Astron. Astrophys. 350, L57-L61 (1999)
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
![[EQUATION]](img18.gif)
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
![[EQUATION]](img22.gif)
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
![[EQUATION]](img30.gif)
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
![[EQUATION]](img32.gif)
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
![[EQUATION]](img44.gif)
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
![[EQUATION]](img47.gif)
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
![[EQUATION]](img49.gif)
yields the average age
![[EQUATION]](img50.gif)
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
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