RADIO MONITORING OF THE TIDAL DISRUPTION EVENT SWIFT J164449.3+573451. II. THE RELATIVISTIC JET SHUTS OFF AND A TRANSITION TO FORWARD SHOCK X-RAY/RADIO EMISSION

The unusual γ-ray/X-ray transient Sw 1644+57 has been broadly interpreted as the first example of a tidal disruption event (TDE) powering a relativistic jet (e.g., Bloom et al. 2011; Burrows et al. 2011; Levan et al. 2011; Zauderer et al. 2011). As such, Sw 1644+57 provides unique insight into the formation (and potentially termination) of relativistic jets in supermassive black holes (SMBHs), a process that is not observed in active galactic nuclei (AGNs) due to long lifetimes of ≳ 10⁷ yr. One of the primary observations supporting the TDE relativistic jet scenario in Sw 1644+57 is the long-term evolution of the X-ray light curve, roughly following a t^−5/3 power law decline (Burrows et al. 2011) as expected for the fallback rate of tidally disrupted material (e.g., Rees 1988). In addition, the mean X-ray luminosity at early time, L_{X, iso} ≈ 10⁴⁷ erg s⁻¹ (flaring to ≈3 × 10⁴⁸ erg s⁻¹ on a ∼10² s timescale; Burrows et al. 2011), exceeded the Eddington limit of a ∼10⁶–10⁷ M_☉ black hole by about 2–3 orders of magnitude, supporting the presence of a collimated relativistic outflow. Independently, our discovery of bright radio synchrotron emission from Sw 1644+57 established the presence of a relativistic outflow with a Lorentz factor of Γ ∼ few, launched at the same time as the onset of γ-ray emission (Zauderer et al. 2011; Berger et al. 2012). The basic picture, therefore, is of X-ray emission likely from internal dissipation in the inner part of the jet (at r ∼ 10¹⁵–10¹⁶ cm) and radio emission from the expanding forward shock (at r ∼ 10¹⁸–10¹⁹ cm).

While the formation of relativistic jets was not predicted in TDE models, a super-Eddington accretion phase was expected (e.g., Evans & Kochanek 1989; Ulmer 1999; Strubbe & Quataert 2009) and the potential for jets was discussed (Giannios & Metzger 2011). The latter paper considered two distinct possibilities for jet formation, during the super-Eddington phase, or at a later time when the accretion rate drops below a few percent of the Eddington rate (motivated by observations of steady jets in X-ray binaries). The rapid formation of the relativistic jet in Sw 1644+57 points to the former scenario. The peak mass accretion rate and duration of the super-Eddington phase are expected to depend on the mass of the black hole, with $\dot{M}_p\approx 1.4$ M_☉ yr⁻¹ and τ_SE ≈ 1.5 yr for a 3 × 10⁶ M_☉ black hole (e.g., Evans & Kochanek 1989; De Colle et al. 2012), the mid-range inferred mass of the disrupting SMBH in Sw 1644+57 (Bloom et al. 2011; Burrows et al. 2011; Levan et al. 2011; Zauderer et al. 2011). Although it is unclear what, if anything, happens to a TDE jet when the accretion declines below the Eddington limit, an analogy with X-ray binaries indicates that relativistic jet ejections will likely be restricted to the super-Eddington phase (e.g., Fender et al. 1999; De Colle et al. 2012).

To take advantage of this unique opportunity to study the birth and evolution of a relativistic jet from an SMBH, and to track the jet properties of a TDE, we have been carrying out a long-term monitoring campaign of the radio emission from Sw 1644+57, in conjunction with X-ray data (Zauderer et al. 2011; Berger et al. 2012). Here we present new radio observations that extend to t ≈ 600 days, and use these data to determine the continued evolution of the integrated forward shock energy. We combine these measurements with public Swift/XRT and Chandra observations over the same timescale to show that the relativistic jet has shut off at t ≈ 500 days, marked by a steep decline in the X-ray luminosity (Sbarufatti et al. 2012; Levan & Tanvir 2012). The radio data allow us to uniquely determine that the X-ray flux measured in the Chandra data is consistent with emission from the forward shock; a model of thermal emission from the accretion disk can be ruled out by the flux and spectrum of the X-ray emission. Associating the rapid decline with the timescale at which $\dot{M}\approx \dot{M}_{\rm Edd}$, we infer the peak mass accretion rate and the total accreted mass at t ≲ 500 days.

Previous radio observations of Sw 1644+57 extending to t ≈ 26 days were presented in Zauderer et al. (2011), while data extending to t ≈ 216 days were presented in Berger et al. (2012, hereafter Paper I). Here we report new observations extending to t ≈ 600 days. All times are measured relative to a γ-ray onset date of 2011 March 25.5 UT. Throughout the paper we use the standard cosmological constants with H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.27 and Ω_Λ = 0.73.

We observed Sw 1644+57 with the Karl G. Jansky Very Large Array (JVLA⁷) using the Wideband Interferometric Digital Architecture (Perley et al. 2011) correlator to obtain up to 2 GHz of bandwidth at several frequencies. At all frequencies we used 3C286 for bandpass and flux calibration, while phase calibration was performed using J1634+6245 at 1.8 GHz and J1638+5720 at all other frequencies. We reduced and imaged the data with the Astronomical Image Processing System (Greisen 2003) software package. The observations are summarized in Table 1.

We also observed Sw 1644+57 with the AMI Large Array (AMI-LA) at 15.4 GHz with a bandwidth of 3.75 GHz using J1638+5720 for phase calibration and 3C48 and 3C286 for flux calibration. The AMI-LA observations are summarized in Table 1.

Chandra/ACIS-S observations of Sw 1644+57 (PI: Tanvir; Levan & Tanvir 2012) started on 2012 November 26.42 UT (t ≈ 610 days), with a total exposure time of 24.7 ks. We analyzed the public data with the CIAO software package (v4.4), using the calibration database CALDB (v4.5.3) and standard ACIS data filtering. Using wavedetect we detect Sw 1644+57 at a significance level of 2.8σ with a count rate of (2.0 ± 0.9) × 10⁻⁴ count s⁻¹ (0.5–8 keV; 15 radius aperture). We note that emission is detected with a roughly flat distribution in counts s⁻¹ keV⁻¹ at ≈1–3.5 keV (Figure 1); formally, the spectral index is only weakly constrained, with Γ = 1.0 ± 1.3.

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To convert the observed count rate to a flux we note that starting at t ≈ 23 days the X-ray emission from Sw 1644+57 undergoes spectral hardening,⁸ with the photon index evolving to Γ ≈ 1.3 at t ≳ 230 days. We therefore use an absorbed power law spectrum with an index of Γ = 1.3, intrinsic absorption of N_{H, int} = 1.4 × 10²² cm⁻², and Galactic absorption of N_{H, MW} ≈ 1.7 × 10²⁰ cm⁻² (Kalberla et al. 2005). With this model, the unabsorbed flux is (5.8 ± 2.0) × 10⁻¹⁵ erg s⁻¹ cm⁻² (0.3–10 keV). For a power law model⁹ with Γ = 2.2 the resulting flux is only ≈5% lower. Finally, a multi-temperature accretion disk blackbody model (diskbb in xspec) can also fit the data, with a resulting temperature at the inner disk radius of kT ≈ 1 keV; thermal disk models with a temperature appropriate to a ∼10⁶–10⁷ M_☉ SMBH (kT ≲ 60 eV) cannot reproduce the Chandra data (Figure 1) and furthermore require an inconsistent radius (see Section 5).

We model the radio emission from Sw 1644+57 following the approach detailed in Paper I, which is based on the afterglow formulation of Metzger et al. (2012) and Granot & Sari (2002). For details of the model we refer the reader to these papers. For the purpose of estimating the X-ray emission from the forward shock we also include in the analysis here the effects of the synchrotron cooling frequency, given by (Granot & Sari 2002):

$$\begin{equation} \nu _c=2.5\times 10^{14}\, \epsilon _{B,-2}^{-3/2}\, L_{\rm j,iso,48}^{0.5}\, t_{j,6}\, n_{18}^{-2}\, \left(\frac{t}{t_j} \right)^{0.5}\,\, {\rm Hz}, \end{equation} \tag{ 1 }$$

where _B is the fraction of post-shock energy in the magnetic fields, L_{j, iso} is the kinetic luminosity of the outflow, t_j is the timescale over which L_{j, iso} is assumed to be constant (followed by L_{j, iso}∝t^−5/3 at t ⩾ t_j), n₁₈ is the circumnuclear density (n_CNM) at a fiducial radius of r = 10¹⁸ cm, and we use the notation X ≡ 10^y X_y, as described in Paper I. We further assume¹⁰ that _B = 0.01 and find from the radio data that p = 2.45 ± 0.05.

As in Paper I, we independently model each broadband radio spectral energy distribution (SED) to extract the temporal evolution of the synchrotron parameters, and in turn the evolution of L_{j, iso}, the emission radius, the jet Lorentz factor (Γ_j), and the radial density profile. The individual SED fits are shown in Figure 2 and the relevant extracted parameters are listed in Table 2. In Figure 3 we plot the light curves at frequencies of 1.8–43 GHz, extending to ≈600 days. Finally, in Figure 4 we plot the X-ray data from Swift/XRT¹¹ and Chandra along with the predicted forward shock emission in the X-ray band based on the radio SED modeling.

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Table 2. Results of Broadband Spectral Energy Distribution Fits

t	log(νa)	log(νm)	log(νc)	${\rm log}(F_{\nu _a})$	log(r18)	log(Γsh)	log(Γj)	log(Lj, iso, 48)	log(n18)	log(nCNM)
(days)	(Hz)	(Hz)	(Hz)	(mJy)	(cm)			(erg s−1)	(cm−3)	(cm−3)
244	10.04	9.67	13.00	1.99	0.59	0.31	0.35	0.22	1.08	−0.10
301	9.96	9.54	13.09	1.92	0.66	0.30	0.33	0.24	1.07	−0.24
390	9.71	9.38	13.45	1.72	0.79	0.31	0.33	0.25	0.92	−0.66
457	9.62	9.28	13.56	1.64	0.85	0.30	0.33	0.26	0.88	−0.81
582	9.58	9.13	13.58	1.60	0.90	0.28	0.30	0.28	0.90	−0.90

Notes. Measured and inferred parameters of the relativistic outflow and environment of Sw 1644+57 from model fits of the individual multi-frequency SEDs shown in Figure 2. The model is described in Paper I, Metzger et al. (2012), and Section 4.

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The X-ray light curve at t ≈ 15–500 days follows a power law decline, with the expected F_X∝t^−5/3 (Figure 4; Burrows et al. 2011; Paper I). However, beyond this point the X-ray flux rapidly declines by a factor of about 15 in the span of only 25 days, followed by an additional (slower) decline of about a factor of 11 in the subsequent 95 days (see also Sbarufatti et al. 2012; Levan & Tanvir 2012). While the X-ray light curve exhibits order of magnitude variability in the first few days, followed by milder variability at later time, a decline by a factor of ≈170 in a narrow span of δt/t ≲ 0.2 (and by a factor of 15 in δt/t ≈ 0.05) is unprecedented and points to a fundamental change in the nature of the emission. In particular, we conclude that the mechanism powering the X-ray emission at δt ≲ 500 days has ceased to operate. The absence of a similar rapid decline in the radio band supports earlier conclusions that the radio and X-ray emission arise from distinct physical components (Bloom et al. 2011; Zauderer et al. 2011; Metzger et al. 2012; Liu et al. 2012).

In addition, the rapid decline rules out models in which the X-ray emission at t ≲ 500 days is due to the forward shock or to reprocessing of radiation by the forward shock, since processes at the forward shock are expected to occur on a timescale comparable to the duration of the event, δt/t ≈ 1. Thus, given the rapid decline we conclude that the early X-ray emission originated at a smaller radius than the forward shock, presumably from internal dissipation in the inner part of the relativistic outflow (at r ∼ few × 10¹⁵ cm; e.g., De Colle et al. 2012). On the other hand, the low X-ray flux following the steep decline, as measured in the Chandra observation, is fully consistent with emission from the forward shock at r ≈ 8 × 10¹⁸ cm (Figure 4 and Table 2), the same component powering the long-term radio emission. While residual emission from the inner jet cannot be definitively ruled out, the observed flattening in the decline rate between the final XRT measurement and the Chandra measurement points to a transition to forward shock dominated emission.

An alternative explanation for the low X-ray flux at t ≈ 610 days is thermal emission from the accretion disk itself. In this scenario, for a 3 × 10⁶ M_☉ black hole the effective temperature is kT ≈ 25 eV for an inner radius at the tidal disruption radius, R_t ≈ 12 R_s ≈ 1.1 × 10¹³ cm (e.g., Ulmer 1999); here R_s is the Schwarzschild radius. The resulting SED severely under-predicts the observed X-ray flux density, and cannot accommodate the X-ray spectrum at ≳ 1 keV due to the expected steep Wien spectrum. Even a model with a temperature of kT ≈ 60 eV (corresponding to an inner disk radius of only 2 R_s) cannot accommodate the detected X-ray emission at ≳ 1 keV (Figure 1). In particular, for this model to even fit the flux normalization of the Chandra data at ≲ 1 keV requires an inconsistent inner disk radius of about 40 R_s (using the standard disk blackbody model with $L_{\rm disk}=4\pi R_{\rm in}\sigma T_{\rm in}^4$). A thermal model only fits the data for a high temperature of kT ≈ 1 keV, but this is not expected for an SMBH.

Finally, the late-time X-ray emission may also be due to Comptonization of the disk UV photons (for example, by a hot corona). This effect is seen in AGNs, with a typical resulting soft X-ray luminosity of L_X/ν_UVL_{ν, UV} ≈ (ν_X/ν_UV)^−0.5 (e.g., Steffen et al. 2006). Using the disk model above (kT ≈ 25 eV and R_in ≈ R_t ≈ 1.1 × 10¹³ cm), we find an expected peak UV luminosity of ν_UVL_{ν, UV} ≈ 4 × 10⁴⁴ erg s⁻¹, and hence an expected X-ray luminosity of L_X ≈ 5 × 10⁴³ erg s⁻¹. This is about an order of magnitude larger than the observed value, suggesting that Comptonization typical of quasars is not relevant here, although this does not rule out the Comptonization scenario. Still, since the forward shock emission is inevitable and provides an excellent match to the observed luminosity, we conclude that forward shock emission is the most natural explanation for the late-time X-ray flux.

While the nature of relativistic jet generation in TDEs is not fully understood, an analogy with X-ray binaries suggests that a powerful jet can be supported as long as the disk is geometrically thick, with an accretion rate of $\dot{M}\gtrsim \dot{M}_{\rm Edd}$. De Colle et al. (2012) recently presented simulations of the tidal disruption of a 1 M_☉ star and showed that for a 3 × 10⁶ M_☉ black hole, the peak mass accretion rate is about $240\,\dot{M}_{\rm Edd}$ (for order unity efficiency), while $\dot{M}\approx \dot{M}_{\rm Edd}$ at t ≈ 1.5 yr. This timescale is remarkably similar to the time of rapid X-ray decline for Sw 1644+57, about 370 days in the rest-frame. Associating this timescale with an accretion rate of about $\dot{M}_{\rm Edd}$, we find that the beaming-corrected X-ray luminosity prior to the rapid decline, L_X ≈ 2 × 10⁴² erg s⁻¹ (for θ_j = 0.1), is about 0.01 L_Edd for a 3 × 10⁶ M_☉ black hole. However, the resulting low efficiency is not surprising given the hard power index of Γ ≈ 1.3 at ≲ 500 days, which suggests that the bulk of the energy is radiated above the XRT band.

With the inference that $\dot{M}(500\,{\rm d{\rm ays}})\approx \dot{M}_{\rm Edd}\approx 0.006$ M_☉ yr⁻¹ we can also determine the total accreted mass. Using a simple model with $\dot{M}(t)=\dot{M}_p$ at t ≲ 15 days and $\dot{M}(t)=\dot{M}_p\, (t/t_j)^{-5/3}$ at t ≳ 15 days, motivated by the X-ray light curve (Burrows et al. 2011; De Colle et al. 2012; Metzger et al. 2012), we find $\dot{M}_p\approx 350\,\dot{M}_{\rm Edd}$, in good agreement with the predictions of De Colle et al. (2012) for a 3 × 10⁶ M_☉ black hole. Integrating the mass accretion rate to t ≈ 370 days in the rest-frame, we find a total accreted mass of ≈0.15 M_☉. This result is consistent with the disruption of a ≲ 1 M_☉ star.

In addition to the rapid decline in X-ray emission, which marks the jet turning off, we also find a change in behavior in the integrated energy of the forward shock. Following an increase in E_{j, iso} by about a factor of 15 at t ≈ 30–250 days, our measurements at t ≈ 250–600 days point to a mild rise or a plateau at a level of E_{j, iso} ≈ 2 × 10⁵⁴ erg (Figure 5). For an assumed jet opening angle of θ_j ∼ 0.1, this corresponds to a beaming-corrected kinetic energy of E_K ≈ 10⁵² erg. The flattening in the temporal evolution of E_{j, iso} is unlikely to be related to the cessation of jet activity since it begins at an earlier phase. Instead, it is more likely related to the velocity profile of the ejecta, as discussed in Paper I, or to a delayed response of the forward shock to the drop in mass accretion rate below the peak rate (De Colle et al. 2012). As a result, we expect that the turn off of the relativistic jet will have only a mild impact on the forward shock energy, on a timescale of t ≈ 10³ days.

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We present a joint analysis of radio and X-ray observations of Sw 1644+57 extending to t ≈ 600 days. From the multi-frequency radio data we determine the integrated energy of the forward shock as a function of time and find that following an increase in E_{j, iso} by about a factor of 15 at t ≈ 30–250 days, measurements to t ≈ 600 days reveal a mild rise or plateau with E_{j, iso} ≈ 2 × 10⁵⁴ erg. X-ray observations with Swift/XRT and Chandra reveal a dramatic change in the light curve evolution, with a sharp decline by about a factor of 170 at t ≳ 500–610 days following a steady t^−5/3 decline at t ≈ 15–500 days. Using the radio data, we conclude that the low X-ray flux measured by Chandra is consistent with emission from the forward shock. The alternative explanation of thermal disk emission is ruled out by the X-ray flux and spectrum, which instead require a temperature of kT ≈ 1 keV, compared to an expected value of ≲ 60 eV for an SMBH accretion disk.

The rapid decline suggests that the relativistic jet has turned off, most likely as a result of a decline in the mass accretion rate below ${\sim }\dot{M}_{\rm Edd}$. With this interpretation, the overall accreted mass by t ≈ 500 days is ≈0.15 M_☉, consistent with the disruption of a solar mass star. Moreover, the rapid decline, with δt/t ≲ 0.2, indicates that the X-ray emission at t ≲ 500 days did not originate from the forward shock or from radiation reprocessed by the forward shock. Instead it was likely due to internal dissipation in the inner part of the jet.

Projecting forward, we expect that the X-ray flux evolution will track the decline rate in the optically thin high-frequency radio bands with a potential dispersion of about ±0.25 due to the response of the synchrotron cooling frequency to variations in the radial density profile. Additional Chandra or XMM-Newton observations in the coming year will test this prediction.

We thank Ramesh Narayan, Ryan Chornock, and Martin Elvis for detailed and helpful discussions. E.B. acknowledges support from the National Science Foundation through Grant AST-1107973. A.M.S. acknowledges support from the David and Lucile Packard Foundation Fellowship for Science and Engineering. A.B. was supported by a Marie Curie Outgoing International Fellowship (FP7) of the European Union (project number 275596). The AMI arrays are supported by the University of Cambridge and the STFC. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester.