Rotational Behaviour of Exotic Compact Objects

TL;DR

The paper investigates solar-mass exotic compact objects composed of self-interacting asymmetric fermionic dark matter with a repulsive Yukawa mediator, and contrasts their static and slow-rotating properties against neutron stars described by the unified SLy4 EOS. Static configurations are computed via the Tolman–Oppenheimer–Volkoff equations, while slow rotation to second order is treated with the Hartle–Thorne formalism for DM masses $m_\chi = 1\,\mathrm{GeV}$ and $m_\chi = 10\,\mathrm{GeV}$; the study analyzes tidal deformability through $k_2$ and $\Lambda$, and rotational observables such as the spin-induced quadrupole $\tilde{Q}$ and eccentricity $e$. The results show that dark-matter stars generally have larger radii and higher tidal deformabilities than NSs at fixed mass, with high-density limits pushing toward an effectively linear equation of state and causing convergence in $k_2$ and $\tilde{Q}$. Rotational diagnostics reveal EOS-driven I–Love–Q trends, and the DM tracks can mimic heavy NS in the mass–radius plane, suggesting that future gravitational-wave observations—particularly with third-generation detectors—could discriminate exotic DM compact objects from baryonic neutron stars in mergers without electromagnetic counterparts.

Abstract

We construct exotic compact objects composed entirely of self-interacting asymmetric fermionic dark matter governed by a repulsive Yukawa potential with massive dark interaction boson. By considering the structural, tidal, and rotational properties of solar mass self-gravitating dark matter systems, and contrasting them against purely baryonic neutron stars, described by the well understood SLy4 equation of state, we hope to shed some light on the place of dark compact systems in the context of gravitational wave astronomy, specifically due to the difficulty parsing mass and radius data from events with no electromagnetic counterpart. Here we consider systems composed of 1 GeV and 10 GeV dark matter. Relevant compact objects are then analysed and simulated as both static bodies, and rotating systems governed by the Hartle-Thorne formalism to second order. Here within we highlight the differences in key tidal and rotational properties encoded in gravitational wave signals, and analyse how dark objects may mimic or distinguish themselves to current and future gravitational wave observatories.

Figures (8)

• Figure 1: Graph of dark fermion mass and dark interaction mass scale, $m_\chi$ and $m_I$. Curves indicate the parameter space of dark fermion and dark interaction boson masses that produce dark compact objects whose maximum mass is similar to the mass of other cold compact objects, for example neutron stars. Dashed lines indicate parameter configurations that produce objects that can attain the same indicated maximum mass across the parameter space. The distinct gradient change present in the curves is most likely determined by which term is a dominant factor in equations \ref{['rhoeos']} and \ref{['peos']}, where the leftmost region is dominated by the dark interaction, and rightmost dominated by fermionic nature of the dark matter particles.
• Figure 2: Mass radius relations of static (solid) and rotating (dashed) compact objects based on the equations of state discussed in Sec. \ref{['sec:SPAEOS']}. The yellow stripe refers to the 1$\sigma$ constraint on the mass of PSR J1810+1744 2021ApJ...908L..46R, and the brown stripe to the 1$\sigma$ constraint on PSR J0348+0432 2013Sci...340..448A. The maroon region corresponds to PSR J0740+6620 2024ApJ...974..295D, the gray to PSR J0030+0451 2019ApJ...887L..24M, tan to GW170817 2018PhRvL.121p1101A, red to J0437-4715 at the $95\%$ confidence level (CL) for the outer region and $68\%$CL inner 2024ApJ...971L..20C, the teal regions to J1231-1411($68\%$CL inner,$95\%$CL outer)2024ApJ...976...58S, and the blue regions to HESS J1713-347($68\%$CL inner,$95\%$CL outer)2022NatAs...6.1444D. Rotating objects revolve at a frequency of 400Hz in all cases, and objects composed entirely of dark matter are indicated in red and blue, with the relevant respective masses indicated.
• Figure 3: Graph of dimensionless $k_2$ love number against object mass for static systems in Figure \ref{['fig:MR']}.
• Figure 4: Compactness-mass curves for static objects in Figure \ref{['fig:MR']}.
• Figure 5: Graph of the dimensionless tidal deformability number $\Lambda$ against Mass. Shaded in gold is the EOS insensitive tidal deformability constraints placed by GW170817 2018PhRvL.121p1101A without a maximum mass constraint. The NS benchmark strongly adheres to observation at all relevant masses, whereas the dark matter objects only fit within these constraints for the highest mass systems.