Title: Prospects for the Observation of Continuous Gravitational Waves from Deformed Fast-spinning White Dwarfs

Abstract: There has been a growing interest within the astrophysics community in highly magnetized and fast-spinning white dwarfs (WDs), commonly referred to as HMWDs. WDs with these characteristics are quite uncommon and possess magnetic fields $\geqslant 10^6$ G, along with short rotation periods ranging from seconds to just a few minutes. Based on our previous work, we analyze the emission of Gravitational Waves (GWs) in HMWDs through two mechanisms: matter accretion and magnetic deformation, which arise due to the asymmetry surrounding the star's rotational axis. Here, we perform a thorough self-consistent analysis, accounting for rotation and employing a realistic equation of state to investigate the stability of stars. Our investigation focuses on the emission of gravitational radiation from six rapidly spinning WDs: five of them are situated within binary systems, while one is an AXP, proposed as a magnetic accreting WD. Furthermore, we apply the matter accretion mechanism alongside the magnetic deformation mechanism to assess the influence of one process on the other. Our discoveries indicate that these WDs could potentially act as GW sources for BBO and DECIGO, depending on specific parameters, such as their mass, the angle ($\alpha$) between the magnetic and rotational axes, and the accumulated mass ($\delta m$) at their magnetic poles, which is influenced by the effect of matter accretion. However, detecting this particular class of stars using the LISA and TianQin space detectors seems unlikely due to the challenging combination of parameters such as a large $\delta m$, a large $\alpha$ angle and a small WD mass value.