MESA-QUEST: Quasi-Star Modeling Framework

• MESA-QUEST is a computational framework for quasi-star evolution that employs novel inner boundary conditions and advanced accretion models.
• It implements both Bondi and saturated-convection prescriptions to predict black hole growth and envelope dynamics under variable wind scenarios.
• The framework is fully integrated with MESA’s post-processing tools, enabling robust, predictive studies testable by JWST and other observatories.

The MESA-QUEST Modeling Framework refers to an advanced computational toolkit for simulating the structure and evolution of quasi-stars—objects consisting of massive, radiation-supported envelopes surrounding accreting black holes—and for exploring broader questions in stellar astrophysics, such as the formation of direct collapse black hole (DCBH) seeds in the early universe. Built atop the Modules for Experiments in Stellar Astrophysics (MESA) code, MESA-QUEST leverages the modularity, numerical sophistication, and extensibility of MESA to implement novel treatments for inner boundary conditions, accretion physics, convective energy transport, and mass loss. This framework is designed to support physically motivated and numerically robust studies of exotic objects, thereby constraining the parameter space for heavy seed formation and providing predictive models testable by JWST and other observatories (Santarelli et al., 13 Oct 2025, Campbell et al., 16 Jul 2025).

1. Origin and Theoretical Motivation

MESA-QUEST was developed to bridge the gap between classic quasi-star modeling—initially undertaken with codes such as the Cambridge STARS code—and the need for a flexible, open-source, and high-fidelity platform capable of incorporating the latest advances in stellar evolution, hydrodynamics, and microphysics. Quasi-stars are hypothesized to arise in primordial, low-metallicity environments where rapid accretion leads to the formation of radiation-dominated envelopes around black holes (which may themselves result from failed supermassive star collapse or direct gas infall). The viability of such objects as progenitors of the first observed SMBHs at redshifts $z \geq 9$ motivates a framework permitting flexible experimentation with the physical conditions leading to their formation and growth (Campbell et al., 16 Jul 2025, Santarelli et al., 13 Oct 2025).

Central to MESA-QUEST’s design philosophy is the need to depart from conventional stellar boundary conditions. Instead of imposing $m(r=0)=0$ and $l(r=0)=0$, the inner boundary can be set at a finite radius $R_0$, with enclosed mass $m(r=R_0)=M_{\rm BH}+M_{\rm cav}$ and luminosity $l(r=R_0)=L_{\rm BH}$, making it possible to model the transfer of energy and mass between the envelope and the central black hole (Santarelli et al., 13 Oct 2025).

2. Inner Boundary Conditions and Accretion Models

A defining feature is the implementation of distinct inner boundary prescriptions:

• Bondi Accretion Boundary: The inner boundary is positioned at the Bondi radius $R_B=2GM_{\rm BH}/c_s^2$, where $M_{\rm BH}$ is the black hole mass and $c_s$ the local sound speed. The accretion rate is expressed as

$$\dot{M}_{\rm BH} = 16\pi \frac{\eta}{\epsilon\Gamma} \frac{(GM_{\rm BH})^2}{c_s c^2} \rho,$$

where $\epsilon$ and $\eta$ are efficiency parameters (often $\sim 0.1$), $\Gamma$ is the adiabatic index, and $\rho$ the local density.

• Saturated-Convection Boundary: More recent theoretical developments support an alternative regime where convective energy transport operates at maximal efficiency, leading to a density profile $\rho \propto r^{-1/2}$. The inner boundary location is set by solving the ODE

$$K_i \frac{d}{d \xi} \left[ \xi^{-2} \left( \frac{d m_i}{d\xi} \right)^{1/3} \right] = -m_i \xi^4 \frac{d m_i}{d\xi},$$

with $K_i$ fixed by envelope properties and black hole luminosity.

The impact of these inner boundaries is directly reflected in the attainable fraction of the envelope mass accumulated by the black hole. For Bondi-limited accretion, the black hole typically reaches no more than $\sim$11% of the total mass before convective instabilities eject the envelope, while saturated-convection models can grow the black hole to a mass ratio $M_{\rm BH}/M_* \sim 0.55$—a fivefold increase (Santarelli et al., 13 Oct 2025). This flexible boundary treatment is central to exploring the physical limits of quasi-star stability and heavy seed production.

3. Mass Loss, Stellar Winds, and Envelope Evolution

A critical element in determining quasi-star fate is the competition between accretion/growth and envelope depletion due to stellar winds. MESA-QUEST incorporates several wind prescriptions:

• Reimers Wind: $$\dot{M}_{\rm wind} = 4 \times 10^{-13} \eta (L R/M)$$, where $\eta \sim 0.5$ (in solar units). This prescription typically leads to modest wind mass-loss rates.
• Dutch Wind: A composite of temperature-dependent wind models with effective transitions at $T_{\rm eff} \sim 10^4$ K, suitable for massive stars; may result in rapid envelope stripping at high luminosity.
• Super-Eddington Radiation-Driven Winds (e.g., Dotan 2011): $$\dot{M}_{\rm wind} = 1.4 \times 10^{-4} M_*^{0.96} M_{\rm BH}^{0.17}$$ $(M_\odot\,\mathrm{yr}^{-1})$, which can lead to complete envelope evacuation on timescales $\sim10^3$ yr unless counterbalanced by ongoing inflow.

The modeled mass-loss rates set the upper limit on the lifetime of quasi-stars and the maximum attainable $M_{\rm BH}$. Strong winds, particularly in models with enhanced accretion luminosity (high $\alpha$ parameter in $L_0 = \alpha L_{\rm Edd}$), can quickly eject the envelope and quench heavy seed formation (Santarelli et al., 13 Oct 2025). The interplay between mass-loss, accretion mode, and envelope accretion is thus a principal determinant in the efficacy of the quasi-star channel for early SMBH formation.

4. Numerical Controls, Stability, and Physical Limits

The regime near the inner boundary is numerically challenging due to steep gradients and potential for noise. MESA-QUEST employs several stabilizing and diagnostic mechanisms:

• Averaging of the local sound speed over the innermost 50 mesh zones to smooth fluctuations near $r_0$.
• Enforcement of step-size controls, such as limiting the fractional change in $r_B$ per timestep to 5%, to avoid spurious excursions and maintain physical realism.
• Use of the Ledoux criterion for convective stability, which is more appropriate for these highly stratified, radiation-dominated envelopes.

The envelope's response to black hole growth—either stable swelling or runaway ejection—depends sensitively on the adopted inner boundary prescription and wind physics. This enables systematic exploration of when a quasi-star can remain hydrostatically stable and under what conditions the black hole mass fraction approaches its theoretical upper bound.

5. Validation, Interoperability, and Post-processing

The performance of MESA-QUEST has been validated by reproducing key results from prior quasi-star studies (e.g., density profiles, radius evolution, and $M_{\rm BH}/M_*$ growth as reported by Ball et al. 2011). The framework is fully interoperable with MESA’s modular post-processing ecosystem, including integration with the NuGrid nucleosynthetic pipeline and third-party analysis tools (such as MESAlab for automated evolutionary phase identification and GYRE for asteroseismic diagnostics) (Denissenkov, 2012, Tarczay-Nehéz, 10 Sep 2025).

Table: Key Inner Boundary Treatments and Expected Limits

Boundary Model	Max $M_{\rm BH}/M_*$	Growth Limiter
Bondi Accretion	$\sim$0.11	Convective envelope ejection
Saturated Convection	$\sim$0.55	Efficiency of convective transport

These values are not strict physical limits but rather outcomes dependent on integration schemes, microphysics, and granularity of accretion/wind models.

6. Scientific Impact and Future Extensions

MESA-QUEST provides a robust platform for studying the formation of heavy-seed black holes, pivotal for understanding the rapid emergence of SMBHs in the early universe. By systematically varying wind schemes, accretion boundary conditions, and envelope accretion rates, the framework delineates the parameter space for viable quasi-star evolution and the circumstances for successful DCBH production (Santarelli et al., 13 Oct 2025).

Planned enhancements include:

• Rotation: To refine both convective transport and embedding disk structure,
• Magnetic Fields: To enable studies of jet formation and wind channeling,
• General Relativistic Radiation Hydrodynamics: For full coupling of GR effects and radiative transfer near the event horizon.

A plausible implication is that only a restricted window of parameter space—characterized by favorable mass inflow and moderate wind strength—permits quasi-stars to remain stable long enough for their seed black holes to reach $\gtrsim 10^3\,M_\odot$ (Santarelli et al., 13 Oct 2025). Incorporation of future microphysics and observational priors from JWST and Chandra is expected to further constrain this channel and its significance for SMBH formation.