Selected topics in the evolution of low-mass stars

Low-mass stars play a key role in many different areas of astrophysics. In this article, I provide a brief overview of the evolution of low-mass stars, and discuss some of the uncertainties and problems currently affecting low-mass stellar models. Emphasis is placed on the following topics: the solar abundance problem, mass loss on the red giant branch, and the level of helium enrichment associated to the multiple populations that are present in globular clusters.Comment: 10 pages, 5 figures. Invited review, to appear in "Ageing low-mass stars: from red giants to white dwarfs", LIAC40 proceeding

A Semi-Empirical Study of the Mass Distribution of Horizontal Branch Stars in M3 (NGC 5272)

Horizontal branch (HB) stars in globular clusters offer us a probe of the mass loss mechanisms taking place in red giants. For M3 (NGC 5272), different shapes for the HB mass distribution have been suggested, including Gaussian and sharply bimodal alternatives. Here we study the mass distribution of HB stars in M3 by comparing evolutionary tracks and photometric observations. Our approach is thus of a semi-empirical nature, describing as it does the mass distribution that is favored from the standpoint of canonical stellar evolutionary predictions for the distribution of stars across the CMD. We locate, for each individual HB star, the evolutionary track whose distance from the star's observed color and magnitude is a minimum. Artificial tests reveal that our method would be able to detect a bimodal mass distribution, if present. We study the impact of different procedures for taking into account the evolutionary speed, and conclude that they have but a small effect upon the inferred mass distribution. We find that a Gaussian shape, though providing a reasonable first approximation, fails to account for the detailed shape of M3's HB mass distribution: the latter may have skewness and kurtosis that deviate slightly from a perfectly Gaussian solution. Alternatively, the excess of stars towards the wings of the distribution may also be accounted for in terms of a bimodal distribution in which both the low- and the high-mass modes are normal, the former being significantly wider than the latter. However, we also show that the inferred distribution of evolutionary times is inconsistent with theoretical expectations. This result is confirmed on the basis of three independent sets of HB models, suggesting that the latter underestimate the effects of evolution away from the zero-age HB. (abridged)Comment: 12 pages, 13 figures. A&A, in pres

Kurtosis and Large--Scale Structure

We discuss the non--linear growth of the excess kurtosis parameter of the smoothed density fluctuation field $\delta$, S_4\equiv[\lan\delta^{\,4}\ran-3\lan\delta^{\,2}\ran^2]/ \lan\delta^{\,2}\ran^3 in an Einstein--de Sitter universe. We assume Gaussian primordial density fluctuations with scale--free power spectrum $P(k)\propto k^{\,n}$ and analyze the dependence of $S_4$ on primordial spectral index $n$, after smoothing with a Gaussian filter. As already known for the skewness ratio $S_3$, the kurtosis parameter is a {\it decreasing function} of $n$, both in exact perturbative theory and in the Zel'dovich approximation. The parameter $S_4$ provides a powerful statistics to test different cosmological scenarios.Comment: 11 pages in Latex (plus 1 figure), SISSA 127/93/

Velocity Differences as a Probe of Non--Gaussian Density Fields

We examine the multi--point velocity field for non--Gaussian models as a probe of non--Gaussian behavior. The two--point velocity correlation is not a useful indicator of a non--Gaussian density field, since it depends only on the power spectrum, even for non--Gaussian models. However, we show that the distribution of velocity differences \bfv_1 - \bfv_2, where \bfv_1 and \bfv_2 are measured at the points \bfr_1 and \bfr_2, respectively, is a good probe of non--Gaussian behavior, in that p(\bfv_1 - \bfv_2) tends to be non--Gaussian whenever the density field is non--Gaussian. As an example, we examine the behavior of p(\bfv_1 - \bfv_2) for non--Gaussian seed models, in which the density field is the convolution of a distribution of points with a set of density profiles. We apply these results to the global texture model.Comment: 18 pages, LATEX style, SISSA-37-94-A, OSU-TA-4-9