A long-standing problem in astronomy is the so-called dark-energy problem (previously known as the dark-matter problem). We can estimate the mass of a galaxy in two ways: we can measure the velocities of the stars within the galaxy, which measures the gravitational field of the galaxy, and therefore the mass within the galaxy, or we can measure the starlight, and from theoretical calculations of how a star's luminosity depends on its mass calculate the mass of the galaxy. These two methods give different results, with a galaxy's gravitational mass exceeding the light-emitting mass by roughly a factor of five. The straightforward interpretation is that most of the mass within a galaxy is in a form that does not emit observable amounts of radiation. What form does the dark mass take? Is part of this mass in low-luminosity stars, brown dwarfs, and Jupiters?
The gravitational lens possessed by every gravitating object provides us with a method for detecting the invisible bodies within our own Galaxy. We can detect a lens when it passes in front of a luminous star, making that star appear temporarily brighter. If we observe enough such events, we have a measure of the density of low mass stars, brown dwarfs, and Jupiters within our Galaxy. To make the problem simple, the star we observe should be in another galaxy. Such a star is effectively at infinity for a gravitational lens within our own galaxy.
The first difficulty in applying this technique is that the probability is tiny of seeing this brightening occur by observing a single bright star in another galaxy; the probability that the light of this star is passing through a gravitational lens in a single observation is around one in ten million. If we are to find a gravitational lens within our Galaxy, we need to examine tens of millions of extragalactic stars on a regular basis. This became possible in the late 1980s as the cost of computers, computer memory, and digital cameras fell, making it possible to automate for several hundred thousand dollars in equipment the search for gravitational lenses. Today better equipment can be bought for several hundred dollars.
The signature of a gravitational lens is the change in luminosity of a distant source. How can we distinguish this change from the changes that occur naturally within a star? Many stars are variable stars, so we need more than simply a change in magnitude to signal the presence of a gravitational lens.
The first characteristic of variability from the passage of a gravitational lens in front of an extragalactic star is that the change in luminosity is independent of frequency. This is because the effect of gravity on light is independent of the energy carried by the light, much as the effect of gravity on object with a rest mass is independent of its mass. So if a star's luminosity increases by 50% at a blue frequency, it must also increase by 50% at a red frequency if the increase is caused by a gravitational lens. Stars that exhibit different amounts of brightening at different frequencies can therefore be eliminated as a lens candidate.
The second characteristic of lens-induced variability is that the distant star brightens and then dims in a very predictable and symmetric fashion. A gravitational lens moves across the sky at a constant rate and in a straight line. The maximum magnification occurs when the distance on the sky from the lens source to the extragalactic star is at its minimum. The magnitude of the star falls as one moves away from this peak, with the magnitude at time t after the peak equal to the magnitude at -t. Because the extragalactic star is so small on the sky relative to the size of the gravitational lens, the shape of the magnitude curve created by the lens depends on only two free parameters: the size of the lens on the sky and the velocity of the lens on the sky. If the magnitude of an extragalactic star cannot be fit by this simple model, then it can be eliminated as a lens candidate.
The time it takes for an extragalactic star to brighten and dim as a gravitational lens passes in front depends on the time it takes the lens to travel the diameter of its Einstein ring. This time is given by
where G is the gravitational constant, M is the mass of the star creating the lens, D is the distance of the lens from us, c is the speed of light, and Vtrans is the velocity transverse to us of the star creating the lens. A lens created by a one solar mass star at 100 parsecs with a transverse velocity of 50 km s-1 causes an extragalactic star to brighten and then dim over about 4 years. A lens source of same distance and velocity, but with a mass of only 10-4 solar masses, causes a change in luminosity over 15 days. More distant lenses, such as lenses at 10 kpc, would have larger velocities, around 250 km s-1, so they would brighten more distant stars on timescales comparable to those of nearby lenses. These numbers suggest that a gravitational lenses can be detected by observing the same extragalactic stars every several days.
The search for gravitational lenses must be automated. The system of telescope, digital camera, and computer must observe tens of million of stars every several nights if it is to find gravitational lens. The systems that currently exist accomplish this by observing the stars in one or two nearby galaxies. Systems in the Northern Hemisphere observe the brightest stars in the Andromeda galaxy, while the systems in the Southern Hemisphere observe the brightest stars in the Large and Small Magellanic Clouds.
Every night, the magnitude of millions of stars are measured and stored. This data is compared to the magnitudes of these stars on previous nights. Stars that are variable are tested to see if they behave as they should if a lens is responsible. These systems have found a number of stellar gravitational lenses within our galaxy.