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Not enough stellar mass objects to fill the galactic halo?

17 April 2000

The universe contains a lot more than meets the eye.
Sophisticated experiments search diligently for this invisible
dark matter. Here Alain Milsztajn of Saclay describes
the latest results to emerge from the microlensing technique.

The mass of our galaxy (the Milky Way) can be computed
from the dynamics of its rotation and of the motion of its
satellites. It can also be evaluated by adding up its visible
components, primarily stars. That these two estimates disagree
by a factor of 5-10 constitutes the problem of galactic dark
matter.

Either the Newtonian/Einsteinian laws of
dynamics are wrong at the galactic scale, or there exists some
form of galactic matter that does not emit or absorb enough
electromagnetic radiation to be directly “visible”. Studies of
many other spiral galaxies confirm that this problem is not
unique to the Milky Way.

Originally proposed in 1986
by B Paczynski of Princeton, gravitational microlensing is a
novel and indirect way to search for galactic dark matter
through the deflection and magnification of the light of
extragalactic stars. The search for microlensing has recently
shed new light on the galactic dark matter
puzzle.

In 1990, three groups
began the search for gravitational microlensing. The main
problem was the inherent large scale of such surveys. To
produce a detectable magnification of the light of a distant star,
an intervening compact massive object has to come closer to
the star’s line of sight than one milli-arcsecond, or five
nanoradians (the angle subtended on Earth by an Apollo
mission lunar jeep); the tighter the alignment, the larger the
magnification.

This happens so seldom that one expects
less than one star in a million to be affected significantly at any
given time, hence the necessity to survey some 10 million stars
over many years. In contrast, variable stars are more than a
thousand times as frequent and constitute a serious
experimental background.

The shape of microlensing
magnification is predictable and does not depend on the
wavelength, contrary to most variable stars. The phenomenon
is transient, because of the motion of the dark lensing object
with respect to the distant star. Its duration scales as the square
root of the lensing object mass, and this can be used to
estimate these masses.

To simplify, one could say that
two of the groups, EROS (Expérience de Recherche d’Objets
Sombres – an experiment to search for dark objects) and
MACHO (Massive Astronomical Compact Halo Objects), were
most concerned with the dark matter problem. To probe the
content of the galactic halo, they chose to monitor stars in the
Magellanic Clouds – two irregular dwarf galaxies, satellites of
the Milky Way, that lie close to the celestial South
Pole.

The third group, OGLE (Optical Gravitational
Lensing Experiment), chose to look first for microlensing
where it was bound to find some – the centre of our galaxy.
The microlensing rate there owing to known low-mass stars
was expected to be about one in a million per year. In contrast,
the rate towards the Magellanic Clouds could be anywhere
between zero, if there are no compact dark objects in the
galactic halo, and about a thousand times the galactic centre
rate, if the halo is swarming with lunar mass dark
bodies.

The main goal of EROS and MACHO was to
detect a few microlensing events caused by brown dwarfs –
would-be stars not massive enough to burn via thermonuclear
reactions. These objects, between a tenth and a hundredth the
size of the Sun, would give rise to a microlensing rate of the
order of the expected galactic centre
rate.

In September 1993 the
discovery of the first microlensing candidates by the three
groups aroused high hopes that the galactic dark matter
problem was about to be solved. However, in the following
years a gradual divergence appeared between the EROS and
MACHO results. Based on two years of Large Magellanic
Cloud (LMC) CCD camera images, the MACHO group
presented its result as pointing to a galactic halo half-full of 0.5
± 0.2 solar mass objects, and compatible with being totally
comprised of such objects.

In contrast the EROS group
observed such a small number of candidate microlensing
events that it published only upper limits, first based on a
photographic plate LMC survey (1990-4), and then on a
survey, started in 1996, of the Small Magellanic Cloud (SMC),
which uses two large CCD cameras. The EROS limits
excluded, in particular, a halo full of 0.5 solar mass
objects.

Despite these somewhat inconsistent results,
agreement was reached on one important point: because all
microlensing candidates observed by MACHO and EROS
lasted longer than a month, the halo could contain no more
than 10-20% of dark objects in the wide mass range between
the mass of planet Mercury and one-tenth that of the Sun, that
is from 10-7 to 0.1 solar masses. This excluded
brown dwarfs – the dark matter candidate that had been the
main motivation for this search (figure
1).

Fortunately the past
months have witnessed a reconciliation of the MACHO and
EROS findings. The latter presented results from the first two
years of an ongoing six-year survey of 17 million LMC stars
that produced a meagre crop of two new microlensing
candidates. Combined with their previous limits, this enables
them to exclude a galactic halo fully comprised of objects of up
to four solar masses – quite a respectable mass for a stellar
object. (For a halo of 0.5 solar mass objects, the upper limit is
now near 30%; figure 1.)

MACHO has analysed almost
six years of LMC images out of seven-and-a-half years of
surveying, and it has now stopped taking data. From its 13-17
observed microlensing candidates, it now favours a 20%
contribution of 0.5 solar mass objects to the halo mass budget,
but these are compatible with halo mass fractions ranging from
8% to 50%.

The duration of the candidates is similar, so
that both results are compatible. However, the two groups
interpret them differently. The MACHO collaboration favours
an interpretation in terms of galactic halo objects. The
distribution of stellar luminosities of its microlensing candidates
agrees with that of LMC stars, which is to be expected given
that the dark lensing objects do not choose the LMC star that
they will lens for. The distribution of magnifications is also
compatible with a random distance of the lens to the star’s line
of sight.

These two tests could have revealed a possible
contamination of the sample by intrinsic variable stars, but they
do not shed light on the position of the dark lenses. This can be
achieved by studying the spatial distribution of microlensing
candidates, which should follow that of LMC stars in the case
of halo lenses, or be more peaked towards the LMC centre if
the lenses are low-mass LMC stars.

The MACHO group
finds that the observed distribution favours halo lenses, but that
it cannot completely exclude LMC lenses. The two options are,
of course, very different in terms of the galactic dark matter
composition.

With three to four microlensing candidates
towards the Magellanic Clouds over eight years, EROS has a
harder time comparing measured and expected distributions.
However, it makes the following observations: compared with
MACHO, EROS has chosen to monitor less frequently more
stars, spread over a three times wider solid angle. Thus the
smaller EROS lensing rate could be interpreted as a spatial
dependence of the event rate, favouring the LMC-lens
hypothesis. Moreover, while MACHO seems rather confident
that its sample is background free, no such claim is heard from
EROS.

Small Magellanic Cloud

Finally,
there is the question of the SMC, where one candidate was
seen by both groups in 1997. This event is longer than those of
all EROS or MACHO LMC candidates, which does not favour
its interpretation as a halo lens: as the Magellanic Clouds are
separated by only 20° in the sky and are at comparable
distances from us, one would expect the characteristics of
(halo) microlensing events towards both clouds to be very
similar.

More quantitatively, the probability of this event
being compatible with the LMC event durations is only 3%.
On the contrary, as stellar velocities in the SMC are smaller
than in those the LMC, it would be natural for SMC
microlensing events to last longer if the lenses belong to the
Magellanic Clouds.

In addition, the SMC event lasted
long enough that the Earth had time to complete
three-quarters of its orbit around the Sun during the
magnification. This could have led to observable microlensing
deformations. Such effects are not seen in EROS and MACHO
data, implying that the lens is either a low-mass SMC star or a
few solar-mass halo object. In the latter case its mass would not
be compatible with that deduced from lenses towards the
LMC.

Thus EROS concludes that this particular lens lies
in the SMC. Much is expected from the comparison of LMC
and SMC events but, because there are only a fifth the number
of stars in the latter, no definitive conclusion can yet be
reached. Nevertheless, EROS expects to be able to make a
statement with an analysis of four years of data. The MACHO
analysis of SMC images is also eagerly awaited.

If the
MACHO interpretation is correct and there are plenty of half a
solar mass objects in the galactic halo, the next challenge is to
find out what they are. They cannot be ordinary stars, because
these would be bright enough to be visible. One exotic
scenario is primordial black holes made in the early universe at
the time of the quark-hadron transition. Old white dwarf stars
are another possibility: there are counter-arguments to their
abundant presence in the halo, but they have the advantage
that they could be detected by looking for nearby, dim
high-velocity objects. Some groups are conducting such
searches, including EROS. One group, led by R Ibata (Max
Planck, Heidelberg), has claimed the detection of a few halo
white dwarfs, but their interpretation as halo objects is
unconfirmed.

Valuable results

Whatever the
future developments involving galactic dark matter,
microlensing surveys have already provided concrete results.
The lensing probability towards the centre of the galaxy was
found by the OGLE and MACHO groups to be three times as
large as expected, so that microlensing can teach us much
about galactic structure.

The surveys have also yielded
many variable stars. This has allowed, for example, studies with
unprecedented statistics of Magellanic Cloud Cepheids, a
pivotal cosmic yardstick, as well as the discovery of new types
of variable stars.

Finally, the monitoring of long
microlensing events of bright stars provides a novel way to
look for planets around the lenses. Compared with the current,
highly successful searches that use precise measurements of
stellar radial velocities, microlensing should be sensitive to
lower-mass planets orbiting more distant and more typical
stars.

There is a good chance that, after reconciling their
results, EROS and MACHO will soon agree. A conclusion that
can already be drawn is that the largest part of galactic dark
matter does not comprise of dark astronomical objects lighter
than a few solar masses.

As far as microlensing is
concerned, the search should now be extended to longer
events corresponding to heavier lensing objects. In parallel, the
groups looking for other dark matter candidates, such as
Weakly Interacting Massive Particles, with underground or
underwater detectors or at large particle accelerators, will
certainly be encouraged by the recent microlensing
results.

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