Single radio pulsars have characteristic space velocities of hundreds of km/s, yet the double neutron stars (DNS) in the Galactic disk mostly have small orbital eccentricities (e ~ 0.08-0.27) and low second-born neutron-star masses (about 1.18-1.30 solar masses), implying that their second supernovae delivered only small natal kicks. Van den Heuvel (2010) synthesized these facts into a two-channel picture: low-mass, low-kick neutron stars form by electron-capture collapse of a degenerate O-Ne-Mg core (an electron-capture supernova, ECSN, of a helium star of initial main-sequence mass roughly 8-11 solar masses, in a binary), whereas high-mass, high-kick neutron stars form by iron-core collapse. The unresolved core, after two of the source's five strands (the iron-core explosion mechanism and individual DNS mass determinations) were largely settled by later work, is quantitative: (i) the natal-kick amplitude distribution of the low-kick channel - modern simulations give hydrodynamic kicks of at most a few km/s but neutrino-induced kicks of tens of km/s, and population-synthesis studies still must assume a value; (ii) the metallicity-dependent progenitor mass boundaries that fix the relative fractions of the two channels; and (iii) a confrontation of model predictions with the observed DNS eccentricity/mass/velocity distributions and the single-pulsar velocity distribution that quantitatively validates or falsifies the dichotomy.

Background

A pulsar is a rapidly rotating, magnetized neutron star (NS) emitting beams of radio emission; its space velocity today traces back largely to the 'natal kick' the NS received at birth, when asymmetric mass ejection and anisotropic neutrino emission during the supernova explosion imparted momentum to the remnant. A double neutron star (DNS) is a binary containing two NSs, at least one observed as a radio pulsar; its orbital eccentricity ee (deviation of the orbit from a circle, 0 = circular) records the violence of the second supernova: a symmetric explosion with little mass loss leaves the orbit nearly circular, while a large kick or sudden mass loss raises ee. Because radio timing gives extremely precise masses for relativistic DNS, the observed combination of low eccentricities, low second-born NS masses, and (from timing of the double pulsar J0737-3039) a small systemic velocity - the space velocity of the binary's center of mass - sits in sharp tension with the high birth velocities of ordinary single radio pulsars, whose proper motions are well fit by a Maxwellian speed distribution with one-dimensional dispersion of a few hundred km/s (Hobbs et al. 2005, a statistical study of 233 pulsar proper motions).

Van den Heuvel (2010; earlier version 2007) proposed the reconciliation now standard in the field: there are two NS formation channels. In the first, a helium star in a binary with initial main-sequence mass of roughly 8-11 solar masses develops a degenerate oxygen-neon-magnesium core; when that core reaches the Chandrasekhar mass (the limiting mass of a degenerate stellar core, about 1.4 solar masses), electron capture on Mg and Ne triggers collapse ('electron-capture supernova', ECSN). The collapse of the small, dense O-Ne-Mg core ejects little mass and, in the nearly symmetric simulations of Kitaura et al. (2006), yields a low-mass NS (about 1.25 M⊙M_\odot) with essentially no kick - so ECSN in binaries preserves low eccentricities. In the second channel, more massive progenitors build iron cores that collapse and explode violently, giving both higher NS masses and the large kicks of single pulsars - and, when they occur in binaries, they disrupt or strongly perturb them. The absence of a substantial population of slow single pulsars is consistent with low-kick ECSNe occurring only in binaries (where the companion strips the envelope, the ECSN-born NS is later recycled - spun up by accreting matter from its companion - and the binary is eventually disrupted or accelerated by the companion's own iron-core-collapse supernova). A later refinement is the 'ultra-stripped supernova' (Tauris et al. 2015): a second supernova in a close binary whose progenitor has been stripped of nearly all its envelope by the companion's wind and accretion, exploding with little ejecta and weak kicks.

The picture, however, is only qualitatively established. Its quantitative completion - the questions left open by the source's argument and by the later literature - comprises: the precise natal-kick amplitude distribution produced by each channel (including how far small departures from spherical symmetry in ECSN can still generate non-negligible kicks); the exact main-sequence mass boundaries separating ECSN progenitors from iron-core-collapse progenitors, which depend on metallicity (the star's fraction of elements heavier than helium) and on convective-transport prescriptions in stellar evolution and set the population ratio of the two channels; a settled iron-core explosion mechanism (shock revival by neutrino heating, and fallback, i.e. material falling back onto the newborn star) from which remnant masses and kicks could be predicted rather than tuned; accurate masses for the individual DNS used as tests; and population-synthesis predictions (merger rates, binary survival fractions, pulsar velocity and mass distributions, obtained by numerically evolving large ensembles of binary stars under prescribed physics) confronted with observations. Gravitational-wave astronomy has since added a new observable class: GW170817 (Abbott et al. 2017) confirmed DNS mergers, and GW190425 (Abbott et al. 2020), with total mass about 3.4 M⊙M_\odot well above the Galactic DNS sample, already stresses the standard channel accounting.

Problem Statement

Determine, quantitatively and per formation channel, the neutron-star natal-kick amplitude distribution and remnant-mass distribution produced by (a) electron-capture collapse of degenerate O-Ne-Mg cores in binaries (helium stars of initial main-sequence mass roughly 8-11 solar masses, with the precise limits of this range depending on metallicity and on the assumed model for convective energy transport), versus (b) iron-core collapse of more massive stars, together with the metallicity-dependent main-sequence mass boundaries that fix the relative contribution of each channel; and validate or falsify the resulting two-channel picture - in which neutron stars formed by electron-capture collapse receive hardly any natal kick at birth, whereas neutron stars formed by iron-core collapse receive large kicks - by confronting model predictions with the observed orbital eccentricities, masses, and systemic velocities of double neutron stars and the velocity distribution of single radio pulsars.

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