Jet and counter-jet in transonic pulsar wind nebulae

X-ray observations show that a jet and a counter-jet in pulsar wind nebulae often differ one from another. Sometimes one of the jets is not observed at all. We show that the most likely reason for this difference is the relative motion of a pulsar and an ambient matter. Even the slow (subsonic or transonic) ambient matter stream in the pulsar rest frame strongly affects the jets, making the windward jet bright and dynamic, and the leeward jet dim and diffuse. The effect is illustrated using a relativistic MHD model of a double-torus pulsar wind nebula. The model is shown to explain reasonably well the observational appearance of the jets in the Vela nebula - a double-torus object which evolves in a transonic stream initiated by the passage of the reverse shock of the parent supernova.

Constraining the geometry of PSR J0855−4644: A nearby pulsar wind nebula with double torus/jet morphology

Aims. PSR J0855−4644 is a fast-spinning, energetic pulsar discovered at radio wavelengths near the south-eastern rim of the supernova remnant RX J0852.0−4622. A follow-up XMM-Newton observation revealed the X-ray counterpart of the pulsar and a slightly asymmetric pulsar wind nebula, which suggests possible jet structures. Lying at a distance d ≤ 900 pc, PSR J0855−4644 is a pulsar with one of the highest Ė/d2 from which no GeV γ-ray pulsations have been detected. With a dedicated Chandra observation we aim to further resolve the possible jet structures of the nebula and study the pulsar geometry to understand the lack of γ-ray pulsations. Methods. We performed detailed spatial modelling to constrain the geometry of the pulsar wind nebula and in particular the pulsar line of sight (observer angle) ζPSR, which is defined as the angle between the direction of the observer and the pulsar spin axis. We also performed geometric radio and γ-ray light-curve modelling using a hollow-cone radio beam model together with two-pole caustic and outer gap models to further constrain ζPSR and the magnetic obliquity α defined as the angle between the magnetic and spin axes of the pulsar. Results. The Chandra observation reveals that the compact XMM source, thought to be the X-ray pulsar, can be further resolved into a point source surrounded by an elongated axisymmetric nebula with a longitudinal extent of 10′′. The pulsar flux represents only ~1% of the XMM compact source, and its spectrum is well described by a blackbody of temperature kT = 0.2 keV, while the surrounding nebula has a much harder spectrum (Γ = 1.1 for a power-law model). Assuming the origin of the extended emission is a double torus yields ζPSR = 32.5° ± 4.3°. The detection of thermal X-rays from the pulsar may point to a low value of | ζ−α | if this emission originates from a heated polar cap. Independent constraints from geometric light-curve modelling yield α ≲ 55° and ζ ≲ 55°, and 10° ≲ | ζ−α | ≲ 30°. A χ2 fit to the radio light curve yields a best fit at (α,ζPSR) = (22°,8°), with an alternative fit at (α,ζPSR) = (9°,25°) within 3σ. The lack of non-thermal X-ray emission from the pulsar further supports low values for α and ζ under the assumption that X-rays and γ-rays are generated in the same region of the pulsar magnetosphere. Such a geometry would explain, in the standard caustic pulsar model picture, the radio-loud and γ-ray-quiet behaviour of this high Ė/d2 pulsar.

Derrida's Limits: Aporias between ‘Ousia and Grammē’

This essay considers the ‘limit’ in Derrida's work from the early consideration of linearisation in ‘Ousia and Grammē’ to the conception of limit as aporia in Aporias. Developing Derrida's tripartite definition of the limit via a reading of Being and Time as closure, border and demarcation, the essay then considers the earlier presentation of limit in Heidegger as temporal primordiality. Developing the metaphysics of line as presentation of presence in terms of Aristotle's aporetics of time as line, the circle is then considered as representing the closed field of presence and its definition via the negation of being's other. This leads to Derrida's early, foundational definition of the law of metaphysics as submission-subtraction, and his proposal of the trace as an alternate way of thinking spatially about being, nonbeing and difference. The second half of the essay then proposes a series of alternative ways of thinking geometrically to those of the traditional metaphysics of point-line-circle topography. Thus topology is proposed as an alternate means of thinking field enclosure, similarity and difference. The figures of the double torus and mathematical limit are proposed as a potential alternative geometry for Western thought. Finally the essay concludes on the apotropaic logic of the problem which echoes that of the trace and is developed in contradistinction to the aporia. Proposing the edge as an interim state between the metaphysics of the line and the deconstructive impossibilities of the aporia, it suggests that the limits of metaphysics are to be found not merely in the apotropaic law of submission-subtraction, but also across alternate geometries which facilitate the bringing together of the two central elements of the totality of Derrida's thinking the limit: différance and singularity.

On the Genus Distribution of $(p,q,n)$-Dipoles

There are many applications of the enumeration of maps in surfaces to other areas of mathematics and the physical sciences. In particular, in quantum field theory and string theory, there are many examples of occasions where it is necessary to sum over all the Feynman graphs of a certain type. In a recent paper of Constable et al. on pp-wave string interactions, they must sum over a class of Feynman graphs which are equivalent to what we call $(p,q,n)$-dipoles. In this paper we perform a combinatorial analysis that gives an exact formula for the number of $(p,q,n)$-dipoles in the torus (genus 1) and double torus (genus 2).