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Astron. Astrophys. 352, 489-494 (1999)

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3. Analysis and results

For the analysis of the profile frequency dependence we combine our 102 MHz profiles with high frequency data at several frequencies in the range between 400 and 1400 MHz. The data is taken from Bailes et al. (1997), Camilo et al. (1996), Foster et al. (1993), Foster et al. (1995), Gould & Lyne (1999), Kramer et al. (1998), Lorimer (1994), Lorimer et al. (1995), Nicastro et al. (1995), Nice et al. (1993), Nice et al. (1996), Sayer et al. (1997), Wolszczan & Frail (1992).

The initial analysis of the frequency dependence of the profile width was made qualitatively, by visual comparison of profiles. The multifrequency alignment was done visually by superposition of profiles.

A typical frequency development of the pulse profile for a normal pulsar is illustrated in Fig. 2. Here the integrated profiles of PSR 1133+16 at 102, 406 and 1380 MHz are plotted. As can be seen the profile narrows with frequency.

[FIGURE] Fig. 2. Integrated profiles of normal pulsar PSR 1133 + 16 at frequencies 102 MHz (top line), 406 MHz (middle line) and 1380 MHz (bottom line). Alignment is arbitrary.

The frequency dependence of the integrated profiles of the millisecond pulsars in our sample at the same frequency range is shown in Fig. 3. The horizontal bars in this figure denote the actual resolution at 102 MHz, which was limited by the dispersion broadening [FORMULA] as listed in Table 1. High frequency profiles are smoothed out to obtain the same dispersion broadening, equal to that observed at 102 MHz. As can be seen in this figure, the profile width of millisecond pulsars at a near zero level remains roughly constant with frequency.

[FIGURE] Fig. 3. Integrated profiles of millisecond pulsars at frequencies 102 MHz (top line), [FORMULA] 400 MHz (middle line) and [FORMULA] 1400 MHz (bottom line). High frequency profiles were smoothed out to obtain the same dispersion broadening, equal to that observed at 102 MHz (see text). Alignment is arbitrary. For pulsars PSR J1518+4904, B1534+12, J1713+0747, J1730+2304 and B1855+09 the high frequency profiles are shown in multiplied scale.

In order to quantify our analysis we employed the component separation method, outlined by Foster et al. (1991), Wu et al. (1992), and further elaborated by Kramer et al. (1994) and Kuzmin & Izvekova (1996). The integrated profile was decomposed into several Gaussian-shaped individual components

[EQUATION]

where [FORMULA], [FORMULA] and [FORMULA] denote the intensity, half-power width and pulse phase respectively of the components. The analytical profile [FORMULA] was compared with the observed one in order to obtain the residual level between these two. This was done by means of a least square iterative fitting procedure resulting in values of [FORMULA], [FORMULA] and [FORMULA] that match the observed and analytical profiles best. As a criterion for the number of Gaussian components we required that the residuals (the difference between the observed and the analytical profiles) should be comparable to the off-pulse noise, similar to the method explained in Kramer et al. (1994). This means that the residuals should not have any regular component-like structures, which exceed the off-pulse noise. The residual noise level should be comparable to that of the off-pulse noise. To set a uniform condition in our analysis, we strove for the decomposition into the same number of Gaussian components at each frequency.

We refer the widths of the integrated profiles to the 10[FORMULA] level of the peak intensity of the leading and the trailing profile components.

[EQUATION]

Here [FORMULA] and [FORMULA] are pulse phases and widths of the leading and trailing components (at 10[FORMULA] level). The frequency dependence of the profile widths of millisecond pulsars are presented in Fig. 4.

[FIGURE] Fig. 4. Frequency dependence of the width of integrated profiles of millisecond pulsars. Solid lines represent the results of a power law fit to the data. The index resulting from this regression is also presented for each pulsar.

In our quantitative analysis we have approximated this dependence with power low [FORMULA] similar to Thorsett (1991). The value of the exponent [FORMULA], its regression error [FORMULA] and a reference for sources of the information on high-frequency profiles are presented in Table 2. The mean value of [FORMULA] is [FORMULA] with a standard deviation 0.03.


[TABLE]

Table 2. Frequency dependence of the profile's width Notes: References: 1 -Nicastro et al. (1995); 2 -Kramer et al. (1998); 3 -Sayer et al. (1997); 4 -Camilo et al. (1996); 5 -Bailes et al. (1997); 6 -Wolszczan & Frail (1992); 7 -Nice et al. (1996); 8 -Gould & Lyne (1999); 9 -Nice et al. (1993); 10 -Lorimer (1994); 11 -Foster et al. (1993); 12 -Lorimer et al. (1995); 13 -Foster et al. (1995).


A similar profile analysis was performed for a sample of 27 normal pulsars from the catalogue of Kuzmin et al. (1998) and also Izvekova et al. (1993). The mean value of [FORMULA] for normal pulsars is [FORMULA] with a standard deviation 0.08. It should be noted that low frequency 102 MHz observations of normal pulsars were performed with the same Large Phased Array BSA radio telescope in Pushchino Radio Astronomy Observatory.

The comparison of the indices [FORMULA] of the profile frequency dependence between millisecond and normal pulsars is presented in Fig. 5. As can be seen in this figure there is an obvious difference between these two distributions. The statistical test confirms that these are two different populations (Kolmogorov- Smirnov test yields a probability of 0.1% that they are drawn from the same parent distribution).

[FIGURE] Fig. 5. Distribution of [FORMULA] indices of the frequency dependence of the integrated profile width of millisecond and normal pulsars.

Thus, the frequency dependence of the width of integrated profiles of millisecond pulsars is much weaker, than that of normal ones.

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© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999
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