A MULTIWAVELENGTH STUDY OF THE RELATIVISTIC TIDAL DISRUPTION CANDIDATE SWIFT J2058.4+0516 AT LATE TIMES

The X-ray data of Sw J2058+05 used in this study were acquired with three different instruments: the X-Ray Telescope (XRT; Burrows et al. 2005) on the Swift Gamma-Ray Burst Explorer (Gehrels et al. 2004), the European Photon Imaging Camera (EPIC; Strüder et al. 2001; Turner et al. 2001) on the XMM-Newton Observatory (Jansen et al. 2001), and the ACIS (Garmire et al. 2003) on the Chandra X-ray observatory (Weisskopf et al. 2002). We describe the data from each of these facilities below.

2.1.1. Swift/XRT Observations

Sw J2058+05 was discovered by the BAT (Barthelmy et al. 2005) on board Swift on 2011 May 17 (Krimm et al. 2011). Soon after the BAT detection, starting 2011 May 27, a Target of Opportunity program was initiated to monitor this source. Between 2011 May 27 and 2012 July 19 (a temporal baseline of 419 days), Swift observed the source on 32 occasions for about 2–3 ks per observation. The data from the first 60 days of this monitoring program have already been reported by C12. They find that the source's hard X-ray flux falls below the BAT detection limits soon after reaching its peak luminosity (see the top panel of Figure 1 of C12). Here we extended the analysis to late times and use only the XRT X-ray (0.3–10 keV) data from Swift.

We started our data analysis with the raw, level-1 XRT data products. Using the latest HEASARC calibration database (CALDB version 20140709) files, we ran xrtpipeline to extract the level-2 (scientific) event files. As suggested by the XRT data-analysis guide,¹³ we extracted the exposure maps to take into account the bad pixels and columns (xrtpipeline with the qualifier createexpomap = yes). These exposure maps were then used to correct the ancillary response files (arfs: effective area, using xrtmkarf) of each of the 32 observations.

Twenty-two of the monitoring observations were taken in the photon-counting (PC) mode, with the remainder in the windowed-timing (WT) mode (see Table 1 for more details). As recommended by the XRT user guide, we only used events with grades 0–12 in the case of PC-mode observations and grades 0–2 for WT-mode data. We then used XSELECT to extract energy spectra from each of the individual observations. For the PC-mode data we extracted the source spectra from a circular region centered on J2000.0 coordinates $\alpha ={{20}^{{\rm h}}}{{58}^{{\rm m}}}19\buildrel{\rm{s}}\over{.}90$ and $\delta =+05{}^\circ 13^{\prime} 32\buildrel{\prime\prime}\over{.} 0$, as derived by C12 using the Chandra/High-Resolution Camera data. We chose an extraction radius of 471 to include roughly 90% (at 1.5 keV) of the light from the source (as estimated from XRT's fractional encircled energy function). A background region free of point sources was extracted from a nearby area. Given the low count rates, we chose a radius twice that of the source region in order to better estimate the background. For the WT-mode source region we chose a square box of width 94 3 and oriented along the roll angle of the spacecraft—that is, parallel to the WT-mode readout streak. Background was estimated from two square regions (width = 94 3) on either side of the source region. The orientation of the square regions (both the source and the background) was adjusted between individual observations to align with the roll angle of the spacecraft during that particular exposure.

Table 1.  Summary of X-ray Spectral Modeling of Sw J2058+05

Instrument	ObsID	MJD Datea	X-ray Fluxb	Notesc
Swift/XRT	00032004001	55,708.915	48.12$_{-1.70}^{+1.61}$	PC Mode
Swift/XRT	00032004002	55,711.582	64.49$_{-2.19}^{+2.20}$	WT Mode
Swift/XRT	00032004003	55,714.412	59.37$_{-2.08}^{+2.24}$	WT Mode
Swift/XRT	00032004004	55,717.879	48.78$_{-1.51}^{+1.62}$	WT Mode
Swift/XRT	00032004005	55,720.568	31.78$_{-1.59}^{+1.66}$	WT Mode
Swift/XRT	00032004007	55,726.045	12.61$_{-0.88}^{+0.90}$	WT Mode
Swift/XRT	00032004008	55,729.110	15.17$_{-1.02}^{+1.08}$	WT Mode
Swift/XRT	00032004009	55,735.539	9.58$_{-0.78}^{+0.84}$	WT Mode
Swift/XRT	00032004010	55,738.548	8.01$_{-0.89}^{+0.79}$	WT Mode
Swift/XRT	00032026001	55,743.760	3.33$_{-0.64}^{+0.74}$	WT Mode
Swift/XRT	00032026002	55,748.457	2.85$_{-0.43}^{+0.38}$	WT Mode
Swift/XRT	00032026003	55,753.531	1.59$_{-0.34}^{+0.38}$	PC Mode
Swift/XRT	00032026004	55,760.699	1.90$_{-0.34}^{+0.36}$	PC Mode
Swift/XRT	00032026005	55,763.907	2.69$_{-0.64}^{+0.64}$	PC Mode
Swift/XRT	00032026006	55,768.723	0.99$_{-0.23}^{+0.25}$	PC Mode
Swift/XRT	00032026007	55,773.203	1.30$_{-0.32}^{+0.28}$	PC Mode
Swift/XRT	00032026009	55,783.373	1.05$_{-0.24}^{+0.24}$	PC Mode
Swift/XRT	00032026010–012	55,806.229	0.64$_{-0.15}^{+0.17}$	PC Mode
Swift/XRT	00032026013–015	55,853.296	0.37$_{-0.11}^{+0.09}$	PC Mode
Swift/XRT	00032026016–021	55,885.110	0.14$_{-0.05}^{+0.05}$	PC Mode
XMM-Newton/EPIC	0679380801	55,885.635	0.19$_{-0.02}^{+0.02}$	Exposure: 23 ks
XMM-Newton/EPIC	0679380901	55,887.787	0.16$_{-0.02}^{+0.02}$	Exposure: 29 ks
XMM-Newton/EPIC	0694830201	56,049.048	0.17$_{-0.01}^{+0.01}$	Exposure: 55 ks
Chandra/ACIS	14975	56,383.806	≤1.05 × 10−3	Exposure: 30 ks
Chandra/ACIS	16498	56,594.972	≤1.76 × 10−3	Exposure: 20 ks
Chandra/ACIS	14976	56,597.639	≤1.63 × 10−3	Exposure: 30 ks

Notes.

^aThe source was discovered on MJD 55,698. ^bThe X-ray fluxes were estimated in the bandpass of 0.3–10 keV and have units of 10⁻¹² erg s⁻¹ cm⁻². These represent the values just outside our Galaxy. The X-ray luminosities in the top panel of Figure 1 were estimated as flux $\times 4\pi {{D}^{2}}$, where D is 8200 Mpc. See text for details on the modeling. ^cPC refers to photon counting and WT to windowed timing.

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2.1.2. XMM-Newton Observations

2.1.3. Chandra/ACIS Observations

Soon after discovery, we started a campaign to carry out multiband photometry of Sw J2058+05 in the UV, optical, and NIR wavebands using multiple instruments. These include the High Acuity Wide field K-band-imager (HAWK-I; Pirard et al. 2004) and the FOcal Reducer and Spectrograph 2 (FORS2; Appenzeller et al. 1998) on the 8.2 m Very Large Telescope (VLT), and the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) mounted on the 8 m Gemini-South telescope. VLT data were reduced via the standard instrument pipelines for FORS and HAWK-I in esorex, while Gemini data were processed using the gemini IRAF¹⁴ package. Photometric calibration was performed relative to nearby point sources from the Sloan Digital Sky Survey (SDSS) (optical) and Two Micron All Sky Survey (2MASS) (NIR). The resulting photometry, all in the AB magnitude system, is presented in Table 2. The reported magnitudes are not corrected for foreground Galactic extinction along the line of sight to Sw J2058+05 [$E(B-V)=0.095$ mag; Schlafly & Finkbeiner 2011], but such corrections were applied before all subsequent analysis. The observations prior to 2011 August 12 can be found in Table 1 of C12.

Table 2.  A Summary of UV/Optical/IR Observations of Sw J2058+05

UTC	MJD Date	Telescope	Filter	Exposure	AB Magnitudea
Date				(seconds)
2011 Aug 12.05	55,785.05	VLT–HAWK-I	J	1020	22.72 ± 0.33
2011 Aug 12.07	55,785.07	VLT–HAWK-I	K	1080	$\gt 21.6$
2011 Aug 20.07	55,793.07	VLT–FORS 2	u	840.0	22.86 ± 0.13
2011 Aug 20.07	55,793.07	VLT–FORS 2	g	120.0	22.69 ± 0.11
2011 Aug 20.07	55,793.07	VLT–FORS 2	r	120.0	23.07 ± 0.11
2011 Aug 20.08	55,793.08	VLT–FORS 2	i	200.0	22.84 ± 0.11
2011 Aug 20.08	55,793.08	VLT–FORS 2	z	720.0	22.79 ± 0.14
2011 Aug 30.56	55,803.56	HST–WFC3	F160W (H band)b	1196.9	23.36 ± 0.02
2011 Aug 30.58	55,803.58	HST–WFC3	F475W (SDSS g)c	1110.0	23.06 ± 0.02
2011 Sep 2.21	55,806.21	VLT–HAWK-I	J	1020	22.22 ± 0.22
2011 Sep 2.21	55,806.21	VLT–HAWK-I	K	1080	21.87 ± 0.25
2011 Sep 22.06	55,826.06	VLT–FORS 2	r	120.0	22.98 ± 0.10
2011 Sep 22.07	55,826.07	VLT–FORS 2	u	840.0	23.11 ± 0.11
2011 Sep 22.07	55,826.07	VLT–FORS 2	g	120.0	22.97 ± 0.13
2011 Sep 22.08	55,826.07	VLT–FORS 2	i	200.0	23.10 ± 0.14
2011 Sep 22.08	55,826.07	VLT–FORS 2	z	720.0	23.32 ± 0.08
2011 Sep 24.99	55,828.99	VLT–HAWK-I	J	1020	22.46 ± 0.16
2011 Sep 25.01	55,829.01	VLT–HAWK-I	K	1080	21.60 ± 0.20
2011 Nov 20.02	55,885.02	Gemini-S–GMOS	u	300.5	$\gt 24.5$
2011 Nov 20.02	55,885.02	Gemini-S–GMOS	g	100.5	23.93 ± 0.21
2011 Nov 20.03	55,885.02	Gemini-S–GMOS	r	100.5	23.53 ± 0.16
2011 Nov 30.96	55,894.96	HST–WFC3	F160W (H band)b	1196.9	23.56 ± 0.02
2011 Nov 30.99	55,894.99	HST–WFC3	F475W (SDSS g)c	1110.0	23.89 ± 0.02
2012 Jun 16.32	56,094.32	VLT–FORS 2	r	400.0	24.24 ± 0.17
2012 Jun 16.33	56,094.33	VLT–FORS 2	g	400.0	24.78 ± 0.15
2012 Jun 16.34	56,094.34	VLT–FORS 2	u	840.0	25.14 ± 0.38
2012 Jun 16.35	56,094.35	VLT–FORS 2	i	240.0	24.32 ± 0.17
2012 Jun 16.35	56,094.35	VLT–FORS 2	z	720.0	23.99 ± 0.23
2012 Jul 18.27	56,126.27	VLT–FORS2	u	840	25.39 ± 0.26
2012 Jul 18.26	56,126.26	VLT–FORS2	g	400	24.97 ± 0.14
2012 Jul 18.26	56,126.26	VLT–FORS2	r	400	24.48 ± 0.14
2012 Jul 18.28	56,126.28	VLT–FORS2	i	240	24.20 ± 0.15
2012 Jul 18.29	56,126.29	VLT–FORS2	z	720	23.81 ± 0.25
2012 Aug 22.09	56,161.09	VLT–FORS2	u	840	$\gt 25.8$
2012 Aug 22.08	56,161.08	VLT–FORS2	g	400	$\gt 26.4$
2012 Aug 22.08	56,161.08	VLT–FORS2	r	400	$\gt 26.0$
2012 Aug 22.10	56,161.10	VLT–FORS2	i	240	$\gt 24.9$
2012 Aug 22.10	56,161	VLT–FORS2	z	720	$\gt 25.2$
2012 Oct 09.01	56,209.01	VLT–FORS2	u	840	$\gt 26.0$
2012 Oct 09.01	56,209.01	VLT–FORS2	g	400	$\gt 26.3$
2012 Oct 09.00	56,209.00	VLT–FORS2	r	400	$\gt 26.2$
2012 Oct 09.02	56,209.02	VLT–FORS2	i	240	$\gt 24.8$
2012 Oct 09.03	56,209.03	VLT–FORS2	z	720	$\gt 25.2$
2013 Dec 10.58	56,636.58	HST–WFC3	F160W (H band)b	2611.8	25.99 ± 0.08
2014 Aug 31.48	56,900.48	HST/ACS–WFC	F606W	5236.0	26.78 ± 0.10

Notes.

^aReported magnitudes have not been corrected for Galactic extinction ($E(B-V)$ = 0.095 mag; Schlafly & Finkbeiner 2011). Upper limits represent 3σ uncertainties. ^bHST/F475W filter has a bandpass similar to SDSS's g band. ^cHST/F160W filter has a bandpass similar to the standard H band.

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We observed the location of Sw J2058+05 with the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) in three separate epochs: 2011 August 30, November 30 (Proposal GO-12686; PI Cenko), and 2013 December 10 (Proposal GO-13479; PI Levan). Observations were obtained with the ${\rm F}160{\rm W}$ filter through the IR channel in all three epochs, as well as with the ${\rm F}475{\rm W}$ filter through the UVIS channel in the first two epochs. An additional epoch of imaging was obtained on 2014 August 31 in the ${\rm F}606{\rm W}$ filter with the WFC detector on the Advanced Camera for Surveys (ACS). These data were downloaded after on-the-fly processing from the HST archive and subsequently drizzled using astrodrizzle (Fruchter & Hook 2002) to final pixel scales of 65 mas (${\rm F}160{\rm W}$), 30 mas (${\rm F}475{\rm W}$), and 33 mas (${\rm F}606{\rm W}$). We performed aperture photometry at the location of Sw J2058+05 in all images using the prescriptions from the various HST handbooks. The resulting photometry, all corrected to the AB system, is displayed in Table 2.

We obtained optical and NIR spectra of Sw J2058+05 with the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the 10 m Keck I telescope, FORS2 on the 8 m VLT UT1 (Antu), and the XSHOOTER (Vernet et al. 2011) spectrograph on the 8 m VLT UT2. Details of the configuration for each spectrum are provided in Table 3. For the Keck/LRIS and FORS2 data, one-dimensional spectra were optimally extracted, a wavelength solution was generated from observations of lamps, and flux calibration was performed via spectrophotometric standards. The XSHOOTER spectra were processed through the reflex environment. For all spectra the slit was oriented at the parallactic angle to minimize losses caused by atmospheric dispersion (Filippenko 1982).

We obtained a single epoch of imaging of Sw J2058+05 with the National Radio Astronomy Observatory's (NRAO¹⁵ ) Very Long Baseline Array (VLBA) to search for spatially extended radio emission (project code BC0199). Observations were obtained on 2011 August 12 (${\Delta }t\approx 40$ days after discovery, in the rest frame) at central frequencies of 8.4 and 22 GHz with a recording rate of 512 Mb s⁻¹. All 10 stations (SC, HN, NL, FD, LA, PT, KP, OV, BR, and MK) were planned for both frequencies; however, the NL station was lost for our 8 GHz observation (owing to a receiver problem).

Initial data processing was performed using the AIPS software package (Greisen 2003). J2101+0341 was used for primary phase and astrometric calibration, while J2050+0407 and J2106+0231 were used as secondary calibrators and for evaluation and correction of tropospheric effects on astrometry. The resulting images achieved an angular resolution of ∼1 mas at 8.4 GHz and 0.3 mas at 22 GHz.

A faint (${{f}_{\nu }}=350\pm 70$ μJy), unresolved source is detected in the 8.4 GHz image at the J2000.0 position $\alpha ={{20}^{{\rm h}}}{{58}^{{\rm m}}}19\buildrel{\rm{s}}\over{.}897282\;\pm$ 0000006, $\delta =+05{}^\circ 13^{\prime} 32\buildrel{\prime\prime}\over{.} 24306$ $\pm \;0\buildrel{\prime\prime}\over{.} 00016$.¹⁶ No emission is detected at this location in the 22 GHz image to a 3σ upper limit of ${{f}_{\nu }}\lt 580$ μJy. Both measurements suggest a decline in radio luminosity by a factor of a few from VLA observations of Sw J2058+05 presented by C12 (∼20 days rest frame).

The individual Swift/XRT observations do not have enough counts to constrain the source's spectral parameters. Hence, we extracted an average energy spectrum by combining all of the XRT PC-mode data.¹⁷ This was achieved by first extracting a source spectrum and a background energy spectrum from each of the 22 observations (most of these observations were at epochs 25–86 days after discovery; rest frame) and then combining them all using the ftool sumpha. Similarly, we combined all of the individual ancillary response files, weighted by total counts per observation, using the ftool addarf. The response files (RMF) were averaged using the ftool addrmf. The combined spectrum was then rebinned using the grppha tool to have a minimum of 25 counts per spectral bin.

With the latest version of the X-ray spectral fitting package XSPECv12.8.2 (Arnaud 1996), we then fitted this combined 0.3–10 keV energy spectrum with a power-law model modified by absorption (phabs∗zwabs∗pow in XSPEC). The Galactic column density was fixed at $0.088\times {{10}^{22}}$ cm⁻² (Kalberla et al. 2005; Willingale et al. 2013)¹⁸ , while the power-law index and the intrinsic absorption column at z = 1.1853 (C12) were free to vary. The best-fit power-law index and intrinsic absorption column density were ${\Gamma }=1.47\pm 0.08$ and ${{n}_{{\rm H}}}=(0.30\pm 0.15)\times {{10}^{22}}$ atoms cm⁻², respectively (with a reduced ${{\chi }^{2}}=0.74$ for 102 degrees of freedom (dof)).

We then used these best-fit power-law model parameters (fixing the power-law index and the absorbing column density but keeping the power-law normalization free) and extracted the source flux from each of the individual observations. We only considered observations with a total number of counts greater than 50. In cases where the total number of counts was less than 50, we averaged neighboring observations. The best-fit absorbed power-law model (with fixed power-law index and absorbing column) yielded a reduced ${{\chi }^{2}}$ in an acceptable range of 0.5–1.3 for these individual epochs.

We then fitted each of the three XMM-Newton/EPIC (both pn and MOS simultaneously) X-ray spectra of Sw J2058+05 using the same model as above (phabs∗zwabs∗pow). We generated the EPIC response files using the arfgen and rmfgen tools, which are part of XMM-Newton's SAS software. Given that each of these observations had total counts in excess of 1600, we left all the model parameters free to vary except for the redshift and the Milky Way column density. The best-fit model parameters are indicated in Table 4. It is interesting to note that while the best-fit absorbing column densities are consistent with the value derived from the combined Swift XRT data acquired at early times, the power-law indices are slightly steeper at late times. The luminosity values derived from modeling the XMM-Newton spectra are indicated by the magenta squares in Figure 1.

Table 4.  Summary of XMM-Newton X-ray (0.3–10 keV) Spectral Modeling of Sw J2058+05

ObsIDa	Absorbing	Power-law	Power-law	χ2/dof	X-ray Fluxd
	Columnb	Indexc	Normalization
0679380801	0.23$_{-0.13}^{+0.15}$	1.89$_{-0.13}^{+0.15}$	3.6$_{-0.4}^{+0.4}$	53/48	0.19$_{-0.02}^{+0.02}$
0679380901	0.15$_{-0.16}^{+0.18}$	1.81$_{-0.16}^{+0.18}$	2.8$_{-0.3}^{+0.4}$	55/64	0.16$_{-0.02}^{+0.02}$
0694830201	0.19$_{-0.12}^{+0.13}$	1.67$_{-0.10}^{+0.10}$	2.5$_{-0.2}^{+0.2}$	86/94	0.17$_{-0.01}^{+0.01}$

Notes.

^aXMM-Newton assigned observation ID. ^bUnits of 10²² atoms cm⁻². ^cThe X-ray spectra were modeled with phabs∗zwabs∗pow in XSPEC. The Galactic column (phabs) was fixed at $0.088\times {{10}^{22}}$ atoms cm⁻² (Kalberla et al. 2005; Willingale et al. 2013), and the redshift in zwabs was fixed at 1.1853 (C12). ^dThe X-ray fluxes were estimated in the bandpass of 0.3–10 keV and have units of 10⁻¹² erg s⁻¹ cm⁻².

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The source was not detectable in the Chandra/ACIS images with the naked eye. Nevertheless, using the CIAO task srcflux, we estimated an upper limit to the 0.3–10 keV X-ray flux for Poisson statistics. In doing so, we assumed that the source spectrum is defined by an absorbed power-law model with the parameters estimated from the XMM-Newton data (see Table 4). The power-law index and the intrinsic absorption column density were set to 1.79 and $0.19\times {{10}^{22}}$ atoms cm⁻², respectively (mean of the XMM-Newton values). The isotropic luminosity upper limits are indicated by the blue squares in Figure 1.

In addition, we studied the short-term variability of the source on timescales of a few hundred to a few thousand seconds using the XMM-Newton data. We first extracted a combined EPIC (pn and MOS) light curve from each of the three XMM-Newton observations. One such light curve (black), along with the background (red) binned with a time resolution of 500 s, is shown in Figure 2. It is clear that the source varies significantly, with the most drastic variation around 32,000 s when the overall count rate changes by a factor of 2.5 within a timescale of ≲1000 s. To further confirm the variability, we modeled the light curve with a constant. The best-fit model gave 0.073 counts s⁻¹ with a reduced ${{\chi }^{2}}$ of 2.3 (${{\chi }^{2}}=236$ for 102 dof). Again, this suggests that a constant count rate model is strongly disfavored. Rapid X-ray variability on similar timescales has also been observed from Sw J1644+57 (e.g., Krolik & Piran 2011) and also nonrelativistic TDE candidates such as SDSS J120136.02+300305.5 (see Figure 5 of Saxton et al. 2012a).

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Finally, to test for any possible coherent oscillations in the X-rays (0.3–10 keV), we extracted a power density spectrum using the longest XMM-Newton observation (ObsID: 0694830201) with an effective exposure of roughly 48 ks. We find that the power spectrum is flat (white noise) and is consistent with being featureless (see Figure 3).

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Dynamical friction within a galaxy ensures that supermassive black holes sink to the center within a few Gyr after formation (e.g., Equation (4) of Miller & Colbert 2004). Therefore, if Sw J2058+05 is an event caused by a supermassive black hole, it should arise from the center of the host galaxy. To constrain the (projected) offset between the transient emission from Sw J2058+05 and its underlying host, we took three approaches.

First, we compared the VLBA position for Sw J2058+05 (Section 2.5) with the host localization derived from HST. We used the ${\rm F}606{\rm W}$ image from 2014 for this purpose (as opposed to the ${\rm F}160{\rm W}$ images obtained in 2013 December), owing to its higher S/N and smaller native pixel scale. While the VLBA position for Sw J2058+05 is the most precise available, the dominant source of uncertainty results from alignment of the HST images onto the FK5 reference grid using common point sources from 2MASS (60 mas in each coordinate). After alignment, we measured a position for the host centroid in the HST images of $\alpha ={{20}^{{\rm h}}}{{58}^{{\rm m}}}19\buildrel{\rm{s}}\over{.}898$, $\delta =+05{}^\circ 13^{\prime} 32\buildrel{\prime\prime}\over{.} 30$. As this is offset from the VLBA position by 58 mas, we conclude that the radio position is consistent with the host nucleus, within our uncertainties.

Next, we performed digital image subtraction on our ${\rm F}160{\rm W}$ images obtained on 2011 August 30 (top-left panel of Figure 4) and 2013 December 10 (top-right panel of Figure 4) to more precisely constrain the relative transient-host offset (e.g., Levan et al. 2011). The resulting subtraction image is displayed in the bottom left panel of Figure 4. Assuming that the flux in the final epoch of imaging is dominated by the host galaxy, we measured a radial offset between the transient emission and the host centroid of 0.34 pixels (i.e., 22 mas). Including contributions to the relative astrometric uncertainty from image alignment (0.18 pixel in each coordinate) and measurement of the host centroid (0.10 pixel in each coordinate), we find a null probability of measuring such an offset of 27% (assuming a Rayleigh distribution for the radial offset). Thus, we conclude that the transient emission is consistent with the host nucleus at this level of precision, as well.

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Finally, we measured the relative offset between the 2011 ${\rm F}475{\rm W}$ images of Sw J2058+05 (dominated by transient emission) and our 2014 ${\rm F}606{\rm W}$ image of the field (presumed to be host dominated). We find that the centroids in the two images are offset by 10 mas, while our alignment uncertainty is only 15 mas in each coordinate. This method offers the most precise constraint on the relative transient-host offset, and we formally place a 90% confidence limit of Δθ ≲ 45 mas, corresponding to a projected distance of ≲400 pc at z = 1.1853. This is comparable to the limits on the transient-host offset derived for Sw J1644+57 ($d\lt 150$ pc (1σ) at z = 0.354; Levan et al. 2011).

The UVOIR SED of Sw J2058+05 at early times (${\Delta }t\lesssim 1$ yr, observer frame) is quite blue, significantly more so than one would expect from simple forward-shock models (e.g., Granot & Sari 2002). Motivated by the observed SEDs in nonrelativistic TDEs (e.g., Gezari et al. 2012), we fit, wherever possible, the UVOIR SEDs with a single-temperature blackbody. The best-fit model parameters from the six epochs are indicated in Table 5. Including host-galaxy extinction as an additional free parameter in modeling these SEDs did not improve the fits. Formally, we limit the host extinction to ${{A}_{V}}\lesssim 0.2$ mag (90% confidence), assuming that it has an extinction law similar to that in the Milky Way (Pei 1992).

All of the SEDs, along with the best-fit model, are shown in the top panel of Figure 5. We show the evolution of the temperature and the radius of the blackbody in the bottom left and bottom right panels, respectively. There is clear evidence for a decrease in the blackbody temperature at late times before the X-ray flux drops off, and marginal evidence for an increase in the radius. But given the large error bars in the radii, we cannot strongly rule out the possibility that the radius remains constant throughout. We also note, however, that with reduced ${{\chi }^{2}}$ values as low as we find in several epochs, the quoted uncertainties should be treated with some degree of caution. Regardless, it is clear that the emission has become much redder in our final epoch, with a largely flat SED in $\nu {{L}_{\nu }}$.

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Our highest-S/N spectrum, obtained with Keck/LRIS on 2011 August 28, is plotted in Figure 6. We also fit our Keck/LRIS spectra to single-temperature blackbody models and find ${{T}_{{\rm BB}}}=(1.8\pm 0.2)\times {{10}^{4}}$ K on 2011 August 2 and ${{T}_{{\rm BB}}}=(2.3\pm 0.1)\times {{10}^{4}}$ K on 2011 August 28 (solid green line in Figure 6). These results are largely consistent with the values derived from our broadband photometry, providing additional confidence in the above analysis.

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For comparison, in Figure 6 we also plot the composite quasar (QSO) spectrum from SDSS (Vanden Berk et al. 2001), and a spectrum taken near maximum light of the TDE PS1–10jh (Gezari et al. 2012). In all cases the spectra of Sw J2058+05 are dominated by a blue, featureless continuum. No obvious emission or absorption features are detected in any spectra, with the exception of the initial spectrum from 2011 June 1 presented in C12, from which the redshift of z = 1.1853 was derived from narrow Mg ii and Fe ii absorption lines. Clearly, the strong, broad emission lines that dominate QSOs in the near-UV (e.g., Mg ii, C iii], and C iv) are not present in our spectra of Sw J2058+05. In addition to a hot (${{T}_{{\rm BB}}}\approx 3\times {{10}^{4}}$ K) blackbody continuum, PS1–10jh displayed high-ionization He ii λλ4686 and 3203 emission lines. Our Keck/LRIS spectra do not probe sufficiently far into the rest-frame optical to cover the stronger He ii λ4686 feature. We see no evidence for broad emission at this location in our XSHOOTER spectra; however, the S/N is quite low in these data. A number of optically discovered TDEs also display broad Hα emission (Arcavi et al. 2014; Holoien et al. 2014), although it is unclear if the presence/absence of H is due to properties of the disrupted star (Gezari et al. 2012) or the radial extent of the newly formed accretion disk (Guillochon et al. 2014). Again, we detect no evidence for broad emission lines at rest-frame Hα (or any other Balmer lines, for that matter), but are limited by the low S/N at these wavelengths.

We can also limit the presence of narrow, nebular emission lines from the underlying host galaxy. In particular, we do not detect either [O ii] λ3727 or Hα. If we assume unresolved emission lines at these wavelengths, we calculate limiting flux values of f(O ii) $\lt \;4.8\times {{10}^{-17}}$ erg s⁻¹ cm⁻² and f(Hα) $\lt \;6.5\times {{10}^{-17}}$ erg s⁻¹ cm⁻². Using the relations from Kennicutt (1998) between emission-line luminosity and star formation rate (SFR), we limit the presence of recent star formation in the host of Sw J2058+05 to be ≲5 M$_{\odot }$ yr⁻¹ (uncorrected for extinction). This is consistent with an estimate of the SFR derived from the UV (${\rm F}606{\rm W}$) luminosity of the host galaxy, for which we find 0.8 M$_{\odot }$ yr⁻¹ (using the calibration from Kennicutt 1998).

The detection of radio emission from Sw J2058+05 confirms the presence of nonthermal electrons in the circumnuclear ejecta. We can apply standard equipartition arguments (Readhead 1994; Kulkarni et al. 1998) to place a lower limit on the size of the radio-emitting region. Using the formulation valid for relativistic outflows from Barniol Duran et al. (2013), our VLBA detection at ${\Delta }t\approx 40$ days (rest frame) implies ${{R}_{{\rm eq}}}\gtrsim 7\times {{10}^{16}}$ cm. Similarly, these observations, though not as constraining as those presented by C12,¹⁹ imply at least transrelativistic expansion (${{{\Gamma }}_{{\rm eq}}}\gtrsim 0.6$) from an energetic outflow (${{E}_{{\rm eq}}}\gtrsim 3\times {{10}^{49}}$ erg).

The above limit on the physical size of the radio-emitting region corresponds to a lower limit on the angular size of Θ ≳ 3Ψ μas, where Ψ is the jet opening angle. For any feasible jet opening angle, this result is consistent with the unresolved nature of the source in the VLBA imaging (Θ ≲ 1 mas).

To better understand the nature of Sw J2058+05, we first consider the origin of the emission in the three regimes probed here: radio, UVOIR, and X-ray. We derived a robust lower limit on the size of the radio-emitting region (based solely on equipartition arguments in Section 3.5), ${{R}_{{\rm radio}}}\gtrsim 7\times {{10}^{16}}$ cm. Together with more stringent limits on the bulk Lorentz factor from C12 (Γ ≳ 1.5), we conclude that the radio emission is generated by the forward shock of a newly formed, at least mildly relativistic jet. An identical conclusion was reached by several authors (e.g., Bloom et al. 2011; Zauderer et al. 2011) in the case of Sw J1644+57.

The X-rays, on the other hand, must clearly have a distinct origin. The rapid variability on a rest-frame timescale of ≲500 s requires the size of the X-ray-emitting region to be ${{R}_{{\rm X}-{\rm ray}}}\lesssim c\;\delta t\approx 2\times {{10}^{13}}$ cm. This clearly rules out a forward-shock origin. However, the tremendous peak X-ray luminosity, many orders of magnitude above Eddington for any feasible black hole, suggests some association with the newly formed jet (as does the rapid turnoff; see below). One possibility is that the X-rays are generated in the base of the jet (e.g., Bloom et al. 2011; Zauderer et al. 2011), though the process by which this occurs remains a mystery. Again, the analogy with Sw J1644+57 holds well.

Finally, we have demonstrated that the UVOIR data, both photometry and spectra, are well fit by a single-temperature blackbody with ${{T}_{{\rm BB}}}\approx {\rm few}\times {{10}^{4}}\;{\rm K}$. The inferred blackbody radius, which appears to remain roughly constant, is ${{R}_{{\rm opt}}}\approx {{10}^{15}}$ cm. Together with the long-lived blue colors, the radius also seems to disfavor a forward-shock origin for the UVOIR component. Similarly, the derived blackbody spectrum severely underpredicts the observed X-ray flux.

Instead, these values are consistent with spectral studies of nonrelativistic TDE candidates in the literature with apparent blackbody temperatures and radii in the range of (1–10) $\times {{10}^{4}}$ K and (0.1–20) $\times {{10}^{15}}$ cm, respectively (e.g., Gezari et al. 2009b, 2012; Cenko et al. 2012a; Armijo & De Freitas Pacheco 2013; Arcavi et al. 2014; Chornock et al. 2014; Guillochon et al. 2014; Holoien et al. 2014), although there are some TDE candidates that tend to show higher disk temperatures of $\gtrsim {{10}^{5}}$ K accompanied by smaller emitting regions of size $\lesssim {{10}^{13}}$ cm (e.g., Gezari et al. 2008). However, for any plausible black hole mass, the blackbody radius is orders of magnitude larger than the radius at which disruption should occur. Such large radii have been attributed to reprocessing in some external region (see, e.g., the numerical simulations of Guillochon et al. 2014).

It is important to note here that while Sw J1644+57 lacked detectable UV and optical emission, the high degree of polarization observed in the NIR was attributed to jetted emission from the forward shock (Wiersema et al. 2012), and not from the (presumably largely isotropic) accretion disk. Naively, unless the reprocessing region was nonisotropic, we would expect a low degree of optical polarization from Sw J2058+05 if this simplistic picture is correct. For future relativistic TDE candidates, polarization observations would be an important test of this model.

Using the best-fit blackbody luminosities and integrating the resulting light curve (using the trapezoidal rule) in the rest frame between epochs 5.7 and 181.4 days, we estimate the total UVOIR energy radiated to be $\sim 5\times {{10}^{51}}$ erg. Similarly, we integrated the X-ray light curve (top panel of Figure 1) and estimate the total isotropic energy to be $\sim 4\times {{10}^{53}}$ erg. Assuming an opening angle of ∼0.1 rad, similar to what has been estimated for Sw J1644+57 (Metzger et al. 2012; Zauderer et al. 2013), we measure the total, beaming-corrected X-ray energy output to be $\sim 4\times {{10}^{51}}$ erg. The bolometric luminosity is, however, expected to be a factor of a few higher than the X-ray luminosity. Assuming that the bolometric value is a factor of 3 (similar to that of Sw J1644+57; Burrows et al. 2011), one can estimate the total accreted mass onto the black hole using Equation (5) of the supplemental information of Burrows et al. (2011). We find this value to be ∼0.1 M$_{\odot }$, which is comparable to Sw J1644+57's 0.2 M$_{\odot }$ (Burrows et al. 2011; Zauderer et al. 2013), both appropriate for disruption of a ∼1 M$_{\odot }$ star.

The X-ray emission from Sw J2058+05 drops abruptly between days 200 and 300 (rest frame), consistent with what was seen for Sw 1644+57 (top panel of Figure 1). More specifically, Sw J2058+05's intensity decreases by a factor of ≳160 within a span of ${\Delta }t/t\leqslant 0.95$ compared to Sw J1644+57's factor of ∼170 decline over a span of ${\Delta }t/t\lesssim 0.2$ (Levan & Tanvir 2012; Sbarufatti et al. 2012; Zauderer et al. 2013). Interestingly, in both of these sources, the X-ray dimming occurs on a comparable timescale after disruption.

In the case of Sw J1644+57, Zauderer et al. (2013) interpreted this sudden decrease in the flux as an accretion-mode transition from a super-Eddington to a sub-Eddington state. This is consistent with the transitioning timescale predicted from numerical simulations (e.g., Figures 2 and 4 of Evans & Kochanek 1989 and De Colle et al. 2012, respectively). Assuming that the same process is responsible for the abrupt flux change in Sw J2058+05, we can attempt to estimate the mass of the black hole by equating the luminosity at turnoff to the Eddington luminosity. From the X-ray light curve (see Tables 1 and 4), it is evident that the isotropic X-ray luminosity drops from $1.3\times {{10}^{45}}$ erg s⁻¹ to less than $8.4\times {{10}^{42}}$ erg s⁻¹, suggesting an Eddington value somewhere in between these two limits. Using these two values and assuming radiative efficiency, beaming angle, and bolometric correction values of 0.1, 0.1 rad, and 30%, respectively (similar to Sw J1644+57; Burrows et al. 2011), we constrained the black hole mass ${{M}_{{\rm BH}}}$ to be 10⁴ M$_{\odot }\lesssim {{M}_{{\rm BH}}}\lesssim 2\times {{10}^{6}}$ M$_{\odot }$. Furthermore, numerical simulations suggest that the time to drop-off (transition from super-Eddington to sub-Eddington) since the disruption is shorter for more massive black holes (see Figure 2 of De Colle et al. 2012). The X-ray drop-off in Sw J2058+05 occurs ∼100 days earlier than that in Sw J1644+57, suggesting that its black hole may be more massive.

However, it is interesting to note that even the optical light curves of Sw J2058+05 undergo an abrupt change during an epoch roughly consistent with the X-ray dimming (see the bottom panel of Figure 1). We find that the optical flux, for instance in the r band, drops by a factor of at least 5 within a narrow span of ${\Delta }t/t\approx 0.16$. We speculate, within the context of the following simple model, that the X-rays are coming from the base of the jet and the optical originates from the reprocessed UV/soft-X-ray disk photons in the ambient medium. In such a scenario, the proposed super-Eddington to sub-Eddington accretion transition would presumably change the accretion-disk structure to lower its emission, thus explaining the reduction in the amount of the reprocessed light. Obviously, the true situation is more complicated, with specific details about the radiative efficiency, beaming, and other factors. It can be better understood with more detailed modeling, but this is beyond the scope of the current paper.

On the other hand, the long-term X-ray light curve of Sw J2058+05 does not exhibit the numerous sudden dips observed in Sw J1644+57 (see Figure 1). In the case of Sw J1644+57, it has been argued that the X-ray dips originate from jet precession and nutation, which causes it to briefly go out of our line of sight (e.g., Saxton et al. 2012b). We speculate, based on the lack of such dips in Sw J2058+05, that its jet may be more stable compared to Sw J1644+57. However, given the poor sampling of the X-ray light curve, the current data cannot completely rule out the presence of dips in Sw J2058+05.

The mass limits derived above based on the X-ray turnoff are consistent with other methods of estimating ${{M}_{{\rm BH}}}$. First, we can use the X-ray variability timescale to place an upper limit on black hole mass. Equating the limit on the size of the X-ray-emitting region with a Schwarzschild radius suggests a compact object of mass less than $5\times {{10}^{7}}$ M$_{\odot }$.

Also, assuming that the optical flux in our final two HST epochs is dominated by the host galaxy (and not transient emission), we can constrain the mass of the central supermassive black hole using the well-known bulge luminosity vs. black hole mass relations (e.g., Lauer et al. 2007). Neglecting for the moment K-corrections [aside from the cosmological $-2.5\;{\rm log} (1+z)$ factor], the distance modulus at z = 1.1853 implies an absolute magnitude of −18.7 from the ${\rm F}606{\rm W}$ observation (approximately rest-frame U band) and −19.4 from the ${\rm F}160{\rm W}$ observation (approximately rest-frame I band). Both suggest ${{M}_{V}}\approx -19$ mag, or an inferred supermassive black hole mass of ${{M}_{{\rm BH}}}\lesssim 3\times {{10}^{7}}$ M$_{\odot }$. While there is significant scatter in the bulge luminosity vs. black hole mass relation, our limits are conservative in the sense that they assume that all of the observed luminosity derives from the bulge (and none from, say, a disk). At the very least, we can robustly conclude that ${{M}_{{\rm BH}}}\lt {{10}^{8}}$ M$_{\odot }$, the limit above which a nonspinning black hole cannot tidally disrupt a solar-mass main-sequence star (Rees 1988).