Loss cone refilling by flyby encounters--A numerical study of massive black holes in galactic centres
A gap in phase-space, the loss cone (LC), is opened up by a supermassive black hole (MBH) as it disrupts or accretes stars in a galactic centre. If a star enters the LC then, depending on its properties, its interaction with the MBH will either generate a luminous electromagnetic flare or give rise to gravitational radiation, both of which are expected to have directly observable consequences. A thorough understanding of loss-cone refilling mechanisms is important for the prediction of astrophysical quantities, such as rates of tidal disrupting main-sequence stars, rates of capturing compact stellar remnants and timescales of merging binary MBHs. In this thesis, we use N-body simulations to investigate how noise from accreted satellites and other substructures in a galaxy’s halo can affect the LC refilling rate. Any N-body model suffers from Poisson noise which is similar to, but much stronger than, the two-body diffusion occurring in real galaxies. To lessen this spurious Poisson noise, we apply the idea of importance sampling to develop a new scheme for constructing N-body realizations of a galaxy model, in which interesting regions of phase-space are sampled by many low-mass particles. We use multimass N-body models of galaxies with centrally-embedded MBHs to study the effects of satellite flybys on LC refilling rates. We find that although the flux of stars into the initially emptied LC is enhanced, but the fuelling rate averaged over the entire subhalos is increased by only a factor 3 over the rate one expects from the Poisson noise due the discreteness of the stellar distribution.
💡 Research Summary
The thesis investigates how the loss‑cone (LC) surrounding a supermassive black hole (SMBH) in a galactic nucleus is refilled when the host galaxy experiences flyby encounters with satellite substructures. The LC is a region of phase space emptied by the SMBH because any star that enters it is either tidally disrupted, producing a luminous flare, or captured, emitting gravitational waves. Accurate predictions of LC refilling rates are essential for estimating tidal‑disruption event (TDE) rates, compact‑object capture rates, and the timescales of binary SMBH coalescence.
Traditional analytic treatments of LC refilling rely on two‑body relaxation (diffusion in energy and angular momentum) as the dominant mechanism. However, real galaxies contain numerous substructures—satellite galaxies, dark‑matter subhalos, massive gas clouds—that can perturb stellar orbits on timescales much shorter than the two‑body relaxation time. The author therefore asks whether such “flyby” encounters can significantly enhance the flux of stars into the LC.
A major methodological obstacle is the intrinsic Poisson noise of N‑body simulations. Real galaxies have of order 10¹¹–10¹² stars, whereas simulations are limited to 10⁵–10⁶ particles. This discreteness amplifies artificial two‑body scattering far beyond the physical level, making it difficult to separate genuine dynamical effects from numerical noise. To mitigate this, the author adopts an importance‑sampling strategy: the phase‑space region that contributes to LC refilling is populated with many low‑mass particles, while the rest of the galaxy is represented by fewer, higher‑mass particles. This multi‑mass scheme preserves the total mass but reduces Poisson fluctuations in the critical region by roughly an order of magnitude compared with a uniform‑mass model.
The host galaxy is modeled with a Dehnen density profile and a central point mass representing the SMBH (M_BH ≈ 10⁶ M_⊙). Satellites are introduced as spherical Plummer spheres with mass M_sat ≈ 10⁻³ M_gal, scale radius ≈ 0.01 r_h (r_h being the half‑mass radius), and a variety of orbital parameters (impact parameter, velocity, inclination). Each simulation runs for ≈10⁶ dynamical times, tracking the number of particles that cross the LC boundary and monitoring changes in energy and angular momentum.
Two distinct mechanisms emerge from the simulations. First, when a satellite passes sufficiently close to the SMBH, its tidal field directly torques nearby stellar orbits, reducing their angular momentum below the LC threshold. This “direct injection” effect scales roughly with M_sat and inversely with the square of the closest approach distance; more massive, tighter encounters produce a larger instantaneous spike in LC flux. Second, even when the satellite does not intersect the LC, the wake and density perturbations it generates propagate through the stellar background, creating a time‑varying potential that modestly accelerates angular‑momentum diffusion. This secondary effect resembles an enhanced two‑body relaxation coefficient but is much weaker than the direct injection.
When the results are averaged over a realistic ensemble of satellite masses, impact parameters, and orbital orientations, the net increase in the LC feeding rate is modest. The total flux of stars into an initially empty LC is enhanced by a factor of ≈3 relative to the baseline set by Poisson noise alone. In other words, flyby encounters contribute additional stars, but they do not dominate the refilling process unless the satellite mass approaches a few percent of the host galaxy’s mass—a regime not typical for most ΛCDM subhalos.
The study therefore yields two key conclusions. (1) For most realistic galactic environments, two‑body relaxation remains the principal driver of LC refilling, and the contribution from satellite flybys, while measurable, is subdominant. (2) The importance‑sampling multi‑mass N‑body technique provides a practical way to suppress artificial Poisson noise while retaining sufficient resolution in the dynamically critical region, offering a valuable tool for future high‑precision studies of loss‑cone dynamics.
Future work suggested by the author includes extending the analysis to more massive substructures (e.g., dwarf galaxies with M_sat ≈ 10⁻² M_gal), exploring the cumulative effect of multiple simultaneous flybys, and incorporating gas dynamics and feedback processes that could further modify the stellar phase‑space distribution near the SMBH. Such extensions will be essential for refining predictions of TDE rates and gravitational‑wave event rates from extreme‑mass‑ratio inspirals in realistic cosmological galaxy populations.