Quasi-stars and the Sch\"onberg-Chandrasekhar limit

TL;DR

This paper investigates quasi-star models and their connection to the Sch"onberg-Chandrasekhar limit, revealing new insights into black hole growth constraints and stellar evolution under different accretion flow assumptions.

Contribution

It demonstrates that the fractional mass limit in quasi-star models is equivalent to the Sch"onberg-Chandrasekhar limit and introduces a test for identifying such limits in composite polytropes.

Findings

Black hole mass in certain models is limited to about one-tenth of the envelope mass.

Alternative models show black holes can accrete all envelope material without fractional mass limits.

Existence of fractional mass limits is linked to stellar evolution into red giants.

Abstract

The mechanism by which the supermassive black holes that power bright quasars at high redshift form remains unknown. One possibility is that ... the monolithic collapse of a massive protogalactic disc ... leads to the formation of a quasi-star: a growing black hole, initially of typical stellar-mass, embedded in a hydrostatic giant-like envelope. Quasi-stars are the main object of study in this dissertation. ... In Chapter 1, I introduce the problem posed by the supermassive black holes that power high-redshift quasars. ... In Chapter 2, I outline the Cambridge STARS code and the modifications that are made to model quasi-star envelopes. In Chapter 3, I present models of quasi-stars where the base of the envelope is located at the Bondi radius of the black hole. The black holes in these models are subject to a robust upper fractional mass limit of about one tenth. In addition, the final black hole mass is sensitive to the choice of the inner boundary radius of the envelope. In Chapter 4, I construct alternative models of quasi-stars by drawing from work on convection- and advection-dominated accretion flows ... The evolution of these quasi-stars is qualitatively different from those described in Chapter 3. ... [T]he core black holes are no longer subject to a fractional mass limit and ultimately accrete all of the material in their envelopes. In Chapter 5, I demonstrate that the fractional mass limit found in Chapter 3 ... is in essence the same as the Sch\"onberg-Chandrasekhar limit. The analysis demonstrates ... that limits exist under a wider range of circumstances than previously thought. A test is provided that determines whether a composite polytrope is at a fractional mass limit. In Chapter 6, I apply this test to realistic stellar models and find evidence that the existence of fractional mass limits is connected to the evolution of stars into the red giants.