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4 Summary and conclusions

The main conclusion of this paper is that the single power law spectrum is a rule and the two power law spectrum is a rare exception to this rule. One could therefore think that the nature of this exception is that the spectrum just becomes steeper starting from some, relatively high frequency. However, inspection of Fig. 1 indicates that this might not be a case. The distribution of $\alpha _1$ seems different from that of $\alpha $, meaning that in pulsars with two power law spectra the average spectral index $<\alpha_1>$ is typically much larger than the average $<\alpha>$ (Fig. 1b) and of course, the high frequency index $<\alpha_2>$ is much smaller than $<\alpha>$ (Fig. 1c). Thus, it seems that the two power law spectra are qualitatively different from the typical single power law spectra. In this paper we obtained spectral index for a large sample of pulsars in a wide frequency range (form 400 MHz to 23 GHz). The average spectral index of pulsars $<\alpha>$ with simple power-law spectrum in our sample is $\rm -1.8~\pm~0.2$ which agrees with results obtained by other authors (see Table 4). The distribution of spectral indices is symmetric and almost Gaussian. The average indices for the broken-type spectra are $<\alpha_1>\,\,= -0.9~\pm~0.5$ and $<\alpha_2>\,\,=
-2.2~\pm~0.9$, respectively, with a break frequency of $<{\nu}_{\rm b}>
\,\,\approx$ 1.5 GHz on the average. We have not found any correlations between spectral index and rotation period P, spin-down rate $\dot P$, characteristic age $\tau$, polarization and profile type for pulsars with both simple power law spectra and two-power-law spectra. We have found 2 young, nearly fully polarized pulsars which indicate turn-over at unusually high frequency ($\sim$ 1 GHz). We have also found 15 pulsars which definitely require two-power-law spectra. The comparison of pulsar spectra analysis for slow and millisecond pulsars indicates that both groups have the same emission mechanism (Table 4).


Table 4: Spectral indices obtained by different authors
Spectral No. of Freq. range References
index PSRs [GHz]  
-1.6 27 0.1-10 Sieber 1973
-1.9 20 0.1-30 Malofeev et al. 1994
-1.6 280 0.3-1.6 Lorimer et al. 1995
-1.7 284 0.1-10 Malofeev et al. 1996
-1.8 32 0.3-4.9 Kramer et al. 1998, 1999
      (millisecond PSRs)
-1.7 216 0.4-1.5 Toscano et al. 1998
      (southern PSRs)
-1.9 19 0.4-1.5 Toscano et al. 1998
      (millisecond PSRs)
-1.9 144 1.4-4.9 Kijak et al. 1998
-1.8 281 0.4-23 this paper

Postscript files of spectra are available at and our spectra are also presented in EPN Database at

We thank Christoph Lange for his help with our observations in August 1998. OM thanks the director of the MPIfR Prof. Dr. R. Wielebinski for invitation and support. OM and JK gratefully acknowledge several discussions with J. Gil in the course of this work. The authors also thank V.M. Malofeev for unpublished data at 102 MHz and his helpful comments. This work was supported in part by the Polish State Committee for Scientific Research Grant 2 P03D 008 19.

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