2. The age bias
The red clump population will illustrate the main thrust of our argument. Clump stars have burning helium cores whose size is approximately independent of the total mass of the object. They also have the same luminosity and hence they spend a fixed amount of time in the clump, irrespective of their mass m. Such objects are evolved post-MS stars, which does not mean that they are necessarily old. We have assumed a Salpeter Initial Mass Function for the various LMC stellar populations
with . The stellar formation history has been borrowed from Geha et al. (1998). Their preferred model (e) corresponds to a stellar formation rate that has remained constant for 10 Gyr since the formation of the LMC 12 Gyr ago. Then, two Gyr ago, has increased by a factor of three. The number of stars that formed at time t and whose mass is comprised between m and may be expressed as
We have assumed a mass-luminosity relation on the MS so that the stellar lifetime may be expressed as (since ). With these oversimplified but natural assumptions, a star whose initial mass is is still today on the MS and cannot have reached the clump. Conversely, a heavier star with may well be today in a helium core burning stage provided that its formation epoch lies in the range between (the object has just begun core helium burning) and (the star is about to leave the red clump). The number of RC stars observed today with progenitor mass in the range between m and is therefore given by
To get more insight into the age bias at stake, we can parameterize the progenitor mass m in terms of the age . The previous relation simplifies into
where . This may be directly compared to the age distribution of the bulk of the LMC stars that goes like . With a Salpeter mass function and , we get a value of . The excess of young RC stars goes as and the bias is obvious. Other IMF are possible and a spectral index as large as would be required to invalidate the effect. HST data analyzed by Holtzman et al. (1997) nevertheless point towards a spectral index that extends from 0.6 up to 2.1 for stars in the mass range . The average value corresponds actually to a Salpeter law.
There has been furthermore a recent burst in the LMC stellar formation rate. In order to model it, we may express the total number of today's RC stars as an integral where the progenitor mass m runs from up to the tip of the IMF whose actual value is irrelevant and has been set equal to infinity here for simplicity. Notice that the specific progenitor mass corresponds to stars born 2 Gyr ago, when the stellar formation rate increased by a factor of 3. Stars which formed before that epoch will be referred to as old. Their number is given by
On the other hand, the number of young clump stars is obtained similarly, with masses in excess of . We readily infer a fraction of young stars
Three quarters of the clump stars observed today in the LMC have thus formed less than 2 Gyr ago, during the recent period of stellar formation mentioned above. Integrating over the RC population
yields the average age
This gives a numerical value of Gyr. We thus conclude that today's clump stars are, on average, much younger than the LMC disk.
© European Southern Observatory (ESO) 1999
Online publication: October 14, 1999