Astron. Astrophys. 322, 489-492 (1997)

4. Inclusion in population synthesis

In the population synthesis as computed by Hartman et al. (1997) the dispersion measure is assumed to be an exact measure of the distance and therefore the derived and actual distance of a radio pulsar are the same. We implement our simple model in this synthesis as follows. The synthesis gives the actual distance of a simulated radio pulsar, and from this distance a flux measured at Earth is derived. From the actual distance, we calculate the smooth dispersion measure according to the model by Taylor & Cordes (1993), and then randomly choose the simulated dispersion measure DM from a Gaussian distribution centered on and with width given by Eq.  6, where we use . The value of DM is also used to compute the scatter broadening of the pulse profile. From DM and the Taylor & Cordes model we find a derived distance, and a derived luminosity. These values are used for the pulsar in the remainder of the simulation, and in particular its derived distance is used to determine whether the pulsar is within the volume selected for the comparison with observation.

In Fig. 2 we compare the results relating to the simulated and observed distributions of the dispersion measures for the synthesis model B, with decay time Myr, with and without inclusion of small scale structure in the electron distribution. It is seen that our simple model leads to a significantly better description of the distributions of the dispersion measure DM, of the vertical component of the dispersion measure , and of the galactic latitude distribution b.

Fig. 2. Comparison between cumulative distributions of the dispersion measure DM, galactic latitude b and the product of real pulsars (dots) and 2000 simulated pulsars (solid line) for the population synthesis according to model B from Hartman et al. (1997), without (upper row) and with (bottom row) the model for the variance in the dispersion measure. The Kolmogorov-Smirnov probabilities Q that the real and simulated distributions are drawn from the same population are indicated in the frames. (The values of Q vary somewhat between runs with different random number initializations; the improvement shown in this figure is more dramatic than for most other initializations.)

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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