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

This paper presents a generalized time-dependent model of viscously spreading accretion disks around black holes that incorporates outflows, non-conservative circularization, and irradiation effects to explain late-time emission plateaus in tidal disruption events and the optical-UV behavior of luminous fast blue optical transients like AT2018cow, while favoring thermally stable, magnetically dominated disk models over radiation-pressure dominated ones.

Original authors: Mila Winter-Granic, Eliot Quataert

Published 2026-07-23

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CC BY 4.0

Original authors: Mila Winter-Granic, Eliot Quataert

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a cosmic kitchen where gravity is the ultimate chef, whipping up spectacular storms of gas and dust. When a star wanders too close to a black hole—a region of space so dense that not even light can escape its grasp—the star gets ripped apart by tidal forces, like a piece of dough stretched too thin. This event, known as a Tidal Disruption Event (TDE), creates a swirling, glowing disk of debris that spirals inward, heating up and shining brightly across the universe. But here's the mystery: while we can see the initial flash, the behavior of this cosmic dough after the first few years is a bit of a puzzle. Does the disk spread out slowly like butter melting on toast? Does it stay put? And what happens when the black hole eats so fast that it chokes and spits out material in powerful winds? Understanding these late-time behaviors is crucial because they act as a unique laboratory, letting us weigh the invisible black holes hiding in the centers of galaxies and test the laws of physics under extreme conditions.

In this paper, the authors build a new, flexible "recipe" to simulate how these accretion disks evolve over time, specifically looking at what happens years after the initial disaster. They take the standard model of a spinning disk and add several new ingredients that previous models often ignored: the possibility that the disk loses mass and spin due to powerful winds (outflows) when it's eating too fast, the idea that the inner part of the disk might shine a spotlight on the outer part (irradiation), and the fact that the disk might not be a simple, flat pancake but could be warped and twisted.

The authors run these simulations to see if they can explain two types of cosmic fireworks: the long-lasting "plateaus" of light seen in TDEs and the strange, fading afterglows of objects called Luminous Fast Blue Optical Transients (LFBOTs), like the famous AT2018cow.

Here is what they find:

1. The "Spreading" Mystery Solved (Sort Of)
For a long time, scientists thought the long, steady glow (the plateau) seen in TDEs years later was caused by the disk slowly spreading out over time, like a drop of ink diffusing in water. The authors' simulations show that this can happen, but it's not the only explanation. They discover that if the disk forms with a huge spread of angular momentum—meaning the debris is already scattered far out from the start—it can stay bright for years without needing to spread much at all. It's like having a giant, pre-spread blanket that stays warm without needing to be unfolded further. This suggests that many of the observed plateaus might be disks that formed with a wide initial spread, rather than disks that are slowly spreading out over years.

2. The "Unstable" Disk is Out, The "Magnetic" Disk is In
The paper explicitly rules out a popular idea: that these disks are dominated by radiation pressure (the pressure of light itself). Standard physics suggests that if a disk is dominated by radiation pressure, it should be unstable and collapse into a much dimmer state. However, the observed TDEs are far too bright for this to be true. The authors argue that the only way to keep these disks stable and bright is if they are supported by strong magnetic fields. Think of it as the disk being held up by invisible magnetic scaffolding rather than just the pressure of hot gas or light. This magnetic support keeps the disk stable and thermally consistent with what we see.

3. The "Spotlight" Effect
The authors also show that if the inner disk is tilted relative to the outer disk (which is likely because the star's orbit and the black hole's spin don't line up), the inner disk can act like a spotlight, shining light onto the outer disk. This "irradiation" heats up the outer edges, making them brighter and keeping the plateau glowing for a few years longer than it would otherwise. It's like a cosmic lighthouse keeping the outer rim of the disk warm.

4. The Case of AT2018cow
The paper also tackles the mystery of AT2018cow, a transient that looked like a star being eaten by a black hole but was much fainter in X-rays than expected. The authors suggest this event was likely a star merging with a smaller black hole (about 10 to 100 times the mass of our Sun). Their model shows that if the black hole is eating too fast, it blows away most of the material in powerful winds before it can form a thick disk. This explains why the object is bright in visible light (from the outer disk) but faint in X-rays (from the inner region). They suspect the X-rays are being absorbed and reprocessed by the winds, turning high-energy X-rays into lower-energy visible light.

5. What's Next?
The authors predict that if we wait long enough, the winds around these objects will thin out, and we should eventually see the hidden X-rays from the center, shining at a level of roughly $10^{39}$ to $10^{40}$ erg s $^{-1}$ . They also suggest that future telescopes like the James Webb Space Telescope (JWST) could spot a specific "break" in the light spectrum of AT2018cow, which would act as a fingerprint confirming the presence of a low-mass black hole and helping us understand the thermodynamics of the outer disk.

In short, this paper doesn't just offer one single answer; it provides a toolkit of scenarios. It tells us that the universe is messy: disks can form with wide spreads, they can be held up by magnetic fields, and they can be lit up by their own inner cores. By accounting for these complex, real-world effects, the authors offer a much better explanation for why these cosmic events shine the way they do years after the initial explosion.

Technical Summary: Viscously Spreading Accretion Disks Around Black Holes: Implications for TDEs, LFBOTs and Other Transients

Problem Statement
Tidal Disruption Events (TDEs) and Luminous Fast Blue Optical Transients (LFBOTs), such as AT2018cow, provide unique laboratories for studying accretion physics around black holes (BHs). While early-time emission in these events remains theoretically uncertain due to complex circularization processes, late-time emission is often interpreted as originating from a viscously spreading, geometrically thin, optically thick accretion disk. However, standard models face several challenges:

Instabilities: Standard radiation-pressure dominated Shakura-Sunyaev disks are thermally and viscously unstable, predicting limit-cycle behavior or collapse to gas-pressure dominated states that underpredict observed plateau luminosities by orders of magnitude.
Initial Conditions: The assumption that TDE disks form with a mass of $\sim 0.5 M_*$ and specific angular momentum equal to the disrupted star is not well-motivated. Simulations suggest significant angular momentum redistribution and mass loss via super-Eddington outflows during circularization.
Geometry and Irradiation: Parabolic TDEs involve stars on orbits uncorrelated with the BH spin, leading to misaligned disks. The Bardeen-Petterson effect aligns the inner disk with the BH spin, potentially causing the inner disk to irradiate a warped outer disk, altering thermal properties.
LFBOT Discrepancies: For LFBOTs like AT2018cow, standard thin-disk extrapolations to X-rays overpredict emission, creating tension with observed faint X-ray limits.

Methodology
The authors develop a simple, time-dependent 1D model of viscously spreading accretion disks around BHs with masses ranging from $10$ to $10^8 M_\odot$ . The model generalizes previous work by incorporating several physical ingredients often neglected in simplified analyses:

Viscous Stress Prescriptions: The model compares standard gas-pressure dominated disks ( $\nu \propto \alpha c_s H$ ) with magnetically dominated disks ( $\nu \propto \alpha v_A H$ ), where the latter assumes MRI suppression when the Alfvén speed exceeds a critical threshold, potentially stabilizing the disk against radiation pressure instabilities.
Mass and Angular Momentum Loss: The model includes source and sink terms for mass ( $\dot{\Sigma}_{fb}$ and $\dot{\Sigma}_{out}$ ) to account for fallback and super-Eddington outflows. For super-Eddington phases, a parameterized outflow model (following Blandford & Begelman 1999) is used, where only a fraction of material accretes while the rest is lost to winds.
Irradiation: A heating term is added to the outer disk flux to account for irradiation by the inner disk, assuming a misalignment between the outer disk (set by the stellar orbit) and the inner disk (aligned with the BH spin via the Bardeen-Petterson effect).
Numerical Implementation: The authors employ both a full radial, time-dependent solution to the disk diffusion equation and a simplified "one-zone" model. The one-zone model approximates the disk as a ring at radius $R_d$ containing mass $M_d$ and angular momentum $J_d$ , allowing for efficient exploration of parameter spaces involving outflows.

Key Contributions and Results

TDE Plateaus and Disk Spreading:
- The authors demonstrate that many late-time optical/UV plateaus in TDEs can be explained by disks that form with a large initial spread in angular momentum (large initial radii, $R_{d,0} \gg 2r_t$ ).
- Contrary to the requirement for active viscous spreading on year timescales to match observations, the data is consistent with "non-spreading" disks where the viscous time is long. The Rayleigh-Jeans tail luminosity depends weakly on viscous time ( $\propto t_{visc}^{-1/4}$ ), meaning disks with large initial radii can maintain high luminosities without significant evolution.
- However, the wide range of observed peak X-ray luminosities suggests a corresponding range of viscous timescales, implying that some systems are indeed undergoing significant spreading.
Thermal Stability and Magnetic Support:
- The collapse of radiation-pressure dominated thin disks to the gas-pressure dominated branch predicts plateau luminosities orders of magnitude lower than observed.
- The results strongly favor thermally stable, magnetically dominated disk models. These models naturally produce the observed luminosities without requiring thermal instability cycles.
Role of Irradiation:
- Irradiation of the outer warped disk by the inner aligned disk increases plateau luminosities and durations by factors of a few. This effect is significant if the disk misalignment persists into the thin-disk phase.
LFBOTs and AT2018cow:
- Applying the model to LFBOTs (specifically stellar mergers with stellar-mass BHs), the authors find that super-Eddington outflows are critical, removing $\gtrsim 3/4$ of the disk mass and angular momentum before the outer disk becomes sub-Eddington.
- Models favoring BH masses of $\sim 10 - 100 M_\odot$ and stellar companions of $1 - 30 M_\odot$ can reproduce the late-time optical/UV emission of AT2018cow.
- X-ray Absorption: The faint late-time X-ray emission in AT2018cow is not necessarily a failure of the model but likely due to ongoing X-ray absorption by outflows from the outer disk. The ionization parameter of the surrounding gas is low enough ( $\xi \ll \xi_c$ ) to allow efficient absorption and reprocessing of X-rays into UV/optical wavelengths.
- The models predict that late-time X-rays ( $\sim 10^{39-40}$ erg s $^{-1}$ ) should eventually become detectable as the ionization parameter increases over decades.

Significance and Claims
The paper claims that continued study of late-time TDE and LFBOT emission offers a unique opportunity to constrain poorly understood aspects of disk physics, including:

Disk Formation and Circularization: The initial spread in angular momentum and mass retention during the super-Eddington phase.
Angular Momentum Transport: The viability of magnetically supported, stable disk models over standard gas-pressure models.
Disk Warps and Irradiation: The persistence of misalignment and its impact on thermal structure.
BH Mass Function: The potential to use late-time plateaus to constrain BH masses, provided the uncertainties in disk physics are better understood.

For LFBOTs, the work suggests that the origin of AT2018cow is likely a stellar-mass BH merger, with the observed spectral energy distribution (SED) shaped by the interplay of a thin outer disk and reprocessed super-Eddington outflows. The authors propose that future HST and JWST observations could detect a break in the SED at near-IR-optical wavelengths, serving as a powerful probe of the outer accretion disk thermodynamics.

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