Binary-supernova Scenario (BSS)

• Binary-supernova Scenario (BSS) is defined as the binary system disruption mechanism where a supernova explosion causes instantaneous mass loss and a natal kick, resulting in runaway or bound compact-object binaries.
• The approach models the event as an impulsive mass loss in a two-body system, yielding companion ejection speeds that closely match the pre-supernova orbital velocity.
• BSS also encompasses a range of phenomena including companion impact signatures and chemical pollution, underlining its broad applicability in understanding supernova outcomes and runaway-star demographics.

Binary-supernova Scenario (BSS) denotes, in its classical Blaauw sense, the supernova outcome of a binary in which the initially more evolved star undergoes core collapse, instantaneously loses mass, and imparts a natal kick to the newly formed compact remnant; the system is then either disrupted, ejecting the non-exploding companion as a runaway or walkaway star, or it survives as a post-supernova compact-object binary (Wagg et al., 22 Apr 2025). In contemporary usage, the same binary-supernova setting also underlies a broader set of problems—companion-impact signatures, chemically polluted survivors, stripped-envelope progenitors, and post-supernova interacting binaries—which suggests that BSS is both a kinematic runaway-star channel and a more general binary-conditioned supernova framework (Gray et al., 2016).

1. Classical meaning and scope

In the classical Blaauw picture, BSS is a post-stellar-evolution binary-disruption channel. A binary has typically already undergone mass transfer and tidal circularization before the first core-collapse supernova. At core collapse, the exploding primary instantaneously loses mass and the newly formed neutron star or black hole receives a natal kick. The post-supernova system is then either still bound on a new Keplerian orbit or unbound on a hyperbolic relative orbit; if unbound, the companion escapes and becomes a runaway or walkaway star (Wagg et al., 22 Apr 2025).

The core terminology is precise. A natal kick is the velocity impulse imparted to the newly formed neutron star or black hole at birth by asymmetries in the explosion or neutrino emission. A disrupted binary companion is the non-exploding star ejected when the binary is ionized by the supernova. A runaway star is a star with unusually large peculiar velocity relative to its surroundings; somewhat lower-velocity objects are often called walkaways. Population synthesis, in this context, means rapidly evolving large ensembles of binaries with approximate prescriptions for stellar and binary physics to predict statistical outcomes (Wagg et al., 22 Apr 2025).

BSS is one of the two classical runaway-star channels, the other being the dynamical ejection scenario (DES), in which few-body encounters convert orbital binding energy into kinetic energy and expel one or more stars. Some recent work also introduces a third channel, the subcluster ejection scenario (SCES), in which stars are ejected when infalling subclusters are tidally disrupted by the assembling cluster potential. In that taxonomy, BSS remains the standard post-supernova binary-disruption mechanism and is sometimes referred to as Blaauw kicks (Polak et al., 2024).

2. Dynamical formulation

The standard BSS treatment models the supernova as an impulsive event in a point-mass two-body system. For the circular pre-supernova binaries usually adopted after mass transfer and tidal circularization, the companion’s pre-supernova orbital speed is

$$v_{\rm 2, preSN}=\frac{m_1}{m_1+m_2}\,v_{\rm orb}, \qquad v_{\rm orb}=\sqrt{\frac{G(m_1+m_2)}{a}},$$

where $m_1$ and $m_2$ are the pre-supernova masses and $a$ is the pre-supernova semimajor axis (Wagg et al., 22 Apr 2025).

If the exploding star leaves a remnant of mass $m_1'$, then the instantaneous mass lost is

$\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$

With pre-supernova relative position and velocity $\mathbf r$ and $\mathbf v$, and natal kick $\mathbf v_{\rm kick}$ applied only to the exploding star, the post-supernova relative velocity is

$\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$

The post-supernova specific orbital energy is

$m_1$0

The binary is unbound if $m_1$1, equivalently if the post-supernova eccentricity satisfies $m_1$2; it remains bound if $m_1$3 (Wagg et al., 22 Apr 2025).

For disrupted systems, the asymptotic relative speed satisfies

$m_1$4

This distinction is important because BSS ejection velocity is not merely the companion’s instantaneous speed at core collapse. It is the final velocity after the short-lived residual gravitational interaction with the compact remnant has ended. In the post-supernova center-of-mass frame, the asymptotic velocities partition as

$m_1$5

up to rotations set by the orbital geometry (Wagg et al., 22 Apr 2025).

The physical consequence is that, once the compact remnant departs sufficiently quickly, the companion is essentially released with the velocity it already had. The kick primarily decides whether disruption occurs; it only weakly modifies the final companion speed through the remnant’s brief post-supernova gravitational tug (Wagg et al., 22 Apr 2025).

3. Ejection velocities, code comparisons, and algorithmic validation

A recent cross-code comparison made the classical BSS result unusually sharp. Using COSMIC, COMPAS, and binary_c, with the same delayed remnant-mass prescription of Fryer et al. (2012), natal kicks drawn from a Maxwellian with $m_1$6, and isotropic kick directions, the authors evolved a representative binary with

$m_1$7

repeating the evolution $m_1$8 times with different kick magnitudes and directions (Wagg et al., 22 Apr 2025).

The three codes did not produce identical pre-supernova binaries, because their default prescriptions for mass transfer, winds, and related binary physics differ. In COSMIC, mass transfer is almost fully conservative and the secondary reaches about $m_1$9, with the orbit widening from $m_2$0 d to $m_2$1 d. In COMPAS, mass transfer is much less conservative, the secondary ends up at about $m_2$2, and the orbit reaches $m_2$3 d. In binary_c, the mass-transfer history is similar to COSMIC but winds are weaker, giving $m_2$4 d at the end of mass transfer and somewhat larger final stellar masses. Despite these differences, all three codes found that disrupted companions are ejected with velocities narrowly distributed around $m_2$5 (Wagg et al., 22 Apr 2025).

Quantitatively, the mean companion ejection velocity in each code lies within roughly $m_2$6 of the pre-supernova orbital velocity, even though the natal kick magnitudes span about three orders of magnitude. The disruption fractions for the representative binary are high: $m_2$7 for COSMIC, COMPAS, and binary_c, respectively. The scatter around $m_2$8 is geometry-dependent: strong kicks make the relation tighter because the remnant leaves more quickly; in-plane weak kicks, especially $m_2$9, broaden the distribution and skew it slightly below $a$0; kicks perpendicular to the plane have much less effect, and almost no such cases deviate by more than about $a$1 (Wagg et al., 22 Apr 2025).

This comparison also functioned as a code-validation exercise across two independent post-supernova orbital algorithms. COSMIC and COMPAS use the vector formalism of Pfahl et al. (2002), whereas binary_c uses Tauris & Takens (1998). Agreement between them showed that the narrow ejection-speed distribution is not a code-specific artifact. During the comparison, however, bugs were found in all three implementations. In COSMIC, the inherited Kiel & Hurley (2009) prescription omitted a $a$2 contribution to the final $a$3-velocity; in COMPAS, spurious vector indexing and incorrect rotation algebra had overestimated companion ejection speeds by a factor of 2; in binary_c, kick magnitudes and azimuthal angles were not sampled independently because one random number was reused. These issues were fixed, and the episode has become a concrete demonstration that open-science code comparison is essential for reliable BSS inference (Wagg et al., 22 Apr 2025).

4. Runaway-star demographics and competing channels

Runaway-star observations do not isolate BSS automatically; they separate channels only statistically. In one recent SMC analysis using Gaia DR3 proper motions for RIOTS4 field OB stars, OBe stars and HMXBs occupy the low-velocity, supernova-related side of the distribution, while normal OB stars and non-compact binaries retain the DES-like high-velocity tail. The median transverse velocities are $a$4 for OBe stars, $a$5 for HMXBs, and $a$6 for normal OB stars. The OBe and HMXB distributions are statistically similar, with a K–S $a$7, and the study concludes that OBe stars appear to be dominated by BSS and are likely post-supernova binary systems. At the population level, however, DES still dominates runaways, with DES/BSS $a$8 in the model, and the two-step channel—dynamical ejection followed by later supernova acceleration—accounts for over half of BSS runaways in that framework (Phillips et al., 2024).

A complementary Galactic study of 203 LAMOST DR8 B-type runaway stars obtained an observed spectroscopic binary fraction of $a$9, corrected it with Monte Carlo modeling to an intrinsic binary fraction of $m_1'$0, and inferred a BSS-to-DES ratio of $m_1'$1. In that study, the best-fit intrinsic distributions are

$m_1'$2

which indicates a preference for short periods and low-mass companions within the modeled parameter space. The paper interprets this as evidence that BSS and DES contribute comparably to Galactic B-type runaway stars, rather than one channel dominating decisively (Chen et al., 30 Jul 2025).

SCES adds a further layer. In star-by-star cluster-formation simulations, SCES can eject runaway binaries and harden them during subcluster infall and tidal disruption, thereby preparing them for a later BSS event. The later supernova phase was not simulated in that work—the run ended at $m_1'$3 Myr, before any supernova occurred, and there were no primordial binaries—but the inferred SCES-BSS sequence provides a plausible two-step route in which a binary is first displaced from its birth cluster and then later receives a second velocity kick from the classical BSS (Polak et al., 2024).

5. Companion interaction, ejecta shadows, and polluted survivors

Beyond stellar kinematics, the binary-supernova setting produces direct companion signatures. For core-collapse supernovae, the collision of ejecta with a surviving companion excavates a low-density cone and can brighten the earliest light curve, but the viewing-angle penalty is severe. Using binary_c/nucsyn population synthesis and a simple cone model with

$m_1'$4

the predicted observable fraction of collision-brightened light curves is only $m_1'$5 for all CCSNe. The subtype fractions are $m_1'$6 for Type II, $m_1'$7 for Type IIb, and $m_1'$8 for Type Ibc. The paper therefore concludes that companion-collision brightening is real but intrinsically rare, and not a good explanation for common early slow declines (Moriya et al., 2015).

In the single-degenerate SN Ia channel, the companion leaves a more persistent remnant-scale imprint. Three-dimensional SPH simulations with a $m_1'$9 carbon–oxygen white dwarf and a $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$0–$\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$1 evolved non-degenerate companion find that the companion carves out a cone-like low-density hole in the ejecta. In the $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$2 model, by $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$3 minutes after explosion the hole has an apex angle of $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$4, corresponding to a solid angle of $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$5. The impact strips $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$6–$\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$7 from the companion, but that gas is too slow and too centrally concentrated to refill the cavity. The hole survives interaction with a uniform ISM for many centuries and remains detectable in $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$8-based X-ray proxies at all tested viewing angles $\Delta m = m_1-m_1', \qquad M_b' = m_1'+m_2.$9 (Gray et al., 2016).

A chemically focused BSS branch appears in the SN-polluted giant channel. For binaries with primaries of roughly $\mathbf r$0–$\mathbf r$1, secondaries within about $\mathbf r$2–$\mathbf r$3 of the primary, and separations $\mathbf r$4–$\mathbf r$5–$\mathbf r$6, the secondary can already be a giant when the primary explodes. The paper models pollution with

$\mathbf r$7

where $\mathbf r$8 is the captured ejecta fraction and $\mathbf r$9 is the retention efficiency, and argues that $\mathbf v$0 can account for the calcium abundance of HV2112 if $\mathbf v$1. This channel is rare, about $\mathbf v$2 of all CCSNe, but long-lived enough that about $\mathbf v$3 SN-polluted giants should exist in the Galaxy and about $\mathbf v$4 in the Magellanic Clouds at any given time (Sabach et al., 2014).

6. Binary stripping, specialized post-supernova variants, and unresolved issues

Binary interaction also shapes what kind of supernova occurs in the first place. On GMC scales, Type II and Type Ic supernovae inhabit environments with essentially indistinguishable molecular gas surface densities, with a Type II vs Type Ic K–S statistic of $\mathbf v$5 and $\mathbf v$6. Modeling the local gas surface density as

$\mathbf v$7

with $\mathbf v$8 Myr, gives a lifetime difference

$\mathbf v$9

consistent with zero. Combined with directly detected Type II progenitor masses, this yields inferred Type Ic progenitor masses of $\mathbf v_{\rm kick}$0 or $\mathbf v_{\rm kick}$1, far below the $\mathbf v_{\rm kick}$2 range usually invoked for single-star wind stripping. The result supports binary interaction as the dominant origin of ordinary Type Ic progenitors (Solar et al., 2024).

That environmental result is consistent with direct explosion calculations of binary-stripped donors. In a solar-metallicity MESA+FORNAX survey of $\mathbf v_{\rm kick}$3–$\mathbf v_{\rm kick}$4 stars, binary-stripped stars generally have less compact cores, deeper Si/O interfaces, and explode preferentially to the corresponding single stars of the same initial mass. The compactness parameter

$\mathbf v_{\rm kick}$5

was evaluated at $\mathbf v_{\rm kick}$6, and stripped models often show significantly smaller $\mathbf v_{\rm kick}$7 than same-$\mathbf v_{\rm kick}$8 singles. This implies that binary stripping changes not only the envelope but the explodability, remnant-mass distribution, and the possible occupation of the mass gap between the heaviest neutron stars and lightest black holes (Vartanyan et al., 2021).

Some recent work extends BSS into the immediate post-supernova phase. In a model proposed for SN2022jli, a stripped-envelope star explodes, forms a $\mathbf v_{\rm kick}$9 neutron star, and leaves an eccentric NS + main-sequence companion binary with $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$0 d. SN ejecta temporarily inflate the companion envelope to a few $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$1, engulfing the neutron star and driving super-Eddington accretion. Hydrodynamical modeling finds that sustained high accretion requires geometrically confined feedback and eccentricity $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$2, while the observed low undulation amplitude of SN2022jli requires a viewing angle close to edge-on. This is not the classical runaway-star branch of BSS; it is a surviving-binary variant in which post-supernova interaction powers the transient itself (Hirai et al., 14 Jul 2025).

A persistent unresolved issue is that the environmental evidence for a binary can be stronger than the evidence for a surviving companion. Kepler’s supernova remnant is a Type Ia remnant interacting with nitrogen-rich, silicate-bearing circumstellar material at high Galactic latitude, a combination that strongly suggests a CO white dwarf accreting from a $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$3–$\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$4 AGB or post-AGB donor, with $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$5, $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$6, and systemic velocity $\mathbf v'=\mathbf v+\mathbf v_{\rm kick}.$7. Yet no surviving donor has been found. This does not invalidate the binary-shaped interpretation, but it shows that BSS-related progenitor inference can remain tensioned between circumstellar evidence, remnant morphology, and ex-companion searches (Vink, 2016).

In aggregate, the literature converges on a narrow classical result and a broad astrophysical one. Classically, when a binary is disrupted at the first supernova, the companion’s asymptotic ejection speed is tightly tied to its pre-supernova orbital speed rather than the natal-kick magnitude (Wagg et al., 22 Apr 2025). More broadly, binary interaction before, during, and after core collapse alters envelope stripping, core structure, transient power sources, circumstellar geometry, and long-term observables; this suggests that BSS is best understood not only as a runaway-star mechanism, but also as a general framework for binary-conditioned supernova phenomenology.