Probing the surface magnetic field structure in RX J1856.5-3754

The evolution of magnetic field in isolated neutron stars is one of the most important ingredients in the attempt to build a unified description of these objects. A prediction of field evolution models is the existence of an equilibrium configuration, in which the Hall cascade vanishes. Recent calculations have explored the field structure in this stage, called the Hall attractor. We use X-ray data of near-by, cooling neutron stars to probe this prediction, as these sources are surmised to be close to or at Hall attractor phase. We show that the source RX J1856.5-3754 might be closer to the attractor than other sources of its class. Our modelling indicates that the properties of surface thermal emission, assuming that the star is in the Hall attractor, are in contradiction with the spectral data of RX J1856.5-3754.Comment: 9 pages, accepted to MNRA

Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

Transient heat flux measurement using a surface junction thermocouple

A new form of surface junction thermocouple sensor has been developed and tested. The novel feature of the design is the use of a tapered fit between two coaxial thermocouple elements to form a thin, robust junction. The gauge has a response time on the order of 1 µs and is suitable for measuring large transient heat fluxes in hypervelocity wind tunnels. Asymptotic analysis is used to demonstrate the operating principles and to assess the errors associated with the finite thickness of the surface junction. Spectral deconvolution methods are used to infer a mean square optimal estimate of the surface heat flux from time resolved surface temperature measurements. This improved signal processing method is applicable to transient heat flux gauges of all types. Potential reducible error sources and other systematic errors are described. Measurements of the heat flux about the forebody of a cylindrical body in a hypervelocity flow demonstrate the functioning of the gauge and are used to obtain statistical estimates of the repeatability of the technique. The measured heat fluxes are compared with established theoretical predictions