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

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 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&