Helium Merger Model in Stellar Evolution

• The Helium Merger Model is a framework describing the coalescence of helium cores (e.g., white dwarfs or helium-burning cores) that leads to a variety of stellar remnants and transients.
• It integrates hydrodynamic and magnetohydrodynamic simulations with population synthesis to model outcomes such as hot subdwarfs, low-mass white dwarfs, and peculiar supernovae.
• The model quantitatively explains observable features—like hydrogen survival rates, magnetic field amplification, and luminosity functions—in merger products spanning from Ca-rich events to gamma-ray bursts.

The Helium Merger Model encompasses a diverse set of stellar merger scenarios in which at least one degenerate helium core (typically a helium white dwarf or a helium-burning stellar core) participates in a physical coalescence. These mergers yield a wide array of astrophysical phenomena, including the formation of hydrogen-rich and helium-rich hot subdwarfs, single low-mass white dwarfs, chemically peculiar giants, Ca-rich and Type Ia supernovae, and transients involving compact objects. The model is anchored in binary stellar evolution theory, nucleosynthesis, stellar hydrodynamics, and population synthesis calculations. Below, the key regimes and predictive frameworks of the Helium Merger Model are surveyed.

1. Double Helium White Dwarf Mergers and Hot Subdwarfs

The canonical helium merger channel involves the coalescence of two helium white dwarfs (He WDs) with masses in the typical range $0.15 \lesssim M_{1,2}/M_\odot \lesssim 0.45$. Prior to merger, each He WD possesses a $\sim10^{-3}\,M_\odot$ hydrogen-rich envelope, the mass of which depends on age and precise progenitor history. At coalescence, hydrodynamic simulations reveal that the lighter WD is wholly disrupted, yielding a structure with a cold core (mainly from the primary), a hot envelope, and an extended disk/tidal tail. Hydrogen in shock-heated (hot) regions is assumed to be destroyed, but fractions residing in cooler or extended regions survive. The surviving hydrogen mass is quantified by

$$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$

where $\epsilon_{\rm surv}\approx 0.4$–$0.6$ for typical mergers. The maximum $M_{\rm H, surv}$ is $\sim2 \times 10^{-3}\,M_\odot$, peaking near $M_{\rm tot} \approx 0.5 M_\odot$.

Post-merger, models constructed as generalized main-sequence (GMS) stars—with a He core and residual H envelope—accurately reproduce the locus in ($T_{\rm eff}$, $\log g$) observed for the majority of isolated H-rich hot subdwarfs (sdB/sdO): $\sim10^{-3}\,M_\odot$0–$\sim10^{-3}\,M_\odot$1 kK, $\sim10^{-3}\,M_\odot$2–$\sim10^{-3}\,M_\odot$3. The characteristic hydrogen envelope ($\sim10^{-3}\,M_\odot$4–$\sim10^{-3}\,M_\odot$5) directly leads to the observed atmospheric properties. The theoretical distribution envelopes $\sim10^{-3}\,M_\odot$690% of observed H-rich sdBs; only a small fraction of low-gravity outliers remain unexplained by this mechanism (Hall et al., 2016).

2. Remnant Magnetic Fields and Their Dependence on Merger Mass Ratio

Three-dimensional, high-resolution MHD simulations demonstrate that mergers of He WDs efficiently generate both small-scale and large-scale magnetic fields through turbulence and the magnetorotational instability (MRI). In equal-mass mergers ($\sim10^{-3}\,M_\odot$7), turbulence rapidly amplifies the field to a root-mean-square $\sim10^{-3}\,M_\odot$8 G, followed by large-scale field growth via the MRI, which produces a coherent azimuthal field of $\sim10^{-3}\,M_\odot$9 dominating the remnant. These ordered fields are expected to survive the subsequent evolution if helium ignites centrally, as in fully mixed, equal-mass configurations.

In contrast, unequal-mass mergers ($$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$0) lead to helium-shell ignition and convective shell burning enveloping the region of magnetic energy, rapidly destroying the large-scale field. Only a tangled small-scale field remains, which ohmic dissipation erases on $$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$1 yr timescales. Consequently, strongly magnetized hot subdwarfs are rare—$$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$2 of the population—consistent with observational incidence (Pakmor et al., 2024).

3. Helium White Dwarf–Main Sequence Mergers: Single Low-mass White Dwarfs and Hot Subdwarfs

A significant fraction of single low-mass ($$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$3) white dwarfs are produced by the merger of a He WD and a low-mass main-sequence star. Rapid, highly super-Eddington accretion forms an RGB-like star whose degenerate core grows until envelope ejection, producing a WD with

$$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$4

for typical wind strengths. The mass distribution for such WDs is sharply peaked, $$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$5–$$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$6 (range $$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$7–$$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$8), aligning with the observed single low-mass WD population. The Galactic formation rate is $$M_{\rm H, surv} = \epsilon_{\rm surv} (M_{\rm H,WD1} + M_{\rm H,WD2}),$$9 yr$\epsilon_{\rm surv}\approx 0.4$0, matching the inferred prevalence of isolated low-mass WDs (Zhang et al., 2017).

In systems where the merged core ignites helium, evolutionary calculations reproduce the observed properties of certain intermediate He-rich and standard H-rich hot subdwarfs. Merger products follow evolutionary paths producing an intermediate He-rich surface phase (few Myr), then settle onto the extreme horizontal branch (hot subdwarf proper) for $\epsilon_{\rm surv}\approx 0.4$1 Myr (Zhang et al., 2017).

4. CO+He White Dwarf Mergers and Peculiar Transients

Mergers between carbon-oxygen (CO) and helium WDs synthesize distinctive post-merger objects and transients:

• RCB and EHe stars: Linear mixing of He WD and stratified CO WD layers during dynamical merger, potentially augmented by hot ($\epsilon_{\rm surv}\approx 0.4$2–$\epsilon_{\rm surv}\approx 0.4$3 K) burning, converts CNO-processed and AGB-inter shell matter into an envelope matching the observed high [C], [O], [F], [Ne], and s-process element abundances of R Coronae Borealis and extreme helium (EHe) stars. The "destroyed-disk" accretion model efficiently enhances $\epsilon_{\rm surv}\approx 0.4$4C enrichment, aligning theory with observed numbers and surface compositions (Zhang et al., 2014, Jeffery et al., 2011).
• Calcium-rich transients: Hydrodynamical and non-LTE radiative transfer studies show that CO+He WD mergers (e.g., $\epsilon_{\rm surv}\approx 0.4$5 CO WD + $\epsilon_{\rm surv}\approx 0.4$6 He WD) can reproduce the key nebular-phase calcium II and [Ca II] features observed in Ca-rich optical transients. The synthetic spectra match the broad velocity structure and He I/Ca signatures, with limitations (He line strength, Ti II blanketing, emission profile widths) suggesting further 3D modeling and tailoring of merger parameters is required (Callan et al., 15 Mar 2025).
• Type Ia Supernovae: In the helium-ignited violent-merger regime, a thin helium shell ($\epsilon_{\rm surv}\approx 0.4$7) on a CO WD detonates—either via shock convergence or dynamic accretion flows—triggering a CO core detonation, unifying normal and rapidly declining (1991bg-like) Type Ia events within a single physical framework. Synthetic light curves and delay-time distributions from population synthesis naturally yield the observed bimodal luminosity function and fraction of fast-declining SNe Ia. The envelope threshold for detonation, $\epsilon_{\rm surv}\approx 0.4$8, presents tension with observational upper limits on helium-burning ash, indicating that multi-dimensional deflagration-to-detonation transitions are likely a necessary ingredient (Pakmor et al., 2013, Iwata et al., 2022).

5. Mergers Involving Giants and the Formation of Chemically Peculiar Giants

Mergers of He WDs with red giant branch (RGB) stars yield lithium-rich red clump stars and early-R carbon stars. Following common-envelope evolution and spiral-in, rapid accretion and mixing ignite helium shell flashes, activating the Cameron–Fowler mechanism (for high Li) and 3$\epsilon_{\rm surv}\approx 0.4$9 burning (for high C/O). Grid-based population synthesis predicts space densities, evolutionary lifetimes, and surface abundance patterns that closely replicate observational samples of Li-rich and R-type giants (Zhang et al., 2020, Tylenda et al., 2023).

Specific historical transients, most notably Nova 1670 (CK Vulpeculae), are attributed to mergers of first-ascent red giants with He WDs. Energetics (total $0.6$0 erg), nucleosynthetic signatures ($0.6$1C, $0.6$2C, $0.6$3O, $0.6$4Al), and the present-day luminosity and composition of the remnant agree with detailed models of this scenario (Tylenda et al., 2023).

6. Helium-Core Mergers in Massive Stars and Gamma-Ray Bursts

Mergers involving compact stellar remnants (neutron star or black hole) and the helium core of an evolved companion offer a high angular-momentum reservoir and rapid accretion, enabling the formation of engine-driven transients, notably long gamma-ray bursts (GRBs). Population synthesis indicates that low-metallicity environments ($0.6$5) favor the production of rapidly rotating, massive helium cores (post-merger naked helium stars), efficiently forming GRB progenitors. The model matches observed GRB rates and redshift evolution with minimal tuning (Kinugawa et al., 2017, Fryer et al., 2012). Additionally, the ejection of dense common-envelope shells at $0.6$6–$0.6$7 cm, a generic feature of these mergers, imprints distinct thermal emission on the early afterglow of GRBs.

7. Summary Table: Key Helium Merger Regimes

Merger Configuration	Stellar Product / Transient	Key Observables / Surface Properties
He WD + He WD	H-rich sdB/sdO subdwarf	$0.6$8–$0.6$9 kK, $M_{\rm H, surv}$0
CO WD + He WD	RCB/EHe stars, Ca-rich SN, fast SN Ia	Enhanced C, O, F, Ne, $M_{\rm H, surv}$1O,$M_{\rm H, surv}$2F; Ca (Callan et al., 15 Mar 2025)
He WD + MS star	Single low-mass WD, hot subdwarf	$M_{\rm H, surv}$3; short He-rich then long H-rich subdwarf phase
He WD + RGB star	Li-rich clump; early-R carbon star	High Li (A(Li)>3.2), C/O$M_{\rm H, surv}$4, $M_{\rm H, surv}$5–$M_{\rm H, surv}$6 K
NS/BH + He core	Long GRB, superluminous SN	High angular momentum, circumburst shell, engine-driven emission

This taxonomy underscores the breadth of stellar phenomena tied to helium mergers, the critical importance of mass ratios, initial composition, and evolutionary context, and the close correspondence between detailed evolutionary modeling, hydrodynamical simulations, population synthesis, and observed astrophysical populations (Hall et al., 2016, Pakmor et al., 2024, Zhang et al., 2017, Zhang et al., 2014, Pakmor et al., 2013, Iwata et al., 2022, Zhang et al., 2020, 2332.07433, Kinugawa et al., 2017, Fryer et al., 2012).