Quasistars: Accreting black holes inside massive envelopes (0711.4078v2)

Abstract: We study the structure and evolution of "quasistars", accreting black holes embedded within massive hydrostatic gaseous envelopes. These configurations may model the early growth of supermassive black hole seeds. The accretion rate onto the black hole adjusts so that the luminosity carried by the convective envelope equals the Eddington limit for the total mass. This greatly exceeds the Eddington limit for the black hole mass alone, leading to rapid growth of the black hole. We use analytic models and numerical stellar structure calculations to study the structure and evolution of quasistars. We derive analytically the scaling of the photospheric temperature with the black hole mass and envelope mass, and show that it decreases with time as the black hole mass increases. Once the photospheric temperature becomes lower than 10,000 K, the photospheric opacity drops precipitously and the photospheric temperature hits a limiting value, analogous to the Hayashi track for red giants and protostars, below which no hydrostatic solution for the convective envelope exists. For metal-free (Population III) opacities this limiting temperature is approximately 4000 K. After a quasistar reaches this limiting temperature, the envelope is rapidly dispersed by radiation pressure. We find that black hole seeds with masses between 1000 and 10000 solar masses could form via this mechanism in less than a few Myr.

Accreting Black Holes within Massive Envelopes: The Quasistar Model

The paper by Begelman, Rossi, and Armitage investigates the theoretical construct of quasistars, an intriguing configuration featuring accreting black holes embedded in massive gaseous envelopes. The paper explores the growth dynamics of these structures, which may serve as precursors to supermassive black holes, especially in the context of early universe cosmology. Utilizing both analytic models and numerical simulations, the authors delineate the evolutionary pathway and characteristic features of quasistars.

Quasistars represent a stage in the theoretical framework proposed for the formation of supermassive black holes. In this model, an accreting black hole is enshrouded by a substantial convective envelope, through which it accretes at a rate limited by the Eddington luminosity applicable to the entire quasistar mass (envelope plus black hole). This broader constraint allows the black hole to effectively bypass the conventional Eddington limit associated solely with its mass, promoting a rapid accretion process and significant mass growth within a relatively short timescale.

The paper reveals a scaling law for the photospheric temperature of the envelope, demonstrating a relationship inversely proportional to the black hole mass and directly influenced by the envelope mass. As the black hole accrues more mass, the envelope's photospheric temperature decreases. Once this temperature falls beneath a critical threshold, approximately 4000 Kelvin for metal-free compositions (Population III), the opacity of the envelope drops sharply. This critical point, akin to the Hayashi limit for red giants, marks a phase beyond which no stable hydrostatic solution is feasible for the quasistar configuration.

Numerically, quasistars exhibit photospheric temperatures that remain above this minimal threshold throughout most of their evolutionary course. The authors calculate that black hole seeds with masses between $10^3 M_\odot$ and $10^4 M_\odot$ may feasibly form within these structures over timescales of a few million years. They explore scenarios of continuous mass accretion onto the quasistar, positing that such accretion influences the eventual mass of the black hole. Moreover, the paper incorporates the effects of variable accretion efficiency, represented by the parameter $\alpha$, affecting the luminosity and resultant evolutionary path.

The coverage of super-Eddington zones within the envelope underscores a nuanced aspect of the quasistar structure, suggesting the potential for mass loss through mechanisms not fully captured in the modeling. The authors posit that mass loss could commence via wind breakouts prompted by such zones, though a comprehensive assessment necessitates further hydrodynamic exploration.

In application, understanding quasistars offers insights into the early stages of black hole evolution in low-metallicity environments, pertinent to the high-redshift universe. As potential seed structures for supermassive black holes observed at high redshifts, quasistars illuminate a plausible evolutionary course within primordial environments, an area ripe for exploration with next-generation astronomical observatories. The constraints posed by the opacity floor indicate a fundamental limit to black hole growth within this framework, critical for modeling the formation and eventual unbinding of these structures.

Future developments in this field may involve probing the stability and mass retention characteristics of quasistars in environments with varying metallicity and angular momentum distributions, certainly a compelling domain for forthcoming astrophysical research. As quasistars illustrate a viable initial exponential growth phase for black holes, this research lays foundational groundwork for deeper cosmological investigations into the origins of supermassive black holes.