Mountain building of solid quark stars

One of the key differences between normal neutron and (bare) quark stars is relevant to the fact that the former are gravitationally bound while the latter self-confined unless their masses approach the maximum mass. This difference results in the possibility that quark stars could be very low massive whereas neutron stars cannot. Mountains could also be build on quark stars if realistic cold quark matter is in a solid state, and an alternative estimation of the mountain building is present. As spinning compact objects with non-axisymmetric mass distribution will radiate gravitational waves, the equations of states of pulsars could be constraint by the amplitude of gravitational waves being dependent on the heights of mountains. We then estimate the maximum mountains and thus quadrupole moment on solid quark stars, to be consistent with that by Owen (2005) if the breaking strain is 0.1, addressing that a solid quark star with mass < 10^{-2} Msun could be `potato-like’. We estimate the gravitational wave amplitude of solid quark stars with realistic mountains to be order of h0 ~ 10^{-27}.