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The permanent ellipticity of a millisecond pulsar
The transitional millisecond pulsar PSR J1023+0038 is unique, because this is the only millisecond pulsar for which the spin-down rate has been measured in both accreting and non-accreting states. This provides two torque budget equations, and a third equation can be written from the observation of gamma-rays in both the states. Solutions of these equations infer, for the pulsar magnetospheric origin of observed gamma-rays in the two states, that PSR J1023+0038 should emit gravitational waves due to an ellipticity of the pulsar. I will discuss how this formalism, which is basically independent of accretion, infers accretion disc penetration into the pulsar magnetosphere, and explains the observed X-ray pulsations in the accreting state using the standard and well-accepted scenario, which was not possible earlier. This, in turn, naturally and self-consistently infers the larger pulsar spin-down power in the accreting state, which explains the observed larger gamma-ray emission in this state. I will also discuss how large ranges of parameter values can be explored to estimate the permanent misaligned mass quadrupole moment of the pulsar