Stellar populations in the dwarf spheroidal galaxy Leo I

We present a detailed study of the color magnitude diagram (CMD) of the dwarf spheroidal galaxy Leo I, based on archival Hubble Space Telescope data. Our photometric analysis, confirming previous results on the brighter portion of the CMD, allow us to obtain an accurate sampling of the stellar populations also at the faint magnitudes corresponding to the Main Sequence. By adopting a homogeneous and consistent theoretical scenario for both hydrogen and central helium-burning evolutionary phases, the various features observed in the CMD are interpreted and reliable estimations for both the distance modulus and the age(s) for the main stellar components of Leo I are derived. More in details, from the upper luminosity of the Red Giant Branch and the lower luminosity of the Subgiant Branch we simultaneously constrain the galaxy distance and the age of the oldest stellar population in Leo I. In this way we obtain a distance modulus (m-M)_V=22.00$\pm$0.15 mag and an age of 10--15 Gyr or 9--13 Gyr, adopting a metallicity Z=0.0001 and 0.0004, respectively. The reliability of this distance modulus has been tested by comparing the observed distribution of the Leo I anomalous Cepheids in the period-magnitude diagram with the predicted boundaries of the instability strip, as given by convective pulsating models.Comment: 19 pages, 3 tables, 14 figures To be published in A

Relaxation time of LL-reversal chains and other chromosome shuffles

We prove tight bounds on the relaxation time of the so-called $L$-reversal chain, which was introduced by R. Durrett as a stochastic model for the evolution of chromosome chains. The process is described as follows. We have $n$ distinct letters on the vertices of the ${n}$-cycle (${{\mathbb{Z}}}$ mod $n$); at each step, a connected subset of the graph is chosen uniformly at random among all those of length at most $L$, and the current permutation is shuffled by reversing the order of the letters over that subset. We show that the relaxation time $\tau (n,L)$, defined as the inverse of the spectral gap of the associated Markov generator, satisfies $\tau (n,L)=O(n\vee \frac{n^3}{L^3})$. Our results can be interpreted as strong evidence for a conjecture of R. Durrett predicting a similar behavior for the mixing time of the chain.Comment: Published at http://dx.doi.org/10.1214/105051606000000295 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fractional Fokker-Planck Equation for Ultraslow Kinetics

Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability distribution of particle's position at long times is a double-sided exponential. We show that such behaviors can be adequately described by a distributed-order fractional Fokker-Planck equations with a power-law weighting-function. We discuss the equations and the properties of their solutions, and connect this description with a scheme based on continuous-time random walks

RR Lyrae variables in Galactic globular clusters - I: The observational scenario

In this paper we revisit observational data concerning RR Lyrae stars in Galactic globular clusters, presenting frequency histograms of fundamentalized periods for the 32 clusters having more than 12 pulsators with well recognized period and pulsation mode. One finds that the range of fundamentalized periods covered by the variables in a given cluster remains fairly constant in varying the cluster metallicity all over the metallicity range spanned by the cluster sample, with the only two exceptions given by M15 and NGC6441. We conclude that the width in temperature of the RR Lyrae instability strip appears largely independent of the cluster metallicity. At the same time, it appears that the fundamentalized periods are not affected by the predicted variation of pulsators luminosity with metal abundance, indicating the occurrence of a correlated variation in the pulsator mass. We discuss mean periods in a selected sample of statistically significant "RR rich" clusters with no less than 10 RRab and 5 RRc variables. One finds a clear evidence for the well known Oosterhoff dichotomy in the mean period of ab-type variables, together with a similarly clear evidence for a constancy of the mean fundamentalized period in passing from Oosterhoff type II to type I clusters. On this basis, the origin of the Oosterhoff dichotomy is discussed, presenting evidence against a strong dependence of the RR Lyrae luminosity on the metal content.Comment: 9 pages, 6 figures. Accepted for publication on A&

Pulsational M_V versus [Fe/H] relation(s) for globular cluster RR Lyrae variables

We use the results from recent computations of updated non-linear convective pulsating models to constrain the distance modulus of Galactic globular clusters through the observed periods of first overtone RRc pulsators. The resulting relation between the mean absolute magnitude of RR Lyrae stars and the heavy element content [Fe/H] appears well in the range of several previous empirical calibrations, but with a non linear dependence on [Fe/H] so that the slope of the relation increases when moving towards larger metallicities. On this ground, our results suggest that metal-poor ([Fe/H]-1.5) variables follow two different linear -[Fe/H] relations. Application to RR Lyrae stars in the metal-poor globular clusters of the Large Magellanic Cloud provides a LMC distance modulus of the order of 18.6 mag, thus supporting the "long" distance scale. The comparison with recent predictions based on updated stellar evolution theory is shortly presented and discussed.Comment: 8 pages, 4 postscript figures, accepted for publication on MNRA

RR Lyrae variables in M5 as a test of pulsational theory

We present B and V CCD photometry for variables in the cluster central region, adding new data for 32 variables and giving suitable light curves, mean magnitudes and corrected colors for 17 RR Lyrae. Implementing the data given in this paper with similar data already appeared in the literature we discuss a sample of 42 variables, as given by 22 RRab and 20 RRc, to the light of recent predictions from pulsational theories. We find that the observational evidence concerning M5 pulsators appears in marginal disagreement with predictions concerning the color of the First Overtone Blue Edge (FOBE), whereas a clear disagreement appears between the ZAHB luminosities predicted through evolutionary or pulsational theories.Comment: 7 pages, 7 postscript figures, accepted for publication on MNRA

Theoretical models for classical Cepheids. VIII. Effects of helium and heavy elements abundance on the Cepheid distance scale

Previous nonlinear fundamental pulsation models for classical Cepheids with metal content Z <= 0.02 are implemented with new computations at super-solar metallicity (Z=0.03, 0.04) and selected choices of the helium-to-metal enrichment ratio DeltaY/Delta Z. On this basis, we show that the location into the HR diagram of the Cepheid instability strip is dependent on both metal and helium abundance, moving towards higher effective temperatures with decreasing the metal content (at fixed Y) or with increasing the helium content (at fixed Z). The contributions of helium and metals to the predicted Period-Luminosity and Period-Luminosity-Color relations are discussed, as well as the implications on the Cepheid distance scale. Based on these new results, we finally show that the empirical metallicity correction suggested by Cepheid observations in two fields of the galaxy M101 may be accounted for, provided that the adopted helium-to-metal enrichment ratio is reasonably high (Delta Y/Delta Z ~ 3.5).Comment: 23 pages, including 6 postscript figures, accepted for publication on Ap

RR LYRAE VARIABLE STARS: PULSATIONAL CONSTRAINTS RELEVANT TO THE OOSTERHOFF CONTROVERSY

A solution to the old Oosterhoff controversy is proposed on the basis of a new theoretical pulsational scenario concerning RR Lyrae cluster variables (Bono and coworkers). We show that the observed constancy of the lowest pulsation period in both Oosterhoff type I (OoI) and Oosterhoff type II (OoII) prototypes (M3, M15) can be easily reproduced only by assuming the canonical evolutionary horizontal-branch luminosity levels of these Galactic globular clusters and therefore by rejecting the Sandage period shift effect (SPSE).Comment: postscript file of 7 pages and 2 figures; one non postcript figure is available upon request; for any problem please write to [email protected]