Partial and Repeating Disruptions

A partial tidal disruption removes part of a star while leaving a self-bound remnant. Repetition requires much more: the remnant must stay bound to the black hole, return to a pericenter permitting further stripping, and remain susceptible to mass loss. Phase-coherent recurring nuclear flares motivate an orbital clock, but recurrence alone proves neither an orbit nor a surviving star: accretion cycles can also repeat. Generic stellar dynamics and exact geodesic derivations are outside scope.

Required background. Geodesics and Jacobi Fields supplies affine geodesics, deviation, and the meaning of a bound orbit.

Helpful background. Black-Hole Geometry and Mechanics supplies capture boundaries; Relativistic Matter and Compact Objects supplies stellar structure and mass–radius response; Black-Hole Astrophysics supplies transient and nuclear-environment context.

A surviving core changes the encounter

Write the penetration factor as $\beta=r_t/r_{\rm p}$. A grazing encounter strips layers whose local self-gravity loses to the black hole’s differential acceleration, while a denser interior can reassemble into a core. There is no universal critical $\beta$: the outcome depends on the stellar density profile, evolutionary state, rotation, mass ratio, relativistic capture boundary, and numerical definition of “bound.” In Newtonian polytropic calculations, centrally concentrated $\gamma=4/3$ models remain partial over a wider interval than $\gamma=5/3$ models. The 43-run FLASH study and its cross-method comparisons establish this structural dependence, not a composition-independent threshold; see Guillochon & Ramirez-Ruiz 2013, §§2–4, Figs. 2, 4, and 12 and Rossi et al. 2021, §4, Figs. 4–6.

The remnant and debris exchange momentum asymmetrically. Let the pre-encounter orbital specific energy be

$$\varepsilon_{\rm orb}=-\frac{GM}{2a}, \qquad P=2\pi\sqrt{\frac{a^3}{GM}}.$$

If a kick changes the energy by $\delta\varepsilon$, the core returns only if $\varepsilon_{\rm orb}+\delta\varepsilon<0$. For a small change that remains bound,

$$\frac{\delta P}{P} =-\frac{3}{2}\frac{\delta\lvert\varepsilon_{\rm orb}\rvert} {\lvert\varepsilon_{\rm orb}\rvert}.$$

This makes a measured period derivative informative but not unique: hydrodynamic recoil, tidal-mode dissipation, drag through an accretion disk, relativistic radiation reaction, and perturbations by another massive body can all alter the clock.

For a velocity impulse $\delta\boldsymbol v$ at fixed position, $\delta\varepsilon=\boldsymbol v\cdot\delta\boldsymbol v+\lvert\delta\boldsymbol v\rvert^2/2$. A kick is not automatically a positive energy change: its direction matters. Energy loss makes the orbit more tightly bound and shortens the period; energy gain lengthens the period or unbinds the remnant. The black-hole mass $M$ is treated as fixed and $a$ is the remnant orbit’s semimajor axis.

Repeated stripping also depends on the remnant’s mass–radius response. Define $\zeta_*=d\ln R_*/d\ln m_*$. At fixed pericenter,

$$r_t\propto R_*m_*^{-1/3}, \qquad \frac{d\ln\beta}{d\ln m_*}=\zeta_* - \frac13.$$

Because mass loss has $d\ln m_*<0$, a star with $\zeta_*<1/3$ becomes more vulnerable after stripping and can run away toward total disruption; one with $\zeta_*>1/3$ tends to become less vulnerable. Thermal relaxation between passages, composition gradients, rotation, and shock heating make $\zeta_*$ history-dependent, so a single equilibrium mass–radius law is only a diagnostic.

Results and limitations through 2026-08-18

The durable observations are recurrence times, nuclear positions, calibrated fluxes, spectra, and their uncertainties. Claims about the stellar type, mass lost per orbit, or even the existence of a surviving core remain model-dependent, and the physical origin of the repeating-transient class is unresolved. Results published after 2026-08-18 are outside this evidence snapshot.

Evidence	Result	Scope and limitations
FLASH 4.0 Newtonian disruption grid, 43 runs	Mass loss and fallback depend strongly on stellar concentration and $\beta$; a surviving core steepens late fallback	Polytropes and first passages; no relativistic capture, realistic repeated stellar evolution, or radiative transfer
ASASSN-14ko, ASAS-SN/TESS/Swift and public VizieR catalog J/ApJ/910/125	Seventeen reported optical outbursts gave $P_0=114.2\pm0.4$ d and $\dot P=-0.0017\pm0.0003$ in the stated timing model	Recurrence and evolving phase are durable; an active host permits star–disk and accretion alternatives, while inferred mass loss is mutable
eRASSt J045650.3−203750, eROSITA/XMM-Newton/Swift/NICER/Chandra through cycle 5	Five X-ray/UV flares; fitted recurrence shortened from roughly 300 d toward about 190 d	Heterogeneous cadence and responses; hydrodynamic mapping requires a particular star, hole mass, efficiency, and per-passage loss
Surviving-core and multiple-encounter calculations	Core kicks, post-stripping expansion, and loss-cone perturbations determine whether another passage occurs	Long sequences couple hydrodynamics, stellar evolution, and nuclear dynamics; current simulations sample only restricted axes

For ASASSN-14ko, the timing fit, bootstrap peak uncertainties, and alternative scenarios are documented in Payne et al. 2021, §§IV.1 and VI, Eq. 1 and Figs. 1–3; its machine-readable photometry is VizieR J/ApJ/910/125. For J0456−20, instrument reductions, selection bands, Cash-statistic fits, and cycle timing are explicit in Liu et al. 2024, §§2–3, Figs. 1–2 and Table 1. Those papers support recurrence; their preferred physical interpretations do not convert into direct images of a remnant.

Competing explanations and discriminants

Repeated partial stripping. A bound star loses matter near each pericenter. It naturally supplies a clock and related flare morphologies, but must reproduce the measured $P$ evolution, survival time, energetics, and spectral changes with one evolving stellar model.

Star–disk impacts or drag. An orbiting star crosses a pre-existing active-galaxy disk. This can generate periodic shocks and change the orbit without tidal mass loss. Disk crossings predict geometric phase relations and dependence on disk state that repeated stripping need not share.

Accretion variability. Thermal, radiation-pressure, magnetic, or other disk cycles can recur without an orbiting donor. Such models must explain long-term phase coherence and any stable, orbit-like timing evolution rather than fitting flare shape alone.

Binary-mediated encounters. A companion black hole or a disrupted stellar binary can impose recurrence or sequential feeding. These scenarios predict additional velocity, astrometric, or secular timing signatures and need not preserve identical debris composition.

Useful discriminants are phase-coherent multi-band timing, line-abundance evolution, flare-to-flare energy, quiescent disk diagnostics, and whether a single dynamical model predicts the next flare before it occurs. A declining amplitude alone is ambiguous: it can mean dwindling stellar mass, evolving circularization, changing reprocessing, or disk-state drift.

What could change the conclusion. The interpretation could change when a public, uniformly selected repeating-transient sample with injection–recovery completeness appears, when long-baseline timing decisively excludes one orbital alternative, or when relativistic multi-passage simulations converge remnant mass, kick, radius, and flare energetics across realistic stellar structures.

Diagnostic: choose the evolution variable

A remnant loses 10% of its mass on each passage and responds locally as $R_*\propto m_*^{-1/3}$. Assume $r_{\rm p}$ remains fixed. Does the next encounter become deeper or shallower, and why is holding $r_t$ fixed the wrong formulation?

Solution

Here $\zeta_*=-1/3$, so

$$\frac{d\ln\beta}{d\ln m_*}=-\frac23.$$

After one passage $m_2/m_1=0.9$, hence

$$\frac{\beta_2}{\beta_1} =\left(0.9\right)^{-2/3}\simeq1.073.$$

The encounter becomes about 7.3% deeper in dimensionless terms even though the geometric pericenter is unchanged. Holding $r_t$ fixed erases the feedback between structural response and stripping; the correct formulation evolves $m_*$, $R_*$, orbital energy, and pericenter together.

References

• Guillochon, James, and Enrico Ramirez-Ruiz. 2013. “Hydrodynamical Simulations to Determine the Feeding Rate of Black Holes by the Tidal Disruption of Stars: The Importance of the Impact Parameter and Stellar Structure.” The Astrophysical Journal 767, 25. https://doi.org/10.1088/0004-637X/767/1/25.
• Liu, Zhu, Taeho Ryu, A. J. Goodwin, et al. 2024. “Rapid Evolution of the Recurrence Time in the Repeating Partial Tidal Disruption Event eRASSt J045650.3−203750.” Astronomy & Astrophysics 683, L13. https://doi.org/10.1051/0004-6361/202348682.
• Payne, Anna V., Benjamin J. Shappee, Jason T. Hinkle, et al. 2021. “ASASSN-14ko Is a Periodic Nuclear Transient in ESO 253-G003.” The Astrophysical Journal 910, 125. https://doi.org/10.3847/1538-4357/abe38d.
• Rossi, Elena M., Nicholas C. Stone, Jamie A. P. Law-Smith, et al. 2021. “The Process of Stellar Tidal Disruption by Supermassive Black Holes: The First Pericenter Passage.” Space Science Reviews 217, 40. https://doi.org/10.1007/s11214-021-00818-7.