  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 drops substantially, from \epsilon ~ 3e-4 (isothermal) to
\epsilon ~ 9e-7 (non-relativistic degenerate neutrons), 6e-8 (relativistic
degenerate electrons) and 1e-8 (non-relativistic degenerate electrons)
(assuming a magnetic field of 3e12 G at birth). The characteristic mass M_{c}
at which the magnetic dipole moment halves from its initial value is also
modified, from M_{c}/M_{\sun} ~ 5e-4 (isothermal) to M_{c}/M_{\sun} ~ 2e-6,
1e-7, and 3e-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.
