Improvement of solar cycle prediction: Plateau of solar axial dipole moment

Aims. We report the small temporal variation of the axial dipole moment near the solar minimum and its application to the solar cycle prediction by the surface flux transport (SFT) model. Methods. We measure the axial dipole moment using the photospheric synoptic magnetogram observed by the Wilcox Solar Observatory (WSO), the ESA/NASA Solar and Heliospheric Observatory Michelson Doppler Imager (MDI), and the NASA Solar Dynamics Observatory Helioseismic and Magnetic Imager (HMI). We also use the surface flux transport model for the interpretation and prediction of the observed axial dipole moment. Results. We find that the observed axial dipole moment becomes approximately constant during the period of several years before each cycle minimum, which we call the axial dipole moment plateau. The cross-equatorial magnetic flux transport is found to be small during the period, although the significant number of sunspots are still emerging. The results indicates that the newly emerged magnetic flux does not contributes to the build up of the axial dipole moment near the end of each cycle. This is confirmed by showing that the time variation of the observed axial dipole moment agrees well with that predicted by the SFT model without introducing new emergence of magnetic flux. These results allows us to predict the axial dipole moment in Cycle 24/25 minimum using the SFT model without introducing new flux emergence. The predicted axial dipole moment of Cycle 24/25 minimum is 60--80 percent of Cycle 23/24 minimum, which suggests the amplitude of Cycle 25 even weaker than the current Cycle 24. Conclusions. The plateau of the solar axial dipole moment is an important feature for the longer prediction of the solar cycle based on the SFT model.Comment: 5 pages, 3 figures, accepted for publication in A&A Lette

Self-Consistent MHD Modeling of a Coronal Mass Ejection, Coronal Dimming, and a Giant Cusp-Shaped Arcade Formation

We performed magnetohydrodynamic simulation of coronal mass ejections (CMEs) and associated giant arcade formations, and the results suggested new interpretations of observations of CMEs. We performed two cases of the simulation: with and without heat conduction. Comparing between the results of the two cases, we found that reconnection rate in the conductive case is a little higher than that in the adiabatic case and the temperature of the loop top is consistent with the theoretical value predicted by the Yokoyama-Shibata scaling law. The dynamical properties such as velocity and magnetic fields are similar in the two cases, whereas thermal properties such as temperature and density are very different.In both cases, slow shocks associated with magnetic reconnectionpropagate from the reconnection region along the magnetic field lines around the flux rope, and the shock fronts form spiral patterns. Just outside the slow shocks, the plasma density decreased a great deal. The soft X-ray images synthesized from the numerical results are compared with the soft X-ray images of a giant arcade observed with the Soft X-ray Telescope aboard {\it Yohkoh}, it is confirmed that the effect of heat conduction is significant for the detailed comparison between simulation and observation. The comparison between synthesized and observed soft X-ray images provides new interpretations of various features associated with CMEs and giant arcades.Comment: 39 pages, 18 figures. Accepted for publication in the Astrophysical Journal. The PDF file with high resplution figures can be downloaded from http://www.kwasan.kyoto-u.ac.jp/~shiota/study/ApJ62426.preprint.pdf

Acute Geometric Changes of the Mitral Annulus after Coronary Occlusion: A Real-Time 3D Echocardiographic Study

We performed real-time 3D echocardiography in sixteen sheep to compare acute geometric changes in the mitral annulus after left anterior descending coronary artery (LAD, n=8) ligation and those after left circumflex coronary artery (LCX, n=8) ligation. The mitral regurgitation (MR) was quantified by regurgitant volume (RV) using the proximal isovelocity surface area method. The mitral annulus was reconstructed through the hinge points of the annulus traced on 9 rotational apical planes (angle increment=20°). Mitral annular area (MAA) and the ratio of antero-posterior (AP) to commissure-commissure (CC) dimension of the annulus were calculated. Non-planar angle (NPA) representing non-planarity of the annulus was measured. After LCX occlusion, there were significant increases of the MAA during both early and late systole (p<0.01) with significant MR (RV: 30±14 mL), while there was neither a significant increase of MAA, nor a significant MR (RV: 4±5 mL) after LAD occlusion. AP/CC ratio (p<0.01) and NPA (p<0.01) also significantly increased after LCX occlusion during both early and late systole. The mitral annulus was significantly enlarged in the antero-posterior direction with significant decrease of non-planarity compared to LAD occlusion immediately after LCX occlusion

Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral

In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the reciprocal of the order of the automorphism group of a tiling of a Riemann surface. The second method is based on the classical analysis of orthogonal polynomials. A rigorous asymptotic method is established, and a special case of the matrix integral is computed in terms of the Riemann $\zeta$-function. The third method is derived from a formula for the $\tau$-function solution to the KP equations. This method leads us to a new class of solutions of the KP equations that are \emph{transcendental}, in the sense that they cannot be obtained by the celebrated Krichever construction and its generalizations based on algebraic geometry of vector bundles on Riemann surfaces. In each case a mathematically rigorous way of dealing with asymptotic series in an infinite number of variables is established