arXiv subjects

Wenkang Xin

Publications and source records attributed to Wenkang Xin.

3 recordsLinked to original sources

arXiv2026

Inclination Diffusion in Relativistic Loss Cones

Relativistic capture and tidal disruption around a spinning black hole depend on both the magnitude and direction of the star's angular momentum, yet loss-cone models often assume fixed orbital inclinations by ignoring the associated diffusion. We show that this is not justified: for isotropic two-body relaxation near a small loss threshold, angular-momentum magnitude $L$ and inclination $x = L_{z}/L$ diffuse on comparable timescales, $t_{E} \gg t_{L} \sim t_{x}$. For Kerr capture, retaining inclination diffusion significantly amplifies the prograde--retrograde contrast while leaving the total inclination-integrated flux nearly unchanged. An almost correct integrated flux can hide a badly wrong angular distribution. The three-dimensional diffusion problem nevertheless retains enough angular structure to permit analytic treatment. By representing pericenter removal as a continuous sink, we obtain a closed-form loss flux solution for a nearly linear Kerr tidal-disruption boundary, finding close agreement with phase-resolved calculations. Inclination-dependent loss therefore requires inclination-resolved diffusion even when integrated rates appear robust.

astro-ph.HE↗

arXiv2026

A Semi-Analytical Loss Cone Theory for Tidal Disruption Event Rates Around Kerr Black Holes

A tidal disruption event (TDE) occurs when a star is scattered onto a near-radial orbit and is torn apart by a black hole (BH)'s tidal field. The angular momentum threshold for disruption is set by general relativistic tidal dynamics, while the supply of stars to the disruption zone is governed by Newtonian stellar dynamics. A spinning BH breaks the spherical symmetry of the disruption boundary, so a star's survival depends on both the magnitude and the orientation of its angular momentum. Existing treatments either assume a non-spinning BH or rely on numerical simulations of spinning BHs. We develop the first semi analytical framework that incorporates spin-dependent loss cone boundaries into TDE rate theory. Using a novel tidal tensor formalism, we compute inclination-dependent thresholds for tidal disruption and direct capture by the event horizon. We then revisit the classical one dimensional loss cone problem with nested disruption and capture boundaries, deriving a closed form capture fraction valid across all loss cone regimes. Finally, we formulate a two dimensional Fokker--Planck equation describing simultaneous diffusion in angular momentum magnitude and orientation. Through a perturbative treatment, we demonstrate that while the Kerr disruption boundary induces a first-order bias favouring the disruption of retrograde stars, the global TDE rate is remarkably insensitive to black hole spin. This approach offers a tractable route to including spin and orbital inclination in population-level TDE studies.

astro-ph.HE↗

arXiv2025

The relativistic tidal tensor: general solutions for stationary axisymmetric spacetimes and the Hills mass of naked singularities

The tidal forces experienced on an orbit contain, in principle, information about the underlying spacetime an object is moving through. Astronomical observations often probe the properties of tidal forces in the relativistic regime, and could thus in principle be leveraged to examine the properties of strong-field gravity, provided that a general procedure for computing the relativistic tidal tensor is known. Existing techniques for deriving the tidal tensor rely on cumbersome, case-by-case methods. This paper introduces a unified analytical approach to deriving the tidal accelerations experienced by a test particle in any stationary, axisymmetric spacetime. This technique uses standard relativistic frame transformations and is built around the zero angular momentum observer frame. The method's utility is demonstrated in the four traditional black hole metrics: Schwarzschild, Reissner-Nordstrom, Kerr, and Kerr-Newman, as well as a particular wormhole metric. As an example of a possible astronomical application of this work, we discuss the concept of the Hills mass, the maximum mass at which a black hole can disrupt a star, and extend its definition to various naked singularity metrics.

gr-qc↗