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Tidal Disruptions and Stellar Encounters

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A close stellar encounter with a massive black hole is a sequence of decisions made on different scales. The tidal tensor first competes with stellar self-gravity; relativistic capture can end the event before disruption; bound debris then returns, intersects, and may circularize; a surviving core can come back; compact remnants can instead become plunges or long gravitational-wave inspirals. This chapter develops that sequence and shows which observed quantities can support black-hole inference. Generic stellar dynamics and exact geodesic derivations are outside scope.

Helpful background. Geodesics and Jacobi Fields supplies geodesic deviation; Black-Hole Geometry and Mechanics supplies horizons, capture, and Kerr spin; Relativistic Matter and Compact Objects supplies stellar structure and remnants; Black-Hole Astrophysics supplies the volume-wide observational setting.

Enter this chapter

Section titled “Enter this chapter”

The governing scales should be kept separate:

rt∼R∗(Mm∗)1/3,Rg=GM,tmin⁡∼π2GM1/2R∗3/2m∗.r_t\sim R_*\left(\frac{M}{m_*}\right)^{1/3}, \qquad R_g=GM, \qquad t_{\min}\sim\frac{\pi}{\sqrt{2G}} \frac{M^{1/2}R_*^{3/2}}{m_*}.

Here MM is the black-hole mass, m∗m_* and R∗R_* are the stellar mass and radius, rtr_t is the tidal radius, and tmin⁡t_{\min} is the first debris-return time. The first relation compares differential gravity with self-binding, the second sets relativistic compactness, and the third is the orbital period of the most-bound debris under a stated energy-freezing prescription. None alone predicts a light curve. An electromagnetic transient also depends on debris-energy distribution, stream intersection, radiation transport, viewing direction, and survey selection. A gravitational-wave source adds the competition between radiation reaction and orbital scattering.

Throughout the chapter, MM denotes physical black-hole mass, Rg=GMR_g=GM, and a∗=J/(GM2)a_*=J/(GM^2). Quantities inferred from data are stated in the source frame unless a detector or cosmological frame is explicitly named. The observational and frontier snapshot closes on 2026-08-18; later results require a fresh review.

The six-stage route

Section titled “The six-stage route”

Read the pages in the listed order because each one changes the initial conditions for the next:

  1. Tidal Radius and Hills Mass derives the tidal-tensor estimate, penetration factor, and capture-first ordering. It explains why the Newtonian equality rt∼Rgr_t\sim R_g is a scaling argument rather than the Kerr answer.
  2. Debris Energy Distribution and Fallback converts dM/dεdM/d\varepsilon into dM/dtdM/dt and shows exactly when t−5/3t^{-5/3} follows. Its public simulation-grid contract separates numerical fallback from observed luminosity.
  3. Relativistic Precession and Circularization locates ballistic stream intersections, tests them with a convergent calculation, and identifies nodal misses and hydrodynamic failure modes. Intersection is treated as a possible dissipation site, not as proof of a disk.
  4. Partial and Repeating Disruptions follows the surviving core, its kick, mass–radius response, and evolving orbital clock. A dated evidence matrix compares repeated stripping with star–disk, accretion-cycle, and binary alternatives.
  5. Stellar Capture and EMRI Sources distinguishes an empty from a full loss cone and a prompt plunge from an adiabatic inspiral. It keeps the GALACTICNUCLEUS tracer catalog separate from the adopted LISA detector selection.
  6. Black-Hole Inference from Tidal Events assembles event and population likelihoods using the frozen TDECat release. It exposes the degeneracies among mass, spin, star, encounter depth, emission geometry, and classification completeness.

This ordering prevents two common shortcuts: interpreting a fallback law before establishing that the star was disrupted outside capture, and fitting a black-hole parameter before choosing what physical clock or radius the observable represents.

What is robust and what remains conditional

Section titled “What is robust and what remains conditional”

The most robust theoretical statements are conditional ones. A flat debris-energy distribution near zero gives late fallback proportional to t−5/3t^{-5/3}. Relativistic apsidal advance rotates the outbound stream; misaligned spin can displace it vertically. A compact remnant becomes an EMRI candidate only where tGW<tJt_{\rm GW}<t_J outside capture. These statements have explicit hypotheses and limiting checks.

The robust data are calibrated times, fluxes or upper limits, spectra, positions, redshifts, and versioned catalog membership. Black-hole mass from a flare, spin from a high-mass event, penetration factor from a light-curve shape, and a surviving core from recurrence are conditional inferences. Gezari 2021, §§3.1 and 4.3, Eqs. 1–5 and 16 summarizes the central observational tensions. Rossi et al. 2021, §§2.2, 4 and 8.3 reviews energy freezing, partial disruption, and multiple encounters; Bonnerot & Stone 2021, §3 develops circularization.

Three boundaries recur across the pages:

  • Dynamical boundary: disruption, partial stripping, direct capture, or inspiral depend on the stellar model and orbit, not mass alone.
  • Radiative boundary: fallback, accretion, shocks, reprocessing, and jets need not share a time dependence.
  • Selection boundary: a literature compilation is not a rate-complete survey, and an intrinsic source population is not a detector-selected population.

From observations to inference

Section titled “From observations to inference”

Start with the raw data product and its calibration. State the detection and classification selection, preserve upper limits, and identify the source, detector, and cosmological frames. Then choose an encounter model and an emission model as separate components. Fit nuisance parameters rather than silently fixing stellar structure, extinction, inclination, efficiency, or delay. Finally, compare with an independent host-mass constraint or a held-out band and propagate selection through a hierarchical population model.

For a numerical calculation, convergence of a root finder does not validate stream hydrodynamics; refine the stream, shocks, capture treatment, and conserved quantities. For a catalog calculation, a narrow posterior does not overcome missing survey efficiency. For a frontier claim, state what new observation or simulation would change the conclusion. Stone et al.’s loss-cone treatment gives the phase-space foundation in Stone et al. 2020, §§3.1–3.6 and 4.1–4.2; Bonnerot and Stone map the accretion-flow uncertainties in Bonnerot & Stone 2021, §§3.1–3.4.

Chapter diagnostic: classify before interpreting

Section titled “Chapter diagnostic: classify before interpreting”

A nuclear transient repeats every 200 days. Each flare has a 40-day optical rise, but X-rays appear 80 days after optical maximum. Host scaling suggests M∼106M⊙M\sim10^6M_\odot. Which conclusions are direct, which are conditional, and which chapter tests come first?

Solution

The direct results are the calibrated recurrence, optical rise, X-ray delay, nuclear localization, and the stated host measurement. “A surviving star is stripped every 200 days” is conditional: a star–disk interaction or accretion cycle can also recur. “The 40-day rise is tmin⁡t_{\min}” is likewise conditional because circularization and diffusion can set the optical clock. The host mass is an external scaling-relation estimate, not a dynamical truth.

First use the tidal-radius/capture test to verify that plausible stars disrupt outside capture. Next compare the rise with the debris-energy clock without forcing luminosity to equal fallback. Then test apsidal/nodal intersection and whether an 80-day accretion delay is credible. The repeating-event page supplies competing clock models; the inference page combines them with host information and selection. EMRI machinery is relevant only if the donor is a compact remnant and radiation reaction outruns scattering. This order prevents a precise mass posterior from being built on an unchosen physical clock.

References

Section titled “References”