Spectral analysis of the sdO K 648, the exciting star of the planetary nebula Ps 1 in the globular cluster M 15 (NGC 7078)

We present a spectral analysis of the sdO central star K 648 based on medium-resolution optical and high-resolution UV spectra. The photospheric parameters are determined by means of state-of-the-art NLTE model atmosphere techniques. We found Teff = 39 +/- 2 kK and log g = 3.9 +/- 0.2. The helium (He/H=0.08) and oxygen (O/H=0.001) abundances are about solar while carbon is enriched by a factor of 2.5 (C/H=0.001). Nitrogen (N/H = 10**(-6), [N/H] = -2.0) appears at a sub-solar value. However, these metal abundances are much higher than the cluster's metallicity M 15: [Fe/H] = -2.25). The surface composition appears to be a mixture of the original hydrogen-rich material and products of helium burning (3 alpha process) which have been mixed up to the surface. The abundances of He, C, and N are consistent with the nebular abundance, while O is considerably more abundant in the photosphere than in the nebula. From a comparison of its position in the log Teff - log g plane with evolutionary calculations a mass of 0.57 (+0.02, -0.01) Msun and a luminosity of 3810 +/- 1200 Lsun are deduced. Our spectroscopic distance d = 11.1 (+2.4, -2.9) kpc is in agreement with the distance of M 15 as determined by Alves et al. (2000). From the GHRS spectra we measure a radial velocity of vrad = -130 km/sec.Comment: 8 pages, 13 figure

Luminosities of AGB Variables

The prevailing evidence suggests that most large-amplitude AGB variables follow the period luminosity (PL) relation that has been established for Miras in the LMC and galactic globular clusters. Hipparcos observations indicate that most Miras in the solar neighbourhood are consistent with such a relation. There are two groups of stars with luminosities that are apparently greater than the PL relation would predict: (1) in the LMC and SMC there are large amplitude variables, with long periods, P> 420 days, which are probably undergoing hot bottom burning, but which are very clearly more luminous than the PL relation (these are visually bright and are likely to be among the first stars discovered in more distant intermediate age populations); (2) in the solar neighbourhood there are short period, P<235 days, red stars which are probably more luminous than the PL relation. Similar short-period red stars, with high luminosities, have not been identified in the Magellanic Clouds.Comment: 8 pages, 2 figure, to be published in Mass-Losing Pulsating Stars and their Circumstellar Matter, Y. Nakada & M. Honma (eds) Kluwer ASSL serie

UV (IUE) spectra of the central stars of high latitude planetary nebulae Hb7 and Sp3

We present an analysis of the UV (IUE) spectra of the central stars of Hb7 and Sp3. Comparison with the IUE spectrum of the standard star HD 93205 leads to a spectral classification of O3V for these stars, with an effective temperature of 50,000 K. From the P-Cygni profiles of CIV (1550 A), we derive stellar wind velocities and mass loss rates of -1317 km/s +/- 300 km/s and 2.9X10^{-8} solar mass yr^{-1} and -1603 km/s +/- 400 km/s and 7X10^{-9} solar mass yr^{-1} for Hb7 and Sp3 respectively. From all the available data, we reconstruct the spectral energy distribution of Hb7 and Sp3.Comment: 4 pages, 3 figures, latex, accepted for publication in Astronomy & Astrophysic

Element Abundance Determination in Hot Evolved Stars

The hydrogen-deficiency in extremely hot post-AGB stars of spectral class PG1159 is probably caused by a (very) late helium-shell flash or a AGB final thermal pulse that consumes the hydrogen envelope, exposing the usually-hidden intershell region. Thus, the photospheric element abundances of these stars allow us to draw conclusions about details of nuclear burning and mixing processes in the precursor AGB stars. We compare predicted element abundances to those determined by quantitative spectral analyses performed with advanced non-LTE model atmospheres. A good qualitative and quantitative agreement is found for many species (He, C, N, O, Ne, F, Si, Ar) but discrepancies for others (P, S, Fe) point at shortcomings in stellar evolution models for AGB stars. Almost all of the chemical trace elements in these hot stars can only be identified in the UV spectral range. The Far Ultraviolet Spectroscopic Explorer and the Hubble Space Telescope played a crucial role for this research.Comment: To appear in: Recent Advances in Spectroscopy: Theoretical, Astrophysical, and Experimental Perspectives, Proceedings, Jan 28 - 31, 2009, Kodaikanal, India (Springer

Speckle interferometry and radiative transfer modelling of the Wolf-Rayet star WR 118

WR 118 is a highly evolved Wolf-Rayet star of the WC10 subtype surrounded by a permanent dust shell absorbing and re-emitting in the infrared a considerable fraction of the stellar luminosity. We present the first diffraction-limited 2.13micron speckle interferometric observations of WR 118 with 73 mas resolution. The speckle interferograms were obtained with the 6m telescope at the Special Astrophysical Observatory. The two-dimensional visibility function of the object does not show any significant deviation from circular symmetry. The visibility curve declines towards the diffraction cut-off frequency to 0.66 and can be approximated by a linear function. Radiative transfer calculations have been carried out to model the spectral energy distribution, given in the range of 0.5-25micron, and our 2.13micron visibility function, assuming spherical symmetry of the dust shell. Both can be fitted with a model containing double-sized grains (``small'' and ``large'') with the radii of a = 0.05micron and 0.38micron, and a mass fraction of the large grains greater than 65%. Alternatively, a good match can be obtained with the grain size distribution function n(a)~a^-3, with a ranging between 0.005micron and 0.6micron. At the inner boundary of the modelled dust shell (angular diameter (17 +/- 1)mas), the temperature of the smallest grains and the dust shell density are 1750K +/- 100K and (1 +/- 0.2)x10^-19 g/cm^3, respectively. The dust formation rate is found to be (1.3 +/- 0.5)x10^-7 Msol/yr assuming Vwind = 1200 km/s.Comment: 6 pages including 4 PostScript figures, also available from http://www.mpifr-bonn.mpg.de/div/ir-interferometry/publications.html; accepted for publication in Astronomy & Astrophysic

Post-AGB Stars in Globular Clusters and Galactic Halos

We discuss three aspects of post-AGB (PAGB) stars in old populations. (1) HST photometry of the nucleus of the planetary nebula (PN) K 648 in the globular cluster (GC) M15 implies a mass of 0.60 Msun, in contrast to the mean masses of white dwarfs in GCs of ~0.5 Msun. This suggests that K 648 is descended from a merged binary, and we infer that single Pop II stars do not produce visible PNe. (2) Yellow PAGB stars are the visually brightest stars in old populations (Mv ~ -3.3) and are easily recognizable because of their large Balmer jumps; thus they show great promise as a Pop II standard candle. Two yellow PAGB stars in the GC NGC 5986 have the same V magnitudes to within +/-0.05 mag, supporting an expected narrow luminosity function. (3) Using CCD photometry and a u filter lying below the Balmer jump, we have detected yellow PAGB stars in the halo of M31 and in its dwarf elliptical companion NGC 205. With the Milky Way zero point, we reproduce the Cepheid distance to M31, and find that NGC 205 is ~100 kpc further away than M31. The star counts imply a yellow PAGB lifetime of about 25,000 yr, and their luminosities imply masses near 0.53 Msun.Comment: 6 pages, 2 figures. To appear in proceedings of Torun, Poland, workshop on "Post-AGB Objects (Proto-Planetary Nebulae) as a Phase of Stellar Evolution," ed. S.K. Gorn

On the linear fractional self-attracting diffusion

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection local time exists in L^2 if $\frac12<H<\frac3{4}$.Comment: 14 Pages. To appear in Journal of Theoretical Probabilit