A New, Faint Population of X-ray Transients

TL;DR

This paper reports the discovery of a new faint X-ray transient with unique properties, challenging existing classifications and suggesting the existence of an unrecognized class of high-energy transient phenomena.

Contribution

It presents the detection and analysis of a novel, faint X-ray transient, expanding the known diversity of high-energy transient events and highlighting potential new astrophysical phenomena.

Findings

Detected a faint, fast X-ray transient in the Chandra Deep Field-South.

The transient's properties do not match known high-energy transients.

Estimated event rate suggests a new or rare class of phenomena.

Abstract

We report on the detection of a remarkable new fast high-energy transient found in the Chandra Deep Field-South, robustly associated with a faint ($m_{\rm R}=27.5$ mag, $z_{\rm ph}$$\sim$2.2) host in the CANDELS survey. The X-ray event is comprised of 115$^{+12}_{-11}$ net 0.3-7.0 keV counts, with a light curve characterised by a $\approx$100 s rise time, a peak 0.3-10 keV flux of $\approx$5$\times$10$^{-12}$ erg s$^{-1}$ cm$^{-2}$, and a power-law decay time slope of $-1.53\pm0.27$. The average spectral slope is $\Gamma=1.43^{+0.23}_{-0.13}$, with no clear spectral variations. The \hbox{X-ray} and multi-wavelength properties effectively rule out the vast majority of previously observed high-energy transients. A few theoretical possibilities remain: an "orphan" X-ray afterglow from an off-axis short-duration Gamma-ray Burst (GRB) with weak optical emission; a low-luminosity GRB at high redshift with no prompt emission below $\sim$20 keV rest-frame; or a highly beamed Tidal Disruption Event (TDE) involving an intermediate-mass black hole and a white dwarf with little variability. However, none of the above scenarios can completely explain all observed properties. Although large uncertainties exist, the implied rate of such events is comparable to those of orphan and low-luminosity GRBs as well as rare TDEs, implying the discovery of an untapped regime for a known transient class, or a new type of variable phenomena whose nature remains to be determined.

Tables

Table 1. Table 1: X-ray timing properties of CDF-S XT1 . Col. 1 : Bayesian block time bin, in seconds, following (Scargle et al., 2013 ) . Col. 2 : Time bin half width, in seconds. Col. 3 : 0.3–7 keV count rate, in cnts s -1 . Col. 4 : 0.3–10 keV flux, in erg cm -2  s -1 . Col. 5 : Hardness ratio (HR) defined as ( H − S 𝐻 𝑆 H-S )/( H + S 𝐻 𝑆 H+S ) where H 𝐻 H and S 𝑆 S are the 2–7 and 0.3–2 keV counts, respectively (Park et al., 2006 ) .

Time	Bin Half	CR	$F_{0.3-10\mathrm{keV}}$	HR
Bin	Width
16	16	$4.24\times {10}^{-2}$	${8.5}_{-6.4}^{+15.4}\times {10}^{-13}$	$-$${0.23}_{-0.43}^{+0.74}$
64	32	$3.82\times {10}^{-2}$	${7.7}_{-4.6}^{+8.8}\times {10}^{-13}$	$-$${0.50}_{-0.43}^{+0.49}$
160	64	$2.45\times {10}^{-1}$	${5.1}_{-0.9}^{+1.1}\times {10}^{-12}$	$-$${0.21}_{-0.18}^{+0.16}$
352	128	$1.14\times {10}^{-1}$	${2.3}_{-0.4}^{+0.5}\times {10}^{-12}$	$-$${0.14}_{-0.21}^{+0.14}$
832	352	$3.59\times {10}^{-2}$	${7.2}_{-1.4}^{+1.7}\times {10}^{-13}$	${0.07}_{-0.24}^{+0.16}$
1664	480	$1.03\times {10}^{-2}$	${2.1}_{-0.6}^{+0.9}\times {10}^{-13}$	$-$${0.19}_{-0.25}^{+0.35}$
3568	1424	$3.19\times {10}^{-3}$	${6.4}_{-2.1}^{+2.9}\times {10}^{-14}$	${0.02}_{-0.33}^{+0.48}$
18000	13008	$2.69\times {10}^{-4}$	${5.4}_{-2.0}^{+2.9}\times {10}^{-15}$	$-$${1.00}_{-0.00}^{+1.42}$
138320	12496	$3.70\times {10}^{-5}$	${7.5}_{-6.9}^{+18.7}\times {10}^{-16}$	$-$${1.00}_{-0.00}^{+1.50}$

Table 2. Table 2: CANDELS F160W Data Release 1 (DR1) catalog parameters Col. 1 : Object number. Col. 2 : CANDELS catalog number. For completeness, the equivalent 3D- HST v4.1 catalog numbers are 10718, 10709, 10670, and 10685, respectively. Col. 3 : J2000 Right Ascension and Declination in degrees. Col. 4 : Angular offset between X-ray and optical positions. Col. 5 : observed R 𝑅 R -band magnitude. Col. 6 : observed J 𝐽 J -band magnitude. Col. 7 : Kron radius. a FWHM ≈ \approx 0 . ′ ′ \aas@@fstack{\prime\prime} 12 is consistent with point source. Col. 8 : Photometry redshift and 95% limit range in parentheses from best-fitting template. b The photometry for 28572 can also be fit with a Galactic M-star template. Col. 9 : Absolute R 𝑅 R -band magnitude. Col. 10 : Estimated logarithm of stellar mass at best-fitting z ph subscript 𝑧 ph z_{\rm ph} . Col. 11 : Estimated star formation rate (SFR) at best-fitting z ph subscript 𝑧 ph z_{\rm ph} .

#	CANDELS	R.A, Dec.	offset	$R$	$J$	$r_{\mathrm{Kron}}$	$z_{\mathrm{ph}}$	$M_R$	$\log \left(M/M_{\odot }\right)$	SFR ($M_{\odot }$ yr-1)
1	28573	53.161575, -27.859375	0.13	27.51	27.31	0.56	2.23 (0.39–3.21)	-18.7	$7.99\pm 0.20$	$1.15\pm 0.04$
2	28572	53.161841, -27.859427	1.09	27.38	27.34	0.50a	0.31 (0.07–6.81)b	-13.7	$6.84\pm 0.18$	$0.40\pm 0.07$
3	5438	53.161095, -27.859668	1.99	26.89	26.16	0.76	0.53 (0.18–2.89)	-15.5	$7.82\pm 0.33$	$1.20\pm 0.60$
4	5448	53.162391, -27.859707	3.29	25.78	25.27	0.69	0.15 (0.10–0.26)	-13.5	$7.47\pm 0.12$	$0.03\pm 0.01$

Table 3. Table 3: Intrinsic constraints on CDF-S XT1 for several example redshifts. Col. 1 : Example redshift. The photometric redshift of the nearby galaxy is nominally 2.23, but extends between 0.39–3.21 at 95%, so we provide a wide range. Col. 2 : 2–10 keV X-ray luminosity within the initial 400 s, in units of 10 45 superscript 10 45 10^{45}  erg s -1 . Col. 3 : Absolute F ​ 606 ​ W 𝐹 606 𝑊 F606W -band magnitude of the tentative host galaxy. Col. 4 : Absolute R 𝑅 R -band magnitude limit for epoch E1. Col. 5 : Absolute R 𝑅 R -band magnitude limit for epoch E2. Col. 6 : Absolute r ′ superscript 𝑟 ′ r^{\prime} -band magnitude limit for epoch E3. Col. 7 : Absolute F ​ 110 ​ W 𝐹 110 𝑊 F110W -band magnitude limit for epoch E4.

Redshift	$L_{2-10\mathrm{keV}}$	$M_{\mathrm{F606W},\mathrm{Host}}$	$M_{R,\mathrm{E1}}$	$M_{R,\mathrm{E2}}$	$M_{r,\mathrm{E3}}$	$M_{\mathrm{F110W},\mathrm{E4}}$
	(${10}^{45}$ erg s-1)	(mag)	(mag)	(mag)	(mag)	(mag)
2.23	67.5	$-$18.7	$>$$-$20.5	$>$$-$19.3	$>$$-$20.3	$>$$-$17.9
0.30	0.5	$-$13.5	$>$$-$15.3	$>$$-$14.0	$>$$-$15.0	$>$$-$12.6
0.50	1.7	$-$14.8	$>$$-$16.6	$>$$-$15.3	$>$$-$16.3	$>$$-$13.9
1.00	9.4	$-$16.6	$>$$-$18.4	$>$$-$17.1	$>$$-$18.1	$>$$-$15.7
2.00	51.7	$-$18.5	$>$$-$20.3	$>$$-$19.0	$>$$-$20.0	$>$$-$17.6
3.00	138.5	$-$19.5	$>$$-$21.3	$>$$-$20.0	$>$$-$21.0	$>$$-$18.6

Table 4. Table 4: Light curve characterization for 184 candidates from CSC search. Col. 1 : Light curve category ( criterion #2 ). Col. 2 : Number found. Col. 3 : Variability characteristics. Col. 4 : Number within | b | 𝑏 |b| ≤ \leq 10 ∘ (i.e., considered Galactic). Col. 5 : Number with clear optical counterparts or associations with globular clusters, star forming regions, or galaxies ( criterion #1 ). Col. 6 : Number that exhibit a best-fitting X-ray spectral slope of Γ Γ \Gamma < < 2.0. In many cases, the spectra and hardness ratios are not of sufficient quality to robustly determine a spectral slope. Therefore we provide the possible range. ( criterion #3 ).

Cat.	#	Var. type	GalPlane?	Opt?	Hard?
1	129	recurrent/persistent transients (flaring, eclipsing, gradual, etc.).	20	123	14–47
2	29	non-recurrent transients with marginal or no prior/post detections; exhibit $\gtrsim 4$ ks rises and/or decay time-scales several times longer than CDF-S XT1.	7	29	12
3	7	non-recurrent transients with no prior/post detections; exhibit 2–4 ks rise times, decay time-scales several times longer than CDF-S XT1 and/or flattening either early or late in the transient decay.	3	7	4
4	5	non-recurrent transients with no prior/post detections similar to Cat 3, but time series terminates or is of insufficient statistical quality to assess further.	2	4	2–4
5	4	non-recurrent transients with no prior/post detections and show consistent X-ray light curve shapes with peak of $\lesssim$103.	2	4	2
6	6	non-recurrent transients potentially similar to Cat 5, but have significant low-level activity in the $\sim$103–104.5 s prior to Cat 5 light curve shapes.	4	5	1–3
7	4	non-recurrent transients with no prior/post detections; exhibit weak short rise and fall behavior within 100–500 s and dominated by noise at late times.	1	3	0–4

Full text

††pubyear: 2017††pagerange: A New, Faint Population of X-ray Transients–A New, Faint Population of X-ray Transients

1 Introduction

The ever-improving depth and sky coverage of modern telescopes have opened the floodgates to the transient universe and enabled the discovery and characterization of several new classes of exotic variable phenomena over the past decades (e.g., Klebesadel et al., 1973; Bade et al., 1996; Galama et al., 1998; Kouveliotou et al., 1998; Gezari et al., 2006; Lorimer et al., 2007; Soderberg et al., 2008; Bloom et al., 2011; Thornton et al., 2013; Garnavich et al., 2016). A distinct subset of such variable and transient objects can only be understood from their high-energy properties as determined by past and current space missions (e.g., CGRO, Einstein, ROSAT, ASCA, BeppoSAX, HETE-2, RXTE, INTEGRAL, Chandra, XMM-Newton, Swift, NuSTAR). While the bulk of X-ray transients relate to accretion processes onto black holes (BHs), neutron stars (NSs), and white dwarfs (WDs), there are several emerging classes of exotic X-ray transients whose nature and driving mechanisms remain unclear or unknown (e.g., Metzger et al., 2011; Woosley & Heger, 2012; Loeb et al., 2014; Tchekhovskoy et al., 2014; Zhang, 2014; Ciolfi, 2016; Irwin et al., 2016). Such objects provide critical challenges to our conventional paradigms, and offer the potential for insight into poorly understood physics.

Here we report the discovery of a new fast X-ray transient found in the Chandra Deep Field-South (CDF-S). The unique multi-wavelength properties of this transient appear to set it apart from any known class of variable observed to date, suggesting that the event either represents a new class of X-ray transient or probes a new regime for a previously known class. While the estimated rate of such transients remains modest and subject to large uncertainties, their origin could have implications for future high-energy and/or gravitational wave (GW) searches.

We have organised the paper as follows: data and analysis methods are detailed in $\S$2; possible intrepretations are discussed in $\S$3; rate estimates are assessed in $\S$4; and finally a summary and exploration of future prospects in $\S$5. We adopt a Galactic neutral column density of N_{\rm H}$$=8.8$\times$1019 cm*-2* (Kalberla et al., 2005) toward the direction of the transient. Unless stated otherwise, errors are quoted at 1$\sigma$ confidence, assuming one parameter of interest. All magnitudes are reported in the AB system.

2 Data and Analysis

We describe below the primary datasets used to detect and characterize the transient, as well as detail the variety of constraints obtained.

2.1 Chandra 0.3–10 keV on 2014 October 01

The CDF-S is the deepest survey of the X-ray sky, with published observations spanning 4 Ms ($\approx$46 days; Xue et al., 2011) and an additional 3 Ms added in 2014–2016 (Chandra proposal number: 15900132; PI: W. N. Brandt). While analyzing the new CDF-S ACIS-I X-ray data in near real-time, we discovered a fast X-ray transient (Luo et al., 2014) midway through one of the observations starting at 2014 October 01 07:04:37 UT (obsid 16454, $\sim$50 ks exposure). X-ray analysis was performed using CIAO (v4.6) tools and custom software. Details regarding the data processing, cleaning, photometry and alignment to the alignment to the VLA radio and TENIS near-infrared astrometric reference frame can be found in Xue et al. (2011) and Luo et al. (2017). We rule out all previously known Chandra instrumental effects; the transient has a normal event grade and energy distribution, and is detected in many dozens of individual pixels tracing out portions of Chandra’s 32$\times$32 pixel (16*′′$\times$16′′*) Lissajous dither pattern over a long time duration (indicating the source is celestial).

No X-rays above the background rate are detected at this position in any other individual Chandra or XMM-Newton obsid or combined event lists, which total 6.7 Ms for Chandra (Luo et al., 2017) and 2.6 Ms for XMM-Newton (Comastri et al., 2011). Here we assumed the 90% encircled energy region to derive the source limit, while for XMM-Newton we adopted a circular aperture of 6*′′* radius. These limits imply quiescent 0.3–10, 0.3–2.0, and 2–10 keV flux limits of 3.1$\times$10*-17*, 1.6$\times$10*-17*, and 5.4$\times$10*-17* erg cm*-2* s*-1*, respectively, at 3$\sigma$ confidence. The first count from CDF-S XT1 arrives $\approx$16.8 ks into the observation, offering immediate precursor 0.3–10, 0.3–2.0, and 2–10 keV flux limits of 5.2$\times$10*-15*, 2.9$\times$10*-15*, and 7.9$\times$10*-15* erg cm*-2* s*-1*, respectively.

The transient has a J2000 position of $\alpha$=53$\aas@@fstack{\circ}$161550, $\delta$=-27$\aas@@fstack{\circ}$859353 and an estimated 1$\sigma$ positional uncertainty of 0$\aas@@fstack{\prime\prime}$26. We extracted 115 net counts in the 0.3–7 keV band for the transient from a 3*′′* radius circular aperture (97% encircled energy fraction at 1.5 keV at the source position and zero expected background counts), from which we constructed an X-ray light curve (Fig. 1) and spectrum (Fig. 2) following standard procedures. We arbitrarily set the light curve zeropoint as 10 s prior to the arrival of the first photon.

The count rate of the transient near the peak of its X-ray light curve is $\approx$0.3–0.4 cts s*-1* (equivalent to a readout of $\gtrsim$1 count per 3.2 s frame). As such, there is some potential for photons to suffer pile-up (two incident photons count as one higher energy photon or possibly even rejected), which would harden the spectrum and lower the observed count rate at early times. Fortunately, the transient lies at an off-axis angle of 4$\aas@@fstack{\prime}$3 from the ACIS-I aimpoint, and thus has an extended point spread function (PSF), such that only $\approx$50% of the photons lie within $\approx$1$\aas@@fstack{\prime\prime}$0–1$\aas@@fstack{\prime\prime}$2 (for energies of 1.5–6.4 keV, respectively). Such a PSF should be $\approx$4 times less affected by pileup compared to an on-axis PSF, implying that CDF-S XT1 should be minimally affected by pileup (a few percent at most). We verified this result empirically by examining the source frame by frame and based on simulations with the MARX (Davis et al., 2012).

The X-ray light curve (Fig. 1) shows a fast rise of 110$\pm$50 s to a peak 0.3–10 keV flux of $5.1\times 10^{-12}$ erg s*-1* cm*-2* and a power-law decay of the form $F_{\rm 0.3-10keV}=F_{0}(t/t_{0})^{a}$, where $t$ is time, F_{0}$$=$$0.364\pm 0.083 erg s*-1* cm*-2*, t_{0}$$=$$146\pm 12 s, and slope a$$=$$-1.53\pm 0.27, fit using a least-squares method. Dividing the light curve into logarithmic time bins of 0.2 dex, we see marginal evidence for spectral hardening in one bin around 1000 s. However this is not strong enough to rule out a constant model at $>$3$\sigma$, and thus no significant spectral variations with time are found given the limited statistics (Fig. 1; see also Table 1 using Bayesian block binning). The $T_{\rm 90}$ duration parameter, which measures the time over which the event emits from 5% to 95% of its total measured counts, is $5.0^{+4.2}_{-0.3}$ ks, with an associated fluence of ($4.2^{+3.5}_{-0.2}$)$\times$10*-9* erg cm*-2*.

Given the low number of counts, the X-ray spectrum was fit using the Cash statistic (Cash, 1979) with relatively simple continuum models. The data are well-fitted by either an absorbed power law ($dN/dE\propto E^{-\Gamma}$) with \Gamma$$=1.43${}^{+0.26}_{-0.15}$ or a relatively unconstrained 20.2${}^{+27.6}_{-11.3}$ keV absorbed thermal plasma (apec) model, with a best-fitting absorption limit of N_{\rm H}$$<4.5$\times$1021 $(1+z)^{2.5}$ cm*-2* (3$\sigma$). The latter is formally consistent with the Galactic value of 8.8$\times$1019 cm*-2* (Kalberla et al., 2005), but intrinsic absorption cannot be ruled out. These values should be used with caution, as there is some possible degeneracy between the best-fitting photon index $\Gamma$ and column density $N_{\rm H}$, such that a softer value of $\Gamma$ ($\sim$2) cannot be excluded; see Fig. 2. The absorption limit implies A_{\rm V}$$\lesssim0.7 $(1+z)^{2.5}$ mag assuming a Galactic dust-to-gas ratio (Güver & Özel, 2009), which could become substantial at large distances due to the strong redshift dependence. The observed 0.3–10 (2–10) keV flux from the total spectrum, which we extracted from the first 12 ks only to optimise the inclusion of source versus background photons, is $2.0\times 10^{-13}$ ($1.4\times 10^{-13}$) erg cm*-2* s*-1*.

To investigate further the possibility of spectral variance with time, we split the spectrum in two parts with roughly equal photon counts: $<$400 s (“early”) and $>$400 s (“late”). This cut roughly coincides with the harder tine bin at $\sim$1000 s seen in Fig. 1. The best-fitting absorbed power law models yielded $\Gamma_{\rm early}=1.63^{+0.42}_{-0.21}$ and N_{\rm H,early}$$<$$7.2\times 10^{21}(1+z)^{2.5} cm*-2* at early times and $\Gamma_{\rm late}=1.50^{+0.42}_{-0.33}$ and N_{\rm H,late}$$<$$1.0\times 10^{22}(1+z)^{2.5} cm*-2* at late times, respectively (3$\sigma$). The corresponding observed early and late time fluxes at 0.3–10 (2–10) keV are $2.9\times 10^{-12}$ ($1.8\times 10^{-12}$) and $4.0\times 10^{-14}$ ($2.9\times 10^{-14}$ ) erg cm*-2* s*-1*, respectively; we find a factor of $\approx$70 decrease in the 0.3–10 keV flux between the early and late regimes. If the column density $N_{\rm H}$ is left free but required to be the same at early and late times, there is no change to the early time slope while the late time spectral index drops to $\Gamma_{\rm late}=1.41^{+0.33}_{-0.23}$ with $N_{\rm H,early+late}<5.5\times 10^{21}(1+z)^{2.5}$ cm*-2* (3$\sigma$). Again, there is no evidence for significant spectral hardening of the transient with time, within the statistical limitations of the data. Based on the confidence contours assessed for the complete spectrum, the source is consistent with Galactic absorption only, although it could be absorbed by as much as $7.2\times 10^{21}(1+z)^{2.5}$ cm*-2* at early times. The 2–10 keV X-ray luminosity for a variety of redshifts is provided in Table 3.

2.2 Previous imaging

The high Galactic latitude (l$$=223*∘*, b$$=$$-54^{\circ}), low extinction CDF-S region has been the subject of many intensive observing campaigns, and has some of the deepest coverage to date at nearly all observable wavelengths. We used in particular the images from the Hubble Space Telescope (HST) GOODS (Giavalisco et al., 2004) and CANDELS (Grogin et al., 2011; Koekemoer et al., 2011) surveys to identify and constrain the potential host galaxy of the X-ray transient. Both the CANDELS F160W DR1 (Guo et al., 2013) and 3D-HST v4.1 (Skelton et al., 2014) catalogs detect several sources in the vicinity of the X-ray transient with comparable brightnesses. We adopt values from CANDELS, which provides TFIT (Laidler et al., 2007) photometry measured on calibrated images, while 3D-HST fit their spectroscopic data with a set of templates and then correct the photometry; there are magnitude differences as large as $\sim$1 mag between catalogs, as well as detections in CANDELS but not in 3D-HST, despite clear visual confirmation. Table 2 lists the optical sources in the vicinity of the X-ray transient, in order of distance.

Given the error in the X-ray position, source #1 is clearly the favoured counterpart and we can exclude all other detected sources at $\gtrsim$4$\sigma$. Based on the source density of the CANDELS $F160W$-band catalog (Guo et al., 2013), the probability of a random alignment between CDF-S XT1 and a source as bright as #1 within a radius of 0$\aas@@fstack{\prime\prime}$13 is $<$0.1%.111Even adopting a 3$\sigma$ radius of 0$\aas@@fstack{\prime\prime}$78, the probability of a random match remains quite low ($<$4%). At the best-fitting photometric redshift of z_{\rm ph}$$=2.23, SED fitting of the CANDELS DR1 optical/NIR photometry suggests that the nearest counterpart is a dwarf galaxy with M_{R}$$=$$-17.3 mag (i.e., a few times smaller than the Large Magellanic Cloud, but with a stronger star formation rate of 1.5 $M_{\odot}$ yr*-1*). The 1$\sigma$ and 2$\sigma$ ranges on the photometric redshift from the CANDELS $F160W$-band catalog are 1.57–2.81 and 0.39–3.21, respectively. The reported 1$\sigma$ errors on the other derived properties listed in Table 2 are only statistical, measured at the best-fitting photometric redshift, which is fixed. Incorporating the $z_{\rm ph}$ error distribution and other systematic errors, which are difficult to quantify, are likely to increase the errors substantially. The absolute magnitude of the host for a variety of redshifts is provided in Table 3. The host does not appear to be particularly dusty. Three $R$-band images and one HST Wide Field Camera 3 (WFC3) $F110W$-band image of the field have been acquired since the X-ray detection, spanning 0.06 and 111 days post-transient (see Fig. 3). As outlined in $\S$2.3–2.6, no clear transient counterpart is detected at m_{\rm R}$$\lesssim25.5–26.5 mag (Luo et al., 2014; Treister et al., 2014a, b) in the optical and $\lesssim 28.4$ mag in the $F110W$ band.

2.3 VLT/VIMOS $R$ on 2014 October 1 (E1)

Serendipitously, the field of the fast X-ray transient was observed almost simultaneously ($\approx$80 minutes after) at optical wavelengths by the 8.2m Very Large Telescope (VLT) of the European Southern Observatory (ESO) using the VIsible MultiObject Spectrograph (VIMOS), as part of the VANDELS222http://vandels.inaf.it public survey (PIs: R. McLure and L. Pentericci). A 550 s $R$-band image (program ID 194.A-2003A) was obtained starting at 2014 October 1 08:20:09.6 UT with an optical seeing of $\approx$0$\aas@@fstack{\prime\prime}$7 FWHM and an average airmass of 1.03 (hereafter epoch ’E1’). The data were retrieved from the ESO archive and reduced using standard procedures. After aligning the X-ray and $R$-band images to $\approx$0$\aas@@fstack{\prime\prime}$1, no object is detected at the location of the X-ray flare, with an estimated magnitude limit of m_{\rm R}$$\approx25.7 mag (2$\sigma$, 0$\aas@@fstack{\prime\prime}$5 radius aperture). There is evidence for a marginal detection of source #4, as seen in the deep HST data, but nothing fainter. No variable sources are found within at least 20–30*′′* of the X-ray transient. The absolute magnitude limit of the transient for a variety of redshifts is provided in Table 3.

2.4 VLT/FORS2 $R$ on 2014 October 19 (E2)

Following the Chandra detection and initial serendipitous observation, the field of the fast X-ray transient was observed again with the 8.2m VLT using the FOcal Reducer and low dispersion Spectrograph (FORS2), 18 days after the X-ray transient was detected, as part of DDT program 294.A-5005A (PI: Franz Bauer). A 2900 s $R$-band image was obtained starting at 2014 October 19 05:37:15.6 UT under photometric conditions with an optical seeing of $\approx$0$\aas@@fstack{\prime\prime}$8 FWHM in the optical and an average airmass of 1.01 (hereafter epoch ’E2’). The $R$ filter was chosen as a compromise between the potential expectation for a blue transient, possible obscuration, and the relative sensitivity of the detector. The $\sim$7’$\times$7’ field of view covered by FORS2 was centred on the reported coordinates of the X-ray transient. The data were retrieved from the ESO archive and reduced using standard procedures. After aligning the X-ray and $R$-band images to $\approx$0$\aas@@fstack{\prime\prime}$1, no source is formally detected at the position of the X-ray transient, with an estimated magnitude limit of m_{\rm R}$$\approx27.0 mag (2$\sigma$, 0$\aas@@fstack{\prime\prime}$5 radius aperture). The nearest detected source is #3. No variable sources are apparent within at least 20–30*′′* of the X-ray transient. The absolute magnitude limit of the transient for a variety of redshifts is provided in Table 3.

2.5 Gemini-S/GMOS-S $r$ on 2014 October 28 (E3)

The field of the X-ray transient was observed a third time by the 8m Gemini-South Telescope using the imager on the Gemini Multi-Object Spectrograph (GMOS-S), 27 days after the X-ray transient was detected, as part of DDT program GS-2014B-DD-4 (PI: Ezequiel Treister). A 4500 s $r$-band image was obtained starting at 2014 October 28 07:36:25.7 UT under clear conditions with an optical seeing of $\approx$0$\aas@@fstack{\prime\prime}$6 FWHM and an average airmass of 1.2 (hereafter epoch ’E3’). The $r$ filter was chosen as a compromise between the potential expectation for a blue transient, possible obscuration, the relative sensitivity of the detector, and to crudely match the previous two observations. With the new Hamamatsu CCDs installed, GMOS-S covers a $\approx$5$\aas@@fstack{\prime}$5$\times$5$\aas@@fstack{\prime}$5 field of view, which was centred on the X-ray transient. The data were retrieved from the Gemini archive and reduced using standard procedures. After aligning the X-ray and $r$-band images to $\approx$0$\aas@@fstack{\prime\prime}$1, no source is formally detected at the position of the X-ray transient, with an estimated magnitude limit of m_{\rm r}$$\approx26.0 mag (2$\sigma$, 0$\aas@@fstack{\prime\prime}$5 radius aperture).333This limit is roughly 0.6 mag brighter than estimated by the Gemini-South GMOS-S ITC, possibly due to early background problems associated with the newly installed Hamamatsu CCDs. The nearest detected source to the X-ray position is #4. No variable sources are apparent within at least 20–30*′′* of the X-ray transient. The absolute magnitude limit of the transient for a variety of redshifts is provided in Table 3.

2.6 HST/WFC3 $F110W$ on 2015 January 20 (E4)

The field of the X-ray transient was observed a fourth time by HST using WFC3, 111 days after the X-ray transient was detected, as part of DDT program HST-GO-14043 (PI: Franz Bauer). A 2612 s $F110W$-band image was obtained on 2015 January 20 11:00:13 UT, with a dithered field of view of $\approx$140*′′$\times$124′′* centred on the X-ray transient (hereafter epoch ’E4’). We switched to the $F110W$ filter to test whether the X-ray transient might have been exceptionally red due to strong extinction or high-redshift, and owing to the excellent sensitivity of this band for faint NIR emission. The data were retrieved from the Mikulski Archive for Space Telescopes and reduced using standard procedures. After aligning the X-ray and $F110W$-band images to $\approx$0$\aas@@fstack{\prime\prime}$1, we recover nearly all of the objects from the deep HST $F125W$ image of CANDELS, including the associated counterpart source #1, with m_{\rm F110W}$$=27.43 mag. Based on difference imaging with the CANDELS $F105W$ and $F125W$ images using the High Order Transform of PSF and Template Subtraction code (HOTPANTS; Becker, 2015), we place a limit of m_{\rm F110W}$$\approx28.4 mag (2$\sigma$, 0$\aas@@fstack{\prime\prime}$2 radius aperture), comparable to the expected magnitude limit based on the HST exposure time calculator. To place this value in context for Fig. 5, we assume a colour dependence of m_{\rm R}$$-$$m_{\rm F110W}$$\approx0.4–0.7 mag based on GRB afterglow power-law spectral slopes in the range of $-$0.6 to $-$1.1 (Kann et al., 2010, 2011) and 0.4–1.0 mag for CCSNe between $z=0.0$–1.0 (Poznanski et al., 2002; Drout et al., 2011; Bianco et al., 2014). This implies an equivalent limit of m_{\rm R}$$=28.8–29.4 mag. Again, no variable sources are detected within at least 20–30*′′* of the X-ray transient. The absolute magnitude limit of the transient from the difference imaging is provided in Table 3 for a variety of redshifts.

2.7 ATCA/CABB 2–19 GHz on 2014 October 08

Radio observations of the field of the X-ray transient were made on 2014 October 08 with the Australian Telescope Compact Array (ATCA) in the 1.5 km configuration using the Compact Array Broadband Backend (CABB) at 2.1, 5, 9, 17, and 19 GHz (Burlon et al., 2014). No radio emission was detected in the vicinity of the transient, with $3\sigma$ limits of $S_{\rm 2.1\,GHz}<174$ $\mu$Jy, $S_{\rm 5\,GHz}<81$ $\mu$Jy, $S_{\rm 9\,GHz}<75$ $\mu$Jy, $S_{\rm 17\,GHz}<105$ $\mu$Jy, and $S_{\rm 19\,GHz}<99$ $\mu$Jy, respectively. Radio limits based on observations obtained prior to the transient are S_{\rm 1.4\,GHz}$$\lesssim24 $\mu$Jy and S_{\rm 5\,GHz}$$\lesssim27 $\mu$Jy (Miller et al., 2013; Burlon et al., 2014).

3 Possible Interpretations

We detail below a set of possible scenarios that might produce a fast X-ray transient such as the one we observed. In many cases, we are able to exclude these scenarios based on our available multi-wavelength constraints. This list may not account for every possibility and should not be interpreted as complete.

3.1 Gamma-Ray Bursts (GRBs)

One possibility is that CDF-S XT1 is connected with a GRB afterglow or a brighter GRB flare on top of an otherwise standard GRB afterglow. GRB emission is characterized by time-scales of $\sim$20 s for long-duration bursts and $\sim$0.2 s for short-duration bursts (hereafter lGRBs and sGRBs, respectively; Meegan et al., 1996). Although many questions remain, the commonly accepted lGRB model is that of a relativistically expanding fireball with associated internal and external shocks (Mészáros & Rees, 1997). After generating the $\gamma$-ray emission, the expanding fireball shocks the surrounding material, producing a broadband X-ray-to-radio afterglow that decays in time as $t^{-a}$ with $a\sim 1.2\pm 0.3$ unless the Doppler boosting angle of the decelerating fireball exceeds the opening angle of the associated jet, at which point the light curve is expected to steepen (a so-called “jet break”; Rhoads, 1999; Zhang & Mészáros, 2004). Alternatively, the currently favoured sGRB progenitor scenario features a compact NS-NS or a NS-BH binary merger (e.g., Eichler et al., 1989; Narayan et al., 1992), induced by angular momentum and energy losses due to GW radiation resulting in a GW burst (e.g., Abbott et al., 2016). The NS-NS case could produce either a millisecond magnetar (e.g., Zhang, 2013) or a BH surrounded by a hyper-accreting debris disk, while the NS-BH case should yield a larger BH with or without a debris disk, depending on whether the NS was tidally disrupted outside of the BH event horizon. When a debris disk is present, the combination of the high accretion rate and rapid rotation can lead to energy extraction via either neutrino-antineutrino annihilation or magnetohydrodynamic processes (e.g., Blandford & Znajek, 1977; Rosswog & Ramirez-Ruiz, 2002; Lee & Ramirez-Ruiz, 2007), which in turn can drive a collimated relativistic outflow. The accretion event should also produce more isotropic thermal, supernova-like emission on timescales of $\sim$104–106 s known as a ’kilonova’ (e.g. Metzger, 2016; Sun et al., 2017). Unfortunately, with only a few dozen well-characterized SGRBs to date, the parameter range of possible properties remains rather open.

To extend the high-energy data available on the transient, we searched for a possible $\gamma$-ray counterpart in the Swift and Fermi archives. Unfortunately, neither satellite had coverage in the direction of the Chandra transient in the few hours surrounding CDF-S XT1 (D. Palmer, H. Krimm, E. Göğüş, Y. Kaneko, A. J. van der Horst, private communications), and thus it is not well-constrained above 10 keV. The field was covered by the Interplanetary Network (Atteia et al., 1987), although no counterpart was detected with a fluence above $10^{-6}~{}{\rm erg~{}cm}^{-2}$ and a peak flux limit of above 1 photon cm*-2* s*-1*, both in the 25–150 keV range (K. Hurley, private communication), which excludes any association with a strong GRB but fails to exclude a faint GRB or orphan afterglow (Yamazaki et al., 2002; Ghirlanda et al., 2015).

For comparison, we retrieved the X-ray light curves of $\sim$760 Swift GRBs with detected X-ray afterglows from the Swift Burst Analyser (Evans et al., 2010b). Identical to Schulze et al. (2014), we resampled these light curves on a grid defined by the observed range of X-ray brightnesses and the timespan probed by the data. If no data were available at a particular time, we interpolated between adjacent data points (but do not extrapolate). Figure 4 presents the light curve of CDF-S XT1 compared to this Swift GRB distribution in greyscale.

The peak X-ray flux and full X-ray light curve of CDF-S XT1 are fainter than almost any known GRB X-ray afterglow (Dereli et al., 2015). Thus CDF-S XT1 would need to be an intrinsically low-luminosity, misaligned, or high-redshift GRB. The light curve decay time slope of CDF-S XT1 (a$$=$$-1.53\pm 0.27) appears fairly constant and marginally steeper than the median afterglow decay time slope for GRBs (a$$\approx-1.2; Evans et al., 2009; Racusin et al., 2009), while its X-ray spectral slope (\Gamma$$=1.43${}^{+0.26}_{-0.15}$) lies in the hardest $\approx$10% of the standard afterglow distribution over comparable energy bands (\Gamma$$\approx1.70$\pm$0.15; Wang et al., 2015). While few GRBs have been well-characterized below 10 keV as they initially exploded, a substantial subset of lGRBs have been observed within 10–100 s of the prompt burst, at which point the low-energy tail of the prompt emission has been seen (Tagliaferri et al., 2005; Barthelmy et al., 2005); this feature is likely responsible for the steeper initial decline seen in the greyscale histogram distributions of Swift-detected GRBs shown in Fig. 4.444We note that a handful of Swift-detected GRBs do show initial rises and peaks around 100–500 s, similar to CDF-S XT1, but their subsequent behaviour appears quite distinct from that of CDF-S XT1, with multiple strong flares and clear breaks. Early observational constraints of sGRBs are far more difficult to obtain due to their limited durations, although they also are expected to show early contributions from the prompt emission (Villasenor et al., 2005). Thus a critical discriminator in CDF-S XT1’s X-ray light curve is its $\approx$100(1$$+$$z)^{-1} s rest-frame rise time (where $z$ is redshift), which contrasts sharply with the strong early emission and spectral softening expected from both lGRBs and sGRBs. Any burst of photons associated with the prompt emission would have been detected easily by Chandra, if they extended below 10–20 keV in the rest-frame.

During the first several hours after a GRB, the X-ray afterglow is frequently characterized by flaring episodes (Chincarini et al., 2007, 2010; Margutti et al., 2011). The peak time of CDF-S XT1 is consistent with that for GRB flares, although the spectral slope and decay time slope are on the hard and slow ends of their respective distributions. The duration of CDF-S XT1, however, is substantially longer than those seen in GRB flares (i.e., $\sim$10-300 s), and thus is unlikely to fit cleanly into such a scenario.

In the optical, we compare to composite $R$-band light curves derived from a database of optical and NIR measurements of 166 GRBs with known redshifts (Kann et al., 2006, 2010, 2011; Nicuesa Guelbenzu et al., 2012). These data were gridded in an identical manner to the X-ray data; Figure 5 shows the corresponding density distribution (cropped at a lower limit of 10*-3* days, since that is the regime most relevant for our observed contraints and allows better visualization of the “busy” 10–100 day region). Comparing the initial $R$-band limit (m_{\rm R}$$\gtrsim25.7 mag at $\approx$80 minutes post-transient) to this optical density distribution, the transient is again fainter than $\gtrsim$99% of known GRB afterglows. As seen in Fig. 5, the early 2$\sigma$ limit lies only $\sim$1 magnitude above a $\nu^{-0.43}$ power-law extrapolation of the X-ray light curve into the optical band (dashed red curve in Fig. 5), thereby providing a relatively stringent constraint on any excess emission above this estimate. Given the prompt X-ray emission, the early limit rules out a standard off-axis jet scenario, wherein we would expect to find a relatively normal, bright optical GRB afterglow associated with weak X-ray emission (van Eerten et al., 2010; van Eerten & MacFadyen, 2011). In fact, based on synchrotron closure relations between the X-ray and optical emission, a large fraction of parameter space can be excluded. Thus to explain the observations in a GRB scenario, the transient would need to be intrinsically low-luminosity, reddened by at least a few magnitudes, and/or at redshift z$$\gtrsim3.6–5.0 (and hence not associated with the apparent host).

Each of these possibilities shares a relatively low probability (Jakobsson et al., 2012; Covino et al., 2013). The strong association with the z_{\rm ph}$$\sim2.2 host galaxy appears to rule out the high redshift option and lowers the probability of the low-luminosity option. Alternatively, a small fraction of sGRBs show extremely weak optical emission, as seen in Fig. 5, allowing an off-axis sGRB with weak optical emission to remain a viable option (Lazzati et al., 2016).

To put the radio limits into context with radio GRB afterglows, we compared the reported limits listed previously to the work of Chandra et al. (2012). In particular, the ATCA 9 GHz limit implies a faint afterglow, although a significant number of GRBs have evaded detection with deeper observations.

Based on the above considerations, the X-ray transient does not appear to be fully consistent with the properties of most known GRBs, nor the predictions for off-axis or weaker ones. The relatively low X-ray fluxes exclude all but low-luminosity, off-axis, or z$$\gtrsim4 GRB solutions, while the optical transient limits further exclude most standard off-axis GRB solutions and necessitate weak or absorbed optical emission. The strong association with a z_{\rm ph}$$\sim2.2 host galaxy appears to exclude the high-z solution. The lack of prompt emission below $\sim$20 keV rest-frame further excludes any on-axis / strongly beamed scenario. Taken together, only a few tentative options may remain.

One is an “orphan” off-axis sGRB, which furthermore must have exceptionally weak optical and radio emission. Based on predictions, such objects could exist, although none has yet been confirmed. Models of compact object mergers (e.g., Metzger & Piro, 2014; Sun et al., 2017) suggest that the initial X-ray light curves are likely to be optically thick and “turn-on” over timescales of many hours to days as it expands, with peak X-ray luminosities in the range of \sim$$10^{44}–$10^{46}$ erg s*-1* followed by a $\sim$t*-2* decay. While such peak luminosities are naively compatible with CDF-S XT1, the peak times are 2–3 dex longer. Among the many X-ray models of Sun et al. (2017), some allow for for earlier turn-ons, but with correspondingly higher peak X-ray luminosities. Some compact object merger models (e.g., Metzger & Piro, 2014) are additionally expected produce strong optical/near-IR emission, which we do not see. Considerable fine-tuning and/or revision of sGRB models may be required in order to more satisfactorily match the observational constraints of CDF-S XT1.

Another possibility is an explanation as a low-luminosity GRB at z$$\gtrsim2, although the X-ray light curve and spectral properties of CDF-S XT1 remain distinct from the best-studied low-luminosity GRBs.

3.2 Shock Breakout (SBO)

One intriguing possibility is that the X-ray transient represents the SBO from a core-collapse supernova (CCSN). An initial flash of thermal UV (or soft X-ray) radiation is expected when the CCSN shock wave emerges from the stellar surface of the progenitor (Falk & Arnett, 1977; Klein & Chevalier, 1978; Matzner & McKee, 1999; Schawinski et al., 2008; Ganot et al., 2016). The character of the SBO depends primarily on the density structure of the progenitor and the explosion energy driving the shock (Chevalier & Irwin, 2011; Gezari et al., 2015), resulting in SBOs with expected initial temperatures of \sim$$10^{5} to 5$\times$106 K and durations of $\sim$100–5000 s. The typical bolometric luminosity associated with an SBO is generally of order $\sim$1044–1045 erg s*-1* (Ensman & Burrows, 1992; Tominaga et al., 2011), while the emission in a given X-ray band (e.g., 0.3–10 or 2–10 keV) will be less ($\sim$1–87% for quoted temperature range). Moreover, a sufficiently compact progenitor with an energetic explosion could produce relativistic effects that substantially harden the X-ray spectrum and lead to significant $>1$ keV emission, although only for a relatively short time (1–100 s) and with dramatic spectral and temporal evolution (Tolstov et al., 2013). After the SBO, the outer layers of the star should enter an adiabatic expansion and cooling phase for $\sim$1–2 days, followed by a plateau phase thereafter as radiative diffusion takes over (Chevalier, 1992; Popov, 1993). If the stellar wind or circumstellar material (CSM) is sufficiently dense, it could intensify or prolong the SBO (by up to factors of $\sim$10) and delay the subsequent phases (Moriya et al., 2011; Balberg & Loeb, 2011; Svirski et al., 2012).

While the duration of the X-ray transient is consistent with that of longer SBOs, the hard observed spectrum (e.g., kT$$>5 keV at 3$\sigma$) appears inconsistent with the relatively low expected temperatures (kT$$\sim0.01–1 keV) for such typical SBOs. For a fixed total energy budget from a SNe, there should be a tradeoff between luminosity and temperature, whereby a larger radius at which the SBO occurs could give a higher luminosity, but a lower blackbody temperature. This makes an SBO interpretation hard to satisfy with the observed properties. The most promising models are explosions of blue supergiants like SN 1987A, which can achieve bolometric luminosities as high as $10^{45}$ erg s*-1* and SEDs peaking at $\sim$10 keV, however only for durations of $\sim$100 s (A. Tolstov, private communication). Alternatively, a relativistic scenario might be able to explain the observed X-ray photon index, but we do not observe the characteristic strong spectral and temporal evolution (a power-law decay time slope of $a>2$). Additionally, by $z\sim 0.4$ the peak X-ray luminosity of the transient already exceeds the predicted bolometric peak luminosity for a SBO associated with a E_{\rm explosion}$$\approx$$10^{51} erg progenitor. Thus the SBO scenario is only viable at low redshift, which remains possible but unlikely based on the photometric redshift probability distribution. To accommodate the best-fitting redshift of z$$=2.23 with a SBO scenario requires an explosion energy of $\gtrsim$1052 erg and/or an optically thick CSM.

The best-studied SBO candidate to date is X-ray Flash (XRF) 080109/SN 2008D (27 Mpc), which compared to CDF-S XT1 has a mildly different X-ray light curve evolution (more gradual rise, broader “peak”, and broken decline) but much softer X-ray spectrum (with kT$$\sim0.7 keV or \Gamma$$\sim2.1; Soderberg et al., 2008; Modjaz et al., 2009). We can also compare to the XRFs 031203/SN 2003lw (475 Mpc), 060218/SN 2006aj (145 Mpc) and 100316D/SN 2010bh (263 Mpc), which are also proposed to have SBO-driven origins. While the high-energy ($>$2 keV) X-ray spectral slopes over comparable bands are consistent, the latter two XRFs show significant soft thermal components (kT$$\sim0.1–0.2 keV) which become dominant beyond $\sim$1000 s (Campana et al., 2006; Starling et al., 2011; Barniol Duran et al., 2015), while CDF-S XT1 appears to marginally harden at late times.555XRF 031203/SN 2003lw was observed in the pre-Swift era and hence has substantially sparser and later X-ray and optical follow-up constraints. Notably, the portions of the X-ray and optical light curves that are well sampled appear similar to those of XRF 060218/SN 2006aj (Watson et al., 2004; Mazzali et al., 2006). As such, we do not include it in Figs. 4 and 5 for clarity. In addition, the early X-ray light curves of these two events lie in stark contrast to CDF-S XT1, as they are substantially flatter and longer lasting, with steeper late time declines (Campana et al., 2006; Starling et al., 2011; Barniol Duran et al., 2015).

Another critical aspect of the SBO scenario is, of course, the expectation of subsequent strong UV/optical emission associated with the standard CCSN light curve. Our combined optical/NIR constraints, shown in Fig. 5, appear to rule out several of the faintest known SNe light curves (Richardson et al., 2014) if placed closer than z$$\sim0.5, and more luminous ones out to z$$\lesssim1–2, with the most critical constraints arising from the initial VIMOS and latest HST data points. Adopting the X-ray to optical flux ratios of XRFs 080109/SN 2008D, 031203/SN 2003lw, 060218/SN 2006aj and 100316D/SN 2010bh, the associated SNe light curves would also all have been easily detected. The most sub-luminous SNe are thought to have extremely low nickel yields (i.e., nickel masses of $\approx$0.002–0.075 $M_{\odot}$; Hamuy, 2003), suggesting that if this event were an SBO, it would potentially require little nickel production, and consequently strong fallback. We also show the theoretical light curve for a Ni-poor core-collapse SN with strong fallback, from a ZAMS M$$=25 $M_{\odot}$ progenitor and a nickel mass of 0.02 $M_{\odot}$. To evade the optical/NIR limits would require a rather contrived scenario of nearly complete fallback. Alternatively, if we redden the comparison light curves by A_{\rm R}$$=0.3–1.3 mag, they can fit the early ground-based limits, although all are still strongly excluded by the NIR HST limit at high significance unless significantly stronger reddening is assumed.

3.3 Tidal Disruption Event (TDE)

A further possibility is that the transient was a TDE. TDEs occur when a star passes exceptionally close to a \gtrsim$$10^{4} $M_{\odot}$ BH (Rees, 1988; Phinney, 1989; Burrows et al., 2011), such that it experiences tidal forces which exceed its self-gravity, allowing the star to be shredded. Luminous thermal emission at soft X-ray through optical wavelengths is generated either by the accretion of this gas onto the BH [often limited to L_{\rm Bol}$$\approx$$L_{\rm Edd}$$\approx$$1.3\times 10^{44} erg s*-1* ($M_{\rm BH}/10^{6}$ $M_{\odot}$)] and/or the initial shocks due to colliding stellar debris streams (Guillochon & Ramirez-Ruiz, 2015). The tidal disruption radius is given by $r_{\rm TDE}$ $\approx$ $(2M_{\rm BH}/m_{*})^{1/3}R_{*}$, where $M_{\rm BH}$ is the mass of the BH, while $m_{*}$ and $R_{*}$ are the mass and radius of the star, respectively. This radius effectively dictates in what band the thermal radiation will peak, with the effective temperature given by T_{\rm eff}$$\approx2.5\times$$10^{5} K  ($M_{\rm BH}/10^{6}$ $M_{\odot}$)1/12 ($R_{*}/R_{\odot}$)-1/2 ($m_{*}/M_{\odot}$)-1/6. For normal main-sequence stars disrupted around $10^{6}$–$10^{8}$ $M_{\odot}$ BHs, the radiation should peak between T_{\rm eff}$$\sim104–106 K. The time-scale for the emission to rise to maximum is given by $t_{\rm min}\approx$0.11 yr (M_{\rm BH}/10^{6}$$M_{\odot})1/2 ($R_{*}/R_{\odot}$)-3/2 ($m_{*}/M_{\odot}$)-1, after which the bolometric light curve is predicted to follow a $\approx t^{-5/3}$ power-law decay. In rare cases, material accreting onto the BH may produce a relativistic jet which gives rise to non-thermal $\gamma$-ray, X-ray and radio emission which can appear orders of magnitude more luminous and can be strongly variable (e.g., Burrows et al., 2011; Bloom et al., 2011; Cenko et al., 2012).

The decay time slope of the transient is fully consistent with the predictions for TDEs. However, the fast rise time and hard X-ray flux of CDF-S XT1 strongly exclude all “normal” stars and supermassive BHs (>$$10^{6} $M_{\odot}$). The only viable remaining parameter space is for a TDE comprised of a white dwarf (WD: 0.008–0.02$R_{\odot}$, 1 $M_{\odot}$) and an intermediate-mass BH (IMBH; $\sim$103–104 $M_{\odot}$), although even in such a scenario it may be difficult to explain the hard observed X-ray spectral slope. Furthermore, the resulting Eddington luminosity for this TDE scenario would be at least two orders of magnitude too low compared to what is expected for the redshift range of the associated host galaxy (Table 3). One alternative could be that the emission arises from a relativistic jet produced by the TDE, although then we might expect substantially stronger variability fluctuations than is observed from the relatively smooth power-law decay of the transient’s X-ray light curve (Levan et al., 2011). Moreover, the ratio of X-ray emission to the optical and radio limits is $\gtrsim 100$ times larger than those from the beamed TDEs Swift J1644$+$57 and Swift J2058$+$0516 (Bloom et al., 2011; Cenko et al., 2012). Moreover, the beaming requirements become quite extreme with increasing redshift. Thus, relativistically beamed emission from a TDE comprised of a WD and an IMBH remains only a remote possibility.

3.4 Galactic Origin

There are at least some similarities between the reported characteristics of CDF-S XT1 and a wide variety of X-ray emitting Galactic phenomena. We limit the discussion here only to the possibilities which have similar X-ray transient time-scales and are unlikely to require bright optical or NIR counterparts, as these are easily excluded by our imaging and line-of-sight through the Galaxy (for instance, this removes most high and low-mass X-ray binary systems).

One remaining possibility is an origin as an M-dwarf or brown-dwarf flare. Magnetically-active dwarfs ($\sim$30% of M dwarfs, $\sim$5% of brown dwarfs) are known to flare on time-scales from minutes to hours, exhibiting flux increases by factors of a few to hundreds in the radio, optical blue, UV, and/or soft X-ray (Schmitt & Liefke, 2004; Mitra-Kraev et al., 2005; Berger, 2006; Welsh et al., 2007). The flares can be short “compact” (L$$\lesssim$$10^{30} erg s*-1*, $<1$ h) or “long” (L$$\lesssim$$10^{32} erg s*-1*, $\geq 1$ h). Flares are often recurrent on time-scales of hours to years, and in the X-ray band at least typically have thermal X-ray spectral signatures with kT$$=0.5–1 keV, both of which are inconsistent with CDF-S XT1. M dwarfs tend to be more X-ray active than brown dwarfs (Berger, 2006; Williams et al., 2014), with \log(L_{\rm R}/L_{\rm X})$$\sim$$-15.5 in units of $\log{{\rm(Hz}^{-1}{\rm)}}$ for a wide range of stars down to spectral types of about M7, after which this ratio rapidly climbs to \sim$$-12 for brown dwarfs. Thus, relative to the observed X-ray peak flux, the radio survey limits mentioned previously should have been more than sufficient to detect radio flares from a brown dwarf and most M-dwarfs, if any occurred during the radio observations. While the best counterpart for the transient, source #1, is clearly extended in multiple images, there remains a low probability ($<$0.3%) that that the transient could be matched to source #2, which is potentially consistent with a m_{\rm R}$$=27.38 mag M-dwarf star. Alternatively, an even fainter dwarf could lie below the HST detection threshold, although the low random probability of spatial coincidence with a background galaxy strongly argues against this. Notably, M dwarfs typically have absolute magnitudes of M_{\rm R}$$\sim8–14 mag (Bochanski et al., 2011), such that source #2 would have to lie at $\gtrsim$5–75 kpc (i.e., in the halo), while an undetected M dwarf would lie even further away. Similarly, brown dwarfs have typical absolute magnitudes of M_{\rm J}$$\sim15–25 (Tinney et al., 2014), such that an undetected source must lie at $\gtrsim$30 pc–3 kpc. However, such distances would imply an M-dwarf X-ray luminosity of L_{\rm X}$$\gtrsim(3.4–850)$\times$1035 erg s*-1* or a brown dwarf X-ray luminosity of L_{\rm X}$$\gtrsim(5.5–54903)$\times$1029 erg s*-1*, which are at least factors of $\gtrsim$103–105 larger than typical flares seen from M dwarfs (Pandey & Singh, 2008; Pye et al., 2015) and brown dwarfs (Berger, 2006), respectively. Thus the observed transient properties appear inconsistent with those of dwarf flares.

Another possibility is that the transient was the result of a magnetar outburst. Magnetars are spinning-down, isolated neutron stars which have relatively slow rotation rates ($\sim$1–10 s) and possess extremely strong magnetic fields that are considered to power characteristic and recurrent bursts of X-rays and $\gamma$-ray radiation (hence their designations as “soft gamma repeaters”, SGRs, or “anomalous X-ray pulsars”, AXPs; Mereghetti et al., 2015). They lack obvious companions from which to accrete, yet have apparent X-ray luminosities during outbursts which can often be super-Eddington and reach luminosities as high as $\sim$1047 erg s*-1* (Palmer et al., 2005); these cannot be explained by rotation power alone. Their strong magnetic fields are predicted to decay on time-scales of $\lesssim$10,000 years, after which their activity ceases. Among the $\approx$26 magnetars known (Olausen & Kaspi, 2014), many are found near OB associations and/or SN remnants and all lie in the thin disk of the Galaxy or the Magellanic clouds, implying magnetars are possibly a rare by-product of massive O stars. Roughly half of the magnetars are persistent X-ray sources with fluxes of $\sim$10*-14*–10*-10* erg s*-1* cm*-2* (or equivalently quiescent X-ray luminosities of order \sim$$10^{35} erg s*-1*). The rest were primarily discovered during bright, short outbursts (0.1–1.0 s) or giant flares (0.5–40 s), $\sim$10–1000 times brighter than their anticipated quiescent phases, whose properties still remain relatively poorly known. The rises and decays of these outburst/flare episodes show different durations and shapes ($\sim$1 week to months), but the decays are generally characterized by a spectral softening. The outburst duty cycle remains poorly known, as multiple distinct outburst episodes have only been detected from a few magnetars to date. The X-ray spectra are generally fit with two-component blackbody (kT_{\rm BB}$$\sim0.5 keV) and power-law (\Gamma$$\sim1–4) models. A subset of magnetars have optical and radio counterparts. Based primarily on the strong association with recent star forming regions and SN remnants (the high Galactic latitude CDF-S field is far from any known Galactic star-forming region), as well as the more sporadic and longer duration rise and decay times expected, CDF-S XT1 appears highly unlikely to be a Galactic magnetar.

Finally, the X-ray properties of CDF-S XT1 could be related to compact object such as an asteroid hitting an isolated foreground NS (Colgate & Petschek, 1981; van Buren, 1981; Campana et al., 2011). This possibility, which was originally suggested to explain GRBs, is difficult to rule out based on the observational data alone due to the wide parameter range of transients that can be produced. However, the combined probability that such an event occurs on a NS which just happens to align with a faint extragalactic source to better than 1$\sigma$ is quite low ($\ll$0.1%), given an expected NS number density out to 30 kpc of $\sim$1000 deg*-2* (Sartore et al., 2010) and the source density of m_{\rm F160W}$$<27.5 mag galaxies in the CANDELS field (0.088 arcsec*-2*).

4 Event Rates

Regardless of origin, the fact that this event occurred in a pencil-beam survey field like the CDF-S naively implies a relatively high occurrence rate. However, although a handful of high-amplitude, fast X-ray transients have been reported in the literature to date (Jonker et al., 2013; Glennie et al., 2015; De Luca et al., 2016), none appears to have the X-ray and optical transient properties of CDF-S XT1 nor an association with such a faint optical host. To quantify this, we first perform a search of the Chandra archive to determine the frequency of events such as CDF-S XT1, and then estimate their occurrence rate.

4.1 Comparable Events

To determine the uniqueness of this transient, we conducted an archival search for similar variable events. Due to the limited variability information available (e.g., no easy access to individual source photon tables) in the most recent XMM-Newton 3XMM DR5 and Swift 1SXPS source catalogs (Rosen et al., 2016; Evans et al., 2014), we found it infeasible to assess properly whether such a source was detected by either observatory, and thus only conducted a search for similar events observed by Chandra using the Chandra Source Catalog (CSC v1.17; Evans et al., 2010a). Most critically, the CSC is the only source catalog that provides easy and straightforward access to photon event lists and light curves, which we considerd absolutely essential to characterize the nature of the variability of each source. Even so, the current version of the CSC only contains relatively bright sources from the first 11 cycles (up to 2010 August 10), which factors into our rate calculations below.

We began by searching the CSC for all securely variable sources with a peak flux of $F_{\rm 2-10\,keV}>1\times 10^{-12}$ erg s*-1* cm*-2* (or their count-rate equivalent, adopting the best-fitting spectral slope of the transient) and which varied in flux by at least a factor of 10. This should find any similar transients down to a factor of five weaker than CDF-S XT1, if they exist. Such a transient should be easily detectable in virtually any Chandra observation. At this flux, it would also be detectable in XMM-Newton or Swift/XRT, although it might be difficult to characterize it in Swift/XRT data due to the typically short (1–2 ks) observations this instrument executes. The above critieria are obviously conservative, as Chandra’s sensitivity could allow a search up to a factor of 10 deeper. However, with so few observed counts ($\sim$10 photons), it would be impossible to determine with much certainty whether the transient truly is similar to CDF-S XT1.

To select sources similar to CDF-S XT1, we adopted the following CSC parameters for sources observed with the ACIS-I and ACIS-S detectors, as well as the High Resolution Camera (HRC): variability probability var\_prob$$>0.9; maximum variability count rate o.var\_max$$>0.06 cnt/s; and minimum variability count rate o.var\_min$$<0.006 cnts/s. We found 184 unique matches. Of these, 39 lie within |b|$$<10*∘* and are presumably Galactic in nature, while at a minimum a further 19 and 82 can be spatially associated with Milky Way globular clusters and young star-forming regions outside the Galactic plane (|b|$$>10*∘*), respectively. Based on the Chandra positional errors, 149 candidates have Digitized Sky Survey (DSS), Two Micron All-Sky Survey (2MASS), and/or Wide-Field Infrared Survey Explorer (WISE) counterparts, while a further 3, 10, 8, and 4 candidates are likely associated with the Galactic Plane, nearby globular clusters, star-forming regions, or local galaxies, respectively, even though they do not have clear, single counterparts. In total, only nine candidates show no sign of a counterpart to the limits of these surveys, no association with extended objects, and/or a location outside of the Galactic Plane (hereafter criterion #1.

The benefit of using the CSC is that we can inspect individual data products for each catalog source. To determine if the variability of the CSC sources shows the same basic signatures as CDF-S XT1 (i.e., non-recurrent, $\lesssim$1 ks rise, \sim$$t^{-1.5} decline), we visually inspected and classified the X-ray light curves of all 184 sources into one of seven categories. Category 1 sources appear to be recurrent or persistent transients, exhibiting single or multiple flares, eclipses, and/or gradual variations on top of otherwise quiescent rates. Recurrence/persistence was determined directly from the Chandra data in some cases, or based on previously known variability in the SIMBAD666http://simbad.u-strasbg.fr/simbad/sim-fid database catalog. We consider category 1 sources to have distinctly different variability behavior from CDF-S XT1.

Category 2–7 sources, on the other hand, were not considered to be recurrent or persistent transients, with only marginal or no prior and post detection of photons during the observations. We regard this as a minimum requirement for similarity to CDF-S XT1, although we caution that such a designation is strongly dependent on how frequently a source is observed as well as the level to which an assessment of variability is carried out. Cross-matching category 2–7 sources with all known X-ray archives and carefully investigating variability across all possible instruments goes well beyond the scope of this project, and would likely result in recategorization of at least some fraction of these sources as Category 1 sources.

Beyond a basic estimate of recurrence or persistence, we further divided the remaining Category 2–7 sources up based on their variability properties. Category 2 sources exhibit $\gtrsim$4 ks rises and/or decay time-scales several times longer than CDF-S XT1. Category 3 sources exhibit $\sim$2–4 ks rise times and decay timescales several times longer than CDF-S XT1 and/or flattening either early or late in the transient decay. Category 4 sources exhibit similar $\sim$2–4 ks rise times like category 3, but have time series which terminate or are of insufficient statistical quality to assess their decay rates properly. Given the strongly disparate rise and decay timescales, category 2, 3 and 4 sources all seem unlikely to be related to CDF-S XT1.

Category 5 sources show X-ray light curve shapes consistent with that of CDF-S XT1 with peaks of \lesssim$$10^{3} s. As such, they represent the most likely potential CDF-S XT1 analogs. Category 6 sources are similar to category 5, but have significant low-level activity in the \sim$$10^{3}–$10^{4.5}$ s prior to their “category 5” light curve shapes. This precursor emission is not seen in CDF-S XT1 and may suggest that these objects have a different physical origin and/or are recurrent or persistent. All likely have Galactic origins. Therefore, they seem much less likely to be potential CDF-S XT1 analogs. Finally, category 7 sources exhibit weak short rise and fall behavior within $\sim$100–500 s, and are dominated by noise at late times. Thus, they could represent fainter versions of CDF-S XT1. While two likely have Galactic origins, one is associated with a faint SDSS+WISE galaxy with z_{\rm ph}$$\sim0.14 and another appears to be a strong radio source with a WISE-only counterpart. Neither of the latter two identification seems like a clear CDF-S XT1 analog. In summary, after assessing the X-ray light curves of all 184 CSC candidates (hereafter criterion #2), we find that category 5 and 7 objects may be potential analogs, while all others categories show substantially different variability behavior.

Finally, approximately 20–40% of the 184 candidates have hardness ratios or best-fitting spectral slopes consistent with $\Gamma<2.0$ (hereafter criterion #3); this fraction also holds for the candidates associated with categories 5 and 7.

A compilation of the results, broken down by category, is listed in Table 4, while the individual light curves of all Category 3–7 sources are shown in Figure 6. Factoring all three (imaging, timing and spectral) criteria together, we find that there is not a single candidate that is comparable to CDF-S XT1. For instance, among all 26 candidates in category 3–7, 21 sources appear to have a Galactic origin. Even amongst the most likely candidates in categories 5–7 which show similar light curves, roughly half have spectral slopes which are too soft and all have an obvious Galactic or bright nearby galaxies origin. We thus conclude that transients like CDF-S XT1 appear to be rare or alternatively hard to find based on relatively simple selection criteria.

We note that Glennie et al. (2015) recently reported the detection of two unusual high-amplitude, fast X-ray transients (FXRT) in the Chandra archive, FXRT 110103 and FXRT 120830. However, both of these exhibit strong X-ray flare behavior above constant quiescent X-ray emission of $\sim$10*-13*–10*-12* erg s*-1* cm*-2*, which is inconsistent with the X-ray behavior (strong quiescent limits) from CDF-S XT1. FXRT 120830 appears to be associated with a bright flare from a nearby late M or early L dwarf star, and thus appears to have a Galactic origin. FXRT 110103 lies at high Galactic latitude (b=32$$\aas@@fstack{\circ}7) and has no counterpart to $J>18.1$, $H>17.6$ and $K_{s}>16.3$. These limits are not too constraining and FXRT 110103 is tentatively associated by Glennie et al. with the galaxy cluster ACO 3581 at 94.9 Mpc. Jonker et al. (2013) also report the discovery of FXRT 000519, which has similar X-ray light curve properties to FXRT 110103 (including apparent quiescent emission at a flux level of $\sim$10*-13*–10*-12* erg s*-1* cm*-2*) and is associated with M86 at 16.2 Mpc. Jonker et al. favor a tidal disruption of a WD by an IMBH, but cannot rule out alternative scenarios such as the accretion of an asteroid by a foreground NS or an off-axis GRB. Given their associations with relatively nearby galaxies, FXRT 110103 and FXRT 000519 are factors of $10^{3}$–$10^{5}$ less luminous than CDF-S XT1, and it is not immediately obvious how they might be manifestations of the same phenomenon as CDF-S XT1. Hence for the moment, we do not consider them to be similar.

4.2 Rate Estimation

Under the above criteria, we find no transients similar to CDF-S XT1 in the entire CSC. If we relax some of the criteria, for instance to allow for bright galaxy counterparts and a broader range of light curve peaks, there are a few additional potential candidates which could boost the rate by up to a factor of 3–4. However, until there is a stronger understanding of the physics involved, we prefer to remain conservative. With only one detected source, the rate of such events is subject to large uncertainties. We adopt the above characterization of the CSC as our baseline and estimate the coverage of the CSC as follows.

For Chandra, there are two main configurations, ACIS-I and ACIS-S, with as many as six 8$\aas@@fstack{\prime}$5$\times$8$\aas@@fstack{\prime}$5 detectors operational for each; in recent years, Chandra has advocated that users turn off at least two detectors. Alternatively, the HRC has a field-of-view (FOV) of $\approx$30*′$\times$30′. The point spread function and effective area of all these detectors degrade substantially beyond a few arcminutes from the aimpoint. For reference, on-axis and with the current sensitivity, a source with $F_{\rm 0.3-10\,keV}=4.2\times 10^{-13}$ erg s-1* cm*-2* and the spectral slope of the transient will yield $\approx$100 counts for ACIS-I, $\approx$150 counts for ACIS-S, and $\approx$64 counts for HRC in 5.0 ks, respectively. Given the degradation in sensitivity over the lifetime of Chandra, early cycles would have detected $\approx$1.5 times more photons. At 15*′* off-axis, vignetting alone will decrease the photon yields by $\approx$40% for a source with $\Gamma=1.5$, while the 90% encircled energy PSF area will likewise grow by a factor of $\approx$400, such that considerably more background is included. The combination of these effects makes reliable detection of a transient like CDF-S XT1 difficult beyond the primary four detectors I0-I3 for ACIS-I (289 arcmin2), the S2+S3+S4 detectors for ACIS-S (217 arcmin2), or the central 100 arcmin2 for HRC. We will assume the shortest Chandra exposure, $\approx$2 ks, is sufficient to detect such a transient (and thus all Chandra exposures are useful), although over such short intervals it may be difficult to characterize the light curve properly.

Summing up the total on-sky exposure time (livetime) examined in the above CSC query up to 2010 August 10 with |b|$$>10*∘*, there is 46.6 Ms, 62.1 Ms, and 3.7 Ms for the ACIS-I, ACIS-S, or HRC detectors, respectively.

Such exposures imply a total potential occurrence rate of up to $4.2^{+9.7}_{-3.4}$ events deg*-2* yr*-1*, adopting errors following Gehrels (1986). We convert this to a volumetric rate ( yr*-1* Gpc*-3*) in Fig. 7, assuming an increasing volume as a function of redshift between the 95% confidence bounds of the photometric redshift of the associated host. Following Sun et al. (2015), we quote event rates at the minimum peak luminosity to which they are probed. The Chandra observations within our CSC archive search should allow detection of “CDF-S XT1”-like events to a peak flux limit of $\sim$(5–10)$\times$10*-13* erg s*-1* cm*-2*, or a peak X-ray luminosity of \sim$$10^{44}–$10^{46}$ erg s*-1* over a redshift range of z_{\rm ph}$$=0.39–3.21.

Although we have already largely excluded an identification with most known types of transients, it is still informative to compare the above rate to the expected rates of other major transients, such as sGRBs and lGRBs, SNe, and TDEs.

For lGRBs, we adopt a simple broken power law shape to model the intrinsic rate of beamed lGRBs (Wanderman & Piran, 2010; Lien et al., 2014), assuming they roughly trace the shape of the cosmic star formation rate as shown in Fig. 7. At z$$=0, the rate is anchored at a value of $\sim$0.84 yr*-1* Gpc*-3* above a peak X-ray luminosity of \sim$$10^{49} erg s*-1* based on simulations matched to the observed rate of lGRBs from Swift/BAT (Lien et al., 2014), with an uncertainty within a factor of $\sim$2. Given that lGRBs are thought to be beamed and highly anisotropic (Harrison et al., 1999; Levinson et al., 2002), it may be more appropriate to compare with the rate of unbeamed, or “orphan”, lGRB explosions, which should be larger by the inverse of the beaming factor. For simplicity, we adopt a beaming correction of $\approx$75$\pm$25 based on large samples of lGRBs (Piran, 2004; Guetta et al., 2005), although we caution that these corrections are often non-trivial, with low- and high-luminosity GRBs likely to have different average half-opening angles. For several well-studied lGRBs, for instance, the beaming corrections were estimated to lie between 450–500 (Frail et al., 2001; van Putten & Regimbau, 2003), implying a much higher orphan rate and at least a factor of $\sim$6–7 uncertainty.

Given some of the potential similarities between CDF-S XT1 and the low-luminosity XRFs 060218/SN 2006aj (145 Mpc), 080109/SN 2008D (27 Mpc), and 100316D/SN 2010bh (263 Mpc), we estimate their cumulative observed rate assuming a volume of 300 Mpc, a 10 yr Swift/BAT search window with 90% efficiency, a 2 steradian Swift/BAT FOV, and a 10% detection rate based on complex trigger criteria (Lien et al., 2014). This yields a rate of $\sim$185${}^{+181}_{-100}$ yr*-1* Gpc*-3* above a peak X-ray luminosity of \approx$$10^{46} erg s*-1*, with the quoted errors being purely statistical, and likely severely underestimating systematic uncertainties. Such rates and luminosity limits are roughly consistent with the lGRB beaming factors mentioned above.

For sGRBs, there are fewer robust identifications and characterizations, leaving rate estimates substantially more uncertain. Based on available samples of $\sim$20 objects, the estimated observed rate is 4.1${}^{+2.1}_{-1.9}$ yr*-1* Gpc*-3* above a peak X-ray luminosity of \sim$$10^{49} erg s*-1* (Wanderman & Piran, 2015). The beaming corrections lie in the range $\sim$70$\pm$40 (Berger, 2014), implying an intrinsic unbeamed or orphan sGRB rate of $\sim$290${}^{+530}_{-230}$ yr*-1* Gpc*-3* between $z$=0.1–1.3 above a peak X-ray luminosity of \sim$$10^{47} erg s*-1*.

For CCSNe, the rate at z$$=0 is estimated to be $\sim$105 yr*-1* Gpc*-3* above a peak X-ray luminosity of \sim$$10^{44} erg s*-1* and is expected to track the cosmic star formation rate as shown in Fig. 7 (Dahlen et al., 2004; Lien & Fields, 2009; Taylor et al., 2014). The uncertainties are likely within a factor of $\sim$2 (Horiuchi et al., 2011). Based on the expected X-ray luminosities for SBOs, the local (z$$<0.5) rates provide the most sensible comparison.

Finally, for TDEs, we note that the rates are still highly uncertain due to limited number of detections and large uncertainties in the underlying assumptions, such that estimates range between $\sim$300–6800 yr*-1* Gpc*-3* (Stone & Metzger, 2016) above a peak X-ray luminosity of \sim$$10^{42} erg s*-1*. The rates of TDEs accompanied by relativistic jets should be significantly smaller and with much higher X-ray luminosity limits (Bower et al., 2013; van Velzen et al., 2016).

From Fig. 7, one can see that the estimated rates for transients like CDF-S XT1 appear similar to some other transient populations. A major caveat here is that the luminosity limits for these various transient populations are quite different. After matching luminosity limits following Sun et al. (2015) and references therein, we find that the CDF-S XT1 rate is most similar to the rates of unbeamed/orphan and/or low-luminosity lGRBs and sGRBs between z$$\sim0.4–2.0. This provides further indirect evidence that CDF-S XT1 may be somehow related to the GRB phenomenon. Although the rates of “CDF-S XT1”-like events remain highly uncertain, we note that they are still likely to be substantially more common than extremely luminous, beamed TDEs out to moderate redshift (z$$\sim1–2).

5 Conclusions

To summarize, during the acquisition of the final 3 Ms of the observations of the CDF-S 7 Ms survey, we detected an exceptional X-ray transient event, CDF-S XT1, at high-significance. The X-ray light curve of CDF-S XT1 shows a fast rise [$\approx$100$(1+z)^{-1}$ s] and a power-law decay time slope of a$$=$$-1.53$$\pm$$0.27, with little spectral variation and a peak flux of F_{\rm 0.3-10\,keV,peak}$$=$$5.1$$\times$$10^{-12} erg cm*-2* s*-1*. The average spectrum can be modeled as an absorbed power law with a spectral slope of \Gamma$$=$$1.43^{+0.26}_{-0.15} and an absorption limit of N_{\rm H}$$<$$1.5$$\times$$10^{21}(1$$+$$z)^{2.5} cm*-2*. The location of the event shows no prior or subsequent X-ray emission, allowing us to place 0.3–10 keV quiescent and precursor limits that are factors of $10^{5}$ and $10^{3}$ times fainter, respectively.

CDF-S XT1 is robustly matched, within $\approx$0$\aas@@fstack{\prime\prime}$13$\pm$0$\aas@@fstack{\prime\prime}$26, to a single optical counterpart, which lies in the CANDELS region and thus benefits from deep HST, Spitzer, and ground-based imaging. The host is a resolved $m_{\rm R}$=27.5 mag galaxy at z_{\rm ph}$$=2.23 (0.39–3.21 at 2$\sigma$ confidence). At this nominal redshift, the host SED is consistent with that of a M_{\rm R}$$\sim$$-18.7 mag, \log{M/M_{\odot}}$$\sim$$8.0$$\pm$$0.2, $1.15\pm 0.04$ $M_{\odot}$ yr*-1* dwarf galaxy. The inferred observed 2–10 keV peak luminosity of the event at this redshift is (6.8^{+0.7}_{-1.6})$$\times$$10^{46} erg s*-1*.

The combination of the X-ray light curve properties, non-recurrence to deep quiescent X-ray limits, robust faint quiescent optical counterpart (or limits if somehow not associated) and lack of associated multi-wavelength (optical/NIR, radio, $>$10 keV) transient emission to sensitive limits appear to exclude nearly all known types of Galactic and extragalactic X-ray variables and transients. A few theoretical possibilities remain: an “orphan” X-ray afterglow from an off-axis sGRB with weak optical emission; a low-luminosity GRB at high redshift with no prompt emission below $\sim$20 keV rest-frame; or a strongly beamed TDE involving an intermediate-mass black hole and a white dwarf with little variability. We stress that each scenario likely requires considerable fine-tuning to comply with all of the constraints. We encourage more efforts to explore and limit parameter space for CDF-S XT1. This situation bears parallels with the discovery of fast radio bursts (Lorimer et al., 2007), which represented a completely new source class, discovered by chance, with no clearcut physical explanation. “CDF-S XT1”-like events are indeed related to unbeamed/orphan sGRBs, then they will be relevant as sources of GW emission.

After failing to find any events identical to CDF-S XT1 in the Chandra Source Catalog (comprised of the first 11 cycles of Chandra), we estimate a rate of “CDF-S XT1”-like events as $<$4.2${}^{+9.7}_{-3.4}$ events deg*-2* yr*-1*. Although highly uncertain due to the small number statistics and wide photometric redshift range of its associated host, this potential rate appears crudely comparable at matched luminosity to that of unbeamed/orphan and low-luminosity lGRBs and sGRBs between z$$\sim0.4–2.0, lending additional weight to a possible link with this transient class. Alternatively, the rate appears substantially higher than that expected for extremely luminous, beamed TDEs at moderate redshifts (z$$\sim1–2), although this class of TDEs likewise suffers from small number statistics at present. Regardless of whether these events belong to an untapped regime for a known transient class, or represent a new type of variable phenomena, the predicted rates imply that “CDF-S XT1”-like events should be a relatively common physical phenomenon that we are just beginning to observe or understand.

Although beyond the scope of the current work, the peak 0.3–10 keV flux of CDF-S XT1 is sufficiently bright to be detected by several of the currently operating X-ray observatories. This could lead to the discovery of further similar transients and would certainly place more stringent limits on the rate estimates. For instance, incorporating the remainder of the Chandra archive would increase coverage by $\sim$50%, while searching through the archives of XMM-Newton (FOV$\approx$0.25 deg2, $\approx$260 Ms observed over 16 years based on the master observation list catalog) and Swift (FOV$\approx$0.15 deg2, $\approx$250 Ms over 11 years based on the master observation list catalog) could increase the areal$+$temporal coverage by factors of $\sim$7.6 and $\sim$4.9, respectively. Moreover, these observatories could last another 5–15 years, pending funding extensions. Alternatively, a few upcoming X-ray observatories may be able to make significant further progress. The eROSITA mission (Merloni et al., 2012) has a FOV of $\approx$0.833 deg2 and sensitivity sufficient to detect transients like CDF-S XT1 in each one of its eight passes over the sky during the nominal four year mission. Thus, eROSITA should effectively provide an equivalent coverage in sky area per time to the current XMM-Newton archive. Each individual “pass” will provide an average exposure of $\sim$320 s, built up from a few short exposures every 4 hours, such that rapid triggers can be performed. Given the relatively weaker hard energy response of eROSITA compared to XMM-Newton, however, rapid X-ray follow-up within 1–2 hrs will likely be necessary to properly characterize transients. Another prospect is the wide-field telescope planned for the Chinese Academy of Sciences’ Einstein Probe (Yuan et al., 2015), which will have a FOV of 60*∘$\times$60∘* and sensitivity of $\sim$10*-11* in 1000 s. While this may be insufficient to detect CDF-S XT1 outright, it could potentially detect bright versions ($\gtrsim$10$\times$) if they exist. Taken together, we thus might expect at least a handful of “CDF-S XT1”-like sources to be discovered in the next decade.

Looking further into the future, next-generation observatories like ESA’s Athena (Barret et al., 2013), the proposed X-ray Surveyor (Weisskopf et al., 2015) or any other wide-field X-ray observatory aim to provide FOVs of order $\sim$0.6–1 deg2 and substantially better sensitivity than Chandra or XMM-Newton, so they may detect several dozen transients like CDF-S XT1 over their lifetimes. However, these observatories will be in a much better position to characterize the light curves in detail and probe factors of at least 10 deeper to study fainter (and perhaps more abundant) versions of CDF-S XT1. In all of the above cases, “CDF-S XT1”-like events will strongly benefit from rapid multi-wavelength follow-up to help constrain their physical nature.

Acknowledgements

We acknowledge the staffs of ESO, Gemini, and HST, and in particular Nancy Levenson, Blair Conn, Rodolfo Angeloni, Rene Rutten, Christian Hummel, Linda Schmidtobreick, Claus Leitherer, Denise Taylor, and Shantavia Sturgis for their help in promptly accepting our DDT requests, preparing the observations and carrying them out. We thank Belinda Wilkes and the Chandra staff for help investigating Chandra instrumental effects. We would like to thank David Palmer, Hans Krimm, Ersin Göğüş, Yuki Kaneko, Alexander J. van der Horst, Shri Kulkarni, and Avishay Gal-Yam for their help and stimulating conversations, and the Fermi LAT team for providing LAT data products. We also thank the anonymous referee for several comments which help improve the manuscript.

We acknowledge support from: CONICYT-Chile grants Basal-CATA PFB-06/2007 (FEB, ET, SS), FONDECYT Regular 1141218 (FEB) and 1160999 (ET), FONDECYT Postdoctorado 3140534 (SS), PCCI 130074 (FEB), “EMBIGGEN” Anillo ACT1101 (FEB, ET); the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS (FEB, FF, SS); Swiss National Science Foundation Grants PP00P2_138979 and PP00P2_166159 (KS); National Natural Science Foundation of China grant 11673010 (BL); Ministry of Science and Technology of China grant 2016YFA0400702 (BL); support from TLS Tautenburg, MPE Garching and DFG Kl/766 16-1 and 16-3 (DAK); Chandra X-ray Center grant GO4-15130A (BL, WNB); NASA through Hubble Cycle 22 grant HST-GO-14043 (FEB) awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555; World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan (KM); Japan Society for the Promotion of Science (JSPS) KAKENHI Grant 26800100 (KM) and JSPS Open Partnership Bilateral Joint Research Projects (KM); 973 Programs 2015CB857005 (JXW) and 2015CB857004 (YQX); CAS Strategic Priority Research Program XDB09000000 (JXW, YQX); CAS Frontier Science Key Research Program QYZDJ-SSW-SLH006 (JXW, YQX); NSFC-11421303 (JXW, YQX); National Thousand Young Talents program (YQX); NSFC-11473026 (YQX); and Fundamental Research Funds for the Central Universities (YQX).

The scientific results reported in this article are based in part or to a significant degree on observations made by the Chandra X-ray Observatory, on observations obtained at the Gemini Observatory acquired through the Gemini Observatory Archive and processed using the Gemini IRAF package, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil), on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 294.A-5005, and on observations made with the NASA/ESA Hubble Space Telescope, obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program HST-GO-14043. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This work also made use of the Rainbow Cosmological Surveys Database, which is operated by the Universidad Complutense de Madrid (UCM), partnered with the University of California Observatories at Santa Cruz (UCO/Lick,UCSC). This research has made use of NASA’s Astrophysics Data System Bibliographic Services.