Gravothermal Pile-Up of Collisional Dark Matter Around Compact Objects

Abstract

The dark matter may consist of multiple species that interact differently. We show that a species that is cosmologically subdominant but highly collisional can pile up and become dominant in deep gravitational wells, such as those of white dwarfs and neutron stars.

Figures (9)

• Figure 1: Gravothermal pile-up mechanism. Collisionless cold dark matter (CDM) transiting through a gravitational well gets mildly focused. Collisional DM subcomponent $\chi$ instead piles up gravothermally: as heat flows out through conduction, decreased pressure lets more $\chi$ particles to flow in. Around a sufficiently deep gravitational well $\Phi$, the subcomponent $\chi$ can be locally dominant over the CDM.
• Figure 2: Results of a gravothermal simulation of subcomponent particles $\chi$ accumulating around the benchmark WD of Table \ref{['tab:co_sources']}. Left: Snapshots of $\chi$'s density $\rho_\chi$, $\chi$'s temperature per unit mass $T_m$, and the WD's gravitational potential $\Phi$, rescaled by the ambient values, $\rho_\chi^\infty$ and $T_m^\infty$, as indicated. The color scale (light to dark) indicates the direction of time evolution. The radius $R_\star$ and gravitational-influence radius $\lambda_{\rm grav}$ of the WD as well as the radius $r_{\rm iso}(t_{\rm end})$ and temperature $T_m^{\rm iso}(t_{\rm end})$ of the isothermal core at the end of the simulation are marked. Right: Central density $\rho_\chi(R_\star)$ vs isothermal-core temperature $T_m^{\rm iso}$ phase space, rescaled as indicated. The system first evolves adiabatically to reach the hydrostatic state of Eq. \ref{['eq:adiabatic']}, before proceeding to cool and pile up gravothermally. The orange circles are representative points from the simulation. The purple curves are analytical expectations based on three different assumptions on the $T_m$ profile outside of the isothermal core: (1) the initial adiabatic profile (dashed), (2) the steady-state profile with $\dot{s}\propto -\vec{\nabla}.\vec{\mathcal{F}}\approx 0$ (dotted), and (3) $\eta_{\rm eff}=1$, a simplifying assumption used in the main text (solid). Subcomponents with different $f$ and $\sigma_m$ values evolve along the same evolution curve at rates proportional to $f\sigma_m$ and reach different terminal points after $10\text{ Gyr}$ (the age of the WD), as indicated in gray dots. Apart from that, other features of both plots apply equally for all $f$ and $\sigma_m$ values.
• Figure 3: Subcomponent $\chi$ parameter space. Here, $f$ is $\chi$'s galactic DM fraction, $\sigma_m$ is $\chi$'s cross-section-to-mass ratio, and $\rho_\chi(R_\star)/\rho_\chi^\infty$ is $\chi$'s final density-enhancement factor at the radius $R_\star$ of the central compact object: white dwarf (left) and neutron star (right). Regions of the parameter space ruled out by Bullet Cluster observations and favored by the SIDM paradigm are shown in gray and purple, respectively. Below the dashed lines, $\tau_{\rm col}\gtrsim 10\text{ Gyr}$, and so the assumptions of the gravothermal formalism are not satisfied. Above the dotted lines, the ambient subcomponent behaves as a perfect fluid on galactic scales. The $\rho_\chi(R_\star)/\rho_\chi^\infty$ are obtained by integrating Eq. \ref{['eq:simpheatEq']} using Eq. \ref{['eq:rhoiso']} with $\eta_{\rm iso}=\bar{\eta}=\eta_{\rm eff}=1$. Above the solid lines, the final central densities of the accumulated $\chi$ particles satisfy $\rho_\chi(R_\star)/(0.4\mathinner{\mathrm{GeV}}/\text{cm}^3)\gtrsim 20\text{ (WD)}, 600\text{ (NS)}$, and thereby locally dominate over gravitationally focused cold collisionless DM inside the compact objects.
• Figure 4: Snapshots of simulated $\eta$ profile (defined in Eq. \ref{['eq:etadefinitions']}) for a subcomponent pile around the benchmark white dwarf of Table \ref{['tab:co_sources_sm']}. The radius $r$ from the center of the white dwarf ranges from $r_{\rm iso}$ (defined in Eq. \ref{['eq:riso']}) to $\lambda_{\rm grav}$ (defined in Eq. \ref{['eq:etadefinitions']}. The scale time $t_0$ is defined in Eq. \ref{['eq:scalet']}. Also shown are the adiabatic and steady profiles, $\eta_{\rm ad}(r)$ and $\eta_{\rm st}(r)$, defined in Eq. \ref{['eq:etaad']} and \ref{['eq:etast']}. It can be seen that the simulated $\eta$ profile begins with $\eta_{\rm ad}(r)$ and approaches $\eta_{\rm st}(r)$.
• Figure 5: Snapshots of simulated outward heat-conduction luminosity $L$ profiles (defined in Eq. \ref{['eq:gravothermal2']}) for a subcomponent pile around the benchmark white dwarf of Table \ref{['tab:co_sources_sm']}. The radius $r$ from the center of the white dwarf ranges from $r_{\rm iso}$ (defined in Eq. \ref{['eq:riso']}) to $\lambda_{\rm grav}$ (defined in Eq. \ref{['eq:etadefinitions']}. The scale quantities $L_0$ and $t_0$ are defined in Eqs. \ref{['eq:scaleluminosity']},\ref{['eq:scalerho']}\ref{['eq:scalev']},\ref{['eq:scalet']}, and \ref{['eq:scalesigma']}. It can be seen that the $L$ profile evolves toward and settles at a spatially-uniform steady-state.