Birth Properties of Neutron Stars

The evolution of massive OB stars beyond the main sequence, leading to supernova explosions and ultimately to compact neutron stars or black holes is a process that is not well understood. In particular, the forces in play during the final moments of a star before it explodes are crucial for understanding the physics of supernovae. The signature of those forces is imprinted onto the 3D spin orientation and velocity of neutron stars and can be measured through observations of the radio emission of pulsars. Observations of the polarised radio emission of pulsars allow us to directly infer the projected orientation of the spin axis of a pulsar onto the plane of the sky. In addition, changes in the arrival times of pulsar signals over several years have allowed us to track the tiny motions of pulsars across the sky.
Fig. 1: Probability density of the angle between spin and velocity, derived from radio polarisation and timing observations of pulsars. It can be seen that the highest probability corresponds to angles near 0 degrees, denoting the preference towards alignment and/or orthogonality between those two vectors. Note that radio polarisation and timing observations alone cannot distinguish between those two configurations. The schematics on the right show the two preferred configurations, i.e. that of orthogonality and of alignment between spin and velocity. Zoom Image
Fig. 1: Probability density of the angle between spin and velocity, derived from radio polarisation and timing observations of pulsars. It can be seen that the highest probability corresponds to angles near 0 degrees, denoting the preference towards alignment and/or orthogonality between those two vectors. Note that radio polarisation and timing observations alone cannot distinguish between those two configurations. The schematics on the right show the two preferred configurations, i.e. that of orthogonality and of alignment between spin and velocity. [less]
Fig. 2: X-ray image of the Vela pulsar-wind nebula, hosting the Vela pulsar at its centre. The projected direction of the pulsar's motion and that of its spin is shown with a green and blue arrow, respectively. Zoom Image
Fig. 2: X-ray image of the Vela pulsar-wind nebula, hosting the Vela pulsar at its centre. The projected direction of the pulsar's motion and that of its spin is shown with a green and blue arrow, respectively. [less]

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

Fig. 3: 3D schematic of the positions and velocity directions of pulsars (blue points with red arrows) in the Galactic volume. The velocity vectors shown assume that the unknown radial velocity of pulsars is of the same order as that of the observed transverse velocity. The greyscale disc in this image represents the electron density of the Galactic plane, based on the NE2001 free-electron density model. The position of the Sun is shown as a yellow point. The fastest-moving pulsars known can have a velocity of a few thousands km/s. Zoom Image
Fig. 3: 3D schematic of the positions and velocity directions of pulsars (blue points with red arrows) in the Galactic volume. The velocity vectors shown assume that the unknown radial velocity of pulsars is of the same order as that of the observed transverse velocity. The greyscale disc in this image represents the electron density of the Galactic plane, based on the NE2001 free-electron density model. The position of the Sun is shown as a yellow point. The fastest-moving pulsars known can have a velocity of a few thousands km/s. [less]
Fig. 4: Distribution of birth velocities of Galactic pulsars (boxes), based on observations of 233 pulsar proper motions. The distribution is well described by a Maxwellian curve with a mean of 400 km/s and an RMS of 265 km/s. Zoom Image
Fig. 4: Distribution of birth velocities of Galactic pulsars (boxes), based on observations of 233 pulsar proper motions. The distribution is well described by a Maxwellian curve with a mean of 400 km/s and an RMS of 265 km/s. [less]

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..

Figs. 5a-5c:Example distributions of (a) pulsar age, (b) spin period at birth and (c) braking index, derived from our simulations. The vertical lines in these figures show the most probable value in each case (solid black line) and the 1σ confidence interval (dashed lines). Zoom Image
Figs. 5a-5c:Example distributions of (a) pulsar age, (b) spin period at birth and (c) braking index, derived from our simulations. The vertical lines in these figures show the most probable value in each case (solid black line) and the 1σ confidence interval (dashed lines). [less]
 
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