From Main Sequence Binary to Blast: MESA Modeling of the Double-Detonation Progenitor PTF1~J2238+7430

TL;DR

This study uses MESA binary evolution to reproduce the history of the sdB+WD system PTF1 J2238+7430, a candidate double-detonation Type Ia supernova progenitor. The authors show that the sdB forms via stable Roche-lobe overflow from a ~2.70 M⊙ donor, while the WD arises from the companion through a subsequent common-envelope phase, yielding the observed components in a ~76.3-minute orbit. A key result is that matching the present-day configuration requires a high common-envelope ejection efficiency, α_CE ≈ 0.87, suggesting unusually efficient envelope removal for this system. The work maps preliminary regions of initial masses and orbital periods that can lead to sdB+WD systems capable of double-detonation progenitors, providing a foundation for future systematic studies and population-synthesis assessments of their contribution to Type Ia supernova rates.

Abstract

Hot subdwarf B (sdB) stars in close binaries with white dwarf (WD) companions are potential progenitors of double-detonation thermonuclear supernovae. The recently discovered system PTF1 J2238+7430 is a candidate for this evolutionary channel, hosting a low-mass sdB and a comparatively massive WD in a compact orbit. We aim to reproduce the evolutionary history of PTF1 J2238+7430, in which the sdB forms first via stable mass transfer, followed by the formation of the WD through a subsequent common-envelope (CE) phase. Additionally, we seek to constrain the range of initial binary parameters that can lead to such double-detonation progenitors. Using the Modules for Experiments in Stellar Astrophysics (MESA), we performed detailed binary evolution simulations from the zero-age main sequence to the present-day configuration. We explored initial stellar masses, orbital periods, and mass-loss fractions, including the effects of angular momentum transfer, tidal synchronization, and gravitational-wave-driven orbital evolution. The post-CE binary properties were derived using the standard energy formalism. Our models successfully reproduce the observed properties of PTF1 J2238+7430, consisting of a 0.406 solar-mass sdB and a 0.72 solar-mass WD in a 76.34-minute orbit. Stable Roche-lobe overflow of an approximately 2.7 solar-mass donor produces the sdB, while the WD forms from the initially less massive companion during an episode of CE evolution. We find that the CE ejection efficiency must be high to match the observed orbit, exceeding canonical values for similar systems. We further delineate the allowed parameter space for initial binaries that can evolve into sdB+WD systems consistent with double-detonation progenitors. These limits are preliminary; a systematic exploration of all parameters is needed for robust constraints, but our results provide a useful starting point for future work.

Figures (5)

• Figure 1: MESA evolutionary track of the sdB progenitor in a binary system with initial stellar masses of $2.7\,M_\odot$ (primary) and $2.6\,M_\odot$ (secondary), and an initial orbital period of 3 days. Point “1” marks the start of the simulation at the zero-age main sequence. Point “2” corresponds to the onset of hydrogen shell burning, while circle “3” indicates the beginning of stable mass transfer, which terminates at point “4.” At point “5,” the stripped primary becomes an sdB star. Finally, point “6” marks the onset of the common-envelope phase initiated by the secondary. The color of the track represents the mass evolution of the primary star. The blue star indicates the observed position of the sdB component of PTF1 J2238+7430, as reported by Kupfer22.
• Figure 2: Evolution of the $2.7\,M_\odot$ main-sequence star during the stable mass-transfer episode. Top panel: Mass-transfer rate, with colors indicating the change in mass of the sdB progenitor. Bottom panel: Stripping of the H-rich envelope, with colors indicating the stellar radius as the star evolves to reveal its core (sdB).
• Figure 3: Evolutionary track of the $2.6,M_\odot$ star, i.e., the white dwarf progenitor, as obtained from two MESA simulations. The left panel, which corresponds to the same simulation shown in Figure \ref{['fig:HRD']}, illustrates the pre-common-envelope evolution, starting at the zero-age main sequence, followed by the onset and termination of stable mass transfer, and culminating in the initiation of the common-envelope phase. The right panel shows the post-common-envelope evolution: the white dwarf cooling track was simulated by removing the red giant envelope, the system emerges as a compact binary, the secondary contracts to form a white dwarf, and the track continues until it reaches the present-day configuration of PTF1 J2238+7430, marked with a yellow star. The color bar indicates the change in the mass of the WD progenitor in both panels.
• Figure 4: Common-envelope efficiency ($\alpha_{\mathrm{CE}}$) versus final orbital period. The solid line shows the possible post–common-envelope orbital configurations. The horizontal dashed line indicates the predicted orbital period of $95.04$ minutes for PTF1 J2238+7430 Kupfer22, while the vertical orange dashed line marks the corresponding $\alpha_{\mathrm{CE}}=0.872$. The recombination energy was fixed to $\lambda=1$.
• Figure 5: Allowed and excluded regions for the formation of an sdB + WD binary through stable mass transfer similar to PTF1 J2238+7430. The central green-shaded region indicates combinations of initial donor mass ($M_{1,\mathrm{init}}$) and orbital period ($P_{\rm init}$) that lead to sdB formation consistent with observations. The hatched and colored regions correspond to physically forbidden configurations: violet (left side) indicates donors too low in mass (no He ignition), red (right side) shows donors too massive (oversized core or Roche-lobe overflow in the subgiant phase), blue (bottom part) denotes systems at risk of common-envelope or merger events, and orange (upper part) represents donors with a thick hydrogen shell preventing sdB formation. The black star marks the parameters of the observed system PTF1 J2238+7430, while black squares represent model systems that produced potential double-detonation supernova progenitors with slightly different masses from the observed system.