Partial tidal disruption of White Dwarfs in off-equatorial orbits around Kerr black holes

TL;DR

Partial TDEs of spinning white dwarfs on off‑equatorial orbits around Kerr IMBHs are explored with SPH coupled to exact Kerr geodesics for orbital motion and Newtonian hydrodynamics. The study finds spin–orbit coupling and orbital inclination modulate core mass loss, debris energy distributions, and gravitational wave signals, yet observable quantities show degeneracies with equatorial cases, limiting single‑messenger discrimination. Key results include a late‑time fallback slope of $t^{-9/4}$ and gravitational‑wave amplitudes of order $|h|\sim 1.83\times10^{-22}$ at a distance of $d=20$ Mpc, with off‑equatorial outcomes filling the intermediate regime between prograde and retrograde equatorial cases. The authors argue these behaviors generalize to TDEs around spinning BHs across IMBH and SMBH scales and suggest multi‑messenger observations to break parameter degeneracies and better constrain system properties.

Abstract

We present the results of a suite of numerical simulations using smoothed particle hydrodynamics to study partial tidal disruption events (TDEs) of white dwarfs (WDs) in off-equatorial orbits in intermediate mass spinning (Kerr) black hole backgrounds. We carry out this analysis for both parabolic and eccentric WD orbits and also take into account possible initial WD spins. Our objective here is to quantify the differences in variables like the mass of the self-bound core, the peak fallback rate of debris and gravitational wave signature in off-equatorial orbits compared to equatorial ones. The analysis is carried out using a hybrid numerical scheme, one which involves integrating the exact Kerr geodesics while adopting a Newtonian formalism for the stellar fluid dynamics, justified by our choice of simulation parameters. We find that the physics of TDEs in off-equatorial orbits present several interesting and novel features due to black hole spin, which in some cases enhances when coupled with the rotation of the WD. However, numerical values of observable quantities in TDEs involving off-equatorial orbits cannot possibly distinguish between such orbits from equatorial ones. We further comment on the genericness of our results and argue that these should extend to a general TDE scenario involving a spinning BH.

Figures (16)

• Figure 1: The tidal radius $r_t$ plotted as a function of $n$ where the WD mass $M_{\rm WD}=n\times M_{\odot}$. The curved lines from top to bottom indicate BHs of $10^3,10^4,5\times 10^4$ and $10^5$ solar masses. The brown and pink horizontal lines indicate $r_t=10$ and $1.2$ respectively, while the vertical line indicates $n=0.8$.
• Figure 2: The core mass fraction, $M_{\text{core}} / M_{\text{wd}}$ , is plotted against the normalized time $t/t_p$ where $t_p\approx28$ sec for the specified values of inclination angle, $\theta_a$ and BH spin, $a^{\star}$. Left Panel shows the variation for a parabolic orbit, whereas Right Panel shows the variation for an eccentric orbit with $e = 0.9$.
• Figure 3: The differential mass distribution, $\text{dM}/\text{d}\epsilon$, is plotted against the normalized specific energy $\epsilon$ for the specified values of inclination angle, $\theta_a$ and BH spin, $a^{\star}$. Left Panel shows the variation for a parabolic orbit, whereas Right Panel shows the variation for an eccentric orbit with $e = 0.9$
• Figure 4: Geodesics and accelerations for a test particle orbiting in an off-equatorial parabolic orbit around a Kerr BH at the origin with spin $a^{\star}=\pm0.98$. The coordinates and distances are normalized with tidal radius, $r_t$ of the BH. Top Left Panel: The $y$--$z$ projection of the test particle’s trajectory in the inclined orbit $\theta_a = 1^{\circ}$. Bottom Left Panel: The trajectory of the test particle for $\theta_a = 90^{\circ}$, i.e., on the $x$--$y$ plane (equatorial orbit). Right Panel: The variation of the magnitude of the acceleration with radial distance for all the specified cases.
• Figure 5: Angle subtended by the orbital angular momentum of a test particle with the $z$-axis. Left Panel: For the $\theta_a = 1^\circ$ case, the orbital motion of the test particle is not strictly confined to a plane around the spinning BH; however, it remains well restricted to $\theta_a=1^\circ$ off-equatorial plane around non-spinning BH. Right Panel: For the equatorial case ($\theta_a = 90^\circ$), the orbital motion lies entirely within the plane for both spinning and non-spinning BH.