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.
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 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.
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
where , and denote the intensity, half-power width and pulse phase respectively of the components. The analytical profile 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 , and 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 level of the peak intensity of the leading and the trailing profile components.
Here and are pulse phases and widths of the leading and trailing components (at 10 level). The frequency dependence of the profile widths of millisecond pulsars are presented in Fig. 4.
In our quantitative analysis we have approximated this dependence with power low similar to Thorsett (1991). The value of the exponent , its regression error and a reference for sources of the information on high-frequency profiles are presented in Table 2. The mean value of is with a standard deviation 0.03.
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 for normal pulsars is 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 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).
Thus, the frequency dependence of the width of integrated profiles of millisecond pulsars is much weaker, than that of normal ones.
© European Southern Observatory (ESO) 1999
Online publication: December 2, 1999