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Repeated Tidal Interactions between Stars and Supermassive Black Holes: Mass Transfer, Stability, and Implications for Repeating Partial Tidal Disruption Events

T0 review · 2 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read When a star loses a few percent of its mass to a supermassive black hole, its surviving core keeps an energy set by its own binding structure, not by tidal heating — and stars above roughly 0.7 solar masses come back denser and harder to…

desk verdict A well-validated analytic model for partial mass loss in rpTDEs; the constant-Γ assumption deserves a sensitivity check before the quantitative threshold is taken at face value. read the letter →

arxiv 2504.18614 v2 pith:KAWCTHUR submitted 2025-04-25 astro-ph.HE astro-ph.GA

Ananya Bandopadhyay , Eric R. Coughlin , C. J. Nixon This is my paper · ORCID
classification astro-ph.HEastro-ph.GA
keywords tidaldisruptioneventsrepeatingpartialsupermassiveblackholesstellarmasslossheatingoscillationsstructurehydrodynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Stars that graze a supermassive black hole can lose a few percent of their mass and keep orbiting, producing a flare on every passage — but a standing worry has been that tidal heating over repeated encounters would inflate the star and destroy it. This paper builds an analytical model of mass loss as a drop in the confining pressure on the star's surviving core, and claims the worry is misplaced: the core's final energy is set almost entirely by the binding energy of the mass that remains, not by heat deposited through tides. The model predicts a sharp mass divide — stars above roughly $0.7\,M_\odot$ emerge denser and harder to disrupt after each stripping, while lighter stars emerge puffier and more fragile. If correct, this explains why some repeating flares fade from outburst to outburst, why others brighten, and why moderately massive, evolved stars are the best candidates to power long-lived repeaters.

What carries the argument

The engine of the model is a Lagrangian, spherically symmetric description of the star as a Bonnor-Ebert sphere: an inner core containing $(100-x)\%$ of the mass, held in by the pressure of an outer confining medium that contains the remaining $x\%$ ($x \lesssim 10$). Mass loss is mimicked by lowering that external pressure at the core radius on roughly a dynamical timescale. The background state is a sequence of quasi-steady hydrostatic equilibria parameterized by the declining surface pressure $h_c$, and the oscillations about the final state are expanded in the eigenmodes of a Sturm–Liouville problem, which yields the surface motion and the small kinetic energy that would become heat. The quantity that controls the physics is $R_{0,c}/R_\star$, the radius in the original star that encloses the surviving mass: it determines whether the post-stripping average density rises or falls, and it is why centrally concentrated, evolved stars become denser while low-mass stars become puffier.

What would settle it

Run a multi-encounter partial-TDE simulation with a realistic equation of state — one whose effective adiabatic index drops below $5/3$ in the ionizing outer layers — and check the two quantitative predictions: the average density of a $1.5\,M_\odot$ survivor should still rise above its pre-stripping value after each passage, and the accumulated oscillatory energy should stay negligible against the binding-energy shift; a departure in either would falsify the mass-dependent stability picture.

Watch

Extended reading notes

Core claim

The paper's central claim is that when a star loses a small fraction ($\lesssim 10\%$) of its mass to a supermassive black hole, the surviving core's final energy is effectively the binding energy of the original star's matter interior to the radius from which mass was removed: $\Delta E \simeq E_{c,0} - E_{\star}$, with a small negative correction from the $p\,dV$ work of the expanding surface. The process that removes the mass is nearly irrelevant at leading order; in particular, the kinetic energy of the oscillations left in the star — the conventional 'tidal heating' — is orders of magnitude smaller than the changes in its gravitational and thermal energies. The same formalism predicts that the survivor's average density rises for stars with $M_\star \gtrsim 0.7\,M_\odot$, most strongly for evolved stars near $1.5$–$2\,M_\odot$ where a $10\%$ mass loss can multiply the mean density severalfold, while low-mass stars become less dense. Because the tidal radius scales as $\rho^{-1/3}$, a denser survivor sheds less mass on the next encounter, so successive flares naturally fade, whereas a puffier low-mass star becomes progressively more vulnerable.

Load-bearing premise

The load-bearing premise is that every layer of the star responds to expansion with the stiffness of a monatomic ideal gas (adiabatic index $\Gamma = 5/3$), even in the outer layers where partial ionization makes the real gas substantially softer, and the paper's quantitative results for post-stripping density and oscillation frequencies rest on that choice without a test of its sensitivity.

Editorial extensions

If this is right

  • Tidal heating does not produce runaway inflation: the oscillatory energy is orders of magnitude below the binding-energy shift, so a partially disrupted star can survive tens to hundreds of repeated encounters.
  • Fading repeaters such as AT2018fyk and eRASSt-J045650 follow naturally from structure alone: the survivor gets denser, its tidal radius shrinks, and each passage removes less mass.
  • Low-mass stars ($\lesssim 0.7\,M_\odot$) become less dense after stripping, so repeat flares from such stars should brighten, matching events whose second outburst outshines the first, such as AT2020vdq.
  • A star that powers many flares, such as the roughly twenty outbursts of ASASSN-14ko, must be comparatively massive and evolved ($M_\star \gtrsim 1.5\,M_\odot$), since only such stars stiffen against further stripping.
  • The pressure-deconfinement formalism transfers to other mass-ejection settings — classical novae, luminous blue variable outbursts, X-ray bursts — giving an inexpensive way to compute the post-ejection structure of a remnant.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The energy result implies a weak universality: any process that peels off the outer $\lesssim 10\%$ of a star — tidal stripping, a wind, Roche-lobe overflow — should leave a remnant with the same leading-order internal structure, set only by the mass that remains; a test would compare a tidally stripped star with one that lost the same fraction through an unrelated channel.
  • For massive stars the effect is self-limiting: each stripping raises the density, which lowers the tidal radius, so the stripped fraction should decay from one encounter to the next; this predicts a specific, quantifiable decay pattern in the flare luminosities of long-lived repeaters.
  • Rotation is the largest term the model neglects, and for very tight orbits the tidal spin-up could outweigh the density stabilization and move the $0.7\,M_\odot$ divide, so extending the background-state calculation to rotating equilibria would show where the stability boundary actually lies.
  • The constant $\Gamma = 5/3$ equation of state is the obvious sensitivity to probe: recomputing the density response with an effective adiabatic index below $5/3$ in the ionizing outer layers could shift the $1.5$–$2\,M_\odot$ peak and change which stars survive.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper develops a semi-analytic Lagrangian model for the response of a star to the removal of a small fraction (less than about 10%) of its mass, motivated by repeating partial tidal disruption events (rpTDEs). The original star is divided into an inner core and an outer envelope; the envelope is replaced by a time-dependent pressure boundary condition, and the core response is decomposed into a quasi-static background state plus linear eigenmode perturbations. Applied to MESA stellar models, the model predicts that the volume-averaged density of low-mass stars (approximately less than 0.7 solar masses) decreases after mass loss, whereas higher-mass and evolved stars become denser, with the largest effect near 1.5-2 solar masses. The paper further predicts that the final energy of the surviving core is essentially the binding energy of the original core interior to the mass-loss radius, so that oscillatory-mode (tidal heating) energy is subdominant. These predictions are compared with two FLASH 1D simulations and three PHANTOM 3D partial-TDE simulations, and the paper concludes that partially disrupted stars are not significantly heated, that evolved and moderately massive stars can survive many repeated stripping events, and that progressively dimmer repeating TDE flares can be explained by post-mass-loss densification.

Significance. If the claims hold, this is a valuable contribution. It provides a cheap predictive framework for a parameter space that would otherwise require expensive simulations, it makes falsifiable statements about which stellar masses and ages can power repeating TDEs, and it cleanly separates binding-energy bookkeeping from genuine tidal heating. The paper deserves credit for testing the analytic model against two independent numerical codes (FLASH and PHANTOM), including a resolution test, and for reporting explicit power-law fits and energy decompositions. The energy-agnostic claim is a derived prediction rather than a fit to the simulations, which strengthens its status. The principal reservation is that the dynamical equation of state is fixed to Gamma = 5/3 in both the analytic model and in the validating simulations, leaving the sensitivity to real envelope thermodynamics unquantified; this is a load-bearing issue for the survivability and dimming-flare conclusions, although not for the energy bookkeeping claim itself.

major comments (2)
  1. [Section 2 (Eqs. 5, 15, 26) and validation in Sections 2.6 and 3] The central quantitative predictions are made with a constant adiabatic index Gamma = 5/3 throughout the star. This Gamma enters the background-state equation (Eq. 5), the eigenmode problem (Eq. 15), and the p-dV work integral (Eq. 26), and the FLASH validation in Section 2.6 explicitly imposes Gamma = 5/3 while the PHANTOM runs reuse the adiabatic setup of previous work. However, the MESA initial models contain outer layers in partial-ionization zones where the effective adiabatic exponent is substantially below 5/3, and those layers are exactly the ones removed for Delta M/M_star less than about 10%. The agreement between the model and the simulations therefore demonstrates self-consistency under the idealized EOS but does not test whether a real envelope responds the same way. A lower Gamma changes the pressure support of the expanded core and hence the density ratios in Figures 5, 6, and 8 and the threshold near 0.7 solar masses that separates destabilizing from stabilizing mass loss. I ask the authors to quantify this sensitivity, for example by rerunning the background-state calculation with Gamma = 4/3 or with the local first adiabatic index profile from MESA, or by giving an analytic bound on the shift of the density ratio and threshold. This is load-bearing for conclusions 1 and 3 (survivability and progressively dimmer flares), while the energy-agnostic claim is less exposed because it is primarily binding-energy bookkeeping.
  2. [Section 4.1 and Section 5, Conclusions 2-3] The stability conclusions are single-encounter statements that are extrapolated to multiple repeated stripping events using the sign of the density change. The paper does not follow the core through multiple pericenter passages; the only repeated-passage evidence cited is from prior simulations (Bandopadhyay et al. 2024) for specific stars. Consequently, the proposed explanation for progressively dimmer flares (a per-encounter density increase) is plausible but not directly demonstrated by the simulations in this manuscript. A short quantitative extrapolation, such as an iterative map using the model's Delta M/M_star to density relation over several encounters, would turn this inference into a testable prediction and would strengthen the claim.
minor comments (5)
  1. [Title] The title as typeset contains spacing artifacts such as 'Mass T ransfer' and 'Stability ,'; these should be corrected in the final version.
  2. [Section 2.3, Eq. (13)] The symbol xib is used for both the time-dependent background state and its asymptotic, pressure-free limit; introducing a distinct notation such as xib_infinity for the latter would improve clarity.
  3. [Figure 9] The left and right panels show overlapping information, and the legend density makes it difficult to identify which curves are analytical versus SPH. Reorganizing into a single panel with a zoom inset or a cleaner legend would help the reader.
  4. [Section 4.2 and Figure 11] The per-orbit specific-energy requirement for Pdot approximately -0.001 in ASASSN-14ko is compared directly with the binding energy of the stripped envelope. Given the authors' own caveats about energy retained in tidal tails and quasi-ballistic reformation, I suggest presenting this comparison explicitly as an upper limit in the main text.
  5. [Section 4.3] The discussion of Yao and Quataert (2025) is a single sentence; since that work directly addresses the same stability question, a more detailed comparison of assumptions and conclusions would be useful to the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the energy and density predictions are computed responses of the stated fluid equations and are tested against independent hydrodynamics, with acknowledged modeling limitations that do not reduce to the paper's own inputs.

full rationale

The derivation is self-contained. The paper begins with the Lagrangian fluid equations (Eqs. 1-2), imposes a Bonnor-Ebert-like split into a core and an envelope whose confining pressure is reduced, and solves for a sequence of hydrostatic background states (Eq. 5) plus linear eigenmodes about the asymptotic state (Eqs. 13-18). The density and energy predictions are computed from the initial MESA stellar structure and the specified fractional mass loss; no parameter is fitted to the FLASH or PHANTOM outcomes. The central result Delta E approximately Ec,0 - E* follows from the energy bookkeeping in Eqs. 21-27, not from an externally imported claim, and the p-dV correction is evaluated from the background-state sequence rather than imposed. The FLASH runs provide an independent nonlinear integration of the same physical setup, and the 3D PHANTOM runs supply a separate benchmark in which mass loss is selected by the impact parameter rather than by the analytical boundary prescription; Section 3 explicitly notes that rotation is absent from the analytic model and is measured in the SPH runs, which is an honest limitation rather than an input. The self-citations (Golightly et al. 2019b; Bandopadhyay et al. 2024) supply MESA initial models and the SPH setup, but the analytic predictions and the comparisons are not defined by those citations. The shared constant-Gamma = 5/3 assumption between the analytic model and FLASH does limit how strongly the validation constrains real partial-ionization envelopes, but that is a modeling-assumption/robustness concern, not circularity; the same applies to the acknowledged neglect of nonlinear terms and rotation. The paper also does not fit the target rpTDE observations, instead comparing qualitative trends to them. Accordingly, no circular step is identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The model's central input is the fractional mass loss and the rate at which the external pressure is removed. The remaining assumptions are standard idealizations (constant Γ, spherical symmetry, no rotation, linear perturbations) that are partially validated by the SPH comparison. No new physical entities are introduced.

free parameters (3)
  • Fractional mass loss ΔM/M⋆ = 0.01-0.10
    The model predicts the stellar response for a specified amount of mass removal; it does not predict how much mass is stripped in a given encounter. In the SPH comparison, ΔM/M⋆ is taken from the simulations; in the analytical model it is an input that sets the initial core radius R0,c.
  • Pressure-drop rate ω = ∂hc/∂τ at τ=0 = 1 (assumed)
    Sets the amplitude of the oscillatory kinetic energy. The authors argue ω ~ 1 for a TDE because mass is removed on the dynamical time, and set ω = 1 in the FLASH comparison. The dominant energy and density predictions are independent of ω, so it is not a central fitted value.
  • SPH core-definition cutoff Δlogρ < 0.01 = 0.01
    Post-processing choice used to separate the surviving core from the tidal stream in phantom simulations. The authors checked that Δlogρ < 0.05 gives almost identical core radii, so it is not a sensitive fitted parameter.
assumptions (5)
  • domain assumption The gas is adiabatic with a constant adiabatic index Γ = 5/3 throughout the core and during the mass-loss response.
    Invoked in Eq. (1) and used in the FLASH setup (Section 2.6); real stellar envelopes have a varying effective Γ.
  • domain assumption Mass loss is represented as a spherically symmetric reduction of the pressure at the core boundary to zero; the tidal field's non-spherical structure is ignored in the analytical model.
    Central physical approximation (Sections 2.1-2.4); the authors test it against 3D SPH and find it captures the dominant behavior.
  • domain assumption The background state proceeds through a sequence of hydrostatic equilibria and the perturbations about it are linear; nonlinearities and mode damping are neglected.
    Used in Sections 2.2-2.3; requires the pressure drop timescale to be comparable to the dynamical time so that velocities remain small.
  • domain assumption The analytical model ignores stellar rotation; rotation is only accounted for in the SPH simulations.
    The paper later shows rotation contributes about 10% of the energy budget, so it is a subdominant but non-negligible effect.
  • domain assumption The core's self-gravity is Newtonian and spherically symmetric, and the black hole's gravity appears only as the agent that removes the envelope.
    The model computes the response of the core alone; the ejection of the envelope and the orbital dynamics are not modeled.

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Pith. "Pith review of Repeated Tidal Interactions between Stars and Supermassive Black Holes: Mass Transfer, Stability, and Implications for Repeating Partial Tidal Disruption Events." pith.science (2026). https://pith.science/paper/KAWCTHUR

@misc{pith2026250418614,
  author       = {Pith},
  title        = {Pith review of: Repeated Tidal Interactions between Stars and Supermassive Black Holes: Mass Transfer, Stability, and Implications for Repeating Partial Tidal Disruption Events},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KAWCTHUR}},
  note         = {Machine review of arXiv:2504.18614}
}
abstract

Stars orbiting supermassive black holes can generate recurring accretion flares in repeating partial tidal disruption events (TDEs). Here we develop an efficient formalism for analyzing the time-dependent response of a star to the removal of a fraction ($\lesssim 10\%$) of its mass. This model predicts that mass loss results in a decrease in the average density of low-mass ($\lesssim 0.7 M_{\odot}$) stars. Contrarily, higher-mass stars exhibit an increase in their average density, such that the change is more pronounced for larger mass losses, and stars with masses $\sim 1.5-2 M_{\odot}$ experience the largest such increase. We predict that the final energy of the star post-mass-loss (i.e., the ``surviving core'') is effectively given by the binding energy of the original star interior to the radius from which mass is removed, i.e., the final core energy is agnostic to the process that removes the mass and -- as a corollary -- tidal heating is comparatively insignificant. We find excellent agreement between our predictions and one-dimensional Eulerian simulations of a star undergoing mass loss, and three-dimensional Lagrangian simulations of partial TDEs. We conclude that 1) partially disrupted stars are not significantly heated via tidal dissipation, 2) evolved and moderately massive ($\gtrsim 1.5 M_{\odot}$) stars can most readily survive many repeated stripping events, and 3) progressively dimmer flares -- observed in some repeating partial TDE candidates -- could be explained by the increase in the density of the star post-mass-loss.

Figures

Figures reproduced from arXiv: 2504.18614 by the authors.

Figure 1
Figure 1. Left: the background state of the star, ξb, as a function of the initial Lagrangian radius in the core, ξ0, for the relative surface pressures hc shown in the legend and a mass loss of 10%. As the pressure declines the system approaches a final equilibrium, and ∂ξb/∂ξ0(ξ0 = 1) → ∞. Right: the dimensionless density of the background state, gb, as a function of the instantaneous/current positions of the fluid elements… view at source ↗
Figure 2
Figure 2. The core radius as a function of surface pressure, showing that the radius expands as the pressure drops (i.e., time goes from right to left on the horizontal axis) and ap￾proaches a limiting value as hc → 0. The different curves are appropriate to the core masses in the legend, while the black-dashed line is the initial radius of the star. For this star, the final core radius is therefore always less than the initi… view at source ↗
Figure 3
Figure 3. Left: the first four eigenmodes describing the background state of the star for a 1M⊙, ZAMS star with 1% mass loss, after the pressure at the surface is reduced by a factor of 10−6 . The eigenvalues appropriate to the modes are shown in the legend. Right: the initial velocity profile of the core normalized by ω, shown by the black-dashed curve. The orange, green, and yellow curves illustrate the reconstruction of th… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: The time-dependent radius of the core of a 1M⊙ ZAMS star, following a 1% mass-loss (left) and a 1.5M⊙ ZAMS star, following a 10% mass-loss (right). In each case, the solid blue curve shows the analytical solution, and the solid orange curve shows the result of a hydrod…
Figure 5
Figure 5. Figure 5: The time-averaged density of a star post– mass-loss, normalized by the average density of the original star, for the range of stars in the legend. The black dashed line demarcates ⟨ρav⟩t/ρ⋆ = 1. stars respectively. Generally, stars that are further along their main-seq…
Figure 6
Figure 6. Figure 6: Left: the relative change in the average density with respect to the original average density, ⟨ρav⟩t/ρ⋆, as a function of stellar mass, M⋆, for a ∆M = 3% mass loss. The stars, clovers and spades represent ZAMS, MAMS and TAMS stars respectively. Right: the relative cha…
Figure 7
Figure 7. Figure 7: The time-averaged change in the kinetic energy (violet), the total energy (orange) and the p−dV work done by the expansion of the core (green) for a 1M⊙ ZAMS star as a function of the relative mass loss. Also shown are the second-order changes to the potential energy (…
Figure 8
Figure 8. Figure 8: shows the corresponding density4 of the sur￾viving core, i.e., ⟨ρav⟩t = 3Mc/(4πR3 c ), normalized by the average density prior to mass loss, for all three stars 4 We use the same notation as the analytical section, namely that the density is “time-averaged,” but we not…
Figure 9
Figure 9. Figure 9: Left: the change in the kinetic, rotational, potential and internal energies of the 1M⊙ ZAMS star on a β = 0.7 orbit around a 106M⊙ SMBH, and the total energy imparted to the surviving core, calculated from the SPH simulation. Also shown are the predictions for the dif…
Figure 10
Figure 10. Figure 10: Left: same as [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: The per-orbit change in the specific energy of the core, in units of GM⊙/R⊙, as a function of the total frac￾tional mass lost, for stars losing 1% of their original mass per encounter with an SMBH. The black dashed line depicts the required per-orbit change in specifi…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    astro-ph.HE 2025-05 conditional novelty 7.0 of 10

    For stars orbiting close to a supermassive black hole, tidal heating can set a stable mass transfer rate orders of magnitude above gravitational-wave-driven rates, powering repeating nuclear transients and low-luminosity AGN.

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