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

Aims. The systemic recoil velocity (vsys) 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 vsys 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 vsys using the observed v1 sample. Under the ‘isotropic- vsys’ assumption that vsys directions are uniformly distributed, we derived the MSP vsys distribution from the distribution of the v1 component of vsys. Based on the derived vsys distribution, we tested the stable- v1 assumption with dynamical population synthesis (DPS). In addition, by matching the observed z and the Galactic-latitude components, vb, 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 vsys 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 vsys 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 vsys 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.