On soft capacities, quasi-stationary distributions and the pathwise approach to metastability

Motivated by the study of the metastable stochastic Ising model at subcritical temperature and in the limit of a vanishing magnetic field, we extend the notion of ($\kappa$, $\lambda$)-capacities between sets, as well as the associated notion of soft-measures, to the case of overlapping sets. We recover their essential properties, sometimes in a stronger form or in a simpler way, relying on weaker hypotheses. These properties allow to write the main quantities associated with reversible metastable dynamics, e.g. asymptotic transition and relaxation times, in terms of objects that are associated with two-sided variational principles. We also clarify the connection with the classical "pathwise approach" by referring to temporal means on the appropriate time scale.Comment: 29 pages, 1 figur

Thermodynamic Limit for Mean-Field Spin Models

If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$\omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2})$$ for every decomposition $N_1+N_2=N$, then its free energy density increases with $N$. We prove such a condition for a wide class of spin models which includes the Curie-Weiss model, its p-spin generalizations (for both even and odd p), its random field version and also the finite pattern Hopfield model. For all these cases the existence of the thermodynamic limit by subadditivity and boundedness follows.Comment: 15 pages, few improvements. To appear in MPE

Monte Carlo Predictions of Far-Infrared Emission from Spiral Galaxies

We present simulations of Far Infrared (FIR) emission by dust in spiral galaxies, based on the Monte Carlo radiative transfer code of Bianchi, Ferrara & Giovanardi (1996). The radiative transfer is carried out at several wavelength in the Ultraviolet, optical and Near Infrared, to cover the range of the stellar Spectral Energy Distribution (SED). Together with the images of the galactic model, a map of the energy absorbed by dust is produced. Using Galactic dust properties, the spatial distribution of dust temperature is derived under the assumption of thermal equilibrium. A correction is applied for non-equilibrium emission in the Mid Infrared. Images of dust emission can then be produced at any wavelength in the FIR. We show the application of the model to the spiral galaxy NGC 6946. The observed stellar SED is used as input and models are produced for different star-dust geometries. It is found that only optically thick dust disks can reproduce the observed amount of FIR radiation. However, it is not possible to reproduce the large FIR scalelength suggested by recent observation of spirals at 200 um, even when the scalelength of the dust disk is larger than that for stars. Optically thin models have ratios of optical/FIR scalelengths closer to the 200um observations, but with smaller absolute scalelengths than optically thick cases. The modelled temperature distributions are compatible with observations of the Galaxy and other spirals. We finally discuss the approximations of the model and the impact of a clumpy stellar and dust structure on the FIR simulations.Comment: 19 pages, 6 figures, accepted by A&

The broad-band X-ray spectrum of the Seyfert 1 galaxy, MCG+8-11-11

We present a long (100 ks) Suzaku observation of one of the X-ray brightest AGN, MCG+8-11-11. These data were complemented with the 54-month Swift BAT spectrum, allowing us to perform a broad-band fit in the 0.6-150 keV range. The fits performed in the 0.6-10 keV band give consistent results with respect to a previous XMM-Newton observation, i.e. the lack of a soft excess, warm absorption along the line of sight, a large Compton reflection component (R~1) and the absence of a relativistic component of the neutral iron K$\alpha$ emission line. However, when the PIN and Swift BAT data are included, the reflection amount drops significantly (R~0.2-0.3), and a relativistic iron line is required, the latter confirmed by a phenomenological analysis in a restricted energy band (3-10 keV). When a self-consistent model is applied to the whole broadband data, the observed reflection component appears to be all associated to the relativistic component of the iron K$\alpha$ line. The resulting scenario, though strongly model-dependent, requires that all the reprocessing spectral components from Compton-thick material must be associated to the accretion disc, and no evidence for the classical pc-scale torus is found. The narrow core of the neutral iron K$\alpha$ line is therefore produced in a Compton-thin material, like the BLR, similarly to what found in another Seyfert galaxy, NGC7213, but with the notable difference that MCG+8-11-11 presents spectral signatures from an accretion disc. The very low accretion rate of NGC7213 could explain the lack of relativistic signatures in its spectrum, but the absence of the torus in both sources is more difficult to explain, since their luminosities are comparable, and their accretion rates are completely different.Comment: 8 pages, 6 figure, accepted for publication in Astronomy and Astrophysic

Four dimensional Lie symmetry algebras and fourth order ordinary differential equations

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.Comment: 12 page