Spark Model for Pulsar Radiation Modulation Patterns

A non-stationary polar gap model first proposed by Ruderman & Sutherland (1975) is modified and applied to spark-associated pulsar emission at radio wave-lengths. It is argued that under physical and geometrical conditions prevailing above pulsar polar cap, highly non-stationary spark discharges do not occur at random positions. Instead, sparks should tend to operate in well determined preferred regions. At any instant the polar cap is populated as densely as possible with a number of two-dimensional sparks with a characteristic dimension as well as a typical distance between adjacent sparks being about the polar gap height. Our model differs, however, markedly from its original 'hollow cone' version. The key feature is the quasi-central spark driven by pair production process and anchored to the local pole of a sunspot-like surface magnetic field. This fixed spark prevents the motion of other sparks towards the pole, restricting it to slow circumferential drift across the planes of field lines converging at the local pole. We argue that the polar spark constitutes the core pulsar emission, and that the annular rings of drifting sparks contribute to conal components of the pulsar beam. We found that the number of nested cones in the beam of typical pulsar should not excced three; a number also found by Mitra & Deshpande (1999) using a completely different analysis.Comment: 31 pages, 8 figures, accepted by Ap

Time-scales of Radio Emission in PSR J0437-4715 at 327 MHz

Time-scales of radio emission are studied in PSR J0437-4715 at 327 MHz using almost half a million periods of high quality data from Ooty Radio Telescope. The radio emission in this milli second pulsar occurs on a short (s) time-scale of approximately 0.026 +- 0.001 periods, and on a (l) time-scale that is much longer than the widths of the components of the integrated profile (approximately 0.05 periods). The width of the s emission increases with its increasing relative contribution to the total radio emission. This may provide constraints for the details of discharge of vacuum gaps above pulsar polar caps. The s emission occasionally takes place in the form of intense spikes, which are confined to the main component of the integrated profile for 90 per cent of the time. The positions of spikes within a component of the integrated profile have no simple relation to the shape of that component. This may have impact on the interpretation of the integrated profile components in terms of independent regions of emission on the polar cap.Comment: Accepted for publication in Vol 543 (1 Nov 2000) of The Astrophysical Journa

Frequency dependence of pulsar radiation patterns

We report on new results from simultaneous, dual frequency, single pulse observation of PSR B0329+54 using the Giant Metrewave Radio Telescope. We find that the longitude separation of subpulses at two different frequencies (238 and 612 MHz) is less than that for the corresponding components in the average profile. A similar behaviour has been noticed before in a number of pulsars. We argue that subpulses are emitted within narrow flux tubes of the dipolar field lines and that the mean pulsar beam has a conal structure. In such a model the longitudes of profile components are determined by the intersection of the line of sight trajectory with subpulse-associated emission beams. Thus, we show that the difference in the frequency dependence of subpulse and profile component longitudes is a natural property of the conal model of pulsar emission beam. We support our conclusions by numerical modelling of pulsar emission, using the known parameters for this pulsar, which produce results that agree very well with our dual frequency observations.Comment: 24 pages, 8 figures. Accepted for publication in Ap

Spot-like Structures of Neutron Star Surface Magnetic Fields

There is growing evidence, based on both X-ray and radio observations of isolated neutron stars, that besides the large--scale (dipolar) magnetic field, which determines the pulsar spin--down behaviour, small--scale poloidal field components are present, which have surface strengths one to two orders of magnitude larger than the dipolar component. We argue in this paper that the Hall--effect can be an efficient process in producing such small--scale field structures just above the neutron star surface. It is shown that due to a Hall--drift induced instability, poloidal magnetic field structures can be generated from strong subsurface toroidal fields, which are the result of either a dynamo or a thermoelectric instability acting at early times of a neutron star's life. The geometrical structure of these small--scale surface anomalies of the magnetic field resembles that of some types of ``star--spots''. The magnetic field strength and the length--scales are comparable with values that can be derived from various observations.Comment: 4 pages, 2 figures, accepted by Astronomy & Astrophysics Letters; language improved, 2nd para of Sect. 3 change

Asymptotic approximations to the nodes and weights of Gauss-Hermite and Gauss-Laguerre quadratures

Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a standalone method of computation of Gaussian quadratures for high enough degrees, with Gaussian weights computed from asymptotic approximations for the orthogonal polynomials. We provide numerical evidence showing that for degrees greater than $100$ the asymptotic methods are enough for a double precision accuracy computation ($15$-$16$ digits) of the nodes and weights of the Gauss--Hermite and Gauss--Laguerre quadratures.Comment: Submitted to Studies in Applied Mathematic

Computation of the Marcum Q-function

Methods and an algorithm for computing the generalized Marcum $Q-$function ($Q_{\mu}(x,y)$) and the complementary function ($P_{\mu}(x,y)$) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory, where they are called the non-central chi-square or the non central gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to $10^{-12}$ can be obtained in the parameter region $(x,y,\mu) \in [0,\,A]\times [0,\,A]\times [1,\,A]$, $A=200$, while for larger parameters the accuracy decreases (close to $10^{-11}$ for $A=1000$ and close to $5\times 10^{-11}$ for $A=10000$).Comment: Accepted for publication in ACM Trans. Math. Soft

Discovery of a remarkable subpulse drift pattern in PSR B0818-41

We report the discovery of a remarkable subpulse drift pattern in the relatively less studied wide profile pulsar, B0818-41, using high sensitivity GMRT observations. We find simultaneous occurrence of three drift regions with two different drift rates: an inner region with steeper apparent drift rate flanked on each side by a region of slower apparent drift rate. Furthermore, these closely spaced drift bands always maintain a constant phase relationship. Though these drift regions have significantly different values for the measured P2, the measured P3 value is the same and equal to 18.3 P1. We interpret the unique drift pattern of this pulsar as being created by the intersection of our line of sight (LOS) with two conal rings on the polar cap of a fairly aligned rotator (inclination angle alpha ~ 11 deg), with an ``inner'' LOS geometry (impact angle beta ~ -5.4 deg). We argue that both the rings have the same values for the carousel rotation periodicity P4 and the number of sparks Nsp. We find that Nsp is 19-21 and show that it is very likely that, P4 is the same as the measured P3, making it a truly unique pulsar. We present results from simulations of the radiation pattern using the inferred parameters, that support our interpretations and reproduce the average profile as well as the observed features in the drift pattern quite well.Comment: 5 pages and 7 figures, Accepted for publication in MNRAS Letter

Alaska mining and water quality

The Institute of Water Resources has sought financial assistance for some time in an attempt to initiate research relative to the impact of mining on water quality. Attempts were made as early as 1971 by Dr. Timothy Tilsworth and later by Dr. Donald Cook and Dr. Sage Murphy. These investigators anticipated growth in placer gold mining and the development of natural resources in Alaska during a period of national and environmental concern. The subsequent energy "crisis," the major increase in the price of gold on the world market, and dwindling nonrenewable resource supplies have resulted in large-scale mineral exploration in Alaska. This exploration, coupled with development of the trans-Alaska oil pipeline, has attracted considerable capital for potential investment and development in Alaska. Expected industrial growth has already started and major new projects are "just around the corner." Yet, as of 1976, no major research effort has occurred to determine the extent of or potential for water quality impacts from mining operations in Alaska. Recently a series of interdisciplinary research projects have been completed in Canada; however, the application of Canadian data to Alaskan problems is uncertain. Although, state and federal government agencies have been advised and are aware of this potential problem and lack of baseline data they have not sought out new information or rational solutions. Even now, with deadlines of Public Law 92-500 at hand, some regulatory agencies give the impression of attempting to ignore the situation. Interim limitations are proposed and permits are issued with no discernible rationale or basis. Data have not been obtained relative to the Alaskan mining operations and thus are not available for use in seeking solutions compatible with mining and environmental protection. Numbers appear to have been arbitrarily assigned to permits and water quality standards. When permits are issued, self-monitoring requirements are negligible or nonexistent. Nor have regulatory agencies demonstrated the ability or inclination to monitor mining operations or enforce permits and water quality standards. It was hoped that the project would bring together miners, environmentalists, and regulators in a cooperative effort to identify the problems and seek solutions. The investigators recognized the political sensitivity of the subject matter but proceeded optimistically. Relatively good cooperation, though not total, occurred early in the project. In April 1976, a symposium was held to exchange ideas and determine the state-of-the-art. Although the symposium had good attendance and an exchange of information occurred, the symposium itself was somewhat of a disappointment. With few exceptions, the participants aligned on one side or the other in preconceived fixed positions. Some even chose not to attend and were therefore able to avoid the issues. Little hard data was presented. Optimistically, some of the miners, environmentalists, and regulators are prepared to resolve their differences. This report, hopefully, will be of benefit to them. It is our experience that miners and environmentalists share a love of the land that is uniquely Alaska. We feel that technology is available for application to this problem for those who care about doing the job right in the "last frontier." Whether or not it will be effectively applied to protect Alaska's water resources is a question which remains unanswered.The work upon which this report is based was supported in part by funds provided by the United States Department of the Interior, Office of Water Resources Research Act of 1964, Public Law 88-379, as amended (Project A-055-ALAS)