Initial periods and magnetic fields of neutron stars

Initial distributions of pulsar periods and magnetic fields are essential components of multiple modern astrophysical models. Not enough work has been done to properly constrain these distributions using direct measurements. Here we aim to fill this gap by rigorously analysing properties of young neutron stars associated to supernova remnants. In order to perform this task, we compile a catalogue of 56 neutron stars uniquely paired to supernova remnants with known age estimate. Further, we analyse this catalogue using multiple statistical techniques. We found that distribution of magnetic fields and periods for radio pulsars are both well described using the log-normal distribution. The mean magnetic field is $\log_{10} [B/\mathrm{G}] = 12.44$ and standard deviation is $\sigma_B = 0.44$. Magnetars and central compact objects do not follow the same distribution. The mean initial period is $\log_{10} P_0 [P / \mathrm{s}] = -1.04_{-0.2}^{+0.15}$ and standard deviation is $\sigma_p = 0.53_{-0.08}^{+0.12}$. We show that the normal distribution does not describe the initial periods of neutron stars sufficiently well. Parameters of the initial period distribution are not sensitive to the exact value of the braking index.