and Cosmology

2. The Milky Way as a Galaxy
74
produce such a large number of white dwarfs as a final
stage of stellar evolution, the total star formation
in our Milky Way, integrated over its lifetime, needs
to be significantly larger than normally assumed. In
this case, many more massive stars would also have
formed, which would then have released the metals they
produced into the ISM, both by stellar winds and in supernova
explosions. In such a scenario, the metal content
of the ISM would therefore be distinctly higher than is
actually observed. The only possibility of escaping this
argument is with the hypothesis that the mass function
of newly formed stars (the initial mass function, IMF)
was different in the early phase of the Milky Way compared
to that observed today. The IMF that needs to be
assumed in this case is such that for each star of intermediate
mass which evolves into a white dwarf, far fewer
high-mass stars, responsible for the metal enrichment
of the ISM, must have formed in the past compared
to today. However, we lack a plausible physical model
for such a scenario, and it is in conflict with the starformation
history that we observe in the high-redshift
Universe (see Chap. 9).
Neutron stars can be excluded as well, because
they are too massive (typically > 1M ⊙ ); in addition,
they are formed in supernova explosions, implying that
the aforementioned metallicity problem would be even
greater for neutron stars. Would stellar-mass black holes
be an alternative? The answer to this question depends
on how they are formed. They could not originate in SN
explosions, again because of the metallicity problem.
If they had formed in a very early phase of the Universe
(they are then called primordial black holes), this
would be an imaginable, though perhaps quite exotic,
alternative.
However, we have strong indications that the
interpretation of the MACHO results is not as straightforward
as described above. Some doubts have been
raised as to whether all events reported as being due to
microlensing are in fact caused by this effect. In fact,
one of the microlensing source stars identified by the
MACHO group showed another bump seven years after
the first event. Given the extremely small likelihood of
two microlensing events happening to a single source
this is almost certainly a star with unusual variability.
As argued previously, by means of t E we only measure
a combination of lens mass, transverse velocity,
and distance. The result given in Fig. 2.29 is therefore
based on the statistical analysis of the lensing events
in the framework of a halo model that describes the
shape and the radial density profile of the halo. However,
microlensing events have been observed for which
more than just t E can be determined – e.g., events in
which the lens is a binary star, or those for which t E
is larger than a few months. In this case, the orbit of
the Earth around the Sun, which is not a linear motion,
has a noticeable effect, causing deviations from the
standard curve. Such parallax events have indeed been
observed. 13 Three events are known in the direction of
the Magellanic Clouds in which more than just t E could
be measured. In all three cases the lenses are most likely
located in the Magellanic Clouds themselves (an effect
called self-lensing) and not in the halo of the Milky
Way. If for those three cases, where the degeneracy between
lens mass, distance, and transverse velocity can
be broken, the respective lenses are not MACHOs in the
Galactic halo, we might then suspect that in most of the
other microlensing events the lens is not a MACHO either.
Therefore, it is currently unclear how to interpret
the results of the microlensing surveys. In particular, it
is unclear to what extent self-lensing contributes to the
results. Furthermore, the quantitative results depend on
the halo model.
The EROS collaboration used an observation strategy
which was sightly different from that of the MACHO
group, by observing a number of fields in very short time
intervals. Since the duration of a lensing event depends
on the mass of the lens as Δt ∝ M 1/2 – see (2.88) – they
were also able to probe very small MACHO masses.
The absence of lensing events of very short duration
then allowed them to derive limits for the mass fraction
of such low-mass MACHOs, as is shown in Fig. 2.30.
Despite this unsettled situation concerning the interpretation
of the MACHO results, we have to emphasize
that the microlensing surveys have been enormously
successful experiments because they accomplished
exactly what was expected at the beginning of the observations.
They measured the lensing probability in
the direction of the Magellanic Clouds and the Galactic
bulge. The fact that the distribution of the lenses differs
from that expected by no means diminishes the success
of these surveys.
13 These parallax events in addition prove that the Earth is in fact
orbiting around the Sun – even though this is not really a new insight.