Aims. An asteroseismological study of PG 1159−035, the prototype of the GW Vir variable stars, has been performed on the basis of detailed and full PG1159 evolutionary models presented by Miller . Methods. We carried out extensive computations of adiabatic g-mode pulsation periods on PG1159 evolutionary models with stellar masses spanning the range 0.530 to 0.741M⊙. These models were derived from the complete evolution of progenitor stars, including the thermally pulsing AGB phase and the born-again episode. We constrained the stellar mass of PG 1159−035 by comparing the observed period spacing with the asymptotic period spacing and with the average of the computed period spacings. We also employed the individual observed periods reported by Costa et al. (2007) to find a representative seismological model for PG 1159−035.Results. We derive a stellar mass in the range 0.56 − 0.59M⊙ from the period-spacing data alone. We also find, on the basis of a period-fit procedure, an asteroseismological model representative of PG 1159−035 that reproduces the observed period pattern with an average of the period differences of δΠi = 0.64 − 1.03 s, consistent with the expected model uncertainties. The model has an effective temperature T eff = 128 000 +8 600 −2 600 K, a stellar mass M * = 0.565 +0.025 −0.009 M⊙, a surface gravity log g = 7.42 +0.21 −0.12 , a stellar luminosity and radius of log(L * /L⊙) = 2.15 ± 0.08 and log(R * /R⊙) = −1.62 +0.06 −0.09 , and a He-rich envelope thickness of Menv = 0.017M⊙. The results of the period-fit analysis carried out in this work suggest that the surface gravity of PG 1159−035 would be 1 σ larger than the spectroscopically inferred gravity. For our best-fit model of PG 1159−035, all of the pulsation modes are characterized by positive rates of period changes, at odds with the measurements by .

GW Vir (PG 1159[035) is the prototype of the class of multiperiodic, nonradially pulsating hot white dwarfs, and shows a strong pulsation mode at 516 s. All measurements to date of the secular variation of the 516 s pulsation quote as best value s s~1. The original measurement P0 \ ([2.49^0.06) ] 10~11 gave two best solutions, and a s2 analysis indicated that the quoted value was preferred at the level of 0.97 probability. On other hand, the best-developed models for planetary nebula nuclei (PNNs), using models from the asymptotic giant branch as starting points and simulating the observed mass loss, provide positive values for any model with as PG 1159[035. This conÑict between the log (L /L _ ) [ 3, measurement and the theoretical models has been a challenge to stellar evolution theory.Exploiting a much larger data set and computational techniques previously unavailable, we show that the earlier analysis of the data grossly underestimated the true uncertainties due to interferences between frequencies. Using new data along with the old, and more accurate statistical methods, we calculated the secular period change of the 516 s pulsation, and obtained a positive value : P0 \ (]13.07^0.03) ] 10~11 s s~1. We show that three additional methods yield the same solution. This new value was the second best of the original possible solutions ; it was eliminated on the basis of statistical arguments that we show to be invalid. It is an order of magnitude larger than the theoretical predictions.Additionally, from rotational splitting analysis, we were able to estimate, for the Ðrst time, a limit to the secular variation of the rotational period s s~1, leading to a contraction P0 rot \ ([1.0^3.5) ] 10~11 timescale upper limit of s~1 with 99.5% probability.

Context. PG 1159-035, a pre-white dwarf with T eff ≃ 140 000 K, is the prototype of the PG 1159 spectroscopic class and the DOV pulsating class. Pulsating pre-white dwarf stars evolve rapidly: the effective surface temperature decreases rapidly, the envelope contracts and the inner structure experiences stratification due to gravitational settling. These changes in the star generate variations in its oscillation periods. The measurement of temporal change in the oscillation periods, Ṗ, allows us to estimate directly rates of stellar evolutionary changes, such as the cooling rate and the envelope contraction rate, providing a way to test and refine evolutionary models for pre-white dwarf pulsating stars. Aims. Previously, only two pulsation modes of the highest amplitudes for PG 1159-035 have had their Ṗ measured: the 516.0 s and the 539.3 s modes. We measured the Ṗ of a larger number of pulsation modes, increasing the number of constraints for evolutionary studies of PG 1159-035. We attempted to use the secular variations in the periods of multiplets to calculate the variation in the rotational period, the envelope contraction rate, and the cooling rate of the star. Methods. The period variations were measured directly from the PG 1159-035 observational data and refined by the (O-C) method. Results. We measured 27 pulsation mode period changes. The periods varied at rates of between 1 and 100 ms/yr, and several can be directly measured with a relative standard uncertainty below 10%. For the 516.0 s mode (the highest in amplitude) in particular, not only the value of Ṗ can be measured directly with a relative standard uncertainty of 2%, but the second order period change, P, can also be calculated reliably. By using the (O-C) method, we refined the Ṗs and estimated the Ps for six other pulsation periods. As a first application, we calculated the change in the PG 1559-035 rotation period, Ṗrot = (−2.13 ± 0.05) × 10 −6 ss −1 , the envelope contraction rate Ṙ = (−2.2 ± 0.5) × 10 −13 R ⊙ s −1 , and the cooling rate Ṫ = −1.42 × 10 −3 Ks −1 .

We report our study of features at the observed red end of the white dwarf cooling sequences for three Galactic globular clusters: NGC 6397, 47 Tucanae and M 4. We use deep colour-magnitude diagrams constructed from archival Hubble Space Telescope (ACS) to systematically investigate the blue turn at faint magnitudes and the age determinations for each cluster. We find that the age difference between NGC 6397 and 47 Tuc is 1.98 +0.44 −0.26 Gyr, consistent with the picture that metal-rich halo clusters were formed later than metal-poor halo clusters. We self-consistently include the effect of metallicity on the progenitor age and the initial-to-final mass relation. In contrast with previous investigations that invoked a single white dwarf mass for each cluster, the data shows a spread of white dwarf masses that better reproduce the shape and location of the blue turn. This effect alone, however, does not completely reproduce the observational data -the blue turn retains some mystery. In this context, we discuss several other potential problems in the models. These include possible partial mixing of H and He in the atmosphere of white dwarf stars, the lack of a good physical description of the collision-induced absorption process and uncertainties in the opacities at low temperatures. The latter are already known to be significant in the description of the cool main sequence. Additionally, we find that the present day local mass function of NGC 6397 is consistent with a top-heavy type, while 47 Tuc presents a bottom-heavy profile.

We report the discovery of two new variable stars in the metal-poor globular cluster NGC 288, found by means of time-series CCD photometry. We classified the new variables as SX Phoenicis due to their characteristic fundamental mode periods (1.02± 0.01 and 0.69 ± 0.01 hours), and refine the period estimates for other six known variables. SX Phe stars are known to follow a well-defined Period-Luminosity (P-L) relation and, thus, can be used for determining distances; they are more numerous than RR Lyraes in NGC 288. We obtain the P-L relation for the fundamental mode M V = (−2.59 ± 0.18) log P 0 (d) + (−0.34 ± 0.24) and for the first-overtone mode M V = (−2.59 ± 0.18) log P 1 (d) + (0.50 ± 0.25). Multi-chromatic isochrone fits to our UBV color-magnitude diagrams, based on the Dartmouth Stellar Evolution Database, provide [Fe/H] = -1.3 ± 0.1, E(B-V) = 0.02 ± 0.01 and absolute distance modulus (m-M) 0 = 14.72 ± 0.01 for NGC 288.