Congruity of Crab pulsar's gamma-ray spectrum with the spectral distribution of the radiation by the current sheet in its magnetosphere

The spectrum derived here for the most tightly-focused component of the radiation generated by the superluminally moving current sheet in the magnetrosphere of a non-aligned neutron star has a distribution function that fits the entire gamma-ray spectrum of the Crab pulsar on its own. This is the first time that the undivided breadth of this spectrum, from 10^2 to 10^6 MeV, is not only described by a single distribution function but is also explained by means of a single emission mechanism.Comment: 3 pages, 1 figur

The electromagnetic radiation whose decay violates the inverse-square law: detailed mathematical treatment of an experimentally realized example

I analyse and numerically evaluate the radiation field generated by an experimentally realized embodiment of an electric polarization current whose rotating distribution pattern moves with linear speeds exceeding the speed of light in vacuum. I find that the flux density of the resulting emission (i) has a dominant value and is linearly polarized within a sharply delineated radiation beam whose orientation and polar width are determined by the range of values of the linear speeds of the rotating source distribution, and (ii) decays with the distance $d$ from the source as d^{-\unicode[STIX]{x1D6FC}} in which the value of \unicode[STIX]{x1D6FC} lies between $1$ and $2$ (instead of being equal to $2$ as in a conventional radiation) across the beam. In that the rate at which boundaries of the retarded distribution of such a source change with time depends on its duration monotonically, this is an intrinsically transient emission process: temporal rate of change of the energy density of the radiation generated by it has a time-averaged value that is negative (instead of being zero as in a conventional radiation) at points where the envelopes of the wave fronts emanating from the constituent volume elements of the source distribution are cusped. The difference in the fluxes of power across any two spheres centred on the source is in this case balanced by the change with time of the energy contained inside the shell bounded by those spheres. These results are relevant not only to long-range transmitters in communications technology but also to astrophysical objects containing rapidly rotating neutron stars (such as pulsars) and to the interpretation of the energetics of the multi-wavelength emissions from sources that lie at cosmological distances (such as radio and gamma-ray bursts). The analysis presented in this paper is self-contained and supersedes my earlier works on this problem.</jats:p

Radio spectra of pulsars fitted with the spectral distribution function of the emission from their current sheet

In their catalogue of pulsars' radio spectra, Swainston et al. (2022, PASA, 39, e056) distinguish between five different forms of these spectra: those that can be fitted with (i) a simple power law, (ii) a broken power law, (iii) a low-frequency turn-over, (iv) a high-frequency turn-over or (v) a double turn-over spectrum. Here, we choose two examples from each of these categories and fit them with the spectral distribution function of the caustics that are generated by the superluminally moving current sheet in the magnetosphere of a non-aligned neutron star. In contrast to the prevailing view that the curved features of pulsars' radio spectra arise from the absorption of the observed radiation in high-density environments, our results imply that these features are intrinsic to the emission mechanism. We find that all observed features of pulsar spectra (including those that are normally fitted with simple or broken power laws) can be described by a single spectral distribution function and regarded as manifestations of a single emission mechanism. From the results of an earlier analysis of the emission from a pulsar's current sheet and the values of the fit parameters for each spectrum, we also determine the physical characteristics of the central neutron star of each considered example and its magnetosphere.Comment: 7 pages, 12 figures. arXiv admin note: text overlap with arXiv:2312.0347

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

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 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 proportional to mu^alpha) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4

Morphology of the nonspherically decaying radiation generated by a rotating superluminal source: reply to comment

The fact that the formula used by Hannay in his Comment is "from a standard text on electrodynamics" neither warrants that it is universally applicable, nor that it is unequivocally correct. We have explicitly shown [J. Opt. Soc. Am. A 25, 543 (2008)] that,since it does not include the boundary contribution toward the value of the field, the formula in question is not applicable when the source is extended and has a distribution pattern that rotates faster than light in vacuo. The neglected boundary term in the retarded solution to the wave equation governing the electromagnetic field forms the basis of diffraction theory. If this term were identically zero, for the reasons given by Hannay, the iffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible. If this term were identically zero, for the reasons given by Hannay, the diffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible

The fundamental role of the retarded potential in the electrodynamics of superluminal sources

We calculate the gradient of the radiation field generated by a polarization current with a superluminally rotating distribution pattern and show that the absolute value of this gradient increases as R^(7/2) with distance R within the sharply focused subbeams constituting the overall radiation beam. This result not only supports the earlier finding that the azimuthal and polar widths of these subbeams narrow with distance (as R^(-3) and R^(-1), respectively), but also implies that the boundary contribution to the solution of the wave equation governing the radiation field does not always vanish in the limit where the boundary tends to infinity. There is a fundamental difference between the classical expressions for the retarded potential and field: while the boundary contribution for the potential can always be made zero via a gauge transformation preserving the Lorenz condition, that for the field may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a rotating superluminal source, however, the boundary term in the retarded solution for the field is by a factor of order R^(1/2) larger than the source term of this solution in the limit, which explains why an argument based on the solution of the wave equation governing the field that neglects the boundary term (such as that presented by J. H. Hannay) misses the nonspherical decay of the field. Given that the distribution of the radiation field of an accelerated superluminal source in the far zone is not known a priori, the only way to calculate the free-space radiation field of such sources is via the retarded solution for the potential. Finally, we apply these findings to pulsar observational data: the more distant a pulsar, the narrower and brighter its giant pulses should be

A new mechanism for generating broadband pulsar-like polarization

Observational data imply the presence of superluminal electric currents in pulsar magnetospheres. Such sources are not inconsistent with special relativity; they have already been created in the laboratory. Here we describe the distinctive features of the radiation beam that is generated by a rotating superluminal source and show that (i) it consists of subbeams that are narrower the farther the observer is from the source: subbeams whose intensities decay as 1/R instead of 1/R^2 with distance (R), (ii) the fields of its subbeams are characterized by three concurrent polarization modes: two modes that are 'orthogonal' and a third mode whose position angle swings across the subbeam bridging those of the other two, (iii) its overall beam consists of an incoherent superposition of such coherent subbeams and has an intensity profile that reflects the azimuthal distribution of the contributing part of the source (the part of the source that approaches the observer with the speed of light and zero acceleration), (iv) its spectrum (the superluminal counterpart of synchrotron spectrum) is broader than that of any other known emission and entails oscillations whose spacings and amplitudes respectively increase and decrease algebraically with increasing frequency, and (v) the degree of its mean polarization and the fraction of its linear polarization both increase with frequency beyond the frequency for which the observer falls within the Fresnel zone. We also compare these features with those of the radiation received from the Crab pulsar.Comment: 8 pages, 8 figure

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

We show that the proportionately spaced emission bands in the dynamic spectrum of the Crab pulsar (Hankins T. H. & Eilek J. A., 2007, ApJ, 670, 693) fit the oscillations of the square of a Bessel function whose argument exceeds its order. This function has already been encountered in the analysis of the emission from a polarization current with a superluminal distribution pattern: a current whose distribution pattern rotates (with an angular frequency $\omega$) and oscillates (with a frequency $\Omega>\omega$ differing from an integral multiple of $\omega$) at the same time (Ardavan H., Ardavan A. & Singleton J., 2003, J Opt Soc Am A, 20, 2137). Using the results of our earlier analysis, we find that the dependence on frequency of the spacing and width of the observed emission bands can be quantitatively accounted for by an appropriate choice of the value of the single free parameter $\Omega/\omega$. In addition, the value of this parameter, thus implied by Hankins & Eilek's data, places the last peak in the amplitude of the oscillating Bessel function in question at a frequency ($\sim\Omega^3/\omega^2$) that agrees with the position of the observed ultraviolet peak in the spectrum of the Crab pulsar. We also show how the suppression of the emission bands by the interference of the contributions from differring polarizations can account for the differences in the time and frequency signatures of the interpulse and the main pulse in the Crab pulsar. Finally, we put the emission bands in the context of the observed continuum spectrum of the Crab pulsar by fitting this broadband spectrum (over 16 orders of magnitude of frequency) with that generated by an electric current with a superluminally rotating distribution pattern