Evolution of Main Sequence Stars Transferring Mass to a Supermassive Black Hole

RESUMO

We consider main-sequence stars orbiting close to a supermassive black hole (SMBH), which are potential gravitational wave (GW) sources for LISA if their orbital periods are of the order of an hour. At such a short orbital period, mass transfer from the star to the SMBH occurs. The evolution of the semi-major axis and GW frequency depends on the evolution of the stellar mass and radius. We use MESA to study stars that transfer mass to SMBHs similar to Sagittarius A* starting on the zero-age main sequence (MS). We identify 4 evolutionary phases. (I) Stars initially with mass $>2 M_\odot$ remain on the MS as their mass and radius decrease. (II) Below $2 M_\odot$, the separation is sufficiently small so that the GW timescale is too short for the stars to maintain thermal equilibrium. They evolve adiabatically off the MS and shrink rapidly as they lose their high-entropy envelope. (III) Below $0.5-1 M_\odot$, depending on the initial mass, the uniform low-entropy core is exposed and stars expand adiabatically. (IV) Below $0.15-0.4 M_\odot$, the thermal and GW timescales become comparable, and stars cool and shrink while maintaining this balance. Overall, mass transfer causes the orbit to expand, slowing down the orbital evolution and leading to GW emission at lower frequencies making the GW signal harder to detect. If located around Sagittarius A*, mass transferring stars spend most of the time relatively close to the LISA sensitivity curve, with maximal SNR reaching around 600 during the transition between stages II and III.