Pulsational Instability of Quasi-Stars

Companion data and code repository for:

Pulsational Instability of Quasi-Stars: Interpreting the Variability of Little Red Dots

Matteo Cantiello, Jake B. Hassan, Rosalba Perna, Philip J. Armitage, Mitchell C. Begelman, Yan-Fei Jiang, Taeho Ryu, Richard H. D. Townsend

Submitted to ApJL (arXiv:2512.17997)

Overview

This repository contains the MESA stellar evolution models, GYRE pulsation analysis, and Jupyter notebooks needed to reproduce the results of the paper. We model quasi-stars -- supermassive stellar envelopes powered by accretion onto a central black hole -- across a mass range of 10^4 to 5x10^5 solar masses. We perform linear non-adiabatic pulsation calculations to identify a "Quasi-Star Instability Strip" where the kappa-mechanism drives radial pulsations with periods of ~20-180 years.

Repository Structure

quasistars-zenodo/
|
|-- quasistars-mesa-template/   MESA work directory template for quasi-star models
|-- pulsations/                 GYRE pulsation analysis and Jupyter notebooks
|-- figures/                    Publication figures (PDF)
|
|-- 1e4Msun/                    Quasi-star model: M = 10^4 Msun
|-- 2e4MsunIC/                  Quasi-star model: M = 2x10^4 Msun
|-- 5e4MsunIC/                  Quasi-star model: M = 5x10^4 Msun
|-- 1e5Msun/                    Quasi-star model: M = 10^5 Msun
|-- 2e5Msun/                    Quasi-star model: M = 2x10^5 Msun
|-- 5e5MsunIC/                  Quasi-star model: M = 5x10^5 Msun
|
|-- 2e5Msun_283000_567/         MESA hydro run: unstable model (Teff ~ 4682 K)
|-- 2e5Msun_33000_67/           MESA hydro run: stable model (Teff ~ 5445 K)

Software Requirements

• MESA (Modules for Experiments in Stellar Astrophysics), version r24.08.1
  • https://docs.mesastar.org
  • The MESA SDK is required to compile and run MESA.
• GYRE version 8.1 (stellar oscillation code, included in MESA)
  • https://gyre.readthedocs.io
• Python 3 with the following packages:
  • numpy, scipy, pandas, matplotlib, seaborn, h5py
  • mesa_reader -- for reading MESA output files
  • pygyre -- for reading GYRE HDF5 output
  • astropy -- for physical constants and units

Quasi-Star MESA Template

The quasistars-mesa-template/ directory is a complete MESA work directory configured to evolve a quasi-star model. Key features of the setup:

• Central black hole: modeled as a point mass (M_center) that grows by accreting from the stellar envelope. The black hole luminosity L_center is set by the accretion rate and a radiative efficiency parameter (x_ctrl(1)).
• TOV correction: General-relativistic corrections to gravity are enabled via use_other_cgrav = .true. (see src/other_cgrav.inc).
• Custom physics: The Fortran source in src/run_star_extras.f90 implements the quasi-star energy source, black hole growth, and optional eruptive mass loss.
• GYRE output: MESA is configured to write GYRE-compatible pulse data with each saved profile (write_pulse_data_with_profile = .true.).
• Zero metallicity: Models use primordial composition (Z = 0, Y = 0.3).

Running a Model

The simulation proceeds in two stages:

1. Initial model (inlist_initial): Creates a pre-main-sequence model of the desired mass and saves it as start.mod.
2. Evolution (inlist_evolve): Loads start.mod, relaxes a central point mass (the seed black hole), and evolves the quasi-star.

To change the quasi-star mass, edit initial_mass in inlist_common. To change the initial black hole mass, edit new_core_mass in inlist_evolve. For example:

! In inlist_common:
initial_mass = 1d5    ! Total quasi-star mass in Msun

! In inlist_evolve:
new_core_mass = 1d2   ! Initial seed BH mass in Msun

To compile and run:

cd quasistars-mesa-template
./mk        # Compile
./rn        # Run (uses inlist_initial then inlist_evolve)

Key Control Parameters (in inlist_common)

Parameter	Description
x_ctrl(1)	Radiative efficiency of BH accretion (default: 0.1)
x_ctrl(2)	Convective efficiency parameter (default: 0.1)
x_ctrl(4)	Efficiency factor for eruptive mass loss (default: 0.1)
x_logical_ctrl(1)	Enable accretion onto the black hole
x_logical_ctrl(2)	Enable mass loss from rest-energy conversion

Pre-Computed MESA Models

Each model directory (e.g., 1e5Msun/) contains:

• LOGS/history.data -- time-resolved stellar evolution output (luminosity, Teff, BH mass, etc.)
• LOGS/profiles.index -- maps model numbers to profile numbers
• LOGS/profileN.data -- detailed stellar structure snapshots
• LOGS/profileN.data.GYRE -- GYRE-compatible pulse data files
• instability_strip_filtered.csv -- GYRE pulsation results (growth rates, periods) for selected profiles

The two MESA hydrodynamic runs (2e5Msun_283000_567/ and 2e5Msun_33000_67/) are restarts from specific snapshots of the 2e5Msun model, evolved with MESA's implicit hydrodynamics to verify the pulsational instability predicted by linear analysis.

Pulsation Analysis

The pulsations/ directory contains the analysis pipeline and four Jupyter notebooks that reproduce the paper figures.

Notebooks

Notebook	Description	Paper Figures
quasistar_HRD.ipynb	HR diagram with evolutionary tracks colored by M_BH	Fig. 1
pulsation_analysis.ipynb	GYRE mode analysis: eigenfunctions, work integrals, opacity derivatives	Figs. 2, 3
instability_strip.ipynb	Constructs the quasi-star instability strip with RBF interpolation; growth rates and periods vs. Teff	Figs. 4, 5
MESA_hydro.ipynb	Analyzes MESA hydrodynamic runs: HRD loops, radius pulsations, surface Mach number	Fig. 6

GYRE Configuration

The file gyre.in is the GYRE input template used for both adiabatic and non-adiabatic radial mode calculations (l=0). Key settings:

• Frequency scan: 0.01 to 20 cycles/day (real axis), -10 to 2 (imaginary axis)
• Solver: MAGNUS_GL2 differencing scheme
• Non-adiabatic search seeded from adiabatic solutions (nad_search = 'AD')
• Output includes work integrals (dW_dx), opacity derivatives (kap_T, kap_rho), and eigenfunctions

Batch GYRE Processing

The script run_gyre_batch.py automates running GYRE across many MESA profiles:

import run_gyre_batch as gb

# List of GYRE-compatible profile files
file_list = ['path/to/profile10.data.GYRE', 'path/to/profile20.data.GYRE', ...]

# Run GYRE on each profile and save results
gb.process_gyre_profiles(file_list, output_filename='instability_strip_filtered.csv')

Note: You must edit the GYRE_CMD path in run_gyre_batch.py to point to your local GYRE installation.

Supporting Python Files

• astro_setup.py -- imports, physical constants, and plot styling (loaded by all notebooks via from astro_setup import *)
• Constants.py -- CGS physical constants class
• strip.py -- instability strip analysis utilities

Pre-Computed Data Files

• summary_ad.h5, summary_nad.h5 -- GYRE adiabatic and non-adiabatic mode summaries for the 2x10^5 Msun reference model
• mode_nad.l0.n+*.h5 -- detailed non-adiabatic eigenfunctions for individual modes
• instability_strip.csv -- compiled pulsation data across all models
• quasistars_data.pkl -- cached processed data from all MESA models (used by instability_strip.ipynb to avoid re-reading large ASCII files; set LOAD_FROM_PICKLE = False to regenerate)
• hrd_data_cache.pkl -- cached HRD track data (used by quasistar_HRD.ipynb)

Reproducing the Paper

1. Install prerequisites: MESA r24.08.1, Python packages listed above.
2. Inspect pre-computed models: The MESA model outputs are included in this repository. To re-run a model from scratch, copy quasistars-mesa-template/ to a new directory, adjust the mass and BH parameters, compile with ./mk, and run with ./rn_nomodfiles inlist_evolve_header
3. Run the notebooks: Open the Jupyter notebooks in pulsations/ and execute them in the following order:
   • quasistar_HRD.ipynb (Fig. 1)
   • pulsation_analysis.ipynb (Figs. 2-3)
   • instability_strip.ipynb (Figs. 4-5)
   • MESA_hydro.ipynb (Fig. 6)
4. Re-run GYRE analysis (optional): To recompute the pulsation mode data from the MESA profiles, use run_gyre_batch.py as described above, or run GYRE manually with the provided gyre.in template.