Toward a unified light curve model for multi-wavelength observations of V1974 Cygni (Nova Cygni 1992)

We present a unified model for optical, ultraviolet (UV), and X-ray light curves of V1974 Cygni (Nova Cygni 1992). Based on an optically thick wind model of nova outbursts, we have calculated light curves and searched for the best fit model that is consistent with optical, UV, and X-ray observations. Our best fit model is a white dwarf (WD) of mass 1.05 M_\sun with a chemical composition of X=0.46, C+N+O=0.15, and Ne = 0.05 by mass weight. Both supersoft X-ray and continuum UV 1455 \AA light curves are well reproduced. Supersoft X-rays emerged on day ~ 250 after outburst, which is naturally explained by our model: our optically thick winds cease on day 245 and supersoft X-rays emerge from self-absorption by the winds. The X-ray flux keeps a constant peak value for ~ 300 days followed by a quick decay on day ~ 600. The duration of X-ray flat peak is well reproduced by a steady hydrogen shell burning on the WD. Optical light curve is also explained by the same model if we introduce free-free emission from optically thin ejecta. A t^{-1.5} slope of the observed optical and infrared fluxes is very close to the slope of our modeled free-free light curve during the optically thick wind phase. Once the wind stops, optical and infrared fluxes should follow a t^{-3} slope, derived from a constant mass of expanding ejecta. An abrupt transition from a t^{-1.5} slope to a t^{-3} slope at day ~ 200 is naturally explained by the change from the wind phase to the post-wind phase on day ~ 200. The development of hard X-ray flux is also reasonably understood as shock-origin between the wind and the companion star. The distance to V1974 Cyg is estimated to be ~ 1.7 kpc with E(B-V)= 0.32 from the light curve fitting for the continuum UV 1455 \AA.Comment: 8 pages, 4 figures, to appear in the Astrophysical Journa

A combinatorial Li-Yau inequality and rational points on curves

We present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field.We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-called finite harmonic graph morphisms to trees, that originate from any refinement of the dual graph of the stable model of the curve. Next comes our main result: we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the Laplacian and some “volume” of the original graph; this can be seen as a substitute for graphs of the Li–Yau inequality from differential geometry, although we also prove that the strict analogue of the original inequality fails for general graphs. Finally,we apply the results to give a lower bound for the gonality of arbitraryDrinfeld modular curves over finite fields and for general congruence subgroups Γ of Γ (1) that is linear in the index [Γ (1) : Γ ], with a constant that only depends on the residue field degree and the degree of the chosen “infinite” place. This is a function field analogue of a theorem of Abramovich for classical modular curves. We present applications to uniform boundedness of torsion of rank two Drinfeld modules that improve upon existing results, and to lower bounds on the modular degree of certain elliptic curves over function fields that solve a problem of Papikian

Coulomb analogy for nonhermitian degeneracies near quantum phase transitions

Degeneracies near the real axis in a complex-extended parameter space of a hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.Comment: 4 page

Norm kernels and the closeness relation for Pauli-allowed basis functions

The norm kernel of the generator-coordinate method is shown to be a symmetric kernel of an integral equation with eigenfunctions defined in the Fock--Bargmann space and forming a complete set of orthonormalized states (classified with the use of SU(3) symmetry indices) satisfying the Pauli exclusion principle. This interpretation allows to develop a method which, even in the presence of the SU(3) degeneracy, provides for a consistent way to introduce additional quantum numbers for the classification of the basis states. In order to set the asymptotic boundary conditions for the expansion coefficients of a wave function in the SU(3) basis, a complementary basis of functions with partial angular momenta as good quantum numbers is needed. Norm kernels of the binary systems 6He+p, 6He+n, 6He+4He, and 8He+4He are considered in detail.Comment: 25 pages; submitted to Few-Body System