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

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

Theoretical insights into the RR Lyrae K-band Period-Luminosity relation

Based on updated nonlinear, convective pulsation models computed for several values of stellar mass, luminosity and metallicity, theoretical constraints on the K-band Period-Luminosity (PLK) relation of RR Lyrae stars are presented. We show that for each given metal content the predicted PLK is marginally dependent on uncertainties of the stellar mass and/or luminosity. Then, by considering the RR Lyrae masses suggested by evolutionary computations for the various metallicities, we obtain that the predicted infrared magnitude M_K over the range 0.0001< Z <0.02 is given by the relation MK=0.568-2.071logP+0.087logZ-0.778logL/Lo, with a rms scatter of 0.032 mag. Therefore, by allowing the luminosities of RR Lyrae stars to vary within the range covered by current evolutionary predictions for metal-deficient (0.0001< Z <0.006) horizontal branch models, we eventually find that the infrared Period-Luminosity- Metallicity (PLZK) relation is MK=0.139-2.071(logP+0.30)+0.167logZ, with a total intrinsic dispersion of 0.037 mag. As a consequence, the use of such a PLZK relation should constrain within +-0.04 mag the infrared distance modulus of field and cluster RR Lyrae variables, provided that accurate observations and reliable estimates of the metal content are available. Moreover, we show that the combination of K and V measurements can supply independent information on the average luminosity of RR Lyrae stars, thus yielding tight constraints on the input physics of stellar evolution computations. Finally, for globular clusters with a sizable sample of first overtone variables, the reddening can be estimated by using the PLZK relation together with the predicted MV-logP relation at the blue edge of the instability strip (Caputo et al. 2000).Comment: 8 pages, including 5 postscript figures, accepted for publication on MNRA

Atmospheric models from GPS data

We modeled the atmosphere of the Earth, to 60 km elevation, with ten layers whose refractivity is given by N4ki exp [2h/hi] with h elevation over the surface of the Earth, ki and hi defining the refractivity of the layer. The refractivity is assumed continuous between layers, and this reduces the number of free parameters to 11 only. A programme is designed to generate synthetic travel times and from satellites distributed in space to a station on the Earth, travel times are generated with a standard atmospheric model. Stocastic errors are then assigned to the data. A programme is then designed to invert the synthetic data and to fit the travel time to the given satellite positions. The inverted atmospheric model, obtained with 60 satellite positions, deviates from the standard model by less than 4% of N; however, the deviations are positive and negative, the total effect is at most 0.01 ns in the travel time or 0.1 cm in the length of the path. The discrepancies between the model determined and the standard reference model are therefore almost irrelevant in the determination of the coordinates of the points on the surface of the Earth. The distribution of N is then used to infer tentatively the atmospheric water vapor content, the pressure and the temperature. The discrepancies resulting in the comparison obtained by fixing with standard models two of the 3 parameters, are not relevant and very encouranging for the use of GPS data to infer physical properties of the atmosphere. The discrepancy in the model water vapor content and that computed with the inversion is at most 1.2 mbar. A 10% variation of water pressure in the first 10 km of the atmosphere gives a variation 0.1 cm when measuring the elevation of the observing station. It also seen that restricting the observations to a 107 the arc of the orbit of the satellite, the atmospheric model obtained would not lose accuracy. The model suggested, determined by means of observations to GPS satellites, because of its 11 free parameters, instead of the two parameters of the standard model, will allow a more precise description of the real distribution of N at the time when the observations are taken and will therefore allow more precise corrections for the definition of the coordinates of the points on the surface of the Earth and of the positions of the GPS satellites

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&

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.Comment: 18 page

RR Lyrae variables in Galactic globular clusters: IV. Synthetic HB and RR Lyrae predictions

We present theoretical predictions concerning horizontal branch stars in globular clusters, including RR Lyrae variables, as derived from synthetic procedures collating evolutionary and pulsational constraints. On this basis, we explore the predicted behavior of the pulsators as a function of the horizontal branch morphology and over the metallicity range Z=0.0001 to 0.006, revealing an encouraging concordance with the observed distribution of fundamentalised periods with metallicity. Theoretical relations connecting periods to K magnitudes and BV or VI Wesenheit functions are presented, both appearing quite independent of the horizontal branch morphology only with Z greater or equal than 0.001. Predictions concerning the parameter R are also discussed and compared under various assumptions about the horizontal branch reference luminosity level.Comment: 11 pages, 10 figures. Accepted for publication in "Astronomy and Astrophysics

From Diffusion to Anomalous Diffusion: A Century after Einstein's Brownian Motion

Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term memory. The coarse-grained behavior of such processes is described by the diffusion equation. However, many natural processes do not possess the Markovian property and exhibit to anomalous diffusion. We consider here the case of subdiffusive processes, which are semi-Markovian and correspond to continuous-time random walks in which the waiting time for a step is given by a probability distribution with a diverging mean value. Such a process can be considered as a process subordinated to normal diffusion under operational time which depends on this pathological waiting-time distribution. We derive two different but equivalent forms of kinetic equations, which reduce to know fractional diffusion or Fokker-Planck equations for waiting-time distributions following a power-law. For waiting time distributions which are not pure power laws one or the other form of the kinetic equation is advantageous, depending on whether the process slows down or accelerates in the course of time