Impact of energetic particle orbits on long range frequency chirping of BGK modes

Long range frequency chirping of Bernstein-Greene-Kruskal modes, whose existence is determined by the fast particles, is investigated in cases where these particles do not move freely and their motion is bounded to restricted orbits. An equilibrium oscillating potential, which creates different orbit topologies of energetic particles, is included into the bump-on-tail instability problem of a plasma wave. With respect to fast particles dynamics, the extended model captures the range of particles motion (trapped/passing) with energy and thus represents a more realistic 1D picture of the long range sweeping events observed for weakly damped modes, e.g. global Alfven eigenmodes, in tokamaks. The Poisson equation is solved numerically along with bounce averaging the Vlasov equation in the adiabatic regime. We demonstrate that the shape and the saturation amplitude of the nonlinear mode structure depends not only on the amount of deviation from the initial eigenfrequency but also on the initial energy of the resonant electrons in the equilibrium potential. Similarly, the results reveal that the resonant electrons following different equilibrium orbits in the electrostatic potential lead to different rates of frequency evolution. As compared to the previous model [Breizman B.N. 2010 Nucl. Fusion 50 084014], it is shown that the frequency sweeps with lower rates. The additional physics included in the model enables a more complete 1D description of the range of phenomena observed in experiments.Comment: Submitted to Nuclear Fusion 25/01/201

RR Lyrae stars in Galactic globular clusters. VI. The Period-Amplitude relation

We compare theory and observations for fundamental RR Lyrae in the solar neighborhood and in both Oosterhoff type I (OoI) and type II (OoII) Galactic globular clusters (GGCs). The distribution of cluster RR_ab in the PA_V plane depends not only on the metal abundance, but also on the cluster Horizontal Branch (HB) morphology. On average the observed k_puls parameter, connecting the period to the visual amplitude, increases when moving from metal-poor to metal-rich GGCs. However, this parameter shows marginal changes among OoI clusters with intermediate to red HB types and iron abundances -1.8<= [Fe/H] <=-1.1, whereas its value decreases in OoII clusters with the bluer HB morphology. Moreover, at [Fe/H]=-1.7+-0.1 the OoI clusters present redder HB types and larger values than the OoII clusters. The RR_ab variables in Omega Cen and in the solar neighborhood further support the evidence that the spread in [Fe/H], at fixed k_puls, is of the order of +-0.5 dex. Synthetic HB simulations show that the PA_V plane can provide accurate cluster distance estimates. The RR_ab variables in OoI and in OoII clusters with very blue HB types obey a well-defined M_V(RR)-k_puls relation, while those in OoII clusters with moderately blue HB types present a zero-point that is ~0.05 mag brighter. Regarding field variables, we show that with [Fe/H]=> -1.0 a unique M_V(RR)-k_puls relation can be adopted, independently of the parent HB morphology. Current findings suggest that the PA_V distribution does not seem to be a robust diagnostic for the metal abundance of RR_ab variables. However, the same observables can be used to estimate the absolute magnitude of globular cluster and field RR_ab variables. We show that over the metallicity range -2.4<= [Fe/H] <= 0.0 the M_V(RR)-[Fe/H] relation shows a parabolic behavior.Comment: Paper accepted on A&A, 13 pages, 18 figure

Approximating RR Lyrae light curves using cubic polynomials

In this paper, we use cubic polynomials to approximate RR Lyrae light curves and apply the method to HST data of RR Lyraes in the halo of M31. We compare our method to the standard method of Fourier decomposition and find that the method of cubic polynomials eliminates virtually all ringing effects and does so with significantly fewer parameters than the Fourier technique. Further, for RRc stars the parameters in the fit are all physical. Our study also reveals a number of additional periodicites in this data not found previously: we find 23 RRc stars, 29 RRab stars and 3 multiperiodic stars.Comment: 6 pages, MNRAS accepte

Deep Photometry of the Globular Cluster M5: Distance Estimates from White Dwarf and Main Sequence Stars

We present deep VI photometry of stars in the globular cluster M5 (NGC 5904) based on images taken with the Hubble Space Telescope. The resulting color-magnitude diagram reaches below V ~ 27 mag, revealing the upper 2-3 magnitudes of the white dwarf cooling sequence, and main sequence stars eight magnitudes and more below the turn-off. We fit the main sequence to subdwarfs of known parallax to obtain a true distance modulus of (m-M)_0 = 14.45 +/- 0.11 mag. A second distance estimate based on fitting the cluster white dwarf sequence to field white dwarfs with known parallax yielded (m-M)_0 = 14.67 +/- 0.18 mag. We couple our distance estimates with extensive photometry of the cluster's RR Lyrae variables to provide a calibration of the RR Lyrae absolute magnitude yielding M_V(RR) = 0.42 +/- 0.10 mag at [Fe/H] = -1.11 dex. We provide another luminosity calibration in the form of reddening-free Wasenheit functions. Comparison of our calibrations with predictions based on recent models combining stellar evolution and pulsation theories shows encouraging agreement. (Abridged)Comment: AASTeX, 29 pages including 5 figures. Complete photometry data and FITS-format images are available at http://physics.bgsu.edu/~layden/ASTRO/PUBL/published.html . Accepted for publication in the Astrophysical Journal, 2005 October 20. Replaced errant wording in last sentence of paragraph 4 of conclusion

The Age of Globular Clusters

I review here recent developments which have affected our understanding of both the absolute age of globular clusters and the uncertainties in this age estimate, and comment on the implications for cosmological models. This present estimate is in agreement with the range long advocated by David Schramm. The major uncertainty in determining ages of globular clusers based upon the absolute magnitude of the main sequence turn-off remains the uncertainty in the distance to these clusters. Estimates of these distances have recently been upwardly revised due to Hipparcos parallax measurements, if one calibrates luminosities of main sequence stars. However, it is important to realize that at the present time, different distance measures are in disagreement. A recent estimate is that the oldest clusters are $11.5 \pm 1.3$ Gyr, implying a one-sided 95% confidence level lower limit of 9.5 Gyr, if statistical parallax distance measures are not incorporated. Incorporating more recent measures, including Hipparcos based statistical parallax measures, raises the mean predicted age to $12.8 \pm 1$ Gyr, with a 95 % confidence range of 10-17 Gyr. I conclude by discussing possible improvements which may allow a more precise age distribution in the near future.Comment: latex (using elsart macro for Physics Reports), 16 pages including 4 figures. To appear in Physics Reports, David Schramm Memorial Volum

Stellar evolution through the ages: period variations in galactic RRab stars as derived from the GEOS database and TAROT telescopes

The theory of stellar evolution can be more closely tested if we have the opportunity to measure new quantities. Nowadays, observations of galactic RR Lyr stars are available on a time baseline exceeding 100 years. Therefore, we can exploit the possibility of investigating period changes, continuing the pioneering work started by V. P. Tsesevich in 1969. We collected the available times of maximum brightness of the galactic RR Lyr stars in the GEOS RR Lyr database. Moreover, we also started new observational projects, including surveys with automated telescopes, to characterise the O-C diagrams better. The database we built has proved to be a very powerful tool for tracing the period variations through the ages. We analyzed 123 stars showing a clear O-C pattern (constant, parabolic or erratic) by means of different least-squares methods. Clear evidence of period increases or decreases at constant rates has been found, suggesting evolutionary effects. The median values are beta=+0.14 day/Myr for the 27 stars showing a period increase and beta=-0.20 day/Myr for the 21 stars showing a period decrease. The large number of RR Lyr stars showing a period decrease (i.e., blueward evolution) is a new and intriguing result. There is an excess of RR Lyr stars showing large, positive $\beta$ values. Moreover, the observed beta values are slightly larger than those predicted by theoretical models.Comment: 15 pages, 9 figures; to be published in Astronomy and Astrophysics; full resolution version available at http://dbrr.ast.obs-mip.fr/tarot/publis/publis.htm

Long-term photometric behaviour of XZ Dra Binarity or magnetic cycle of a Blazhko type RRab star

The extended photometry available for XZ Dra, a Blazhko type RR Lyrae star, makes it possible to study its long-term behavior. It is shown that its pulsation period exhibit cyclic, but not strictly regular variations with approx. 7200 d period. The Blazhko period (approx. 76 d) seems to follow the observed period changes of the fundamental mode pulsation with dP_B/dP_0=7.7 x 10^4 gradient. Binary model cannot explain this order of period change of the Blazhko modulation, nevertheless it can be brought into agreement with the O-C data of the pulsation. The possibility of occurrence of magnetic cycle is raised.Comment: 13 pages, 11 figures (submitted to A&A

The Variable Stars and Blue Horizontal Branch of the Metal-Rich Globular Cluster NGC 6441

We present time-series VI photometry of the metal-rich ([Fe/H] = -0.53) globular cluster NGC 6441. Our color-magnitude diagram shows that the extended blue horizontal branch seen in Hubble Space Telescope data exists in the outermost reaches of the cluster. The red clump slopes nearly parallel to the reddening vector. A component of this slope is due to differential reddening, but part is intrinsic. The blue horizontal branch stars are more centrally concentrated than the red clump stars. We have discovered about 50 new variable stars near NGC 6441, among them eight or more RR Lyrae stars which are very probably cluster members. Comprehensive period searches over the range 0.2-1.0 days yielded unusually long periods (0.5-0.9 days) for the fundamental pulsators compared with field RR Lyrae of the same metallicity. Three similar long-period RR Lyrae are known in other metal-rich globulars. With over ten examples in hand, it seems that a distinct sub-class of RR Lyrae is emerging. The observed properties of the horizontal branch stars are in reasonable agreement with recent models which invoke deep mixing to enhance the atmospheric helium abundance, while they conflict with models which assume high initial helium abundance. The light curves of the c-type RR Lyrae seem to have unusually long rise times and sharp minima. Reproducing these light curves in stellar pulsation models may provide another means of constraining the physical variables responsible for the anomalous blue horizontal branch extension and sloped red clump observed in NGC 6441.Comment: 30 pages plus 6 EPS and 6 JPEG figures; uses AAS TeX. Accepted by the Astronomical Journal. Minor changes include computing He abundance, modifications to Figs 1 and 8, and expansion on idea that blue HB stars may be produced in binarie