The young radio pulsars within the the Milky Way appear confined to a thick disk centered on the Galactic plane, but this apparent confinement is misleading. The motion of radio pulsars within the Galaxy is very different from the motions of most other stars in the Galaxy. The young radio pulsars are moving away from the Galactic plane at a very high velocity. Despite this motion out of the plane, the young radio pulsars are all found within 1 kpc of the plane. The high velocity is a consequence of a pulsar's birth in a supernova explosion. The absence of pulsars more than 1 kpc from the Galactic plane is a consequence of the short lifetime of a radio pulsar.
To know how fast a pulsar is traveling, we must first know how far away it is. For most isolated objects within the Galaxy, this bit of information is a difficult to come by. The distance to nearby stars has been derived from parallax measurements, but this method becomes inaccurate for stars that are farther than about 200 parsecs from Earth. With radio pulsars, the limitations of parallax are less severe, because positions on the sky can be measured much more precisely with radio telescopes than is possible with optical telescopes. Still, parallaxes have only been measured for pulsars within 1 kpc of Earth. For more distant pulsars, other techniques must be used. The distances to pulsars behind spiral arms can be derived by measuring the absorption of radio waves by neutral hydrogen within the spiral arms. A small number of radio pulsars have distances derived indirectly through their association with objects such as supernova remnants. These various methods provide distances to only a small fraction of radio pulsars. Fortunately, a method unique to radio pulsars is available to derive a distance to every radio pulsar in the Galaxy: the dispersion of pulsar radio waves by free electrons within the Galaxy.
The space between the stars in our Galaxy is filled with a hot, very tenuous gas of hydrogen and helium. With a density of around one atom per cubic centimeter, the gas that fills this space would count as a pure vacuum by Earthly standards, but over kiloparsecs, this gas is dense enough to slow the velocity of radio waves slightly below the speed of light. The interaction that causes this slowing is between the electric field of the radio wave and the free electrons (electrons not bound to atoms) within the gas; the passage of the radio waves causes the free electrons to oscillate, which retards the progress of the radio waves. What is interesting about this effect is that the amount of the delay depends on only two parameters: the frequency of the radio wave and the density of electrons integrated over the distance between the pulsar and Earth. More precisely, the delay is proportional to nD/μ2, where n is the density of electrons, D is the distance, and μ is the frequency of the radio waves. The electrons between us and a pulsar therefore cause the high-frequency radio pulses from a pulsar to arrive before the low-frequency radio pulses.
The effect of electrons on the radio waves from a pulsar is analogous to the separation in high and low frequency sound waves in a thunder clap. Close to a lightning bolt, we hear a single crack, but far from the bolt, we hear a long rumble starting at a high frequency and dropping to low frequency. We could derive the distance to the lightning bolt by measuring the time it takes the thunder's pitch to drop.
By measuring the time delay in the arrival of low-frequency radio pulses compared to the high-frequency radio pulses, astronomers can derive the value nD, a quantity that is called the dispersion. If we know the density of electrons, then the dispersion gives us a direct measure of the distance to a pulsar.
The issue then becomes one of estimating the number of hot electrons along the line of sight. This is done using a model for how hot electrons fill the galaxy. In the grand tradition of astronomy of bootstrapping from one measure of distance to another, the model for hot electrons is derived from the dispersion measure of pulsars with distances derived through other methods.
The derivation of a pulsar's distance through its dispersion measure enables us to see the distribution of pulsars in three dimensions. The young radio pulsars constitute a thick disk that envelopes the Galactic disk of stars. While main-sequence stars and red giant are confined to a relatively narrow disk of 100 parsecs thickness, the pulsars form a disk that extends to 1 kpc on either side of the Galactic plane, with most pulsars confined within the central 1 kpc of this disk.
The motion of the pulsars within this disk is much different that of the main sequence stars within their disk. The fusion-powered stars in the Galactic disk orbit the galactic center in nearly-circular orbits at a velocity of 208±16 km s-1. This velocity applies to all star in the Galactic disk regardless of distance form the Galactic center. The velocities of these stars perpendicular to the plane is very smaller, typically around 10 km s-1. This velocity permits no more than a 100 pc excursion above the galactic plane by a star before gravitational forces pull the star back to the Galactic plane. Because the stars are confined to the Galactic disk, we find star in equal numbers that are moving away from and moving towards the galactic plane. In contrast, the young radio pulsars are all moving away from the galactic plane with velocities of several hundred km s-1. Even though the radio pulsar disk is an order of magnitude larger than the disk of the fusion-powered stars, the velocities of the pulsars are so high that they can travel much farther than 1 kpc above the galactic disk. These factors imply that a pulsar's life of radio emission ends before it leaves the 1 kpc pulsar disk; beyond the radio pulsar disk there should be many neutron stars that are too old to generate radio emission.
This picture of radio pulsars moving away from the galactic plane at high velocity fits within the theory that a radio pulsar receives a considerable kick when it is born in a supernova. The progenitors of neutron stars, the blue giants, are confined to the Galactic disk. If core collapse gave no kick to the resulting neutron star, all the radio pulsars see near supernova remnants would be sitting at the centers of their remnants; this is not the case. We see pulsars with large offsets from the centers of their supernovae, and we see pulsars that have left their remnants behind entirely. What we can say is that pulsars are born in the Galactic disk. We can derive a “kinetic age” for a pulsar by setting its birthplace to the Galactic plane. For pulsars hundreds of parsecs away from the Galactic plane, this kinetic age should be close to the true age of the pulsar. One finds that the radio pulsars have kinetic ages of no more than 10 million years.
For the youngest pulsars, the kinetic age of the pulsar is in close agreement with the “characteristic age” the age derived from the slowing of the pulsar's rotation. As the kinetic age of a pulsar exceeds 1 million years, the two methods of estimating an age diverge, with the kinetic age being smaller than the characteristic age by a factor ranging from 10 to 100. This divergence in value is taken as evidence that the magnetic field of a pulsar weakens over time. As the magnetic field weakens, the pulsar loses rotational energy more slowly. This slowing of energy loss causes the timescale for the pulsar to lose half of its energy to lengthen, causing the characteristic age to lengthen.