Pulsar Magnetospheric Emission Mapping: Images and Implications of Polar-Cap Weather

The beautiful sequences of ``drifting'' subpulses observed in some radio pulsars have been regarded as among the most salient and potentially instructive characteristics of their emission, not least because they have appeared to represent a system of subbeams in motion within the emission zone of the star. Numerous studies of these ``drift'' sequences have been published, and a model of their generation and motion articulated long ago by Ruderman & Sutherland (1975); but efforts thus far have failed to establish an illuminating connection between the drift phemomenon and the actual sites of radio emission. Through a detailed analysis of a nearly coherent sequence of ``drifting'' pulses from pulsar B0943+10, we have in fact identified a system of subbeams circulating around the magnetic axis of the star. A mapping technique, involving a ``cartographic'' transform and its inverse, permits us to study the character of the polar-cap emission ``map'' and then to confirm that it, in turn, represents the observed pulse sequence. On this basis, we have been able to trace the physical origin of the ``drifting-subpulse'' emission to a stably rotating and remarkably organized configuration of emission columns, in turn traceable possibly to the magnetic polar-cap ``gap'' region envisioned by some theories.Comment: latex with five eps figure

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

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

Sources of variability in cartographers' deconstruction of fractals : paper presented at the 18 November 1998 meeting of the British Cartographic Society's Design Group at the University of Glasgow

CISRG discussion paper ; 1

The `Periodic Nulls' of Radio Pulsar J1819+1305

We present a single-pulse study of the four-component pulsar J1819+1305, whose ``null'' pulses bunch at periodic intervals of around 57 times the rotation period. The emission bursts between the null bunches exhibit characteristic modulations at two shorter periodicities of approximately 6.2 and 3 times the rotation period, the former found largely in the two outer components, and the latter only in the first component. Many bursts commence with bright emission in second component, exhibit positive six-period drift across the full profile width, and end with 3-period modulation in the leading component. The 57-period cycle can be modelled geometrically as a sparsely filled subbeam carousel with nulls appearing whenever our line of sight intersects a circulating empty region. This interpretation is compatible with other recent evidence for periodic, carousel-related nulling and appears to support the physics of a polar-gap emission model for ``drifting'' subpulses, but the subtle structure of the emission bursts defies an easy explanation.Comment: 8 pages, 9 figure

Exploring Deep Learning for deformative operators in vector-based cartographic road generalization

Cartographic generalisation is the process by which geographical data is simplified and abstracted to increase the legibility of maps at reduced scales. As map scales decrease, irrelevant map features are removed (selective generalisation), and relevant map features are deformed, eliminating unnec- essary details while preserving the general shapes (deformative generalisation). The automation of cartographic generalisation has been a tough nut to crack for years because it is governed not only by explicit rules but also by a large body of implicit cartographic knowledge that conven- tional automation approaches struggle to acquire and formalise. In recent years, the introduction of Deep Learning (DL) and its inductive capabilities has raised hope for further progress. This thesis explores the potential of three Deep Learning architectures — Graph Convolutional Neural Network (GCNN), Auto Encoder, and Recurrent Neural Network (RNN) — in their application on the deformative generalisation of roads using a vector-based approach. The generated small- scale representations of the input roads differ substantially across the architectures, not only in their included frequency spectra but also in their ability to apply certain generalisation operators. However, the most apparent learnt and applied generalisation operator by all architectures is the smoothing of the large-scale roads. The outcome of this thesis has been encouraging but suggests to pursue further research about the effect of the pre-processing of the input geometries and the inclusion of spatial context and the combination of map features (e.g. buildings) to better capture the implicit knowledge engrained in the products of mapping agencies used for training the DL models

Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps