  We have studied the spin-down induced phase transition in cold, isolated
neutron stars in this work. After birth, as the star slows down, its central
density rises and crosses the critical density of phase transition, and a quark
core is seeded inside the star. Intermediate mass stars are more likely to have
a quark seeding in their lifetime at birth. Smaller neutron stars do not have a
quark core and remain neutron stars throughout their life, whereas in massive
stars, a quark core exists at their center from birth. In intermediate and
massive stars, the quark core grows further as the star slows down. The
appearance of a quark core leads to a sudden change in the moment of inertia of
the star in its evolutionary history, and it is also reflected in a sudden
discontinuity in the braking index of the star (at the frequency where the
quark core first seeds). The energy released during the phase transition
process as the quark core is seeded can excite the f-mode oscillation in the
star and is emitted in the form of the gravitational wave, which is in the
range of detection with present operating detectors; however, future detectors
will enable a more clean extraction of this signals. Also, neutrinos and bursts
of gamma-rays can originate from phase transition events. The spin-down induced
phase transition could be gradual or in the form of subsequent leaps producing
persistent or multiple transient emissions.
