Birth Properties of Neutron Stars
By combining measurements of pulsar velocities and spins for several tens of pulsars, we have shown that there is a strong preference for alignment or orthogonality between those two vectors. This is an important discovery, as it shows us that the supernova process imparts kicks onto a pulsar that are not random in nature but are statistically orientated along or perpendicularly to the pulsar's spin axis. Figure 1 shows the probability distribution of the angle between spin and velocity, ψ. The value of ψ ranges from 0° to 45°, because the spin-axis orientation derived from polarisation measurements is ambiguous between perpendicular orientations. The higher probability near ψ = 0° denotes preference towards alignment and/or orthogonality between those two vectors. A good example of such a mechanism in operation is the case of the Vela pulsar in the Vela SNR (figure 2), where X-ray imaging of the pulsar-wind-nebula has revealed a nearly aligned configuration between the pulsar's spin and its velocity. This work has been published in Noutsos et al. (2012), MNRAS, 423, 3, 2736.
The properties of pulsars at birth, right after the parent star gives off a supernova, are very difficult to measure, as supernovae are rare events: the famous example of the birth of the Crab pulsar observed by Chinese monks in 1054 AD is one of only a few historical records of such an event. Yet, the ages of pulsars, their spin frequencies at birth, and the rates at which they spin down during their lifetimes is valuable information. Knowledge of pulsar ages is central in pulsar-population studies, as it allows us to calculate the birth rates of Galactic pulsars, which in turn is important in theories of stellar evolution and furthermore for our understanding of the balance between gas and stars in spiral galaxies. In addition, the longterm rate of spin-down of pulsars is directly related to the neutron-star physics: the standard model of magnetic-dipole braking predicts that all pulsars should spin down entirely due to dipolar electromagnetic emission, with their spin down being proportional to the third power of the their spin frequency (i.e. braking index of 3). Nevertheless, so far the few pulsars for which this measurement is possible all have values significantly different from 3. Finally, the standard model for pulsars assumes that pulsars are born having spin periods that are much shorter than those observed today. There are examples of pulsars, like PSR J0538+2817, for which a kinematic analysis of its outward motion from its supernova birth place provides a precise estimate of its age; the derived age is roughly an order of magnitude smaller than that predicted by the standard model. Hence, the standard model fails to predict the properties of pulsars in several cases.
The measured proper motions of hundreds of pulsars (red arrows, Fig. 3) can be used to estimate the birth properties of pulsars through kinematics, if one assumes that pulsars are born near the Galactic plane. Our group has performed a simulation of the pulsar motions through the Galactic volume, which uses the derived distribution of birth velocities of pulsars (Fig. 4) as a prior, as well as a model of the Galactic gravitational potential. The simulation has allowed us to calculate the time interval between the pulsar's present position and its position at birth, for a range of unknown parameters, like the pulsar's current radial velocity and its vertical distance from the Galactic plane at birth. An example distribution of a pulsar's age, from our simulation, can be seen in figure 5a. Having a distribution for the pulsar age, one can then derive the distributions of the birth spin period under the assumption of magnetic-dipole braking (figure 5b) and conversely the distribution of the braking index, assuming the pulsar was spinning at birth much faster than it does today (figure 5c). This work has been published in Noutsos et al. (2013), MNRAS, 430, 3, 2281.