$g$-mode oscillations of dark matter admixed neutron stars

TL;DR

This paper shows that DM admixing in neutron stars systematically raises $g$-mode frequencies, with the frequency shift $\ig\Delta\nu_{g_i}\big$ showing a near-universal linear dependence on the DM fraction $f_{DM}$ regardless of the nuclear EoS. Using a RMF hadronic EoS coupled with a self-interacting DM sector motivated by the neutron decay anomaly, the authors compute equilibrium and adiabatic speeds of sound and solve the $g$-mode spectrum in the Cowling approximation, finding principal and first overtone frequencies that can reach up to ~900 Hz. They demonstrate that DM fraction, not microscopic nuclear parameters, dominantly controls the $g$-mode shifts, and provide EOS-independent fits linking $\ u_{g}$ to $f_{DM}$. The results imply that high-frequency $g$-modes in NSs, especially at lower masses, could serve as signatures of DM in the stellar interior and motivate using future gravitational-wave observations to constrain DM content in NSs.

Abstract

We investigate $g$-mode oscillations in dark matter admixed neutron stars employing a relativistic mean field model to describe hadronic matter and a model for self-interacting fermionic dark matter motivated by the neutron decay anomaly. Following the construction of such admixed configurations, we derive the equilibrium and adiabatic speeds of sound therein, leading to a computation of the star's $g$-mode spectrum in the Cowling approximation. In particular, we explore the effect of dark matter self-interaction, the nucleon effective mass and dark matter fraction on the principal $g$-mode frequency, and its first overtone. We show that the effect on $g$-mode frequency depends predominantly on the dark matter fraction, and demonstrate an equation of state-independent constraint for the latter. Prospects of identifying the presence of dark matter in neutron stars using $g$-mode are discussed.

Figures (10)

• Figure 1: a) The EoS bands and corresponding b) mass-radius bands for DM admixed NS for "RMF" set parameters satisfying the two solar mass constraint. The widest (faintest) band corresponds to $m^*/m=0.55$, and the narrowest (darkest) corresponds to $m^*/m=0.75$. The intermediate ones are for increasing values of $m^*/m$ in steps of 0.05 as we go from the widest to the narrowest. See text for more details.
• Figure 2: Sound speed difference $c^2_s-c^2_e$ plotted for the various effective mass values of the "RMF" set. The solid curves are for the EoSs without any DM and the dashed ones are for DM admixed EoSs with $G=30$ fm$^2$.
• Figure 3: The fundamental mode a) $g_1$ and first overtone b) $g_2$ of $g$-mode frequency as a function of mass for DM admixed NS with hadronic matter modeled by "RMF" set of parameters as enlisted in \ref{['table:parameters']}. $m^*/m$ has been fixed to 0.65. We show the variation of $\nu_{g_1}$ and $\nu_{g_2}$ for different values of $G$. The colour bar denotes the DM fraction.
• Figure 4: The increase in fundamental $g1$ and first overtone $g_2$ of $g$-mode frequency as a function of mass for DM admixed NS with hadronic matter modelled by "RMF" set of parameters as enlisted in \ref{['table:parameters']}. $m^*/m$ has been fixed to 0.65. We show the variation of $\nu_{g_1}$ (solid) and $\nu_{g_2}$ (dashed) for different values of $G$.
• Figure 5: The fundamental $g1$ and first overtone $g_2$ of $g$-mode frequency for a) pure hadronic NS with "RMF" EoS and b) DM admixed NS with hadronic matter modeled by the RMF EoS and the DM self-interaction strength set to $G=30$ fm$^2$. This has been shown for the different effective masses of the RMF EoS in the range [0.55,0.75]. As $G=30$ fm$^2$, the DM fraction is approximately given by $f_{DM} = \frac{1}{30}(\frac{M}{M_{\odot}})$ using the relation proposed in Shirke2024.