Stellar Evolution and Mass Transfer from a Star to a Supermassive Black Hole

Supermassive black holes (SMBHs) reside in the centers of most galaxies and are surrounded by millions of stars that orbit them. LISA would be able to detect emission of gravitational waves (GWs) from stars orbiting close enough to the SMBH, with orbital periods of order an hour. At such a period, mass transfer would take place from the star into the SMBH. We show that in the case of orbital angular momentum conservation, mass transfer is likely to be stable. For stable systems, evolution of the semi-major axis of the orbit of the star and the frequency of the emitted GWs, depends on the mass-radius relation of the star as it loses mass. We use MESA code to study the mass-radius relation of a massive star that starts transferring mass while on the main sequence (MS). We show that stars, above about 2 solar masses, remain in the MS as their mass shrinks. Once below approximately 2 solar masses, the GW timescale is too short to allow heat transfer to adjust the stellar structure and the star evolves adiabatically (each mass element preserves its entropy) off the MS. We find that contrary to previous estimates, such stars shrink, rather than expand. We show analytically, that this discrepancy stems from the structure of a two solar mass star as a dense core containing most of the mass surrounded by a low density envelope which occupies most of the volume with negligible mass. We discuss the evolution of the resulting GW signal