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Gravitational waves from r-mode instability of massive young sub- and super-Chandrasekhar white dwarfs

In the present work we investigate the r-mode instability windows, spindown and spindown rates of sub- and super-Chandrasekhar magnetized white dwarfs in presence of Landau quantization of the electron gas and magnetic braking. The gravitational wave strain amplitudes due to r-mode instability is also calculated. The dominant damping mechanism is taken to be the shear viscosity arising due to scattering of the degenerate electrons from the ion liquid. We find that the critical frequencies of Landau quantized magnetized white dwarfs are the lowest, those of non-Landau quantized ones are higher and those of non-magnetized ones are the highest at the same temperature. This implies that magnetic braking and Landau quantization both enhance r-mode instability. We have also seen that there is rapid spindown of magnetized white dwarfs due to additional magnetic braking term but there is no considerable effect of Landau quantization on the spindown and spindown rates for magnetic field strengths relevant for white dwarf interiors. We find that the r-mode gravitational wave strain amplitude for a rapidly rotating super-Chandrasekhar white dwarf at 1 kpc is $\sim 10^{-27}$, making isolated massive rapidly rotating hot magnetized white dwarfs prime candidates for search of gravitational waves in the future.