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 $$a(a+1)m~{\rm sn}^2(x,m)+b(b+1)m~{\rm cn}^2(x,m)/{\rm dn}^2(x,m)$$ consists of a finite number of bound bands followed by a continuum band when both $a$ and $b$ take integer values. Further, if $a$ and $b$ 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 $a$ and $b$ are not integers, but either $a + b$ or $a - b$ is an integer ($a \ne b$), we again show that several of the band-gaps vanish due to degeneracy of states with the same number of nodes. Finally, when either $a$ or $b$ 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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