Next Contents Previous


Discovered in 1967, pulsars are the rapidly rotating core left behind by exploding Type II supernovae. More than a thousand have now been observed in our Galaxy, in halo globular clusters, and in the LMC and SMC. Radio observations of these rapidly pulsating stars provide information on the plasma densities and magnetic field strengths of the intervening interstellar medium over base lines of tens of kiloparsecs.

The electrodynamic properties of a plasma are functions of the frequency of the electromagnetic wave that traverses the plasma. The group velocity of a wave in a plasma is

Equation 3 (3)

where omega is the angular frequency and omegap is the plasma frequency defined by omega2p = 4pi n e2 / m, for which n, e and m are the number density, charge and mass of the free electrons.

Because the group velocity of a wave depends on its frequency, the fourier components of a pulse will traverse a total distance d through a plasma in a time tomega given by

Equation 4 (4)

where s defines a small increment of distance through the plasma. Plasma frequencies in interstellar space are typically very low so we can expand eqn. 3 and substitute into eqn. 5 such that the time taken for the fourier component of a pulse to traverse a plasma is

Equation 5 (5)

The first term is the time taken to traverse a distance d in vacuo, and the second term is the plasma correction.

Studies of the arrival times of the various fourier components indicate that the highest frequencies arrive ahead of the low frequency components. What is actually measured is the derivative of eqn. 5,

Equation 6 (6)

The dispersion measure, defined as Dm = integ0d ne ds, is a measure of the total column of free electrons along the path to the pulsar in units of pc cm-3. A column of 1020 electrons results in a Dm of 30 pc cm-3 and a delay of 12 sec for a signal at 100 MHz relative to infinite frequency. Dispersion measures were first obtained by the pulsar discovery team. Since then, we have come to learn (Fig. 5) from pulsars in distant globular clusters and the Magellanic Clouds that the warm atmosphere in the Galaxy extends to about a kiloparsec above the Galactic plane.

Figure 5

Figure 5. Dispersion measures from pulsars, Dm sin b where b is galactic latitude, versus z-distance above the Galactic plane. The horizontal lines show the distance uncertainty for different pulsars. The black circles and stars refer to pulsars in globular clusters and the Magellanic clouds respectively. The sloping line corresponds to a model electron distribution which is uniform in density 0.03 cm-3, and the two dashed lines are for models in which the electron layer has the same density at z = 0 but falls off with increasing z as sech2(z/h) where h is 500 pc and 800 pc. (Courtesy of R.N. Manchester, Australia Telescope National Facility.

The radio signals reveal other important properties about the diffuse gas. In the presence of a magnetic field along the path to the pulsar, B||, the plane of polarization of the propagating wave will rotate by an angle chi equal to the phase delay between the ordinary and extraordinary components of the electric field. The so-called Faraday rotation angle is given by

Equation 7 (7)

for which omegaB is the cyclotron frequency. We define a quantity called the rotation measure,

Equation 8 (8)

in the traditional units of rad m-2, and where B|| is in units of microgauss (µG). The ratio of Rm to Dm is the average galactic magnetic field strength along the path,

Equation 9 (9)

Next Contents Previous