Numerical calculations of neutron star mountains supported by crustal lattice pressure

Abstract

Gravitational waves may set the spin frequencies of neutron stars in low-mass X-ray binaries (LMXBs). One mechanism for facilitating such emission is the formation of a mass asymmetry - or 'mountain' - supported by elastic strains driven by thermal gradients. Most studies have focused either on the origin of the elastic strains or the temperature asymmetry in isolation, and have not considered the entire formation process. In previous work, we showed that anisotropic heat transport in magnetised accreting neutron stars can source a significant temperature asymmetry, and made rough estimates that suggested temperature-induced perturbations in the pressure supplied by the crustal lattice may be competitive with the widely known model of temperature-induced capture-layer shifts. In this paper we carry out detailed calculations to properly explore this scenario. We self-consistently calculate both the temperature asymmetries, the perturbations in crustal lattice pressure, and the mass asymmetries within a single framework. For the first time, we make use of the set of realistic equations of state from the Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21 which describe all regions of accreting neutron stars in a thermodynamically consistent, unified way. We find these mountains are too small to be dictating the spin-equilibrium of LMXBs, and estimate the level of gravitational wave emission they produce.

Figures (5)

• Figure 1: Upper panels: Analytical fits to the pressure-density relations predicted by the BSk19 (left), BSk20 (centre) and BSk21 (right) equations of state for 'AC' accreted (coloured lines; Fantina_2018Fantina_2022) and 'GC' ground-state non-accreted (black lines; Goriely_2010Pearson_2011Pearson_2012) neutron stars. Crosses denote (rarefied) tabular data points for the accreted crust. Coloured lines are obtained via Equation \ref{['eq: Analytic EOS Fit']} together with Table \ref{['tab:Analytic Fit Parameters']}, while black lines are obtained via Equation \ref{['eq: Analytic EOS Fit']} and Table 2 in Potekhin_2013. Lower panel: Relative percentage difference between the tabulated data and analytic fit of the accreted crust. Vertical dotted lines indicate the location of each capture layer from Tables A1 - A3 of Fantina_2018.
• Figure 2: Temperature profiles (in units of 10$^8$ K) of neutron stars assuming the BSk21 equation of state as a function of density, accreting at $\dot{M} = 7 \times 10^{-11}$ M$_{\odot}$ yr$^{-1}$ (Left), $\dot{M} = 8 \times 10^{-10}$ M$_{\odot}$ yr$^{-1}$ (center), and $\dot{M} = 2 \times 10^{-9}$ M$_{\odot}$ yr$^{-1}$ (Right). We also consider different amounts of shallow crustal heating, ranging from 1.5 - 10 MeV, as indicated in the legend. The solid lines indicate fluid regions of the star, while dashed lines indicate regions where the star forms a solid Coulomb lattice. The crust begins at the point where the Coulomb parameter $\Gamma_{\text{Coul}} = 175$ - assuming a one component plasma; Eq. \ref{['eq:Coulomb to Thermal']}, and ends at the crust-core transition (Table \ref{['tab:Model properties']}).
• Figure 3: Magnitude of the fractional temperature perturbation $\delta T / T$ inside weakly magnetised neutron stars for the NS configurations considered in Fig. \ref{['fig:BSk20 Background Temperature Profiles']}. In this figure we assume a $B = 2 \times 10^{12}$ G internal crustal toroidal magnetic field.
• Figure 4: Same as Fig. \ref{['fig:BSk20 Perturbed Temperature Profiles Crust']} but for a $B = 10^{8}$ G internal core toroidal magnetic field.
• Figure 5: Ellipticity of a number of magnetised neutron stars assuming the BSk19 (left), BSk20 (centre) and BSk21 (right) equations of state (with properties listed in Table \ref{['tab:Model properties']}) as a function of the mass accretion rate $\dot{M}$. Different amounts of assumed shallow crustal heating, ranging from 1.5 - 10 MeV, are indicated in the legend. Solid lines (filled circles) denote NS models that assume a $B = 10^8$ G internal core toroidal magnetic field, while dashed lines (crosses) denote models that assume a $B = 2\times 10^{12}$ G internal crustal toroidal magnetic field. Dashed-dotted lines show the ellipticity required for gravitational-wave torques to determine the spin-equilibrium - via Eq. \ref{['eq: Torque Balance Ellipticity']} - of accreting neutron stars with spin frequencies 300 Hz (filled stars) and 700Hz (filled diamonds), as a function of $\dot{M}$.