2,302 research outputs found
The Small-scale Structure in Interstellar HI: A Resolvable Puzzle
During the past decade or so, measurements of Galactic HI absorption using
VLBI against extra-galactic sources, as well as multi-epoch observatios in
pulsar directions, have detected small-scale transverse variations
corresponding to tens of AU at the distance of the absorbing matter. Hitherto
these measurements have been interpreted as small-scale structure in the HI
distribution with densities n_{HI} ~ 10^4-10^5 per cc, orders of magnitude
greater than those of the parsec-scale structure. Naturally it is difficult to
imagine how such structures could exist in equilibrium with other components of
the ISM.
In this paper we show that structure on all scales contributes to the
differences on neighbouring lines of sight, and that the observed differences
can be accounted for by a natural extension of the distribution of
irregularities in the distribution of HI opacities at larger scales, using a
single power law. This, in our opinion, should put an end to the decades long
puzzle of the so-called small-scale structure in HI and other species in the
Galaxy.Comment: 7 pages including 3 figures, Latex format. Accepted for publication
in MNRAS, 200
Fluctuation Properties and Polar Emission Mapping of Pulsar B0834+06 at Decameter Wavelengths
Recent results regarding subpulse-drift in pulsar B0943+10 have led to the
identification of a stable system of sub-beams circulating around the magnetic
axis of the star. Here, we present single-pulse analysis of pulsar B0834+06 at
35 MHz, using observations from the Gauribidanur Radio Telescope. Certain
signatures in the fluctuation spectra and correlations allow estimation of the
circulation time and drift direction of the underlying emission pattern
responsible for the observed modulation. We use the `cartographic transform'
mapping technique to study the properties of the polar emission pattern. These
properties are compared with those for the other known case of B0943+10, and
the implications are discussed.Comment: (v3: minor changes); 9 pages, 6 figures (11 ps files); To appear in
MNRA
Topology and Polarisation of Subbeams Associated With Pulsar 0943+10's ``Drifting''-Subpulse Emission: I. Analysis of Arecibo 430- and 111-MHz Observations
The ``drifting'' subpulses exhibited by some radio pulsars have fascinated
both observers and theorists for 30 years, and have been widely regarded as one
of the most critical and potentially insightful aspects of their emission.
Here, we report on detailed studies of pulsar B0943+10, whose nearly coherent
sequences of ``drifting'' subpulses have permitted us to identify their origin
as a system of subbeams that appear to circulate around the star's magnetic
axis. We introduce several new techniques of analysis, and we find that both
the primary and secondary features in the star's fluctuation spectra are
aliases of their actual values. We have also developed a method of tracing the
underlying pattern responsible for the observed sequences, using a
``cartographic'' transform and its inverse, permitting us to study the
characteristics of the polar-cap emission ``map'' and to confirm that such a
``map'' in turn represents the observed sequence. We apply these techniques to
the study of three different Arecibo observations. The ``B''-mode sequences are
consistent in revealing that the emission pattern consists of 20 subbeams,
which rotate around the magnetic axis in about 37 periods or 41 seconds. Even
in the ``Q'' mode sequence, we find evidence of a compatible circulation time.
The similarity of the subbeam patterns at different radio frequencies strongly
suggests that the radiation is produced within a set of columns, which extend
from close to the stellar surface up though the emission region and reflect
some manner of a ``seeding''phenomenon at their base. The subbeam emission is
then tied neither to the stellar surface nor to the field.Comment: 25 pages with 26 figures; in press in MNRA
Some Exact Results for Mid-Band and Zero Band-Gap States of Associated Lame Potentials
Applying certain known theorems about one-dimensional periodic potentials, we
show that the energy spectrum of the associated Lam\'{e} potentials
consists of
a finite number of bound bands followed by a continuum band when both and
take integer values. Further, if and are unequal integers, we show
that there must exist some zero band-gap states, i.e. doubly degenerate states
with the same number of nodes. More generally, in case and are not
integers, but either or is an integer (), we again
show that several of the band-gaps vanish due to degeneracy of states with the
same number of nodes. Finally, when either or is an integer and the
other takes a half-integral value, we obtain exact analytic solutions for
several mid-band states.Comment: 18 pages, 2 figure
Cyclic Identities Involving Jacobi Elliptic Functions
We state and discuss numerous mathematical identities involving Jacobi
elliptic functions sn(x,m), cn(x,m), dn(x,m), where m is the elliptic modulus
parameter. In all identities, the arguments of the Jacobi functions are
separated by either 2K(m)/p or 4K(m)/p, where p is an integer and K(m) is the
complete elliptic integral of the first kind. Each p-point identity of rank r
involves a cyclic homogeneous polynomial of degree r (in Jacobi elliptic
functions with p equally spaced arguments) related to other cyclic homogeneous
polynomials of degree r-2 or smaller. Identities corresponding to small values
of p,r are readily established algebraically using standard properties of
Jacobi elliptic functions, whereas identities with higher values of p,r are
easily verified numerically using advanced mathematical software packages.Comment: 14 pages, 0 figure
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