Resolved stellar population of distant galaxies in the ELT era

The expected imaging capabilities of future Extremely Large Telescopes (ELTs) will offer the unique possibility to investigate the stellar population of distant galaxies from the photometry of the stars in very crowded fields. Using simulated images and photometric analysis we explore here two representative science cases aimed at recovering the characteristics of the stellar populations in the inner regions of distant galaxies. Specifically: case A) at the center of the disk of a giant spiral in the Centaurus Group, (mu B~21, distance of 4.6 Mpc); and, case B) at half of the effective radius of a giant elliptical in the Virgo Cluster (mu~19.5, distance of 18 Mpc). We generate synthetic frames by distributing model stellar populations and adopting a representative instrumental set up, i.e. a 42 m Telescope operating close to the diffraction limit. The effect of crowding is discussed in detail showing how stars are measured preferentially brighter than they are as the confusion limit is approached. We find that (i) accurate photometry (sigma~0.1, completeness >90%) can be obtained for case B) down to I~28.5, J~27.5 allowing us to recover the stellar metallicity distribution in the inner regions of ellipticals in Virgo to within ~0.1 dex; (ii) the same photometric accuracy holds for the science case A) down to J~28.0, K~27.0, enabling to reconstruct of the star formation history up to the Hubble time via simple star counts in diagnostic boxes. For this latter case we discuss the possibility of deriving more detailed information on the star formation history from the analysis of their Horizontal Branch stars. We show that the combined features of high sensitivity and angular resolution of ELTs may open a new era for our knowledge of the stellar content of galaxies of different morphological type up to the distance of the Virgo cluster.Comment: 21 pages, 17 figures, PASP accepted in pubblicatio

Program logics for homogeneous meta-programming.

A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself. Meta-programming has been used extensively since macros were introduced to Lisp, yet we have little idea how formally to reason about metaprograms. This paper provides the first program logics for homogeneous metaprogramming – using a variant of MiniMLe by Davies and Pfenning as underlying meta-programming language.We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics

Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I

We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer operator is a perturbation of a normal one. Then the transfer operator is studied using methods of semi-classical analysis. In this paper we concentrate on the second step, the main technical result being a semi-classical estimate for powers of an integral operator which is approximately normal.Comment: 28 pp, improved the presentatio

A numerical investigation of the solution of a class of fourth-order eigenvalue problems

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied since it is known that this has an unbounded number of oscillations when approaching certain types of corners on domain boundaries. Recent computational results of Bjorstad & Tjostheim, using a highly accurate spectral Legendre-Galerkin method, have demonstrated that a number of these sign changes may be accurately computed on a square domain provided sufficient care is taken with the numerical method. We demonstrate that similar accuracy is also achieved using an unstructured finite-element solver which may be applied to problems on domains with arbitrary geometries. A number of results obtained from this mixed finite-element approach are then presented for a variety of domains. These include a family of circular sector regions, for which the oscillatory behaviour is studied as a function of the internal angle, and another family of (symmetric and non-convex) domains, for which the parity of the least eigenfunction is investigated. The paper not only verifies existing asymptotic theory, but also allows us to make a new conjecture concerning the eigenfunctions of the biharmonic operator