the inner accretion disk will be initially blocked, and may escape at later times as the density and opacity of the expanding outflow decreases Metzger & Stone (2016); Wevers et al. (2019).In the model, efficient circularization of the returning debris is assumed, resulting in rapid onset of disk accretion and reprocessed emission in the optical and UV bands.However, the increase in the X-ray flux of AT2018cqh lasts at least 550 days after the optical flare has decayed to the quiescent level.This is much longer than the time scale for the ionization break out of X-ray radiation for a black hole of M BH ∼ 10 6 M ⊙ (Metzger & Stone 2016).In addition, assuming that the X-rays were produced at the time of optical flare, we fitted the X-ray light curve using the data after the current peak (t >1000 days) with the canonical t −5/3 decline law.Extrapolating the model backwards in time results in a unlikely peak luminosity of > 10 50 erg s −1 , several orders of magnitudes above the Eddington luminosity.On the other hand, the X-ray spectra are dominated by a soft blackbody component whose temperature remains little changed between the eROSITA observations, indicating no clear evidence for the decrease in absorbing column density with the increasing X-ray luminosity as expected in the reprocessing scenario.Therefore, the scenario that the late time X-ray brightening is due to the ionization break out of disk emission is disfavored .

Origin of the delayed radio flare
Upon its radio detection, the steep rise in the flux density at 0.88 GHz (and possibly at 3 GHz as well) between ≈ 175 days, F ν ∝ t α with α = 6.6, is not consistent with the theoretical predictions for an on-axis relativistic jet or a sub-relativistic outflow launched promptly after stellar disruption in AT2018cqh.For instance, the fastest rise in the flux density is F ν ∝ t 3 for an on-axis relativistic jet interacting with circumnuclear material (CNM) with a steep density profile of ρ CNM ∝ r −2.5 (Horesh et al. 2021b).Instead, to reconcile with the observed increase in flux density with the predictions of standard CNM shockwave models, a radioemitting process that occurs at late times should be invoked.
To achieve an ∼ t 3 increase in flux density requires a delayed launch of the outflow by ∼ 600 days after optical discovery.
In comparison with X-ray light curve, the evolution of the radio emission is clearly not paralleled, as the X-ray emission faded away after the peak, while the radio emission was still rising.In the context of TDEs, both theory and simulations suggest that the accretion rate of stellar debris onto a BH can vary by several orders of magnitudes (e.g., Rees 1988;Curd & Narayan 2019).The combined X-ray and radio properties of AT2018cqh appear to be reminiscent of the observed behavior of accretion state transition in X-ray bina-ries (XRBs, Fender et al. 2004).In XRBs, a state transition in accretion occurs when the accretion rate increases above a critical threshold, typically ∼10 − 30% of the Eddington luminosity (Done et al. 2007).During the transition, the X-ray emission gradually becomes disk dominated.Given the peak X-ray luminosity of L 0.3−2keV ∼ 5.5 × 10 42 erg s −1 and BH mass M BH ∼ 10 6 M ⊙ , AT2018cqh is likely accreting at a rate of L Bol /L Edd ∼ 0.1 − 0.5 (depending on the bolometric correction factor).X-ray spectral analysis revealed that the X-ray spectra during the peak phase are dominated by a blackbody emission component (kT bb ∼ 60 eV), with a non-thermal hard tail that accounts for ∼10% of the X-ray flux (Bykov et al. 2024).The non-thermal emission can be described by a powerlaw with Γ = 1.9, likely from the lowluminosity AGN in the quiescent state (Section 4.1).It is therefore possible that a low-hard to high-soft phase transition occurred in AT2018cqh, resulting in the delayed launch of an outflow that led to rapidly rising radio emission at late times.Similar scenarios have been invoked to explain the late-time radio flares in the TDE ASASSN15-oi (Horesh et al. 2021a) and AT2019azh (Sfaradi et al. 2022).However, standard accretion models can hardly explain the following evolution of radio flux after the initial steep rise, including a flattening lasting about 544 days and a phase with another steep rise.
On the other hand, one may consider the possibility that the delayed radio emission from AT2018cqh may be produced by a relativistic jet viewed off-axis, which is potentially relevant for TDEs in which the radio emission is still rising (Matsumoto & Piran 2023;Sfaradi et al. 2023).In this model, the off-axis jet was initially launched at the time of TDE, which remains collimated with the emitting area increasing over time.The evolution of radio emitting region eventually intersects the light of sight to the observer, resulting in a delayed radio flare.On a basis of the best-fit synchrotron model to the radio SED evolution (Figure 4), we find both the peak flux densities and frequencies are increasing over time, with F peak ∝ t 4.2 and ν peak ∝ t 1.8 .Following the formalism of Matsumoto & Piran (2023), the apparent velocity of the radio emitting source is found to evolve with β eq,N ∝ t −0.8 .Therefore, β eq,N will continue to decrease monotonically unless either F peak rises or ν peak decreases more rapidly, and the transition to the Newtonian branch will never happen, disfavoring the off-axis jet as the origin of delayed radio flares.
Recently, Teboul & Metzger (2023) proposed a unified model for jet production in TDEs, which can be used to explain the delayed mildly-relativistic outflow observed in AT2018hyz (see also Lu et al. 2023b).In the model, the late-time radio brightening in AT2018hyz can be attributed to the break out of jet emission that was initially choked by the disk-wind ejecta, and its interaction with the CNM.However, once the decelerating jet expands into the CNM, the ra-dio emission from the shock should follow a SED evolution similar to ASASSN-14li (Alexander et al. 2016), which is inconsistent with what is observed in AT2018cqh (Figure 4).A similar scenario in which an outflow from the TDE interacts with dense clouds in an inhomogeneous CNM seems also less plausible.In this latter case, the peak frequency in the radio SED is predicted to decrease as a function of time, while the peak flux remains almost constant (Bu et al. 2023).Such a SED evolution was not observed in AT2018cqh, at least with the current data.In addition, it would be challenging to explain the non-detection of infrared flares in the context of outflow-cloud interaction model.It should be noted that we have only quasi-simultaneous observations at two frequencies for a given epoch, so the current constraints on the SED evolution (hence F peak and ν peak ) might not be robust.Since the radio flux is still rising, future radio observations covering a broader frequency range will be crucial to explore the exact evolution of peak flux densities and frequencies, allowing to better distinguish between different models in explaining the radio behaviour in AT2018cqh.

CONCLUSION
We present the discovery of delayed radio flare in an optical and X-ray detected TDE occurred in a dwarf galaxy.Both the optical light curve fitting and galaxy scaling relationships suggest a central black hole mass in the range of 5.9 < logM BH /M ⊙ < 6.4.The temporal evolution of radio emission is peculiar, including an initial steep rise of at least 175 days, a flattening lasting about 544 days, and a phase with another steep rise.Although limited in the frequency coverage, the radio SED is found to evolve toward higher peak flux and frequencies over a period of ≈480 days.These properties make it challenging to explain the delayed radio brightening with an off-axis jet launched promptly after the TDE, the break out of a choked jet, or outflow-cloud interaction.The rapid rise in flux density coupled with the slow decay in the X-ray emission points to a delayed launching of outflow, perhaps due to a transition in the accretion state of the black hole.However, none of known accretion models can predict the radio variability behavior after the initial flare, including the flattening and secondary flare that is rising even more rapidly in comparison with the initial one.Since AT2018cqh 's radio emission is still rising, continued multi-frequency monitoring observations are required and crucial to understand the odd spectral and temporal properties of the delayed radio flares.
The data presented in this paper are based on observations made with the Karl G. Jansky Very Large Array, the Australian SKA Pathfinder, the Zwicky Transient Facility, and the European Space Agency space mission Gaia.The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.The Australian SKA Pathfinder is part of the Australia Telescope National Facility which is managed by CSIRO.Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy.This paper includes archived data obtained through the CSIRO ASKAP Science Data Archive, CASDA (http://data.csiro.au).The Zwicky Transient Facility Project is supported by the National Science Foundation under Grant No. AST-1440341.Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been pro-vided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.We acknowledge ESA Gaia, DPAC and the Photometric Science Alerts Team (http://gsaweb.ast.cam.ac.uk/alerts), and the use of the Hale 200-inch Telescope through the Telescope Access Program (TAP), under the agreement between the National Astronomical Observatories, CAS, and the California Institute of Technology.The work is supported by the SKA Fast Radio Burst and High-Energy Transients Project (2022SKA0130102), and the National Science Foundation of China (NSFC) through grant No. 12192220 and 12192221.

Figure 2 .
Figure 2. Left panel: P200/DBSP spectrum observed on 2023 Oct 6, as compared with the archival SDSS spectrum taken on 2000 Oct 3. The corresponding stellar continuum models are also shown (purple and blue).Middle panel: a zoomed-in view of the emission-line profile fittings for the H β , [O III], and Hα+[N II] doublet lines.Gaussian line models are plotted in red.Right panel: The optical classification of AT2018cqh in the BPT diagram based on the emission line ratios of [O III]/Hβ vs. [N II]/H α.The optical spectrum displays Seyfert-like narrow emission-line ratios which have not changed between P200 and SDSS observations.

Figure 3 .
Figure3.Left Panel: Light curves of AT2018cqh in the optical (ZTF r-band and Gaia G-band), X-ray (0.3-2 keV), and radio (0.89, 1.36 and 3 GHz).Note that the optical light curves include the flux contributed by host.It is clear that there is a delayed brightening in the X-rays, while AT2018cqh has faded in the optical to a quiescent level.The radio emission appears even later, for which the flux in still rising in both 0.89 GHz and 3 GHz.For the non-detections, the corresponding 3σ upper limits on flux density are shown.Right Panel: The radio luminosity evolution of AT2018cqh (red), including the upper limits.Since the date of VLASS epoch I observations (2017 Nov 30) is before the time of optical discovery, it was shown for the purpose of illustrating the upper limit on the radio flux.Also shown for comparison are the light curves of the relativistic TDE Sw J1644+57 (dark orange,Cendes et al. 2021), and other three TDEs with late-rising radio emission: ASASSN-15oi (blue; Horesh et al. 2021a), AT2018hyz (green;Cendes et al. 2022) and iPTF16fnl (gray;Horesh et al. 2021b).

Figure 4 .
Figure4.The radio SEDs for two epochs which have quasisimultaneous observations at different frequencies.For the nondetections, the corresponding 3σ upper limits on flux density are shown.The red and green lines represent the best-fit to each SED from our MCMC modeling (Section 3.2), which are the model realizations on a basis of 500 random samples from the MCMC chains.There is a steadily rising in both peak flux density and frequency between the two epochs.

Figure 5 .
Figure 5.The evolution of radius (left), kinetic energy (middle), and ambient density (right) as a function of time from our equipartition analysis assuming a single outflow is launched into the CNM around the time of optical discovery.Red and blue filled circles indicate parameters for a spherical homogeneous and a collimated, conical outflow, respectively.

Table 1 .
Summary of the radio observations of AT2018cqh The upper limit was measured by stacking the VAST images observed between 2019 Aug 27 and 2020 Aug 28. ‡