LATE TIME MULTI-WAVELENGTH OBSERVATIONS OF SWIFT J1644+5734: A LUMINOUS OPTICAL/IR BUMP AND QUIESCENT X-RAY EMISSION

We have continued to monitor Swift J1644+57 in the IR from the United Kingdom Infrared Telescope (UKIRT) and Gemini-North. A log of our new photometric observations is shown in Table 1. The UKIRT images were obtained with the Wide Field Camera (WFCAM) and reduced through the standard CASU pipeline. The data were retrieved in calibrated form from the WFCAM science archive.¹⁰ The Gemini-North images were reduced using the standard Gemini IRAF package. Photometric calibration was performed relative to several 2MASS stars, with the zeropoint tied to the star at R.A. = 16:44:50.96, decl. = +57:35:31.6 (J = 13.121, H = 12.798, K = 12.727) as in Levan et al. (2011) such that the photometric observations should be directly comparable between earlier work and this one.

We also include in our analysis other published IR photometry from Burrows et al. (2011). Observations taken at similar times provide reasonable agreement with our measured photometry within ∼0.1–0.2 mag and hence should be on a comparable scale. There is no apparent systematic offset that could be applied to reduce this scatter significantly, and so it is likely that the differences in measurements reflect a combination of measurement error (often significant at later times) and true variation within the source (often significant at earlier times).

We have also obtained further observations of Swift J1644+57 with the Hubble Space Telescope (HST). These observations were obtained in the F606W and F160W bands using the WFC3 camera with both UVIS and IR channels, matching the earlier data presented in Levan et al. (2011). The images were retrieved from the archive after standard post-processing. The UVIS observations were corrected for pixel-dependent CTE utilizing the method of Anderson (2014). The images were then drizzled (Fruchter & Hook 2002) onto a common frame, utilizing a pixel scale of 0.025 arcsec pixel⁻¹ for F606W and 0.07 arcsec pixel⁻¹ for F160W. The first and last epochs, as well as a subtraction, are shown in Figure 1. To obtain magnitudes of the counterpart only the final epoch of HST observations was subtracted from the earlier data and the resulting residual measured. The photometry is shown in Table 2, where both transient fluxes and combined host plus transient magnitudes are listed. To avoid including additional sky noise, which may impair the estimation of transient contributions, the combined magnitudes were measured in an aperture of radius 15 pixels for F160W (105) and corrected assuming a pointlike aperture correction. In practice this underestimates the true host galaxy magnitude, and so the host galaxy magnitude itself is calculated based on the Sérsic profile fit to the host galaxy, yielding a magnitude approximately 0.2 mag brighter. The resulting magnitudes for the host galaxy are comparable to those obtained by Yoon et al. (2015) from an independent analysis of our data. The relatively bright point sources in subtractions were measured in small apertures (2 × FWHM), and aperture corrected, while due to possible galaxy residuals we measured the F606W subtractions in apertures of 04. We note that as expected the choice of aperture size has little impact on our final photometry.

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A clear residual is seen in both bands. In fact, this is the first detection of transient optical emission in the r-band, previous detections having only been possible in the z band and longwards (Levan et al. 2011), likely due to the strong extinction within the host galaxy. Interestingly, the optical light appears to rise between the first two epochs (6.6 and 23 days post-outburst) during which time the IR appears to show a decline. This is puzzling if both the optical and IR are arising from the same component and is discussed further below.

We can determine the location of the transient within the host galaxy by comparing the centroid in the subtracted frames with the center of the host galaxy in late epoch images, utilizing compact sources in the field for astrometric purposes. This is best done in the IR since the signal to noise for the transient is much higher, does not risk any systematic shift due to poorer subtraction of the host galaxy light, and minimizes the risk of mis-identifying the centroid due to differential extinction within the host galaxy. We compared our first and last epoch, using eight sources in common between the two frames for alignment. As the first and last images were taken at the same orientation we can utilize a direct shift between the two rather than more complex fits (which may underestimate the errors for the small number of sources considered). This yields an offset of (0.010 ± 0.012)'', equivalent to a spatial offset of <60 pc from the centroid of the galaxy. Although it has limitations this approach can also be used in the F606W observations, which yields an offset of (0.033 ± 0.010)''. This is formally inconsistent with the nucleus at the 3σ level, but may be due to a combination of the effects described above. However, this technique is based on utilizing compact sources (predominantly stars) in the field of view and so proper motion can be a significant factor. A new technique, employing cross correlation with galaxies, can improve this and will be presented separately (R. Hounsell et al. 2015, in preparation).

We also observed Swift J1644+57 with the Spitzer Space Telescope at four epochs. The first three roughly span a year after the outburst, with a final epoch obtained in 2014 March for host subtraction. Observations were obtained in both the 3.6 and 4.5 μm bands. Photometry was performed directly on the PBCD mosaics and on aligned and subtracted images to isolate the transient flux utilizing a 4 pixel (2 native pixel) aperture and correcting for excluded light. The IRAC observations suggest a bright mid-IR outburst, consistent with a highly extinguished source, which fades by by a factor of 10 over the course of the first year. A log of observations and resulting photometry is shown in Table 2.

In addition to the early spectroscopy reported in Levan et al. (2011) we obtained further optical spectroscopy with Gemini-N/GMOS on 2011 July 23 and 2012 March 23 to April 4. Observations were obtained in the R400 filter spanning a wavelength range from ∼5900 to 10000 Å and utilizing the nod-and-shuffle mode to improve sky subtraction. The data were reduced via the Gemini GMOS pipeline appropriate for simple longslit (for our earlier observations) or nod and shuffle (for later data). The previously reported emission lines of Hα, Hβ, [O iii], and [O ii] (Levan et al. 2011) remain visible and no clear evolution is seen. In particular, the lines remain narrow with no sign of the development of broad lines around Hα, where some recently identified TDF candidates have shown transient broad features (Gezari et al. 2012; Arcavi et al. 2014). This is unsurprising given the low level of broadband optical variability in the source and may be indicative of a lack of broad features, or could suggest that the lines seen are from relatively unobscured star formation within the host galaxy, while any broadline region remains highly obscured.

We obtained several epochs of late time observations of Swift J1644+57 with both XMM-Newton and Chandra. A log of these observations with exposure times is shown in Table 3. All XMM-Newton observations utilized the thin filter for both PN and MOS observations. Chandra observations used ACIS-S in very faint mode with the source placed at the default aim point on the S3 chip.

Table 3.  Late Time X-Ray Observations of Swift J1644+57

Date-obs	MJD-obs	ΔT	Telescope	ks	Count Rate	Flux
		(days)			(0.3–10 keV)	(erg s−1 cm−2)
2012 Sep 27	56197.81	549.27	XMM	22.7	(1.9 ± 0.3) × 10−3	9.93 × 10−15
2012 Oct 05	56205.80	557.26	XMM	28.7	(1.2 ± 0.2) × 10−3	6.27 × 10−15
2012 Nov 26	56257.44	608.90	Chandra	24.7	(3.0 ± 1.1) × 10−4	4.18 × 10−15
2013 Jul 17	56490.70	842.16	XMM	44.1	(8.1 ± 1.5) × 10−4	4.21 × 10−15
2015 Feb 17	57070.20	1421.66	Chandra	27.8	(4.6 ± 1.3) × 10−4	6.40 × 10−15
2015 Apr 06	57118.85	1470.31	Chandra	18.7	(2.7 ± 1.3) × 10−4	3.76 × 10−15
2012 Sep 02	56172.86	${524.32}_{-17}^{+34}$	XRT	110.7	(1.90 ± 0.69) × 10−4	9.19 × 10−15
2013 Mar 15	56366.85	718.31${}_{-160}^{+251}$	XRT	146.4	(1.61 ± 0.67) × 10−4	7.79 × 10−15

Note. Log of late time observations of Swift J1644+57 obtained with XMM-Newton, Chandra, and the Swift-XRT. The XMM-Newton and Chandra observations were obtained as single observations. In contrast, the Swift-XRT observations were based on stacking multiple observations over a long period and so have a significant time error bar. The dates given for these observations correspond to the ΔT given, as determined by the methods described in Evans et al. (2007, 2010).

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For our Chandra observations we extracted images from the cleaned event files in the 0.3–10 keV energy band. We then determined count rates in an aperture of 2'' radius. Although faint, the source is detected in each individual image with between 7 and 17 source counts and within our aperture the background is negligible (<1 count expected). Given the small number of counts it is not possible to determine detailed spectral parameters for our data, although as noted by Berger et al. (2012) the X-ray photons arise across the energy range and are not dominated by soft photons as would be expected for a thermal blackbody typically thought to underly TDFs.

The XMM-Newton data were reduced with SAS 14.0.0 using epchain and emchain to extract the event lists. All the XMM-Newton observations utilized the thin filter for both pn and MOS observations; single- and double-pixel events (patterns 0–4) for pn and all events up to quadruple pixels (patterns 0–12) for MOS were selected. The event lists were screened for times of high, flaring background and an energy range of 0.3–10 keV was then considered. Source count rates were extracted using a 10'' radius circle centered on the source position and corrected for point-spread function (PSF) losses caused by the small region size. The background was estimated from a nearby, larger, source-free region. The numbers given in Table 3 for the XMM-Newton observations are from the pn data sets in each case.

We convert the measured X-ray count rates in the 0.3–10 keV bands into fluxes assuming a simple model determined from the fit to the late time X-ray spectra measured by the Swift-XRT, namely, an absorbed power law of index Γ = 1.99 and contributions from Galactic and host galaxy absorption (N_H,gal = 1.75 × 10²⁰, N_H,host = 2.07 × 10²²; (Willingale et al. 2013)). We note this does differ in detail from the fit found by more detailed spectral fitting when the source was brighter, which required an additional thermal component providing a few percent of the soft flux. However, the errors associated with the choice of spectrum are small compared to the photon counting errors for the source at this brightness. It is possible to fit the XMM-Newton PN observations directly since the combined observations contain 130 counts (of which approximately half are from the source). Doing so with the absorption fixed to the values determined by the XRT yields a power-law index of ${\rm{\Gamma }}\;=\;{1.85}_{-0.73}^{0.51}$ (at 90% confidence), consistent with the earlier observations and implying no strong hard to soft evolution.

The updated X-ray light curve of Swift J1644+57 is shown in Figure 2 on both logarithmic and linear time axes. Our late time observations have been supplemented by the ongoing observations with the Swift-XRT, taken from the Swift UK data center¹¹ , processed via the techniques described in Evans et al. (2007, 2010). As previously noted (Bloom et al. 2011b; Burrows et al. 2011; Levan et al. 2011) the early light curve is dominated by pronounced flaring and variability, which then settles into a steady decay, punctuated by notable dips, which have been suggested to show some signs of periodicity (Saxton et al. 2012). The ongoing variability means that attempts to fit any simple decay model to the data inevitably lead to poor quality fits, although the data from ∼100–500 days, if fit with a single power-law do favor a slope of −5/3 (Levan 2015). More complex fits could be attempted to investigate the presence or absence of additional breaks in the light curve, but these require some attempt to remove dipping activity, and so are necessarily limited in statistical power.

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The final good detection reported by the Swift-XRT is at around 500 days, with a flux of (5.5 ± 0.8) × 10⁻¹³ erg s⁻¹ cm⁻², based on the stacking of images obtained ∼4 days either side of this midpoint. After this, the X-ray flux decreased markedly. By the time of our XMM-Newton observations the source had declined by a factor of at least 50 in flux. In a factor of ΔT/T = 0.08 in time a fall of a factor of 50 corresponds to a decay index of around t⁻⁷⁰. In practice, the decay was too fast to be resolved since beyond the steep drop-off, XRT observations cannot recover the flux in short exposure times and there was a significant delay before the XMM-Newton and Chandra observations were scheduled. Hence we conclude that the power-law decay rate was faster than t⁻⁷⁰. Assuming we are observing X-ray activity from the base of the jet this suggests that activity suddenly shut off, due to either a switch of accretion mode or the cessation of accretion. Given the size of emitting regions at the head of the jet at this late time it is difficult to envision a scenario in which this shut off was not due to the cessation of activity close to the base of the jet since otherwise it would have smeared out over a much longer time period.

It is interesting to note that such rapid cessation of X-ray activity was explicitly predicted in the massive star models of Quataert & Kasen (2012) since this represents the point at which all of the star has accreted onto the central compact object. Such predictions were not made for jetted TDF-like events prior to the detection of the rapid drop in Swift J1644+57, although can potentially be explained via magnetic processes within the disk (Tchekhovskoy et al. 2014). In particular, once the black hole accretion rate becomes sub-Eddington and radiatively efficient (geometrically thin), it enters a thermally dominant accretion state, which is empirically not observed to produce powerful jets in Galactic X-ray binaries (e.g., Russell et al. 2011).

After this rapid decay, X-rays of luminosity L_X ∼ 5 × 10⁴² erg s⁻¹ continue to be detected until at least 2015 April (day 1500). These X-rays appear to be approximately constant in luminosity with little sign of a decay. A fit to the available Swift-XRT, XMM-Newton, and Chandra observations with a constant source is not especially good (χ²/dof = 13.7/7). The fit is not improved by allowing for a power-law model, which gives a best fit decay of $\alpha \;=\;{0.5}_{-0.2}^{+0.7}$ (χ²/dof = 10.22/6), with an F-test probability of chance improvement of 20%. However, these data are dominated by observations immediately after the break and may contain additional systematic errors from comparison between three different instruments. If instead we compare the Chandra count rates then a constant source provides a very good description (χ²/dof = 1.27/2), and the power-law slope of $\alpha \;=\;-{0.2}_{-0.4}^{+0.8}$ rules out a continuing decay around t^−5/3 at >2.3σ (and t^−4/3 at 1.9σ). This is at first sight surprising since it is reasonable to assume that after the cessation of jet activity we begin to observe forward shock emission at all wavelengths (Zauderer et al. 2013). The absence of continued decay of this emission would then suggest that these X-rays either do not originate from the forward shock or that it is somehow continuing to be energized despite the cessation of jet activity. It is hence interesting to compare this late time behavior to the general expectations of differing progenitor models.

In a TDF scenario, once the jet turns off, thermal X-ray emission from the inner accretion disk could be observed (which was originally considered the hallmark signature of TDFs; e.g., Rees 1988). For stellar tidal disruption by a black hole of mass ∼10⁶M_⊙, the fall-back time of the most tightly bound tidal debris (i.e., the time at which we expect accretion to start and an observable electromagnetic transient to be produced) is t_fb ∼ 1 month, similar to the duration of peak hard X-ray activity in Swift J1644+57 and J2058+05. The accretion luminosity is then some fraction, η, of the rest mass of the disrupted star (M_⋆) accreted. Since this mass returns as t/t_fb)^−5/3 (Rees 1988; Phinney 1989), this luminosity can be expressed as

$$\begin{eqnarray}{L}_{{\rm{X}}} & \approx & \eta \dot{M}{c}^{2}\approx \eta \displaystyle \frac{{M}_{\star }{c}^{2}}{3{t}_{{\rm{fb}}}}{\left(\displaystyle \frac{t}{{t}_{{\rm{fb}}}}\right)}^{-5/3}\\ & \approx & 3\times {10}^{43}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\left(\displaystyle \frac{\eta }{0.1}\right)\left(\displaystyle \frac{{M}_{\star }}{0.5{M}_{\odot }}\right)\\ & & \times {\left(\displaystyle \frac{{t}_{{\rm{fb}}}}{{\rm{month}}}\right)}^{2/3}{\left(\displaystyle \frac{t}{\text{1000 day}}\right)}^{-5/3}.\end{eqnarray} \tag{ 1 }$$

To order of magnitude, the predicted luminosity at 500–1000 days is similar to that observed in J1644+57 after the steep drop (once a bolometric correction is included). However, the predicted $\propto {t}^{-5/3}$ decay is steeper than the observed light curve between 500 and 1000 days. A dimmer and flatter light curve than predicted by Equation (1) could be explained if the black hole accretion rate after the jet shut off no longer tracks the mass fall-back rate due to the viscous spreading of the disk (Cannizzo et al. 1990; Shen & Matzner 2014). Such a transition from rapid to slow processing by the disk is naturally instigated by the sudden and large increase in the viscous timescale ∝H⁻² once the disk scale height H shrinks following the sub-Eddington state transition (Shen & Matzner 2014). However, the apparently relatively hard X-ray spectrum after the rapid decay is not in keeping with the very soft thermal spectrum expected in TDFs, and so it seems less likely that this is the observed origin of the late time X-ray emission.

In the case where all the material from a collapsing star has been accreted (Quataert & Kasen 2012) it seems unlikely that an essentially quiescent source would persist. One possibility is that some level of ongoing accretion may occur from the dense region in which the SN occurred, although the luminosity is orders of magnitude larger than possible from either Bondi-Hoyle accretion in a giant molecular cloud or from accretion from a companion star. Indeed, the luminosity of ∼5 × 10⁴² erg s⁻¹ remains ∼3 orders of magnitude larger than possible from a stellar mass black hole, and would require both a continued high accretion rate and a significant degree of beaming unless the supernova had been from an extremely massive star that had created an exceptionally massive black hole (e.g., Portegies Zwart et al. 2004).

Finally, it is possible that the late time X-rays represent ongoing AGN activity, separate to the transient outburst. The X-ray luminosity itself would be fairly typical for a low-luminosity AGN, however, the host galaxy would be unusual in this case since the majority of AGNs are hosted in rather more luminous galaxies. This is illustrated in Figure 3 which, following Levan et al. (2011), shows the comparative luminosity evolution of Swift J1644+57 in the X-ray luminosity against the optical/IR absolute magnitude plane. The track of the counterpart of Swift J1644+57 is shown at several characteristic times and shows that it evolves from extreme X-ray luminosity through to rather fainter luminosities in both the optical/IR and X-ray. However, at late times it does not fall within the locus of X-ray emitting galaxies, either of local galaxies harboring relatively quiescent black holes or of more luminous AGNs. For example, in the comparison of Pineau et al. (2011) of SDSS with 2XMM, only a handful of matches have optical absolute magnitudes fainter than −19 and in most of these galaxies the X-ray luminosity is sufficiently low (10^38–40 erg s⁻¹) that discrete X-ray emission from binaries, etc. could be responsible for the observed flux. Indeed, the optical absolute magnitude of the host galaxy of Swift J1644+57 of M_V ∼ −18.5 is fainter than the cases of Heinze 2–10 (Reines et al. 2011) or Mrk 709 (Reines et al. 2014), both nearby dwarf galaxies thought to harbor massive black holes. Thus, despite the apparent plateau in X-ray luminosity, this argues against the presence of a standard AGN within the host galaxy, as supported by the absence of obvious AGN features in either optical spectroscopy (see above) or late time radio follow-up (Zauderer et al. 2013). Further X-ray observations over increasingly long time periods should ultimately offer a sensitive test of any variability within the source.

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A striking feature of the optical/IR light curves is the presence of an apparent upturn to a peak in the light curve around 30 days after the outburst. Initially the plateauing seen at these times was assumed to be due to the source fading into its host galaxy light, but later observations clearly demonstrate further fading by a factor of >3 from this time. There is significant point-to-point scatter in the IR observations at many epochs, possibly due to intrinsic variation in the source on short timescales. Direct comparison of observations taken with the same instrument and telescope combination implies that this variability is real, at least at early times. There is also likely to be some scatter due to slight systematic differences between our photometry and that reported by Burrows et al. (2011). This means that as with the X-ray, simple fits to the data do not yield high-quality fits and will provide only an approximation of the true behavior. However, the host-subtracted K-band data can be described by a multiply broken power law as shown in Figure 4. The counterpart declines with α₁ ≈ 1.3 (where F_ν ∝ t^−α), then rises with α₂ ≈ −0.7 to a peak at 30 days. From this point a decline with α₃ ≈ 0.8 describes the final fading into the host galaxy, although there are significant errors on the late time points due to the uncertainty in host subtraction. This crude model of three power-law segments also provides a reasonable fit to the H- and J-band observations if an arbitrary offset is applied (see Figure 4). If this offset is scaled to provide a good match to the early data (<10 days post-burst) then it significantly underpredicts the strength of the bump in the H and J bands. This suggests that the bump does not have the same underlying spectral energy distribution (SED) as the earlier counterpart and is much bluer with relatively weak IR emission.

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The HST observations provide the best measurements of this bump since they can cleanly be subtracted for host contribution without the need for PSF matching or differences between cameras or filters. However, the HST observations also provide extremely poor temporal sampling. Nonetheless, it is striking to note that the F606W optical observations show an apparent rise between 6 and 23, with the 23 day flux ∼1.5 times brighter than at day 6, while the IR light at 23 days is 0.9 times as bright as at 6 days (see Figure 5). This offers further evidence that the bump is a separate feature rather than a simple, achromatic re-brightening. The HST observations also suggest that at later times the decay cannot be well fit as a single power-law decay, although this is again based on very small sampling (3 points per band).

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In Figure 6 we show the evolution of the SED of Swift J1644+57. It can be seen to be extremely red, as previously noted. Its SED, combined with the significant X-ray column density, favors an optical extinction in the region 1.5 < E(B − V) < 2 (Bloom et al. 2011b; Burrows et al. 2011; Levan et al. 2011). To highlight the possible impact of extinction, we then also plot the SED corrected for a maximal extinction of E(B − V) = 2 assuming a Milky Way extinction law, although since none of our wavelengths are close to the rest-frame 2175 Å bump, the choice of extinction law has minimal impact on the correction. The peak of the bump at 30 days has an absolute magnitude of M_B ∼ −22 for a maximal extinction, comparable to the peak magnitude in the K band (which is far less affected by host extinction).

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Perhaps the most plausible explanation is that the optical bump originates as the hot thermal component of the tidal flare. Such components are typically those expected based on non-relativistic models (e.g., Rees 1988). This peak luminosity occurs well after the disruption itself since the peak accretion rate is after the return of the most bound debris. Indeed, numerical models of mass return suggest that luminous UV flares may peak on timescales of ∼20–50 days at optical and UV wavelengths (Lodato & Rossi 2011) with luminosities rather similar to those of normal SNe. This is broadly borne out by observations of candidate disruptions to date, with many of the most promising candidates showing such rises. However, suggested examples of TDFs actually show a surprisingly large variation in their properties. Some peak early and very bright (M_V < −20 and rise times of a few days, e.g., PTF10iya (Cenko et al. 2012a)) while those with much longer lifespans are also significantly fainter (M_V > −18 with rise times of 20–50 days). There are no examples that apparently match the energy output for Swift J1644+57, although there remains significant uncertainty about both the extinction and the contribution of any non-thermal component. We plot the light curves of Swift J1644+57 (after subtraction of the host contribution and correction for host extinction) against those of candidate TDFs in Figure 5. Unfortunately, such a comparison is non-trivial since Swift J1644+57 is predominantly observed in the rest-frame IR, while the thermal flares are strong UV and optical emitters. Therefore, the poorly sampled optical light curve of Swift J1644+57 (cyan line in Figure 5) is probably the best comparison with known examples. However, the strong evolution in the optical/IR SED of the source occurs primarily at early times, where the IR light is falling as the optical rises. As this is before the peak of the bump, we can compare the later evolution by scaling the well sampled K-band light curve to the optical. It should also be noted that this comparison is further complicated since the origin of many suggested TDFs remains uncertain, for example, some may be unusual SNe and others due to partial disruption (e.g., Chornock et al. 2014; Holoien et al. 2014) or the disruption of unusual stars (e.g., Gezari et al. 2012).

Another possibility is that the re-brightening is due to the optical/IR contribution of the second synchrotron component identified by Berger et al. (2012). This peaks at radio wavelengths at ∼100 days, although plausible synchrotron models could result in an earlier peak for the optical/IR emission (as seen in GRBs for example (Sari et al. 1998)), depending on the location of spectral breaks. This would have the appeal of representing the manifestation of a feature known at other wavelengths and might also explain the relatively high polarization (7.4 ± 3.5%) seen in the IR 17 days after the outburst as the bump is beginning to dominate (Wiersema et al. 2012). Indeed, as noted by De Colle et al. (2012), the delay between viewing energy injection at the base of the jet in X-rays and radio emission from the jet head is naturally expected in models of jetted TDFs, and this "lag" in which the optical/IR peak is between these two extremes may have some appeal. However, the parameters would necessarily require some tuning to provide the brightening without the presence of any moving spectral breaks in the optical/IR since while the relative strength of the bump emission varies with wavelength, the shape of the bump is broadly similar. The bump colors would also be unusually blue-corrected for host extinction: the spectrum would follow F_ν ∼ ν² or steeper, much bluer than expected for GRB-blast waves in this wavelength regime. The polarization measurement could also represent underlying asymmetry in the source, as is seen in some SNe (e.g., Patat et al. 2011), while its intrinsic value is significantly uncertain since interstellar polarization within the host could also play an important role (Wiersema et al. 2012). To date there do not exist polarimetric observations of the thermal components of TDF flares, and so this cannot be compared directly.

An alternative hypothesis is that the optical bump could be due to reverberation of the X-ray light. Yoon et al. (2015) claim that the morphology of the optical is similar to that of the X-ray, but with a delay of ∼15 days. While this does not appear the case in a detailed comparison (for example, the X-ray rise is rapid while the optical/IR rise apparently takes place over the timescale of several days) it is possible that a prompt injection of energy in the X-ray could be smoothed out should the reverberating material be spread out at an average distance of ∼15 light days from the central engine. While the lags to the broadline region can be of this size (Peterson et al. 2004) simultaneous optical/X-ray monitoring of AGNs typically yields much smaller lags (∼1 day) between X-ray and optical emission (e.g., Breedt et al. 2009, 2010), while lags due to processes within the disk are also short (∼1 day) and should increase with increasing wavelength (McHardy et al. 2014). Hence the properties of the light curves do not naturally match the expectations of reverberation seen in AGNs and would require an unusual, pre-existing AGN-like geometry to exist within the host. On the other hand, the unexpectedly high optical luminosities and low effective temperatures of many optically selected TDFs have also been attributed to "reprocessing" of the inner disk emission by debris from the merger, either bound debris still returning to the BH (Guillochon et al. 2014) or an unbound outflow from the accretion disk (e.g., Strubbe & Quataert 2011; Metzger & Stone 2015).

The other class of astrophysical transient that can reach such extreme luminosities are the superluminous supernovae (SLSNe; e.g., Gal-Yam 2012). These events peak at magnitudes of M_V < −21 and have slow rise times of 30–100 days, followed by slow decays. The peak luminosity of Swift J1644+57 is comparable to these events and given the uncertainty in both the explosion date of SLSNe and the true "trigger" time for Swift J1644+57, it is possible to obtain a reasonable match in both light curve shape and luminosity. For the case of E(B − V) = 2 the luminosity would be among the highest for SLSNe, although the recent discovery of the most luminous SLSNe ASASSN-15lh would be comparable (in fact, it should also be noted that ASASSN-15h is apparently coincident with the nucleus of its host galaxy (Dong et al. 2016), as is the second brightest SLSNe, CSS 100217, (Drake et al. 2011), perhaps offering further hints of similarities between classes of astrophysical transient). Given the uncertainties in host extinction one can also find a reasonable match in terms of spectral shape between hydrogen poor SLSNe and Swift J1644+57 (see Figure 6).

At first sight, the strong simultaneous X-ray emission would appear to rule out an SLSNe origin, however, two recent developments may be important in this regard. First, the apparently normal hydrogen poor SLSNe, SCP 06F6 has a strong X-ray detection >100 days after its discovery, with a luminosity very similar to that of Swift J1644+57 at the same epoch (Gänsicke et al. 2009; Levan et al. 2013). X-ray observations were not obtained of SCP 06F6 until very late, but it is possible that it is due to jetlike emission that could have been persistent but undetected over a long period in a system similar to Swift J1644+57. Although it is also possible that the X-ray detection of SCP 06F6 was due to a shorter breakout of magnetar emission (Levan et al. 2013) and the possibilities cannot be distinguished between with the paucity of earlier X-ray observations. Second, in the case of one ultra-long GRB, GRB 111209A (Gendre et al. 2013; Levan et al. 2014) there has recently been the identification of a luminous supernova signature (Greiner et al. 2015), indicating that one can simultaneously observe strong X-ray emission and a luminous SNe bump. If these SNe are in fact powered by either a black hole or long-lived magnetar central engines then one might expect to sometimes observe them down a jet axis, in which case events like Swift J1644+57 or GRB 111209A could be observed. Motivated in part by these results Metzger et al. (2015) have shown that the full variety of luminous SNe and extremely long-lived high-energy transients can be explained (although not necessarily uniquely) by magnetars with differing magnetic fields and spin-down times, extending the suggestion by Mazzali et al. (2014) that most GRBs can be explained by such a mechanism. Indeed, they note that this model would naturally predict the luminosity of Swift J2058+0516. The case of Swift J1644+57 would then also fit on the extrapolation of these models.

Indeed, it is instructive to consider Swift J2058+0516 in this regard, since it exhibited similar high-energy properties to Swift J1644+57, but lacked the heavy extinction. Thus we might expect to be able to test any SN hypothesis, especially as the redshift was almost identical to the SLSNe SCP 06F6. In this case the luminosity of the optical afterglow was comparable to SLSNe, and the inferred temperature (T ∼ 2 × 10⁴ K, Pasham et al. 2015) was similar to both GRB 111209A/SN2011kl and ASASSN-15lh (Dong et al. 2016; Greiner et al. 2015). However, there was only rather minimal evidence of any optical rise (although observations started late) and optical spectroscopy did not yield any sign of the strong absorption features seen in most SLSNe. This casts some doubt on any model linking events such as Swift J1644+57 and Swift J2058+0516 with stellar core collapse, although it should equally be noted that in the case of GRB 111209A/SN2011kl (Greiner et al. 2015) the high ejecta velocities diluted any absorption features such that they were not obvious in the observed spectra. The final case of Swift J1112–8238 (Brown et al. 2015) unfortunately does not yield such strong constraints due to rather patchy follow-up, although the absolute magnitude of the transient of M_B ∼ −21.4, 20 days after the BAT detection is in keeping with the absolute magnitudes seen in both Swift J1644+57 and Swift J2058+0516.

Finally, the observed rates of different events could potentially provide some discrimination between progenitor models. Before correction for beaming, GRBs likely show a volumetric rate of a few Gpc⁻³, corrected for likely beaming this becomes ∼300 Gpc⁻³ (e.g., Kanaan & de Freitas Pacheco 2013), rather comparable to the rate of SLSNe (Quimby et al. 2013). The rate of Swift J1644+57-like transients, or ultra-long GRBs is significantly lower than the GRB rate, although poorly constrained given the small population observed, and observational biases against their detection as long-lived, low peak-flux events (Levan et al. 2014). Brown et al. (2015) estimate a rate of 3 × 10⁻¹⁰ galaxy⁻¹ yr⁻¹ for Swift J1644+57-like events. Accounting for biases in their detection could give an order of magnitude larger rate, with a similar boost given if shorter events, such as the ultra-long GRBs are included (Levan et al. 2014). Given the volume density of galaxies in the relatively local universe (or more specifically massive black holes) is ∼10⁻²–10⁻³ Mpc⁻³ the inferred volumetric rate of the Swift J1644+57-like events is ∼3 × 10⁻³ Gpc⁻³ yr⁻¹, or allowing for the various selections against their discovery perhaps as high as ∼0.1 Gpc⁻³ yr⁻¹. Hence, even with very small beaming angles (e.g., the factor of ∼10^2–3 needed to bring the observed luminosity below the Eddington limit for a 10^7–8 M_⊙ black hole) such jets need only be launched from a small fraction of SLSNe. This would explain why evidence for their existence in X-ray monitoring of SLSNe is rare to date (Levan et al. 2013). Equally, these rates are significantly below the rates of TDFs, whose canonical rate of 1 × 10⁻⁵ galaxy⁻¹ yr⁻¹ is 5 orders of magnitude higher than that of the relativistic counterparts. As noted by Cenko et al. (2012b) and Brown et al. (2015) it is therefore unlikely that any significant fraction of TDFs could launch such powerful relativistic jets as seen in Swift J1644+57 and other examples. Overall, the rate arguments suggest that these very long duration transients could arise from some small subset of either TDFs or SLSNe.

After the X-ray break it is likely that the observed flux in all bands is now dominated by the host galaxy, affording us the opportunity to investigate it in more detail than previously possible. Indeed, this is supported by the analysis of Yoon et al. (2015) who attempt to fit a point source onto the host, concluding that at later times the point source contribution is minimal. The galaxy is detected in 12 photometric bands from 0.45–4.5 μm, with upper limits available from GALEX in the UV (Gezari et al. 2011) and WISE in the mid-IR (Levan et al. 2011), although in practice the upper limits are weak and do not aid in the determination of galaxy properties since they lie well above any plausible galaxy model fitted through the bands in which the host is detected. The photometric detections and limits are shown in Table 4. From this we can derive the physical properties of the host galaxy based on template fitting to the available SED shown in Figure 7. Considering the Binary Population and Spectral Synthesis (BPASS) library of models (Eldridge & Stanway 2009), we find the SED to be well reproduced by a relatively old dominant stellar population (age = 3.2 × 10⁹ years), although the emission lines clearly indicate the presence of a younger population as well (Figure 7). Importantly, the fitting also provides a much more robust determination of the stellar mass than was previously possible, since earlier attempts were significantly contaminated at red wavelengths by transient light. Specifically we find a stellar mass of M_* = 5.5 × 10⁹ M_⊙. This value is somewhat larger than that found by Yoon et al. (2015) from their more detailed study (${M}_{*}\;=\;{1.38}_{-0.27}^{+0.48}\times {10}^{9}$). However, this may be explained by the use of differing spectral models, and our use of later time Spitzer observations, free from transient contamination. This stellar mass can be used to infer an approximate mass for the central black hole. Scott et al. (2013) find that for core-Sérsic profiles the scaling is roughly linear (${M}_{\mathrm{BH}}\propto {M}_{*}^{0.97\pm 0.14}$), but for galaxies with low masses (they define low to be M_* < 3 × 10¹⁰ M_⊙) they find a much steeper relation of ${M}_{\mathrm{BH}}\propto {M}_{*}^{2.22\pm 0.58}$. Under the assumption that the galaxy stellar mass is equal to its spheroid mass (which seems a reasonable assumption given the surface brightness profile, see below) the implied black hole mass is then M_BH ∼ 3 × 10⁶ M_⊙, which could be taken as an upper limit on the likely BH mass.

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Despite its luminosity appearing very similar to the LMC (M_B ∼ −18), the morphological properties of the host of Swift J1644+57 are rather different. The core of the galaxy is barely resolved by the HST IR observations, although is reasonably resolved in the optical. The galaxy has little ellipticity e ≈ 0.1 and is very concentrated, with R_20,50,80 = 0.077, 0.184, 0388 = 0.39, 0.92, 1.95 kpc at z = 0.354. Its surface brightness profile is well fit with a Sérsic fit with n = 4 (i.e., a de Vaucouleurs profile) in both the optical and IR, suggesting it is dominated by a spheroidal component (see also Yoon et al. 2015). However, a subtraction of a rotated image does reveal some asymmetry with a knotlike structure extending ∼01 from the galaxy nucleus, but interestingly including the location of the transient. These are potentially the star-forming regions creating emission lines and lead to a formal concentrated asymmetry measure of C ≈ 3.5, A ≈ 0.1, placing the host in a region of in the concentration asymmetry plane similar to many GRB hosts (Conselice et al. 2005).