FIRST J153350.8$+$272729: the radio afterglow of a decades-old tidal disruption event

We now interpret these observations in terms of three hypotheses for J1533+2727:

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  AGN variability.

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  An engine-driven transient associated with a supernova.⁸⁸8We do not consider standard supernovae because the peak radio luminosity of J1533+2727 ($1.6\times 10^{30}$ erg s^-1 Hz^-1) is a factor of eight greater than even the most luminous radio supernova (PTF 11qcj; Palliyaguru et al., 2019).

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  A jet or outflow powered by a TDE.

We first augment the observations presented above with archival ROSAT/PSPC pointings that included J1533+2727 in the field of view. We highlight two observations in particular: a 415 s pointing on MJD 48102 (1990 July 30; sequence id rs931238n00; around three years after the last Green Bank detection) obtained as part of the ROSAT All-Sky Survey, and a 13932 s pointing a year later on MJD 48449 (1991 July 12; sequence id RP201103N00) obtained as part of a long exposure on $\alpha$ Cor Bor. We used the sosta tool in the XIMAGE package, and the exposure maps associated with the observations, to derive $3\sigma$ upper limits on the count rates at the position of J1533+2727. These were 0.125 cts s^-1 and 0.0108 cts s^-1 on the respective dates (in the standard PSPC 0.1–2.4 keV band). We then converted these to upper limits on the 2–10 keV luminosity assuming a photon index of 2, and a Galactic neutral-hydrogen column density of $n_{H}=2.9\times 10^{20}$ cm^-2 derived from the HI4PI neutral hydrogen column map (HI4PI Collaboration et al., 2016). These upper limits were $L_{X}<3.0\times 10^{42}$ erg s^-1 and $L_{X}<2.6\times 10^{41}$ erg s^-1 on the respective dates.

These X-ray upper limits are low in comparison with the radio luminosity of J1533+2727, if J1533+2727 represents an active black hole. The black hole fundamental plane relates the mass, 5 GHz radio luminosity, and 2–10 keV X-ray luminosity of actively accreting objects across nine orders of magnitude in black hole mass, and hints at a fundamental link between accretion rate and jet power. We used the latest iteration of this relation (Gültekin et al., 2019) to derive predicted upper limits on the 5 GHz radio luminosity of J1533+2727 at the epochs of the X-ray observations. Given the derived SMBH mass, by assuming Poisson statistics for the X-ray upper limits, and by using a Monte Carlo technique to account for the uncertainty and intrinsic scatter in the black hole fundamental plane, we calculated 95% confidence upper limits on the expected radio luminosity of $4.8\times 10^{38}$ erg s^-1 and $9.8\times 10^{37}$ erg s^-1 corresponding to the two X-ray observations. These in turn imply radio flux-density upper limits of 3.7 mJy and 0.8 mJy respectively, where we divided the luminosities by the frequency to derive the spectral luminosities following Gültekin et al. (2019). If J1533+2727 was indeed this faint during the X-ray observations, a much more rapid evolution is implied between the Green Bank 4.85 GHz detection and these epochs than at later times. Furthermore, unless the source re-brightened between the X-ray observations and the NVSS and FIRST detections, an unrealistic spectral index steeper than $-2$ is implied between 1.4 GHz and 5 GHz for the FIRST detection. We conclude that J1533+2727 was inconsistent with the black hole fundamental plane when the ROSAT X-ray observations were undertaken.

This suggests that J1533+2727 was not actively accreting as an AGN at this time, which is in tension with the hypothesis of ongoing AGN variability. This is however not in tension with the TDE hypothesis, because the accretion could have ceased (e.g., Levan et al., 2016). When detected in the Green Bank survey, J1533+2727 was also more luminous at a wavelength of 6 cm than the cores of any of the 52 nearby Seyfert galaxies observed by Ho & Ulvestad (2001), besides Perseus A (NGC 1275; Seyfert 1.5) and NGC 1167 (Seyfert II; beyond the magnitude-completeness limit of the survey). Additionally, J1533+2727 is likely more variable than any of the 12 Seyferts observed by Mundell et al. (2009), within whose sample the maximum variability in seven years at 8.4 GHz was a factor of three. We therefore proceed to consider hypotheses (2) and (3) given above.

Some insight can be gained by analyzing J1533+2727 as a synchrotron transient, despite the lack of detailed spectral information. That J1533+2727 represents synchrotron emission is evident given the brightness temperature ($\gtrsim 5.3\times 10^{9}$ K) implied by the extreme variability of the source.⁹⁹9A useful working definition of a variability timescale that can be used to calculate a light-crossing time is a timescale over which the modulation index, defined as the variability range divided by the mean source flux density, is greater than unity. Adopting a timescale of six years (between the FIRST/NVSS observations and L-band VLA observations in 2001), we find a brightness temperature in excess of $5.3\times 10^{9}$ K. We can also derive rough constraints on the source radius, $R$, the energy required to power the source, $E$, and the electron number density, $n_{e}$, of the medium into which the source is expanding. The constraints are based on a fiducial $65$ mJy maximum flux density measured at $4.85$ GHz, and the assumption that the optically thin spectral index observed in our 2019 observations of the source of $\alpha=-0.84$ is representative of a non-evolving relativistic electron energy distribution $N(E)\propto E^{-p}$ with $p=-2\alpha+1=2.68$. In the following, we assume (a) equipartition between the energy in relativistic electrons and in magnetic fields within the source, (b) that the source is expanding sub-relativistically, (c) that the source is spherically symmetric with a filling factor of unity, and (d) that the relativistic electrons are accelerated in a strong (forward) shock that deposits 10% of its energy in the electrons, and 10% of its energy in magnetic fields (i.e., $\epsilon_{e}=\epsilon_{B}=0.1$ in usual terms).¹⁰¹⁰10In our calculation, we adopt $c_{5}=9.68\times 10^{-24}$ and $c_{6}=8.10\times 10^{-41}$ from Pacholczyk (1970). The non-relativistic assumption further implies that the spectral peak was associated with synchrotron self-absorption rather than the minimum relativistic-electron energy (e.g., Chevalier, 1998).

In this scenario, following Chevalier (1998), $R\propto S_{p}^{(p+6)/(2p+13)}\nu_{p}^{-1}$, and $E\propto S_{p}^{(3p+14)/(2p+13)}\nu_{p}^{-1}$, where $\nu_{p}$ is the peak frequency and $S_{p}$ is the peak flux density. If we are simply constraining the values of $R$ and $E$ when $\nu_{p}=4.85$ GHz, we are setting lower limits on both quantities. This is also essentially the case if we are constraining the values of $R$ and $E$ during the 1986 Green Bank observations.¹¹¹¹11If the spectrum was optically thick and $\nu_{p}>\nu=4.85$ GHz, $S_{p}\propto(\nu_{p}/\nu)^{2}$ implies a nearly fixed estimate of $R$ regardless of the true value of $\nu_{p}$, and a larger value of $E$. If the spectrum was optically thin, $R$ and $E$ would clearly both be larger. The electron number density is derived by applying the Rankine-Hugoniot jump conditions in the strong shock limit (Equation (15) of Ho et al., 2019), with the further assumption of the shock velocity being given by the source size divided by its lifetime, $T$. In this case, $n_{e}\propto S_{p}^{-(2p+16)/(2p+13)}\nu_{p}^{4}$. In summary, using the 1986 measurement, we find

These equations, including the constants of proportionality, directly reproduce Equations (8), (12), and (16) of Ho et al. (2019), for our value of $p$. Although the radius estimate is only mildly sensitive to the assumptions above, a departure from equipartition like that observed for Sw J1644$+$57 (Eftekhari et al., 2018), where $\epsilon_{B}=0.001$ was inferred assuming $\epsilon_{e}=0.1$, would increase the energy estimate by two orders of magnitude.

These results provide evidence that J1533+2727 represents a relativistic jet/outflow from a TDE. First, the lower limit on the energy in the outflow is greater than that of any known stellar cataclysm (e.g., Mattila et al., 2018) besides classical, on-axis long gamma-ray bursts (LGRBs).¹²¹²12Radio calorimetry of the ejecta of cosmic explosions traces the fastest ejecta, and therefore cannot be directly related to the total energies in outflows with a range of velocities, like supernovae (e.g., Berger et al., 2003). Additionally, most LGRBs have apparent expansion velocities of $\Gamma\beta\gtrsim 3$ (here, $\Gamma$ is the bulk Lorentz factor of the emitting material, and $\beta=v/c$ is the normalized expansion velocity). However for J1533+2727, following Sari et al. (1998), the characteristic frequency corresponding to radiation from the lowest-energy relativistic electrons, $\nu_{m}$, was likely lower than 4.85 GHz in 1986, because the source declines between 1986 and 1987. This frequency is related to $E$ and $T$ in the case of adiabatic evolution, which implies a lifetime:

This in turn implies $\Gamma\beta\lesssim 4$, and $n_{e}\lesssim 0.8\,{\rm cm}^{-3}$. Although this makes the LGRB scenario somewhat fine-tuned, the derived parameters are consistent with some GRBs (e.g., GRB 980703; Perley et al., 2017). Indeed, GRB 980703 exhibits late-time emission 16 years post-burst that is similar to J1533+2727 (Perley et al., 2017). However, the projected offset between J1533+2727 and the center of light of its host galaxy of $\approx 100$ pc is inconsistent with more than 95% of the LGRB population (Lyman et al., 2017). Additionally, the high stellar mass and lack of evidence for an ongoing starburst in the host galaxy of J1533+2727 are inconsistent with typical LGRB hosts (Taggart & Perley, 2019). We therefore favor the TDE scenario.

A comparison between the radio lightcurve of J1533+2727 and the remainder of the TDE population is shown in Figure 2. The post-explosion time of the 1986 epoch (88 days) was derived assuming a nominal expansion velocity of $c$, which would imply $n_{e}\sim 12$ cm^-3. Please note however that sub-relativistic expansion was assumed to derive the constraints above, and this is therefore for illustrative purposes only. The high radio luminosity and outflow energy relative to several radio-detected TDEs is suggestive of a relativistic jet, rather than a wide-angle outflow (Alexander et al., 2020). We note that if the emission region were significantly aspherical, with a non-unity filling factor, some of the above conclusions would be altered by factors of a few (Barniol Duran et al., 2013).

We have established that J1533+2727 is a remarkable radio transient and a likely TDE afterglow. Using the FIRST survey, and assuming the detection of just one such source, we can calculate a lower limit on the occurrence of sources like J1533+2727. The 1 mJy minimum flux density of the FIRST catalog and the peak luminosity of J1533+2727 in FIRST implies a detectable distance of 452 Mpc. The FIRST and VLASS 1.1 sky surveys have an overlapping sky coverage of $\sim 6000$ deg², and thus the detectable distance corresponds to an observable volume of 0.056 Gpc³. J1533+2727 emitted above its detected FIRST luminosity for at least 8 years between the Green Bank and FIRST detections. We can therefore infer a lower limit on the volumetric rate of approximately 2.2 Gpc^-3yr^-1, or $\sim 1$% of the observed TDE rate (van Velzen, 2018). We do not take this analysis further because the search for TDEs detected in FIRST is ongoing.

Our results add to the emerging picture of the diversity of TDE-driven jets/outflows from supermassive black holes. Although it has long been known that $\sim 50\%$ of the mass of a disrupted star is likely to be unbound (e.g., Rees, 1988), the geometry and kinematics of such outflows are poorly constrained, as are any jets/outflows powered by the accretion of the remaining 50% of the mass. The radio luminosity and derived outflow energy of J1533+2727 fills the gap between the three relativistic TDEs identified through their prompt high-energy emission, and the remaining TDE sample (Figure 2). The host galaxy of J1533+2727 and its central supermassive black hole appear otherwise unremarkable with respect to the TDE population (French et al., 2020; Wevers et al., 2017). Although the black hole mass is somewhat high relative to optically selected TDEs (Wevers et al., 2017), stars with a wide range of masses ($\gtrsim 0.3M_{\odot}$) are expected to be disrupted by such black holes (Kochanek, 2016). The optical spectrum of the host of J1533+2727 shows emission lines characteristic of the narrow-line regions of Type II Seyferts; this nuclear activity must have been ongoing prior to the transient event, given the large expected sizes of narrow-line regions (e.g. Bennert et al., 2006). This is similar to the host of the radio-discovered TDE CNSS J0019$+$00 (Anderson et al., 2019). The presence of nuclear activity in the spectrum of the J1533+2727 host makes it difficult to determine whether or not it is a post-starburst galaxy, although we note that TDEs are found to be over-represented in galaxies that are evidently post-starburst from their optical spectra (Figure 3; French et al., 2016, 2020). We speculate that TDEs discovered in radio transient surveys will have substantially different selection effects, especially with regards to AGN activity and extinction, than the selection effects present in optical and soft X-ray surveys that dominate TDE discoveries today.