How realistic are solar model atmospheres?

Recently, new solar model atmospheres have been developed to replace classical 1D LTE hydrostatic models and used to for example derive the solar chemical composition. We aim to test various models against key observational constraints. In particular, a 3D model used to derive the solar abundances, a 3D MHD model (with an imposed 10 mT vertical magnetic field), 1D models from the PHOENIX project, the 1D MARCS model, and the 1D semi-empirical model of Holweger & M\"uller. We confront the models with observational diagnostics of the temperature profile: continuum centre-to-limb variations (CLV), absolute continuum fluxes, and the wings of hydrogen lines. We also test the 3D models for the intensity distribution of the granulation and spectral line shapes. The predictions from the 3D model are in excellent agreement with the continuum CLV observations, performing even better than the Holweger & M\"uller model (constructed largely to fulfil such observations). The predictions of the 1D theoretical models are worse, given their steeper temperature gradients. For the continuum fluxes, predictions for most models agree well with the observations. No model fits all hydrogen lines perfectly, but again the 3D model comes ahead. The 3D model also reproduces the observed continuum intensity fluctuations and spectral line shapes very well. The excellent agreement of the 3D model with the observables reinforces the view that its temperature structure is realistic. It outperforms the MHD simulation in all diagnostics, implying that recent claims for revised abundances based on MHD modelling are premature. Several weaknesses in the 1D models are exposed. The differences between the PHOENIX LTE and NLTE models are small. We conclude that the 3D hydrodynamical model is superior to any of the tested 1D models, which gives further confidence in the solar abundance analyses based on it.Comment: 17 pages, 15 figures. Accepted for publication in A&

Spectral degeneracy and escape dynamics for intermittent maps with a hole

We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron-Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds, and demonstrate $L^1$ convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations.Comment: 34 page

A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

Eigenfunctions for smooth expanding circle maps

We construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.Comment: 10 pages, 2 figure

Can we trust elemental abundances derived in late-type giants with the classical 1D stellar atmosphere models?

We compare the abundances of various chemical species as derived with 3D hydrodynamical and classical 1D stellar atmosphere codes in a late-type giant characterized by T_eff=3640K, log g = 1.0, [M/H] = 0.0. For this particular set of atmospheric parameters the 3D-1D abundance differences are generally small for neutral atoms and molecules but they may reach up to 0.3-0.4 dex in case of ions. The 3D-1D differences generally become increasingly more negative at higher excitation potentials and are typically largest in the optical wavelength range. Their sign can be both positive and negative, and depends on the excitation potential and wavelength of a given spectral line. While our results obtained with this particular late-type giant model suggest that 1D stellar atmosphere models may be safe to use with neutral atoms and molecules, care should be taken if they are exploited with ions.Comment: Poster presented at the IAU Symposium 265 "Chemical Abundances in the Universe: Connecting First Stars to Planets", Rio de Janeiro, 10-14 August 2009; 2 pages, 1 figur

Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show unexpected smooth oscillations with a period growing logarithmically and can be fitted assuming corrections to the scaling laws with complex exponents.Comment: 10 pages, Latex , uses revtex. 2 figures not included (hard copies available on request

A Two-Parameter Recursion Formula For Scalar Field Theory

We present a two-parameter family of recursion formulas for scalar field theory. The first parameter is the dimension $(D)$. The second parameter ($\zeta$) allows one to continuously extrapolate between Wilson's approximate recursion formula and the recursion formula of Dyson's hierarchical model. We show numerically that at fixed $D$, the critical exponent $\gamma$ depends continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a guide to construct improved recursion formulas.Comment: 7 pages, uses Revtex, one Postcript figur

On the spectrum of Farey and Gauss maps

In this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced version, the Gauss map, respectively. By means of a suitable operator-valued power series we are able to study simultaneously the spectrum of both these operators along with the analytic properties of the associated dynamical zeta functions.Comment: 23 page

Dual Fronts Propagating into an Unstable State

The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into {\em two} fronts propagating with {\em different} velocities was observed numerically in a magnetic system. The intermediate state is unstable and grows linearly in time. We first establish rigorously the existence of this phenomenon, called ``dual front,'' for a class of structurally unstable one-component models. Then we use this insight to explain dual fronts for a generic two-component reaction-diffusion system, and for the magnetic system.Comment: 19 pages, Postscript, A