What Are The Effects of Dark Matter On the Inspiral Properties of the Binary Neutron Star? (Planetary Science)

The binary neutron star (BNS) in its inspiral phase tidally interact with each other, which affects their stellar structure. Each star’s tidal property depends on the macroscopic properties, such as mass M, radius R, second Love number k2 etc. which are all model-dependent.

Now, Das and colleagues studied the properties of the binary neutron star (BNS) systems in the inspiral phase. To calculate the equation of state (EOS) of the neutron star (NS), they take the relativistic mean-field (RMF) model. The RMF model, namely NL3 (stiff) and two extended RMF model IOPB-I (less stiff) and G3 (soft) are taken to explore the properties of the NS.

They assumed that the dark matter (DM) particles are accreted inside the NS due to its enormous gravitational field. Different macroscopic properties of the NS such as mass M, radius R, tidal deformability λ and dimensionless tidal deformability Λ are calculated at different DM fractions. They found that with the addition of DM inside the NS, the value of the quantities like M, R, λ and Λ decreases.

FIG. 1. (colour online) (2,2) mode waveform, frequency, phase and PN-parameters are shown for three (NL3, G3 and IOPB-I) parameter sets of the EMBNS in the retarded time interval calculated for D = 100 Mpc. © Das et al.

To explore the BNS properties in the inspiral phase, they also considered post-Newtonian (PN) formalism because it is suitable up to the last orbits in the inspiral phase. They calculated the strain amplitude of the polarization waveforms h+ and h×, (2,2) mode waveform h22, orbital phase Φ, frequency of the gravitational wave f and PN parameter x with DM as an extra candidate inside the NS..

“We find that the BNS with soft EOS sustains more time in their inspiral phase as compare to stiff EOS. In the case of DM admixed NS, the BNS with high DM fractions survives more time in the inspiral phase than lesser fraction of DM. The magnitude of f, Φ and x are almost the same for all the assumed parameter sets, but their inspiral time in the last orbit is different. We find a significant change in the BNS systems properties in the inspiral phase with DM inside the NS.”

— told Das, first author of the study.

They found that stiff EOS, like NL3, predicts higher mass and tidal deformability compared to the soft EOS like G3. Therefore, the massive NS easily deformed by the presence of tidal fields created by its companion star. Hence, a less massive BNS system sustains a longer time than a more massive BNS system in the inspiral phase. This is because the tidal interactions accelerate the orbital evolution in the late inspiral phases due to increase in the interactions forces between two NSs.

FIG. 2. (colour online) Same as Fig. 1, but for DM admixed NS with IOPB-I parameter set as a representative case. © Das et al.

Furthermore, they found that, with the addition of DM inside the NS, the inspiral properties such as h22, f, Φ and x are changing significantly (as shown in Fig. 2). The BNS with IOPB-I+DM5 sustains more time in the inspiral orbits as compare to IOPB-I+DM3. The magnitude of f, Φ and x are almost the same, but their inspiral time is different. Therefore, they concluded that DM has significant effects on inspiral properties of BNS.

Reference: H. C. Das, Ankit Kumar, S. K. Patra, “Effects of dark matter on the inspiral properties of the binary neutron star”, ArXiv, pp. 1-10, 2021. https://arxiv.org/abs/2104.01815

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