Lense–Thirring precession after a supermassive black hole disrupts a star

An accretion disk formed around a supermassive black hole after it disrupts a star is expected to be initially misaligned with respect to the equatorial plane of the black hole. This misalignment induces relativistic torques (the Lense–Thirring effect) on the disk, causing the disk to precess at early times, whereas at late times the disk aligns with the black hole and precession terminates1,2. Here we report, using high-cadence X-ray monitoring observations of a tidal disruption event (TDE), the discovery of strong, quasi-periodic X-ray flux and temperature modulations. These X-ray modulations are separated by roughly 15 days and persist for about 130 days during the early phase of the TDE. Lense–Thirring precession of the accretion flow can produce this X-ray variability, but other physical mechanisms, such as the radiation-pressure instability3,4, cannot be ruled out. Assuming typical TDE parameters, that is, a solar-like star with the resulting disk extending at most to the so-called circularization radius, and that the disk precesses as a rigid body, we constrain the disrupting dimensionless spin parameter of the black hole to be 0.05 ≲ ∣a∣ ≲ 0.5.

nates.Here, using high-cadence X-ray monitoring observations of a TDE, we report the discovery of strong, quasi-periodic X-ray flux and temperature modulations from a TDE.These X-ray modulations are separated by 17.0 +1.2 −2. 4 days and persist for roughly 130 days during the early phase of the TDE.
Lense-Thirring precession of the accretion flow can produce this X-ray variability, but other physical mechanisms, such as the radiation-pressure instability, cannot be ruled out.Assuming typical TDE parameters, i.e., a solar-like star with the resulting disk extending at-most to so-called circularization radius, and that the disk precesses as a rigid body, we constrain the disrupting black hole's dimensionless spin parameter to be 0.05 ≲ |a| ≲ 0.5.
AT2020ocn/ZTF18aakelin is an optical transient from the center of a previously-quiescent galaxy at a redshift of 0.0705 (1) (Extended Data Figure, EDF 1).Follow-up optical spectra taken 1-2 months post-discovery revealed a blue continuum and a broad He II line (Fig. 16 of (2)).Based on these properties it was classified as a TDE (1,2).We measured the host galaxy's stellar velocity dispersion using an optical spectrum taken 12 years prior to the outburst (section 2).Assuming the scaling relation between the host stellar velocity dispersion and black hole mass implies a disrupting SMBH mass of 10 6.4±0.6 M ⊙ , where the errorbar includes both the measurement and the systematic uncertainties in the scaling relation.
Roughly a day after the TDE classification NICER started a high-cadence (multiple visits per day) monitoring program on MJD 59041.Here we focus on the first ≈4 months of monitoring data during which multiple soft X-ray (0.3-1.0 keV) flares are evident (Fig. 1a and EDF 2).
A visual inspection suggests that they are regularly spaced, roughly 15-d apart, and similar modulations are not present in the optical/UV bands (Fig. 1b).
To quantify the variability we extracted a Lomb Scargle Periodogram (LSP; (3,4)) of the background-subtracted 0.3-1.0keV count rate (Fig. 2).As expected, there is a broad peak at comparable to observations if a magnetic field ∼10 4 Gauss is present in the inner disk.Thus RPI can, in principle, explain the X-ray modulations, but requires fine-tuning of multiple parameters (see SM).
In a TDE the stellar orbit and SMBH spin axis will be misaligned, and disk material will undergo Lense-Thirring precession in which the plane of the orbit precesses around the black hole's spin vector.Emission from the central accretion disk, combined with Lense-Thirring precession of the disk, may provide a straightforward explanation for the soft X-ray spectrum, flux and temperature modulations, and the lack of similar modulations in the optical/UV bands.Indeed, Lense-Thirring precession is commonly accepted to be the cause of some X-ray QPOs of the order of seconds from accreting stellar mass compact objects (11)(12)(13).The shape of the outbursts we have detected in AT2020ocn are similar to some of those exhibited by the X-ray binaries GRS 1915+105 and IGR J17091-3624.These systems show quasi-periodically repeating state cycles (e.g., (14)(15)(16)), and this behavior has often been interpreted as evidence for the radiation pressure instability (10,17), but it has also been suggested that it may arise from Lense-Thirring precession of a radially narrow region of the disc close to the black hole horizon (18).We therefore consider Lense-Thirring precession of a newly formed accretion disk around a SMBH.This can manifest in two modes: 1) if the accretion rate is sufficiently high, and thus the disk geometrically thick such that the disk angular semi-thickness H/R is larger than the disk viscosity parameter α ≈ 0.1 (19), then the precession can be efficiently communicated via pressure waves (20).This allows a significant portion of the disk to precess as a rigid body (21,22); or 2) for lower accretion rates, where the disk is thin, the inner disk can tear into discrete annuli that precess individually (23).In the former case the observed X-ray modulations are a result of the changing orientation of the system, while in the latter scenario the X-ray modulations result from a combination of changing orientation and accretion of discrete precessing annuli.We focus on the first mode here because the accretion rate is, in general, expected to be high following a TDE (e.g., Fig. 1 of ( 24)), and discuss the second mode in SM.
When the disk precesses as a rigid body, both the observed flux and the disk temperature can exhibit modulation over the precession period (e.g., see Fig. 4 of ( 25)).This is because, during certain phases of the precession, our line of sight enables us to observe the hot/inner disk, whereas during other phases, our view of the inner disk becomes obstructed, allowing mostly the outer/cooler disk to be visible (EDF 7).Also, Fig. 3c suggests that the cool component's variability roughly traces the warm component-albeit with large error bars.This is consistent with precession of an extended disk rather than a narrow ring.While the origin of optical/UV emission from TDEs is still debated, it is, in general, not thought to be direct disk emission.Some current models include stream-stream collisions (e.g., (7)) and X-ray reprocessing (e.g., (26,27)).Thus, a precessing inner disk that produces soft X-rays should not modulate the optical/UV flux originating far away from the hole.Furthermore, theoretical studies have estimated that, for SMBH masses weighing 10 5−7 M ⊙ , such rigid body precession should last between 0.4-0.7 years before the accretion rate declines to the point that rigid precession is no longer possible and instead the disk aligns with the black hole spin (Fig. 2 of ( 21)).This is consistent with the observed lifetime of AT2020ocn's X-ray modulations, t lifetime ∼ 130 days (Fig. 1a).AT2020ocn's first few X-ray flares are asymmetric, and this can be interpreted as a precessing disk that is warped, rather than planar, which can lead to an abrupt obscuration of the inner hot gas.Also, the second peak in the total X-ray flux (close to 90 days in Fig. 1a) appears blended with the third peak.However, it is more pronounced in the luminosity and the temperature evolution of the warm component (Fig. 3a,b).You can explain this in the precession model if the disc initially has a significant geometric thickness.This can shield the inner warm material more when compared to other time periods.
If rigid body disk precession is indeed driving these modulations, we can use the observed period to constrain the disrupting SMBH's spin (21).We calculated the precession period fol-lowing (21), taking the power-law of the surface density profile to be s = −3/2, which corresponds to the radiation pressure dominated inner region of the standard disk model (28,29).
In this case the timescale is principally determined in the outer disk regions and we find that , where a is the dimensionless black hole spin, R g = GM/c 2 is the gravitational radius of the black hole, and ξ(R in /R out ) is a dimensionless function that is weakly dependent on the ratio of the inner and outer disk radii (for R in /R out → 0, we have ξ → 1/4).Using this approximation, taking R out to be the circularisation radius of the debris, and inverting the equation for the precession timescale, we can calculate the black hole spin as a ≈ 0.1 t p 15.9 days where β = R t /R p ≃ 2 is the impact parameter of the stellar orbit required to just fully disrupt a solar-like star (30), M ⋆,⊙ and R ⋆,⊙ are the mass and radius of the star in solar units, and M 7 is the SMBH mass scaled by 10 7 M ⊙ .
From this equation we can see that to accurately constrain the spin with this model we require accurate constraints on the parameters β, M ⋆,⊙ , R ⋆,⊙ and M .However, if we take standard TDE parameters (as above), and an SMBH mass estimate of 10 6.4 M ⊙ , then we find that a ≈ 0.15 is required to generate the 15 day period.We also explored varying the surface density profile's power-law index, s, in the range −3/2 to 3/4, finding that for SMBH masses ∼ 10 7 M ⊙ the value of s makes little difference to this estimate, while at the lower end of the black hole mass range the value of s can make a significant difference with s = −3/2 providing the largest spin estimate.Thus considering a range of possible models, we conclude that 0.05 ≲ |a| ≲ 0.5 (Fig. 4).Future modelling of AT2020ocn's multi-wavelength emission, especially the high-cadence X-ray observations with numerical simulations, will provide a more detailed understanding of the accretion flow structure and should provide even tighter constraints on the SMBH spin.
The accretion of stellar debris following a TDE can be highly chaotic owing to various physical effects, and this is evident in the plethora of low-cadence X-ray TDE light curves (e.g., (31,32)).Our work demonstrates that high-cadence X-ray monitoring can unveil regular processes happening amongst the chaos from the highly-relativistic regions close to the disrupting SMBHs.If regular modulations like the ones identified here are indeed caused by rigid body disk precession, this enables an independent avenue to measure SMBH spins.Especially exciting is the prospect that upcoming all-sky surveys like the Rubin observatory could detect hundreds of TDEs per year (e.g., (33)).Even if only a fraction of them show early X-rays and quasi-periodic precession-like modulations, this could result in independent constraints on SMBH spin distribution in the local Universe.Archival Swift X-ray (0.3-1.0 keV) 3σ upper limit from prior to MJD 58274 is 3×10 −14 erg s −1 cm −2 (4×10 41 erg s −1 ).The first X-ray/XRT data point is a non-detection with a 3σ upper limit of 1.7×10 −13 erg s −1 cm −2 .(b) AT2020ocn's optical and UV evolution.All values are host-subtracted.All the other errorbars represent 1σ uncertainties.The data are provided as a supplementary file.b) and (c) show the precession period-spin relations for the upper-limit, best-fit and the lower-limit on the SMBH mass inferred from the M-σ * relation (section 2).Standard TDE parameters, i.e., a solar-like star with the resulting disk extending out to tidal radius, were assumed for these calculations.The shaded grey area captures the uncertainty arising from various disk density profiles.The green dashed horizontal line represents AT2020ocn's rest-frame period (15.9 days) and the green band reflects the uncertainty in the rest-frame period (15.9 +1.1 −2.2 days).For a given SMBH mass, the possible spin values are depicted by the orange-shaded area.The overall spin constraint for AT2020ocn's SMBH across all masses is 0.05 ≲ |a| ≲ 0.5 (see the Extended Data Table 1 for specific values).

X-ray data
NICER is comprised of 52 co-aligned detectors (Focal Plane Modules/FPMs).In any given GTI, some detectors may be "hot", i.e., optical light loading can make them behave anomalously.We identify such "hot" detectors on a per GTI basis by flagging FPMs whose 0.0-0.2keV count rate is more than 3σ above the sigma-clipped median value of all FPMs during that GTI (see (5,6) for more details).
Using the 3c50 background model (7), we first extracted the source and the background spectra on a per GTI basis by excluding the appropriate hot FPMs.We then computed the background-subtracted count rates (counts s −1 FPM −1 ).Because the source is "faint" as per (7), we also applied the so-called level-3 filtering as described in (7).The source was typically above the estimated background in the 0.3-1.0keV band.Therefore, we adopted this energy for the majority of our analysis in this paper.However, because both the source and the background are variable, in some GTIs, the background exceeded the source counts down to 0.6 keV.For those spectra, modeling was restricted to an appropriate value lower than 1 keV.
All spectra were binned using an optimal binning scheme of ( 8) to have at least 25 counts per spectral bin.This was done using the ftgrouppha task of HEASoft: https://heasarc.gsfc.nasa.gov/lheasoft/help/ftgrouppha.html.We performed spectral modeling in XSPEC (9) and Python version of XSPEC, PyXspec, using the χ 2 statistic.

XMM-Newton
XMM-Newton observed AT2020ocn on four occasions, two taken roughly a week after NICER started monitoring the source (2020 July 18 and 21) and the other two taken 1-2 years later.
Here we only use the data from EPIC-pn detector from the first two datasets with observation IDs: 0863650101 (XMM#1) and 0863650201 (XMM#2).We reduced the publicly available raw data using the standard epproc tool of XMM software xmmsas version 19.1.0with the latest calibration files.From these cleaned eventfiles we visually inspected the 10-12 keV count rates from the entire field of view to identify epochs of background flaring.GTIs were chosen to exclude these flaring windows.Using only the events that occurred during the GTIs, we extracted source spectra (corrected for pileup) by using annuli with inner radii of 5 ′′ and 10 ′′ for XMM#1 and XMM#2, respectively.The annuli were centered on optical coordinates: (13:53:53.803,+53:59:49.57)J2000.0 and had an outer radius of 20 ′′ .Background spectra were extracted using events from two nearby circular regions of 50 ′′ each.Finally, spectra were grouped using xmmsas tool specgroup to have a minimum of 1 count per spectral bin.

Swift
Swift started monitoring AT2020ocn on 2020 June 25 at a much lower cadence than NICER, roughly one visit every few days.There were also 14 archival observations with a total exposure of 12.3 ks prior to the outburst, i.e., between MJD 57255.452(2015 Aug 14) and MJD 58268.978(2018 May 30).Using the standard xrtpipeline tool we reduced all the X-Ray Telescope (XRT) observations taken prior to 2020 Nov 17. Source events were extracted from a circular aperture of 47.1 ′′ and background events were chosen from an annulus with an inner and outer radii of 70 ′′ and 210 ′′ , respectively.We only used events with grades 0-12 as recommended by the data analysis guide.Swift data was used for three reasons: 1) to estimate an upper limit on the X-ray flux prior to the outburst, 2) to fill-in NICER data gaps, and 3) to confirm that there are no contaminating sources within NICER's field of view of AT2020ocn (EDF 2).

Optical/UV Observations 1.2.1 Zwicky Transient Facility
AT2020ocn was discovered and reported by ZTF and released as a transient candidate ZTF18aakelin in the Transient Name Server (10).We performed point spread function (PSF) photometry on all publicly available ZTF data using the ZTF forced-photometry service (11) in gand r-band.
We report our photometry, corrected for Galactic extinction of A V = 0.0153 mag (12).

Swift/UVOT
We perform photometry on Swift/UVOT (13) observations of AT2020ocn with the uvotsource task in HEAsoft package v6.29 using a 5 ′′ aperture on the source position.Another nearby region of 40 ′′ free of any point sources was used to estimate the background emission.The host contribution was subtracted using a modeled spectral energy distribution (SED).Similar to ZTF data, UVOT photometry was corrected for Galactic extinction.

Black Hole Mass from Host Galaxy's Stellar Velocity Dispersion
AT2020ocn's host galaxy was observed by SDSS on 2008 Feb 12, i.e., ≈12 years before the flare occurred.No narrow emission lines are visible in the spectrum, indicating that the host is a quiescent galaxy.We divide the flux-calibrated spectrum by the median flux value to quasinormalize the spectrum.Then, we use the penalized pixel fitting routine (14) combined with the MILES single stellar population template library (15) to measure the velocity dispersion of the stellar absorption lines (σ * ).We conservatively mask the locations of prominent emission lines during this process (even though none are apparent).Following (16) we resample the spectrum within the errors and repeat the fitting procedure 1000 times, and take the mean and standard deviation as the velocity dispersion σ * and its uncertainty.We find σ * = 82±4 km s −1 , which translates into a black hole mass of log 10 (M) = 6.4±0.6 M ⊙ using the M-σ * relation of ( 17).
Here we have added the measurement uncertainty in quadrature with the systematic uncertainty in the M-σ * relation.

Estimating the Statistical Significance of the 15-d X-ray Flux Modulations
We employ the following procedure to estimate the global statistical significance of the 15-d quasi-periodicity seen in the X-ray light curve in Fig. 1a.The main steps are: 1. Estimate the nature of the continuum noise in the periodogram.
2. Simulate a large number of light curves that follow the above continuum variability.
3. Sample these simulated light curves exactly as the real/observed data.
4. Compute the Lomb Scargle Periodograms (LSPs) exactly as done on real data and from these estimate the likelihood of finding a quasi-periodic oscillation (QPO) as strong as the one found in real data with a wide range of coherence values.
We describe each of these steps in detail below.

Estimating the nature of the continuum in the periodogram
A quick visual inspection of the X-ray light curve (Fig. 1a) suggests that there are 7-8 prominent flares roughly 15 days apart (see vertical dashed lines in Fig. 1a to guide the eye).The second peak appears to be blended with the third one.These regular flares terminate beyond MJD 59171 as a corona is eventually formed and those observations are discussed in a separate paper.
We started our timing analysis by computing the LSP of the observed, background-subtracted 0.3-1.0keV X-ray light curve using all the data until MJD 59171.The LSP was computed exactly as described in (18) and normalized as per (19).As expected, there is a broad peak in the LSP around 15 days.There are also broad peaks in the LSP at integer harmonics, i.e., 2×15-d, 4×15-d and smaller peaks near 1 2 ×15-d and 1 4 ×15-d (Fig. 2).To assess the nature of the noise, i.e., the distribution of the power values within the LSP, we used the Kolmogorov-Smirnov and Anderson-Darling tests for white noise.To assess the nature of the LSP in the vicinity of ∼15-d, we used the power values that correspond to timescales longer than 3 days and excluded bins near 15-d, 2×15-d, and 4×15-d.Following the procedure outlined in section 2.2.2 of ( 6), both the Kolmogorov-Smirnov and Anderson-Darling tests suggest that the null hypothesis that these LSP powers (normalized by mean) below 3 days are white cannot be rejected at even the 90% confidence level (EDF 3).
The average of the power values corresponding to timescales longer than 3 days (excluding those near 15, 2×15 and 4×15-d) is elevated compared to the average value for shorter than 3 days.This could be due to two reasons: 1) the contribution from the wings of the broad peaks at 15-d and its harmonics, or 2) genuine red noise.Therefore, we compute the FAPs separately for both these cases.
Red noise is a common type of variability noise that is predicted from both general relativistic magnetohydrodynamic simulations (see, for example, ( 20)) and X-ray observations and is, in general, described analytically by a power-law or a bending powerlaw (21).We rebinned the LSP by a factor of 10 and fit it with a powerlaw + constant and a bending powerlaw + constant models.The former and the latter yielded a χ 2 /dof of 26/48 and 24/46, respectively.
It is known that the best-fit powerlaw index value inferred from modeling the LSP can be biased if the time series is unevenly sampled (22).To test whether the current sampling could have biased our estimate of the index we carried out the following tests.
First, using the algorithm of ( 23), we simulated 10,000 time series whose power spectrum is defined by the best-fit powerlaw + constant model of the real data, i.e., an index of unity and a normalization of 1.2×10 −6 .These time series had a resolution of 100 s.To account for red-noise leakage (22) we ensured each of these time series were 10 times longer than the observed baseline of ∼130 days.Then, we sampled each of these 10,000 time series exactly as the observed light curve and computed their LSPs.Then we rebinned them by a factor of 10-similar to the observed LSP-and fit them with a powerlaw + constant model.The bestfit powerlaw index values had a median and standard deviation of 0.93 and 0.07, respectively (EDF 4), i.e., consistent with the best-fit values shown in Fig. 2.This demonstrates that, for the current uneven sampling, the inferred power-law index from modeling the LSP does indeed represent the true shape of the underlying power spectrum.

Monte Carlo Simulations of Time Series
Based on the analysis in the above section we concluded that the underlying continuum can be described as white, a powerlaw or a bending-powerlaw/red noise.The goal in this section is to answer the following question: how often would we see a broad QPO-like feature as strong as the one seen in the observed LSP for each of these underlying noise continuum models.To address this question we use the following methodology for six continuum models: 1) white noise, 2) best-fit powerlaw red noise model corresponding to (index, normalization) = (1.0,1.2×10 −6 ), 3) red noise model corresponding to (index, normalization) = (best-fit index + 1σ error, corresponding normalization) = (1.3,1.0×10 −7 ), 4) a red noise model with (corresponding index, best-fit normalization + 1σ uncertainty) = (0.9, 5.6×10 −6 ), 5) a bending-powerlaw red noise model corresponding to the best-fit parameters, and 6) a bending-powerlaw noise corresponding to the best-fit normalization + 1σ uncertainty.
diskbb).In all the cases, the column density near the host (ztbabs) was pegged by the fit to 0. For each spectrum, we computed the evidence ratio as per the Akaike Information Criterion (AIC) for two disks with respect to a single disk model.If the evidence ratio was less than 10, we fixed the cool disk to a value of 0.062 keV and estimated the cool disk's luminosity.On the other hand, if the evidence ratio was greater than 10, the cool thermal component's temperature was allowed to be free (see Fig. 3).

X-ray flux variations are not driven by neutral column density changes near the TDE
To test whether the observed changes in X-rays are driven by changes in column density, we extracted higher count NICER spectra from near the peaks of the early time flares and compared them with spectra between the flares by letting the neutral column density be a free parameter.In all these cases, the best-fit column density of the host was again close to 0.
For instance, a composite NICER spectrum using data taken between MJDs 59073.lightcurves show evolution on ∼ 30 − 50 day timescales implies that the fallback time is on this order, which would be longer than the 15-day orbit of the star (which is presumably responsible for modulating the X-ray emission).It seems unreasonable for the fallback time to be longer than the orbital time of the star, rendering this scenario extremely unlikely.

Variability from discrete stream collisions
We can expect that some variability in the TDE accretion process comes from the dynamics of the returning debris stream.For example, the recurrent X-ray flares could, in principle, result from the infall of material onto the black hole from self-intersection shocks.In particular, recent simulations (29,30) have shown that the self-intersection of the debris stream from a deep TDE leads to a geometrically inflated, slowly evolving, quasi-spherical flow at large radii that can extend to 100's-1000's of gravitational radii.However, on small scales and very near the horizon of the black hole, where the ∼ keV emission would originate, (30) found that the flow and the accretion is modulated on timescales comparable to the freefall time from the selfintersection shock, as material dissipates energy and periodically falls to the black hole on this timescale.Geometrically it follows that the self-intersection radius r SI -assuming that the selfintersection arises from the general relativistic advance of periapsis -is related to the pericenter distance of the star r p via In this scenario, the material from the self-intersection shock would fall toward the black hole to form a small-scale disk.This disk could generate the higher temperature X-ray emission (i.e., the warmer component revealed by the X-ray analysis of AT2020ocn).The higher disk temperature, and thus additional pressure support, could inflate the disk to the point that it once again obscures our line of sight, resulting in the rapid shutoff of the X-ray emission.However, to make the above estimate of the pericentre distance that is required to generate the 17 d timescale commensurate with the tidal radius of a solar-like star requires the black hole mass to be ∼ 10 5 M ⊙ , which is smaller than that implied by the M − σ * scaling for AT2020ocn.
Another possibility is the variability induced from the stream colliding with the accretion disk.In the case that the disk is misaligned to the black hole spin and precessing, the radius at which the stream hits the disk varies with time.This, in turn, affects the accretion rate through the disk as the angle between the stream and disk angular momentum varies.This affect arises both through the radius at which mass is added to the disk, and through the amount of angular momentum cancellation that is caused by the addition of material with a roughly constant angular momentum direction to a disk with a time-varying angular momentum direction.As noted in the main text, these complications could plausibly explain the more erratic behavior of the X-ray lightcurve than can be explained by a precessing, planar disk, but we leave a detailed investigation of these features to future work.

Radiation-pressure instability
Inner portions of standard thin disks are unstable when dominated by radiation pressure (31).
This can eventually lead to quasi-periodic flares in the accretion rate explaining the behavior of some changing-look AGN.The model proposed by (32) consists of an inner advectiondominated hot flow, which is a stable optically-thin solution, and the outer standard thin disk, whose inner zone with the width of ∆R is radiation-pressure dominated and located on an un-stable branch in the accretion rate-surface density plane.The flares due to radiation-pressure instability recur on the timescale, τ flare , shorter than the standard viscous timescale at the distance R, i.e. τ flare = τ visc ∆R/R, where τ visc is the viscous timescale that depends on the distance R, the viscosity α parameter, and the flow scale-height H.The unstable zone forms for a relative (Eddington) accretion rate larger than ṁ ≳ 0.15(α/0.1) 41/29 (M/10 6 M ⊙ ) −1/29 (32), which can be achieved in AT2020ocn for M ≲ 10 6.7 M ⊙ .
As was shown by (33), via global time-dependent calculations without the assumption of the hot inner advection-dominated accretion flow (ADAF), the model can be fine-tuned enough, including corona and sufficiently strong magnetic field, to produce quasiperiodic flux changes by an order of magnitude on the timescale as short as ∼ 10 days, when the disk is small enough (like for TDEs) or interrupted by a gap.For the early phases of the TDE, we expect Eddington to super-Eddington accretion rates and in that case, the accretion disk is expected to be a geometrically thicker slim disk that is stabilized by advection.The radiation-pressure instability model is still applicable for a standard disk, and the advective terms are included in the calculations via radial derivatives of density and temperature (time-dependent numerical simulations tailored to AT2020ocn will be presented in a separate study).For AT2020ocn this is relevant if its SMBH is heavier, e.g. for M ∼ 10 7 M ⊙ , i.e., if the Eddington ratio is ṁ ∼ 0.1, so that the accretion disk can be of a standard type.The model is applicable as well for higher accretion rates.However, a challenge to the instability model is the fact that AT2020ocn's flares weaken after a few months (Fig. 1a).This can happen if the magnetic field gets sufficiently strong, e.g.due to dynamo effect, which tends to stabilize the disk (34).In that case we would expect the amplitude to gradually decrease with the magnetic field build-up.
with Ṁ / ṀEdd = 0.3), we can expect disk tearing to occur at a radius of ≈ 25R g with a period of ≈ 15 days.Thus it is possible that the variability observed in the X-ray lightcurve from AT2020ocn is due to either Lense-Thirring precession of a rigidly precessing and radially extended portion of the disk (as discussed in the main text) or Lense-Thirring precession of an unstable region of the disk that has broken into discrete rings.

Figure 1 :
Figure 1: AT2020ocn's multiwavelength evolution.(a) 0.3-1.0keV X-ray luminosity vs time since optical discovery.Gaps in NICER monitoring are filled by Swift data.The dashed/vertical lines are separated by 15 d to guide the eye.Archival Swift X-ray (0.3-1.0 keV) 3σ upper limit from prior to MJD 58274 is 3×10 −14 erg s −1 cm −2 (4×10 41 erg s −1 ).The first X-ray/XRT data point is a non-detection with a 3σ upper limit of 1.7×10 −13 erg s −1 cm −2 .(b) AT2020ocn's optical and UV evolution.All values are host-subtracted.All the other errorbars represent 1σ uncertainties.The data are provided as a supplementary file.

Figure 2 :
Figure 2: Lomb Scargle Periodogram of the observed 0.3-1.0keV NICER light curve.(a) The blue, dashed histogram represents the unbinned LSP while the red data points are the binned LSP excluding the peaks near 15 and 2×15 days.The solid blue and orange curves are the best-fit bending powerlaw + constant and powerlaw + constant models, respectively, used to characterize the noise continuum.(b) Unbinned periodogram (same as (a)) but the y-axis is shown on linear scale without overplotting the continuum for clarity.

Figure 3 :
Figure 3: AT2020ocn's X-ray spectral evolution.(a) Temperature evolution of the warm and the cool X-ray thermal components.When the cool component was not statistically required by the data, we froze its temperature to 0.062 keV and compute a 1σ upper limit on the cool component's flux.Logarithm of luminosity of the warm (b) and the cool components (c).All errorbars represent 90% uncertainties.

Figure 4 :
Figure 4: Spin constraints on AT2020ocn's SMBH based on the rigid-body Lense-Thirring precession model.Panels (a), (b) and (c) show the precession period-spin relations for the upper-limit, best-fit and the lower-limit on the SMBH mass inferred from the M-σ * relation (section 2).Standard TDE parameters, i.e., a solar-like star with the resulting disk extending out to tidal radius, were assumed for these calculations.The shaded grey area captures the uncertainty arising from various disk density profiles.The green dashed horizontal line represents AT2020ocn's rest-frame period (15.9 days) and the green band reflects the uncertainty in the rest-frame period (15.9 +1.1 −2.2 days).For a given SMBH mass, the possible spin values are depicted by the orange-shaded area.The overall spin constraint for AT2020ocn's SMBH across all masses is 0.05 ≲ |a| ≲ 0.5 (see the Extended Data Table1for specific values).

1. 1
.1 NICER NICER started monitoring AT2020ocn on 2020 July 11, roughly 10 weeks after ZTF discovered it on 29 April 2020 (MJD 58968.305)(4).NICER continues to monitor AT2020ocn on a daily cadence at the time of writing of this paper.However, for this work, we only consider data taken over the first ≈ 130 days, i.e., until 2020 November 17, when X-ray flares are prominent.

1 : 3 :Extended Data Figure 4 :
54 and 59074.45 had roughly 32,200 counts in the 0.3-1.0keV band.Modeling this spectrum with tbabs*ztbabs*zashift*(diskbb+diskbb) yielded a best-fit column of the ztbabs component to be close to 0. For comparison, the 0.3-1.0keV flux during this time was ∼3×10 −12 erg s −1 cm −2which is a factor of 6 and 4 higher compared to XMM#1 and XMM#2 epochs.Another example is a spectrum obtained using data between MJDs 59087.085and 59087.877which had about 21,650 counts.The source flux during this epoch was 3.5×10 −12 erg s −1 cm −2 and again the best-fit ztbabs column was close to 0. Based on these tests, we concluded that the observed changes in X-ray flux were not driven by changing neutral column near the TDE.SDSS host spectrum of AT2020ocn (black).Overlaid in orange is the best fit MILES model template obtained through pPXF fitting, broadened to a velocity dispersion of 82±4 km s −1 .No narrow emission lines are evident in the spectrum.Extended DataFigure 2: Swift/XRT 0.3-1.0keV image of NICER's FoV.The yellow circle with a radius of 47 ′′ and is centered on AT2020ocn's optical coordinates of 13:53:53.803,+53:59:49.57(J2000.0epoch).The outer cyan circle shows NICER/XTI's approximate field of view of 3.1 ′ radius.There are no contaminating sources within NICER's field of view.The north and east arrows are each 100 ′′ long.The colorbar shows the number of X-ray counts.White noise tests for the distribution of noise powers in the observed Lomb Scargle periodogram (LSP) using power values that correspond to timescales slower than 3 days and excluding bins near 15, 2×15 and 4×15 days.(a) Comparison of the cumulative distribution functions (CDFs) of the observed noise powers and the expected exponential distribution.The CDF of the observed LSP of the observed light curve is represented by the orange histogram, while the solid black line shows the CDF of white noise powers, which follows an exponential distribution.(b) Comparison of the probability density functions of the observed noise powers and the expected exponential distribution.The solid black line is the PDF of white noise distribution, whereas the shaded orange histogram represents the PDF of the observed noise powers in the LSP of the observed light curve.(c)Distribution of the Kolmogorov-Smirnov test statistic derived from simulations.(d) Distribution of the Anderson-Darling test statistic using simulations.In both (c) and (d), the solid red and the dashed black lines represent the median of the distribution and the observed value, respectively and the shaded blue regions indicate the ±1σ values of their respective distributions.The null hypothesis that the noise powers are exponentially distributed, i.e., consistent with white noise, cannot be rejected.0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1Check for powerlaw index bias due to uneven sampling.The distribution represents the powerlaw index values of the simulated LSPs with an input index of 1.0.

( f )Extended Data Figure 5 :
Continuum Model: Bending Powerlaw Red noise with best-fit normalization+1 Estimates of the global false alarm probability (FAP) of finding a broad peak in the simulated LSPs.Each panel is for a different underlying noise continuum: (a) white noise, (b) powerlaw red noise with best-fit powerlaw index, α best−f it , and normalization, Norm best−f it , (c) powerlaw red noise with best-fit powerlaw index + 1σ and its corresponding normalization, (d) powerlaw red noise best-fit normalization + 1σ and its corresponding powerlaw index, (e) bending powerlaw red noise with best-fit parameters, and (f) bending powerlaw red noise with best-fit normalization + 1σ and corresponding parameters.The dashed, vertical line in each panel represent the observed QPO at 15-days.Extended Data Figure7:A simplified schematic of a potential model showing Lense-Thirring precession of an inner disk.In the left precession phase a), view of the inner/warm disk is obstructed and, consequently, we would see lower luminosity and temperature.In the right panel b), the inner/warm disk is visible which leads to higher observed temperature and luminosity.Relative sizes are not to scale.slope M = 10 7 M ⊙ M = 10 6.4 M ⊙ M = 10

√ GM t ff 2 / 3 ,
)where M is the mass of the black hole.If we associate 15 d with the freefall time t ff from the self-intersection shock, then r SI ≃ and letting M = 10 6 M ⊙ , Equation (S2) yields a pericenter distance of r p ≃ 200GM/c 2 .This distance is a factor of a few larger than the classical tidal disruption radius of a solar-like star by a 10 6 M ⊙ black hole, and the self-intersection radius is r SI ≃ 4400GM/c 2 , i.e., highly spatially extended compared to a geometrically thin disk at the tidal radius.

Table 1 :
Summary of spin constraints for AT2020ocn SMBH for different surface-density slopes of the precessing accretion flow and the range of SMBH masses.The negative spin values in parentheses correspond to the retrograde spin.The outer radius of the precessing disk is fixed at the corresponding tidal radius for a Sun-like star.For the radial surface-density profile, we use the prescription Σ ∝ R −s .The last line summarizes the spin interval for a given SMBH mass.