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Delayed radio flares from a tidal disruption event

Abstract . Radio observations of tidal disruption events (TDEs)—when a star is tidally disrupted by a supermassive black hole (SMBH)—provide a unique laboratory for studying outflows in the vicinity of SMBHs and their connection to accretion onto the supermassive black hole. Radio emission has been detected in only a handful of TDEs so far. Here we report the detection of delayed radio flares from an optically discovered TDE. Our prompt radio observations of the TDE ASASSN-15oi showed no radio emission until the detection of a flare six?months later, followed by a second and brighter flare years later. We find that the standard scenario, in which an outflow is launched briefly after the stellar disruption, is unable to explain the combined temporal and spectral properties of the delayed flare. We suggest that the flare is due to the delayed ejection of an outflow, perhaps following a transition in accretion states. Our discovery motivates observations of TDEs at various timescales and highlights a need for new models. You have full access to this article via your institution. Download PDF Download PDF Main . Synoptic time-domain surveys have been increasingly fruitful in discovering nearby tidal disruption events (TDEs) over the past several years 1 . These transient events, which are interpreted as stars being tidally disrupted by supermassive black holes 2 (SMBHs), may provide a window into many diverse astrophysical questions. Uncovering dormant SMBHs is only one of the revelations made through these events. The complex physical process of the accretion of matter onto a SMBH is another. The nature of TDEs and their emission mechanisms are still puzzling. For example, what generates the ultraviolet (UV) and optical emission? Is it a process related to accretion or maybe internal shocks in streams of stellar debris 3 , 4 ? Does an accretion disk form around the SMBH, and if so, when and in which geometry 3 , 5 , 6 ? Panchromatic studies of a growing number of events hold the key to unlocking many of the remaining open questions. An example is the progress made in recent years by uncovering two potentially distinct sub-classes of TDEs: (1) thermal TDEs, discovered via their optical/UV emission, and (2) relativistic events such as Swift J1644+57 (refs.? 7 , 8 , 9 ), which exhibit high-energy non-thermal emission. Until recently, thermal TDEs were not seen to exhibit strong radio emission, but this changed with the discovery of a prompt radio signal 10 , 11 from the nearby event ASASSN-14li (ref. 12 ). The weak radio emission has been interpreted as originating from a sub-relativistic shockwave launched into the SMBH circumnuclear material (CNM), driven by either outflows from an accretion disk 10 or by the unbound stellar debris travelling away from the central SMBH 13 , 14 (another plausible explanation is that the outflow is a jet that slowed down 11 ). On the other hand, Swift J1644+57 exhibited a strong radio afterglow 15 , 16 , orders of magnitude more luminous than the emission in ASASSN-14li, originating from a relativistic jet that is viewed on-axis. The field of TDE radio observations has seen further developments in recent years. Very long baseline radio observations of an infrared (IR) transient that is considered to be a TDE candidate (Arp?299B-AT1), revealed a radio jet 17 . Moreover, a recent radio transient, discovered independently of detection at other wavelengths, is also attributed to a TDE 18 . A recent excitement is the discovery of a coincident neutrino with an optically discovered TDE 19 , AT?2019DSG, which also exhibits radio emission similar to that of ASASSN-14li. These past discoveries represent other pieces of the puzzle, which will hopefully allow a coherent picture of the overall physical processes in play to be built. In search of similar radio emission from other nearby TDEs, we carried out radio (6–22?GHz) observations using the Karl Jansky Very Large Array (VLA) telescope and, recently, the Arcminute Microkelvin Imager (AMI) telescope of a number of optically discovered TDE candidates at various timescales from early to late times (A. Horesh et al., manuscript in preparation). Although most of the observations resulted in null detections, a single event—named ASASSN-15oi—revealed a delayed radio flare, months after its optical discovery, followed by (even more surprisingly) a second flare years later. ASASSN-15oi was discovered in optical wavelengths by the All-Sky Automated Survey for SuperNovae (ASASSN 20 ) on 2015 August 14 (ref.? 21 ) at a distance of 216?Mpc. At the time of discovery it had an optical magnitude of V ?≈?16.2, whereas previously it was not detected on 2015 July 26 down to V ? ?17.2, suggesting that it was discovered relatively young. An optical spectrum obtained by the PESSTO collaboration 22 on 2015 August 20 provided the initial classification of ASASSN-15oi as a TDE 23 . Multiple groups then launched panchromatic monitoring campaigns. In the optical, additional spectroscopy of ASASSN-15oi confirmed the initial classification of the event as a TDE 21 and showed a rapid spectral evolution (compared with other optically discovered TDEs). A search for high-energy emission by the Neil Gehrels Swift Observatory initially showed no significant emission 24 . However, deeper X-ray observations revealed what first seemed to be a non-varying weak X-ray source that later increased in flux 25 , 26 . In the radio, we launched a monitoring campaign using the VLA. Discovery of a delayed radio flare . Our radio campaign began on 2015 August 22, 8?days after the optical discovery. Our initial observation, performed at both 5?GHz and 22?GHz, resulted in null detections with 3 σ limits of ? 33?μJy (1.8?×?10 27 ?erg?s ?1 ?Hz ?1 ) and ~60?μJy (3.3?×?10 27 ?erg?s ?1 ?Hz ?1 ), respectively. Despite the non-detections, we continued to observe the source, motivated by some theoretical models that suggest a delay between the TDE optical flare and the formation of the accretion disk 3 , 27 , 28 . We observed ASASSN-15oi twice more on 2015 September 6 (Δ t ?=?23?days, where Δ t is the time since optical discovery) and November 12 (Δ t ?=?90?days); observations that also resulted in null detections, until the discovery of significant radio emission on 2016 February 12 (Δ t ?=?182?days; Fig. 1 and Extended Data Fig. 1 ), with an approximate flux density of ~1,300?μJy (7.3?×?10 28 ?erg?s ?1 ?Hz ?1 ) at a peak frequency of ~9.6?GHz. Once ASASSN-15oi was detected in the radio, we embarked on a follow-up observing campaign, carrying out observations in multiple radio frequencies to characterize the properties of the broadband radio spectrum and its evolution. Fig. 1: The radio luminosity of a handful of TDEs as a function of time. Note that the time here is after optical discovery (in some cases the actual disruption time, such as in ASASSN-14li, is poorly constrained, thus the light curves of these events may shift in time compared with others). The radio measurements (luminosity densities L ν ) were at a frequency of ~5?GHz (data for AT?2019DSG is at 8.5?GHz). Empty markers represent a phase where the emission is optically thick, whereas filled markers represent optically thin emission. The radio emission of ASASSN-14li (ref.? 10 ) and AT?2019DSG (ref.? 19 ) shows the typical evolution of a shockwave in a CNM, as the emission peaks when the optical depth is about unity at the relevant frequency and thereafter declines (similar to what is also seen in radio supernovae). The radio emission from the radio discovered TDE, CNSSJ0019 (ref. 18 ), exhibits similar behaviour as in the two latter TDEs (the radio peak is not shown here as it is at lower GHz frequencies). The radio observations of XMMSL1 J0740-85 (ref.? 60 ) and IGR J12580+0134 (ref.? 61 ) took place only at later times, when the radio emission is already optically thin and fading. The data available for ARP?299B-AT1 (ref.? 17 ) suggests that the radio emission originated, in that case, from a relativistic jet launched promptly after disruption. In contrast, our radio observations of ASASSN-15oi early after discovery and up to 90?days later resulted in null detections (3 σ limits are represented by red vertical arrows). The delayed radio flare we detect later (red squares) has a peculiar evolution. The light red square at Δ t ?≈?1,400?days is the recent detection of a rebrightening emission from ASASSN-15oi at 3?GHz (lacking spectral information). We also present past events with no detected radio emission (detection limits shown as grey triangles). The emission from Swift J1644+57 (not shown) is a few orders of magnitudes brighter than the emission detected from the TDEs presented in here, and slowly rises in the first 100?days after discovery. Full size image The position of ASASSN-15oi was recently observed separately from our follow-up observing campaign as part of the Very Large Array Sky Survey (VLASS 29 ). Inspection of the quick-look images (produced by the National Radio Astronomy Observatory (NRAO)) reveals a rebrightening of the radio emission at 3?GHz on 2019 July 01 (almost 4?years after the initial optical discovery), to a flux density level of ~8,000?μJy (4.4?×?10 29 ?erg?s ?1 ?Hz ?1 ). The peculiar evolution of the delayed radio flare . Our follow-up campaign (which includes six additional observing epochs since the radio discovery) reveals an unusually evolving radio spectrum (the full spectral evolution is presented in Extended Data Fig. 2 ). During the first 2?weeks after the initial detection of the radio emission, the peak frequency slowly evolved, from ν p ?=?9.6?±?0.9?Ghz to ν p ?=?8.6?±?0.4?GHz (see ‘Radio observations’ in the Methods), while the peak flux density simultaneously dropped by ~25%. In contrast, at later times, the radio flare evolved quickly. As seen in Fig. 2 , the peak frequency of the radio emission decreased to <3?GHz only 2?months after radio discovery. Fig. 2: The evolution of the peak flux density and frequency of the delayed radio emission from ASASSN-15oi. During the first 2?weeks after the radio discovery, the peak frequency evolves slowly, whereas in the 6?weeks that followed, the peak frequency evolves rapidly to an unknown frequency below 3?GHz (the peak limit marked by the blue arrow; error bars show 1 σ uncertainties from the peak best-fit analysis). For comparison, we show the evolution of the peak in both ASASSN-14li (ref.? 10 ) and Swift J1644+57 (ref.? 15 ). This type of diagnostic plot of the radio peak is used to follow the evolution of radio flares from AGNs/blazars. The peak behaviour of ASASSN-15oi is similar to the observed late-stage evolution of two AGN/blazar flares. The inset shows a late-time phase in the evolution of the radio flare from the blazar CTA?102 (ref. 48 ). We emphasize, however, that this behaviour is not observed in all AGN/blazar flares. Full size image Another oddity is the shape of the radio spectrum. In general, the radio spectral peak ( ν p ) observed in transient phenomena is due to either the minimum energy of the emitting electrons (in which case the flux density at ν ?}\,{\nu }_{\mathrm{p}}}\propto {\nu }^{{\alpha }_{\mathrm{syn}}}\) ), is a function of the power-law index ( p ) of the energy distribution ( N e ) of the emitting electrons ( N e ∝ E ? p ). For ASASSN-15oi, the spectral index is initially in the range ?2?≤? α syn ?≤??1, which is steeper than the spectral index observed in both Swift J1644+57 and ASASSN-14li. Later, when the peak flux density decreased to below 3?GHz, the optically thin spectrum became shallower ( α syn ? ??0.6; which is also shallow compared with ASASSN-14li and Swift J1644+57). The nature of the delayed radio flare . The delayed radio emission we observe from the TDE ASASSN-15oi, its properties and evolution raise several key questions. Can the late-time radio emission and the earlier null detections be reconciled under a standard CNM shockwave model? If so, does it originate in a relativistic jet, such as observed in Swift J1644+57 or perhaps an off-axis jet that became visible only at late times? Or does it point to a sub-relativistic shockwave (driven by accretion disk outflows or stellar debris), such as the one observed in ASASSN-14li? Does a delayed radio detection require a delayed outflow formation? To address these questions, first we tested the standard dynamical models that have been used to explain the radio emission from TDEs 31 , 32 , 33 , 34 . In these models, a single shockwave (either relativistic or sub-relativistic) is launched into the CNM around the time of optical discovery. Both the optically thick and optically thin emission have a power-law temporal evolution with a range of values for the power-law indexes (depending on the properties of the shockwave; see ‘Temporal evolution of the radio emission’ in the Methods). The steep rise of the observed radio emission from non-detection on Δ t ?=?90?days to detection on Δ t ?=?182?days requires that the temporal evolution of the flux density is steeper than F ν ∝ t 4 . In the analytical models that we explore, the fastest increase in the rate of the emission occurs in the relativistic jet case. When an on-axis relativistic jet is interacting with CNM profiles in the range between a constant density ρ and ρ CNM ∝ r ?2.5 (which is the steepest density profile found so far in TDEs 35 ), the fastest rise in the flux density is F ν ∝ t 3 , when the emission is optically thick (for comparison, the optically thick radio emission in a sub-relativistic supernova usually results in shallower rise of F ν ∝ t 2.5 ). Extrapolating backwards in time from our initial radio detection in the C band on 2016 February 12 results in a predicted flux density of 0.15?mJy on 2015 November 12, well above our detection limit (see ‘Temporal evolution of the radio emission’ in the Methods). A steeper rise can be obtained if the relativistic jet is observed off-axis. Exploring numerical models of such a scenario 36 , we find that it cannot account for both the steep rise from non-detection to detection, and for the subsequent spectral and temporal evolution of the detected radio emission (see ‘Temporal evolution of the radio emission’ in the Methods). Another possible model, used to explain the rebrightening of radio emission at late times (such as the one observed in the relativistic TDE Swift J1644+57; ref. 16 ) is a structured relativistic jet 37 , 38 launched promptly after stellar disruption. In this case, the slower parts of the jet, will provide an additional power source for the observed emission in late times. However, even in this case, the steepest rise due to such a jet structure will result at most in an ? t 3 increase in flux density, which is not enough to explain the steep rise in the initial radio flare that we observed. The big jump in flux density that we observed from null detection to detection thus does not seem to favour the predictions of the existing models that we discussed above, which invoke the interaction of a relativistic (on or off-axis) or sub-relativistic outflow with the CNM promptly after the disruption of the star, and therefore points to a radio-emitting process that occurs at late times. The temporal evolution of the optically thin emission, following its temporal peak, is inconsistent with the above models. Whether we consider an on- or off-axis relativistic jet or a sub-relativistic outflow, the optically thin radio emission is expected to have a power-law temporal evolution ( F ν ∝ t β ) with a predicted 13 , 34 power-law index of ?1?≥? β ?≥??3. However, here we saw a varying, steep temporal evolution, where the temporal power law reaches a value β ?20, years after the onset of the TDE, is not expected in any of the above scenarios. Even when considering a radio rebrightening in a structured jet model 37 , 38 , none of these models predict a rebrightening of the flux density by more than an order of magnitude over a timescale as long as observed here. Moreover, explaining a rebrightening at late times with a structured jet that has been launched early on requires that the initially observed delayed late-time emission is explained by this outflow as well. However, as we have shown, it cannot. A secondary flare years after the onset of the TDE is therefore not expected in any of the above scenarios. One possibility is that the rebrightening is driven by the same process responsible for the initial delayed flare we detected. One could also consider the possibility of a recurring TDE flare due to repeated partial disruptions of a star 40 , 41 . Another possible explanation is that the TDE occurred around a binary SMBH system. In such a scenario, the accretion rate may be highly variable with multiple peaks that could appear several years after the initial disruption 42 . Still, none of these proposed theoretical explanations offer clear predictions for late-time radio emission that can be tested against our measurements. Unfortunately, further information about the 2019 rebrightening event is also limited (K. Alexander et al., manuscript in preparation). Late-time UV and optical observations show no signature of any renewed activity or a secondary flare during the first year after the optical discovery of ASASSN-15oi (ref. 26 ). UV emission is still detected from the TDE after the time when we discovered the delayed radio flare (with observations ongoing up to a year after optical discovery), and is consistent with a simple power-law decline of the UV emission detected at early times. A series of optical spectra taken starting at Δ t ?=?301?days and up to Δ t ?=?455?days shows that the broad emission lines, which are typical of TDEs and detected early on, have diminished, and no new emission lines are present 26 . We now compare the evolution of the X-ray emission with that of the radio emission (Fig. 3 ). The X-ray emission, which was detected early on, slowly and steadily rose with time and peaked (after an increase in flux by a factor of ~10) about a year after the optical discovery 25 , 26 . A direct comparison with the evolution of the radio emission was somewhat limited by a gap in the X-ray data during the time of the first late-time radio detection and the subsequent follow-up radio observations. It is clear that the radio emission did not increase in parallel with the X-ray emission (Fig. 3 ), as the radio emission faded away at ? 200?days, while the X-ray emission was still rising. Interestingly enough, the X-ray emission after the gap in X-ray observations increased beyond 1% of the Eddington luminosity ( L Edd ), and its thermal (soft) component became brighter 26 .This behaviour is usually observed in X-ray binaries (XRBs), but although this transition is observed at a level of ~1% in some XRBs, it occurs on average at higher Eddington luminosities (~10?30%) 43 , 44 , 45 . A possible explanation for this behaviour in XRBs is that this transition occurs when the accretion rate increases and fresh material with a high Lorentz factor is injected into an existing jet 46 . Following this stage in XRBs, a radio flare is observed 46 . We also note that combined X-ray observations during June–August 2019, the period in which a rebrightening of the radio emission was detected in VLASS, show that the X-ray flux slightly increased, after declining, to a flux level of 8.07?±?1.1?×?10 ?14 ?erg?cm ?2 ?s ?1 . This translates to only 0.4% of the Eddington luminosity (lower than the X-ray luminosity increase to 1% L Edd around the time of the initial delayed radio flare we observed). However, these recent X-ray data are limited and averaged over several months (see ‘A comparison between the X-ray and radio emission temporal evolution’ in the Methods), thus making their interpretation difficult. Fig. 3: Comparison of the temporal evolution of the X-ray luminosity with the optically thin radio luminosity in ASASSN-15oi. The X-ray emission (left y axis) is detected soon after the occurrence of the TDE, whereas the radio emission (right y axis) begins later. Unfortunately, no X-ray data are available when the radio emission was initially detected. The X-ray luminosity, however, increases to a level of ? 1% L Edd when radio emission is detected. The X-ray data are presented as blue circles 25 (error bars show 1 σ ). The radio data are at a frequency of 13?GHz (red squares; uncertainties are the image noise and flux calibration uncertainty added in quadrature as defined in Supplementary Table 1 ). Averaged early radio 3 σ non-detections up to 90?days after optical discovery are represented by red arrows. Full size image Radio emission with a similar spectral shape to the one we observe in ASASSN-15oi and similar temporal behaviour (in contrast to the one in GPS sources), has been observed in some AGN or blazar radio flares (but is not necessarily typical of the whole AGN/blazar flare population). In September 2011, a radio flare from M81 exhibited an inverted radio spectrum with a peak frequency of ~10?GHz. The flare radio flux density slowly decreased on a timescale of weeks with the spectral peak frequency roughly staying the same until a second flare was observed 47 . In another case, a year-long radio flare from the blazar CTA?102 had a complex temporal and spectral behaviour 48 . The late-time evolution phase of this radio flare also shows similar characteristics to those observed in ASASSN-15oi (Fig. 2 ). In general, these AGN/blazar radio flares have been partially explained by the shock-in-jet model 49 in which a shock propagates in an existing radio jet leading to what seems to be a flare. However, a phase in which the radio peak frequency does not vary while the peak flux density decreases, as observed in both the M81 and the CTA?102 flares, is not captured by this model. Nonetheless, it is possible that there is a radio weak quiescent jet associated with the SMBH of ASASSN-15oi that is shocked by a delayed injection of energy by the TDE. Such pre-existing weak quiescent radio emission, which suggests a non-TDE related activity of the SMBH, has been found in ASASSN-14li 10 at a level that is too faint for detection at the distance of ASASSN-15oi. It has been suggested that emission in both XRBs and AGNs is dominated by a weak non-thermal jet when the accretion rate is considerably sub-Eddington (the accretion becomes radiatively inefficient) 50 . A phase transition in accretion occurs when the accretion rate increases above a critical threshold, at which point the emission in the X-ray becomes disk dominated and a high-velocity outflow is launched (sometimes observed as spatially discrete knot ejections 47 , 51 ) resulting in a radio flare. It is therefore possible that such a phase transition occurred in ASASSN-15oi, resulting in the delayed launch of an outflow that led to rapidly rising radio emission at late times. However, what triggers this phase transition, how this transition and the outflow launching coupled to it depend on the nature and properties of the relevant phenomena (for example, TDE versus XRB) and what the typical signatures of this transition in TDEs are (for example, will all TDEs exhibit an increase of their X-ray emission above a certain threshold characterized by some percentage of their Eddington luminosity?) remain open questions. The details of what follows any transition in the accretion phase are also unclear. Recall that, once detected, we observed an initially slowly evolving inverted spectrum but the spectral peak frequency rapidly evolved shortly after. It is possible that the termination of the slow spectral evolution phase marks the point at which the shock reached the edge of a pre-existing jet and that the emission that follows is of the slowly cooling jet. Testing this scenario and answering any other open questions may become possible with the discovery of additional events like ASASSN-15oi. Yet another open question relates to how common such late-time flares (due to a delayed outflow ejection) are in TDEs. There is one other case of a possible late-time radio flare in the IR TDE ARP?299B-AT1 (ref.? 17 ). In that case, a single-frequency (8.4?GHz) radio observation, taken 12?days after the first possible indication of an increase in the IR flux, resulted in a null detection. The next observation, carried out just 48?days later, detected increasingly bright radio emission. The full set of radio measurements (spanning thousands of days) of ARP?299B-AT1 is consistent with a relativistic jet launched briefly after the stellar disruption. The late-time radio spectrum, which is consistent with originating from an electron energy distribution of N e ∝ E ?3 , was also slowly evolving, in agreement with the predictions of known models 17 , but in contrast to the evolution observed in ASASSN-15oi. It is possible that the delayed launch of an outflow, as observed here, has been missed in other TDEs due to limited observational coverage. First, in several past TDEs there is a substantial gap between the time of disruption and the time at which the first radio observation was carried out (for example, the disruption time in the case of ASASSN-14li is poorly constrained). Thus even if radio emission is detected initially in such cases, the exact time at which the outflow was launched with respect to disruption is unknown. Moreover, radio observations in most cases—whether radio emission is detected or not—are curtailed after several months, leaving any flaring event that occurs later on undetected. The peculiar delayed flares we discovered in ASASSN-15oi on timescales of months and years thus motivate carefully planned observational campaigns of TDEs from early times until very late times. Conclusions . Our radio observing campaign of the optically discovered TDE ASASSN-15oi since discovery to over a year later revealed a delayed radio flare with odd spectral and temporal properties. A second, even more luminous radio flare has been detected in VLASS observations. The various models that we explore here, which have been proposed to explain the radio emission originating from TDEs, are unable to explain the combined properties of the observed radio emission. Specifically, it seems that such a delayed bright radio flare following an extended period of null radio detections requires some sort of an outflow to be launched at late times (into a possibly inhomogeneous CNM; Methods), suggesting a delayed onset of enhanced accretion. Some of the properties of the emission have similarities to XRBs and to AGN/blazar radio flares, thus raising the possibility that a transition in the accretion phase state (which has been proposed as an explanation of these latter flares) is also at play in TDEs. The details of this process, which has not previously been observed in TDEs, and what triggers it are yet to be discovered. Understanding this process requires that we first better characterize it. Our discovery thus motivates late-time radio campaigns of TDEs that will hopefully identify additional delayed flares. These could help us to study the process responsible for triggering delayed enhanced accretion, the subsequent outflow launching and the emission that accompanies it, thus helping to unveil the nature of this new puzzling phenomenon in TDEs. Methods . Radio observations . We observed the field of ASASSN-15oi with the VLA on 2015 August 22, September 06 and November 12, and on 2016 February 12, under a Swift-VLA joint programme (SB 4220). Later observations were performed under a director discretionary time programme (16A-422). The four initial observations were performed in only the X and K bands (6?GHz and 22?GHz, respectively) as a detection experiment in search of radio emission. Once radio emission was detected in the fourth observation (Extended Data Fig. 1 ), the follow-up observations were conducted in a wide range of bands from the S band (3?GHz) to the K band, as needed, to characterize and capture the evolution of the broadband radio spectrum (Extended Data Fig. 2 ). We calibrated the radio data using the automated VLA calibration pipeline available in the Common Astronomy Software Applications (CASA) package 52 . Flux density calibration was conducted using 3C48, whereas J2040-2507 was used as a gain calibrator. Images of the ASASSN-15oi field were produced using the CASA task CLEAN. In images where ASASSN-15oi was detected, the source flux density was measured using the CASA task IMFIT, and the image root mean square was calculated using the CASA task IMSTAT. We also added a flux density calibration error at conservative levels of 3% and 5% to frequencies below and at (or above) the Ku band, respectively. The log of the observations and the resulting measurements are listed in Supplementary Table 1 . As mentioned in the main text, a rebrightening of the delayed flare was detected in VLASS data. VLASS data were obtained over a long period of time and will continue to be collected in the coming years. The observation in which ASASSN-15oi was detected was obtained in 2019 July. The data were reduced and imaged by NRAO using a software pipeline designed for VLASS. The flux density from ASASSN-15oi in the VLASS quick-look image is at a level of ? 8?mJy (with an assumed general uncertainty level of 15% for all quick-look images; http://go.nature.com/36nnV5y ). Spectral modelling of the radio emission . Below we attempt to model the observed broadband radio spectra of ASASSN-15oi at the individual observing epochs where a peak in the flux density was observed, but without modelling the temporal evolution. Theoretical models 13 , 31 , 32 , 33 , 34 predict that radio emission in TDEs originates from a forward shockwave (either relativistic or sub-relativistic) travelling in the surrounding environment. This shockwave accelerates free electrons that gyrate in the shockwave-enhanced magnetic field and thus emit synchrotron radiation. Therefore, we first modelled the individual single-epoch broadband radio spectra that we observed according to a SSA spectral emission model 33 , 53 , 54 . This model successfully accounted for the radio emission observed in both Swift J1644+57 and ASASSN-14li (refs. 10 , 13 , 15 , 16 ). In the SSA emission model, the radio spectrum exhibits a peak below which the emission is self-absorbed and thus optically thick, and above which the emission is optically thin. The optically thick emission can be described as $${F}_{\nu }\propto \frac{\uppi {R}^{2}}{{D}^{2}}{B}^{-1/2}{\nu }^{5/2},$$ (1) whereas the optically thin emission is described by $${F}_{\nu }\propto \frac{4\uppi f{R}^{3}}{3{D}^{2}}{N}_{0}{B}^{(p+1)/2}{\nu }^{-(p-1)/2},$$ (2) where R is the radius of the radio-emitting shell, D is the distance to the TDE, f is the emission filling factor and B is the magnetic field strength. The energy density of the magnetic field is a fraction ? B of the energy density of the shocked CNM. Thus, the magnetic field strength also depends on the square root of the CNM density (and its profile). Our SSA best-fit models of each of the ASASSN-15oi radio spectra, separately, in which a radio peak is evident, are presented in Extended Data Fig. 3 . As shown in Extended Data Fig. 3 , the SSA models poorly account for the observed radio spectra (with reduced χ 2 values of \({\chi }_{r}^{2}>8\) at times Δ t ?=?190,197?days). This is no surprise, as the optically thick spectral index of the SSA model is α ?=?5/2, while examination of the data suggests a spectral index of α ?≈?1. A shallower spectral index of the optically thick emission is expected if only internal free–free absorption (FFA) is the dominant absorption mechanism instead of SSA, although still steeper than the observed α ?≈?1 spectral index. In this internal FFA model 53 the flux density is: $${F}_{\nu }\propto {F}_{\nu,{\mathrm{syn}}}\left(\frac{1-{\mathrm{e}}^{-{\tau }_{\mathrm{ff}}}}{{\tau }_{\mathrm{ff}}}\right),$$ (3) where F ν ,syn is the unabsorbed synchrotron emission and τ ff is the FFA optical depth. The results of the FFA modelling are presented in Extended Data Fig. 3 . While the internal FFA models better account for the observed radio spectra than the SSA model ( \({\chi }_{r}^{2}\approx 2.5\) ), they still significantly deviate from the observations. A solution may be found by reverting to the SSA model, but this time, instead of assuming a homogeneous CNM environment, we will assume an inhomogeneous one. Inhomogeneities in the CNM can be modelled as inhomogeneities of the magnetic field and will result in an SSA spectrum with a broader peak and a shallower spectral index 55 . This explanation was also used recently to describe a shallow optically thick radio emission in a stripped envelope supernova 56 . We follow this model (which is an extension of the SSA model but one that is parameterized with a distribution of magnetic fields, P ( B )? ∝ B ? a , instead of a single magnetic field). This model thus adds two degrees of freedom: the range of magnetic field strengths and the power-law index ( a ) of the magnetic field distribution. The best-fit results of this model are presented in Extended Data Fig. 3 . We find that the inhomogeneous SSA model provide a better spectral fit ( \({\chi }_{r}^{2}\approx 0.8\) ) than the previous models. It is important to note that finding a separate good spectral fit to each of the individual observed spectra does not mean that we have found a dynamical single scenario that can explain the combined full observed dataset, as we explain below, when attempting a temporal modelling. At this point, it is worth mentioning that the observed radio spectrum of ASASSN-15oi is reminiscent of GPS sources. These radio sources have a spectrum with a peak frequency in the low gigahertz range, as their name suggests. They are powerful, compact ( ? 1?kpc) radio sources, some of which exhibit a morphology of two sided symmetric sources when resolved with high-angular-resolution observations, and are believed to be young AGN radio jets 57 . On a long timescale, GPS sources can exhibit strong variability up to an order of a magnitude in the radio. However, the complex spectral variations observed here, over a short timescale of 2?months, are atypical of GPS sources. Still, considering that the radio spectral shape of GPS sources is attributed to inhomogeneities and the resemblance of their spectra to that of ASASSN-15oi strengthens the conclusion that the radio emission from ASASSN-15oi may originate from a complex CNM environment. Despite the poor fit by a simple SSA model, assuming that the peak flux density is the result of SSA, we use the peak flux density and frequency to roughly estimate the shockwave radius 58 by $$\begin{array}{lll}{R}_{\mathrm{p}}&=&4.0\times 1{0}^{14}{\left(\frac{{\epsilon }_{\mathrm{e}}}{{\epsilon }_{B}}\right)}^{-1/19}{\left(\frac{f}{0.5}\right)}^{-1/19}{\left(\frac{{F}_{\mathrm{p}}}{{\rm{mJy}}}\right)}^{9/19}{\left(\frac{D}{{\rm{Mpc}}}\right)}^{18/19}\\ &&\qquad{\times} {\left(\frac{{\nu }_{\mathrm{p}}}{5\,{\rm{GHz}}}\right)}^{-1}{\rm{cm}},\end{array}$$ (4) where ? e and ? B are the fractions of shockwave energy deposited into accelerating free electrons and enhancing the magnetic field, respectively. We adopt standard equipartition value of ? e ?=? ? B ?=?0.1 and f ?=?0.5. The radius of the radio-emitting region when we first detected it (2016 February 12, Δ t ?=?182?days), is estimated at R ?≈?4?×?10 16 ?cm, which implies (assuming an outflow was launched at optical discovery) a shockwave velocity of 25,000?km?s ?1 (only slightly higher than the velocity expected for the unbound stellar debris 13 ). Note, however, that if a jet (or an outflow) is launched later, then the velocity estimate will be higher. We also find that the radius of the radio-emitting region remains roughly the same over a two-week period (when evaluated on 2016 February 20 and 27; Δ t ?=?190 and 197?days, respectively, following the initial radius evaluation on Δ t ?=?182?days). Following this period, the estimated radius makes a big jump to R ? ?1.1?×?10 17 ?cm in only 6?weeks. The above radius estimates (as well as the velocity estimates), however, become lower limits if the emission originates from an inhomogeneous source (as discussed above). Temporal evolution of the radio emission . The temporal evolution of the observed radio emission can be compared with main theoretical predictions. We first address the analytical predictions for an on-axis relativistic jet and a sub-relativistic outflow. In the case of an on-axis relativistic jet 32 the optically thick emission is expected to rise as t ( k +2)/(4? k ) , where k is the power-law index of the CNM density profile ( ρ CNM ∝ r ? k ). Adopting the steepest density profiles found in some TDEs 35 of ρ CNM ∝ r ?2.5 (which is steeper than the usual wind-like CNM profile used in most numerical simulations), we obtain F ν ∝ t 3 . In the sub-relativistic case 13 , the optically thick emission evolves as F ν ,thick ∝ t (28+3.5 k )/14 , which is shallower than the relativistic case. We also found that attempting to model the full observed data (including the observed non-detections) with a sub-relativistic spherical outflow model fails. Adopting, therefore, the steepest relation F ν ∝ t 3 (of the relativistic case), the optically thick emission detected on 2016 February 12 can be evolved back in time to 2015 November 12, resulting in a predicted flux density level of 0.15?mJy in the C band, well above the detection threshold of our observation at that time (a 3 σ limit of 60?μJy). As seen in Extended Data Fig. 4 , the jump in flux density from non-detection to detection requires a temporal power law slightly steeper than t 4 , which requires a CNM density profile with a power law steeper than k ?=?2.8. However, note that while this model predicts that the optically thick emission is rising, in fact, upon detection it is declining. The optically thin emission, on the other hand, is expected to be declining according to F ν ∝ t ?3( p +2)/(2(5? k )) or F ν ∝ t (42?28 k )/14 in either the relativistic jet or the sub-relativistic outflow scenario, respectively. The steepest decline in this case for a k ?=?2.5 is t ?3 , while the observed emission decline rate becomes steeper than this. We next turned to examine numerical emission models for off-axis relativistic jets. For that purpose, we use the publicly available ( https://cosmo.nyu.edu/afterglowlibrary/boxfit2011.html ) BoxFit code 36 . In this scenario, a steep rise in the radio emission (steeper than the t 3 above) can occur in large off-axis angles when the relativistic jet travels in a CNM with a constant density (a wind-like density results in a shallower rise 59 ). We therefore explored the constant ISM density scenario next. We found that the numerical model can provide a reasonable fit to individual epochs of the broadband spectra only. However, the best-fit parameters vary substantially between the fitted models of each epoch. For example, the optically thin spectrum observed on day 233 requires an off-axis angle of ~1.1?rad, whereas the radio emission observed on day 197 requires an off-axis angle of 1.57?rad and and an ISM density an order of magnitude higher than the one in the model for day 233. Moreover, no numerical solution that can explain both the initial steep rise in flux density and the spectral and temporal evolution was found. In Extended Data Fig. 4 , we show several temporal power laws for the rise and the decline of the emission, including the above steepest rise and decline rates. As seen in Extended Data Fig. 4 , assuming that a shockwave was launched at the time of optical discovery leading to radio emission that peaks at the time we discovered the radio flare, then the radio emission should have been detectable at the time of the third null detection observation. The observed decline rate of the radio emission after the discovery is also steeper than that expected from standard theoretical models. A comparison between the X-ray and radio emission temporal evolution . The X-ray luminosity of ASASSN-15oi (ref.? 25 ) is shown in Fig. 3 in units of the Eddington luminosity. We estimated the Eddington luminosity using the black hole mass estimate of ~10 6 M ⊙ (refs.? 25 , 26 ) corresponding to L Edd ?≈?1.2?×?10 44 ?erg?s ?1 . As seen in Fig. 3 , there is a gap in the X-ray data when we first detected the radio emission. Despite this, it seems that there is no apparent correlation between the X-ray and radio emissions. The X-ray emission is detectable shortly after the optical discovery of ASASSN-15oi, and slowly increased by a factor of ~10 up to about a year later and crosses the 1% Eddington luminosity level. In addition to previously published X-ray data 25 , 26 , short Swift snapshot observations were undertaken in 2019 and 2020 and are publicly available. The data were analysed following the same procedures used to analyse past Swift observations of ASASSN-15oi (refs. 25 , 26 ). Owing to the limited sensitivity, we combined the datasets obtained over several months in 2019, resulting in an X-ray flux measurement of 8.07?±?1.1?×?10 ?14 ?erg?cm ?2 ?s ?1 . The combined observations in 2020 show that the X-ray emission then faded to a flux level of 1.8?±?1.9?×?10 ?14 ?erg?cm ?2 ?s ?1 . Data availability . The ASASSN-15oi radio data, presented in several figures, can be found in Supplementary Table 1 . The raw VLA data are available via the NRAO archive at https://archive.nrao.edu/archive/advquery.jsp . The collection of radio data of other TDEs can be found in ref.? 35 . The ASASSN-15oi X-ray emission measurements can be found in ref.? 25 . 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A. et al. CHANG-ES V: nuclear outflow in a Virgo Cluster spiral after a tidal disruption event. Astrophys. J. 809 , 172 (2015). ADS ? Article ? Google Scholar ? Download references Acknowledgements . We thank T. Piran, E. Nakar and R. Fender for useful discussions. A.H. was suported by grants from the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation (ISF), and from the US–Israel Binational Science Foundation (BSF). I.A. is a CIFAR Azrieli Global Scholar in the Gravity and the Extreme Universe Program and acknowledges support from that program, from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement number 852097), from the Israel Science Foundation (grant number 2752/19), from the United States – Israel Binational Science Foundation (BSF), and from the Israeli Council for Higher Education Alon Fellowship. We thank the NRAO staff for approving and scheduling the VLA observations. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We thank the Swift TOO team. This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC. This research has made use of the CIRADA cutout service at http://cutouts.cirada.ca/ , operated by the Canadian Initiative for Radio Astronomy Data Analysis (CIRADA). CIRADA is funded by a grant from the Canada Foundation for Innovation 2017 Innovation Fund (Project 35999), as well as by the Provinces of Ontario, British Columbia, Alberta, Manitoba and Quebec, in collaboration with the National Research Council of Canada, the US National Radio Astronomy Observatory and Australia’s Commonwealth Scientific and Industrial Research Organisation. Author information . Affiliations . Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel A. Horesh Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA S. B. Cenko Joint Space-Science Institute, University of Maryland, College Park, MD, USA S. B. Cenko The School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel I. Arcavi CIFAR Azrieli Global Scholars Program, CIFAR, Toronto, Ontario, Canada I. Arcavi Authors A. Horesh View author publications You can also search for this author in PubMed ? Google Scholar S. B. Cenko View author publications You can also search for this author in PubMed ? Google Scholar I. Arcavi View author publications You can also search for this author in PubMed ? Google Scholar Contributions . A.H. led the radio observing campaign, the data analysis and modelling, the interpretation and the manuscript preparation. S.B.C and I.A. contributed to the interpretation of the results and to the manuscript preparation. Corresponding author . Correspondence to A. Horesh . Ethics declarations . Competing interests . The authors declare no competing interests. Additional information . Peer review information Nature Astronomy thanks Miguel Perez Torres, Elad Steinberg and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Extended data . Extended Data Fig. 1 VLA K-band images of the position of the optical TDE candidate ASASSN-15oi, before and after radio detection. . The left panel (a) presents the third VLA image we obtained of this field 3 months after optical discovery on 2015 Nov 12, still showing a null-detection. The right panel (b) presents the image from our forth VLA observation on 2016 Feb 12 which reveals a delayed radio flare, 6 months after optical discovery. The synthesized beam size is shown as a white ellipse at the bottom left corner of the images. The flux density scale is identical in both images. Extended Data Fig. 2 The full observed broadband spectral evolution of the delayed radio flare from ASASSN-15oi. . Each of the radio broadband spectra is from a different observing epoch, starting from the initial detection of the delayed flare on 182 days and up to 576 days after optical discovery. Data from each epoch is represented by a different marker shape and color as noted in the legend (a dashed line connecting the data has been added for convenience). The error bars represent the image noise and flux calibration error added in quadrature (see Supplementary Table 1 ). Extended Data Fig. 3 Best fit single-epoch spectral models of the radio flare. . Observing epochs at Δt=182, 190, 197 days are represented in purple, yellow and red, respectively. The broadband spectrum in each single epoch was fitted independently, thus not including any modeling of the temporal evolution. The errors of the data modeled here include the flux density calibration error and image noise added in quadrature. The left panel (a) presents the best-fit homogeneous SSA model 33 . The middle panel (b) shows the best-fit models of the radio flare spectra using the internal free-free absorption model 53 . The right panel (c) is the best-fit models using the inhomogeneous SSA model 55 . Out of the three models that we try here, the latter model is the best match to the spectral data presented in this figure (see details in Methods). Extended Data Fig. 4 Comparison of the temporal evolution of the observed optically thin radio emission with different rising and declining power-law functions. . The presented radio emission is at a frequency of 15 GHz (black solid line and markers). The various power-law functions for both the rise of the emission (since the last non-detection) and its decline are presented as dashed curves (representing various predictions, see details in Methods). The black triangle represents a 3 σ non-detection limit (based on the average between the 22 GHz and 6 GHz limits). Supplementary information . Supplementary Information . Supplementary Table 1. Rights and permissions . Reprints and Permissions About this article . Cite this article . Horesh, A., Cenko, S.B. & Arcavi, I. Delayed radio flares from a tidal disruption event. Nat Astron (2021). https://doi.org/10.1038/s41550-021-01300-8 Download citation Received : 18 June 2020 Accepted : 05 January 2021 Published : 22 February 2021 DOI : https://doi.org/10.1038/s41550-021-01300-8 .

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