Let us now address the issue of gravitational microlensing.
This is a lensing of stars by other stars.
As you may recall, one possibility for the constituentce of baryonic dark matter
or maybe all of the dark matter was the in the form of some under luminous
substellar objects, which could be brown dwarfs or planets or even little black
holes or neutron stars, and gravitational microlensing offers a
way to test that. So if any such object passes along the
line of sight of some background star, it will cause gravitational magnification
and there, there will be first horizon brightness as it approaches the critical
radius and [UNKNOWN] so it will be a symmetric light curve,
it will also be same at all wavelengths because gravitational lensing is
achromatic. How often will this happen depends
obviously on a cross section and cross sections for stars that are very small,
they're down, because they're so very small compared to interstellar distances.
So in principle for any given star, it'll be extremely rare, and therefore, you'd
have to monitor a large number of stars in order to be able to catch one of
these. Here's some of the model light curves for
microlensing event. The peak magnification will depend on how
well aligned the passage is. The, the closer the better, of course.
And, how long does the event last will depend on the velocity of the lens
relative to the line of sight. Faster moving ones will cause shorter
events, obviously. In order to make this practical, one had
to monitor many millions of stars, and one good solution was to look towards
the large Magellanic Cloud, which is about 50 kiloparsecs away, where
many, many stars can be in the same field of view and then monitor for a whil
looking for such events. This was done by a team called MACHO, for
Massive Compact Halo Object, and also another team called OGLE, and since then,
many others. So there is a probability of seeing
lensing happen to any given star is about one part in 10 million per year, then you
better look at tens of millions of stars. Another possible direction is towards the
galactic bulge where a large number of galactic stars will be the same.
So MACHO and OGLE were just two experiments that started the whole thing.
MACHO monitored almost 12 millions stars for several years and OGLE continues to
monitor about 33 million stars. Many others have been started since then,
and now, this is a really well-established field.
Shown here on the right, is the first MACHO event detected, detected in
microlensing, and the two panels show light curving to
different filters. This was an important discriminator
against variable stars, because variable stars will tend to vary differently in
different filters, whereas gravitational lensing is unique in the sense that it
will work exactly the same for all wavelengths.
And on the left, we see many more different events,
to date there have been probably thousands and thousands of microlensing
discovered by different groups. Recall that Einstein radius essentially
defines the cross section for strong lensing.
And in this case, it would be as a critical impact parameter for lens
passing along the line or close to the line of sight.
Because mass of the lens and there is under square root in Einstein radius in
the area of the cross section is a square of that, it will be directly proportional
to the mass of the lens, thus, we can have an insight into the
masses of the lenses, and if we look at the whole population of
stars, then we can just add them up. So the net total fraction of all stars
that are being lensed per unit time is giving you effectively an optical depth
due to gravitational microlensing. The velocities of lenses are indicative
of the velocity dispersion of their populations, say halo, but they do not by
themselves say anything about lenses, and also, the implification says exactly
nothing about any given lens. Now, since their distances involved in
the expression of the Einstein radius, we have to know where the lenses are, and
so, the interpretation of the result depends critically on where do you assume
the lensing is happening? Are there stars near us? Are there stars in a giant cloud
or somewhere in between, like in a galactic halo?
If you know or assume, somehow, velocities of the lenses,
say we know that the velocity of dispersion of halo stars is couple
hundred kilometers per second, then you can infer masses of lenses from the
durations of the events, and typically, those are measured in days
or tens of days. The shorter the event, the smaller the
mass, so for an, an individual event there are only two things to measure.
We measure duration and the amplitude. The amplitude is simply telling you how
well aligned you are, it doesn't say anything about lenses.
The duration tells you about either their velocity dispersion or the individual
masses, and the total number of lenses you see is
telling you something about their density.
So here are the original MACHO results, they're expressed in probability contours
as a function of the lens mass and a fraction of the mass of the galactic halo
that could be attributed to them, assuming they really are in the galactic
halo. The surprising result here was the
typical mass was supposed to be about half solar mass.
This was unexpected because the only thing that could be like that would be
white dwarfs, which are evolutionary remnants of more massive stars,
but that means that there must have been some huge population of projectors of
those with other consequences which are not seen.
And so most likely the solution of this is that lenses were actually not in
galactic halo. They were either in our disc of our
galaxy or imaginary clouds themselves. But even if they were in a galactic halo,
the sheer frequency of them eliminated the possibility that all of the dark
matter is in form of MACHOs, regardless of what matters are brown dwarfs or black
holes or anything else. This was still a very powerful result.
Sometimes you can't find where the lenses. One it sufficiently close by that
you can use parallax and the other one is there is a binary, because then you can
use geometry of the binary star to infer how far it was.
A more recent twist on this is that this kind of measurement is used to discover
planets around other stars. A complimentery method to those, say
like, say Kepler Satellite that uses eclipses or kinematical measurements with
radial velocities. Next time, we will talk about dark
energy, probably the single most understanding
problem of physical cosmology today.