Spectral properties of the nonspherically decaying radiation generated by a rotating superluminal source

Abstract

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published [J. Opt. Soc. Am. A24, 2443 (2007)] asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (mu) that is by a factor of order mu(2/3) slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: It, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: The focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density S infinity mu(alpha)) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4.

Mechanism of generation of the emission bands in the dynamic spectrum of the Crab pulsar

“…These predictions seem to be borne out both by Geminga (ω/2π 4.5 Hz), which has emission peaked in the ultraviolet to gamma-ray end of the spectrum, and by millisecond pulsars such as 1937+21 (ω/2π 642 Hz) and 1957+20 (ω/2π 622 Hz), both of which show no emission in the GHz range but strong pulses at radiofrequencies (Lyne & Graham-Smith 2006). Furthermore, once it is acknowledged that (as shown in Appendices A and B) the current emitting the observed pulses from pulsars has a superluminally rotating distribution pattern, the results reported in the published literature on the electrodynamics of superluminal sources (Ardavan 1998;Ardavan et al 2003Ardavan et al , 2004aArdavan et al , 2007Schmidt et al 2007;Ardavan et al 2008a,b) can be used to explain the extreme values of the giant pulses' brightness temperature (∼10 40 K) ), temporal width (∼1 ns) and source dimension (∼1 m) (Ardavan et al 2008a), as well as the unique characteristics of the average pulses' polarization (their occurrence as concurrent 'orthogonal' modes with swinging position angles and with nearly 100 per cent linear or circular polarization) ) and spectra (the range −4 to −2/3 of their spectral indices and the breadth of their bandwidth, from radio waves to gamma-rays) (Ardavan et al 2008b).…”

“…Once it is acknowledged that the electric current emitting the observed pulses from pulsars has a superluminally rotating distribution pattern, results from the published literature on the electrodynamics of superluminal sources (Ardavan 1998; Ardavan, Ardavan & Singleton 2003, 2004a; Ardavan et al 2007; Schmidt et al 2007; Ardavan et al 2008a,b) can be applied to pulsars. In this paper, we explain the recently observed emission bands in the dynamic spectrum of the Crab pulsar (Hankins & Eilek 2007) using the calculations of Ardavan et al (2003).…”

“…Note that the electric susceptibility of the magnetospheric plasma (contained in the factor s) does not influence these results, because it depends on the source frequencies µ ± ω, not on the radiation frequency nω [seeArdavan et al (2008b)] …”