On the Post--Asymptotic Giant Branch Model for the Far-Ultraviolet Emission in Elliptical Galaxies

Recently, Burstein and coworkers, studying the nature of the far-UV emission in elliptical galaxies, found a well-defined correlation between the flux (relative to the visual) in the far-UV and the index Mg_2_ for a group of quiescent galaxies. The higher the flux in UV, the higher the Mg_2_ index and hence the metallicity of the galaxy. Furthermore, on the basis of the post-asymptotic giant branch (PAGB) star model for the UV emission, the same authors concluded that the masses of the PAGB stars are in the range 0.53-0.55 M_sun_, if the relation between the residual envelope mass M_env_ and the core mass M_f_ adopted by Schonberner is valid (see the discussion below for more details on this topic), and that the UV flux of metal-poor galaxies like M32 can be accounted for by PAGB stars with mass 0.55 M_sun_, whereas that of metal-rich galaxies like NGC 4649 can be matched by PAGB stars with mass 0.53 M_sun_ This implies that the metallicity-final mass relation suggested by the far-UV emission contradicts the expectation from stellar evolution theory. Other explanations were not considered particularly satisfactory. In this paper we endeavor to show that the above result is not in contradiction to the theory of asymptotic giant branch (AGB) stars, provided that the dependence of the final mass on mass loss and chemical composition is properly taken into account. We also show that the final mass-metallicity relation implied by the UV emission does not contradict the opposite trend shown by globular clusters, where the maximum AGB luminosity, hence core mass (or equivalently, final mass), of AGB stars increases with the metal content. Once more, the chemical composition is the key parameter of the apparent disagreement. In addition to this, we present fundamental relations between final mass and age for various alternatives for the chemical composition and mass-loss efficiency, which are used to date galaxies from the mass of PAGB stars implied by their far-UV emission. Finally, we address the question of the recent activity of star formation suspected to have occurred in some elliptical galaxies. In fact, it has long been debated whether or not the turnoff color of M32 indicates prolonged activity of star formation which terminated about 6 Gyr ago. In the case of giant elliptical galaxies with typical turnoff color (B-V) = 0.65 and [Fe/H] = 0.3-0.5, we find that the age from the UV emission method is consistent with the age from the turnoff, thus implying that star formation went to completion in early epochs and was confined within a narrow age range. In the case of galaxies with bluer turnoff (B-V) color and lower metallicity, such as M32, the ages derived from the two methods may be substantially different. Assuming for M32 the canonical values for the metallicity and turnoff color, [Fe/H] = 0 and (B-V) = 0, respectively, we find that the age inferred from the UV emission is larger by a few Gyr than that derived from the turnoff color--the latter, however, based on an accurate color-age relation. Nonetheless, since the turnoff color and metallicity are the result of photometric synthesis analysis, and uncertainties are always possible, if the metal content of M32 is as low as [Fe/H] = -0.3 as some studies seem to indicate, then the ages derived from the turnoff may be only 25% younger than the age from PAGB stars, thus throwing light on a point of controversy.