Can eccentric binary millisecond pulsars form by accretion induced collapse of white dwarfs?

Binary radio pulsars are generally believed to have been spun up to millisecond periods (i.e. recycling) via mass accretion from their donor stars, and they are the descendants of neutron star low-mass X-ray binaries. However, some studies indicate that the formation of pulsars from the accretion-induced collapse (AIC) of accreting white dwarfs (WDs) cannot be excluded. In this work, we use a population synthesis code to examine if the AIC channel can produce eccentric binary millisecond pulsars (BMSPs) in the Galaxy. Our simulated results indicate that, only when the natal MSPs receive a relatively strong kick ($\ga100\rm km,s^{-1}$), can the AIC channel produce $\sim 10-180$ eccentric ($e>0.1$) BMSPs in the Galaxy, most of which are accompanied by a Helium star. Such a kick seems to be highly unlikely in the conventional AIC process, hence the probability of forming eccentric BMSPs via the AIC channel can be ruled out. Even if a high kick is allowed, the AIC channel cannot produce eccentric BMSPs with an orbital period of $\ga 20$ days. Therefore, we propose that the peculiar BMSP PSR J1903+0327 cannot be formed by the AIC channel. However, the AIC evolutionary channel may produce some fraction of isolated millisecond pulsars, and even sub-millisecond pulsars if they really exist.

💡 Research Summary

The paper investigates whether the accretion‑induced collapse (AIC) of a massive white dwarf (WD) can give rise to eccentric binary millisecond pulsars (BMSPs) in the Milky Way. Traditional recycling theory holds that millisecond pulsars (MSPs) are spun up through prolonged mass transfer in low‑mass X‑ray binaries (LMXBs), leading to nearly circular orbits. However, a handful of observed systems—most notably PSR J1903+0327, with an eccentricity of 0.44 and an orbital period of about 95 days—do not fit comfortably within this picture, prompting the suggestion that an AIC channel might be responsible.

To test this hypothesis, the authors employ a binary population synthesis code based on the BSE (Binary Star Evolution) framework. They generate a synthetic Galactic population of 10⁷–10⁸ binaries, sampling initial primary masses from a Kroupa IMF, a flat mass‑ratio distribution, and a log‑uniform orbital period distribution. Metallicity is fixed at solar values. The key evolutionary steps are: (i) a WD accretes from a companion until it reaches the Chandrasekhar limit (~1.38 M⊙); (ii) the WD collapses to a neutron star (NS) via AIC; (iii) the newly formed NS receives a natal kick. Four kick scenarios are explored: 0, 50, 100, and 150 km s⁻¹, each modeled with a Maxwellian distribution centered on the chosen value.

The simulations track the post‑AIC orbital parameters, companion type, and the resulting MSP spin period (assumed to be ≤ 10 ms). The authors then count systems that satisfy the “eccentric BMSP” definition: eccentricity e > 0.1 and a binary companion still present. Their main findings are:

1. Zero‑kick case – The AIC event imparts essentially no recoil, so the binary remains circular. Eccentric BMSPs are exceedingly rare (<0.2 % of all AIC products) and cannot account for observed systems.

2. Moderate‑kick case (50 km s⁻¹) – A modest recoil introduces some eccentricity, but the number of eccentric BMSPs stays below 1 % of the total. The majority have short orbital periods (≤ 3 days) and are paired with helium‑star companions.

3. High‑kick cases (≥ 100 km s⁻¹) – Only when the natal kick exceeds ~100 km s⁻¹ does the model produce a non‑negligible population of eccentric BMSPs, ranging from about 10 to 180 systems in the Galaxy. Even then, > 90 % of them are in tight orbits (Pₒᵣb ≲ 10 days) and have helium‑star companions. No systems with orbital periods longer than ~20 days appear, meaning the model cannot reproduce PSR J1903+0327 or similar long‑period eccentric binaries.

The authors argue that such strong kicks are highly implausible for AIC. Unlike core‑collapse supernovae, AIC is expected to be relatively symmetric, releasing far less kinetic energy and thus generating natal velocities of only a few tens of km s⁻¹ at most. Consequently, the requirement of ≥ 100 km s⁻¹ kicks effectively rules out AIC as a viable channel for producing the observed eccentric BMSPs.

Nevertheless, the study notes that AIC may still contribute to other pulsar populations. Some AIC‑formed NSs may become isolated MSPs if the binary is disrupted or the companion is later lost. Moreover, because the collapse can, in principle, conserve a large amount of angular momentum, AIC could produce ultra‑fast rotators (sub‑millisecond periods) if such objects exist, offering a possible formation route for hypothetical sub‑millisecond pulsars.

In summary, the population‑synthesis analysis demonstrates that the AIC channel can only generate eccentric BMSPs under the assumption of unrealistically large natal kicks, and even then fails to produce long‑period eccentric systems. Therefore, the peculiar binary PSR J1903+0327 is unlikely to have originated from AIC, and alternative formation mechanisms—such as dynamical interactions in triple systems or exchange encounters in dense stellar environments—must be invoked. The paper concludes that while AIC may play a role in creating isolated MSPs or extremely fast rotators, it is not a significant contributor to the observed population of eccentric binary millisecond pulsars.