THE DEFINITIVE X-RAY LIGHT CURVE OF SWIFT J164449.3+573451

The 0.3−10 keV count rate light curve shown in Figure 1 was produced by binning the net source counts in order to have at least 200 counts per time bin at early times, and progressively decreasing the level of required counts per bin down to at least 10 counts per bin at late times, up to sequence 00032526001, observed on 2012 August 16, 507 days after the trigger. On day 508 the source emission suddenly dropped below the detection threshold for a 1−2 ks single snapshot observation (Sbarufatti et al. 2012). A detailed plot of the abrupt drop is shown in Figure 2, where data from 2012 August and September have been binned daily. The daily count rate measured in the source region (red histogram) is compared to the expected background count rate in the source region on the same day (blue histogram). When Swift J1644+57 is not detected, the 3σ upper limit on source count rate is shown. The plot shows that the count rate drops abruptly on day 508 (2012 August 17). By comparing the count rate on day 507 and the level of the deepest upper limit we see in Figure 2 (on day 537) we can state that we had a drop of more than a factor 11 in one month, i.e., a fraction of 0.06 of the total time elapsed.

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The very last point in the light curve of Figure 1 is the detection obtained from the summed 191 monitoring observations performed from 2012 August 17th (marked by the green dashed vertical line) to 2014 March 28th, for a total of 284.5 ks exposure. We extracted the source counts from a circular region of 10 pixels radius (314 pixel² area) and estimated the background contribution from counts found in the background region (21,143 pixel² area, specifically selected to avoid contamination from any field source detected in the whole PC data set) and rescaled to the source region area. We obtained 78 total counts in the source region in the 0.3−10 keV band with an estimated background of 44 counts and applied the technique of Kraft et al. (1991) to calculate the upper and lower 99% confidence limits on source counts. These correspond to an average count rate of ${1.2}_{-0.7}^{+0.9}\times {10}^{-4}$ s⁻¹. The source is also detected on the summed image of the post-drop monitoring with the ximage command sosta, centered on the position of source with user defined source and background regions, at the level ${\rm{(}}1.5\pm 0.4{\rm{)}}\times {10}^{-4}$ s⁻¹ with 3.8σ significance.

The band ratio and hardness ratio curves of Swift J1644+57 are shown in Figure 3. We have defined the energy range 0.3−1.5 keV as the soft band (S) and the energy range 1.5−10 keV as the hard band (H). We have calculated both the ratio of the counts detected in the two bands (H/S) and the hardness ratio (H–S)/(H+S). The curves have been binned in order to have at least 500 net counts in each band up to day 507 post-trigger. For the last point (covering the time interval from day 508 to day 1096) net counts in the required bands were derived from the summed post-drop observations with the same procedure used for the count rate light curve. Errors have been estimated in the Poisson approximation (Gehrels 1986) and propagated with standard error propagation formulae. At the beginning, both curves show variations tracking the light curve flares, with the hardness rising when the average rate increases, and decaying when the average rate decreases. But later phases with different trends can be identified. We observe a hardness plateau phase from ∼2.4 to ∼16 days post-trigger, corresponding to a phase of average rate decrease (from ∼2.4 to ∼6 days) followed by a rapid rise by a factor ∼10 in ∼0.3 days and a shallow decay afterwards. After 16 days, while the average rate in the light curve goes on decaying steadily, we observe a relatively rapid (∼1 day long) drop (i.e., softening) in the hardness followed by a steep rising (i.e., hardening) phase that lasts up to ∼100 days, when a final hardness plateau phase starts. In both cases the last point represents a clearly different and much softer spectral state compared to the final trend of the curve. A comparable softness is attained only at a few light curve minima between flares (e.g., the first one at ∼0.2 days), which are minima for the band ratio and hardness ratio curves as well. If the abrupt Swift J1644+57 emission drop on day 508 is due to the turn-off of the jet (Zauderer et al. 2013), which might be likely caused by a transition to a thin disk as the accretion rate dropped below a critical value of several tens of percent of the Eddington accretion rate (Zauderer et al. 2013; Tchekhovskoy et al. 2014), then the low-level residual emission we detected later should have a different origin and this discontinuity in the hardness curves would not be surprising.

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We see evidence of different spectral phases during Swift J1644+57 evolution also in Figure 4, where the soft band ratio S/(H+S) is plotted against the total rate (H+S) in the 0.3−10 keV band. Here XRT data in different operation mode are color-coded as in the previous figures, and different markers distinguish early emission (before 2.4 days, filled circles) from intermediate (between 2.4 and 39 days, empty stars) and late emission (after 39 days, empty triangles). According to this plot early data show an anti-correlation between the soft band ratio and the overall count rate i.e., a trend for harder spectra at higher rates. The correlation is tighter for WT data. PC data are more dispersed and seem to lie on a different correlation, also consistent with the harder-when-brighter trend. Late data are in PC mode only, and follow an opposite trend of harder spectra at lower rates despite the large dispersion. Intermediate data populate the central part of the plot. Part of these (WT data up to 23 days, dark blue empty stars) were included in the corresponding plot in Paper I (Supplementary Figure 4) and are interpreted as a second branch of the WT harder-when-brighter correlation after a count-rate discontinuity at ∼4 s⁻¹. The inclusion of the remaining WT data (light blue empty stars) has not completed the correlation in the left upward direction as expected, but simply thickened the data cloud on the left direction. Note that count rates as low as those reached by the WT data in Figure 1 are not seen in this plot because of the different binning criterion used. The intermediate PC data populate the bottom of the central cloud, spanning a range in rates comparable to the intermediate WT data, but with much less spread in softness (consistent with the plateau observed in Figure 3 between 2.4 and 16 days). With the possible exception of intermediate PC data, intermediate WT and late PC data in Figure 4 may be interpreted as a single component obtained by shifting leftwards and downwards with time an anti-correlation law similar to the one followed by the early WT data. This result could be obtained with a global hardening with time superimposed on a strict hardness-tracking-brightness rule on the smaller variability timescales of flares and dips.

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The XRT team's on-line light curve repository (http://www.swift.ac.uk/xrt_curves/00450158/; Evans et al. 2009) uses a single conversion factor between count rate and flux (ECF), determined using an automated spectral fit of the PC mode data. This works well for GRBs, since there is rarely any significant spectral evolution after the first few ks of the afterglow, but it does not work well for Swift J1644+57, due to the extremely strong spectral variations during the first few hundred days (Figure 3). A more realistic conversion to flux can be obtained via time-dependent spectral analysis. The procedure, which we already applied in Paper I, consists of the following steps: (i) split the data set into a sequence of short time intervals tracking the hardness states of the source but with enough counting statistics to use standard ${\chi }^{2}$ fitting techniques, and extract spectra for each time interval; (ii) fit each spectrum, derive the ECF corresponding to the best-fit model, and create a stepped ECF evolution law; (iii) convert the count rate light curve to flux by applying at each point an ECF obtained through a cubic spline interpolation of the ECF stepped curve.

The conversion applied in Paper I was limited to the first 50 days of the Swift J1644+57 outburst, and was based on spectral modeling with the log-parabola model defined as $A(E)={E}^{(-\alpha +\beta {\mathrm{log}}_{10}(E))}$ where α is the photon index and β is a measure of the curvature compared to a simple power law, which is obtained for $\beta =0$. The complete spectral model we use also includes two absorption components: a Galactic one with ${N}_{{\rm{Hgal}}}$ fixed to 1.7 × 10²⁰ cm⁻² (Kalberla et al. 2005) and an intrinsic one at redshift z = 0.35 with ${N}_{{\rm{H}}}$ allowed to vary with time. The log-parabola model has been introduced as a good empirical fit for broadband spectral distributions of BL Lacs and other blazar sources. The version we use corresponds to the model logpar in xspec (Massaro et al. 2004) with (constant) parameter pivot-E (representing the low end of the energy range used in the fit) fixed to 1 keV, and curvature parameter equal to $-\beta$. In Paper I we reported that the log-parabola spectral model generally provided better fits than a simple power law to both time and intensity-selected spectra of Swift J1644+57, though power-law fits were statistically acceptable. However, in about 74% of cases the best-fit value of the parameter β was consistent with zero within its uncertainties, making the model perfectly equivalent to a power law (see Supplementary Figure 11 in Paper I), but with substantially larger errors on both the intrinsic absorption column and the photon index compared to the power-law fit.

For the present paper, we complete the set of time-dependent spectra used in Paper I with more spectra extracted from the data collected after the first 50 days and before the light curve drop, reaching a total of 215 spectra (163 in WT mode and 52 in PC mode). We have reanalyzed the whole data set with updated spectral response files, fitting each spectrum with both power-law and log-parabola models.⁶ Since these two models are suitable for an F-test (Protassov et al. 2002), we apply it to estimate the probability P of chance improvement of the ${\chi }^{2}$ and reject all the log-parabola fits with P > 0.01. This condition rejects 195 of the log-parabola fits (including all the best-fit solutions with β consistent with zero within errors) i.e., according to this selection the log-parabola model significantly improves the fit only for 20 spectra (15 in WT mode and 5 in PC mode). Thus, for every further calculation, we decided to use the power-law fit results for all the spectra but the 20 for which the log-parabola fit represents a significant improvement.

We also extracted and analyzed a spectrum from the summed PC data collected after the drop in the light curve, choosing source and background extraction regions as we did for the final count rate and hardness ratio calculation. In this case the data were binned to 1 count per energy bin to allow for fitting with Cash statistics (Cash 1979) in xspec (with ${\chi }^{2}$ statistic test evaluation enabled). The very low statistics do not allow for a fit withan absorbed power-law with both intrinsic ${N}_{{\rm{H}}}$ and photon index free or an absorbed log-parabola model in this case. We modeled the spectrum with an absorbed power-law with intrinsic ${N}_{{\rm{H}}}$ fixed to 1.9 × 10²² cm⁻². The best fit photon index is ${\rm{\Gamma }}=2\pm 1$. The fit is poor and the uncertainty is very large. Γ values larger than 2 are likely to be preferred because corresponding models give H/S < 1.5. The correct band ratio may be achieved also with Γ values smaller than 2 and lower intrinsic ${N}_{{\rm{H}}}$. We then performed a second fit with Γ fixed to 1 and free intrinsic ${N}_{{\rm{H}}}$. The fit is apparently equivalent to the previous one and formally gives ${N}_{{\rm{H}}}$ < 0.5 × 10²² cm⁻², but the model cannot reproduce an H/S ∼ 1 unless ${N}_{{\rm{H}}}$ is zero.

Our final best-fit results, including those for the post-drop spectrum, are listed in Table 1 and shown in Figure 5. The log-parabola model is a curved model with a broad minimum in the spectrum at ${E}_{{\rm{crit}}}={10}^{(\alpha -2)\frac{2}{\beta }}$ keV if $\beta \gt 0$, or a broad peak at energy ${E}_{{\rm{crit}}}$ for $\beta \lt 0$. Note that among the log-parabola best-fit models that survive our selection, we have five with positive values of β and all of them correspond to PC spectra. In all cases ${E}_{{\rm{crit}}}$ is in the 2.5−6.0 keV range, well within the Swift/XRT energy band, but the peak/minimum is so broad compared to the band (relative width ∼ $| \alpha /\beta |$) that almost no curvature can be seen by eye in the spectrum. Finally, the 20 log-parabola fits show a strong correlation between ${N}_{{\rm{H}}}$, photon index, and β. This is apparently unrelated to any physical status, because the 20 spectra do not show any common property (e.g., corresponding to peaks or minima, showing pile-up, etc.). We are led to believe that in these 20 special cases the log-parabola fits are merely approximate descriptions that we cannot use for any other purpose than flux estimation.

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Table 1.  Swift J1644+57: Best Fit Parameters of Time-resolved Spectra

Number	XRT Mode	Start (days)a	Stop (days)b	${N}_{{\rm{H}}}$ (cgs)c	Photon Indexd	β	${\chi }^{2}$	dof
1	WT	0.01713861	0.03135739	${1.5}_{-0.2}^{+0.2}$	${0.74}_{-0.28}^{+0.30}$	−0.86 ${}_{-0.24}^{+0.25}$	469.530	470
2	PC	0.07028800	0.41441000	${2.6}_{-0.4}^{+0.4}$	${4.34}_{-0.74}^{+0.71}$	${1.94}_{-0.69}^{+0.65}$	131.768	104
3	PC	0.41559230	0.49312770	${2.3}_{-0.5}^{+0.6}$	${1.73}_{-0.24}^{+0.25}$	⋯	45.600	40
4	WT	0.55755144	0.55925056	${2.0}_{-0.2}^{+0.2}$	${1.63}_{-0.10}^{+0.10}$	⋯	145.590	138
216e	PC	508.39513700	1096.00273100	${1.9}_{-0.0}^{+0.0}$	${1.98}_{-1.08}^{+0.97}$	⋯	23.611	47

Notes.

^aStarting time of data interval, relative to the first BAT trigger at T₀ = 2011 March 28 12:57:45.201 UTC = 55648.5401 MJD. ^bEnding time of data interval, relative to the first BAT trigger at T₀ = 2011 March 28 12:57:45.201 UTC = 55648.5401 MJD. ^cUnits are 10²² cm⁻². ^dGives the value of the parameter α when the value of β is listed. ^eSpectrum of the post-drop phase.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

The ECFs to be used for the final conversion from count rate (Figure 1) to 0.3−10 keV observed flux are derived from the best-fit results listed in Table 1 and are shown in the left panel of Figure 6, while in the right panel of the same figure we show the corresponding ECFs for conversion into 0.3−10 keV unabsorbed flux. Note that in this latter case the five log-parabola best-fit models with $\beta \gt 0$ lead to higher than average values of the ECF, and all those with $\beta \lt 0$ lead to lower than average values of the ECFs. This is due to log-parabola spectra with $\beta \gt 0$ having larger than average ${N}_{{\rm{H}}}$ values and softer than average photon indices, as opposed to the $\beta \lt 0$ solutions, for which the opposite is true. The correction for the absorption leads to a larger scatter in the ECFs. The absolute average deviation of the ECFs (i.e., the average of their differences from the mean value, taken in absolute value) rises from 7% to 15% of the mean value going from the left panel to the right panel in Figure 6.

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The final light curve in observed and unabsorbed flux will be introduced and discussed in Section 3.4. Note that the ECFs for the observed flux after day 15 change systematically, mirroring the strong variations in the band and hardness ratio plots of Figure 3. This could lead to a different slope for the overall decay rate than would be obtained using a single mean ECF. The ECFs for the unabsorbed flux, instead, show an average constant trend after day 15, in better agreement with the standard XRT light curve repository.

A closer look at the temporal evolution of the spectral parameters in Figure 5 shows that the variations of both the intrinsic ${N}_{{\rm{H}}}$ and the photon index approximately track the rate, but with opposite trends: the ${N}_{{\rm{H}}}$ tends to be higher at higher rates, while the photon index tends to be lower at higher rates, at least for the early portions of the light curve.⁷ These different behaviors are visible in Figure 7, where the photon indices and the intrinsic absorption columns of the time-resolved spectra of Swift J1644+57 well fit by an absorbed power-law model are plotted as a function of the 2−10 keV flux. The photon index plot (left panel) shows a structure similar to the soft band ratio versus rate plot in Figure 4, though a larger dispersion in the different groups of data is clearly seen. The intrinsic ${N}_{{\rm{H}}}$ plot (right panel) has a different structure, with early data (filled circles) showing a more-absorbed-when-brighter trend, and late data (empty triangles) suggesting a moderately increasing absorption as the flux decays. The intermediate data (empty stars) are more difficult to interpret because of the large dispersion, but seem to follow a trend similar to early data. A general trend of intrinsic ${N}_{{\rm{H}}}$ decreasing with time is confirmed by a linear fit of ${N}_{{\rm{H}}}$ versus ${\mathrm{log}}_{10}\;t$. With t in units of days we obtain an intercept at 1 day of (1.98 ± 0.02) × 10²² cm⁻² and a linear coefficient of −0.44 ± 0.02, with a ${\chi }_{r}^{2}=1.522$ (213 dof). An analogous fit for the photon index gives an intercept at 1day of 1.82 ± 0.01 and a linear coefficient of −0.40 ± 0.01, with a ${\chi }_{r}^{2}=1.885$ (213 dof), and confirms the general trend for hardening of the spectra we already noted in Section 3.2.

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The final light curves of Swift J1644+57 in observed flux and unabsorbed flux ar e shown in Figure 8. The conversion procedure and the time-dependent ECFs used are described in Section 3.3. Note that discrepancies between the two curves are largest in the time intervals from 0.07 days after the BAT trigger to ∼0.5 days, and from 6 to 15 days. The overall later decay does not seem dramatically affected by the correction for the absorption. Models of TDEs give predictions about the decay of the intrinsic luminosity of the source. For this reason the unabsorbed flux light curve of Swift J1644+57 should be used in testing models. This one is shown alone in Figure 9 and listed in Table 2.

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The X-ray light curve of Swift J1644+57 differs from the typical X-ray afterglow light curve of a GRB in many respects. In Figure 10 we compare the X-ray light curve of Swift J1644+57 to that of GRB 060729, the longest GRB X-ray light curve ever obtained (Grupe et al. 2010). Both curves are shown in terms of the X-ray luminosity, ${L}_{{\rm{X,iso}}}$, calculated assuming isotropic emission, and are plotted in the source rest frame. The ${L}_{{\rm{X,iso}}}$ light curve of GRB 060729 has a canonical afterglow shape, with a flat plateau phase followed by a power-law decay similar to the late average decay of Swift J1644+57, but starting about 30 times earlier and running three orders of magnitude below the Swift J1644+57 light curve for $t\gt 10$ days. As illustrated by GRB 060729, GRB afterglows are typically fairly smooth; they may show flares (usually in the first day, before and/or during the plateau phase) but never show dips, nor has a GRB ever exhibited a range of variability like that seen in Swift J1644+57, which uniformly spans more than one order of magnitude throughout its evolution. Moreover, GRB afterglows rarely exhibit spectral evolution after the first day, while we have shown that Swift J1644+57 exhibits strong spectral evolution for well over a year.

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The overall shape of the X-ray light curve of Swift J1644+57 also differs from typical X-ray light curves from long-term monitoring of blazars, the class of AGN sources with observed radiation dominated by the emission from relativistic jets pointing at the observer. The typical dynamic range of blazar flares in X-rays is a factor of a few, not several orders of magnitude, and the typical activity duty cycle is small compared to that of the initial flares of Swift J1644+57 (Krolik & Piran 2011).

Zauderer et al. (2013) argue that the rapid decline of the X-ray flux at $t\simeq 500$ days heralded the turning off of the relativistic jet in Swift J1644+57. They suggest that at that time, the accretion rate within the jet feeding the BH dropped below the Eddington rate, ${\dot{M}}_{{\rm{Edd}}}\simeq 6\times {10}^{-3}$ ${M}_{\odot }\;{{\rm{yr}}}^{-1}$, assuming ${M}_{{\rm{BH}}}\simeq {10}^{6.5}$ ${M}_{\odot }$ and a conversion efficiency between rest-mass energy and accretion luminosity of ${\epsilon }_{{\rm{acc}}}\simeq 1$. Prior to this time, the ratio of accretion power to jet power was constant, as evidenced by the constancy of the observed power law decay index. During the time it was seen by XRT, the X-ray luminosity of Swift J1644+57 varied over a dynamic range of about a factor of ∼6000, from ∼2.2 × 10⁴⁸ erg s⁻¹ to ∼3.7 × 10⁴⁴ erg s⁻¹. Thus if the switch-off luminosity corresponded to Eddington, at peak luminosity the accretion rate onto the BH would have been ∼6000 times Eddington.

If the conjecture by Zauderer et al. (2013) is correct, one may obtain a constraint on the combination of efficiency parameters relating accretion rate to jet power. The jet power can be expressed as

$$\begin{eqnarray}&&{L}_{J}={\epsilon }_{J}{\dot{M}}_{{\rm{fb}}}{c}^{2},\end{eqnarray} \tag{ 3 }$$

and the observed X-ray luminosity (assuming all the jet power is in X-rays) is

$$\begin{eqnarray}&&{L}_{{\rm{X,iso}}}=\displaystyle \frac{{L}_{J}}{\displaystyle \frac{1}{2}{{\theta }_{J}}^{2}},\end{eqnarray} \tag{ 4 }$$

where ${\theta }_{J}$ is the jet opening angle. Hence,

$$\begin{eqnarray}&&{L}_{{\rm{X,iso}}}=\displaystyle \frac{{\epsilon }_{J}{\dot{M}}_{{\rm{fb}}}{c}^{2}}{\displaystyle \frac{1}{2}{{\theta }_{J}}^{2}}.\end{eqnarray} \tag{ 5 }$$

Assuming that the jet turns off when the accretion rate drops below Eddington, which happens at ${\dot{M}}_{{\rm{fb}}}=6\times {10}^{-3}$ ${M}_{\odot }\;{{\rm{yr}}}^{-1}$ and ${L}_{{\rm{X,iso}}}=3.7\times {10}^{44}$ erg s⁻¹, we obtain the constraint

$$\begin{eqnarray}&&{\epsilon }_{J}{{\theta }_{J}}^{-2}=5.4.\end{eqnarray} \tag{ 6 }$$

According to theory, it is not expected a priori for jet power to track accretion rate in the disk. If the jet is fed via the canonical Penrose–Blandford–Znajek process, the jet power would be

$$\begin{eqnarray}&&{L}_{J}=1.2\times {10}^{46}\ {\rm{erg}}\ {{\rm{s}}}^{-1}{{\rm{\Phi }}}_{*,30}^{2}{M}_{{\rm{BH,}}\;{\rm{6}}}^{-2}{{\omega }_{H}}^{2}f({\omega }_{H}),\end{eqnarray} \tag{ 7 }$$

where ${{\rm{\Phi }}}_{*,30}$ is the magnetic flux threading the BH event horizon in units of 10³⁰ Gauss cm², ${M}_{{\rm{BH,6}}}$ is the BH mass in units of 10⁶ ${M}_{\odot }$, ${\omega }_{H}=a/(1+\sqrt{1-{a}^{2}})$ is the dimensionless angular frequency of the BH horizon, and $f(\omega )=1+0.35{{\omega }_{H}}^{2}\;{\rm{\mbox{--}}}\;0.58{{\omega }_{H}}^{4}$ is a high spin correction (Tchekhovskoy et al. 2010, 2014). For a spin parameter a = 0.9 this becomes

$$\begin{eqnarray}&&{L}_{J}=5\times {10}^{44}\ {\rm{erg}}\ {{\rm{s}}}^{-1}{{\rm{\Phi }}}_{*,30}^{2}{M}_{{\rm{BH,}}\;{\rm{6}}}^{-2}.\end{eqnarray} \tag{ 8 }$$

Tchekhovskoy et al. (2014) argue that in order for the jet power to track the accretion rate, there must exist a "magnetically-arrested" accretion disk (MAD), in which the magnetic flux threading the BH is determined by the ram pressure of the accretion flow. For such disks ${\epsilon }_{J}\simeq 1.3{a}^{2}$, where a is the dimensionless spin of the BH. For a nominal jet opening angle ${\theta }_{J}\simeq 0.1$, our constraint ${\epsilon }_{J}{{\theta }_{J}}^{-2}=5.4$ implies a spin $a\simeq 0.2$ if Tchekhovskoy et al. (2014) are correct. Also, the MAD state may be consistent with super-Eddington accretion.

At some point during the fallback of debris from the TDE an accretion disk is expected to form and to dominate the decay law, due to its slower inherent time scale enforced by an ever-expanding outer edge to the accretion disk (Cannizzo et al. 1990, 2011). Cannizzo et al. (2011) argued that for Swift J1644+57 this transition occurred at $t\simeq 10$ days, such that for $t\gt 10$ days the decay law would be flatter, $s\simeq \frac{4}{3}$. In this work we show that the best fit to the decay of Swift J1644+57 appears to be in line with s = 1.5. Moreover, the quality of the fit is good; therefore $s=\frac{5}{3}$ appears to be excluded, as does the value $s=\frac{4}{3}$ expected from an advective disk. As a caveat on drawing any strong conclusions based on our putative slope s = 1.5 for the unabsorbed flux light curve, we note that we are averaging over large amplitude variations in flux versus time. Although we utilize a multi-time step technique and average values in $\mathrm{log}{F}_{x}-\mathrm{log}t$ space, it may be that our measured s value is not robust enough to warrant a detailed comparison with either of the two canonical theoretical s values. Our small inferred value for the fallback time ${t}_{{\rm{fb}}}\lesssim 1$ day appears to rule out the large ${\rm{\Delta }}{t}_{{\rm{offset}}}$ values that would be required to substantially increase s. The theoretical decay law $s=\frac{4}{3}$ (Kumar et al. 2008; Metzger et al. 2008, 2009; Cannizzo & Gehrels 2009) is dependent on a super-Eddington disk and differs from the $s=19/16$ expected from a standard thin disk (Cannizzo et al. 1990). This flatter decay ($s\simeq 1.19$) can also be strongly excluded from our fit, and would not be expected anyway since $\dot{M}\gg {\dot{M}}_{{\rm{Edd}}}$ for Swift J1644+57.

Two schools of thought have emerged concerning the fallback time ${t}_{{\rm{fb}}}$ for Swift J1644+57. Cannizzo et al. (2011) and Gao (2012) argue for ${t}_{{\rm{fb}}}\lesssim 1$ day, which leads to the inference of a tidal disruption radius to periastron radius ratio ${R}_{T}/{R}_{P}\simeq 10$ for the TDE, whereas Tchekhovskoy et al. (2014) and Shen & Matzner (2014) find ${R}_{T}/{R}_{P}\simeq 1$. Shen & Matzner (2014) also favor a BH mass ${M}_{{\rm{BH}}}\simeq {10}^{4}\mbox{--}{10}^{5}$ ${M}_{\odot }$, lower than most other groups. They advocate ${t}_{{\rm{fb}}}\gtrsim 10$ days and assume that the $s=\frac{5}{3}$ decay starts at ∼10 days, which is not consistent with our results. It is also important to note that Tchekhovskoy et al. (2014) and Shen & Matzner (2014) simply use the Swift J1644+57 data taken from the XRT website (Evans et al. 2009) which assumes a single ECF ($4.8\times {10}^{-11}$ erg cm⁻¹ count⁻¹) and reports the observed flux, whereas we have used the time-dependent ECF for the unabsorbed flux, which is related to the intrinsic luminosity. As we show in Figure 6, the unabsorbed flux ECF is about $9.6\times {10}^{-11}$ erg cm⁻¹ count⁻¹, resulting in fluxes a factor of two higher than those obtained with the standard analysis; this affects the energetics, but not the derived decay slope s of the light curve.

An important caveat to the results of Cannizzo et al. (2011) and Gao (2012) has emerged in the past few years, namely, these studies adopted a theoretical value for ${t}_{{\rm{fb}}}$ from Lacy et al. (1982) and Rees (1988) that derives from relating the spread in specific orbital energy of the debris streams to conditions at periastron, ${\rm{\Delta }}\epsilon \simeq {{GM}}_{{\rm{BH}}}{R}_{*}{{R}_{P}}^{-2}$. However, recent work has shown that this viewpoint is not correct: the stellar shredding by the tidal force is in fact so effective that by the time the star arrives at periastron, its shredded fragments are traveling on ballistic trajectories; therefore the relevant radius in determining ${\rm{\Delta }}\epsilon$ and thus ${t}_{{\rm{fb}}}$ is not the periastron radius R_P, but rather the disruption radius R_T (Guillochon & Ramirez-Ruiz 2013; Stone et al. 2013). This leads to smaller ${\rm{\Delta }}\epsilon$ and larger ${t}_{{\rm{fb}}}$. However, the more recent studies do not consider strong general relativistic effects under the Kerr metric, which would become relevant if an orbit were deeply plunging such that R_P were to lie within the ergosphere of a nearly maximal spin BH. It is conceivable ${t}_{{\rm{fb}}}$ could be shortened dramatically.

Support for this idea may be given by a recent study by Evans, Laguna, & Eracleous (2015), which presents a new class of TDEs showing prompt formation of an accretion torus and hyperaccretion. These TDEs involve ultra-close encounters (R_T/R_P ≃ 10) and high spin BHs. They find a strong influence of general relativistic effects. A caveat to their work is that their large ${\rm{\Delta }}\epsilon$ values may be an artifact of under-resolving the midplane compression of the star.

In any event, the observational inference on the fallback time we derive in this work, ${t}_{{\rm{fb}}}\lesssim 1$ days, is based on two observables, the peak X-ray flux and the total X-ray fluence, and is therefore not subject to the theoretical uncertainties inherent in the aforementioned works. Krimm & Barthelmy (2011) note apparent activity in Swift J1644+57 on 2011 March 25, ∼3 days before the 2011 March 28 Swift/BAT trigger. This interval of time exceeds our nominal ${t}_{{\rm{fb}}}$ estimate. The signal-to-noise ratio (S/N) for the 2011 March 25 was low, $\sim 3.7\sigma$ (0.0059 ± 0.0016 ct s⁻¹ cm⁻²), but the positional coincidence with the larger trigger 3 days later, S/N = 7.6σ, gives strength to the detection. A prior close encounter of the star that became disrupted may have led to a partial disruption, such that an extended train of debris arrived near the BH prior to the main TDE, leading to a weak precursor.

Swift J1644+57 is still detected at the flux level of (1.0 ± 0.8) × 10⁻¹⁴ erg cm⁻² s⁻¹ (0.3−10 keV, observed flux) over an integrated exposure of ∼200 ks accumulated in ∼500 days of weekly XRT monitoring. The Chandra-ACIS ToO observation performed on 2012 November 26, ∼3 months after the XRT drop, also detected Swift J1644+57 with 2.8σ significance. A detailed analysis of the observation is reported in Zauderer et al. (2013). We reproduced their results and estimated a 0.3−10 keV unabsorbed flux⁹ of (7 ± 3) × 10⁻¹⁵ erg cm⁻² s⁻¹, consistent with the final Swift/XRT data point (see Figure 9). This flux value is obtained with the average late XRT spectral parameters estimated and used by (Zauderer et al. 2013): ${N}_{{\rm{Hgal}}}$ fixed to $1.7\times {10}^{20}$ cm⁻², intrinsic ${N}_{{\rm{H}}}$ $\sim \;1.4\times {10}^{22}$ cm⁻², and ${\rm{\Gamma }}\sim 1.3$. A fit with ${N}_{{\rm{H}}}$ fixed to $1.9\times {10}^{22}$ cm⁻² gives ${\rm{\Gamma }}={2.1}_{-1.4}^{+1.7}$ (consistent with the spectrum of our XRT last point presented in Section 3.3) and an unabsorbed 0.3−10 keV flux of (8 ± 3) × 10⁻¹⁵ erg cm⁻² s⁻¹.In the second observation performed by Chandra on 2015 February 17 (day 1421 after the BAT trigger), Swift J1644+57 is still detected with 5σ significance and net count rate of (4.2 ± 1.2) × 10⁻⁴ counts s⁻¹ in the 0.5−8 keV range. We modeled the spectrum with an absorbed power-law model as we already did with previous data. Fixing ${N}_{{\rm{Hgal}}}$ to $1.7\times {10}^{20}$ cm⁻², and intrinsic ${N}_{{\rm{H}}}$ to $\sim 1.4\times {10}^{22}$ cm⁻² we obtain ${\rm{\Gamma }}=0.6\pm 1.2$, ${\chi }_{r}^{2}=0.906$ (10 dof), while ${N}_{{\rm{H}}}$ fixed to $1.9\times {10}^{22}$ cm⁻² gives ${\rm{\Gamma }}=0.74\pm 1.2$, ${\chi }_{r}^{2}=0.932$ (10 dof). The unabsorbed flux in the (0.3−10) keV band is equal to $({1.7}_{-1.0}^{+0.4})\;\times$ 10⁻¹⁴ erg cm⁻² s⁻¹. The 2015 Chandra spectrum seems to be harder than both the Swift-post drop spectrum and the Chandra 2012 spectrum, though given the large uncertainties on the photon indices the statistical significance is marginal. Moreover, this 2015 detection is still consistent with the final Swift/XRT data point (see Figure 9).

The residual emission detected by Chandra and Swift is not consistent with thermal emission from the fall-back accretion disk. For ${M}_{{\rm{BH}}}$ in the 5 × 10⁶−10⁷ ${M}_{\odot }$ range, the disk is expected to have a temperature at the inner radius in the ∼20−25 eV range if jet shut-off occurred at a critical accretion rate ∼${\dot{M}}_{{\rm{Edd}}}$, or in the ∼12−15 eV range if the critical accretion rate was ∼0.1 ${\dot{M}}_{{\rm{Edd}}}$. By using the diskbb model in xspec with true inner radius ∼6 G ${M}_{{\rm{BH}}}$/c², face-on disk, and redshift effects properly taken in account, we predict a 0.3−10 keV flux always <10⁻¹⁶ erg cm⁻² s⁻¹, and a bolometric disk luminosity ${L}_{{\rm{disk}}}$ in the 5 × 10⁴³−10⁴⁵ erg s⁻¹ range. By using the standard spectral model for Comptonized X-ray emission from an AGN corona described in Ghisellini & Tavecchio (2009), which consists of a power-law with photon index ∼−1, a high energy exponential cut-off with folding energy of ∼150 keV, and total X-ray luminosity ∼0.3 L_disk, we can easily calculate that the observed 0.3−10 keV flux could be obtained as a result of Comptonization of the disk UV photons by a hot corona for an ${L}_{{\rm{disk}}}\;\lesssim$ 10⁴⁴ erg s⁻¹. However, fine tuning of a number of unmeasurable parameters is required to achieve this result, and this makes the interpretation of residual X-ray emission from Swift J1644+57 as Comptonized emission unlikely, though we cannot rule out contributions from Comptonization effects.

An alternateinterpretation is that the residual X-ray emission detected by Chandra and Swift after jet shut-off originates from the forward shock of the jet still expanding in the ambient medium. In fact, Zauderer et al. (2013) calculate that the low X-ray flux measured by Chandra is consistent with synchrotron emission from the forward shock of a structured jet with time-dependent physical parameters derived by modeling the radio spectra of Swift J1644+57, which they regularly monitored for about 600 days after the outburst.In this scenario we expect the X-ray emission to go on decaying with time as the radio emission. An extrapolation of the 2012 Chandra-ACIS flux to 2015 can be done assuming no spectral variation with time (as guaranteed by the extrapolated value of the cooling frequency based on Zauderer et al. (2013) results still being in the NIR band), and a flux decay rate $\propto {t}^{-\alpha }$ with $\alpha \sim (2{\rm{\mbox{--}}}3p)/4$, where p is the slope of the energy distribution of the electrons accelerated at the shock (Granot & Sari 2002). For a typical value of p ∼ 2.2–2.6, we expect α in the 1.15–1.45 range. Then, an unabsorbed flux lower than $\sim (2.6\pm 1)$ × 10⁻¹⁵ erg cm⁻² s⁻¹ in the 0.3–10 keV band was expected in February 2015. The 2015 Chandra detection clearly shows that the X-ray flux has not decayed according to this prediction. Unfortunately, we have no simultaneous information on radio emission level from Swift J1644+57 and we cannot tell if the two bands are really evolving in an independent way. Only a coordinated X-ray and radio monitoring will be able to answer this question.

A distinctive signature of the two possible scenarios for the origin of residual X-ray emission, i.e., disk/corona related Comptonized emission and forward shock related synchrotron emission, may be the photon index of the X-ray spectrum Γ. In the former case, Γ is expected to lie in the 1.5–2.2 range: values much lower than 1.5 correspond to nonphysical Compton y parameters in standard inverse-Compton scattering scenarios for modeling the X-ray power-law emission from the corona (Zdziarski et al. 1990); values much larger than 2.2 are observationally unlikely based on detailed X-ray spectral analysis of the non-beamed AGNs (Corral et al. 2011; Vasudevan et al. 2013). In the latter case, since the Zauderer et al. (2013) analysis shows that the cooling frequency of the shocked electrons was and is likely still expected to be in the infrared band, the spectral slope in X-rays should be ${\rm{\Gamma }}=\frac{p}{2}+1$, and for a typical value of p ∼ 2.2–2.6, we expect Γ ∼ 2.1–2.3 (Granot & Sari 2002). Unfortunately, none of our Swift or Chandra X-ray spectra has enough statistics to unambiguously constrain the photon index. Even our indication in favor of a ${\rm{\Gamma }}\gt 2$ given by the measure of the XRT band ratio after the shut-off (see Section 3.2) does not allow us to decide between the two cases.

Krolik & Piran (2011) and Bloom et al. (2011) point out that the variability time-scales observed in Swift J1644+57 are orders of magnitude shorter than those found in the relativistic jets of blazars, which presumably have a similar mechanism (Blandford & Znajek 1977). Tchekhovskoy et al. (2014) provide a model that seems able to account for all of the behavior seen in the X-ray light curve of Swift J1644+57, including both the initial rapid and strong variability in 2011 March as well as the sudden shut-off in 2012 August. The uncertainty regarding the long term evolution of the whole system after jet shut-off, the nature and timescales of possible future disk transitions and their observable signatures are related to the uncertainty in the physics of disk accretion and to the detailed accretion disk models adopted by different authors. According to Tchekhovskoy et al. (2014) a reactivation of the jet may occur due to a further transition of the disk to the Advection Dominated Accretion Flow (ADAF) stage expected for $\dot{M}$ $\lesssim$ 0.01 ${\dot{M}}_{{\rm{Edd}}}$. This phenomenon is expected in analogy to state transitions from high/soft to low/hard emission observed in Galactic microquasars, and observationally associated with a jet revival (Fender et al. 2004). The jet reactivation, predicted to occur sometime between 2016 and 2022 at an X-ray flux level of ∼${10}^{-14}\mbox{--}{10}^{-13}$erg cm⁻² s⁻¹ (depending on ${M}_{{\rm{BH}}}$ and the type and the disrupted fraction of the passing star), is expected to be observable for months. The new X-ray bright stage of Swift J1644+57 will likely be detectable by Chandra through all the reactivation period, and possibly even by Swift. In the final analysis, such questions will be decided by observations, and to this end Swift continues to observe Swift J1644+57 regularly, watching for another flare-up of this fascinating object.

We have shown that the shape and the variability timescales in the X-ray light curve of Swift J1644+57 are unlike other known sources with relativistic jets along the line of sight. The spectral behavior of Swift J1644+57 is peculiar as well. For the first several days the source seems to follow a pure harder-when-brighter correlation similar to that observed in blazars, but the later time analysis we have done can be better explained in terms of a superposition of a slow hardening of the spectra along with the global light curve decay, and a harder-when-brighter correlation tracking variability at shorter timescales. The typical harder-when-brighter behavior in blazar flares can be explained in terms of the blazar spectral model (Celotti & Ghisellini 2008) by a rise of the External Compton (EC) component with the accretion rate, associated with an independent different evolution of the Synchrotron Self Compton (SSC) component. It has also been observed that the slope of the correlation between the photon index and the 2−10 keV flux can be different from flare to flare, and can even disappear (Vercellone et al. 2011). This may happen when the SCC and EC components increase proportionally with the accretion rate but maintain balance, so that luminosity rises achromatically.

Paper I successfully explained the early broadband spectra of Swift J1644+57 with a blazar-like spectral model, but no EC component was required by our data. The stringent VERITAS and Fermi upper limits on gamma-ray emission even required a suppression of the Self Compton peak of the spectrum through pair production. The EC component in blazars can be produced by seed photons from the Broad Line Region (BLR) and/or seed photons from the accretion disk interacting with the relativistic electrons in the jet. Actually, it is very unlikely that a BLR had time enough to form in the case of Swift J1644+57, but it is still possible that EC from disk photons contributes to the soft X-ray emission of Swift J1644+57, though the component peak, expected at very high energies, must be highly suppressed. On the other hand, Paper I (e.g., Supplementary Figure 15) showed that both the XRT spectrum extracted at the light curve minimum 4.5 days post-trigger and the later intermediate level spectrum extracted at 8 days post-trigger have an upward kink at higher energies that suggest the presence of an unknown additional hard spectral component, the peak of which they could not constrain. This is also the case for all our XRT spectra fit by a concave log-parabola model. This unknown hard component may play a role similar to the low energy tail of the EC in determining the spectral evolution of Swift J1644+57 in X-rays.

The softness of the average emission of the dips compared to the inter-dip normal emission, without ${N}_{{\rm{H}}}$ variation, agrees with a production mechanism based on a larger contribution of a hard spectral component at larger accretion rate/luminosity. The apparent randomness in temporal distribution, duration, and depths of the dips, as well as in height, duration, and structure of the flares occurring between dips, suggest they originate from random fluctuations in the accretion rate, i.e., instabilities in the accretion flow, like in blazars. However, dynamic range and duty cycle of dips and flares in Swift J1644+57 are extreme compared to blazars, and are difficult to reproduce in this model. Krolik & Piran (2011) suggest that the required extremely compact and short-lived inhomogeneities (i.e., "knots") in the accretion flow, can be obtained if the tidally disrupted star is a white dwarf and the tidal disruption goes on taking away fragments of it at each periastron passage until it is consumed. However, only a central BH mass of ∼10⁴$\;{M}_{\odot }$ would fit the observed timescales, which is not consistent with results from our analysis of the global decay of the Swift J1644+57 light curve.

An alternative mechanism based on random internal shocks propagating along the jet channel has been proposed by De Colle et al. (2012). Based on a hint of possible periodic modulation of the dips, Saxton et al. (2012) proposed they may be due to combined effects of precession and nutation that cause the core of the jet briefly to go out of the line of sight.