24 research outputs found

### 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

### 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

### 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

### 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