Systemic recoil velocity distribution of field millisecond pulsar systems: Implications for neutron star retention in star clusters

¹ Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon, Republic of Korea
² Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, 2-12 Hoshigaoka-cho, Mizusawa, Oshu, Iwate 023-0861, Japan

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
^★★ EACOA Fellow.

Received: 7 May 2025
Accepted: 12 November 2025

Abstract

Aims. The systemic recoil velocity (v_sys) distribution of millisecond pulsars (MSPs) is essential for understanding the MSP formation channel(s) and for estimating the retention fractions of MSPs in star clusters, which can potentially be determined using the precise astrometry of MSPs. However, the determination is complicated by the long-term dynamic evolution of MSPs and the scarcity of radial velocity measurements. The goal of this work is to overcome the complexity and derive the MSP v_sys distribution from high-precision astrometric measurements.

Methods. We compiled 64 field MSP systems (including 52 binary MSPs and 12 solitary MSPs) that have been well determined astrometrically. We calculated their transverse peculiar (or space) velocities, v_⊥, and Galactic heights, z. Assuming that the Galactic-longitude components, v₁, of v_⊥ are statistically stable over time (i.e. the ‘stable- v₁’ assumption), we approached the distribution of the v₁ components of v_sys using the observed v₁ sample. Under the ‘isotropic- v_sys’ assumption that v_sys directions are uniformly distributed, we derived the MSP v_sys distribution from the distribution of the v₁ component of v_sys. Based on the derived v_sys distribution, we tested the stable- v₁ assumption with dynamical population synthesis (DPS). In addition, by matching the observed z and the Galactic-latitude components, v_b, of v_⊥ to the DPS counterparts, we estimated the initial and the current Galaxy-wide scale heights of field MSP systems.

Results. We find that solitary field MSPs have similar v₁ magnitudes to those of binary ones. Additionally, the observed v₁ can be well described by a linear combination of three normal distributions. Accordingly, the MSP v_sys distribution can be approximated by a linear combination of three Maxwellian components. Our DPS analysis verified the stable- v₁ assumption in the parameter space of this work and estimated the initial and the current Galaxy-wide scale heights of field MSP systems to be about 0.32 kpc and 0.68 kpc, respectively.

Conclusions. According to the MSP v_sys distribution, ≈14% of all the MSPs born in a globular cluster with the nominal 50 km s⁻¹ central escape velocity can be retained. Therefore, the v_sys distribution of field MSP systems may account for the high number of MSPs discovered in globular clusters, which implies that MSPs in star clusters might follow the same formation channel(s) as field MSP systems.