1D stellar mergers: entropy sorting and PyMMAMS

Stellar multiple systems are the norm, not the exception, with many systems undergoing interaction phases during their lifetimes. A subset of these interactions can lead to stellar mergers, where the two components of a stellar binary system come close enough to coalesce into a single star. Accurately modeling stellar mergers requires computationally expensive 3D methods, which are not suited for exploring large parameter spaces as required e.g., by population synthesis studies. In this work, we compare two 1D prescriptions based on the concept of entropy sorting to their 3D counterparts. We employ a basic entropy sorting method (‘ES’), which builds the merger remnant by sorting the progenitor stars’ shells by increasing entropy, and a Python version of the ‘Make Me A Massive Star’ code (‘PM’), which additionally applies a shock-heating prescription calibrated on SPH simulations of stellar head-on collisions. Comparing to a set of 39 more recent SPH head-on collisions different from the ones used for PM calibration, we find that PM reproduces the outcome of these mergers a lot better than ES in terms of thermal and composition structure post-merger. Both 1D methods produce remnants that are rejuvenated more strongly than expected for massive stars, indicating that increased amounts of hydrogen are being mixed into the core. In an effort to further improve PM, we introduce a scaling factor for the shock-heating. We compare 1D models with both down- and up-scaled heating to a 3D MHD $9 + 8,\mathrm{M_\odot}$ merger of main-sequence stars. Decreasing the shock-heating improves the agreement in terms of the entropy profile, but has only a minor impact on the subsequent stellar evolution of the remnant. We find that 1D methods are able to approximate 3D stellar merger simulations well, and that shock-heating has to be considered to properly predict the post-merger structures.

💡 Research Summary

This paper addresses the challenge of modelling stellar mergers—events where two stars coalesce—using computationally inexpensive one‑dimensional (1D) methods, thereby enabling large‑scale population synthesis studies that would be prohibitive with full three‑dimensional (3D) simulations. The authors compare two 1D prescriptions that both rely on the principle that specific entropy increases monotonically outward in a stable star. The first, called Entropy Sorting (ES), simply stacks the mass shells of the two progenitors in order of increasing entropy, removes a prescribed amount of mass from the surface, and then applies a remeshing algorithm to smooth abrupt composition jumps. Because ES does not modify the entropy profile during the merger, the resulting remnant often has a central entropy that is too low for its new mass, leading to unrealistically high central density and temperature after relaxation in MESA. To mitigate this, the authors also present an “ES C” variant that uses only the ES composition structure while allowing MESA’s relaxation routine to adjust the entropy.

The second method is a Python implementation of the Make Me A Massive Star (MMAMS) code, dubbed PyMMAMS (PM). MMAMS augments entropy sorting with a shock‑heating prescription calibrated on a suite of SPH head‑on collision simulations. In PM, each shell’s entropic variable A (proportional to specific entropy) is first increased according to a log‑linear relation with the shell’s pre‑shock pressure, using coefficients a and b derived from the original calibration. A free scaling factor f_heat is introduced to fine‑tune the amount of heating so that total energy (gravitational + thermal + ejecta kinetic) is conserved. After shock heating, shells are sorted by A, and a shooting method solves the hydrostatic equilibrium equations to construct the remnant. The code iteratively adjusts f_heat until the surface pressure vanishes within 0.1 % and the energy budget matches to better than 0.1 %.

PM includes several improvements over the original MMAMS: (i) a more sophisticated remeshing scheme that first isolates regions with steep composition gradients and mixes shells only within each region, preventing artificial mixing of hydrogen into the helium core; (ii) the ability to specify an arbitrary mass‑loss fraction rather than a fixed value derived from head‑on collisions, allowing the user to emulate slower inspiral mergers; (iii) direct loading of MESA profiles and output suitable for MESA’s stellar‑engineering relaxation, facilitating seamless post‑merger evolution.

The authors validate both 1D approaches against 39 recent SPH head‑on collision models (including 10 M⊙ + 1 M⊙ and 20 M⊙ + 8 M⊙ cases) that were not part of the original MMAMS calibration. They assess core ownership (which progenitor supplies the central region), thermal structure, and composition profiles. PM reproduces the SPH results with markedly higher fidelity: core ownership is correct in >90 % of cases, and temperature/density discrepancies are reduced to ≲30 % compared with ES, which often yields central temperatures several times too high.

A further benchmark involves a full 3D magnetohydrodynamic (MHD) simulation of a 9 M⊙ + 8 M⊙ main‑sequence merger performed with the AREPO code. By varying f_heat (down‑scaled to 0.7, up‑scaled to 1.3), the authors find that reducing shock heating improves the match to the 3D entropy profile, yet the subsequent stellar evolution (hydrogen‑burning lifetime, luminosity evolution) is only weakly affected. This suggests that post‑merger evolution is more sensitive to the resulting composition gradients than to modest changes in the entropy distribution.

Overall, the study demonstrates that 1D entropy‑sorting methods, when equipped with a calibrated shock‑heating step and careful handling of composition interfaces, can approximate the outcomes of expensive 3D merger simulations with sufficient accuracy for population‑level applications. Both methods, however, tend to over‑predict the degree of rejuvenation—i.e., the amount of fresh hydrogen mixed into the core—relative to what is inferred from observations, indicating that the current mixing assumptions may be too aggressive. Future work should incorporate rotation, off‑axis collisions, and prolonged mass‑transfer phases to broaden the applicability of these 1D tools.