3. Discussion and conclusion
3.1. Shape of emission beams and pulse profiles
The result in this paper shows that slow-rotation pulsars with long period such as or longer, are "double-conal pulsars" with both inner and outer cone beams. This is in agreement with the conclusion given by Rankin (1993a). Rankin's table (1993a) for M pulsars with five components shows, most of these 19 pulsars have long pulse periods. In the Fig. 6a, the opening angle (angular radius) becomes larger when the frequency increases (decreases) for the inner cone (outer cone). Fast pulsars, i.e. , may only have a core and one inner conal emission component (Fig. 4 and Fig. 6b). For this class of pulsars, observations tend to get triple (T) profiles. In Fig. 6b, as the frequency increases, the opening angle for the inner cone always increases. In this case, at higher frequency (from line D to line C), we will get a wider pulse profile (Qiao 1992) in contrast to that in slow pulsars for outer cone. This can be seen for some pulsars, such as PSR B1642-03 and PSR B1933+16 (Sieber et al. 1975; LM88).
We must mention that the theoretical angular radius of the outer conal beam is larger than in previous calculations and the height of the outer conal beam emission region is larger than that of Rankin. This may be related to the parameter in Eq. (13). A detailed calculation shows that the controller is determined by the energy loss of particles, which depends on the strength of the magnetic field and the thermal temperature at the surface of neutron stars (Zhang et al. 1997b).
3.2. Does the "inner" cone radius increase as the observed frequency increases?
One result of this paper is that the inner cone radius increases as the observed frequency increases. This result is supported by analysis of observations. Wu et al.(1992) present a method to deal with the structure of the mean pulse profiles of pulsars. With that method and multi-frequency observational data, a diagram of was given which is very similar to the result of our calculation (see Fig. 6) and Fig. 2 of Qiao (1992). Further analysis of Rankin (1993a) did not emphasize that the angular radius of the inner cone increases when the frequency increases. More analysis of this is needed. A direct method to check the result of this paper is that for pulsars with "inner" and "outer" cones (five components), the pulse profiles should become a triple ("inner" cone and "outer" cone get together) with a smaller central component at very high frequency (Fig. 6, line A) and also become a triple (the inner cone and core get together) with stronger central component at low frequency (Fig. 6, line B). This is in agreement with the observations of PSR 1237+25, e.g. Izvekova et al. (1989), Kuzmin et al. (1997).
Our result shows that the ICS process is a possible radiation mechanism for radio pulsars since it can produce the emission beams naturally and consistent with observations. Rankin (1993a) showed that the angular radii of core, "inner" cone and "outer" cone at a given frequency is a function of P (and only P!). This is just the result of the calculations in this paper. In agreement with the results given by Rankin (1993), we conclude that those pulsars with only "inner" cone (core single and triple in Rankin's classification) are generally faster, those with "outer" cone (conal single and double) much slower, and the group of five-component (M) pulsars falls in between the other two. This paper also supports the conclusion that the "inner" cone is emitted at a lower height along a same group of field lines that produce the "outer" cone. The shapes of pulse profiles change with frequencies in agreement with some pulsars (Qiao 1992). The retardation and aberration effects induce asymmetry and our result fits with observations (McCulloch 1992). These two effects may also change the linear polarization position angle (Xu, et al. 1997). The coherent emission of the ICS process suggested in this paper is an efficient mechanism to produce observed luminosity, and is also a mechanism to produce observed polarization (Qiao et al. 1997; Xu 1997).
© European Southern Observatory (ESO) 1998
Online publication: April 15, 1998