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Accretion disks in (repeating) partial tidal disruption events: rapid state transitions, UV plateaus and flares from disk-remnant collisions

This paper argues that rapid state transitions in repeating partial tidal disruption events are driven by reduced fuel supply leading to a universal Eddington ratio threshold of ~0.01, while explaining that late-time UV plateaus remain unaffected and predicting short-lived, potentially observable X-ray flares from collisions between the stellar remnant and the accretion disk.

Original authors: Andrew Mummery

Published 2026-02-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Andrew Mummery

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

The Big Picture: The Cosmic "Partial" Meal

Imagine a supermassive black hole as a giant, hungry vacuum cleaner floating in the center of a galaxy. Usually, if a star gets too close, the black hole's gravity rips the star apart completely. This is a Full Tidal Disruption Event (TDE). It's like the vacuum cleaner sucking up an entire apple in one go. The debris forms a swirling disk of hot gas that glows brightly for a long time before fading away slowly over years.

But sometimes, the star doesn't get close enough to be eaten whole. It just gets a little "nibble." A small piece of the star is stripped away, but the rest of the star survives and flies back out into space. This is a Partial TDE.

The star is like a cookie that got a bite taken out of it. The cookie survives, but it's now on a new path that will bring it back to the black hole again and again, getting a few more bites every time.

The Main Discovery: The "Fast-Forward" Switch

The author of this paper, Andrew Mummery, noticed something strange about these "nibble" events (Partial TDEs) compared to the "whole meal" events (Full TDEs).

Full TDEs (The Whole Apple): The black hole eats the whole star. The resulting glow is bright and stable for a long time (thousands of days), slowly fading like a candle burning down.
Partial TDEs (The Nibbled Cookie): These events are much more dramatic and unstable. They start bright, but then they suddenly switch off or change color very quickly (in just a few hundred days).

The Analogy: Think of a Full TDE as a large log fire. It burns steadily for a long time. A Partial TDE is like a small pile of dry twigs. It flares up quickly, but because there is so little fuel, it burns out or changes state very fast.

Why Does This Happen? (The Fuel Tank Theory)

The paper argues that the reason Partial TDEs change so fast is simple: They run out of fuel.

When a star is only partially disrupted, the black hole gets a much smaller amount of "food" (gas) to feed its accretion disk.

In a Full TDE, the disk is full of gas, so it can stay bright and "soft" (thermal) for a long time.
In a Partial TDE, the fuel tank is nearly empty. As soon as the gas runs low, the disk undergoes a state transition. It switches from a bright, thermal state (like a glowing stove) to a dim, "hard" state (like a flickering, hot ember), and eventually goes dark.

The paper calculates that this switch happens when the black hole is eating at about 1% of its maximum capacity. Because Partial TDEs have less fuel, they hit this 1% limit much faster than Full TDEs do.

The "Plateau" Surprise: A Bright Spot in the Dark

One of the most interesting findings is about the UV Plateau.

After the initial flash of light, TDEs often settle into a "plateau"—a phase where the brightness stays roughly the same for a year or so. This light comes from the outer edges of the disk.

The author was surprised to find that even though Partial TDEs have much less fuel, their UV plateau brightness is almost the same as Full TDEs.

Why? It's a cosmic balancing act.
- Factor A: Less fuel means the disk is cooler (which should make it dimmer).
- Factor B: But because the star wasn't ripped apart as violently, the disk spreads out wider (which makes it brighter).
- Result: These two effects cancel each other out! So, even a "nibbled" star can produce a UV glow that looks just as bright as a "whole" star, at least for a while.

This is great news for astronomers because it means they can still use the brightness of these UV glows to measure the mass of the black hole, even if the event was only a partial disruption.

The "Remnant Collision": A Short-Lived Spark

Finally, the paper asks: What happens when the surviving piece of the star (the remnant) comes back for its second "bite"?

It has to crash through the disk of gas left behind from the first time. This is like a car driving through a puddle of mud.

The Event: The collision creates a shockwave, heating up the gas and creating a bright flare of X-rays.
The Catch: This flare is incredibly fast. It lasts only 10 minutes to an hour.
The Verdict: It's like trying to photograph a firefly blinking in the dark with a camera that takes a 10-second exposure. Unless you have incredibly good timing and luck, you will likely miss it. The paper concludes that while these flares are theoretically bright, they are probably too short to be seen by current telescopes.

Summary of Key Takeaways

Partial TDEs are the "Fast Food" of the universe: They have less fuel, so they burn out and change states much faster than full disruptions.
The 1% Rule: All TDEs (and even black hole binaries) seem to switch from a bright state to a dim state when they drop to about 1% of their maximum eating speed.
The UV Trick: Even with less fuel, the "afterglow" (UV plateau) of a partial disruption looks surprisingly similar to a full one, helping astronomers measure black hole masses accurately.
The Missed Flare: When the surviving star hits the gas disk on its return trip, it creates a bright flash, but it's so short (less than an hour) that catching it is extremely difficult.

In short, this paper explains why some black hole "meals" are quick, dramatic, and fleeting, while others are long, steady, and slow-fading, and why the leftovers from a partial meal can still tell us a lot about the black hole itself.

1. Problem Statement

Tidal Disruption Events (TDEs) occur when a star is disrupted by a supermassive black hole (SMBH). While full disruptions destroy the star completely, partial TDEs occur when the star passes close to, but outside, the tidal radius, stripping a fraction of its mass while leaving a bound stellar remnant. These remnants can return to pericenter on timescales of months to years, leading to repeating TDEs.

A key observational puzzle is that known repeating partial TDEs (e.g., AT2018fyk, eRASSt J045650.3-203750) exhibit rapid X-ray state transitions (from thermal/soft to non-thermal/hard, followed by dimming to quiescence) on timescales of $\sim 100$ days. In contrast, full TDEs often remain in a soft state for thousands of days. The paper aims to:

Explain the physical mechanism behind these rapid transitions in partial TDEs compared to full TDEs.
Determine if the late-time UV plateau luminosity (used to estimate black hole mass) is affected by the reduced fuel supply in partial TDEs.
Assess the observability of X-ray flares generated by collisions between the returning stellar remnant and the accretion disk.

2. Methodology

The author employs a combination of analytical scaling arguments and numerical simulations using the FitTeD code (a time-dependent relativistic accretion disk solver).

Analytical Framework:
- Mass Fallback: The paper defines the stripped mass ( $M_{fb}$ ) as a function of the impact parameter $\beta$ (ratio of tidal radius to pericenter distance). For partial TDEs ( $\beta < \beta_c$ ), $M_{fb} \propto (\beta/\beta_c)^q M_\star$ , where $q \approx 3$ based on hydrodynamic simulations.
- Disk Evolution: The surface density $\Sigma$ and accretion rate $\dot{M}$ are modeled using time-dependent thin-disk theory. The evolution depends on the viscous timescale $t_{visc}$ and the initial disk mass.
- State Transitions: The paper assumes TDE disks behave like scaled-up X-ray binaries (XRBs), undergoing state transitions at specific Eddington ratios ( $f_{Edd} = L_{bol}/L_{Edd}$ ). The transition to a hard state is assumed to occur at $f_{tr} \sim 0.01$ , and to quiescence at $f_Q \sim 10^{-3}$ .
- Scaling Laws: The author derives scaling relations for the time to reach a specific Eddington ratio ( $t_{tr}$ ) and the late-time UV plateau luminosity ( $L_{plat}$ ) as functions of $\beta$ , black hole mass ( $M_\bullet$ ), and stellar mass ( $M_\star$ ).
Numerical Simulations:
- The FitTeD code solves relativistic disk equations for various $\beta$ values (ranging from partial to full disruptions).
- Parameters include $M_\bullet = 10^6 M_\odot$ , $M_\star = 0.8 M_\odot$ , and a turbulent viscosity parameter $V \sim 1000$ .
- Simulations track X-ray luminosity ($0.3-10$ keV), bolometric luminosity, and UV luminosity over time.
Case Study: The framework is tested against the well-observed repeating partial TDE AT2018fyk.
Collision Modeling: The paper models the collision between the returning remnant and the pre-existing disk using shock-heating physics (following Linial & Metzger 2023) to estimate flare luminosity, duration, and temperature.

3. Key Contributions and Results

A. Rapid State Transitions in Partial TDEs

The paper demonstrates that the rapid state transitions in partial TDEs are a direct consequence of the reduced fuel supply (lower disk mass) compared to full disruptions.

Scaling: The time to reach the hard-state transition ( $t_{tr}$ ) scales strongly with the impact parameter: $t_{tr} \propto \beta^{9/4}$ (for canonical parameters).
Result: For a partial TDE with $\beta/\beta_c \approx 0.5$ , the disk mass is significantly lower, causing the Eddington ratio to drop to the critical $f_{tr} \sim 0.01$ in just $\sim 100-400$ days.
Contrast: Full disruptions ( $\beta \ge \beta_c$ ) have much larger disk masses and remain in the soft state for $\sim 1000$ days or more.
Implication: This supports the paradigm that TDE disks are large-scale analogues of XRBs, undergoing universal state transitions at fixed Eddington ratios.

B. Late-Time UV Plateau Luminosity

A critical question is whether the reduced mass in partial TDEs invalidates the scaling relations used to estimate SMBH masses from UV plateaus.

Result: The late-time UV plateau luminosity ( $L_{plat}$ ) shows a weak dependence on $\beta$ ( $L_{plat} \propto \beta^{7/40}$ ).
Mechanism: While the reduced disk mass lowers the temperature (reducing flux), the partial disruption results in a larger circularization radius (increasing the emitting area). These effects largely cancel out.
Significance: The scaling relationship $L_{plat} \propto M_\bullet^{2/3}$ , calibrated on full TDEs, remains valid for partial TDEs, provided the observation occurs before the disk transitions to a hard state (typically within $\sim 1-2$ years).

C. Disk-Remnant Collision Flares

The paper investigates the observability of flares produced when the stellar remnant returns and collides with the disk formed from the previous passage.

Physics: The collision shock-heats gas, producing a flare. The kinetic energy is set by the star's binding energy, independent of the black hole mass.
Predictions:
- Luminosity: $L_{flare} \sim 10^{42}$ erg/s.
- Duration: Extremely short, $t_{flare} \sim 0.1 - 1$ hour.
- Temperature: $kT_{obs} \sim 100$ eV (Soft X-rays).
Observability: Despite the high luminosity, these flares are unlikely to be detected due to their extremely short duration relative to the return timescale (months/years) and the difficulty of catching such brief events.

D. Case Study: AT2018fyk

The model successfully reproduces the light curve of AT2018fyk:

Predicts the initial soft-to-hard transition at $\sim 100$ days.
Predicts the transition to quiescence at $\sim 600$ days (consistent with the observed factor of 10 drop in Eddington ratio).
Explains the re-brightening and subsequent transitions as a result of the remnant returning and replenishing the disk, with the peak Eddington ratio of the second flare being just above the transition threshold.

4. Significance and Future Directions

Unified Paradigm: The work solidifies the connection between TDEs and X-ray binaries, suggesting that all TDEs undergo state transitions at $f_{Edd} \sim 0.01$ , but the timescale of this transition is dictated by the initial mass supply (partial vs. full).
Mass Estimation: It validates the use of UV plateau luminosity to estimate black hole masses in partial TDEs, removing a potential systematic uncertainty in TDE demographics.
Observational Strategy:
- Radio Emission: Since partial TDEs transition to the hard state (and potentially launch jets) much faster than full TDEs, they are prime targets for radio follow-up campaigns, which often miss full TDEs that stay in the soft state too long.
- Flare Detection: While disk-remnant collisions are theoretically bright, their short duration makes them difficult targets; however, they remain a potential signature for high-cadence X-ray monitoring.

In summary, Mummery provides a robust theoretical framework explaining the unique, rapid evolutionary behavior of repeating partial TDEs, confirming that their differences from full TDEs are driven by fuel supply limitations rather than fundamental differences in accretion physics.