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Astron. Astrophys. 359, 242-250 (2000)

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3. Properties of the simulated pulsar population

The possibility that the magnetic axis could migrate gives not only a possible explanation for the non-canonical braking index observed in some pulsars, but also a mechanism affecting the [FORMULA] and age distributions. In general, objects with small deceleration rates ([FORMULA]) are old and have low magnetic fields in the standard picture. In our scenario the magnetic torque controlling the deceleration rate, depends not only on the field strength but also on the angle between the dipole and the spin axes. Therefore, our simulated catalog contains some young objects born with a small misalignment between those axes, having a high field strength but a small deceleration rate. Unfortunately, it is not possible to disentangle easily both situations and, as a consequence, the derived value of the dipole migration timescale [FORMULA] has a large uncertainty: [FORMULA] = 10000[FORMULA]4000 yr. These values imply migration rates spanning the interval (2-18)[FORMULA] rad/yr, which compare with rates derived by other authors (see Sect. 2.1).

The optimized parameters characterizing the distribution of the initial period and that of the magnetic braking timescale [FORMULA] are given in Table 2 for tmax equal to 24 Myr and 100 Myr. These parameters represent the best compromise able to fit adequately to data, the simulated distributions of period and its derivative, as well as the distribution of distances to the sun. Note that the parameters characterizing the Gaussian representing the initial distribution of rotation periods are not sensitive to the adopted value for [FORMULA], but this is not the case for the parameter [FORMULA].


Table 2. Pulsar population properties

In Fig. 1 we have plotted in the plane XY, which coincides with the galactic plane (the origin of the coordinates is placed at the galactic center), the observed pulsar population and our simulated population. The superposition of both populations is quite good, suggesting that selection effects were adequately taken into account by the model. In Fig. 2 we compare the observed period distribution with simulated data, where error bars correspond to the dispersion derived from five hundred experiments. Fig. 3 shows the comparison between observed and simulated data for the period derivative, whereas Fig. 4 display both heliocentric distance distributions. These figures correspond to simulations with [FORMULA] = 24 Myr and they illustrate the fit quality.

[FIGURE] Fig. 1. Spatial distribution in the galactic plane (origin at the galactic center) of both observed (stars) and simulated (circles) populations of radio pulsars. The position of the sun is also indicated in the diagram.

[FIGURE] Fig. 2. Distribution of rotation periods. Bars represent observed binned data and filled circles indicate the result of our simulations. Error bars give the rmsd after averaging 500 numerical experiments.

[FIGURE] Fig. 3. Distribution of period derivatives. Symbols have the same meaning as in Fig. 1.

[FIGURE] Fig. 4. Distribution of heliocentric distances. Symbols have the same meaning as in Fig. 1.

The last line of Table 2 gives the average magnetic field of the simulated observed population, which is about 2.5[FORMULA] G, in agreement with values derived from a direct application of the "standard" pulsar model. However, the average field of the true or "unseen" population is one order of magnitude higher, namely, 2.5[FORMULA] G. Most of these high-field pulsar have rather long periods and thus are radio-quiet. The relevance of this high-field pulsar population in the context of magnetars will be discussed in a forthcoming paper (Regimbau & de Freitas Pacheco 2000).

Our simulations indicate that the data are better explained if an initial distribution of periods is assumed instead of an unique (mean) initial value. Bhattacharya et al. (1992) assumed an initial period equal to 100 ms, comparable with the average value derived from our simulations (290 ms). Models by Lorimer et al. (1993) are not directly comparable, since they have assumed a magnetic field decay with a timescale of 10 Myr. For the present purposes, we will focus our attention on the pulsar population with periods less than 0.4 s, which contributes to the continuum GW emission from the galactic disc. This upper bound is expected to be attained in a second phase of the VIRGO experiment. In spite of the bulk of the population having higher periods, the dispersion in the initial periods guarantees the existence of objects in that frequency band. From our simulations, we predict about 60-90 (single) pulsars with P [FORMULA] 80 ms in the Galaxy, a number not in contradiction with present data. The period distribution for pulsars satisfying the condition P [FORMULA] 0.4 s is shown in Fig. 5, and their heliocentric distance distribution is given in Fig. 6. The number of this sub-population is in the range 5100-7800, according to our simulations performed with tmax equal to 24 Myr and 100 Myr respectively. The contribution of this population to the gravitational strain is estimated in the next section.

[FIGURE] Fig. 5. Distribution of periods for all pulsars satisfying P[FORMULA]0.4 s.

[FIGURE] Fig. 6. Distribution of heliocentric distances for the pulsar population satisfying P[FORMULA]0.4 s.

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© European Southern Observatory (ESO) 2000

Online publication: June 30, 2000