Gravitational Waves from Mergers of Asymmetric Dark Stars

Abstract

A strongly self-interacting component of asymmetric dark matter (DM) particles can form compact dark stars (DSs). These objects have a broad spectrum of masses and radii, with distinct evolution histories from both neutron stars and black holes (BHs). We argue that these differences allow a population of DSs to contribute significantly to the astrophysical merger rate in unique and discernible ways. Specifically, their merger rate could dominate at low redshifts over other sources, while their mass function may populate windows outside known astrophysical processes. We investigate the structure and formation of DSs within a dissipative model, and calculate the enhancement of their merger cross-section due to tidal deformation effects. From this, we derive the present-day merger rate and its differential mass distribution. These findings open a new window to probe DM substructure and particle interactions through present and future gravitational wave (GW) observatories.

Figures (9)

• Figure 1: Left panel: Number density vs temperature of a dark electron clump in a halo with $M_{\rm halo}=10^{5}M_\odot$ (red rhombus), $M_{\rm halo}=10^{9}M_\odot$ (red solid line) and $10^{13}M_\odot$ (red dotted line), assuming that 10% of the total mass of the halo is in the form of dark electrons. We take the parameter values: $m_{e_D}=2.18~\rm GeV$, $m_{\gamma_D}=60~\rm keV$ and $\alpha_D=0.1$. Solid gray curves: Contours of constant Jeans mass. Red-shaded region: Optical thickness region $R\sigma_c n_{e_D}>1$. Green-shaded region: Region where self-interaction pressure overcomes kinetic pressure $n_{e_D}T_{e_D}<2\pi\alpha_Dn_{e_D}^2/m_{\gamma_D}^2$. Purple-shaded region: BH formation region. Blue-shaded region: Region where bremsstrahlung cooling is inefficient and DSs would not have been formed by today. Right panel: Same as left, but for $m_{e_D}=208.4~\rm GeV$, $m_{\gamma_D}=17~\rm eV$ and $\alpha_D=0.1$.
• Figure 2: Left panel: Range of halo masses leading to DS formation at redshift $z$, for $m_{e_D}=2.18~\rm GeV$ and $m_{\gamma_D}=60~\rm keV$ (red-colored region), $m_{e_D}=1.91~\rm GeV$ and $m_{\gamma_D}=40~\rm keV$ (blue-colored region) and $m_{e_D}=208.4~\rm GeV$ and $m_{\gamma_D}=17~\rm eV$ (cyan-colored region). The rest of parameters are as in Fig. \ref{['fig:Formation_phase_space']}. Right panel: DS mass density as a function of redshift. The colored curves correspond to the benchmark parameters from the left panel.
• Figure 3: Left panel: Mass-radius relation for a DS with EoS \ref{['eq:EOS']} for $\alpha_D=0.1$ and three choices of dark electron and dark photon mass. The star-shaped points correspond to configurations of DS mass of $1000M_\odot$, but with different compactness. The black-colored area shows the unavailable region of compactness $C\geq0.5$, corresponding to BHs. Right panel: Mass density distribution as a function of the radius of the DS. The density distributions correspond to the benchmark points (colored stars) indicated in the left panel.
• Figure 4: Parameter space in dark photon vs dark electron mass for fixed $\alpha_D=0.1$. The red contours correspond to constant DS mass (in units of $\log_{10}(M_{\rm DS}/M_\odot)$), while the light blue ones show the compactness in units of $\log_{10}(C)$. The black-shaded regions are the space where the solutions satisfy $C\geq0.5$, and correspond to BHs.
• Figure 5: Merger cross section contours (cyan, in units of $\log_{10}(\sigma_{\rm merge}/{\rm pc}^2)$) in the DS mass vs radius plane for $v_{\rm rel}=200~\mathrm{km}~\mathrm{s}^{-1}$. The black lines correspond to contours of constant compactness and the black region correspond to BH. The green area shows the region where tidal capture and collision are subdominant and the cross section is given by \ref{['eq:sigma_GW']}, the red area is where tidal effects dominate and the blue area where the geometrical cross section is most important.