1D stellar mergers: entropy sorting and PyMMAMS

TL;DR

The paper tackles the need for fast, reliable 1D approximations of stellar mergers by comparing two 1D schemes—entropy sorting (ES) and PyMMAMS (PM)—against 3D SPH and MHD benchmarks. PM augments ES with a shock-heating prescription calibrated on head-on SPH collisions and orders shells by the entropic variable $A$, improving agreement with 3D results for core ownership, density, and temperature distributions. The authors extend PM with a tunable heating factor $f_ ext{mod}$ to better capture slow inspiral mergers, finding a moderate reduction in shock heating (roughly $f_ ext{mod}\,\approx\,0.3$–$0.5$) yields the best compromise between entropy and composition profiles. While 1D methods cannot capture rotation or magnetic-field effects, PM provides a substantially more accurate and computationally efficient framework for exploring merger outcomes and their subsequent evolution, with direct applicability to population synthesis and interpretation of blue supergiants and rejuvenation signatures.

Abstract

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.

Figures (16)

• Figure 1: Comparison of the merger case between SPH and PM (upper row) and SPH and ES (lower row) for all of the mergers presented in Glebbeek2013. The abscissa shows the initial mass of the primary progenitor star, and the ordinate the mass ratio $q = M_2 / M_1$. Each square field corresponds to one merger, and is subdivided into a lower-left (SPH) and upper-right (PM/ES) triangle. The color of the triangle indicates the merger case, with blue for case 'P', orange for case 'S', and green for case 'M'. If the merger methods disagree on the case, the corresponding field is additionally marked with a black diagonal bar.
• Figure 2: From top to bottom: Hydrogen mass fraction, density, temperature and entropic variable profiles of the half-age main sequence (HAMS) merger of a $10\,{\rm M}_{\odot}$ primary with a $1\,{\rm M}_{\odot}$ secondary star of the same age. We compare the profiles produced by our 1D methods PM, ES and ES$_\mathrm{C}$ with the SPH simulations taken from Glebbeek2013. The hydrogen mass fraction profile of the ES$_\mathrm{C}$ model was not included as it is virtually identical to the ES profile.
• Figure 3: Same as Fig. \ref{['fig_hams_10_1']}, but now for the core-hydrogen exhaustion (CHEX) merger of a $20\,{\rm M}_{\odot}$ primary with an $8\,{\rm M}_{\odot}$ secondary star of the same age.
• Figure 4: Relative remaining core-hydrogen burning lifetime $t_\mathrm{MS}/\tau_\mathrm{MS}$ versus apparent fractional age $f_\mathrm{app}$ of the merger remnant for all of our HAMS and TAMS merger models. The black dashed line corresponds to the $\alpha = 1.14$ prescription for low-mass stars offered by Glebbeek2013, and the blue dashed line to $\alpha = 1.67$ in Glebbeek2008 for low-mass stars. HAMS mergers are indicated by circles, TAMS mergers by squares. The different colors correspond to the mass ratio $q$ of the merger. Figure titles again indicate the merger method used.
• Figure 5: Hertzsprung-Russell diagram showing the post-merger evolution of the $q = 0.7$ HAMS merger remnants (with the exception of the $M_1 = 40\,{\rm M}_{\odot}$ model) until core helium exhaustion. The track marked with 'GS*' represents a genuine single star with a ZAMS mass equal to that of the merger remnant immediately post-merger.