Post Common Envelope BinaryEdit

Post common envelope binaries (PCEBs) are close stellar pairs that have survived a dramatic episode in which one star engulfed its companion within a shared gaseous envelope. During this common-envelope (CE) phase, orbital energy and angular momentum are dumped into the envelope, leading to rapid inspiral and, in favorable cases, ejection of the envelope. The result is a compact binary comprising a stellar remnant—most often a white dwarf or a hot, helium-burning subdwarf—and a companion that may be a main-sequence star, a brown dwarf, or another compact object. The dramatic tightening of the orbit means PCEBs typically have short orbital periods, from hours to days, and their light and velocity signatures reflect intense interactions and extreme evolutionary histories.

The study of post common envelope binaries illuminates several pathways in binary star evolution and informs our understanding of later astrophysical phenomena, including cataclysmic variables, double-degenerate systems, and potential progenitors of some Type Ia supernovae. They also serve as valuable laboratories for testing CE physics, which remains one of the more uncertain phases in binary evolution. Observationally, PCEBs are identified through radial-velocity variations, eclipsing light curves, and, in some cases, irradiation effects or accretion-related emission from the companion. These systems populate the Milky Way in diverse stellar environments and provide key constraints on the frequency and outcomes of CE events.

Overview

Definition and scope: A post common envelope binary is a close binary in which the preceding CE phase has been successfully completed, leaving a compact remnant and a companion in a bound orbit binary star concepts; the CE event itself is described in the common envelope literature.
Typical constituents: The remnant is often a white dwarf or a hot subdwarf (a core-helium burning or helium-core object, e.g., subdwarf B stars), paired with a companion that can be a main-sequence star, a brown dwarf, or another compact object such as a neutron star or a second white dwarf.
Orbital properties: Orbits are compact, with periods ranging from a few hours to a few days, and separations that can be well below the original pre-CE configuration. This compactness makes PCEBs important sources of gravitational waves in the mHz regime for future observatories such as LISA.
Relevance to broader astrophysics: PCEBs are precursors to cataclysmic variables, they contribute to the population of close WD+WD systems that may merge to produce explosive events, and they provide empirical tests for energy- and angular-m momentum-based CE formulations such as the alpha_ce formalism and the gamma formalism.
Observational channels: Surveys such as the Sloan Digital Sky Survey and dedicated radial-velocity campaigns have identified large samples of PCEBs; some are central stars of close planetary nebulae, demonstrating a link between CE evolution and planetary nebula formation planetary nebula.

Formation and evolution

The common-envelope phase is triggered when one star in a binary evolves to fill its Roche lobe, and the ensuing mass transfer cannot be stabilized by the binary orbit. The engulfed companion spirals inward through the donor’s envelope, transferring orbital energy and angular momentum to the envelope. If sufficient energy or angular momentum is deposited, the envelope can be ejected, exposing the exposed core of the donor as the remnant. If the envelope is not ejected, the two stars may merge. The post-CE configuration is then the tight binary that remains.

Two principal formalisms are used to model the outcome of CE evolution: - The α_ce formalism (energy balance): the idea that a portion of the orbital energy released during inspiral is used to unbind the envelope. The efficiency parameter α_CE quantifies how effectively orbital energy contributes to ejection, and the envelope binding energy is often parameterized by λ. Together, α_CE and λ determine the post-CE separation for a given progenitor state. - The γ formalism (angular-momentum balance): an alternative approach focusing on how angular momentum loss during the spiral-in reshapes the orbit, sometimes providing better fits to certain populations.

In practice, both formalisms carry uncertainties and are calibrated against observed populations rather than derived from first principles. A key area of active research is the role of additional energy sources, such as recombination energy stored in ionized gas, and how they contribute to envelope ejection. These considerations influence predictions for the survivability of a binary through CE and the resulting orbital period distribution recombination energy.

Post-CE evolution depends on the nature of the companion and the remnant. A WD+MS PCEB may later interact again if the MS star evolves, potentially becoming a cataclysmic variable. A WD+WD system can evolve under gravitational radiation toward a possible merger, with implications for short-lived transients and gravitational-wave populations. Some CE remnants become central stars of planetary nebulae, linking CE physics to late stages of stellar evolution planetary nebula.

Observed populations and manifestations

WD+MS post-CE binaries: A large fraction of observed PCEBs have a white dwarf primary and a main-sequence companion. Their spectra show radial-velocity shifts and, in favorable cases, eclipses or ellipsoidal variations that constrain the orbital geometry and component masses.
sdB binaries: Hot subdwarf B stars in close orbits with a companion are frequently interpreted as the exposed helium-burning cores of red giants that have shed their hydrogen envelopes during a CE event. These systems illuminate how CE ejection can expose a compact core and leave a short-period binary with a low-mass companion subdwarf B.
WD+WD binaries: Double degenerate systems originate from CE episodes in both stars and are central to discussions of potential Type Ia supernova progenitors in the double-degenerate pathway. Their orbital decay by gravitational waves can bring the stars to contact within a Hubble time double degenerate.
Central binaries of planetary nebulae: Some planetary nebulae host very close binary nuclei, implying a CE event in the recent past. These objects provide direct observational links between CE physics and nebular shaping and ionization structures planetary nebula.

Observationally, PCEBs are identified through: - Radial-velocity monitoring: Periodic Doppler shifts reveal short orbital periods and allow mass estimates. - Time-series photometry: Eclipses, transits, and ellipsoidal variations provide orbital constraints and component radii. - Spectral features: Emission or irradiation signatures from a hot primary or accretion-related activity can indicate ongoing interaction or past CE ejection.

Physical processes and modelling challenges

CE energy budget: The post-CE separation is sensitive to how efficiently orbital energy unbinds the envelope, captured by α_CE, and to the binding energy parameter λ. Accurately predicting outcomes requires understanding the donor's internal structure and envelope binding.
Additional energy sources: Recombination energy and other thermal contributions may participate in envelope ejection, potentially reducing the required orbital energy. The significance of these contributions remains a topic of debate and modeling variation recombination energy.
Angular momentum considerations: The γ formalism emphasizes the role of angular momentum loss, which can affect the remnant orbit in ways not captured by a purely energy-based approach.
Hydrodynamic simulations vs. population synthesis: First-principles simulations of CE events are challenging due to the complexity of turbulent flows, jet-like outflows, and three-dimensional dynamics. Population synthesis attempts to predict the statistical properties of PCEBs across the Galaxy but depends on the adopted CE prescriptions and initial-condition distributions.

Controversies and debates (neutral framing)

Universal α_CE: Whether a single efficiency parameter can describe CE ejection across the full range of binary masses and evolutionary states is uncertain. Different systems may require different efficiencies to reproduce observed post-CE populations.
Role of recombination energy: Some studies argue that recombination energy substantially aids envelope ejection, while others find it insufficient to explain observed CE outcomes on its own. The true contribution likely varies with stellar structure and composition.
Validity of the γ formalism: While useful for certain populations, the angular-momentum–based approach does not always reproduce the full diversity of observed PCEB properties, and its applicability remains a matter of ongoing testing.
Connection to transient events: The extent to which post-CE binaries contribute to Type Ia supernova rates or other transients via mergers in WD+WD systems is debated, with competing observational and theoretical arguments for and against each progenitor channel.
Observational biases: The detected PCEBs represent a slice of the underlying population, with selection effects (brightness, period sensitivity, and geometric alignment) shaping the apparent demographics. Correcting for these biases is essential to robustly compare with CE theory.