Dark Matter

We have established that there must be siginificant amounts of dark matter in the halo of our galaxy. The overall mass-to-light ratio for our galaxy, which is dominated by the massive halo, is somewhere between 10 and 100 Msun/Lsun. What can this halo dark matter be made of?

Low luminosity stars - the main sequence mass-luminosity relation gives L proportional to M^3.5, so the mass-to-light ratio M/L is proportional to M^-2.5. Thus, main sequence stars less massive than the Sun will have a M/L > 1. It is likely that these make up the disk dark matter, which has M/L about 3 Msun/Lsun. However, you would need to have many more faint stars in the halo compared with bright stars than there is in the disk.

Brown Dwarfs - "failed" stars or large planets (Jupiters) are extreme examples of low luminosity stars. They can have very large M/L, though it would be hard to see how there are so many of them to contribute large amounts of total mass to the galaxy halo. This is a general problem with having lots of low-mass, high M/L objects make up the halo.

Compact Objects - non-main sequence stars such as white dwarfs, neutron stars, or black holes. These are high-mass, high M/L objects so you dont need quite so many of them. On the other hand it is still hard to see why there would be a lot of mass in post-main sequence objects. In general, most of the mass in a standard distribution of stars like those near the Sun have most of the mass in stars about the same mass of the Sun, or lower. Thus, you have the opposite problem as with low-mass stars, you need to have predominantly massive stars which then evolve rapidly off the main sequence to compact objects. This leads to the problem of making too many heavy elements in all those supernovae! Not a great solution.

Massive Particles - some strange new particle that interacts only weakly with matter, and not at all with light (except through gravity). Not disallowed by physics, but would be somewhat unexpected, but an exciting prospect for physicists. There have been many searches and theoretical papers on this, and still must be considered a leading possibility. As we see when we talk about dark matter in cosmology, this would have important implications for the fate of our Universe also.

We can break these possibilities into two classes: massive compact halo objects (MACHOS) like stars, brown dwarfs, planets, compact objects, etc., and weakly interacting massive particles (WIMPS). Particle physicists have taken the lead in searching for WIMPS, so far without success. Astronomers have been looking for MACHOS, using techniques such as gravitational microlensing, as described in the next section.

Gravitational Microlensing

If one star passes in front of another, the bending of light by gravity will cause the foreground star to act as a gravitational lens magnifying the background star. Because the splitting of images of the background star by lensing from the foreground star is on the scale of micro-arcseconds and thus too small to be seen with telescopes, this is called microlensing.

If the lens is directly in front of the background star, then it is imaged into a ring of a radius proportional to the square-root of the mass of the lensing star. This is called an Einstein ring. If the foreground star is very close to, but not directly over, the background star, then you get two images of the star, which nevertheless increases the total brightness of the background star. The ring and the two image splitting, as mentioned before, are a few micro-arcseconds, and so not visible in telescopic images. In fact, you cannot separate out the foreground and background star images, you only see the sum of the two brightnesses, and the brightening cause by the lensing magnification.

Given a sample of background stars to look at, the statistics of microlensing tells you about the distribution of the foreground stars doing the lensing, their masses, and their velocities. In a microlensing event, the foreground star passes in front of the background star, which is seen to brighten then fade back to normal. The time it takes to brighten then fade depends on the distance and velocity of the lens in a straightforward manner:

In the last few years there have been several observational programs to look for and measure the statistics of microlensing. One of these, called MACHO after the types of dark matter object they are looking for in the halo, looked at the Large Magellanic Cloud (LMC) which is a nearby (about 53 kpc away) small (about 10^7 stars) companion galaxy to our Milky Way. Since the LMC is out of the plane of our galaxy, this is a good probe of the halo dark (and light) matter in MACHOS. During the times of the year when the LMC was not up at night, MACHO looked at stars in our galactic bulge in a direction of low obscuration called Baade's Window.

The other groups looked at the galactic bulge only. The largest of these projects is called OGLE, or Optical Gravitational Lens Experiment. Both MACHO and OGLE monitor the brightness of 10^6 to 10^7 stars in the LMC or bulge every night! This is no mean feat, and is only possible through the use of automated telescopes, CCD cameras, and computer controlled automated analysis of the huge amounts of data. This has been possible only in the last few years.

Both MACHO and OGLE see dozens of events (more than 60 total) toward the galactic bulge. These are due to stars in the disk and bulge, and have shown the existence of a bar in the center of our galaxy - an elonated distribution of stars as seen in some other galaxies. This is an important find for the study of galactic structure, and was not know before (though some astronomers had postulated its existence). These microlensing events are consistent with being due to the known types of stars, and no strange dark matter is needed to explain this.

The MACHO project has seen around 7 events toward the LMC, at least one of which is due to a lens in the LMC itself. In a recent press release, they claim that their results could be due to as much as 50% of the halo dark matter being in MACHOs of masses from 0.1 to 1 Msun, and thus white dwarfs! Unfortunately, it is likely that they are being a little overambitious in their conclusions, and it is more likely that their results are consistent with what we know is out there in normal halo stars, plus more of the events due to LMC starst themselves. Their claimed dark matter would mean that there is an unexpectedly large number of post-main sequence stars in the halo, and thus there would be a huge amount of heavy elements locked up in them. With so few events, its hard to justify these strong conclusions, only more data over the next few years will tell us the real story. Don't take everything you read about science in the press at face value - look carefully at all the possibilites first!

Stellar Populations

In the early 1940's, during wartime blackouts in Los Angeles, the astronomer Walter Baade at the Mount Wilson observatory was able to take many spectra of faint stars without the glare of city lights. What he discovered was that there were two populations of stars in our galaxy, distinguishable by the elements seen in their spectra.

The Population I stars are stars like our Sun, with similar amounts of heavy elements. The term metals is used to denote elements heavier than helium. Population I stars have solar metallicity, or at least a similar abundance of metals to the Sun. The Population I stars make up the disk of the galaxy, and thus have low velocities relative to the Sun, at least for those stars near the Sun.

The Population II stars are found in the halo of the galaxy. These stars are metal poor, since their spectra have few lines due to elements heavier than helium. The Pop II stars tend to have high velocities with respect to the Sun. This is because they are in the halo, not in the disk which is rotating along with the Sun. Halo stars have random orbits and thus cross the disk star orbits with relatively high velocities.

Pop II stars in the halo tend to be older than their Pop I disk counterparts. They appear to have formed early in the history of the galaxy out of almost pristine hydrogen and helium unenriched in metals by supernovae. This is why they are metal poor. There does appear, at least in the halo and disk, to be a direct correlation between when a star was formed and the abundance of metals in its photosphere. In fact, the most recently formed stars in the Orion Nebula are metal rich, and contain as much as twice the abundance of metals as the Sun!

An anomaly in this age - metallicity relation is the galactic bulge. It contains some of the oldest stars, and was probably one of the first things formed in the galaxy, but these stars are also metal rich! The probable explanation for this is that in the dense gas of the forming bulge, the large number of supernovae quickly enriched the clouds making the bulge stars, thus resulting with old stars (now) with solar or higher metallicities.

Evolution in Star Clusters

We have said that Pop I stars are young, while Pop II and bulge stars are old. How do we know this? How do we find the age of a distant star? We need some sort of stellar clock. The H-R diagram and stellar evolution gives us this clock. Remember, the main sequence lifetime of a star increases with decreasing mass, since M/L is proportional to M^-2.5 measuring the fuel divided by the rate of burning. Thus, if we had a group of stars of a range of masses formed at the same time, we could find the point on the main sequence where the stars more massive than this had evolved off onto the giant branch - this is called the turn off point. Stellar models can give us the time it would take a star of this luminosity and temperature, and thus known mass, to evolve off the main sequence, and thus the age of the cluster.

There are two types of star clusters seen in the galaxy. Open clusters are loose groups of 100 to 1000 stars in a radius of about 3 to 30 parsecs. The open clusters are in the disk of the galaxy, and are Population I objects. The turn-off ages for open clusters are found to be less than 10 billion years.

The globular clusters are dense balls of 100,000 to a million stars contained in a radius of around 10 to 15 pc. Globular clusters belong to the Pop II halo The turn-off ages of globular clusters are 10 to 18 billion years, and thus gives the age of the halo as old.

Some metal rich clusters are found in the bulge and have ages of more than 10 billion years. This gives us the old age for the bulge. Note that since the most massive stars live less than 1 million years, you can have significant enrichment in much less than a billion years in a crowded environment like the bulge. The sparse halo region would take much longer to enrich since the metals from supernovae would need a long time to travel large distances to where new stars were being formed. This is a plausible explanation for the differences in metal content of halo and bulge stars.

Luminosity and Mass Functions

There are many more faint low-mass stars than there are bright high-mass stars. We can quantify this by counting the number of stars of a given mass or luminosity per cubic parsec of the galaxy. We can only do this easily in the neighborhood of the Sun, where we can be sure of seeing all the stars, and of getting good distances (and thus luminosities from brightness). The masses must be estimated from the H-R diagram unless in a binary. The resulting mass and luminosity counts are called the mass function and luminosity function respectively.

We will discuss the mass function, though what we say applies to the luminosity function, through the mass-luminosity relation. We consider only main sequence stars for now. We let N(M)dM represent the number of stars between mass M and M + dM per cubic parsec of space. The function N(M) is the mass function, in units of number of stars per Solar Mass per cubic parsec. If we factor out stellar evolution, and consider the initial mass function as the stars are formed, we find the relation:

The constant N_0 is the number of 1 Msun stars (around 4 per Msun per pc^3). This relation is known as the Salpeter initial mass function.

The Sun is a G2 dwarf star (main sequence stars are called "dwarfs" to distinguish them from giant stars of the same spectral type). There are about 4 Msun/pc^3 in G stars in the solar neighborhood. Likewise, there are around 25 Msun/pc^3 in M dwarf stars, which are much less massive than the Sun but much more numerous.

Steven T. Myers - Last revised 23Apr96