Hamilton-Jacobi Method and Gravitation

Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we possess the instruments to perform exact predictions in special, highly symmetric, conditions. Aim of the present contribution is to show how it is possible to extract quantitative information about a variety of physical phenomena in very general situations by virtue of the so-called Hamilton-Jacobi method. In particular, we shall prove the agreement of such semi-classical method with exact results of quantum field theoretic calculations.Comment: To appear in the proceedings of "Cosmology, the Quantum Vacuum, and Zeta Functions": A workshop with a celebration of Emilio Elizalde's Sixtieth birthday, Bellaterra, Barcelona, Spain, 8-10 Mar 201

On tunneling across horizons

The tunneling method for stationary black holes in the Hamilton-Jacobi variant is reconsidered in the light of various critiques that have been moved against. It is shown that once the tunneling trajectories have been correctly identified the method isfree from internal inconsistencies, it is manifestly covariant, it allows for the extension to spinning particles and it can even be used without solving the Hamilton-Jacobi equation. These conclusions borrow support on a simple analytic continuation of the classical action of a pointlike particle, made possible by the unique assumption that it should be analytic in complexified Schwarzschild or Kerr-Newman spacetimes. A more general version of the Parikh-Wilczek method will also be proposed along these lines.Comment: Latex Document, 5 pages, 2 figures, title changed, abstract changed, added references, results unchange

Evolved stars in the Local Group galaxies. I. AGB evolution and dust production in IC 1613

We used models of thermally-pulsing asymptotic giant branch (AGB) stars, that also describe the dust-formation process in the wind, to interpret the combination of near- and mid-infrared photometric data of the dwarf galaxy IC 1613. This is the first time that this approach is extended to an environment different from the Milky Way and the Magellanic Clouds (MCs). Our analysis, based on synthetic population techniques, shows a nice agreement between the observations and the expected distribution of stars in the colour-magnitude diagrams obtained with JHK and Spitzer bands. This allows a characterization of the individual stars in the AGB sample in terms of mass, chemical composition, and formation epoch of the progenitors. We identify the stars exhibiting the largest degree of obscuration as carbon stars evolving through the final AGB phases, descending from 1-1.25Msun objects of metallicity Z=0.001 and from 1.5-2.5Msun stars with Z=0.002. Oxygen-rich stars constitute the majority of the sample (65%), mainly low mass stars (<2Msun) that produce a negligible amount of dust (<10^{-7}Msun/yr). We predict the overall dust-production rate from IC 1613, mostly determined by carbon stars, to be 6x10^{-7}Msun/yr with an uncertainty of 30%. The capability of the current generation of models to interpret the AGB population in an environment different from the MCs opens the possibility to extend this kind of analysis to other Local Group galaxies.Comment: 14 pages, 6 figures, accepted for publication on MNRA

The helium spread in the Globular cluster 47 Tuc

Spectroscopy has shown the presence of the CN band dicothomy and the Na-O anticorrelations for 50--70% of the investigated samples in the cluster 47 Tuc, otherwise considered a "normal" prototype of high metallicity clusters from the photometric analysis. Very recently, the re-analysis of a large number of archival HST data of the cluster core has been able to put into evidence the presence of structures in the Sub Giant Branch: it has a brighter component with a spread in magnitude by $\sim$0.06 mag and a second one, made of about 10% of stars, a little fainter (by $\sim$0.05 mag). These data also show that the Main Sequence of the cluster has an intrinsic spread in color which, if interpreted as due to a small spread in helium abundance, suggests $\Delta$Y$\sim$0.027. In this work we examine in detail whether the Horizontal Branch morphology and the Sub Giant structure provide further independent indications that a real --although very small-helium spread is present in the cluster. We re--analyze the HST archival data for the Horizontal Branch of 47 Tuc, obtaining a sample of $\sim$500 stars with very small photometric errors, and build population synthesis based on new models to show that its particular morphology can be better explained by taking into account a spread in helium abundance of 2% in mass. The same variation in helium is able to explain the spread in luminosity of the Sub Giant Branch, while a small part of the second generation is characterized by a small C+N+O increase and provides an explanation for the fainter Sub Giant Branch. We conclude that three photometric features concur to form the paradigm that a small but real helium spread is present in a cluster that has no spectacular evidence for multiple populations like those shown by other massive clusters.Comment: Accepted for publication in the MNRAS on 2010 June 8. Received 2010 May 19; in original form 2010 February 9. 7 pages and 3 figures. No table

RR Lyrae stars in Galactic globular clusters.III. Pulsational predictions for metal content Z=0.0001 to Z=0.006

The results of nonlinear, convective models of RR Lyrae pulsators with metal content Z=0.0001 to 0.006 are discussed and several predicted relations connecting pulsational (period and amplitude of pulsation) and evolutionary parameters (mass, absolute magnitude and color of the pulsator) are derived. These relations, when linked with the average mass of RR Lyrae stars, as suggested by horizontal branch evolutionary models, provide a ``pulsational'' route to the determination of the distance modulus, both apparent and intrinsic, of RR Lyrae rich globular clusters. Based on a preliminary set of synthetic horizontal branch simulations, we compare the predicted relations with observed variables in selected globular clusters (M2, M3, M5, M15, M55, M68, NGC 1851, NGC 3201, NGC 5466, NGC 6362, NGC 6934 and IC 4499). We show that the distance moduli inferred by the various theoretical relations are mutually consistent within the errors, provided that the value of the mixing-length parameter slightly increases from the blue to the red edge of the pulsation region. Moreover, we show that the relative ``pulsational'' distance moduli fit well previous empirical results and that the parallax of the prototype variable RR Lyr, as inferred by the predicted Period-Wasenheit relation, is in close agreement with the HST astrometric measurement

The Globular Cluster Luminosity Function and Specific Frequency in Dwarf Elliptical Galaxies

The globular cluster luminosity function, specific globular cluster frequency, S_N, specific globular cluster mass, T_MP, and globular cluster mass fraction in dwarf elliptical galaxies are explored using the full 69 galaxy sample of the HST WFPC2 Dwarf Elliptical Galaxy Snapshot Survey. The GCLFs of the dEs are well-represented with a t_5 function with a peak at M_{V,Z}^0(dE,HST) = -7.3 +/- 0.1. This is ~0.3 magnitudes fainter than the GCLF peaks in giant spiral and elliptical galaxies, but the results are consistent within the uncertainties. The bright-end slope of the luminosity distribution has a power-law form with slope alpha = -1.9 +/- 0.1. The trend of increasing S_N or T_MP with decreasing host galaxy luminosity is confirmed. The mean value for T_MP in dE,N galaxies is about a factor of two higher than the mean value for non-nucleated galaxies and the distributions of T_MP in dE,N and dE,noN galaxies are statistically different. These data are combined with results from the literature for a wide range of galaxy types and environments. At low host galaxy masses the distribution of T_MP for dE,noN and dI galaxies are similar. This supports the idea that one pathway for forming dE,noN galaxies is by the stripping of dIs. The formation of nuclei and the larger values of T_MP in dE,N galaxies may be due to higher star formation rates and star cluster formation efficiencies due to interactions in galaxy cluster environments.Comment: 53 pages, 13 figures, 12 tables, accepted by the Astrophysical Journa

A test for asymptotic giant branch evolution theories: Planetary Nebulae in the Large Magellanic Cloud

We used a new generation of asymptotic giant branch (AGB) stellar models that include dust formation in the stellar winds to find the links between evolutionary models and the observed properties of a homogeneous sample of Large Magellanic Cloud (LMC) planetary nebulae (PNe). Comparison between the evolutionary yields of elements such as CNO and the corresponding observed chemical abundances is a powerful tool to shed light on evolutionary processes such as hot bottom burning (HBB) and third dredge-up (TDU). We found that the occurrence of HBB is needed to interpret the nitrogen-enriched (log(N/H)+12>8) PNe. In particular, N-rich PNe with the lowest carbon content are nicely reproduced by AGB models of mass M >=6 Mo, whose surface chemistry reflects the pure effects of HBB. PNe with log(N/H)+12<7.5 correspond to ejecta of stars that have not experienced HBB, with initial mass below about 3 Mo. Some of these stars show very large carbon abundances, owing to the many TDU episodes experienced. We found from our LMC PN sample that there is a threshold to the amount of carbon accumulated at AGB surfaces, log(C/H)+12<9. Confirmation of this constraint would indicate that, after the C-star stage is reached,AGBs experience only a few thermal pulses, which suggests a rapid loss of the external mantle, probably owing to the effects of radiation pressure on carbonaceous dust particles present in the circumstellar envelope. The implications of these findings for AGB evolution theories and the need to extend the PN sample currently available are discussed.Comment: 12 pages, 4 figures, 1 table, accepted for publication in MNRAS (2015 July 13; in original form 2015 June 9

Planetary Nebulae in the Small Magellanic Cloud

We analyse the planetary nebulae (PNe) population of the Small Magellanic Cloud (SMC), based on evolutionary models of stars with metallicities in the range $10^{-3} \leq Z \leq 4\times 10^{-3}$ and mass $0.9 M\odot < M < 8M\odot$, evolved through the asymptotic giant branch (AGB) phase. The models used account for dust formation in the circumstellar envelope. To characterise the PNe sample of the SMC, we compare the observed abundances of the various species with the final chemical composition of the AGB models: this study allows us to identify the progenitors of the PNe observed, in terms of mass and chemical composition. According to our interpretation, most of the PNe descend from low-mass ($M < 2 M\odot$) stars, which become carbon rich, after experiencing repeated third dredge-up episodes, during the AGB phase. A fraction of the PNe showing the signature of advanced CNO processing are interpreted as the progeny of massive AGB stars, with mass above $\sim 6 M\odot$, undergoing strong hot bottom burning. The differences with the chemical composition of the PNe population of the Large Magellanic Cloud (LMC) is explained on the basis of the diverse star formation history and age-metallicity relation of the two galaxies. The implications of the present study for some still highly debated points regarding the AGB evolution are also commented.Comment: Accepted for publication in MNRAS, 11 pages, 4 figure