Pulse profiles

2.3 Pulse profiles

Pulsars are weak radio sources. Measured intensities at 1.4 GHz vary between 5 $μ$ Jy and 1 Jy (1 Jy $≡$ 10^–26 W m^–2 Hz^–1). As a result, even with a large radio telescope, the coherent addition of many hundreds or even thousands of pulses is usually required in order to produce a detectable “integrated profile”. Remarkably, although the individual pulses vary dramatically, the integrated profile at a given observing frequency is very stable and can be thought of as a fingerprint of the neutron star’s emission beam. Profile stability is of key importance in pulsar timing measurements discussed in Section 4.

The selection of integrated profiles in Figure 4 shows a rich diversity in morphology including two examples of “interpulses” – a secondary pulse separated by about 180 degrees from the main pulse. One interpretation for this phenomenon is that the two pulses originate from opposite magnetic poles of the neutron star (see however [252 ]). Since this is an unlikely viewing angle, we would expect interpulses to be a rare phenomenon. Indeed, the fraction of known pulsars in which interpulses are observed in their pulse profiles is only a few percent [196 ]. Recent work [393 ] on the statistics of interpulses among the known population show that the interpulse fraction depends inversely on pulse period. The origin of this effect could be due to alignment between the spin and magnetic axis of neutron stars on timescales of order 10⁷ yr [393 ]. If we take this result at face value, and assume that all millisecond pulsars descend from normal pulsars (Section 2.6), then the implication is that millisecond pulsars should be preferentially aligned rotators. However, their appears to be no strong evidence in favour of this expectation based on the pulse profile morphology of millisecond pulsars [205 ].

Figure 4: A variety of integrated pulse profiles taken from the available literature. References: Panels a, b, d, f [129 ], Panel c [24

], Panels e, g, i [205

], Panel h [32 ]. Each profile represents 360 degrees of rotational phase. These profiles are freely available from an online database [363 ].

Two contrasting phenomenological models have been proposed to explain the observed pulse shapes. The “core and cone” model [302 ] depicts the beam as a core surrounded by a series of nested cones. Alternatively, the “patchy beam” model [246 , 133 ] has the beam populated by a series of randomly-distributed emitting regions. Recent work suggests that the observational data can be better explained by a hybrid empirical model depicted in Figure 5 which employs patchy beams in a core and cone structure [182 ].

Figure 5: A recent phenomenological model for pulse shape morphology. The neutron star is depicted by the grey sphere and only a single magnetic pole is shown for clarity. Left: a young pulsar with emission from a patchy conal ring at high altitudes from the surface of the neutron star. Right: an older pulsar in which emission emanates from a series of patchy rings over a range of altitudes. Centre: schematic representation of the change in emission height with pulsar age. Figure designed by Aris Karastergiou and Simon Johnston [182

A key feature of this new model is that the emission height of young pulsars is radically different from that of the older population. Monte Carlo simulations [182 ] using this phenomenological model appear to be very successful at explaining the rich diversity of pulse shapes. Further work in this area is necessary to understand the origin of this model, and improve our understanding of the shape and evolution of pulsar beams and fraction of sky they cover. This is of key importance to the results of population studies reviewed in Section 3.2.