What Are Pulsar Companions Made of? Using Gravitational Tides to Probe Their Compositions

Abstract

Low eccentricity, short orbital period pulsar companions may provide a probe to study novel dense and stable exoplanet internal compositions due to the potentially significant orbital evolution they experience caused by strong gravitational tides. We model the tidal characteristics such as apsidal motion constants, orbital precession, and tidal deformability for a variety of equations of state to be compared with values recovered via pulsar timing for a sample of four systems: PSR J1719-1438b, PSR J0636+5128b, PSR J2322+2650b, and PSR J1807-2459A b. With this method, we hope to place stringent limits on the chemical and structural composition of these objects. Through limiting the internal composition of pulsar companions, we aim to elucidate their unique history and formation.

Figures (7)

• Figure 1: Uncertainties on $\dot\omega$ values recovered by PINT for our two pulsar-timing systems of special interest, J1719-1438b and J0636+5128n, as a function of years of consistent pulsar-timing measurements.
• Figure 2: Plot of mass-radius relationships for companions composed of the EOS discussed in Section \ref{['subsec:EOS']}. Note that the curves for H$_2$O, SiC, MgSiO$_3$, and Fe end between $\sim$ 1 and 10 $M_J$, as the EOS described in Seager_2007 are only valid up for central pressures of $P_c \leq 10^{16}$ Pa. The EOS for CO is valid up to $P_c \sim 3 \cdot 10^{14}$ Pa, as described in Podolak_2023. The label polytrope refers to an $n=1.5$ polytrope used to approximate non-relativistic white dwarfs.
• Figure 3: Mass-$k_{2}$ relationships for same EOS described in Figure \ref{['fig:Hydro_Mass-Radius_plot']}. Note that this is the apsidal motion constant, not the second order tidal Love number, and thus a homogeneous body has $k_{2}= 0.75$. It is interesting, but not surprising, to see that at low central pressures/masses most of these EOS tend toward a homogeneous density.
• Figure 4: Plot of the relationship between mass and apsidal motion for the various internal compositions described in Section \ref{['subsec:EOS']}, specifically modeled to PSR J1719-1438b. The greyed out region denotes parameter-space that is ruled out by the Roche-lobe limit of this companion. The vertical pink dashed line denotes the minimum mass of PSR J1719-1438b, as described in Section \ref{['subsec:J1719']}. The apsidal motion returned by even the most deformable bare strange quark stars returns the GR prediction of the apsidal motion, shown in a dash-dotted sea green.
• Figure 5: The same plot as Figure \ref{['fig:Mass-wdot_plot']} but modeled for J0636+5128b. The precession in this system can be as much as almost an order of magnitude higher than possible in J1719-1438B under the Roche-lobe limit. The additional vertical dash-dotted line denotes the measured mass of 19.9 M$_J$ from Draghis_2018, higher than the minimum mass of 7.4 M$_J$.