The Evolution of Pop III.1 Protostars Powered by Dark Matter Annihilation. II. Dependence on WIMP Properties

TL;DR

The paper tests whether DM annihilation heating from WIMP capture can alter Pop III.1 protostellar evolution to form heavy black hole seeds, by surveying a wide parameter space in DM density $ρ_χ$, WIMP mass $m_χ$, and spin-dependent cross section $σ_{SD}$ using the GENEC code with Gould capture. It finds a robust bifurcation: for $ρ_χ \,gtrsim 5×10^{14}$ GeV cm$^{-3}$ and $σ_{SD} \,gtrsim 10^{-41}$ cm$^2$, DM heating inflates protostars onto Hayashi tracks, suppressing ionizing feedback and enabling growth to $\ ilde{M_*} \,\sim 10^5 M_⊙$; lighter $m_χ$ enhances this effect, while heavier $m_χ$ delays or prevents it, with a threshold around $m_χ ∼ 3$ TeV. The total DM mass in equilibrium scales approximately as $M_{χ,tot} ∝ (T_c/ρ_c)^{3/4} m_χ^{-1/4}$, implying heavier WIMPs contribute less DM mass despite higher per-particle energy. These results imply that DM annihilation provides a viable channel for heavy black hole seed formation in plausible early-universe halos, subject to DM microphysics and environmental density. The work outlines robustness limitations and suggests future extensions to include halo contraction, multi-dimensional effects, and observational predictions.

Abstract

The rapid appearance of supermassive black holes (SMBHs) at $z\gtrsim7$ requires efficient pathways to form massive black hole seeds. We investigate whether annihilation of weakly interacting massive particles (WIMPs) can alter primordial (Pop III.1) protostellar evolution sufficiently to enable formation of such `heavy'' seeds. Using the one-dimensional Geneva stellar-evolution code (GENEC) with an implemented Gould single-scatter capture module, we compute a grid of protostellar evolution models covering ambient WIMP mass densities $ρ_χ=10^{12}$-$10^{16}\ \mathrm{GeV\,cm^{-3}}$, WIMP masses $m_χ=30$-$3000\ \mathrm{GeV}$, spin-dependent cross sections $σ_{\rm SD}=10^{-42}$-$10^{-40}\ \mathrm{cm^2}$, and baryonic accretion rates $\dot{M_*}=(1-3)\times10^{-3}\, M_\odot \,{\rm yr}^{-1}$. We find a robust bifurcation of outcomes. For sufficiently high ambient dark matter density ($ρ_χ\gtrsim5\times10^{14}\ \mathrm{GeV\,cm^{-3}}$) and capture efficiency ($σ_{\rm SD}\gtrsim10^{-41}\ \mathrm{cm^2}$) WIMP annihilation supplies enough energy to inflate protostars onto extended, cool (Hayashi-track) configurations that dramatically suppress ionizing feedback and permit uninterrupted growth to $\sim10^{5}\,M_\odot$. Lighter WIMPs and larger $σ_{\rm SD}$ favour earlier and stronger annihilation support; heavier WIMPs delay the effect. For our fiducial case, WIMP masses $<$3 TeV are essential for allowing growth to the supermassive regime, otherwise the protostar evolves to the compact, feedback-limited regime that results in `light'' seeds. These results indicate that, under plausible halo conditions, DM annihilation provides a viable channel for forming heavy black hole seeds.

Figures (7)

• Figure 1: Total WIMPs capture rate $C_c$ as a function of stellar mass for accreting Population III protostar models. Left: Six models at fixed ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, accretion rate $\dot{M} = 3 \times 10^{-3} \, M_\odot \, {\rm yr}^{-1}$, and scattering cross section $\sigma_{\rm SD} = 10^{-41} \, {\rm cm}^2$, for WIMP masses $m_\chi =$ 30, 50, 100, 300, 1000, and 3000 GeV. Right: Three models with fixed WIMP mass $m_\chi = 100 \, GeV$ and ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, varying spin-dependent scattering cross section $\sigma_{\rm SD} = 10^{-42}$, $10^{-41}$, and $10^{-40} \, {\rm cm}^2$ for the same accretion rate.
• Figure 2: Annihilation luminosity $L_\chi = \frac{2}{3} \, m_\chi \, C_c$ as a function of stellar mass for accreting Population III protostar models. Left: Six models at fixed ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, accretion rate $\dot{M} = 3 \times 10^{-3} \, M_\odot \, {\rm yr}^{-1}$, and scattering cross section $\sigma_{\rm SD} = 10^{-41} \, {\rm cm}^2$, for WIMP masses $m_\chi =$ 30, 50, 100, 300, 1000 and 3000 GeV. Right: Three models with fixed WIMP mass $m_\chi = 100 \, {\rm GeV}$ and ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, varying spin-dependent scattering cross section $\sigma_{\rm SD} = 10^{-42}$, $10^{-41}$, and $10^{-40} \, {\rm cm}^2$ for the same accretion rate.
• Figure 3: Radius versus stellar mass for accreting Population III protostar models. Left:$R_*$ is the stellar radius and $r_\chi$ the WIMP characteristic length for six models at fixed ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, accretion rate $\dot{M} = 3 \times 10^{-3} \, M_\odot \, {\rm yr}^{-1}$, and scattering cross section $\sigma_{\rm SD} = 10^{-41} \, {\rm cm}^2$, for WIMP masses $m_\chi =$ 30, 50, 100, 300, 1000 and 3000 GeV. Right: Four models at a fixed WIMP mass $m_\chi = 100 \, GeV$ and ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, for spin-dependent scattering cross sections $\sigma_{\rm SD} = 10^{-42}$, $10^{-41}$, $10^{-40} \, {\rm cm}^2$ and the No-WIMPs model.
• Figure 4: Evolution of central temperature versus central density for accreting Population III protostar models. Left: Seven models at a fixed ambient WIMP density of $10^{15} \, {\rm GeV \, cm}^{-3}$ and accretion rate $\dot{M} = 3\times10^{-3} \, M_\odot \, {\rm yr}^{-1}$, for WIMP masses 30 GeV, 50 GeV, 100 GeV, 300, 1000, 3000 GeV, and the No-WIMPs case (standard Pop III). The colour-shaded regions denote regimes of no nuclear burning ($T_c < 10^6$ K), deuterium burning ($10^6 \lesssim T_c/{\rm K} < 10^{8.15}$), and hydrogen ignition ($T_c \gtrsim 10^{8.15}$ K), respectively. Right: Four models at a fixed WIMP mass $m_\chi = 100$ GeV and ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, for spin-dependent scattering cross sections $\sigma_{\rm SD} = 10^{-42}$, $10^{-41}$, $10^{-40} \, {\rm cm}^2$ and the No-WIMPs case. The colour-shaded regions represent the same nuclear burning temperatures.
• Figure 5: Hertzsprung–Russell diagrams for accreting Population III protostar models. Left: Seven models at a fixed ambient WIMP density of $10^{15} \, {\rm GeV \, cm}^{-3}$ and accretion rate $\dot{M} = 3\times10^{-3} \, M_\odot \, {\rm yr}^{-1}$, for WIMP masses $m_\chi =$ 30 GeV, 50 GeV, 100 GeV, 300 GeV, 1000 and 3000 GeV and the No-WIMPs model (standard Pop III). The black line marks the Pop III Zero-Age Main Sequence (ZAMS). Right: Four models at a fixed WIMP mass $m_\chi = 100$ GeV and ambient dark matter density $\rho_\chi = 10^{15} \, {\rm GeV \, cm}^{-3}$, for spin-dependent scattering cross sections $\sigma_{\rm SD} = 10^{-42}$, $10^{-41}$, and $10^{-40} \, {\rm cm}^2$ and the No-WIMPs case.