Chapter 16: The Expanding Universe

Gravitation (curvature of spacetime) and gyrogravity/gravitomagnetism/gravitoelectromagnetism (analogue of EM field) according to Einstein's theory.

Einstein's general relativity is the theory that accurately describes the way light is affected by mass. In Einstein's theory, mass distorts space — light then bends to follow this distortion of space. More correctly, mass-energy affects the geometry of space-time. Or, as the eminent physicist John Wheeler, who coined the term black hole, said: "Mass tells space-time how to curve, and space-time tells mass how to move." General relativity received its first experimental confirmation in the observed deflection of starlight as it passed close to the edge of the Sun.

Diagram of angles involved in gravitational lensing.

A single galaxy can deflect distant quasar light by 2 arc seconds. It's a happy coincidence that this angle is a bit larger than the amount by which the atmosphere blurs incoming light; if it had been five or ten times smaller we might never have detected lensing! The first lensed quasar was detected in 1979 at the Multiple Mirror Telescope in Arizona when the images of the double quasar 0957+561 were found to be 6 arc seconds apart. The multiple images are a kind of mirage — there is only one object but the light is bent on two different paths around the intervening galaxy so two images are seen. If the quasar is perfectly aligned behind the galaxy and the galaxy is symmetric (a good approximation for an elliptical galaxy), then the deflection will occur equally in every orientation and the deflected rays will trace back to form the image of a ring on the sky. Thus a point source of light — a quasar — is transformed into an Einstein ring. The angular scale Θ_E is known as the Einstein radius.

2004GravitationalLens

Lensing is rare. Only 1 in 300 quasars is gravitationally lensed because the odds of a galaxy or galaxy cluster lying directly in front of a distant quasar are low. However, it is not as rare as you might expect because the second consequence of lensing is the fact that the quasar light is amplified. A gravitational lens will magnify light just as an optical lens will. Lensing, therefore, makes a quasar brighter than it would have been in the absence of a foreground galaxy. This means that a lensed quasar can be seen to a greater distance than a non-lensed quasar. The greater volume out to that larger distance means a larger potential population to be lensed. Thus, there is a selection effect in favor of detecting lensed quasars. Lensing is "nature's telescope." Since lensing can amplify the brightness of the background galaxies by factors of 10-20 or more, lensing can let astronomers see galaxies that would be too faint or too distant to detect otherwise.

Diagram of microlensing

Considering deflection angles leads to an understanding of the phenomenon of gravitational microlensing. Imagine looking for dark matter in the halo of the Milky Way with the suspicion that it is made of sub-stellar objects, like white dwarfs or brown dwarfs. What is the lensing signature of a 0.01 solar mass object observed at a distance of 10 kpc against a backdrop of more distant stars? Scaling from our previous result, we note that Θ_E² ∝ M/D, so Θ_E ∝ (M/D)^½. The mass is 10¹⁴ times smaller and the distance is 2 x 10⁵ times smaller, so the deflection angle is (10¹⁴/2 x 10⁵)^½ = 22,000 times smaller than the deflection angle for lensing by a galaxy. We get 2/22,000 = 10^-4 arc seconds or 100 micro-arc seconds — hence the term microlensing. Since the deflection angle is much smaller than the smallest angle that can be resolved by any telescope (including the Hubble Space Telescope), the Einstein ring is not visible and the image is not noticeably distorted.

Illustration for gravitational lens. Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.

What is the recipe for detecting microlensing? Look for a one-time brightening and fading of a background star with a light curve that does not depend on wavelength (the deflection angle predicted by general relativity is the same for any wavelength of light). This distinctive signature is unlike any variation of the known variable stars. The problem is the low probability of an alignment. Only about one in a million stars is microlensed at any particular time, so at least a million stars per night must be observed to have a chance of catching these rare events. Modern CCD detectors allow this kind of wide-angle survey, and microlensing events have been detected in the halo of our galaxy. However, the rate of microlensing is too low for the dark halo of the Milky Way to be composed mostly of sub-stellar objects.