Chemically Homogeneous Evolution (CHE)

• Chemically homogeneous evolution is a stellar evolution regime in which efficient rotational mixing maintains nearly uniform chemical composition throughout a star’s nuclear-burning lifetime.
• It occurs in massive, rapidly rotating stars—often in tidally locked binaries—with low metallicity, enabling continual mixing and suppression of envelope expansion.
• CHE has significant astrophysical implications, producing Wolf–Rayet stars, gamma-ray burst progenitors, and compact merging binary black holes.

Chemically homogeneous evolution (CHE) is a distinct regime of stellar evolution in which a star remains nearly uniform in its internal chemical composition throughout the majority of its nuclear-burning lifetime. This phenomenon is realized primarily in massive, rapidly rotating stars—most effectively within tidally locked, short-period binary systems—where efficient rotational mixing mechanisms serve to erase the core-envelope chemical gradient that ordinarily builds up during stellar evolution. CHE fundamentally alters the star's structure, evolutionary trajectory, spectrophotometric properties, and final fate, with wide-ranging implications for the formation of Wolf–Rayet (WR) stars, gamma-ray burst (GRB) progenitors, and massive merging binary black holes (BBHs).

1. Physical Basis and Definition

In the CHE regime, rotationally induced instabilities—principally Eddington–Sweet circulation and associated hydrodynamic processes—redistribute the products of nuclear burning (for example, helium produced in core hydrogen fusion) throughout the envelope on timescales shorter than core hydrogen consumption. This condition is succinctly expressed as

$\tau_{\rm mix} \ll \tau_{\rm nuc}$

where $\tau_{\rm mix}$ is the timescale for internal mixing and $\tau_{\rm nuc}$ is the nuclear-burning timescale (Mink et al., 2010). In the idealized limit of perfect mixing, core and surface helium mass fractions remain nearly equal: $X_{\rm He,\,core} \approx X_{\rm He,\,surface}$ The result is the persistent suppression of a steep mean molecular weight gradient and hence the inhibition of radius expansion typical of post-main-sequence stellar evolution. The star evolves along a blueward, high-luminosity track, remaining compact throughout its main-sequence lifetime.

2. Conditions for Chemically Homogeneous Evolution

CHE requires:

• High Initial Mass: The probability and efficacy of rotational mixing, and hence homogeneous evolution, increase strongly with stellar mass due to higher central temperatures and enhanced susceptibility to instability-driven circulation (Mink et al., 2010, Yoon et al., 2012).
• Rapid Rotation: Either primordial or maintained by tidal synchronization in close binaries (orbital periods typically $\lesssim 2-3$ days). In binaries, tidal locking can enforce near-critical rotation for the system lifetime (Mink et al., 2010, Yoon et al., 2012, Martins et al., 2013).
• Low Metallicity: Metal-poor stars ($Z \lesssim 0.004$) experience reduced line-driven winds, thus retaining angular momentum and facilitating sustained rapid rotation and, consequently, efficient internal mixing (Mink et al., 2010, Martins et al., 2013, Cui et al., 2018).
• Binary Interaction: Additional spin-up through episodes of stable mass accretion or post-merger evolution can initiate or reinforce CHE in the accretor (Mink et al., 2010, Ghodla et al., 2022, Dall'Amico et al., 8 Jan 2025).

Notably, the presence of magnetic angular momentum transport (e.g., the Spruit–Tayler dynamo) can support nearly solid-body rotation and thus foster more uniform mixing (Yoon et al., 2012).

3. Dynamical Channels of CHE in Binaries

Multiple evolutionary channels operate within binaries to give rise to CHE:

• Tidal CHE: In extreme short-period binaries, tides synchronize spin with the orbit, maintaining rotation rates near the critical limit; both stars may experience CHE, particularly in mass ratios near unity (Mink et al., 2010).
• Accretion-induced CHE: Spin-up of a secondary via Keplerian disk-fed mass transfer can induce rapid rotation and homogeneous mixing, often requiring the accretor to gain only a small fractional mass when angular momentum accretion is highly efficient (Ghodla et al., 2022, Dall'Amico et al., 8 Jan 2025).
• Merger-induced CHE: Binary mergers deposit significant angular momentum into the merger product, potentially initiating CHE even if neither component initially underwent homogeneous evolution (Mink et al., 2010).
• Triple Dynamics: In hierarchical triples, tertiary-induced perturbations (e.g., von Zeipel–Lidov–Kozai oscillations) can affect the angular momentum evolution, merger dynamics, and subsequent fate of CHE binaries (Dorozsmai et al., 2023, Vigna-Gómez et al., 21 Mar 2025).

The outcome may differ when secondary effects (e.g. post-accretion or post-merger orbital widening via wind mass loss) alter subsequent stages of evolution and observational signatures (Sharpe et al., 19 Feb 2024, Dall'Amico et al., 8 Jan 2025).

4. Astrophysical Consequences and Observational Signatures

CHE leads to several departures from canonical evolutionary theory:

• Suppression of Envelope Expansion: Stars avoid progress toward the red supergiant phase and instead remain compact and hot—this persists even at advanced nuclear burning phases (Mink et al., 2010, Yoon et al., 2012).
• Enhanced Ionizing and UV Output: Homogeneously evolving stars are hotter and more luminous, resulting in UV photon output enhanced by factors of several in both non-ionizing and hydrogen/helium-ionizing bands compared to standard stellar populations (Yoon et al., 2012, Sibony et al., 2022, Liu et al., 2 Dec 2024).
• WR and SN Progenitor Formation: CHE leads naturally to WR stars (often retaining some hydrogen at the surface in early phases) and, should sufficient mass be retained, to core-collapse or pair-instability supernovae (PISNe) (Yoon et al., 2012, Dall'Amico et al., 8 Jan 2025).
• Outcome Diversity in Binaries: CHE suppresses the usual sequence and order of Roche lobe overflow. In some cases, the initially less massive companion will fill its Roche lobe first ("Case M" evolution), highlighting a reversal from the canonical Cases A, B, C (Mink et al., 2010).
• Compact BBH Formation: CHE enables the formation of high-mass, nearly equal-mass binary black holes with short orbital periods, naturally producing merger times less than a Hubble time (Mink et al., 2016, Riley et al., 2020).
• GRB and SLSN Progenitors: The high angular momentum retained in the core of CHE stars is a key ingredient for the collapsar paradigm for long GRBs and magnetar-driven superluminous supernovae (SLSNe-I) (Yoon et al., 2012, Ghodla et al., 2022).

5. Empirical and Modeling Evidence

Observational and theoretical studies corroborate the occurrence and consequences of CHE:

• Stellar Populations: Hydrogen-rich WR stars with blueward HR diagram locations and CN equilibrium surface abundances in the LMC and Milky Way support CHE up to at least solar metallicity, although coupling between core and envelope must be moderate to maintain efficient angular momentum (Martins et al., 2013, Cui et al., 2018).
• Wolf–Rayet and Binary Compact Object Populations: Population synthesis (e.g., SEVN, BPASS, COMPAS, MESA models) indicates a significant increase (up to %%%%4$Z \lesssim 0.004$5%%%%) in the WR fraction at low $Z$ when CHE is included, with a shift toward more massive, luminous WRs and a corresponding increase in BBHs and BH–NS systems—though mergers are often suppressed due to wider final orbits (Dall'Amico et al., 8 Jan 2025, Ghodla et al., 2022, Cui et al., 2018).
• Gravitational Wave Events: The masses and spins of observed BBH mergers (e.g., GW150914, GW231123, GW190517_055101) are well-reproduced by CHE channels, which produce compact, nearly equal-mass, high-spin BBH systems, although the effective spin cannot exceed limits imposed by the critical rotation at collapse (Mink et al., 2016, Popa et al., 29 Aug 2025, Qin et al., 2022, Marchant et al., 2023).
• Constraints from Stellar Winds and Polarimetry: Empirical efforts to find enhanced rotation rates among low-metallicity WR stars (e.g., via spectro-polarimetry) have not confirmed a pronounced increase, potentially challenging the universality of the rotational CHE pathway in all low-$Z$ environments (Vink, 2018).
• Reionization and High-z Galaxies: Models incorporating Pop III CHE stars predict UV and ionizing efficiencies that can explain cosmic reionization with lower total stellar mass densities and produce UV-bright galaxies observed at high redshift with JWST, mitigating the need for extreme star formation efficiencies or top-heavy IMFs (Sibony et al., 2022, Liu et al., 2 Dec 2024, Liu et al., 1 Apr 2025).

6. Quantitative Framework and Scaling Relations

Key theoretical and modeling expressions used to characterize CHE include:

• Mixing Criterion: CHE occurs when

$\tau_{\rm mix} \ll \tau_{\rm nuc}$

with $D_{\rm mix} \sim$ function (rotation rate, gradients) (Mink et al., 2010, Yoon et al., 2012).

• Critical Rotational Velocity: For CHE, the star must maintain

$v_{\rm rot} \gtrsim f_{\rm crit} v_{\rm Kepler}$

where $f_{\rm crit}$ parameterizes mixing efficiency (Riley et al., 2020).

• Wind-Driven Mass Loss Scaling: $\dot{M} \propto Z^\alpha$, with $\alpha$ in the range $0.6$–$0.8$, so that lower $Z$ helps sustain angular momentum and CHE (Martins et al., 2013, Vink, 2018).
• Critical Rotation and Maximum Spin: The upper limit for the BH dimensionless spin is

$a_{\rm BH} = \frac{Jc}{GM^2} \leq 1$

with a strong dependence of $a$ on progenitor mass, e.g., $a \propto M^{-0.9}$ for massive hydrogen-depleted CHE models (Marchant et al., 2023, Popa et al., 29 Aug 2025).

• Impact on Binary Parameters: When mass is lost via stellar winds in a close binary,

$$P_{\rm orb}/P_{\rm orb,0} = (M_{\rm tot}/M_{\rm tot,0})^{-2}$$

characterizes orbital widening (Sharpe et al., 19 Feb 2024).

• Population Synthesis Prediction: CHE can account for up to $\sim$70% of BBH gravitational-wave detections arising from isolated binary evolution, contingent on the adopted assumptions about the prevalence of CHE (Riley et al., 2020).

7. Broader Astrophysical Implications and Open Questions

CHE fundamentally redefines the mapping from initial conditions to final fates for massive stars:

• CHE impacts predictions of the cosmic reionization photon budget, early chemical enrichment, and the appearance of the first galaxies (Sibony et al., 2022, Liu et al., 2 Dec 2024, Liu et al., 1 Apr 2025).
• It provides an efficient pathway for both prompt and delayed BBH mergers in hierarchical triples, where tertiary-driven perturbations can expedite mergers and possibly yield unique multi-messenger signatures (Dorozsmai et al., 2023, Vigna-Gómez et al., 21 Mar 2025).
• While the efficiency and universality of CHE (especially in single stars at high metallicity) remain debated, a non-negligible fraction of massive binaries—especially at low metallicity—are expected to experience CHE, making it a cornerstone channel in theoretical population models of massive stars and black holes.
• Predicted signatures, such as a "pile-up" of BBHs near the critical-spin boundary and a distinct absence of high-chirp-mass, high-spin BBH mergers, provide testable benchmarks for current and next-generation gravitational-wave observatories (Marchant et al., 2023, Popa et al., 29 Aug 2025).
• Recent constraints suggest that WR winds and core-envelope coupling must be modeled with care; overefficient mass loss and mixing can alter evolutionary paths, while polarimetric observations have not confirmed a universal rotation enhancement at low $Z$, highlighting the complexity of CHE's realization in nature (Vink, 2018, Sharpe et al., 19 Feb 2024, Dall'Amico et al., 8 Jan 2025).

In sum, chemically homogeneous evolution stands as a pivotal framework for understanding the evolutionary diversity of massive stars, the formation of WR and GRB progenitors, and the demography of merging BBHs—shaping both the observables and the theoretical landscape in stellar astrophysics and multi-messenger cosmology.