to each pulsar can be made from an effect known as pulse dispersion, the delay in pulse arrival times across a finite bandwidth. Dispersion occurs because the group velocity of the pulsed radiation through the ionised component of the interstellar medium is frequency dependent: pulses emitted at higher radio frequencies travel faster through the interstellar medium, arriving earlier than those emitted at lower frequencies. The delay in arrival times between a high frequency and a low frequency pulse is given  by
where the frequencies are in MHz and the dispersion measure DM () is the integrated column density of free electrons along the line of sight:
Here, d is the distance to the pulsar (pc) and is the free electron density (). From Equation (2) it is obvious that a measurement of the delay across a finite bandwidth yields the DM. Pulsars at large distances have higher column densities and therefore larger DMs than those pulsars closer to Earth so that, from Equation (1), the dispersive delay across the bandwidth is greater. Hence, given the DM, the distance can be estimated from a model of the Galactic distribution of free electrons.
The electron density model is calibrated from the pulsars with independent distance estimates and measurements of scattering for lines of sight towards various Galactic and extragalactic sources. Independent distance estimates now exist for over 100 pulsars based on three basic techniques: neutral hydrogen absorption, trigonometric parallax (measured either with an interferometer or through pulse time-of-arrival techniques) and from associations with objects of known distance (i.e. supernova remnants, globular clusters and the Magellanic Clouds). Based on these data, Taylor & Cordes  have developed an electron density model which is free from large systematic trends and can be used to provide distance estimates with an uncertainty of 30%. However, use of this model to estimate distances to individual pulsars may result in uncertainties by as much as a factor of two. This model is currently being refined following recent pulsar discoveries and independent distance and scattering measurements (J. Cordes, private communication).
|Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
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