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Mass Transfer in Tidally Heated Stars Orbiting Massive Black Holes and Implications for Repeating Nuclear Transients

This paper demonstrates that tidal heating in stars orbiting supermassive black holes can drive stable mass transfer rates sufficient to power low-luminosity active galactic nuclei and explain repeating nuclear transients, with the stability of this process critically dependent on how tidal energy dissipation alters the star's internal convective structure.

Original authors: Philippe Z. Yao, Eliot Quataert

Published 2026-06-26

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CC BY 4.0

Original authors: Philippe Z. Yao, 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

The Big Picture: A Star Dancing Too Close to a Monster

Imagine a star (like our Sun) orbiting a supermassive black hole (a cosmic monster with gravity so strong it eats light). Usually, if a star gets too close, the black hole's gravity rips it apart in a violent event called a "Tidal Disruption Event" (TDE). Think of this like a cookie crumbling into dust when you squeeze it too hard.

However, this paper explores a different, more subtle scenario. What if the star gets close enough to feel the black hole's grip, but not close enough to be ripped apart immediately? Instead of being torn apart instantly, the star starts to heat up from the friction of the black hole's gravity tugging on it.

The Core Discovery: Heating Up Before Breaking

The authors (Philippe Yao and Eliot Quataert) used computer models to see what happens when this "tidal heating" occurs. They found a surprising result:

The star doesn't just sit there; it swells up like a balloon.

Because the black hole is constantly tugging on the star, energy is pumped into the star's interior. This energy makes the star expand. Eventually, the star gets so big that its outer layers start spilling over onto the black hole. This is called mass transfer.

The "Leaky Faucet" vs. The "Firehose"

In most cases where stars orbit black holes, scientists thought the rate at which the star loses mass is determined by how fast the orbit shrinks due to gravitational waves (like a slow leak in a tire).

But this paper argues that for stars near black holes, the heating is the real driver.

The Old View: The orbit shrinks slowly, and the star leaks mass slowly over millions of years.
The New View: The tidal heating acts like a blowtorch. It inflates the star quickly, causing it to pour mass onto the black hole at a much faster rate (a "firehose" rather than a leak).

This "firehose" phase is intense but short-lived, lasting only thousands of years instead of millions.

The Critical Twist: Where the Heat Goes Matters

The paper makes a crucial distinction about where this heat is deposited inside the star, which determines if the mass transfer is stable or chaotic.

Think of the star as a house with two types of rooms:

Radiative Rooms (The Library): Quiet, orderly, and stable.
Convective Rooms (The Dance Floor): Chaotic, swirling, and unstable.

Scenario A (The Dance Floor): If the tidal heat is dumped deep in the center of the star, it turns the core into a "dance floor" (convection). The star becomes unstable. As it loses mass, it expands more, which makes it lose mass even faster. This is a runaway effect—a "firehose" that quickly runs out of water. The star is destroyed quickly.
Scenario B (The Library): If the heat is spread out evenly throughout the star, it actually keeps the outer layers quiet and orderly (radiative). In this case, as the star loses mass, it shrinks slightly or stays stable. This allows for a stable mass transfer, where the star feeds the black hole steadily for a while without exploding immediately.

What Does This Mean for the Universe?

The authors suggest this process could explain some of the mysterious, repeating flashes of light we see coming from the centers of galaxies (called Repeating Nuclear Transients).

Low-Luminosity Active Galaxies: The steady "leak" of mass from a heated star could power dim, long-lasting active galactic nuclei (AGN).
Repeating Flares: The chaotic "runaway" events could look like the repeating X-ray flares (QPEs) or partial tidal disruption events (pTDEs) that astronomers have recently spotted, such as ASASSN-14ko or GSN 069.

The Bottom Line

The paper concludes that tidal heating is a powerful force that can inflate stars and cause them to feed black holes much faster and more dramatically than previously thought.

If the heat is concentrated in the center: The star goes unstable and is destroyed quickly.
If the heat is spread out: The star can feed the black hole steadily for a few thousand years.

However, the authors are honest about the limits of their work. They don't know exactly where the heat is deposited inside the star for sure. Because this detail changes the outcome so drastically (stable vs. unstable), they say we need more detailed studies to know for certain which type of event we are actually seeing in the sky. They also note that many of these events might be too faint for our current telescopes to see, meaning there could be a whole hidden population of these "tidally heated" stars waiting to be discovered.

Technical Summary: Mass Transfer in Tidally Heated Stars Orbiting Massive Black Holes

Problem Statement
Stars orbiting close to supermassive black holes (SMBHs) are subject to complex interactions involving gravitational dynamics and hydrodynamics. While tidal disruption events (TDEs) occur when stars pass within the tidal radius ( $r_t$ ), recent observations of repeating nuclear transients (RNTs)—including quasi-periodic eruptions (QPEs) and partial TDE candidates (pTDEs)—suggest that stars can survive multiple pericenter passages. In these scenarios, even if the pericenter distance ( $r_p$ ) remains outside $r_t$ , the star experiences significant tidal heating. Previous work indicates that this heating can inflate the stellar radius, potentially initiating mass transfer to the SMBH before the orbit decays via gravitational waves (GWs) to the point of disruption. However, the coupled dynamics of tidal heating, stellar structural evolution, orbital decay, and the stability of the resulting mass transfer remain poorly understood, particularly regarding whether the mass transfer is stable or unstable and what luminosity it produces.

Methodology
The authors employ a dual approach combining analytic modeling and numerical simulations using the Modules for Experiments in Stellar Astrophysics (MESA).

Analytic Models: The authors develop a semi-analytic framework for a Sun-like star (main-sequence with a radiative core and convective envelope) orbiting an SMBH ( $M_\bullet \gg M_\star$ ). They consider two orbital regimes: highly eccentric ( $1-e \ll 1$ ) and near-circular ( $e \ll 1$ ).
- Tidal Heating: They utilize linear perturbation theory (Press & Teukolsky 1977; Lai 1997) for highly eccentric orbits and dynamical tidal dissipation via internal gravity waves for near-circular orbits (Linial & Quataert 2024b). The heating rate is parameterized by dimensionless factors ( $f_p$ and $f_c$ ) to account for uncertainties in non-linear mode coupling and dissipation.
- Evolution Equations: The model tracks the evolution of the stellar radius ( $R_\star$ ) and mass ( $M_\star$ ) driven by the balance between tidal energy deposition and stellar binding energy. Crucially, they assume that angular momentum and energy lost via mass transfer are permanently removed from the system (not returned to the orbit), a condition appropriate for high mass-ratio binaries.
- Stability Criteria: Stability is assessed by the stellar response to mass loss. If $R_\star \propto M_\star^\zeta$ with $\zeta \lesssim 1/3$ , mass transfer is unstable; otherwise, it is stable.
MESA Simulations: To address the limitations of analytic models regarding internal stellar structure, the authors perform 1D MESA simulations.
- Setup: Models consist of a $1 M_\odot$ zero-age main sequence (ZAMS) star orbiting an SMBH.
- Tidal Heating Implementation: Since the spatial distribution of tidal dissipation is uncertain, they test two phenomenological heating profiles: (1) Centrally Concentrated (0.1 < $r/R_\star$ < 0.2), motivated by internal gravity wave breaking, and (2) Uniform per unit mass in the outer 75% of the star.
- Orbital Evolution: They incorporate GW orbital decay (Peters 1964) and tidal orbital evolution terms into the MESA binary evolution code.
- Stability Determination: The simulations explicitly track whether the stellar radius expands or contracts in response to mass loss, thereby determining the stability of the mass transfer phase.

Key Contributions and Results

Dominance of Tidal Heating Timescale: The primary finding is that for stars orbiting SMBHs, the stable mass transfer rate ( $\dot{M}_\star$ ) is typically set by the tidal heating timescale ( $\tau_{\text{heat}} \sim E_\star / \dot{E}_{\text{tides}}$ ) rather than the GW orbital decay timescale ( $\tau_{\text{GW}}$ ).
- For highly eccentric orbits, $\dot{M}_\star \sim 10^{-5} - 10^{-3} M_\odot \text{yr}^{-1}$ .
- For near-circular orbits, $\dot{M}_\star \sim 10^{-6} - 10^{-4} M_\odot \text{yr}^{-1}$ (potentially higher if inertial wave excitation is efficient).
- This rate is significantly higher than that predicted by GW-driven orbital decay alone, implying a much shorter stable mass transfer phase ( $\sim 10^3 - 10^4$ years) compared to GW-driven scenarios ( $\sim 10^6 - 10^7$ years).
Stability Dependence on Heating Location: The stability of mass transfer is highly sensitive to where tidal energy is dissipated within the star.
- Centrally Concentrated Heating: Drives the star to become fully convective. In MESA models, this leads to unstable mass transfer, characterized by runaway expansion and a sharp increase in $\dot{M}_\star$ , which the code cannot solve numerically.
- Uniform/Outer Heating: Increases entropy in the outer layers, inhibiting convection and maintaining a radiative core. This leads to stable mass transfer, where the star contracts or expands slowly enough to maintain equilibrium, allowing for a sustained phase of mass loss.
Orbital Evolution: While tidal heating inflates the star, the orbital evolution driven by tides is generally sub-dominant to GW decay prior to the onset of mass transfer for fiducial parameters. However, once mass transfer begins, the orbital evolution is slow compared to the stellar mass loss timescale.

Significance and Implications
The paper argues that tidally heated mass transfer offers a viable mechanism for powering a population of low-luminosity active galactic nuclei (AGN) and specific repeating nuclear transients.

Repeating Nuclear Transients (RNTs):
- pTDE Candidates: The model provides a "gentler" version of partial TDEs for stars on orbits where $r_p$ approaches $r_t$ slowly (e.g., ASASSN-14ko). The authors note that their default models predict rates slightly lower than required for ASASSN-14ko, suggesting many such systems may be fainter than currently detected.
- QPEs: The stable mass transfer phase, particularly for near-circular orbits with enhanced heating rates (e.g., via inertial waves), could power short-period QPEs (e.g., GSN 069, eRO-QPE2). The model qualitatively explains the long-lived quiescent disk emission and the lack of broad AGN lines.
- Low-Luminosity AGN: The predicted mass transfer rates are sufficient to power low-luminosity AGN in many galaxies, potentially representing a significant but currently undetected population.
Theoretical Advancement: The work highlights a critical feedback loop: tidal heating alters stellar structure, which in turn modifies the tidal heating rate and the stability of mass transfer. The authors emphasize that robust conclusions require self-consistent calculations of this coupling, which their current 1D models approximate but do not fully resolve.

Limitations
The authors explicitly state several limitations:

Heating Physics: The total heating rate and spatial distribution of dissipation are uncertain and treated phenomenologically.
Orbital Approximations: The analytic models assume simplified orbital evolution, and MESA models approximate tidal energy deposition as time-averaged rather than impulsive bursts at pericenter.
Hydrodynamics: The models are hydrostatic and do not capture time-dependent pulsations or dynamical mass ejection that might occur during non-linear phases.
Disk Interactions: The interaction between the star and pre-existing accretion disks (from other TDEs) is neglected, though acknowledged as a potential factor in stellar survival.

In conclusion, the paper establishes that tidal heating can initiate mass transfer in stars orbiting SMBHs at rates and timescales distinct from GW-driven evolution, with the stability of this transfer critically dependent on the internal dissipation of tidal energy. This mechanism offers a plausible explanation for a subset of observed repeating transients and suggests a larger population of fainter, undetected systems.