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Crustal lattice pressure as a source of neutron star mountains

D. I. Jones, T. J. Hutchins

TL;DR

This work assesses thermoelastic mechanisms for neutron-star mountains that could power continuous gravitational waves. It critically re-evaluates the traditional capture-layer shift scenario under modern crust equations of state and finds deep-layer possibilities unlikely, especially once elastic sinking is included. The authors then quantify thermal perturbations in the electron and neutron Fermi gases and—in a novel direction—focus on the crustal lattice pressure as a temperature-dependent source of density perturbations, finding it yields small but non-negligible non-spherical pressure changes. They conclude that a self-consistent treatment of temperature asymmetries, lattice-pressure perturbations, and the induced mass quadrupole is needed, with the lattice mechanism offering a broader applicability to both accreting and isolated neutron stars and motivating further study. The results lay groundwork for future work on magnetically induced temperature asymmetries and fully self-consistent elastic-gravity solutions to determine the viability of thermoelastic mountains in explaining observed spin distributions and offering detectable gravitational waves.

Abstract

The spin frequencies of neutron stars in low-mass X-ray binaries may be limited by the emission of gravitational waves. A candidate for producing such steady emission is a mass asymmetry, or "mountain", sourced by temperature asymmetries in the star's crust. A number of studies have examined temperature-induced shifts in the crustal capture layers between one nuclear species and another to produce this asymmetry, with the presence of capture layers in the deep crust being needed to produce the required mass asymmetries. However, modern equation of state calculations cast doubt on the existence of such deep capture layers. Motivated by this, we investigated an alternative source of temperature dependence in the equation of state, coming from the pressure supplied by the solid crustal lattice itself. We show that temperature-induced perturbations in this pressure, while small, may be significant. We therefore advocate for more detailed calculations, self-consistently calculating both the temperature asymmetries, the perturbations in crustal lattice pressure, and the consequent mass asymmetries, to establish if this is a viable mechanism for explaining the observed distribution of low-mass X-ray binary spin frequencies. Furthermore, the crustal lattice pressure mechanism does not require accretion, extending the possibility for such thermoelastic mountains to include both accreting and isolated neutron stars.

Crustal lattice pressure as a source of neutron star mountains

TL;DR

This work assesses thermoelastic mechanisms for neutron-star mountains that could power continuous gravitational waves. It critically re-evaluates the traditional capture-layer shift scenario under modern crust equations of state and finds deep-layer possibilities unlikely, especially once elastic sinking is included. The authors then quantify thermal perturbations in the electron and neutron Fermi gases and—in a novel direction—focus on the crustal lattice pressure as a temperature-dependent source of density perturbations, finding it yields small but non-negligible non-spherical pressure changes. They conclude that a self-consistent treatment of temperature asymmetries, lattice-pressure perturbations, and the induced mass quadrupole is needed, with the lattice mechanism offering a broader applicability to both accreting and isolated neutron stars and motivating further study. The results lay groundwork for future work on magnetically induced temperature asymmetries and fully self-consistent elastic-gravity solutions to determine the viability of thermoelastic mountains in explaining observed spin distributions and offering detectable gravitational waves.

Abstract

The spin frequencies of neutron stars in low-mass X-ray binaries may be limited by the emission of gravitational waves. A candidate for producing such steady emission is a mass asymmetry, or "mountain", sourced by temperature asymmetries in the star's crust. A number of studies have examined temperature-induced shifts in the crustal capture layers between one nuclear species and another to produce this asymmetry, with the presence of capture layers in the deep crust being needed to produce the required mass asymmetries. However, modern equation of state calculations cast doubt on the existence of such deep capture layers. Motivated by this, we investigated an alternative source of temperature dependence in the equation of state, coming from the pressure supplied by the solid crustal lattice itself. We show that temperature-induced perturbations in this pressure, while small, may be significant. We therefore advocate for more detailed calculations, self-consistently calculating both the temperature asymmetries, the perturbations in crustal lattice pressure, and the consequent mass asymmetries, to establish if this is a viable mechanism for explaining the observed distribution of low-mass X-ray binary spin frequencies. Furthermore, the crustal lattice pressure mechanism does not require accretion, extending the possibility for such thermoelastic mountains to include both accreting and isolated neutron stars.
Paper Structure (9 sections, 32 equations, 5 figures, 1 table)

This paper contains 9 sections, 32 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Thermal Mountains from capture layer shifts
  3. Mass quadrupole moment from capture layer shifts
  4. Expected GW emission from capture layer shifts
  5. Thermal corrections to the electron gas pressure
  6. Thermal corrections to the neutron gas pressure
  7. Thermal corrections to the lattice pressure
  8. Comparison between capture layer shifts and thermal crustal pressure
  9. Summary and Discussion

Figures (5)

  • Figure 1: Plots of signal strength $h_0$ (triangles/stars) and minimum detectable amplitudes $h_{0, \, \rm{det}}$ (curves) for various signal models and GW detectors. The minimum detectable amplitudes were obtained from equation (\ref{['eq: Detector_sensitivity']}) with $A=11.4$ and $T_{\rm obs} = 2$ years. In the left panel we plot the torque balance limit as per equation \ref{['eq: Torque Balance Quadrupole']} for the low-mass X-ray binaries listed in Table \ref{['tab:LMXBs_table']}, and estimate the largest thermal mountain that can be created with an assumed maximum temperature asymmetry $\delta T_{22} / T = 1\%$ for different accreted equations of state (UCB: ucb_00, HZ90: hz_90_second, F+18: Fantina_2018, GC20: Gusakov_2020) using the fiducial estimate \ref{['eq: UCB Fiducial Q_22']}. In the right panel we show the effects on mountain sizes which arise from elastic readjustments of the crust to shifting deep (90 MeV) and shallow (25 MeV) capture layers. The bars indicate the range of uncertainty in $Q_{\rm{fid}}$ (and thus $h_0$) that arise due to 'sinking penalties'.
  • Figure 2: Fractional perturbation in pressure due to relativistic electrons for the hz_90_firsthz_90_second (left) and BSk21 (Fantina_2018Fantina_2022; right) equations of state, as a function of density and temperature, for a temperature perturbation $\delta T_{22} / T = 1\%$, computed using equation (\ref{['eq:delta_P_over_P_e']}).
  • Figure 3: Fractional perturbation in pressure due to non-relativistic neutrons for the hz_90_firsthz_90_second (left) and BSk21 (Fantina_2018Fantina_2022; right) equations of state, as a function of density and temperature, for a temperature perturbation $\delta T_{22} / T = 1\%$, computed using equation (\ref{['eq:delta_P_over_P_n']}).
  • Figure 4: Plasma ion temperature $T_{\rm pi}$ for the hz_90_firsthz_90_second (left) and BSk21 (Fantina_2018Fantina_2022; right) equations of state.
  • Figure 5: Fractional perturbation in pressure due to the crustal lattice for the hz_90_firsthz_90_second (left) and BSk21 (Fantina_2018Fantina_2022; right) equations of state, as a function of density and temperature, as computed using the formalism described in Section \ref{['sect:lattice']}, for a temperature perturbation $\delta T_{22} / T = 1\%$.