We argue that comparison with observations of theoretical models for the velocity distribution of pulsars must be done directly with the observed quantities, i.e. parallax and the two components of proper motion. We develop a formalism to do so, and apply it to pulsars with accurate VLBI measurements. We find that a distribution with two maxwellians improves significantly on a single maxwellian. The 'mixed' model takes into account that pulsars move away from their place of birth, a narrow region around the galactic plane. The best model has 42% of the pulsars in a maxwellian with average velocity σ √ 8/π = 120 km/s, and 58% in a maxwellian with average velocity 540 km/s. About 5% of the pulsars has a velocity at birth less than 60 km/s. For the youngest pulsars (τ c < 10 Myr), these numbers are 32% with 130 km/s, 68% with 520 km/s, and 3%, with appreciable uncertainties.

The aim of this work is to study the imprints that different models for black hole (BH) and neutron star (NS) formation have on the Galactic distribution of X-ray binaries (XRBs) which contain these objects. We find that the root mean square of the height above the Galactic plane of BH-and NS-XRBs is a powerful proxy to discriminate among different formation scenarios, and that binary evolution following the BH/NS formation does not significantly affect the Galactic distributions of the binaries. We find that a population model in which at least some BHs receive a (relatively) high natal kick fits the observed BH-XRBs best. For the NS case, we find that a high NK distribution, consistent with the one derived from the measurement of pulsar proper motion, is the most preferable. We also analyse the simple method we previously used to estimate the minimal peculiar velocity of an individual BH-XRB at birth. We find that this method may be less reliable in the bulge of the Galaxy for certain models of the Galactic potential, but that our estimate is excellent for most of the BH-XRBs.

Understanding the natal kicks, or birth velocities, of neutron stars are essential for understanding the evolution of massive binaries as well as double neutron star formation. We use maximum likelihood methods as published in Verbunt et al. to analyse a new large dataset of parallaxes and proper motions measured by Deller et al. This sample is roughly three times larger than number of measurements available before. For both the complete sample and its younger part (spin-down ages τ < 3 Myr), we find that a bimodal Maxwellian distribution describes the measured parallaxes and proper motions better than a single Maxwellian with probability of 99.3 and 95.0 per cent respectively. The bimodal Maxwellian distribution has three parameters: fraction of low-velocity pulsars and distribution parameters σ 1 and σ 2 for low and high-velocity modes. For a complete sample, these parameters are as follows: 42 +17 −15 per cent, σ 1 = 128 +22 −18 km s −1 and σ 2 = 298 ± 28 km s −1 . For younger pulsars, which are assumed to represent the natal kick, these parameters are as follows: 20 +11 −10 per cent, σ 1 = 56 +25 −15 km s −1 and σ 2 = 336 ± 45 km s −1 . In the young population, 5 ± 3 per cent of pulsars has velocities less than 60 km s −1 . We perform multiple Monte Carlo tests for the method taking into account realistic observational selection. We find that the method reliably estimates all parameters of the natal kick distribution. Results of the velocity analysis are weakly sensitive to the exact values of scale-lengths of the Galactic pulsar distribution.

We analyse the origin of the magnetic field decay in normal radio pulsars found by us in a recent study. This decay has a typical time scale ∼ 4×10 5 yr and operates in the range ∼ 10 5 -few×10 5 yr. We demonstrate that this field evolution may be either due to the Ohmic decay related to the scattering from phonons, or due to the Hall cascade which reaches the Hall attractor. According to our analysis, the first possibility seems to be more reliable. So, we attribute the discovered field decay mainly to the Ohmic decay by phonons, which is saturated at the age of a few×10 5 yr when a neutron star cools down to the critical temperature below which the phonon scattering does not contribute much to the resistivity of the crust. Some role of the Hall effect and attractor is not excluded, and will be analysed in our further studies.

Context. The mergers of neutron stars (NSs) and white dwarfs (WDs) could give rise to explosive transients, potentially observable with current and future transient surveys. However, the expected properties and distribution of such events is not well understood. Aims. Here we characterise the rates of such events, their delay-time distributions, their progenitors, and the distribution of their properties. Methods. We use binary population synthesis models and consider a wide range of initial conditions and physical processes. In particular we consider different common-envelope evolution models and different NS natal kick distributions. We provide detailed predictions arising from each of the models considered.Results. We find that the majority of NS-WD mergers are born in systems in which mass-transfer played an important role, and the WD formed before the NS. For the majority of the mergers the WDs have a carbon-oxygen composition (60−80%) and most of the rest are with oxygen-neon WDs. The time-integrated rates of NS-WD mergers are in the range of 3−15% of the type Ia supernovae (SNe) rate. Their delay-time distribution is very similar to that of type Ia SNe, but is slightly biased towards earlier times. They typically explode in young 100 Myr < τ < 1 Gyr environments, but have a tail distribution extending to long, gigayear-timescales. Models including significant kicks give rise to relatively wide offset distribution extending to hundreds of kiloparsecs. Conclusions. The demographic and physical properties of NS-WD mergers suggest they are likely to be peculiar type Ic-like SNe, mostly exploding in late-type galaxies. Their overall properties could be related to a class of recently observed rapidly evolving SNe, while they are less likely to be related to the class of Ca-rich SNe.