Gravitational Waves from Magnetically Confined Mountains on Accreting White Dwarfs
We propose fast-spinning, magnetic white dwarfs in binary systems as promising sources of continuous gravitational waves for future space-based detectors. The aim of this work is to determine the maximum ellipticities and gravitational wave amplitudes achievable by magnetically confined mountains accreted on the star's magnetic poles, and to assess their detectability against predicted sensitivity curves. Self-consistent magnetohydrodynamic equilibrium simulations are used to characterize the structure of the accreted mountain. A parametric search is then performed on these simulations to determine the maximum mass values that can be confined by the star's magnetic field. The stellar ellipticity $\varepsilon$ grows nearly linearly with accreted mass $M_{\rm a}$ up to a maximum, and was found to scale as $\varepsilon_{\rm max} \simeq 1.6\times10^{-2}T_5^{-2} B_{*,8}^{2}$, while the maximum gravitational wave amplitude as $h_{\rm 0, max} \simeq 1.2\times10^{-23}T_5^{-2} B_{*,8}^{2}$, where $T_5$ represents the temperature of the mountain in units of $10^5 \mathrm{K}$ and $B_{*,8}$ represents the star's polar magnetic field intensity in units of $10^8 \mathrm{G}$. Across a representative range of source inclinations, distances and spin periods, magnetically confined mountains on white dwarfs can generate continuous gravitational waves detectable by future space-based interferometers. BBO and DECIGO can probe diverse configurations, whereas LISA, TianQin, and Taiji require highly magnetized systems. Applications to known fast-spinning white dwarfs indicate that cooler accreted mountains favor detectability.