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Abstract

We introduce our approaches, in particular the modifications of the primitive
recovery procedure, to handle bare quark stars in numerical relativity
simulations. Reliability and convergence of our implementation are demonstrated
by evolving two triaxially rotating quark star models with different mass as
well as a differentially rotating quark star model which has sufficiently large
kinetic energy to be dynamically unstable. These simulations allow us to verify
that our method is capable of resolving the evolution of the discontinuous
surface of quark stars and possible mass ejection from them. The evolution of
the triaxial deformation and the properties of the gravitational-wave emission
from triaxially rotating quark stars have been also studied, together with the
mass ejection of the differentially rotating case. It is found that
supramassive quark stars are not likely to be ideal sources of continuous
gravitational wave as the star recovers axisymmetry much faster than models
with smaller mass and gravitational-wave amplitude decays rapidly in a
timescale of $10\,$ms, although the instantaneous amplitude from more massive
models is larger. As with the differentially rotating case, our result confirms
that quark stars could experience non-axisymmetric instabilities similar to the
neutron star case but with quite small degree of differential rotation, which
is expected according to previous initial data studies.