Viscously Spreading Accretion Disks around Black Holes: Implications for TDEs, LFBOTs and other Transients

TL;DR

This paper develops a time-dependent, 1D thin-disk model for viscously spreading accretion disks around black holes across $M_ullet=10$--$10^8\,M_\odot$, incorporating non-conservation during disk formation, super-Eddington outflows, outer-disk irradiation, and multiple viscous-stress prescriptions. Applying the model to TDEs and LFBOTs, it shows that late-time optical/UV plateaus can arise from disks with large initial angular-momentum spreads or from slow viscous spreading, and that thermally unstable gas-pressure disks are inconsistent with observed luminosities, favoring magnetically dominated disks. Irradiation of warped outer disks and misalignment between stellar orbits and BH spin can enhance plateau luminosities and durations by factors of a few. For AT2018cow, the results favor stellar-mass BHs ($\sim 10$--$10^2\,M_\odot$) with substantial super-Eddington outflows, predicting eventual recoverable X-ray emission and a possible near-IR break detectable by JWST, thereby offering a path to constrain disk formation, warps, and angular-momentum transport. The framework provides a versatile tool to probe outer-disk thermodynamics and the late-time behavior of a broad class of transient accretion-powered phenomena.

Abstract

We present a simple time-dependent model of viscously spreading accretion disks around black holes (BHs) with masses between $10-10^8M_\odot$. We apply the results to observations of late-time emission in tidal disruption events (TDEs) and luminous fast blue optical transients (LFBOT) such as AT2018cow. Our model generalizes previous work by incorporating outflows during super-Eddington accretion, non-conservation of mass and angular momentum in TDE circularization, irradiation of the outer disk by the inner accretion flow, and a range of viscous stress models. We show that many late-time plateaus in TDEs can be explained by disks formed with a large spread in angular momentum due to redistribution during circularization. Viscous spreading on year timescales is not required, although it is also compatible with the data. The collapse of radiation pressure dominated thin disks to the stable gas-pressure dominated phase greatly underpredicts TDE plateau luminosities, strongly favoring thermally stable magnetically dominated disk models. Irradiation of the outer disk in TDEs due to misalignment of the stellar orbit and black hole spin increases plateau luminosities and durations by factors of a few. Continued study of late-time TDE emission provides a unique opportunity to constrain the physics of disk formation and circularization, disk warps, angular momentum transport, and other poorly understood aspects of disk physics. The models we develop can also explain the late-time optical-UV emission in the LFBOT AT2018cow for BH masses of ~$10-100M_\odot$. The faint X-ray emission at late times in AT2018cow is likely due to ongoing absorption. Our models predict that late-time X-rays should eventually be detectable again, and that HST/JWST observations of AT2018cow may detect a break in the SED at near-IR-optical wavelengths, providing a powerful probe of outer accretion disk thermodynamics.

Figures (10)

• Figure 1: Full radial, time-dependent evolution of a magnetized disk. Top two panels show the evolution of the disk mass $M_d$ and disk radius $R_d$ respectively, where we have included results obtained using the 1-zone model for comparison purposes. The initial disk mass and radius are set to $M_{d,0}=0.07M_\odot$ (see equation (\ref{['eq:Md0']}) in §\ref{['subsubsec:superedd outflows']}) and $R_{d,0}=2r_t$. Bottom panel shows the temporal evolution of the surface density profile up to $t=500$ years, with the initial state shown with a dot-dashed line.
• Figure 2: Initial luminosities of disks prior to viscous spreading with $R_{d,0}=2r_t$ and $R_{d,0}=10r_t$, for different $M_\bullet$ and $\alpha(H/R)^2$ combinations. All models have disk mass set by equation (\ref{['eq:Md0']}). For reference, a fiducial model with $M_\bullet=10^6M_\odot$ and $\alpha=0.01$ gives $(H/R)_g\sim0.003$ and $(H/R)_\mathrm{mag}\sim0.06$ for a gas and magnetic pressure supported disk, respectively. Black contours show a few reference luminosities, while red contours represent inferred values of plateau luminosities for several observed TDEs from mummery_fundamental_2023. We include in white dashed lines the viscous timescale $t_\mathrm{visc}(R_{d,0})$. Many of the observed late-time TDE luminosities fall within the parameter space of non-spreading disks with long viscous timescales, which suggests that they can be explained by disks that form with a large spread of angular momentum.
• Figure 3: SEDs (top panel) and surface density profiles (bottom panel) at different times for a model with $M_\bullet=10^6M_\odot$, $M_{d,0}=0.07M_\odot$ and $\alpha(H/R)^2=10^{-5}$, with initial radii $R_{d,0}=2r_t$ (purple) and $R_{d,0}=10r_t$ (orange). The vertical dotted line marks $\nu=6\times10^{14}$Hz for reference. For different initial disk radii, the initial SEDs (solid lines) differ considerably in where the Rayleigh-Jeans break occurs, which can be used to determine the initial structure of the disk and identify whether it is in fact viscously spreading; in practice this will be non-trivial given that the key differences are in the far UV. At later times, once the disk has spread significantly, the SEDs and surface density profiles are relatively independent of the initial profile.
• Figure 4: Optical light curves for different TDE models with initial disk mass set by equation (\ref{['eq:Md0']}), and fiducial initial radius of $R_{d,0}=2r_t$. Observed data for the events AT2019qiz, AT2020wey, AT2020ocn and AT2021ehb are plotted for comparison purposes. The shaded region covers the range of inferred luminosity plateau values obtained by mummery_fundamental_2023 over the times the observations were made ($\sim 1-10$yr), which overlaps with the plateaus for our more luminous models.
• Figure 5: Optical light curves for different disk models varying BH mass, initial disk mass, initial disk radius and $\alpha$. The left panel shows models for magnetized disk, while the right panel shows gas pressure supported disks. The fiducial model represents a disk with $M_\bullet=10^6M_\odot$, $R_{d,0}=2r_t$ and $\alpha=0.01$. All models have an initial disk mass calculated according to equation (\ref{['eq:Md0']}) except when $M_{d,0}$ is specified. Magnetized disks produce overall higher luminosities than gas pressure supported disks, which can be further increased by having larger $M_\bullet$, $\alpha$, $M_{d,0}$, or by increasing $R_{d,0}$ as long as the optical-UV emission is still the Rayleigh-Jeans tail i.e. $k_BT_{\rm eff}(R_{d,0})\sim h\nu$. Collapse of an unstable radiation pressure supported disk to the gas pressure supported branch produces optical luminosities much fainter than observed (right panel), favoring magnetically supported disk models.