arXiv subjects

Elisha Modelevsky

Publications and source records attributed to Elisha Modelevsky.

3 recordsLinked to original sources

arXiv2026

Emission line formation in scattering dominated media: implications for LRDs

Recent JWST observations of ``Little Red Dots'' (LRDs) reveal broad and prominent Balmer emission lines. We present a theoretical framework for intrinsic emission line formation and broadening within static, optically thick, scattering-dominated gas envelopes with thermal populations. Using random-walk and diffusion approximations, we derive analytical line profiles for lines forming intrinsically within the scattering medium. We demonstrate that a geometrically thin planar photosphere produces a shallow line profile characterized by a logarithmic plateau and a $v^{-1}$ wing. A radially extended photosphere yields a broken power-law spectrum transitioning from $v^{-\alpha}$ to $v^{-(\alpha+1)}$, with $0 < \alpha < 1$. This is in contrast to a scattering medium external to the line-forming region, which produces an exponential line profile. We show that this broken power-law model can fit the $\mathrm{H}\alpha$ line profiles observed in LRDs. Higher quality spectra may be able to distinguish between intrinsic and extrinsic models for the line broadening in LRDs. In our LTE models, the high contrast between the $\mathrm{H}\alpha$ and continuum flux cannot be explained. Quantitative comparison to LRD spectra requires expanding our models to non-LTE situations.

astro-ph.GA↗

arXiv2024

The unreasonable effectiveness of the $n \Sigma v$ approximation

In kinetic theory, the classic $n \Sigma v$ approach calculates the rate of particle interactions from local quantities: the number density of particles $n$, the cross-section $\Sigma$, and the average relative speed $v$. In stellar dynamics, this formula is often applied to problems in collisional (i.e. dense) environments such as globular and nuclear star clusters, where blue stragglers, tidal capture binaries, binary ionizations, and micro-tidal disruptions arise from rare close encounters. The local $n \Sigma v$ approach implicitly assumes the ergodic hypothesis, which is not well motivated for the densest star systems in the Universe. In the centers of globular and nuclear star clusters, orbits close into 1D ellipses because of the degeneracy of the potential (either Keplerian or harmonic). We find that the interaction rate in perfectly Keplerian or harmonic potentials is determined by a global quantity -- the number of orbital intersections -- and that this rate can be far lower or higher than the ergodic $n \Sigma v$ estimate. However, we find that in most astrophysical systems, deviations from a perfectly Keplerian or harmonic potential (due to e.g. granularity or extended mass) trigger sufficient orbital precession to recover the $n \Sigma v$ interaction rate. Astrophysically relevant failures of the $n \Sigma v$ approach only seem to occur for tightly bound stars orbiting intermediate-mass black holes, or for the high-mass end of collisional cascades in certain debris disks.

astro-ph.HE↗

arXiv2021

Revisiting the Strong Shock Problem: Converging and Diverging Shocks in Different Geometries

Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We study the flow of an ideal gas with adiabatic index $γ$ with initial density $ρ\sim r^{-ω}$, containing a strong shock wave. We characterize the self-similar solutions in the entirety of the parameter space $γ,ω$, and draw the connections between the different geometries. We find that only type II self-similar solutions are valid in converging shocks, and that in some cases, a converging shock might not create a reflected shock after its convergence. Finally, we derive analytical approximations for the similarity exponent in the entirety of parameter space.

astro-ph.HE↗