Prospects of Constraining the Dense Matter Equation of State from Timing Analysis of Pulsars in Double Neutron Star Binaries: The Cases of PSR J0737 ‒ 3039A and PSR J1757 ‒ 1854

Manjari Bagchi

doi:10.3390/universe4020036

Abstract

The Lense-Thirring effect from spinning neutron stars in double neutron star binaries contributes to the periastron advance of the orbit. This extra term involves the moment of inertia of the neutron stars. The moment of inertia, on the other hand, depends on the mass and spin of the neutron star, as well as the equation of state of the matter. If at least one member of the double neutron star binary (better the faster one) is a radio pulsar, then accurate timing analysis might lead to the estimation of the contribution of the Lense-Thirring effect to the periastron advance, which will lead to the measurement of the moment of inertia of the pulsar. The combination of the knowledge on the values of the moment of inertia, the mass and the spin of the pulsar will give a new constraint on the equation of state. Pulsars in double neutron star binaries are the best for this purpose as short orbits and moderately high eccentricities make the Lense-Thirring effect substantial, whereas tidal effects are negligible (unlike pulsars with main sequence or white-dwarf binaries). The most promising pulsars are PSR J0737 − 3039A and PSR J1757 − 1854. The spin-precession of pulsars due to the misalignment between the spin and the orbital angular momentum vectors affect the contribution of the Lense-Thirring effect to the periastron advance. This effect has been explored for both PSR J0737 − 3039A and PSR J1757 − 1854, and as the misalignment angles for both of these pulsars are small, the variation in the Lense-Thirring term is not much. However, to extract the Lense-Thirring effect from the observed rate of the periastron advance, more accurate timing solutions including precise proper motion and distance measurements are essential.

Highlights

Timing analysis of binary pulsars leads to the measurement of pulsar’s spin, Keplerian orbital parameters, as well as post-Keplerian (PK) parameters like the Einstein parameter (γ), Shapiro range (r) and shape (s) parameters, the rate of the periastron advance ω, the rate of change of the orbital period Ṗb, the relativistic deformation of the orbit δθ, etc. [4]
For the purpose of demonstration, I compute the value of the moment of inertia (I p ) for the two most interesting pulsars, PSR J0737−3039A and PSR J1757−1854 using the Akmal-PandharipandeRavenhall (APR) equation of state [27] and the RNS code3 [28]
I use this value in my calculations, remembering the fact that the true values of I p would be different depending on the true Equation of State (EoS), and we are seeking an answer whether it would be possible to know the value of I p by singling out ωLT p from the total observed ωp,obs

Summary

Introduction

The remaining Keplerian parameter, the longitude of the ascending node φ, does not come in the standard pulsar timing algorithm. It can be measured via proper motion only in very special cases; see [1,2,3] for details. Measurement of PK parameters leads to estimation of masses of the pulsars and their companions, as well as tests of various theories of gravity [7,8]. As these neutron stars are rapidly spinning (spin periods of most of the pulsars in DNSs are less than 100 milliseconds), the Lense-Thirring effect is significant. Earth due to its spin-precession [16]

Precession in Double Neutron Star Binaries

Periastron Advance

Results

Summary and Conclusions