Proto-strange quark stars from density-dependent quark mass model

In this paper, we investigate the evolution of strange quark stars (SQS) from birth as proto-strange quark stars to maturity as stable SQSs at a zero temperature. We assume that self-bound free quarks form {entirely the compact} star and study its evolution {through a series of snapshots} using a density-dependent quark mass model. We consider $\beta$-equilibrated stellar matter at two major stages of the star's evolution: neutrino trapped regime and neutrino transparent regime during the deleptonization and cooling processes of the star. We fix the entropy density per baryon and the lepton fraction to investigate the nuclear equation of state (EoS), particle distribution, temperature profile inside the star, sound velocity, polytropic index, and the structure of the star. Our results show that stars with higher neutrino concentrations are slightly more massive than the neutrino-poor ones along the evolution lines of the SQS. We obtain EoSs in agreement with the conformal boundary set through sound velocity, and also the 2 M$_\odot$ mass constraint for NSs was satisfied at all stages of the star's evolution.