The Stellar Activity - Rotation Relationship

Using a new catalog of 824 solar and late-type stars with X-ray luminosities and rotation periods we have studied the relationship between rotation and stellar activity. From an unbiased subset of this sample the power law slope of the unsaturated regime, $L_X/L_{bol}\propto Ro^\beta$, is fit as $\beta=-2.70\pm0.13$. This is inconsistent with the canonical $\beta=-2$ slope to a confidence of 5$\sigma$ and argues for an interface-type dynamo. Super-saturation is observed for the fastest rotators in our sample and its parametric dependencies are explored. Significant correlations are found with both the corotation radius and the excess polar updraft, the latter theory being supported by other observations. We also present a new X-ray population synthesis model of the mature stellar component of our Galaxy and use it to reproduce deep observations of a high Galactic latitude field. The model, XStar, can be used to test models of stellar spin-down and dynamo decay, as well as for estimating stellar X-ray contamination rates for non-stellar studies.Comment: 4 pages, 4 figures. To appear in the proceedings of Cool Stars 17: 17th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, AN 334, 1-2, Eds Klaus Strassmeier and Mercedes Lopez-Morale

An explanation of the Newman-Janis Algorithm

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

The Effects of Turbulence on Three-Dimensional Magnetic Reconnection at the Magnetopause

Two- and three-dimensional particle-in-cell simulations of a recent encounter of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion region at the magnetopause are presented. While the two-dimensional simulation is laminar, turbulence develops at both the x-line and along the magnetic separatrices in the three-dimensional simulation. The turbulence is strong enough to make the magnetic field around the reconnection island chaotic and produces both anomalous resistivity and anomalous viscosity. Each contribute significantly to breaking the frozen-in condition in the electron diffusion region. A surprise is that the crescent-shaped features in velocity space seen both in MMS observations and in two-dimensional simulations survive, even in the turbulent environment of the three-dimensional system. This suggests that MMS's measurements of crescent distributions do not exclude the possibility that turbulence plays an important role in magnetopause reconnection.Comment: Revised version accepted by GR

An Algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations of projective planes and affine planes. We present an algorithm for constructing a projective Hjelmslev planes and affine Hjelsmelv planes using projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv planes can be constructed in this way. As a corollary it is shown that all 2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014, Springer Proceedings in Mathematics & Statistics 13