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

# 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](https://arxiv.org/abs/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: ```fortran ! 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: ```bash 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: ```python 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.