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.

We show that the spectral energy distribution (SED) of the tightly focused radiation generated by the superluminally moving current sheet in the magnetosphere of a non-aligned neutron star fits the gamma-ray spectra of the Crab, Vela and Geminga pulsars over the entire range of photon energies so far detected by Fermi-LAT, MAGIC and H.E.S.S. from them: over $10^2$ MeV to $20$ TeV. While emblematic of any emission that entails caustics, the SED introduced here radically differs from those of the disparate emission mechanisms currently invoked in the literature to fit the data in different sections of these spectra. We specify, moreover, the connection between the values of the fit parameters for the analysed spectra and the physical characteristics of the central neutron stars of the Crab, Vela and Geminga pulsars and their magnetospheres.

By applying the Efron-Petrosian method to the fluxes S and distances D of the magnetars listed in the Magnetar Outburst Online Catalogue, we show that the observational data are consistent with the dependence S proportional to D-3/2, which characterizes the emission from the superluminally moving current sheet in the magnetosphere of a non-aligned neutron star, at substantially higher levels of significance than they are with the dependence S proportional to D-2. This result agrees with that previously obtained by an analysis of the data in the McGill Online Magnetar Catalog and confirms that, contrary to the currently prevalent view, magnetars' X-ray luminosities do not exceed their spin-down luminosities. The X-ray spectra of magnetars, moreover, are congruous with the spectral energy distribution (SED) of a broad-band non-thermal emission mechanism identical to that at play in rotation-powered pulsars: we show that the SED of the caustics that are generated in certain privileged directions by the magnetospheric current sheet single-handedly fits the observed spectra of 4U 0142+61, 1E 1841-045, and XTE J1810-197 over their entire breadths. Magnetars' outbursts and their associated radio bursts are predicted to occur when, as a result of large-scale timing anomalies (such as glitches, quakes, or precession), one of the privileged directions along which the radiation from the current sheet decays more slowly than predicted by the inverse-square law either swings past or oscillates across the line of sight.

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. To illustrate that the derived function describes the spectral distribution of the high-energy emission from any non-aligned neutron star, we analyse, in addition, the spectra of two other gamma-ray pulsars for which sufficiently large datasets are available: PSR J0101-6422 and PSR J1709-4429. From the connection between the parameters of the fitted spectra and the physical characteristics of their sources, we moreover infer certain attributes of the magnetospheres of the analysed pulsars: the angle between the magnetic and spin axes of their central neutron stars, the scale factor of the electric current density that is associated with their current sheet, and the privileged latitudinal direction (relative to the spin axis) in which they are observed.

The prevalent view that the radio-loud gamma-ray pulsars have gamma-ray luminosities that exceed their radio luminosities by several orders of magnitude is based on the assumption that the decay with distance of their gamma-ray fluxes obeys the inverse-square law as does that of their radio fluxes. The results presented here, of testing the hypothesis of independence of luminosities and distances of gamma-ray pulsars by means of the Efron–Petrosian statistic, do not uphold this assumption however: they imply that the observational data in the Fermi-LAT 12-Year Catalog are consistent with the dependence S∝D−3/2 of the flux densities S of the gamma-ray pulsars on their distances D at substantially higher levels of significance than they are with the dependence S∝D−2. These results, which were theoretically predicted in Ardavan (2021), are not incompatible with the requirements of the conservation of energy because the radiation process by which the superluminally moving current sheet in the magnetosphere of a neutron star has been shown to generate the slowly decaying gamma-ray pulses is intrinsically transient: the difference in the fluxes of power across any two spheres centred on the star is balanced by the change with time of the energy contained inside the shell bounded by those spheres. Once the over-estimation of their values is rectified, the luminosities of gamma-ray pulsars turn out to have the same range of values as do the luminosities of radio pulsars. This conclusion agrees with that reached earlier on the basis of the smaller data set in the Second Fermi-LAT Catalog of Gamma-ray Pulsars.

The prevailing view that magnetars' X-ray luminosities exceed their spin-down luminosities is based on the assumption that the decay with distance of the flux of the X-rays received from magnetars obeys the inverse-square law. The results presented here, of testing the hypothesis of independence of luminosities and distances of magnetars by means of the Efron-Petrosian statistic, do not uphold this assumption however: they imply that the observational data in the McGill Magnetar Catalog are consistent with the dependence S∝D^-3/2 of the flux densities S of these objects on their distances D at substantially higher levels of significance than they are with the dependence S∝D^-2. These results are not incompatible with the requirements of the conservation of energy because the radiation process described in Ardavan (2021, MNRAS, 507, 4530), by which the superluminally moving current sheet in the magnetosphere of a neutron star is shown to generate the slowly decaying X-ray pulses, is intrinsically transient. Once their over-estimation is rectified, the ratios of X-ray to spin-down luminosities of known magnetars turn out to be invariably lower than one. A magnetar differs from other rotationally powered pulsars only in that it is observed along a privileged latitudinal direction relative to its spin axis: the closer is the line of sight to a direction in which the radiation from the current sheet is focused, the higher the frequency content and the lower the decay rate with distance of the observed radiation. The outbursts characterizing the emission of a magnetar thus arise from sudden movements of its spin or magnetic axes.

Pulsars' gamma-ray luminosities are thought to exceed their radio luminosities by several orders of magnitude: a notion that is based on the assumption that the decay with distance of the flux of gamma-ray pulses obeys the inverse-square law as does that of the flux of radio pulses. However, results of testing the hypothesis of independence of luminosities and distances of gamma-ray pulsars by means of the Efron--Petrosian statistic imply that the observational data in the second {\it FERMI} catalogue are consistent with the dependence $S\propto D^{-3/2}$ of the flux densities $S$ of these pulsars on their distances $D$ at substantially higher levels of significance than they are with the dependence $S\propto D^{-2}$. This is not incompatible with the requirements of the conservation of energy because the radiation process described in Ardavan [{\it Mon. Not. R. Astron. Soc.}, {\bf 507}, 4530--4563 (2021)], by which the superluminally moving current sheet in the magnetosphere of a neutron star is shown to generate the observed gamma-ray pulses, is intrinsically transient: the difference in the fluxes of power across any two spheres centred on the star is balanced by the change with time of the energy contained inside the shell bounded by those spheres. Once the over-estimation of their values is rectified, the luminosities of gamma-ray pulsars turn out to have the same range of values as do the luminosities of radio pulsars.

The mechanism by which the radiation received from obliquely rotating neutron stars is generated remains an open question half a century after the discovery of pulsars. In contrast, considerable progress has recently been made in determining the structure of the magnetosphere that surrounds these objects: numerical computations based on the force-free, magnetohydrodynamic, and particle-in-cell formalisms have now firmly established that the magnetosphere of an oblique rotator entails a current sheet outside its light cylinder whose rotating distribution pattern moves with linear speeds exceeding the speed of light in vacuum. However, the role played by the superluminal motion of this current sheet in generating the multiwavelength, focused pulses of radiation that we receive from neutron stars is unknown. Here, we insert the description of the current sheet provided by the numerical simulations in the classical expression for the retarded potential and thereby calculate the radiation field generated by this source in the time domain. We find a radiation consisting of highly focused pulses whose salient features (brightness temperature, polarization, spectrum and profile with microstructure and with a phase lag between the radio and gamma-ray peaks) are strikingly similar to those of the emission received from pulsars. In addition, the flux density of this radiation diminishes with the distance D from the star as D−3/2 (rather than D−2) in certain latitudinal directions: a result that suggests that the high energetic requirements normally attributed to magnetars and the sources of fast radio bursts and gamma-ray bursts could be artefacts of the assumption that the radiation fields of all sources necessarily decay as predicted by the inverse-square law.

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.

We analyze pulsar fluxes at 1400 MHz ($S_{1400}$) and distances ($d$) extracted from the Parkes Multibeam Survey. Under the assumption that distribution of pulsar luminosities is distance-independent, we find that either (a) pulsar fluxes diminish with distance according to a non-standard power law, due, we suggest, to the presence of a component with $S_{1400} \propto 1/d$, or (b) that there are very significant (i.e. order of magnitude) errors in the dispersion-measure method for estimating pulsar distances. The former conclusion (a) supports a model for pulsar emission that has also successfully explained the frequency spectrum of the Crab and 8 other pulsars over 16 orders of magnitude of frequency, whilst alternative (b) would necessitate a radical re-evaluation of both the dispersion-measure method and current ideas about the distribution of free electrons within our Galaxy.