Analytically Modeling the Gravitational Radiation Generated from a Quasistar System

We model Quasistars (QSs), which consist of a stellar mass black hole (BH) embedded inside a massive star-like envelope. The accretion rate onto the BH matches the Eddington rate for the entire QS. This quick growth of the BH leads to the outwards transport of energy, causing the envelope to expand. We allow the BH to be displaced from the center of mass of the QS and have some initial velocity, leading the BH to orbit inside of the QS, which generates gravitational waves (GWs) as a result of a sinusoidal Quadrupole moment tensor. We use analytical models to derive formulas for the separation between the BH and the envelope’s center as a function of time and the characteristic GW strain as a function of radiation frequency. We then numerically model these formulas for various initial mass and separation conditions. The characteristic GW strain model can be compared to the noise curves of upcoming GW observatories, such as μAres, in order to determine the detectability of the QS. We find that the BH/envelope separation exhibits an unconventional increase over time. Additionally, our model produces GWs with peak strains between 10-20 and 10-24 at frequencies between 10-5 Hz and 10-9 Hz, 2 to 6 magnitudes below the sensitivity curve of μAres.