MESA-QUEST: Quasi-Star Simulation Toolkit

• MESA-QUEST is a simulation toolkit that models quasi-stars as systems with a central black hole embedded in a massive gaseous envelope.
• It reproduces key results from the STARS framework using 1D stellar structure equations, Bondi radius boundaries, and general relativistic corrections.
• Designed for systematic parameter studies, it bridges theoretical quasi-star models with early supermassive black hole formation research with an open-source, modular code base.

MESA-QUEST is the MESA Quasi-star Evolutionary Simulation Toolkit, an implementation within the 1D stellar evolution code MESA of the quasi-star modeling framework developed with the Cambridge STARS code by Ball et al. (2011, 2012). It is designed to model the structure and evolution of quasi-stars, defined as configurations in which a central black hole (BH) is embedded in a massive, extended gaseous envelope, and to study their role as a heavy-seeding channel for the earliest supermassive black holes (Campbell et al., 16 Jul 2025). In the formulation implemented here, quasi-stars can produce BH seeds in the $10^3$–$10^5\,M_\odot$ range in a single quasi-star episode, a scale relevant to explaining very high-redshift SMBHs without requiring extreme sustained Eddington super-accretion from stellar-mass seeds.

1. Astrophysical context and scientific motivation

The primary scientific context of MESA-QUEST is the unresolved problem of early supermassive black hole formation. The observational motivation is the existence of luminous quasars and overmassive BHs at very high redshift, when the Universe is only a few hundred Myr old. In that regime, growth from stellar-mass seeds via accretion at or below the Eddington rate is difficult because of limited cosmic time, feedback that self-regulates BH accretion, and an uncertain duty cycle and environment (Campbell et al., 16 Jul 2025).

This motivates heavy-seed scenarios, in which BHs are born already massive, typically $\gtrsim 10^4\,M_\odot$, through direct collapse in pre-galactic haloes. Within that broader class, the quasi-star is a specific BH-in-a-star configuration. Its envelope is hydrostatic and extremely massive, typically $\sim 10^4$–$10^6\,M_\odot$, while the central BH grows from an initial seed. The envelope is not powered by nuclear fusion; instead, it is supported by BH accretion luminosity transported outward through a radiation-dominated, largely convective interior. A common misconception is to treat quasi-stars as ordinary supermassive stars with unusual central objects. The model implemented in MESA-QUEST instead follows the quasi-star as a radiation-supported envelope energized by a central accretion source.

The toolkit is explicitly oriented toward reproducing the Ball et al. (2011) fiducial quasi-star and then extending that framework in a modern, modular code base. Parameter ranges inherited from the STARS studies include envelope masses $\sim 10^4$–$10^6\,M_\odot$, low metallicity or primordial composition, and fiducial radiative and convective efficiencies $(\epsilon,\eta)=(0.1,0.1)$.

2. Quasi-star structure and governing physical picture

In MESA-QUEST, the BH is treated as a point mass at the center, while the stellar structure integration begins not at $r=0$ but at a finite inner boundary identified with the BH’s Bondi radius. The enclosed mass at that point is the sum of the BH mass and a cavity mass estimated from an assumed $\rho \propto r^{-3/2}$ profile inside the boundary. This replaces the usual stellar center with a BH-dominated inner boundary condition (Campbell et al., 16 Jul 2025).

The envelope structure is computed with the standard 1D stellar structure equations, modified by the quasi-star inner boundary and by zone-by-zone general relativistic corrections. In conceptual form, the hydrostatic equation is written as

$10^5\,M_\odot$0

where $10^5\,M_\odot$1 is a TOV-like correction factor following Herrington et al. (2023). Energy transport proceeds by radiative diffusion in the outer envelope and by convection in the inner envelope.

BH growth is regulated by a convectively limited accretion prescription inherited from Ball (2011). The corresponding luminosity is coupled back into the envelope as the central energy source. With the fiducial efficiency choices $10^5\,M_\odot$2, the object evolves close to the global Eddington limit,

$10^5\,M_\odot$3

This is a global constraint on the quasi-star as a whole rather than the Eddington limit of the BH alone.

The physical division of the envelope is also central. The inner envelope is convective and radiation-pressure dominated, while the outer layers are radiative. The models are highly extended and can occupy an extreme region of the HR diagram, with high luminosities but relatively low effective temperatures. As the BH grows, the envelope generally becomes larger and cooler at the surface.

3. Implementation inside MESA

MESA-QUEST transplants the Ball et al. physical model from the Cambridge STARS code into MESA’s star module. The implementation is concentrated in MESA’s run_star_extras hook system, which is where quasi-star-specific physics is introduced at each timestep and zone (Campbell et al., 16 Jul 2025).

Several specific controls define the implementation. Convection uses ML1 mixing-length theory in the Böhm-Vitense (1958) flavor with $10^5\,M_\odot$4, matching Ball (2011). Convective stability is evaluated with the Ledoux criterion, with default semi-convective mixing treatment. GR corrections are applied as TOV-like factors zone by zone. The inner radius $10^5\,M_\odot$5, the enclosed inner mass $10^5\,M_\odot$6, the BH accretion rate $10^5\,M_\odot$7, the BH luminosity $10^5\,M_\odot$8, and the numerical stabilizations are all handled in run_star_extras.

The timestep logic follows a specific sequence. At each timestep, the code obtains the BH mass and the thermodynamic state of the inner zones; computes the Bondi-radius inner boundary and the corresponding enclosed mass; integrates the structure outward from those values; calculates $10^5\,M_\odot$9 and $\gtrsim 10^4\,M_\odot$0 with the prescribed efficiencies; applies GR and convection physics; and advances subject to safety constraints. Two stabilizations are explicitly imposed near the BH: the sound speed is averaged over the innermost 50 zones, corresponding to less than 1% of the mass, and the fractional timestep change in the Bondi radius is limited to $\gtrsim 10^4\,M_\odot$1.

The outer boundary remains standard MESA photospheric physics. The surface is treated near $\gtrsim 10^4\,M_\odot$2, with

$\gtrsim 10^4\,M_\odot$3

and the envelope is allowed to expand or contract in response to the balance of gravity and radiation pressure.

4. Initial conditions, validation, and reproduced behavior

The initial configurations are tuned to reproduce the fiducial Ball et al. (2011) quasi-star. The paper does not present a full parameter survey, but it summarizes a typical setup: a massive, centrally concentrated envelope with total mass on the order of the Ball fiducial model, a central BH seed mass chosen to match that evolution, and low-metallicity or primordial composition appropriate to direct-collapse conditions (Campbell et al., 16 Jul 2025).

The validation target is direct comparison with STARS. The comparison includes density profiles versus radius for various BH masses, the evolution of the inner Bondi radius and outer stellar radius with BH mass, the surface luminosity and effective temperature, and core properties. Across these diagnostics, the MESA-QUEST models reproduce the STARS quasi-star behavior: a strongly centrally concentrated envelope, a growing inner boundary radius as the BH grows, steadily increasing surface luminosity, decreasing surface temperature, and numerically stable core evolution.

The agreement is summarized by the final BH mass and the structural trends.

Quantity	STARS target	MESA-QUEST result
Density profiles	Fiducial Ball et al. model	Reproduced with similar evolution
Surface trends	$\gtrsim 10^4\,M_\odot$4 rises, $\gtrsim 10^4\,M_\odot$5 falls	Same qualitative behavior
Final BH mass	Fiducial STARS value	Within 10%

The paper states that the final BH mass is within 10% of the Ball (2011) fiducial result. It further notes that this level of agreement indicates that quasi-star lifetimes and maximum seed masses remain consistent with the earlier STARS predictions.

5. Capabilities and comparison with previous codes

The central result of MESA-QUEST is not a new quasi-star phenomenology but a validated transplantation of the STARS quasi-star framework into a more modern and modular platform. The code can evolve quasi-stars with a central BH and massive envelope, track BH growth via convectively limited accretion, include GR corrections and realistic convection in 1D, and reproduce earlier STARS-based results (Campbell et al., 16 Jul 2025).

The comparison with Cambridge STARS is methodologically important. It shows that the Bondi inner boundary, convectively limited $\gtrsim 10^4\,M_\odot$6, BH-driven central luminosity, and quasi-star envelope structure are not tied to the legacy STARS code. They can be implemented in MESA while preserving the fiducial behavior. This matters because MESA is open-source, widely used, and readily extensible.

The paper also frames MESA-QUEST as an infrastructure for systematic parameter studies. Because the quasi-star physics resides in run_star_extras, new accretion prescriptions, mass-loss prescriptions, envelope accretion, photon trapping, and additional feedback treatments can be introduced without replacing the basic stellar solver. This makes MESA-QUEST a bridge between quasi-star theory, supermassive-star calculations, and direct-collapse studies already carried out in MESA.

6. Repository, limitations, and future extensions

MESA-QUEST is publicly available at http://www.github.com/andysantarelli/MESA-QUEST. The central custom physics is implemented in run_star_extras, and the provided inlist_project reproduces the main example model shown in the paper. The paper states that the key efficiencies are controlled through x_ctrl parameters in the inlist, with $\gtrsim 10^4\,M_\odot$7 reproducing the fiducial setup (Campbell et al., 16 Jul 2025).

As presented, the toolkit is limited to non-rotating, spherically symmetric, 1D, hydrostatic quasi-stars. It does not yet include explicit winds or mass loss, external envelope accretion, detailed photon-trapping treatments, strongly non-solar or complex compositions beyond standard MESA tables, or multidimensional effects such as rotation and anisotropic feedback. A second common misconception is therefore that the public implementation already contains the full direct-collapse phenomenology. The paper instead describes these as natural extensions that the framework is designed to support.

The explicit future directions are mass loss from winds, mass gain through envelope accretion, photon trapping, updated accretion prescriptions, and relativistic corrections beyond the present implementation. More broadly, the toolkit is positioned to connect quasi-star calculations to studies of supermassive primordial stars and other exotic massive objects in MESA. In that sense, MESA-QUEST defines a reusable computational framework for examining whether quasi-stars can supply the heavy BH seeds required by the earliest SMBHs.