Sample genealogies and genetic variation in populations of variable size

We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression, Eq. (27), for the moments of these distributions for an arbitrary smooth dependence of the population size on time. We investigate how the frequency of population-size variations alters the distributions. This allows us to discuss their influence on the distribution of the number of mutations, and on the population homozygosity in populations with variable size.Comment: 19 pages, 8 figures, 1 tabl

Exploring wind-driving dust species in cool luminous giants III. Wind models for M-type AGB stars: dynamic and photometric properties

Stellar winds observed in asymptotic giant branch (AGB) stars are usually attributed to a combination of stellar pulsations and radiation pressure on dust. Shock waves triggered by pulsations propagate through the atmosphere, compressing the gas and lifting it to cooler regions, which create favourable conditions for grain growth. If sufficient radiative acceleration is exerted on the newly formed grains through absorption or scattering of stellar photons, an outflow can be triggered. Strong candidates for wind-driving dust species in M-type AGB stars are magnesium silicates (Mg$_2$SiO$_4$ and MgSiO$_3$). Such grains can form close to the stellar surface, they consist of abundant materials and, if they grow to sizes comparable to the wavelength of the stellar flux maximum, they experience strong acceleration by photon scattering. We use a frequency-dependent radiation-hydrodynamics code with a detailed description for the growth of Mg$_2$SiO$_4$ grains to calculate the first extensive set of time-dependent wind models for M-type AGB stars. The resulting wind properties, visual and near-IR photometry and mid-IR spectra are compared with observations.We show that the models can produce outflows for a wide range of stellar parameters. We also demonstrate that they reproduce observed mass-loss rates and wind velocities, as well as visual and near-IR photometry. However, the current models do not show the characteristic silicate features at 10 and 18 $\mu$m as a result of the cool temperature of Mg$_2$SiO$_4$ grains in the wind. Including a small amount of Fe in the grains further out in the circumstellar envelope will increase the grain temperature and result in pronounced silicate features, without significantly affecting the photometry in the visual and near-IR wavelength regions.Comment: 11 pages, 14 figure

The Calibration of Stromgren uvby-Hbeta Photometry for Late-Type Stars -- a Model Atmosphere Approach

We aim to test the power of theoretical calibrations based on a new generation of MARCS models by comparisons with observational photomteric data. We calculate synthetic uvby-Hbeta colour indices from synthetic spectra. A sample of 388 field stars as well as stars in globular clusters is used for a direct comparison of the synthetic indices versus empirical data and for scrutinizing the possibilities of theoretical calibrations for temperature, metallicity and gravity. We show that the temperature sensitivity of the synthetic (b-y) colour is very close to its empirical counterpart, whereas the temperature scale based upon Hbeta shows a slight offset. The theoretical metallicity sensitivity of the m1 index (and for G-type stars its combination with c1) is somewhat larger than the empirical one, based upon spectroscopic determinations. The gravity sensitivity of the synthetic c1 index shows a satisfactory behaviour when compared to obervations of F stars. For stars cooler than the sun a deviation is significant in the c1-(b-y) diagram. The theoretical calibrations of (b-y), (v-y) and c1 seem to work well for Pop II stars and lead to effective temperatures for globular cluster stars supporting recent claims by Korn et al. (2007) that atomic diffusion occurs in stars near the turnoff point of NGC 6397. Synthetic colours of stellar atmospheres can indeed be used, in many cases, to derive reliable fundamental stellar parameters. The deviations seen when compared to observational data could be due to incomplete linelists but are possibly also due to effects of assuming plane-parallell or spherical geometry and LTE

Exploring wind-driving dust species in cool luminous giants II. Constraints from photometry of M-type AGB stars

The heavy mass loss observed in evolved asymptotic giant branch (AGB) stars is usually attributed to a two-stage process: atmospheric levitation by pulsation-induced shock waves, followed by radiative acceleration of newly formed dust grains. The dust transfers momentum to the surrounding gas through collisions and thereby triggers a general outflow. Radiation-hydrodynamical models of M-type AGB stars suggest that these winds can be driven by photon scattering -- in contrast to absorption -- on Fe-free silicate grains of sizes 0.1--1\,$\mu$m. In this paper we study photometric constraints for wind-driving dust species in M-type AGB stars, as part of an ongoing effort to identify likely candidates among the grain materials observed in circumstellar envelopes. To investigate the scenario of stellar winds driven by photon scattering on dust, and to explore how different optical and chemical properties of wind-driving dust species affect photometry we focus on two sets of dynamical models atmospheres: (i) models using a detailed description for the growth of Mg$_2$SiO$_4$ grains, taking into account both scattering and absorption cross-sections when calculating the radiative acceleration, and (ii) models using a parameterized dust description, constructed to represent different chemical and optical dust properties. By comparing synthetic photometry from these two sets of models to observations of M-type AGB stars we can provide constraints on the properties of wind-driving dust species. Photometry from wind models with a detailed description for the growth of Mg$_2$SiO$_4$ grains reproduces well both the values and the time-dependent behavior of observations of M-type AGB stars, providing further support for the scenario of winds driven by photon scattering on dust.Comment: Accepted for publication in A&A. 15 pages, 14 figure