Bayesian 3D modeling of the orbital dynamics of wide binary stars: gravitational anomaly at low acceleration from a highest-quality sample of 36 wide binaries with accurate 3D velocities

Abstract

Python modules, data files, and MCMC output figures for "Detection of Gravitational Anomaly at Low Acceleration from a Highest-quality Sample of 36 Wide Binaries with Accurate 3D Velocities" (arXiv:2601.21728, submitted to the AAS journals). [Note: Due to upload limitations, MCMC output data files other than corner plot figures are not included. However, MCMC outputs can be produced with the given codes based on the observational data file provided here. Examples of MCMC output files can be found in the previous version.] Python modules: 'MCMCwb3D_newton.py': The module to perform Markov Chain Monte Carlo (MCMC) simulations using the public package 'emcee' for a fixed value of G=gamma*G_N (gamma can be specified by the user). It also has a function that is called in the grid search of the parameter space. [Note: In the previous version, the prior range for inclination was (-90deg,90deg) for this module. It is now fixed to (-180deg,180deg). 'MCMCwb3D_general.py': Same as 'MCMCwb3D_newton.py' but for the generalized gravity case where G (through parameter Gamma) is free. 'jobMCMCfit_wb3Dany_basic.py': The main program to carry out the Bayesian fit for a wide binary from a Gaia sample by calling 'MCMCwb3D_newton.py' or 'MCMCwb3D_general.py'. 'jobGridSearch_wb3D_newton.py' and 'jobGridSearch_wb3D_general.py': The codes to obtain grid-search solutions that are needed as starting values of the MCMC procedure. Gaia samples of wide binaries: 'gaia_purewb_3D_valueadded_basic75_corrected.csv' : The Chae+2026 sample of binaries that is used in the study. The given radial velocities (RVs) were corrected for gravitational redshift (GR) and convective blueshift (CB) for the binaries from APOGEE and HARPS. For the other binaries, realistic errors of the given relative RVs were estimated. For all binaries, perspective effects were corrected for in proper motions and radial velocities. 'gaia_purewb_3D_valueadded_basic75.csv' : The same sample as above but with measured proper motions and radial velocities without any corrections of GR, CB, or perpective effects. The errors of the relative RVs given in this file do not include errors of GR+CB. 'gaia_wb_RV_com2026.csv' : All measured RVs of the raw sample of 306 binaries. Auxiliary files: 'gaia_purewb_3D_valueadded_basic75_corrected_gridsol_newton.csv': The pre-calculated grid solutions for the Newtonian gravity case. 'gaia_purewb_3D_valueadded_basic75_corrected_gridsol_general.csv': The pre-calculated grid solutions for the general gravity case. 'gaia_purewb_3D_valueadded_basic75_corrected_gridsol_newton140.csv': The pre-calculated grid solutions for the pseudo-Newtonian gravity with G=1.4G_N. MCMC output data files: 'fig_corner_basic75.tar.gz': compressed file containing corner plots derived from the MCMC simulations