When a star passes within the tidal radius of a supermassive black hole, it will be torn apart1. For a star with the mass of the Sun (M ⊙) and a non-spinning black hole with a mass <108 M ⊙, the tidal radius lies outside the black hole event horizon2 and the disruption results in a luminous flare3–6. Here we report observations over a period of ten months of a transient, hitherto interpreted7 as a superluminous supernova8. Our data show that the transient rebrightened substantially in the ultraviolet and that the spectrum went through three different spectroscopic phases without ever becoming nebular. Our observations are more consistent with a tidal disruption event than a superluminous supernova because of the temperature evolution6, the presence of highly ionized CNO gas in the line of sight9 and our improved localization of the transient in the nucleus of a passive galaxy, where the presence of massive stars is highly unlikely10,11. While the supermassive black hole has a mass >108 M ⊙ 12,13, a star with the same mass as the Sun could be disrupted outside the event horizon if the black hole were spinning rapidly14. The rapid spin and high black hole mass can explain the high luminosity of this event.
ASASSN-15lh was discovered by the All-Sky Automated Survey for Supernovae (ASAS-SN) on 14 June 2015 at a redshift of z = 0.2326. Its light curve peaked at V ≈ 17 mag implying an absolute magnitude of M = −23.5 mag, more than twice as luminous as any known supernova 7 . Our long-term spectroscopic follow-up reveals that ASASSN-15lh went through three different spectroscopic phases (Fig. 1). During the first phase 7 , the spectra were dominated by two broad absorption features. While these features appear similar to those observed in superluminous supernovae (SLSNe; Supplementary Fig. 1), their physical origin is different. The features in SLSNe are due to O II 8,15 , but this would produce an additional strong feature at ∼4,400 Å (Supplementary Fig. 2). The feature at ∼4,100 Å cannot be easily identified in the tidal disruption event (TDE) framework either. Two possibilities are that it could be due to absorption of Mg ii or high-velocity He ii 16 . After the initial broad absorption features disappeared, the spectra of ASASSN-15lh were dominated by two emission features. A possible identification for these features is He ii λλ3,202 and 4,686 Å, which are both consistently blue-shifted by ∼15,000 km s−1 (Supplementary Fig. 3). He ii emission is commonly seen in optically discovered TDEs 4,5 at different blueshifts, albeit typically at lower velocities, but it has not been seen in H-poor SLSNe. These features disappeared after day +75 (measured in rest frame from the peak) and the later spectra were mostly featureless, with the exception of two emission features at ∼4,000 and 5,200 Å. The spectra remained much bluer than those of SLSNe 17 for many months after the peak and never revealed nebular features, even up to day +256.
A UV spectrum obtained with the HST on day +168 does not show any broad features 18 . At the redshift of the host, we identified weak Lyα absorption and disproportionately strong high-ionization lines (Nv, Ovi, Civ). Combined with the weakness (or absence) of common 19 low-ionization absorption lines (Feii, Siii, Mgii), this aspect seems to be similar to the spectrum of ASASSN-14li, the only available UV spectrum of a TDE 9 (see Methods and Supplementary Fig. 4). The highly ionized gas appears at slightly different velocities, suggesting that it could be due to material in the vicinity of the TDE and ionized by its radiation. In contrast to the case of ASASSN-14li 9 , we do not observe any broad features in the UV range, but the optical spectrum is also mostly featureless at these phases.
In addition, we detect the presence of hydrogen in ASASSN-15lh. A weak Hα emission line is unambiguously detected in our highest signal-to-noise spectra (Fig. 1) and in more spectra at lower significance (Supplementary Fig. 3). Its presence cannot be excluded in any spectrum and its strength (equivalent width ∼4–8 Å) is invariable, within the present errors. The velocity of the Hα line (full-width at half-maximum (FWHM) ∼2,500 km s−1) is different from those of other features, implying that it is formed in a different emitting region.
The light curve evolution of ASASSN-15lh is shown in Fig. 2. After the initial peak and decline, around 10 September (day +60), the UV started rebrightening, an effect that was more prominent in the far-UV bands
. The dense photometric follow-up with the Swift Gamma-Ray Burst Mission (Swift) and the Las Cumbres Observatory Global Telescope Network (LCOGT) revealed that ASASSN-15lh reached a secondary UV maximum at around +110 days, followed by another decline. Interestingly, after day +100, the colours of ASASSN-15lh remained almost constant for over 120 rest-frame days (Supplementary Fig. 5). By fitting a black body to the multiwavelength photometry of ASASSN-15lh, we are able to estimate the temperature evolution, black-body radius and bolometric luminosity (Fig. 3). While the UV region rebrightens and the spectrum changes, the blackbody radius decreases and the temperature increases again, stabilizing at ∼16,000 K. This is neither expected from a supernova photosphere, nor observed for SLSNe
By integrating the bolometric luminosity, we estimate that ASASSN-15lh had radiated a total of 1.88 ± 0.19 × 1052 erg (depending on the assumed bolometric correction) up to 25 May 2016 (day +288). Including kinetic energy, which can reach an additional 1052 erg for SLSNe 15,25 , the total energy budget approaches the theoretical limit of that which supernova explosion models can accommodate 26,27 . It is possible that UV rebrightening could occur in an SLSN, due to either strong circumstellar interaction or the ionization breakout powered by a central magnetar. However, the observed Hα line is much weaker than those in SLSNe that have shown signs of late interaction 28 (Supplementary Fig. 1), and there are no features indicative of interaction in the UV spectrum. In addition, predictions for ionization breakout suggest that the spectrum should turn nebular 26 , although this might apply better to an X-ray rather than a UV breakout. Nevertheless, no detailed model has yet been calculated that can naturally explain the entire spectroscopic and photometric properties observed, either in the SLSN or in the TDE scenario. A single epoch of imaging polarimetry with HST shows low levels of polarization 18 , similar to that obtained for an SLSN 29 and suggesting an only mildly asymmetric geometry (in projection). Polarization measurements and predictions for optical TDEs are still lacking.
Strong evidence for ASASSN-15lh being a TDE comes from its environment. H-poor SLSNe are found in blue, metal-poor dwarf galaxies with average masses of , and none have yet been found to exceed at z < 1 10,11 . These galaxies typically have strong emission lines, pointing to active ongoing star formation and young progenitor ages that do not exceed a few million years 11 . In contrast, the host of ASASSN-15lh is a massive and passive red galaxy. By fitting the available photometry (see Methods), we estimate that the mass of the host is , with a dominant stellar population of age . The spectral energy distribution (SED) fit provides a star formation rate (SFR) of yr−1, consistent with the improved limit on SFR of <0.02 yr−1 that we obtained from our highest signal-to-noise spectrum. The derived specific SFR of yr−1 is thus three orders of magnitude lower than in any H-poor SLSN host (Supplementary Fig. 7). Furthermore, the transient is positionally coincident with the nucleus of its host. By aligning postdiscovery HST Advanced Camera for Surveys (ACS) images with a prediscovery image taken with the Cerro Tololo Inter-American Observatory 4 m Dark Energy Camera (Supplementary Fig. 8), we were able to improve the positional accuracy 7 of ASASSN-15lh by a factor of about four, corresponding to a projected nuclear offset of 131 ± 192 pc.
It has been argued that the large host galaxy mass may imply the presence of a supermassive black hole (SMBH) that is too large to disrupt stars outside its event horizon 7 . Since the tidal radius scales as while the gravitational radius scales as R g ∝ M •, stars can only be disrupted outside the horizon of an SMBH if the black hole is below a certain size, the Hills mass 2 M Hills. Larger SMBHs swallow stars whole. For a non-spinning Schwarzschild SMBH, , where and (see Methods). Using an empirical relationship between SMBH mass and total stellar mass for elliptical and spiral/lenticular galaxies with classical bulges 12 , we find is far above the Schwarzschild M Hills for stars of the same mass as the Sun . Using a mass-luminosity relation for early-type galaxies 13 (M •−L, using the V-band luminosity), we obtain . However, M Hills increases by almost an order of magnitude for rapidly spinning Kerr SMBHs and favourable orbital orientations 14 . For an optimal (prograde equatorial) orbit and our range of SMBH mass estimates, we find that a star with the same mass as the Sun can be disrupted by an SMBH with dimensionless spin parameter a • = 0.68 if , and by an SMBH with dimensionless spin parameter a • = 1 if . We show the exact relativistic M Hills(a •) in Fig. 4. For stars less massive than the Sun, the spin is constrained to even higher values. ASASSN-15lh could be compatible with a TDE by a Schwarzschild SMBH provided . However, the typical tidally disrupted star comes from the lower end of the stellar mass function, and this hypothesis is further challenged by the old age of the galaxy’s stellar population 30,31 . Observations of active galactic nuclei suggest that rapid SMBH spins are common 32 . We demonstrated here that TDEs present a method to probe the SMBH spins of quiescent galaxies. Given the inferred rapid spin of the SMBH, the fact that we did not detect a jet at radio wavelengths implies that black hole spin alone is not sufficient to launch powerful jets (see Methods).
The luminosity and energetics of ASASSN-15lh are also explained by a particularly massive SMBH. The expected radiative efficiency of accretion increases from η ≈ 0.05 (for a Schwarzschild SMBH) to η ≈ 0.42 for a rapidly spinning SMBH disrupting stars on prograde, near-equatorial orbits. A particularly massive SMBH is further biased towards disrupting the most massive stars near the main sequence turn-off mass, increasing accretion rates and total energy release. Finally, it is known that most TDEs only release a small fraction of in accretion power (the so-called ‘missing energy problem’ 30,33 ). One compelling explanation for this is that circularization of debris and formation of the accretion disk is mediated by relativistic apsidal precession, and that the majority of TDEs circularize inefficiently due to weak apsidal precession 34 . For a particularly massive fast-spinning SMBH, efficient circularization is favoured because R t ≈ R g, ensuring large per-orbit precession. The peculiar light curve may also be a natural consequence of tidal disruption by extremely massive black holes. In Methods we combine two competing models (the ‘circularization’ 33 and the ‘accretion/reprocessing’ 35 paradigms) of the optical emission in TDEs and show that the most massive SMBHs produce an unusual hierarchy of tidal disruption timescales. Since the viscous time in the accretion disk is much longer than the debris fallback time when is greater than a few , TDEs around the most massive SMBHs can display an early peak in the light curve from circularization luminosity, and a second peak from reprocessed accretion luminosity.
We describe here the data, methods and theoretical calculations used. We provide details on the localization of ASASSN-15lh and on the host galaxy properties. We present the different data used, and describe the reductions and comment on the implications. Finally, we demonstrate that a TDE can easily accommodate the luminosity and energetics of ASASSN-15lh, we show that combining two luminosity mechanisms for TDEs can result in light curves with two different timescales and we present our derivation of the relativistic M Hills as a function of the SMBH spin. We assume a Planck cosmology 36 .
Astrometric localization of ASASSN-15lh
HST observations of ASASSN-15lh were obtained under programme 14348 (PI: Yang) with ACS and a broadband polarimetry filter (POL0V) and the F606W filter. All analyses were performed on the reduced drizzled image obtained from the Barbara A. Mikulski Archive for Space Telescopes (MAST) archive. The image was taken on 3 August 2015, and the total exposure time for this frame was 366 s. The dark energy camera (DECam) image was a 90 s image taken on 22 October 2014 using an r-band filter. The DECam data were reduced using the Dark Energy Survey Data Management Pipeline and are available online 37 . The measured FWHM was 0.8 arcsec.
Eight sources common to both the DECam and ACS images were used to derive a geometric transformation (allowing rotation, translation and a single scaling factor) between the two frames. Of these sources, five were unresolved in the ACS image and the remaining three had a FWHM of less than about twice that of the point sources. The root mean square error in the transformation was 0.19 DECam pixels, or 52 mas. To measure the position of the host galaxy in the DECam frame, we fitted a model galaxy profile using the GALFIT code; uncertainties in the galaxy centroid were estimated to be only a few hundredths of a pixel from Monte Carlo tests. The position of ASASSN-15lh on the ACS image yielded an accuracy of five hundredths of a pixel (or 3 mas) using three different centring algorithms within the Image Reduction and Analysis Facility PHOT package.
The host galaxy
To derive the physical properties of the host galaxy of ASASSN-15lh through modelling of its SED, we used grizY 37 , J and K s 38 , as well as 3.4 μm and 4.6 μm Wide-Field Infrared Survey Explorer photometry. We also performed aperture photometry on Galaxy Evolution Explorer images, yielding no significant detections.
We fitted the galactic extinction-corrected 39 photometry of the host with stellar population synthesis models 40 using the photometric analysis for redshift estimate (Le Phare) code 41,42 . Our galaxy templates were based on a Chabrier initial mass function 43 , and spanned different stellar metallicities, e-folding timescales τ (0.1–30 Gyr), stellar population ages (0.01–10 Gyr) and dust attenuations 44 . The galaxy stellar mass and SFR are and yr−1, respectively. Physical parameters are given as the median of the probability distribution of all templates, with error bars containing the 1σ probability interval. The best fit model is shown in Supplementary Fig. 6 and it has a low E(B−V)host = 0.02 mag. We assume that the extinction at the host is negligible.
We also constrain the recent star formation in the host by placing limits on the flux of [O ii] and (narrow) Hα. Using the FORS2 spectra (signal-to-noise ratio >200) we obtain flux limits of <1.8 × 10−16 erg s−1 cm−2 for [O ii] and <2.9 × 10−17 erg s−1 cm−2 for Hα (2σ). These limits constrain the SFR to <0.25 and <0.02 yr−1 respectively 45,43 , an improvement by a factor of ten over previous estimates 7 .
HST UV spectroscopy
A UV spectrum of ASASSN-15lh was obtained on day +168 with HST under programme 14450 (PI: Brown). We downloaded the reduced Cosmic Origins Spectrograph (COS) and the Space Telescope Imaging Spectrograph (STIS) spectra from the MAST archive. The spectrum does not display any broad emission or absorption features (at similar phases the optical spectrum is also mostly featureless; Fig. 1). We identified both geocoronal and absorption lines at z = 0 and a number of narrow (FWHM ~200−400 km s−1) absorption features at the redshift of ASASSN-15lh. Supplementary Fig. 4 shows the COS spectrum (the STIS spectrum is more noisy and less interesting). Supplementary Table 1 contains the equivalent widths and kinematic offsets (measured relative to Lyα) for lines that were detected, as well as selected limits.
Low ionization features, such as Fe ii and Si ii, which are common in the star-forming lines of sight of SLSNe 46 or gamma ray bursts (GRBs) 19,47 are weak or absent in ASASSN-15lh. In contrast, absorption from high ionization lines from N v and O vi is remarkably strong, especially relative to the (weak) Lyα. In particular, the ratio of N v to Lyα is about four, while it is >1,000 times lower in GRBs. The same is true for column densities: using Voigt profile modelling, we derived N(H i) = 14.73 ± 0.12, N(O vi) = 15.58 ± 0.03, N(N v) = 15.42 ± 0.06 and N(C iv) = 14.60 ± 0.27, resulting in ratios that are highly unusual for GRB or quasar damped Lyα systems 48,49 , even if the values are lower limits due to saturation. The ratio of N v to Lyα was also observed to be of the order of unity in the spectrum of ASASSN-14li, the only UV spectrum of a TDE 9 . By complementing our measurements with those from optical spectra 7 , we found that the Mg ii absorption is weak, below the value for GRBs 19,47 and SLSNe 46 .
Therefore we suggest that the absorbing gas can be separated into two components: (1) a tenuous mildly ionized medium (Lyα, Mg ii, Si iii at velocities from 0 to +44 km s−1), which is very unusual given the lack of Fe ii and Si ii, and (2) a highly ionized medium (N v, O vi and C iv) at negative velocity offsets of −80 to −120 km s−1. We suggest that the latter is consistent with material from a disrupted low-mass star 9,50 and that it is ionized by the TDE. Despite the absence of broad features, the phenomenological similarity with the UV spectrum of ASASSN-14li strongly favours a TDE origin for ASASSN-15lh. A highly ionized outflow was also detected for ASASSN-14li in X-rays 51 .
Spectra were obtained with the instruments and set-ups listed in Supplementary Table 2. The data from FLOYDS, WIFES and EFOSC2 were reduced using dedicated instrument pipelines
Imaging and removal of the host contribution
The LCOGT gri images were preprocessed using the Observatory Reduction and Acquisition Control Data Reduction pipeline 55 . To remove the host contribution, we performed image subtraction using the prediscovery DECam gri images as templates. The Swift Ultraviolet and Optical Telescope (UVOT) observations were reduced following the standard procedures and software (uvotsource). To extract the photometry, we used a 4 arcsec aperture and a curve of growth aperture correction. For the Swift filters we did not have prediscovery observations, and hence used the model galaxy spectrum from the SED fit (Supplementary Fig. 6) to generate synthetic magnitudes at these wavelengths. For the B and V filters, where host contamination is a concern, we estimated the host uncertainty to be <0.05 mag, increasing to 0.1 mag for the U band. The host uncertainties in the UV filters are more significant, but at these wavelengths the host is many orders of magnitude below the transient luminosity. In the AB system we obtained host magnitudes of V = 18.98, B = 20.43, U = 21.95, UVW1 = 23.21, UVM2 = 23.65 and UVW2 = 23.62 mag, which we subtracted from the Swift measurements to obtain the transient photometry. Two UVOT filters suffered from a red leak but this did not affect blue sources such as ASASSN-15lh to the same degree as, for example, SNe Ia 56 . On the basis of synthetic photometry of blackbody spectra, we estimated that the photometry is affected by <2% for a black body with T = 15,000 K. As this precision is significantly lower than our photometric accuracy, we did not attempt to correct for this effect. Another study 18 has found higher values – but still low – for this maximum contamination.
Radio and X-ray observations
We observed ASASSN-15lh from 05:00 to 14:00 ut on 9 December 2015, using the Australia Telescope Compact Array in configuration 750C, under project code CX340. We observed in two frequency bands of width 2.048 GHz centred at 5.5 and 9.0 GHz. We used B1934-638 as both the flux and bandpass calibrator, and B2205-636 as the phase calibrator. We reduced the data following standard procedures in the Multichannel Image Reconstruction, Image Analysis and Display package 57 , and carried out the imaging and self-calibration using the Common Astronomy Software Application 58 .
The field was dominated by PKS J2203-6130, a 9 mJy source (before primary beam correction) located 15 arcmin away from the target. We performed self-calibration, initially in phase only (down to a timescale of 2 min), and eventually in amplitude and phase, on a timescale of 10 min. Given the non-uniform uv coverage, we tested a variety of image weighting schemes, and found the optimum to be a Briggs robust weighting of 0.5. ASASSN-15lh was not detected down to 3σ upper limits of 25 and 23 μJy per beam at 5.5 and 9.0 GHz, respectively, consistent with a reported upper limit from 3 weeks earlier 59 . Stacking our two frequency bands gave us a slightly deeper 3σ radio upper limit of 17 μJy per beam.
The X-Ray Multi-Mirror Mission (XMM-Newton) satellite observed ASASSN-15lh as part of a Director’s Discretionary Time proposal on 18 November 2015. The on-source time is 11.9 ks, and after filtering epochs of high background, 9 ks of MOS2 and 4 ks of PN data can be used. Given the lower background and the longer net exposure, we used the MOS2 detector for estimating the upper limit on the source flux. In an aperture of radius 32” centred on ASASSN-15lh we derived a 95% confidence upper limit 60,61 of 11 source counts in the 0.15–1 keV band. To convert this to a limit on the flux, we use a temperature of 70 eV found for ASASSN-14li as input, which taking into account that the in ASASSN-15lh is close to 8 × 108 , and that of ASASSN-14li is closer to 2 × 106 , implies a black-body temperature of 18 eV (as T ∝ M −0.25). With this and N H = 3 × 20 cm−2 W3PIMMS provides a 95% upper limit to the 0.3–1 keV X-ray flux of 2 × 10−16 erg cm−2 s−1, yielding an upper limit to the source luminosity of 3 × 1040 erg s−1. This limit depends strongly on the chosen energy band. The 0.3-1 keV band was chosen to allow comparison with ASASSN-14li (ref. 62).
If TDEs do in fact all produce radio jets, as suggested by the recent detection of ASASSN-14li 62 , then applying the same model with appropriate scalings would predict a radio flux of 10 μJy at the time of the observations. The fact that we did not detect a radio jet therefore remains consistent with a TDE origin for ASASSN-15lh, and implies that the jet power of ASASSN-15lh is νL ν≲1038 erg s−1, which is at least two or three orders of magnitude lower than that of the relativistic TDE Swift J1644+57 63 . This difference was probably caused by a combination of misalignment of the jet axis and the line of sight (consistent with our non-detection of X-rays) and differences in accretion flow geometry, interstellar medium density or magnetic field strength 64 . If black hole spin were the dominant factor in setting jet power, we would have expected ASASSN-15lh to host a jet at least comparable in strength to that of ASASSN-14li (as we have inferred a high black-hole spin for ASASSN-15lh). Given that our upper limit is close to the ASASSN-14li model prediction, this jet should have been detectable unless the spin of ASASSN-15lh is significantly less than we have inferred, the interstellar medium density is extremely low, or the SMBH in ASASSN-14li is also rapidly spinning.
Tidal disruption luminosities and energetics
In Newtonian theory, a star with mass and radius will be tidally disrupted when it approaches an SMBH of mass within a distance:
Stars passing within this tidal radius can create a luminous electromagnetic flare provided R t ≳ R IBCO, the location of the innermost bound circular orbit (IBCO) for the SMBH. This occurs for SMBHs smaller than the Hills mass,
If we assume a top-hat distribution of debris energy, then the fallback time (in units of seconds) for the most tightly bound debris is: which gives a peak fallback rate of:
where η = 0.1η −1 is the radiative efficiency of accretion used to calculate the Eddington-limited mass inflow rate . The peak bolometric luminosity is: which is easily compatible with our observations for and η = 0.42, appropriate for Kerr black holes. The radiated bolometric energy is:
Tidal disruption flare timescales
Existing observations do not yet distinguish between two competing theories for producing TDE optical emission. In the accretion/reprocessing paradigm, the bolometric luminosity of a compact (~10R g), efficiently circularized accretion disk is intercepted by an optically thick screen of gas at larger scales (~103 R g). This reprocessing layer may be a slow outflow from the disk 70 , or a more hydrostatic configuration 35,71,72 . However, in both cases it absorbs and re-emits a large fraction of the disk bolometric luminosity at longer wavelengths. Both cases predict a larger reprocessing layer for larger SMBHs: outflow velocities , or, if we assume that a hydrostatic reprocessing layer exists at scales comparable to the semimajor axis of the most tightly bound material, its size is proportional to . Alternatively, in the circularization paradigm, observed optical emission arises from shocks between debris streams 33 , which thermalize and radiate stream kinetic energy at the (generally large) stream self-intersection radius.
The efficiency of circularization (and therefore ) depends sensitively on the dimensionless orbital pericentre R p/R g: small decreases in R p quickly move the self-intersection point inwards, increasing the circularization efficiency 73,74 . The low luminosities seen in many optically selected TDEs may reflect the fact that most TDEs have subrelativistic pericentres and circularize inefficiently, so that their peak luminosity is much less than (ref. 34 ).
For an extremely massive SMBH with M • ≈ M Hills, all TDE pericentres are highly relativistic and circularization is maximally efficient (except possibly if the SMBH spin is rapid and strongly misaligned 75,76 ). Stream self-intersection points will be ~R p, near the IBCO 34 , so the circularization and accretion power will be comparable. It is therefore natural to expect that TDEs from the most massive SMBHs will be brighter and able to attain their theoretical peak luminosity, while smaller SMBHs will often produce TDEs that (due to inefficient circularization) have luminosities well below the peak theoretical luminosity.
We propose that the two peaks in the ASASSN-15lh light curve correspond to two different energy sources: the circularization luminosity, and the accretion luminosity. The former evolves on the fallback timescale t f while the latter evolves on a viscous timescale,
where we have assumed that the disk outer edge is 2R p, α < 1 is the usual Shakura-Sunyaev viscosity parameter, and H/R is the disk aspect ratio. For standard TDEs, these two sources of luminosity are difficult to disentangle, because t v ≪ t f (refs. 77,78 ): as soon as matter circularizes into a disk, it drains rapidly into the SMBH, and the two sources of luminosity rise and fall together.
However, for very massive SMBHs, , and the accretion disk will be geometrically thin, dramatically increasing t v and producing an inverted timescale hierarchy: t v ≳ t f. The circularization luminosity can be released promptly, but accretion luminosity is bottlenecked by the long t v. The range of inferred SMBH masses for ASASSN-15lh yield (unlike for most other TDE hosts), so it is natural to expect two power sources – circularization and accretion – to have two different peaks.
The characteristic decay time of the first peak will be ~t f, while that of the second will be t v, which is a sensitive function of α and H/R. Plausible parameter choices (for example , α = 0.1, H/R = 0.03) give a t v of about 6 months, in agreement with the observed second component of the light curve. However, the first component of the light curve decays on a the timescale of about 1−2 months, unlike the Newtonian estimate of equation (4): t f ≈ 1 yr. In the following subsection, we argue that general relativity effects can increase Δϵ in TDEs with extremely relativistic pericentres, substantially reducing t f for this subset of TDEs.
Relativistic alterations to the fallback time
Highly relativistic tidal disruption will alter the Newtonian Δϵ. The frozen-in energy spread Δϵ can increase by a factor of up to (ref. 79), decreasing t f and increasing modestly. However, Δϵ may increase further by modest spin–orbit misalignments in a TDE for sufficiently relativistic pericentres 66 . Here, we argue that this effect can strongly reduce the fallback time from the Newtonian estimate of equation (4).
The extremity of a TDE is quantified not just by B ≡ R p/R g, but also by the penetration factor β ≡ R t/R p. TDEs with a large β will strongly compress the star orthogonal to the orbital plane, causing a vertical collapse with velocity . The collapse is reversed near the pericentre, once internal pressure in the disrupted star builds up to the point where it ‘bounces’ along this vertical axis 80 , receiving an almost impulsive hydrodynamic kick ~v z along the direction of collapse. The bounce typically has little effect on the energy spread of the debris 65,73 , despite the fact that V p v z ≳ Δϵ for large β or small B (here V p is the orbital velocity at the pericentre). One could define a hydrodynamic component of the energy spread, , but in standard TDEs the misalignment angle θ = π/2.
However, for very low B, modest spin–orbit misalignment will precess the orbital plane as the star passes through the tidal sphere, partially aligning the axis of vertical collapse with the orbital velocity vector. The per-orbit precession in the line of ascending nodes for a parabolic orbit is 81 :
at leading post-Newtonian order. Since most of this shift occurs near the pericentre, we approximate the rotation in the line of ascending nodes between R t and the bounce (near R p) as δΩ/2. The misalignment angle is θ ( , where I is the misalignment between spin and orbital angular momentum). Defining a total energy spread Δϵtot ≡ Δϵ + Δϵh, we find (Stone, Kennon, & Metzger, manuscript in preparation):
The above arguments are approximate, as the post-Newtonian approximation begins to break down for R p ≈ R g, and we have treated the bounce hydrodynamics impulsively. A detailed examination of this spin–orbit coupling is beyond the scope of this paper, but order unity increases in Δϵ and decreases in t f ∝ Δϵ3/2 are expected for TDEs around SMBHs with a • ≈ 1 and B ≈ 1.
Relativistic calculation of Hills mass
Some of the previous Newtonian estimates break down when the star's orbital pericentre R p ≈ R g. In this regime, general relativistic effects are crucial for proper modelling of M Hills 82,14 . The increased M Hills arises from two different effects: first, a large a • will lower the IBCO radius significantly, and second, the Kerr tidal field is somewhat stronger than the Schwarzschild equivalent.
To calculate M Hills(a •), we employ Fermi normal coordinates to write a local, fully general relativistic tidal tensor 83 . We then employ the accepted formalism 14 to estimate relativistic M Hills. The results are shown for equatorial orbits (that maximize M Hills) in Fig. 4, where we see that the relativistic Kerr M Hills can be almost an order of magnitude greater than the Newtonian (or Schwarzschild) equivalent.
How to cite this article: Leloudas, G. et al. The superluminous transient ASASSN-15lh as a tidal disruption event from a Kerr black hole. Nat. Astron. 1, 0002 (2016).
We acknowledge support from the European Union FP7 programme through the following European Research Council grants: 320360 (M.F., H.C.), 647208 (P.G.J.), 291222 (S.J.S.), 615929 (M.S.). We also acknowledge: Einstein Postdoctoral Fellowship PF5-160145 (N.C.S.), Hubble Postdoctoral Fellowship HST-HF2-51350 (S.v.V.), STFC grants ST/I001123/1 ST/L000709/1 (S.J.S.) and ST/L000679/1 (M.S.), Australian Research Council Future Fellowship FT140101082 (J.C.A.M.-J.), a Royal Society University Research Fellowship (J.R.M.), a Sofja Kovalevskaja Award to P. Schady (T.Kr., T.-W.C.), a Ramón y Cajal fellowship and the Spanish research project AYA 2014-58381 (A.de U.P.), CONICYT-Chile FONDECYT grants 3130488 (S.K.), 3140534 (S.S.), 3140563 (H.K.), 3150238 (C.R.-C.), a PRIN-INAF 2014 project (N.E.-R.), support from IDA (D.M.), an Ernest Rutherford Fellowship (K.M.), CAASTRO project number CE110001020 (B.E.T.), National Science Foundation grant AST 11-09881 and NASA grant HST-AR-13726.02 (J.C.W.). This work used observations from the Las Cumbres Observatory Global Telescope Network (LCOGT) and was based upon work supported by National Science Foundation grant 1313484. The Australia Telescope Compact Array is part of the Australia Telescope National Facility which is funded by the Australian Government for operation as a National Facility managed by Commonwealth Scientific and Industrial Research Organisation. This work was based partially on observations collected as part of the Public European Southern Observatory Spectroscopic Survey for Transient Objects Survey (PESSTO) under European Southern Observatory (ESO) programmes 188.D-3003 and 191.D-0935, and on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 095.D-0633. We thank M. Della Valle for comments.
Supplementary Figures 1–8, Supplementary Tables 1–2