A likely decade-long sustained tidal disruption event

TL;DR

This paper reports the discovery of an exceptionally long-lasting super-Eddington tidal disruption event in a dwarf galaxy, providing new insights into black hole accretion processes over a decade.

Contribution

It presents the first observation of a super-long (>11 years) tidal disruption event with sustained super-Eddington accretion, expanding understanding of black hole feeding mechanisms.

Findings

Persistent high X-ray luminosity near Eddington limit over a decade

Spectral softening indicating state transition or transient absorber

Evidence of super-Eddington accretion in a dwarf galaxy

Abstract

Multiwavelength flares from tidal disruption and accretion of stars can be used to find and study otherwise dormant massive black holes in galactic nuclei. Previous well-monitored candidate flares are short-lived, with most emission confined to within ~1 year. Here we report the discovery of a well observed super-long (>11 years) luminous soft X-ray flare from the nuclear region of a dwarf starburst galaxy. After an apparently fast rise within ~4 months a decade ago, the X-ray luminosity, though showing a weak trend of decay, has been persistently high at around the Eddington limit (when the radiation pressure balances the gravitational force). The X-ray spectra are generally soft (steeply declining towards higher energies) and can be described with Comptonized emission from an optically thick low-temperature corona, a super-Eddington accretion signature often observed in accreting stellar-mass black holes. Dramatic spectral softening was also caught in one recent observation, implying either a temporary transition from the super-Eddington accretion state to the standard thermal state or the presence of a transient highly blueshifted (~0.36c) warm absorber. All these properties in concert suggest a tidal disruption event of an unusually long super-Eddington accretion phase that has never been observed before.

Tables

Table 1. Table 1: Spectral fit results for high-quality spectra. The X1 and C10 spectra were rebinned to have at least one count per bin and were fitted by minimizing the C statistic, while the X2, X3, C2, and C3–C9 spectra were rebinned to have at least 20 counts per bin and were fitted by minimizing the χ 2 superscript 𝜒 2 \chi^{2} statistic. The fits used energy channels within 0.3–10 keV for XMM-Newton and energy channels within 0.3–7 keV for Chandra . All models include Galactic absorption of column density N H , Gal = 4.4 × 10 20 subscript 𝑁 H Gal 4.4 superscript 10 20 N_{\mathrm{H,Gal}}=4.4\times 10^{20} cm -2 . The absorption intrinsic to the X-ray source at redshift 0.14542 was also included and fixed at N H , i = 4.2 × 10 21 subscript 𝑁 H i 4.2 superscript 10 21 N_{\mathrm{H,i}}=4.2\times 10^{21} cm -2 , which was the best-fitting value from the simultaneous fit to the C2, X3, and C3–C9 spectra. L abs subscript 𝐿 abs L_{\rm abs} is the source rest-frame 0.34–11.5 keV luminosity, corrected for the Galactic absorption but not intrinsic absorption, and L unabs subscript 𝐿 unabs L_{\rm unabs} is the source rest-frame 0.34–11.5 keV luminosity, corrected for both Galactic and intrinsic absorption. Both L abs subscript 𝐿 abs L_{\rm abs} and L unabs subscript 𝐿 unabs L_{\rm unabs} are in units of 10 43 erg s -1 . All errors are at the 90%-confidence level. Parameters without errors were fixed in the fits. For C10, two models were tested: diskbb+PL and zxipcf(comptt). For the latter model, the CompTT component was fixed at the best fit of this model to C3–C9, and the luminosities L abs subscript 𝐿 abs L_{\rm abs} and L unabs subscript 𝐿 unabs L_{\rm unabs} was simply copied from those of C3–C9. The reduced χ 2 superscript 𝜒 2 \chi^{2} values are given for fits using the χ 2 superscript 𝜒 2 \chi^{2} statistic, but not for those using the C statistic.

Obs.	Model	Parameters	${\chi }_{\nu }^2\left(\nu \right)$	$L_{\mathrm{abs}}$	$L_{\mathrm{unabs}}$
X1	diskbb+PL	$k{T}_{\mathrm{diskbb}}={0.10}_{-0.04}^{+0.06}$ keV, $N_{\mathrm{diskbb}}={210}_{-204}^{+27841}$,	…	${0.08}_{-0.03}^{+0.04}$	${0.55}_{-0.31}^{+0.95}$
		${\Gamma }_{\mathrm{PL}}=2.5$, $N_{\mathrm{PL}}={4.6}_{-3.4}^{+3.9}\times {10}^{-6}$
X2	CompTT	$k{T}_0=0.04$ keV, $k{T}_e={0.35}_{-0.05}^{+0.08}$ keV, $\tau ={10.8}_{-2.1}^{+2.4}$	$1.09\left(106\right)$	${1.16}_{-0.06}^{+0.06}$	${6.18}_{-0.60}^{+0.65}$
X3	CompTT	$k{T}_0=0.04$ keV, $k{T}_e={0.51}_{-0.13}^{+0.30}$ keV, $\tau ={7.3}_{-2.2}^{+2.1}$	$0.90\left(99\right)$	${1.13}_{-0.06}^{+0.06}$	${7.03}_{-0.66}^{+0.71}$
C2	CompTT	$k{T}_0=0.04$ keV, $k{T}_e={0.51}_{-0.14}^{+0.33}$ keV, $\tau ={7.6}_{-2.5}^{+3.0}$	$0.90\left(43\right)$	${1.08}_{-0.09}^{+0.09}$	${6.24}_{-1.32}^{+1.55}$
C3–C9	CompTT	$k{T}_0=0.04$ keV, $k{T}_e={1.33}_{-0.43}^{+1.48}$ keV, $\tau ={3.9}_{-1.7}^{+1.3}$	$0.83\left(138\right)$	${0.60}_{-0.02}^{+0.02}$	${3.38}_{-0.21}^{+0.23}$
C10	diskbb+PL	$k{T}_{\mathrm{diskbb}}={0.13}_{-0.01}^{+0.01}$ keV, $N_{\mathrm{diskbb}}={312}_{-154}^{+310}$,	…	${0.31}_{-0.04}^{+0.05}$	${2.88}_{-0.66}^{+0.86}$
		${\Gamma }_{\mathrm{PL}}=2.5$, $N_{\mathrm{PL}}={2.2}_{-1.2}^{+1.7}\times {10}^{-6}$
	zxipcf(CompTT)	$k{T}_0=0.04$ keV, $k{T}_e=1.33$ keV, $\tau =3.9$,	…	${0.60}_{-0.02}^{+0.02}$	${3.38}_{-0.21}^{+0.23}$
		$N_H=64\pm 10\times {10}^{22}$ cm-2, $\log \left(\xi \right)=2.78\pm 0.04$, $z=-0.36\pm 0.02$

Table 2. Table 1: The X-ray Observation Log . Columns: (1) the observation ID with our designation given in parentheses, (2) the observation start date, (3) the detector, (4) the off-axis angle, (5) the exposures of data used in final analysis, (6) radius of the source extraction region, (7) the net count rate in the source extraction region (0.3–3 keV for XMM-Newton and 0.4–3 keV for Chandra and Swift observations), with 1 σ 𝜎 \sigma error (but for observations rh601125n00, C1 and S2–S5, the 3 ​ σ 3 𝜎 3\sigma confidence bounds are given).

Obs. ID	Date	Detector	OAA	$T$ (ks)	$r_{\mathrm{src}}$	Count rate (10-3 counts s-1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
ROSAT:
rh601125n00	1998-01-18	HRI	13${.}^{\prime }$8	1.9	10′′	$0^{+3.8}$
XMM-Newton:
0302460101(X1)	2005-07-23	pn/M1/M2	13${.}^{\prime }$5	22/33/33	20′′/20′′/20′′	$1.45\pm 0.40$/$0.74\pm 0.20$/$0.21\pm 0.15$
0554680201(X2)	2009-02-12	pn/M2	12${.}^{\prime }$5	43/64	20′′/20′′	$37.4\pm 1.0$/$11.1\pm 0.4$
0554680301(X3)	2009-02-18	pn/M2	12${.}^{\prime }$5	42/64	20′′/20′′	$35.6\pm 0.9$/$9.7\pm 0.4$
Chandra:
5907(C1)	2005-04-02	ACIS-S1	12${.}^{\prime }$4	48	12${.}^{\prime \prime }$4	$0^{+0.28}$
9517(C2)	2008-06-05	ACIS-I3	14${.}^{\prime }$6	99	16${.}^{\prime \prime }$7	$11.1\pm 0.3$
12951(C3)	2011-03-28	ACIS-S1	10${.}^{\prime }$9	74	13${.}^{\prime \prime }$4	$13.8\pm 0.4$
13246(C4)	2011-03-30	ACIS-S1	10${.}^{\prime }$9	45	13${.}^{\prime \prime }$4	$13.9\pm 0.6$
13247(C5)	2011-03-31	ACIS-S1	10${.}^{\prime }$9	36	13${.}^{\prime \prime }$4	$14.2\pm 0.6$
12952(C6)	2011-04-05	ACIS-S1	10${.}^{\prime }$9	143	13${.}^{\prime \prime }$4	$13.4\pm 0.3$
12953(C7)	2011-04-07	ACIS-S1	10${.}^{\prime }$9	32	13${.}^{\prime \prime }$4	$15.3\pm 0.7$
13253(C8)	2011-04-08	ACIS-S1	10${.}^{\prime }$9	118	13${.}^{\prime \prime }$4	$13.8\pm 0.3$
13255(C9)	2011-04-10	ACIS-S1	10${.}^{\prime }$9	43	13${.}^{\prime \prime }$4	$13.3\pm 0.6$
17019(C10)	2015-02-23	ACIS-S3	0${.}^{\prime }$3	37	1${.}^{\prime \prime }$6	$4.9\pm 0.4$
Swift:
00033207001(S1)	2014-03-28	XRT	1${.}^{\prime }$0	8.7	25′′	$1.9\pm 0.5$
00033207002(S2)	2016-02-03	XRT	3${.}^{\prime }$8	3.1	25′′	${0.7}^{+1.3}$
00033207003(S3)	2016-02-04	XRT	2${.}^{\prime }$0	0.3	25′′
00033207004(S4)	2016-02-05	XRT	1${.}^{\prime }$5	2.7	25′′
00033207005(S5)	2016-02-07	XRT	1${.}^{\prime }$3	2.9	25′′
00033207007(S6)	2016-02-10	XRT	1${.}^{\prime }$2	3.0	25′′	$2.8\pm 0.7$
00033207008(S7)	2016-02-12	XRT	1${.}^{\prime }$0	2.3	25′′
00033207009(S8)	2016-02-14	XRT	1${.}^{\prime }$4	1.4	25′′

Table 3. Table 2: Spectral fit results. Columns : (1) the observations; (2) the model; (3) intrinsic absorption column density; (4) the apparent inner disk temperature of the MCD; (5) the MCD normization N MCD ≡ ( ( R MCD / km ) / ( D / 10 ​ k ​ p ​ c ) ) 2 ​ cos ⁡ θ subscript 𝑁 MCD superscript subscript 𝑅 MCD km 𝐷 10 k p c 2 𝜃 N_{\rm MCD}\equiv((R_{\rm MCD}/{\rm km})/(D/{\rm 10kpc}))^{2}\cos\theta , where R MCD subscript 𝑅 MCD R_{\rm MCD} is the apparent inner disk radius, D 𝐷 D is the source distance, θ 𝜃 \theta is the disk inclination; (6) the PL photon index; (7) the PL normalization; (8) the reduced χ 2 superscript 𝜒 2 \chi^{2} and degrees of freedom for fits using the χ 2 superscript 𝜒 2 \chi^{2} statistic (we rebinned the spectra to have at least 20 counts in each bin in order to use the χ 2 superscript 𝜒 2 \chi^{2} statistic; other fits without reduced χ 2 superscript 𝜒 2 \chi^{2} used the C statistic); (9) the 0.34–11.5 keV luminosity, corrected for the Galactic absorption but not instrinsic absorption (10) the 0.34–11.5 keV luminosity (the rest frame), corrected for the Galactic absorption and intrinsic absorption. The fits used spectra within 0.3–10 keV for XMM-Newton and Swift and used spectra within 0.3–7 keV for Chandra . Parameters without errors were fixed in the fits. All errors are at the 90%-confidence level.

Observation	model	$N_H$	$k{T}_{\mathrm{MCD}}$	$N_{\mathrm{MCD}}$	${\Gamma }_{\mathrm{PL}}$	$N_{\mathrm{PL}}$	${\chi }_{\nu }^2\left(\nu \right)$	$L_{\mathrm{abs}}$	$L_{\mathrm{unabs}}$
		(1022 cm-2)	(keV)			(${10}^{-6}$)		(1043 erg s-1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
X1	MCD+PL	$0.42$	${0.10}_{-0.04}^{+0.06}$	${210}_{-204}^{+27841}$	$2.5$	${4.6}_{-3.4}^{+3.9}$	…	${0.08}_{-0.03}^{+0.04}$	${0.55}_{-0.31}^{+0.95}$
	MCD	${0.00}_{0.00}^{+0.17}$	${0.32}_{-0.11}^{+0.15}$	${0.08}_{-0.07}^{+0.93}$	…	…	…	${0.06}_{-0.02}^{+0.02}$	${0.06}_{-0.02}^{+0.05}$
	PL	${0.01}_{-0.01}^{+0.40}$	…	…	${2.71}_{-0.68}^{+2.34}$	${4.4}_{-1.8}^{+7.2}$	…	${0.08}_{-0.04}^{+0.04}$	${0.08}_{-0.03}^{+0.51}$
X2	MCD+PL	${0.24}_{-0.05}^{+0.05}$	${0.29}_{-0.03}^{+0.03}$	${5.67}_{-2.25}^{+4.11}$	$2.5$	${14.8}_{-11.6}^{+11.4}$	$1.03\left(105\right)$	${1.22}_{-0.07}^{+0.07}$	${2.66}_{-0.42}^{+0.51}$
	MCD	${0.21}_{-0.04}^{+0.05}$	${0.31}_{-0.02}^{+0.02}$	${3.94}_{-1.27}^{+1.95}$	…	…	$1.06\left(106\right)$	${1.17}_{-0.06}^{+0.06}$	${2.31}_{-0.27}^{+0.34}$
	PL	${0.64}_{-0.07}^{+0.08}$	…	…	${4.93}_{-0.28}^{+0.30}$	${464}_{-71}^{+94}$	$1.17\left(106\right)$	${1.19}_{-0.06}^{+0.06}$	${25}_{-7}^{+12}$
X3	MCD+PL	${0.20}_{-0.05}^{+0.05}$	${0.28}_{-0.03}^{+0.03}$	${4.93}_{-2.09}^{+4.19}$	$2.5$	${19.3}_{-11.9}^{+11.7}$	$0.88\left(98\right)$	${1.19}_{-0.07}^{+0.07}$	${2.35}_{-0.38}^{+0.47}$
	MCD	${0.16}_{-0.04}^{+0.04}$	${0.32}_{-0.02}^{+0.02}$	${2.91}_{-0.96}^{+1.49}$	…	…	$0.94\left(99\right)$	${1.12}_{-0.05}^{+0.05}$	${1.93}_{-0.22}^{+0.27}$
	PL	${0.55}_{-0.06}^{+0.07}$	…	…	${4.69}_{-0.27}^{+0.29}$	${359}_{-50}^{+61}$	$0.91\left(99\right)$	${1.15}_{-0.06}^{+0.06}$	${16}_{-5}^{+7}$
C2	MCD+PL	${0.15}_{-0.11}^{+0.14}$	${0.32}_{-0.04}^{+0.05}$	${2.22}_{-1.22}^{+3.32}$	$2.5$	${9.9}_{-9.9}^{+10.3}$	$0.98\left(42\right)$	${1.13}_{-0.13}^{+0.17}$	${1.84}_{-0.43}^{+0.67}$
	MCD	${0.09}_{-0.09}^{+0.11}$	${0.35}_{-0.04}^{+0.04}$	${1.43}_{-0.64}^{+1.34}$	…	…	$1.01\left(43\right)$	${1.14}_{-0.14}^{+0.19}$	${1.55}_{-0.27}^{+0.39}$
	PL	${0.72}_{-0.16}^{+0.18}$	…	…	${5.02}_{-0.40}^{+0.47}$	${471}_{-116}^{+185}$	$0.92\left(43\right)$	${1.02}_{-0.10}^{+0.11}$	${27}_{-12}^{+27}$
C3–C9	MCD+PL	${0.14}_{-0.03}^{+0.03}$	${0.34}_{-0.02}^{+0.03}$	${0.80}_{-0.22}^{+0.34}$	$2.5$	${14.5}_{-3.6}^{+3.7}$	$0.97\left(137\right)$	${0.64}_{-0.02}^{+0.02}$	${1.00}_{-0.08}^{+0.09}$
	MCD	${0.07}_{-0.02}^{+0.03}$	${0.40}_{-0.02}^{+0.02}$	${0.39}_{-0.08}^{+0.10}$	…	…	$1.25\left(138\right)$	${0.60}_{-0.02}^{+0.02}$	${0.74}_{-0.04}^{+0.04}$
	PL	${0.47}_{-0.04}^{+0.04}$	…	…	${4.09}_{-0.13}^{+0.13}$	${147}_{-12}^{+13}$	$0.86\left(138\right)$	${0.61}_{-0.02}^{+0.02}$	${4.57}_{-0.62}^{+0.77}$
C10	MCD+PL	${0.46}_{-0.23}^{+0.27}$	${0.13}_{-0.02}^{+0.03}$	${461}_{-411}^{+4660}$	$2.5$	${2.3}_{-1.3}^{+1.8}$	…	${0.31}_{-0.05}^{+0.06}$	${3.52}_{-2.31}^{+9.45}$
	MCD	${0.20}_{-0.18}^{+0.21}$	${0.17}_{-0.03}^{+0.04}$	${27}_{-22}^{+158}$	…	…	…	${0.32}_{-0.06}^{+0.10}$	${0.97}_{-0.53}^{+1.51}$
	PL	${0.81}_{-0.27}^{+0.32}$	…	…	${8.01}_{-1.42}^{+0.99}$	${136}_{-63}^{+134}$	…	${0.31}_{-0.05}^{+0.06}$	${96}_{-81}^{+688}$

Equations

$${\dot{M}}_{\mathrm{d}}(t)=\frac{1}{{\tau }_{\mathrm{visc}}}\left(e^{-t/{\tau }_{\mathrm{visc}}}{\int }_0^t{e}^{t^{\prime }/{\tau }_{\mathrm{visc}}}{\dot{M}}_{\mathrm{fb}}(t^{\prime })d{t}^{\prime }\right),$$

Full text

{affiliations}

Space Science Center, University of New Hampshire, Durham, NH 03824, USA

Harvard-Smithsonian Center for Astrophysics, The Institute for Theory and Computation, 60 Garden Street, Cambridge, MA 02138, USA

QianNan Normal University for Nationalities, Longshan Street, Duyun City of Guizhou Province, China

Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA

Department of Physics and Astronomy, University of Alabama, Box 870324, Tuscaloosa, AL 35487, USA

Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea

Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA

Space Science Center, Morehead State University, 235 Martindale Drive, Morehead, KY 40351, USA

CNRS, IRAP, 9 avenue du Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France

Université de Toulouse, UPS-OMP, IRAP, Toulouse, France

Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 USA

AIM Paris-Saclay Service d’astrophysique, CEA-Saclay, 91191 Gif sur Yvette, France

Gemini Observatory/AURA, Southern Operations Center, Casilla 603, La Serena, Chile

Canadian Astronomy Data Centre, Herzberg Institute of Astrophysics, 5071 West Saanich Road, Victoria, British Columbia, V9E 2E7, Canada

The X-ray source 3XMM J150052.0+015452 (XJ1500+0154 hereafter) was serendipitously detected in frequent observations[7] of the foreground galaxy group NGC 5813 by the X-ray observatories Chandra and XMM-Newton from 2005 to 2011. Our follow-up observation of the source with Chandra on February 23rd 2015 provided a well constrained X-ray position coincident with the center of the galaxy SDSS J150052.07+015453.8, to within 0$.\!\!^{\prime\prime}$18 (Figure 1, see SI). The galaxy lies at a redshift of 0.145, or a luminosity distance of $D_{L}=689$ Mpc (for $H_{0}$=70 km s*-1* Mpc*-1*, $\Omega_{\mathrm{M}}=0.3$, $\Omega_{\Lambda}=0.7$), with strong emission lines indicative of intense star-forming activity. It has a total stellar mass of \sim$$6\times 10^{9} $M_{\odot}$ (see SI), comparable to that of the Large Magellanic Cloud. For such a small galaxy, we expect[8] the central supermassive black hole (SMBH) to have mass \sim$$10^{6} $M_{\odot}$.

The upper panel in Figure 2 shows the long-term evolution of the X-ray luminosity $L_{\rm X}$. Our best fits to the spectra with sufficient counts are shown in the lower panel of the figure and are given in Table 1. One striking property of the source is the fast-rise-very-slow-decay outburst profile. It was not detected in the first Chandra observation on April 2nd 2005, with $L_{\rm X}<4.3\times 10^{41}$ erg s*-1* (3$\sigma$ upper limit, assuming a powerlaw source spectrum of photon index 2.0). Less than 4 months later (July 23rd 2005), the source was detected in the first XMM-Newton observation, with $L_{\mathrm{X}}\sim 5.5\times 10^{42}$ erg s*-1*. It was detected at an even higher luminosity three years later, in one Chandra observation on June 5th 2008 and two XMM-Newton observations in February 2009, with $L_{\rm X}\sim 7.0\times 10^{43}$ erg s*-1*. The luminosity decreased only slightly to $\sim 3.0\times 10^{43}$ erg s*-1* in seven Chandra observations in March–April 2011. Similar luminosities were seen in our follow-up observations later, one by Swift on March 28th 2014, one by Chandra on February 23rd 2015, and seven by Swift in February 2016. Given the probably small central SMBH and correcting for emission outside the X-ray band, the source luminosity has been most likely at around the Eddington limit since it went into the outburst.

Another special property of the source is the generally quasi-soft X-ray spectra, most evident in the XMM-Newton and Chandra observations in 2008–2011. These spectra can be roughly described with a dominant thermal disk of apparent maximum disk temperature $kT_{\mathrm{diskbb}}\sim 0.3$ keV plus a weak powerlaw (see SI). However, such a model is physically unacceptable, because the standard thin accretion disk around a SMBH is expected to produce much cooler thermal emission ($kT_{\mathrm{diskbb}}\lesssim 0.1$ keV)[9]. Instead, the spectra can be described well with the Comptonization model CompTT[10], with an optically thick ($\tau\sim 4$–11) low-temperature ($kT_{\mathrm{e}}\sim 0.4$–1.3 keV) corona (see SI). Such spectral parameters are commonly seen in ultraluminous X-ray sources (ULXs)[11, 12, 6], most of which are believed to be super-Eddington accreting stellar-mass black holes, except that XJ1500+0154 had orders of magnitude higher luminosities. Therefore, we identified the observations in 2008–2011 as being in the super-Eddington accretion state.

Surprisingly, we obtained a much softer X-ray spectrum in the Chandra observation in 2015, mostly due to a drop (by a factor of 7.0) in the count rate above $\sim$1 keV (Figure 2), compared with the observations in 2008–2011. This super-soft spectrum can be described with a dominant thermal disk of $kT_{\mathrm{diskbb}}\sim 0.13\pm 0.01$ keV plus a very weak powerlaw (Figure 2). Such a cool thermal disk is expected from accretion onto a SMBH below the Eddington limit. Then the source could be in the thermal state, which in turn supports the identification of the super-Eddington accretion state in previous observations. In this case the X-ray spectral evolution of XJ1500+0154 is very similar to a transient ULX in M31[6], which changed from a super-Eddington accretion state to a thermal state within 20 days with the X-ray luminosity decreasing only slightly. However, we find that the spectrum can be described equally well with the CompTT model that fits the Chandra observations in 2011, except for additional absorption by a strong ($N_{\mathrm{H}}\sim 6\times 10^{23}$ cm*-2*) ionized ($\log(\xi)=2.8$) absorber with a blueshifted velocity of $0.36c$. Powerful sub-relativistic winds are expected in super-Eddington accreting black holes[13], and highly blueshifted warm absorbers have been detected in ULXs[14]. Therefore, this interpretation for the Chandra observation in 2015 also supports the identification of the super-Eddington accretion state in previous observations. The recent Swift observations in 2016 have poor statistics, but some of them did not seem to show similar super-soft X-ray spectra. Therefore, the source has not completely settled to a new state of super-soft X-ray spectra, and the super-Eddington accretion seems to have lasted for \gtrsim$$11 years (see SI).

No sign of persistent nuclear activity is seen in the optical emission lines of the host galaxy, whose ratios are fully consistent with those expected from a starburst galaxy. There are many other properties of the source that argue against the possibility that it is a standard active galactic nucleus (AGN, see SI). In particular, no AGN is known to show X-ray spectra as soft as XJ1500+0154 within the 1–4.5 keV energy band or show dramatic quasi-soft to super-soft X-ray spectral change. The large X-ray variability (a factor of $>$97) is also extremely rare among AGNs. Therefore, although we cannot completely rule out that XJ1500+0154 is just a highly variable AGN at this point, its X-ray outburst is best explained as tidal disruption of a star by the central black hole. This interpretation is strongly supported by our new discovery of two other sources that seemed to be in X-ray outbursts with similar quasi-soft X-ray spectra as XJ1500+0154 but have host galaxies showing no sign of nuclear activity in optical (see SI).

The super-Eddington accretion phase from tidal disruption of a solar-type star by a $10^{6}$ $M_{\odot}$ black hole can last $t_{\mathrm{Edd}}\approx 2$ years, with the peak mass accretion rate highly super-Eddington[1, 15]. One main property of a super-Eddington accretion disk is a lower radiative efficiency than a standard thermal thin disk, due to significant super-Eddington effects of photon trapping and outflows in the inner disk region[16, 17, 13]. These effects are more serious at higher accretion rates, with the disk luminosity sustained at around the Eddington limit. The Eddington-limited slow decay of our source thus agrees well with the super-Eddington accretion signatures suggested by the X-ray spectra. The long super-Eddington accretion phase of \gtrsim$$11 years in our event would imply disruption of a very massive star (10 $M_{\odot}$) based on the standard theory[15]. However, it has been realized that the evolution of TDEs heavily depends on how the streams of tidal debris intersect each other[18, 19, 20, 21, 22]. It should be common for circularization of the fallback mass onto the accretion disk to occur at a much larger distance, resulting in a much longer viscous time scale, than predicted from the standard theory[19]. Therefore, $t_{\mathrm{Edd}}$ can be very long in a slow circularization process, unless the circularization is so slow that the peak accretion rate drops to be sub-Eddington.

We plot in Figure 2 (solid line) the evolution of the luminosity from a full disruption of a 2 $M_{\odot}$ star by a $10^{6}$ $M_{\odot}$ black hole, with the accretion of the mass slowed relative to the fallback time by 3 years. The super-Eddington effects were taken into account by introducing a logarithmic dependence of the radiative efficiency on the accretion rate above the Eddington limit[13] (see SI). We assumed that 25% of the radiation is in X-rays, as inferred from the spectral modeling. The model describes the data well. The total energy release and the total mass accreted onto the black hole until the last Swift observation would then be $6.4\times 10^{52}$ ergs and 0.89 $M_{\odot}$, respectively, which are orders of magnitude higher than seen in other known events[23, 24, 5].

Although disruption of a very massive star of 10 $M_{\odot}$ with prompt circularization can also describe the data, such disruption is expected to be orders of magnitude rarer than disrupting a star of 2 $M_{\odot}$ with slow circularization (see SI). Therefore our event provides the first convincing evidence of slow circularization effects in TDEs, which are expected to be very common when the black holes are small (\sim$$10^{6} $M_{\odot}$) but were not clearly observed before probably due to observational bias[19].

We calculated the rate of events similar to XJ1500+0154 to be \sim$$4\times 10^{-7} per galaxy per year (see SI), which is about two orders of magnitude lower than estimated for short TDEs[25]. One main reason for the low rate of events like XJ1500+0154 could be the relatively large mass (2$M_{\odot}$) of the disrupted stars required, which is only possible in starburst galaxies[26]. Although events like XJ1500+0154 are rare, their extreme duration and radiative inefficiency mean that their contributions to the luminosity function of active galactic nuclei and to the growth of the black holes are comparable to or even higher than those of short events. TDEs with a shorter super-Eddington accretion phase than XJ1500+0154 could be more common. The discovery of our event opens up a new realm in which to search for super-Eddington accreting TDEs, that is, by investigating sources with quasi-soft X-ray spectra. Our discovery of the other two candidates is the result of applying this scheme.

This is the first time that X-ray spectra resembling typical super-Eddington accreting stellar-mass black holes were observed in an accreting SMBH. If our interpretation of a super-Eddington accreting TDE for XJ1500+0154 is correct, it would have important implications for the growth of massive black holes. The detection of quasars at redshift $z>6$ with black hole masses $\sim 10^{9}$ $M_{\odot}$ poses a problem to explain their growth with accretion via a standard thin disk at the Eddington rate[27]. However, their formation would be possible if the black holes can accrete at a super-Eddington rate during an early phase[28]. Our event shows that super-Eddington accretion onto massive black holes can occur, giving strong observational support to this model. The high absorption in these systems would mean that the search for them should be through radio and infrared[29], because their X-ray spectra, if as soft as XJ1500+0154, would be completely absorbed.

We expect the accretion rate to drop by an order of magnitude to be well sub-Eddington in the next ten years based on our model of full disruption of a 2 $M_{\odot}$ star. By continued monitoring of the event, we will be able to test our TDE interpretation and to determine the duration of the super-Eddington accretion phase and the origin of spectral softening. We will also be given a rare opportunity to observe the spectral evolution of the event across different accretion regimes and to investigate its connection with short super-soft events that are mostly believed to accrete below the Eddington limit.

Method

XMM-Newton observations and data analysis

XJ1500+0154 was serendipitously detected at off-axis angles of $\sim$13′ in three XMM-Newton observations (X1–X3 hereafter; see Supplementary Table 1) of NGC 5813. X1 was made in July 2005, while X2 and X3 were made in February 2009, only six days apart. The source was detected in all three European Photon Imaging Cameras (i.e., pn, MOS1/M1, and MOS2/M2)[1, 2, 3] in the imaging mode in X1, but only in pn and MOS2 in X2 and X3 because the source is outside the field of view (FOV) of MOS1 in these two observations. We used SAS 15.0.0 and the calibration files of 2016 February for reprocessing the X-ray event files and follow-up analysis. The data in strong background flare intervals, seen in all cameras in all observations, were excluded following the SAS thread for the filtering against high backgrounds. The final clean exposures used are given in Supplementary Table 1. We extracted the source spectra from all available cameras using a circular region of radius 20*′′. The background spectra were extracted from a large circular region near the source, using a radius of 100′′* for MOS1 and MOS2 and a radius of 50*′′* for pn. The event selection criteria followed the default values in the pipeline[4]. For X2 and X3, in which the source was bright, we also extracted the pn light curves binned at 500 s using the SAS tool epiclccorr and performed variability tests using the ekstest tool. We used the 0.3–3 keV band, where the source counts dominated over those of the background.

Chandra observations and data analysis

XJ1500+0154 was serendipitously covered in nine Chandra observations (C1–C9 hereafter; see Supplementary Table 1) of NGC 5813, but all at large pointing offsets (11′–15′). The dense observations in 2011 (C3-C9, $\sim$0.5 Ms) are from a Large Program (LP, PI: Dr. Scott Randall) on NGC 5813. All nine observations used the imaging array of the AXAF CCD Imaging Spectrometer (ACIS)[5], and XJ1500+0154 fell in the back-illuminated chip S1 in all observations except C2, in which it fell in the front-illuminated chip I3. We had a Chandra follow-up observation of the source for 37 ks in February 2015 (C10 hereafter), with the aim point at the back-illuminated chip S3. We reprocessed all the data to apply the latest calibration (CALDB 4.6.7) using the script chandra_repro in the Chandra Interactive Analysis of Observations (CIAO, version 4.7) package. No clear background flares were seen, and we used all data for all observations.

The spectra of XJ1500+0154 were extracted for each observation. We used a circular source region enclosing 90% of the point spread function (PSF) at 1.0 keV and a circular background region of a radius of 50\mbox{{}^{\prime\prime}} near the source. However, there are three exceptions. For observations C1 and C2, we used the 70% PSF radius for the source region, considering that the source was not detected in C1 and was near the CCD edge in C2. For our follow-up observation C10, in which the source is near the aim point with minimum background contamination, we used the 95% PSF radius for the source region. We used the CIAO task mkacisrmf to create the response matrix files and the CIAO tasks mkarf and arfcorr to create the point-source aperture corrected auxiliary response files. Considering no significant difference between LP observations, which were taken within 13 days, and in order to improve the statistics for spectral modeling, we created a single spectrum combining LP observations. For observation C1 in which the source was not detected, we used the CIAO task aprates to determine confidence bounds of the flux.

We measured the short-term variability within 0.4–3 keV adopting the Gregory-Loredo algorithm[6] implemented by the CIAO tool glvary[7]. It splits the events into multiple time bins and looks for significant deviations. The variation of the effective area with time was taken into account and was obtained by another CIAO tool dither_region. The different degrees of confidence is indicated by the parameter of “variability index”, which spans values within [0, 10] and is larger for variability of higher confidence[7].

Our C10 observation was intended to provide an accurate position of XJ1500+0154, utilizing the sub-arcsec resolution of Chandra near the aimpoint. We performed the source detection by applying the CIAO wavdetect wavelet-based source detection algorithm[8] on the 0.3–7 keV image binned at single sky pixel resolution. We then carried out the absolute astrometric correction for the X-ray sources by cross-correlating them with optical sources in the Canada-France-Hawaii Telescope (CFHT) MegaPrime/MegaCam[9] r\mbox{{}^{\prime}}-band stacked images. We only used 19 matches that are outside the strong diffuse gas emission in NGC 5813[10] and have X-ray 95% statistical positional errors $\leq$1$.\!\!^{\prime\prime}$2 (based on Equation 12 in Kim et al.[11]) and magnitude m_{r\mbox{{}^{\prime}}}<24.0 AB mag for astrometric correction. These 19 matches do not include XJ1500+0154, in order to reduce the effect of the astrometric correction on the identification of its optical counterpart. The astrometric correction method in Lin et al.[12] was used, by searching for the translation and rotation of the X-ray frame that minimize the total $\chi^{2}$ ($\chi$ is the ratio of the X-ray-optical separation to the total positional error) for 90% (i.e., 17, allowing 2 matches to be spurious or bad) of the matches that have the smallest $\chi$ values. The uncertainties of the translation and rotation and thus the systematic positional errors of the X-ray sources were estimated using 200 simulations. In order to calculate the statistical positional uncertainty for the source, we carried out 2000 ray-trace simulations with MARX 5.1.0 at positions near it and at the same off-axis angle. The spectrum from the thermal disk plus powerlaw fit to C10 was assumed.

Swift observation and data analysis

At our request, Swift[13] observed XJ1500+0154 in two epochs: one observation on March 28th 2014 (S1 hereafter), and seven observations between February 3rd–14th 2016 (S2–S8 hereafter, Supplementary Table 1). We analyzed the data with FTOOLS 6.18 and the calibration files released on July 31st 2015. The X-ray telescope (XRT)[14] was operated in the Photon Counting mode for all observations, and we reprocessed the data with the task xrtpipeline (version 0.13.2). The spectrum was extracted, using radii of 25*′′* and 2\mbox{{}^{\prime}} for the circular source and background regions, respectively. The source was hardly detected by the XRT in S2–S5, and we created a co-added XRT spectrum from these observations. The source was clearly detected in S6–S8, and we also created a co-added XRT spectrum from these observations. The source net count rate was higher in S6–S8 than in S2–S5 at the $3\sigma$ confidence level.

The UV-Optical Telescope (UVOT)[15] in S1 used three standard UV filters W1 (2.3 ks), M2 (2.3 ks), and W2 (2.3 ks). In S2–S8 the UVOT used the “Filter of the Day” mode, and we combined images for different filters, resulting in total exposures of 6.3 ks, 1.4 ks, 3.9 ks and 3.8 ks for the U, W1, M2, and W2 filters, respectively. To obtain the photometry, we used the task uvotsource with radii of 5*′′* and 20*′′* for the circular source and background regions, respectively.

ROSAT Observations

XJ1500+0154 was in the field of view of a ROSAT High-Resolution Imager pointed observation in 1998 for 1.9 ks (Supplementary Table 1). XJ1500+0154 was not detected in the observation, and we extracted the source and background spectra using a circular region of radius 10*′′* and a circular region of radius 50\mbox{{}^{\prime\prime}}, respectively, in order to estimate the flux limit.

CFHT MegaCam observations and data analysis

There are seven CFHT/MegaPrime r\mbox{{}^{\prime}}-band images, with exposure 345 second each and taken on May 5th 2014, and eight g\mbox{{}^{\prime}}-band images, with exposure 345 second each and taken on April 26th 2014. We produced two stacked images, one for the r\mbox{{}^{\prime}} band (the final seeing FWHM is 0$.\!\!^{\prime\prime}$65) and the other for the g\mbox{{}^{\prime}} band (the final seeing FWHM is 0$.\!\!^{\prime\prime}$80), using MegaPipe[16], and aligned their astrometry to the Sloan Digital Sky Survey (SDSS)[17]. The sources detected from these two stacked images were used to compare with the SDSS photometry to detect the source optical variability and to compare with X-ray sources to align the X-ray source astrometry. We also fitted the host galaxy profile in the CFHT/MegaPrime stacked images using GALFIT[18]. Ten stars within 2\mbox{{}^{\prime}} from XJ1500+0154 were used to construct the point spread function of the images.

X-ray spectral fits

The X-ray activity of XJ1500+0154 should be due to accretion onto a BH, and we fitted the X-ray spectra with several models typically used to study such an object. Given that XJ1500+0154 is most likely associated with a galaxy at $z=0.14542$, we applied this redshift to all the spectral models that we tested with the convolution model zashift in XSPEC[19]. All models included the Galactic absorption[20] fixed at $N_{\mathrm{H}}=4.4\times 10^{20}$ cm*-2* using the tbabs model. Possible absorption intrinsic to the source was accounted for using the ztbabs model. The abundance tables from Wilms et al.[21] were used.

Data availability statement The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.