Magnetically confined mountains on accreting neutron stars are promising sources of continuous-wave gravitational radiation and are currently the targets of directed searches with long-baseline detectors like the Laser Interferometer Gravitational Wave Observatory ( LIGO ) .
In this paper , previous ideal-magnetohydrodynamic models of isothermal mountains are generalized to a range of physically motivated , adiabatic equations of state .
It is found that the mass ellipticity \epsilon drops substantially , from \epsilon \approx 3 \times 10 ^ { -4 } ( isothermal ) to \epsilon \approx 9 \times 10 ^ { -7 } ( non-relativistic degenerate neutrons ) , 6 \times 10 ^ { -8 } ( relativistic degenerate electrons ) and 1 \times 10 ^ { -8 } ( non-relativistic degenerate electrons ) ( assuming a magnetic field of 10 ^ { 12.5 } \mathrm { G } at birth ) .
The characteristic mass M _ { \mathrm { c } } at which the magnetic dipole moment halves from its initial value is also modified , from M _ { \mathrm { c } } / \mathrm { M } _ { \sun } \approx 5 \times 10 ^ { -4 } ( isothermal ) to M _ { \mathrm { c } } / \mathrm { M } _ { \sun } \approx 2 \times 10 ^ { -6 } , 1 \times 10 ^ { -7 } , and 3 \times 10 ^ { -8 } for the above three equations of state , respectively .
Similar results are obtained for a realistic , piecewise-polytropic nuclear equation of state .
The adiabatic models are consistent with current LIGO upper limits , unlike the isothermal models .
Updated estimates of gravitational-wave detectability are made .
Monte Carlo simulations of the spin distribution of accreting millisecond pulsars including gravitational-wave stalling agree better with observations for certain adiabatic equations of state , implying that X-ray spin measurements can probe the equation of state when coupled with magnetic mountain models .