arXiv subjects

V. Ripepi

Publications and source records attributed to V. Ripepi.

At least 127 records · Page 7Linked to original sources

arXiv2012

The VMC Survey. V. First results for Classical Cepheids

The VISTA Magellanic Cloud (VMC, PI M.R. Cioni) survey is collecting deep Ks-band time-series photometry of the pulsating variable stars hosted by the system formed by the two Magellanic Clouds (MCs) and the "bridge" connecting them. In this paper we present the first results for Classical Cepheids, from the VMC observations of two fields in the Large Magellanic Cloud (LMC). The VMC Ks-band light curves of the Cepheids are well sampled (12-epochs) and of excellent precision. We were able to measure for the first time the Ks magnitude of the faintest Classical Cepheids in the LMC (Ks\sim17.5 mag), which are mostly pulsating in the First Overtone (FO) mode, and to obtain FO Period-Luminosity (PL), Period-Wesenheit (PW), and Period-Luminosity-Color (PLC) relations, spanning the full period range from 0.25 to 6 day. Since the longest period Cepheid in our dataset has a variability period of 23 day, we have complemented our sample with literature data for brighter F Cepheids. On this basis we have built a PL relation in the Ks band that, for the first time, includes short period pulsators, and spans the whole range from 1.6 to 100 days in period. We also provide the first ever empirical PW and PLC relations using the (V-Ks) color and time-series Ks photometry. The very small dispersion (\sim0.07 mag) of these relations makes them very well suited to study the three-dimensional (3D) geometry of the Magellanic system. The use of "direct" (parallax- and Baade-Wesselink- based) distance measurements to both Galactic and LMC Cepheids, allowed us to calibrate the zero points of the PL, PW, and PLC relations obtained in this paper, and in turn to estimate an absolute distance modulus of (m-M)0=18.46\pm0.03 for the LMC. This result is in agreement with most of the latest literature determinations based on Classical Cepheids.

astro-ph.CO↗

arXiv2012

Initial data release of the Kepler-INT Survey

This paper describes the first data release of the Kepler-INT Survey (KIS), that covers a 116 deg2 region of the Cygnus and Lyra constellations. The Kepler field is the target of the most intensive search for transiting planets to date. Despite the fact that the Kepler mission provides superior time series photometry, with an enormous impact on all areas of stellar variability, its field lacks optical photometry complete to the confusion limit of the Kepler instrument necessary for selecting various classes of targets. For this reason, we follow the observing strategy and data reduction method used in the IPHAS and UVEX galactic plane surveys in order to produce a deep optical survey of the Kepler field. This initial release concerns data taken between May and August 2011, using the Isaac Newton Telescope on the island of La Palma. Four broadband filters were used, U, g, r, i, as well as one narrowband one, Halpha, reaching down to a 10-sigma limit of around 20th mag in the Vega system. Observations covering around 50 deg2, thus about half of the field, passed our quality control thresholds and constitute this first data release. We derive a global photometric calibration by placing the KIS magnitudes as close as possible to the Kepler Input Catalog (KIC) photometry. The initial data release catalogue containing around 6 million sources from all the good photometric fields is available for download from the KIS webpage, as well as via MAST.

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arXiv2012

The Carina Project. V. The impact of NLTE effects on the iron content

We have performed accurate iron abundance measurements for 44 red giants (RGs) in the Carina dwarf spheroidal (dSph) galaxy. We used archival, high-resolution spectra (R~38,000) collected with UVES at ESO/VLT either in slit mode (5) or in fiber mode (39, FLAMES/GIRAFFE-UVES). The sample is more than a factor of four larger than any previous spectroscopic investigation of stars in dSphs based on high-resolution (R>38,000) spectra. We did not impose the ionization equilibrium between neutral and singly-ionized iron lines. The effective temperatures and the surface gravities were estimated by fitting stellar isochrones in the V, B-V color-magnitude diagram. To measure the iron abundance of individual lines we applied the LTE spectrum synthesis fitting method using MARCS model atmospheres of appropriate metallicity. We found evidence of NLTE effects between neutral and singly-ionized iron abundances. Assuming that the FeII abundances are minimally affected by NLTE effects, we corrected the FeI stellar abundances using a linear fit between FeI and FeII stellar abundance determinations. We found that the Carina metallicity distribution based on the corrected FeI abundances (44 RGs) has a weighted mean metallicity of [Fe/H]=-1.80 and a weighted standard deviation of sigma=0.24 dex. The Carina metallicity distribution based on the FeII abundances (27 RGs) gives similar estimates ([Fe/H]=-1.72, sigma=0.24 dex). The current weighted mean metallicities are slightly more metal poor when compared with similar estimates available in the literature. Furthermore, if we restrict our analysis to stars with the most accurate iron abundances, ~20 FeI and at least three FeII measurements (15 stars), we found that the range in iron abundances covered by Carina RGs (~1 dex) agrees quite well with similar estimates based on high-resolution spectra.

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arXiv2012

Stellar Archaeology in the Galactic halo with the Ultra-Faint Dwarfs: VI. Ursa Major II

We present a B, V color-magnitude diagram (CMD) of the Milky Way dwarf satellite Ursa Major II (UMa II), spanning the magnitude range from V ~ 15 to V ~ 23.5 mag and extending over a 18 {\times} 18 arcmin2 area centered on the galaxy. Our photometry goes down to about 2 magnitudes below the galaxy's main sequence turn-off, that we detected at V ~ 21.5 mag. We have discovered a bona-fide RR Lyrae variable star in UMa II, which we use to estimate a conservative dereddened distance modulus for the galaxy of (m-M)0 = 17.70{\pm}0.04{\pm}0.12 mag, where the first error accounts for the uncertainties of the calibrated photometry, and the second reflects our lack of information on the metallicity of the star. The corresponding distance to UMa II is 34.7 {\pm} 0.6 ({\pm} 2.0) kpc. Our photometry shows evidence of a spread in the galaxy subgiant branch, compatible with a spread in metal abundance in the range between Z=0.0001 and Z=0.001. Based on our estimate of the distance, a comparison of the fiducial lines of the Galactic globular clusters (GCs) M68 and M5 ([Fe/H]=-2.27 {\pm} 0.04 dex and -1.33 {\pm} 0.02 dex, respectively), with the position on the CMD of spectroscopically confirmed galaxy members, may suggest the existence of stellar populations of different metal abundance/age in the central region of UMa II.

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arXiv2012

Preliminary results for RR Lyrae stars and Classical Cepheids from the Vista Magellanic Cloud (VMC) Survey

The Vista Magellanic Cloud (VMC, PI M.R. Cioni) survey is collecting $K_S$-band time series photometry of the system formed by the two Magellanic Clouds (MC) and the "bridge" that connects them. These data are used to build $K_S$-band light curves of the MC RR Lyrae stars and Classical Cepheids and determine absolute distances and the 3D geometry of the whole system using the $K$-band period luminosity ($PLK_S$), the period - luminosity - color ($PLC$) and the Wesenhiet relations applicable to these types of variables. As an example of the survey potential we present results from the VMC observations of two fields centered respectively on the South Ecliptic Pole and the 30 Doradus star forming region of the Large Magellanic Cloud. The VMC $K_S$-band light curves of the RR Lyrae stars in these two regions have very good photometric quality with typical errors for the individual data points in the range of $\sim$ 0.02 to 0.05 mag. The Cepheids have excellent light curves (typical errors of $\sim$ 0.01 mag). The average $K_S$ magnitudes derived for both types of variables were used to derive $PLK_S$ relations that are in general good agreement within the errors with the literature data, and show a smaller scatter than previous studies.

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arXiv2012

CORS Baade-Wesselink distance to the LMC NGC 1866 blue populous cluster

We used Optical, Near Infrared photometry and radial velocity data for a sample of 11 Cepheids belonging to the young LMC blue populous cluster NGC 1866 to estimate their radii and distances on the basis of the CORS Baade-Wesselink method. This technique, based on an accurate calibration of the surface brightness as a function of (U-B), (V-K) colors, allows us to estimate, simultaneously, the linear radius and the angular diameter of Cepheid variables, and consequently to derive their distance. A rigorous error estimate on radius and distances was derived by using Monte Carlo simulations. Our analysis gives a distance modulus for NGC 1866 of 18.51+/-0.03 mag, which is in agreement with several independent results.

astro-ph.CO↗

arXiv2011

Stroemgren photometry of the Bulge: the Baade's Window and the globular cluster NGC 6522

We present Ca-uvby Stroemgren photometry of the Baade's Window, including the Galactic globular cluster NGC 6522. We separate field and cluster stars by adopting color-color planes and proper motions. We then estimate the global metallicity of red-giants (RGs) in NGC 6522 by using a new theoretical metallicity calibration of the Stroemgren index hk presented in Calamida et al. (2011). We find that metallicities estimated by adopting the hk index and the (Ca-y) color are systematically more metal-rich than metallicities estimated with hk and the (u-y), (v-y) and (b-y) colors. Current evidence indicate that the hk metallicity index is affected not only by the Calcium abundance, but also by another source of opacity.

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arXiv2011

On a new theoretical calibration of the Stroemgren hk metallicity index: NGC6522 as a first test case

We present a new theoretical calibration of the Stroemgren metallicity index hk by using alpha-enhanced evolutionary models transformed into the observational plane by using atmosphere models with the same chemical mixture. We apply the new Metallicity--Index--Color (MIC) relations to a sample of 85 field red giants (RGs) and find that the difference between photometric estimates and spectroscopic measurements is on average smaller than 0.1 dex with a dispersion of sigma = 0.19 dex. The outcome is the same if we apply the MIC relations to a sample of eight RGs in the bulge globular cluster NGC6522, but the standard deviation ranges from 0.26 (hk, v-y) to 0.49 (hk, u-y). The difference is mainly caused by a difference in photometric accuracy. The new MIC relations based on the (Ca-y) color provide metallicities systematically more metal-rich than the spectroscopic ones. We found that the Ca-band is affected by Ca abundance and possibly by chromospheric activity.

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arXiv2011

The Kepler characterization of the variability among A- and F-type stars. I. General overview

The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars. We propose three main groups to describe the observed variety in pulsating A-F type stars: gamma Dor, delta Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars of different spectral type, or stars that show no clear periodic variability. 23% of the stars (171 stars) are hybrid stars, which is a much larger fraction than what has been observed before. We characterize for the first time a large number of A-F type stars (475 stars) in terms of number of detected frequencies, frequency range, and typical pulsation amplitudes. The majority of hybrid stars show frequencies with all kinds of periodicities within the gamma Dor and delta Sct range, also between 5 and 10 c/d, which is a challenge for the current models. We find indications for the existence of delta Sct and gamma Dor stars beyond the edges of the current observational instability strips. The hybrid stars occupy the entire region within the delta Sct and gamma Dor instability strips, and beyond. Non-variable stars seem to exist within the instability strips. The location of gamma Dor and delta Sct classes in the (Teff,logg)-diagram has been extended. We investigate two newly constructed variables 'efficiency' and 'energy' as a means to explore the relation between gamma Dor and delta Sct stars. Our results suggest a revision of the current observational instability strips, and imply an investigation of other pulsation mechanisms to supplement the kappa mechanism and convective blocking effect to drive hybrid pulsations.

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arXiv2011

Non-Blazhko RR Lyrae Stars Observed with the KEPLER Space Telescope

This paper summarizes the main results of our recent study of the non-Blazhko RR Lyrae stars observed with the Kepler space telescope. These stars offer the opportunity for studying the stability of the pulsations of RR Lyrae stars and for providing a reference against which the Blazhko RR Lyrae stars can be compared. Of particular interest is the stability of the low-dispersion (sigma < 1mmag) light curves constructed from ~18,000 long-cadence (30-min) and (for FN Lyr and AW Dra) the ~150,000 short-cadence (1-min) photometric data points. Fourier-based [Fe/H] values and other physical characteristics are also derived. When the observed periods are compared with periods computed with the Warsaw non-linear convective pulsation code better agreement is achieved assuming pulsational L and M values rather than the (higher) evolutionary L and M values.

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arXiv2011

Fourier analysis of non-Blazhko ab-type RR Lyrae stars observed with the Kepler space telescope

Nineteen of the ~40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. In this paper we present the results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on ~18400 long-cadence observations per star (and ~150000 short-cadence observations for FN Lyr and for AW Dra) are derived. None of the stars shows the recently discovered `period-doubling' effect seen in Blazhko variables; however, KIC 7021124 has been found to pulsate simultaneously in the fundamental and second overtone modes with a period ratio P2/P0 ~ 0.59305 and is similar to the double-mode star V350 Lyr. Period change rates are derived from O-C diagrams spanning, in some cases, over 100 years; these are compared with high-precision periods derived from the Kepler data alone. Extant Fourier correlations by Kovacs, Jurcsik et al. (with minor transformations from the V to the Kp passband) have been used to derive underlying physical characteristics for all the stars. This procedure seems to be validated through comparisons of the Kepler variables with galactic and LMC RR Lyr stars. The most metal-poor star in the sample is NR Lyr, with [Fe/H]=-2.3 dex; and the four most metal-rich stars have [Fe/H] ranging from -0.6 to +0.1 dex. Pulsational luminosities and masses are found to be systematically smaller than L and mass values derived from stellar evolution models, and are favoured over the evolutionary values when periods are computed with the Warsaw linear hydrodynamics code. Finally, the Fourier parameters are compared with theoretical values derived using the Warsaw non-linear convective pulsation code.

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arXiv2011

CoRoT\,102699796, the first metal-poor Herbig Ae pulsator: a hybrid $δ$ Sct-$γ$ Dor variable?

We present the analysis of the time series observations of CoRoT\,102699796 obtained by the CoRoT satellite that show the presence of five independent oscillation frequencies in the range 3.6-5 c/d. Using spectra acquired with FLAMES@VLT, we derive the following stellar parameters: spectral type F1V, T$_{\rm eff}$=7000$\pm$200 K, log(g)=$3.8\pm0.4$, [M/H]=$-1.1\pm0.2$, $v$sin$i$=$50\pm5$ km/s, L/L$_{\odot}$=21$^{+21}_{-11}$. Thus, for the first time we report the existence of a metal poor, intermediate-mass PMS pulsating star. Ground-based and satellite data are used to derive the spectral energy distribution of CoRoT\,102699796 extending from the optical to mid-infrared wavelengths. The SED shows a significant IR excess at wavelengths greater than $\sim5 μ$. We conclude that CoRoT\,102699796 is a young Herbig Ae (F1Ve) star with a transitional disk, likely associated to the HII region [FT96]213.1-2.2. The pulsation frequencies have been interpreted in the light of the non-radial pulsation theory, using the LOSC code in conjunction with static and rotational evolutionary tracks. A minimization algorithm was used to find the best-fit model with M=1.84 M$_{\odot}$, T$_{\rm eff}$=6900 K which imply an isochronal age of t$\sim$2.5 Myr. This result is based on the interpretation of the detected frequencies as $g$-modes of low-moderate $n$-value. To our knowledge, this is the first time that such modes are identified in a intermediate-mass PMS pulsating star. Since CoRoT\,102699796 lies in the region of the HR diagram where the $δ$ Sct and $γ$ Dor instability strips intersect, we argue that the observed pulsation characteristics are intermediate between these classes of variables, i.e. CoRoT\,102699796 is likely the first PMS hybrid $γ$ Dor-$δ$ Sct pulsator ever studied.

astro-ph.SR↗

arXiv2011

Distance to Galactic globulars using the near-infrared magnitudes of RR Lyrae stars: IV. The case of M5 (NGC5904)

We present new and accurate near-infrared (NIR) J, K-band time series data for the Galactic globular cluster (GC) M5 = NGC5904. Data were collected with SOFI at the NTT (71 J + 120 K images) and with NICS at the TNG (25 J + 22 K images) and cover two orthogonal strips across the center of the cluster of \approx 5 \times 10 arcmin^{2} each. These data allowed us to derive accurate mean K-band magnitudes for 52 fundamental (RR_{ab}) and 24 first overtone (RR_{c}) RR Lyrae stars. Using this sample of RR Lyrae stars, we find that the slope of the K-band Period Luminosity (PLK) relation (-2.33 \pm 0.08) agrees quite well with similar estimates available in the literature. We also find, using both theoretical and empirical calibrations of the PLK relation, a true distance to M5 of (14.44 \pm 0.02) mag. This distance modulus agrees very well (1σ) with distances based on main sequence fitting method and on kinematic method (14.44 \pm 0.41 mag, \citealt{rees_1996}), while is systematically smaller than the distance based on the white dwarf cooling sequence (14.67 \pm 0.18 mag, \citealt{layden2005}), even if with a difference slightly larger than 1σ. The true distance modulus to M5 based on the PLJ relation (14.50 \pm 0.08 mag) is in quite good agreement with the distance based on the PLK relation further supporting the use of NIR PL relations for RR Lyrae stars to improve the precision of the GC distance scale.

astro-ph.GA↗

arXiv2011

Regularities in frequency spacings of Delta Scuti stars: The Kepler star KIC 9700322

In the faint star KIC 9700322 observed by the Kepler satellite, 76 frequencies with amplitudes from 14 to 29000 ppm were detected. The two dominant frequencies at 9.79 and 12.57 c/d (113.3 and 145.5 μHz), interpreted to be radial modes, are accompanied by a large number of combination frequencies. A small additional modulation with a 0.16 c/d frequency is also seen; this is interpreted to be the rotation frequency of the star. The corresponding prediction of slow rotation is confirmed by a spectrum from which v sin i = 19 \pm 1 km/s is obtained. The analysis of the spectrum shows that the star is one of the coolest δ Sct variables. We also determine Teff = 6700 \pm 100 K and log g = 3.7 \pm 0.1, compatible with the observed frequencies of the radial modes. Normal solar abundances are found. An \ell = 2 frequency quintuplet is also detected with a frequency separation consistent with predictions from the measured rotation rate. A remarkable result is the absence of additional independent frequencies down to an amplitude limit near 14 ppm, suggesting that the star is stable against most forms of nonradial pulsation. The frequency spectrum of this star emphasizes the need for caution in interpreting low frequencies in δ Sct stars as independent gravity modes. A low frequency peak at 2.7763 c/d in KIC 9700322 is, in fact, the frequency difference between the two dominant modes and is repeated over and over in various frequency combinations involving the two dominant modes. The relative phases of the combination frequencies show a strong correlation with frequency, but the physical significance of this result is not clear.

astro-ph.SR↗

arXiv2011

The VMC Survey - I. Strategy and First Data

The new VISual and Infrared Telescope for Astronomy (VISTA) has started operations. Over its first five years it will be collecting data for six public surveys, one of these is the near-infrared YJKsVISTA survey of the Magellanic Clouds system (VMC). This survey comprises the LMC, the SMC, the Bridge connecting the two galaxies and two fields in the Stream. This paper provides an overview of the VMC survey strategy and presents first science results. The main goals of the VMC survey are the determination of the spatially resolved SFH and 3D structure of the Magellanic system. Therefore, the VMC survey is designed to reach stars as faint as the oldest main sequence turn-off point and to constrain the mean magnitude of pulsating variable stars such as RR Lyrae stars and Cepheids. This paper focuses on observations of VMC fields in the LMC obtained between November 2009 and March 2010. These observations correspond to a 7% completeness of the LMC fields. The VMC observations consist of multi-epoch measurements organised following a specific structure. The data were reduced using the VISTA Data Flow System pipeline whose source catalogues were produced and made available via the VISTA Science Archive. The analysis of the data shows that the sensitivity in each wave band agrees with expectations. Uncertainties and completeness of the data are also derived. The first science results, aimed at assessing the science quality of the VMC data, include an overview of the distribution of stars in colour-magnitude and colour-colour diagrams, the detection of planetary nebulae and of stellar clusters, and the Ks band light-curve of variable stars. The VMC survey represents a tremendous improvement, in spatial resolution and sensitivity, on previous panoramic observations of the Magellanic system in the near-infrared and complements nicely the deep observations at other wavelengths. (Abridged)

astro-ph.CO↗

arXiv2010

CORS Baade-Wesselink method in the Walraven photometric system: the Period-Radius and the Period-Luminosity relation of Classical Cepheids

We present a new derivation of the CORS Baade-Wesselink method in the Walraven photometric system. We solved the complete Baade-Wesselink equation by calibrating the surface brightness function with a recent grid of atmosphere models. The new approach was adopted to estimate the mean radii of a sample of Galactic Cepheids for which are available precise light curves in the Walraven bands. Current radii agree, within the errors, quite well with Cepheid radii based on recent optical and near-infrared interferometric measurements. We also tested the impact of the projection factor on the Period-Radius relation using two different values (p=1.36, p=1.27) that bracket the estimates available in the literature. We found that the agreement of our Period-Radius relation with similar empirical and theoretical Period-Radius relations in the recent literature, improves by changing the projection factor from p=1.36 to p=1.27. Our Period-Radius relation is log(R)=(0.75\pm 0.03)log(P)+(1.10 \pm 0.03), with a rms=0.03 dex. Thanks to accurate estimates of the effective temperature of the selected Cepheids, we also derived the Period-Luminosity relation in the V band and we found Mv=(-2.78 \pm 0.11)log(P)+(-1.42 \pm 0.11) with rms=0.13 mag, for p=1.27. It agrees quite well with recent results in the literature, while the relation for p=1.36 deviates by more than 2sigma. We conclude that, even taking into account the intrinsic dispersion of the obtained Period-Luminosity relations, that is roughly of the same order of magnitude as the effect of the projection factor, the results of this paper seem to favour the value p = 1.27.

astro-ph.SR↗

arXiv2010

NGC 1866: a milestone for understanding the chemical evolution of stellar populations in the LMC

We present new FLAMES@VLT spectroscopic observations of 30 stars in the field of the LMC stellar cluster NGC 1866. NGC 1866 is one of the few young and massive globular cluster that is close enough so that its stars can be individually studied in detail. Radial velocities have been used to separate stars belonging to the cluster and to the LMC field and the same spectra have been used to derive chemical abundances for a variety of elements, from [Fe/H] to the light (i.e. Na, O, Mg...) to the heavy ones. The average iron abundance of NGC 1866 turns out to be [Fe/H]= -0.43+-0.01 dex (with a dispersion of 0.04 dex), from the analysis of 14 cluster-member stars. Within our uncertainties, the cluster stars are homogeneous, as far as chemical composition is concerned, independent of the evolutionary status. The observed cluster stars do not show any sign of the light elements 'anti-correlation' present in all the Galactic globular clusters so far studied, and also found in the old LMC stellar clusters. A similar lack of anti-correlations has been detected in the massive intermediate-age LMC clusters, indicating a different formation/evolution scenario for the LMC massive clusters younger than ~3 Gyr with respect to the old ones. Also opposite to the Galactic globulars, the chemical composition of the older RGB field stars and of the young post-MS cluster stars show robust homogeneity suggesting a quite similar process of chemical evolution. The field and cluster abundances are in agreement with recent chemical analysis of LMC stars, which show a distinctive chemical pattern for this galaxy with respect to the Milky Way. We discuss these findings in light of the theoretical scenario of chemical evolution of the LMC.

astro-ph.SR↗

arXiv2010

A New Census of the variable star population in the Globular Cluster NGC 2419

We present B, V and I CCD light curves for 101 variable stars belonging to the globular cluster NGC2419, 60 of which are new discoveries, based on datasets obtained at the TNG, SUBARU and HST telescopes. The sample includes 75 RR Lyrae stars (of which 38 RRab, 36 RRc and one RRd), one Population II Cepheid, 12 SX Phoenicis variables, 2 DeltaScuti stars, 3 binary systems, 5 long-period variables, and 3 variables of uncertain classification. The pulsation properties of the RR Lyrae variables are close to those of Oosterhoff type II clusters, consistent with the low metal abundance and the cluster horizontal branch morphology,disfavoring (but not totally ruling out) an extragalactic hypotesis for the origin of NGC2419. The observed properties of RR Lyrae and SX Phoenicis stars are used to estimate the cluster reddening and distance, using a number of different methods. Our final value is mo(NGC2419)=19.71+/-0.08mag (D= 87.5+/-3.3kpc), with E(B-V)=0.08+/-0.01mag, [Fe/H]=-2.1dex in the Zinn & West metallicity scale, and a value of Mv that sets mo(LMC)=18.52mag. This value is in good agreement with most recent literature estimates of the distance to NGC 2419.

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