Dark Matter Heating of Compact Stars Beyond Capture: A Relativistic Framework for Energy Deposition by Particle Beams

TL;DR

The paper addresses how directed, high-energy particle fluxes, such as boosted dark matter from blazar jets, deposit energy in compact stars. It builds a fully general relativistic framework that maps an asymptotic beam into local stellar densities via geodesic congruences, incorporating gravitational focusing, multiple-streaming, and optical-depth effects while distinguishing capture-driven heating from through-going energy deposition. It provides explicit formulas for interaction rates in degenerate matter across elastic, DIS, and RES channels and defines the interaction roof and geometric limit to describe saturation of heating, with a concrete application to white dwarfs and neutron stars exposed to a 324-blazar boosted DM flux. The approach is modular and can accommodate arbitrary DM–SM interactions and flux geometries, making it a versatile tool for exploring DM-induced heating of compact objects in regimes beyond conventional halo DM and for informing potential observational signatures.

Abstract

Compact astrophysical objects, such as neutron stars and white dwarfs, can act as detectors of energetic particle fluxes originating from astrophysical accelerators. While most existing capture and heating calculations assume isotropic very low energetic incident fluxes from the halo dark matter, many realistic sources produce highly directional beams or jets, for which gravitational focusing, trajectory multiplicity, and local energy deposition must be treated consistently. In this work, we develop a general relativistic formalism to compute the local density, capture probability, and energy deposition of particles arriving as directed beams onto compact objects. The framework is based on the mapping of an asymptotic particle flux to local densities through geodesic congruences, allowing for gravitational focusing, multi-stream regions, and optical depth effects to be incorporated in a unified way. The formalism applies to arbitrary particle species and interaction models, and separates capture from through-going energy deposition in a frame-consistent manner. As an explicit application, we consider relativistic particle beams generated in astrophysical jets and evaluate their interaction with two compact objects samples: a white dwarf and a neutron star. In particular, we illustrate the framework using boosted dark matter produced in a list of 324 blazars as a representative case study, computing the resulting fluxes and the associated heating in the selected stars. Additional regimes such as the interaction roof and geometric limit are discussed, highlighting the conditions under which compact objects can efficiently convert incident beam energy into observable heating.

Figures (4)

• Figure 1: Example of geodesic trajectories used to determine the number of particles per unit volume for a WD (left) and an NS (right). Each curve represents the trajectory of a BBDM particle with a different impact parameter $b$, originating in the upper half--plane and propagating toward the compact object (grey disk). Region 1 (gold) corresponds to single, non-degenerate trajectories. Regions 2a (orange) and 2b (green) represent overlapping congruences of geodesics that both traverse the lower half--plane. The overlap of these families defines the multi--stream region relevant for computing $dN$.
• Figure 2: Left panel: Fluxes for the vector and axial benchmark cases with $m_\chi =10\,\mathrm{MeV},\, 1\,\mathrm{GeV}$ and $m_{Z^\prime} = 3\,m_\chi$, after excluding contributions from sources whose DM particles would not reach the Galaxy within the blazar lifetime. Right panel: Maximum redshift $z$ from which DM particles of different masses and kinetic energies can arrive within a typical blazar lifetime ($\sim 10\,\mathrm{Gyr}$). The dashed gray line indicates the minimum redshift of the 324 blazars considered, the dotted line the maximum, and the dash-dotted line highlights the blazar providing the dominant contribution.
• Figure 3: Heating of the WD benchmark induced by BBDM, for $m_\chi = 10~\mathrm{MeV}$ and $m_\chi = 1~\mathrm{GeV}$ with $m_{Z^\prime} = 3\,m_\chi$, considering both vector and axial couplings. Dashed lines denote the optically thin limit, the interaction roof, and the geometric limit.
• Figure 4: Heating of the NS benchmark induced by BBDM, for $m_\chi = 10~\mathrm{MeV}$ and $m_\chi = 1~\mathrm{GeV}$ with $m_{Z^\prime} = 3\,m_\chi$, considering both vector and axial couplings. Dashed lines denote the optically thin limit, the interaction roof, and the geometric limit.