X-Ray Evidence of an AGN in M82

An X-ray spectrum of the famous starburst galaxy M82 consists of three components: soft, medium, and hard components (Tsuru et al. 1997). The spectrum of the hard component, which is spatially unresolved, is well represented by an absorbed thermal bremsstrahlung, or an absorbed power-law model. However the origin of the hard component was unclear. Thus, we made a monitoring observation with ASCA in 1996. Although the X-ray flux of the soft and medium components remained constant, a significant time variability of the hard component was found between $3\times10^{40}$ erg/s and $1\times10^{41}$ erg/s at various time scales from 10 ks to a month. The temperature or photon index of the hard component also changed. We proved that the spatial position of the hard component is the center of M82. The spectrum of the variable source obtained by subtracting the spectrum of the lowest state from the highest state suggests the strong absorption of $N_{\rm H} \sim 10^{22}$ cm$^2$, which means the variable source is embedded in the center of M82. All these suggest that a low-luminosity AGN exists in M82.Comment: 15pages for text and tables. 13pages for figure

Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.Comment: Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figure

ASCA observations of massive medium-distant clusters of galaxies. II

We have selected seven medium-distant clusters of galaxies (z ~ 0.1 - 0.3) for multi-wavelength observations with the goal of investigating their dynamical state. Following Paper I (Pierre et al. 1999) which reported the ASCA results about two of them, we present here the analysis of the ASCA observations of the other five clusters; RXJ1023.8-2715 (A3444), RXJ1031.6-2607, RXJ1050.5-0236 (A1111), RXJ1203.2-2131(A1451), and RXJ1314.5-2517. Except for RXJ1031.6, whose X-ray emission turned out to be dominated by an AGN, the ASCA spectra are well fitted by a one-temperature thin thermal plasma model. We compare the temperature-luminosity relation of our clusters with that of nearby ones (z<0.1). Two clusters, RXJ1050.5 and RXJ1023.8, show larger luminosities than the bulk of clusters at similar temperatures, which suggests the presence of a cooling flow. The temperature vs. iron-abundance relationship of our sample is consistent with that of nearby clusters.Comment: 9 pages, 20 figures, A&AS in pres

Generalized β\beta-conformal change and special Finsler spaces

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.Comment: References added, some modifications are performed, LateX file, 24 page

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.Comment: 19 pages, LATEX file with 2 PS figure

Spontaneous Hall effect in chiral p-wave superconductor

In a chiral superconductor with broken time-reversal symmetry a ``spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution originates from the Bernoulli (or Lorentz) force from spontaneous currents running along the surfaces of the superconductor. The other contribution has a topological origin and is related to the intrinsic angular momentum of Cooper pairs. The latter can be described in terms of a Chern-Simons-like term in the low-energy field theory of the superconductor and has some similarities with the quantum Hall effect. The spontaneous Hall effect in a chiral superconductor is, however, non-universal. Our analysis is based on three approaches to the problem: a self-consistent solution of the Bogoliubov-de Gennes equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar is of order h/(e k_F\lambda)^2, where k_F is the Fermi wave vector and \lambda is the London penetration depth; the Hall resistance is substantially suppressed from a quantum unit of resistance. Experimental issues in measuring this effect are briefly discussed.Comment: 22 pages including 12 figure

On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Relic Abundances and the Boltzmann Equation

I discuss the validity of the quantum Boltzmann equation for the calculation of WIMP relic densities.Comment: 5 pages, no figures; talk given at Dark Matter 2000; an important reference is added in the revised versio