S-1. Sunlight & Earth
S-1B. Global Climate
S-3.The Magnetic Sun
S-4. Colors of Sunlight
Optional: Doppler Effect
S-4A-1 Speed of Light
S-4A-2. Frequency Shift
S-4A-3 Rotating Galaxies
and Dark Matter
S-5.Waves & Photons
Optional: Quantum Physics
Q3. Energy Levels
Q4. Radiation from
The M31 Galaxy
The designation "M31" identifies it as No. 31 in the catalogue compiled in 1771 and 1781 by the Frenchman Charles Messier. That catalogue listed cloudy and fuzzy objects in the sky, to warn astronomers searching for new comets (Messier himself discovered 15) off objects which looked like comets but weren't. Viewed through a telescope M31 seems dim and fuzzy, disappointing non-astronomers who see nothing resembling the familiar picture of the Andromeda galaxy, with its slightly tilted disk, bright central core and dark lanes of dust. Actually that picture is a time exposure, seen only by the camera. Galaxies vary in size and shape, but this one appears to be rather similar to ours.
What holds galaxies together? Apparently, gravity, and the disk-like shape suggests that they rotate. It should then be possible to measure the rotation of a galaxy like M31 using the Doppler effect: on the receding side of the disk, the wavelength of spectral lines would be slightly shifted towards the red, on the approaching side, towards the blue. As discussed below, comparing such shifts at various distances from the center, and invoking the laws of gravity and mechanics, can tell about the way density of matter in the galaxy varies with distance.
There is also another way of estimating the distribution of matter, by assuming that its average density at any location is proportional to the brightness of the galaxy there. With that assumption, the rate at which brightness falls off with distance from the center should also give the distribution of mass, except in the dark lanes (see picture) where dust blocks out starlight. Obviously, it is of interest to compare the results of both methods.
The observation of the Doppler effect in M31 is not easy, and becomes even harder in more distant galaxies. As already noted, M31 is a dim object, and observing it in detail requires long time exposures. Furthermore, to observe the Doppler effect, only a small part of the light can be used, just one "spectral line" isolated by a sensitive spectrograph, and taken from just one small part of the galaxy, whose motion we want to detect.
The Period of the Orbit
where k is some constant, related to the mass M of the attracting center. The relation is discussed (with particular attention to Earth satellites) in section #21.
The Doppler effect of course does not measure the period T, but rather, the velocity V, related to it (at any distance r) by
It G is the constant of gravitation, the balance of forces on any mass m in the galaxy is
If the only source of attracting gravity was a central black hole, its mass would provide M, and V2 would diminish with distance like 1/r, as it does in the solar system. Indeed, it was long suspected that the center of M31 contained a black hole, though detailed pictures suggests that here we may actually have a double center. However, galaxies contain a lot more mass than their central bodies: in the Milky Way Galaxy, the central black hole may have the mass of 3.7 million suns, but the galaxy itself contains about 100 billion stars.
The light of M31 is distributed more or less symmetrically around the center, so it is reasonable to assume its mass does likewise (hard to imagine otherwise, given that its components rotate!). As shown by Newton for the spherical Earth, the pull of gravity on a star in the galaxy midplane then depends on all the mass closer to the axis of rotation: that mass (at least if distributed throughout a spherical volume) acts as if it were concentrated at the enter, whereas mass at greater distances has no effect.
Thus the effective value of M increases with distance, and the rotation velocity V in the denser parts of the galaxy may fall off less steeply than like 1/r. However, past the densest part, V should drop off, and the drop-off rate of V2 should be close to that of 1/r.
Previously such observations were hampered by the low intensity of light from M31. This time especially baked photographic plates were used, providing much higher sensitivity. Even then, an operator had to keep the telescope (with its attached spectroscope) manually aligned on the selected part of M31, using for reference a nearby star, a much better defined point of light.
The spectral feature used was the red Hα ("H-alpha") line of hydrogen, also isolated by filters observing the Sun, because solar flares show up very well in H-alpha light (for more detail, see here and here). Between 1967 and 1969, the shift of the H-alpha line was observed at 67 positions on the galaxy.
After some wiggles near the center of the galaxy (where observations also had problems), the curve of V against r was almost flat, as shown schematically on the graph above, from a web site devoted to rotation curves.
What was remarkable was that the near-constancy of V extended even to the far edges of the galaxy, where very little light was emitted. If brightness was an indication of mass, then most of the mass was huddled near the galactic center, and velocities in these outer regions were expected to decrease in accordance to Kepler's law. But they did not. Radio observations (on a hydrogen microwave emission) later confirmed the flatness at even greater distances.
Since then the rotation curves of many more galaxies were studied (bigger telescopes, much more sensitive electronic light detectors) and flat rotation curves were the general rule. Even in our own galaxy, where different methods (also based on the Doppler effect) must be used, even there the rotation curve seems flat. From
What contributes this mass? No one knows for sure. In principle you could have dark, burned out stars, but it would be a very strange universe indeed, if burned-out stars crowded the edges of galaxies, unaccompanied by brightly burning ones like those in the middle. Indeed, no convincing explanation exists. Fritz Zwicky already suggested in the late 1930s that an appreciable part of the mass of the universe was invisible, to explain the clustering of galaxies which he observed. The galaxies did not seem to have enough mass to create the gravity which held together those clusters.
Many astronomers now believe that the mass of invisible "dark matter" may outweigh all other kinds in the universe, and that its attraction may be a major cause of the existence of galaxies. By that view, dark matter clumped early in the history of the universe, and ordinary matter--forming galaxies--followed it into the gravitational "holes" which it formed. The rotation of galaxies suggests that the dark matter is still present, to a large extent holding galaxies together. For more of that story, see John Gribbin's book, "Origins of the Future".
MONDIt is only fair to mention here a possible loophole which could also explain rotation curves. It could be that the decrease of Newtonian gravity with distance does not follow exactly an inverse-square law, but that at very large distances, say 10,000 light years and more, gravity is slightly stronger than such a law predicts. A slight departure from the inverse-square law ("Modified Newtonian Gravity" or MOND for short) then explains the observed discrepamcies.
Most astrophysicists dismiss MOND as inconsistent with general relativity, but ways out of this have recently been proposed (see "Seeing Through Dark Matter" by Stacy McGaugh, "Science" 317, p. 607-8, 3 August 2007). Unfortunately, even if MOND is accepted, there may still remain a need for dark matter to explain the clustering of galaxies first observed by Fritz Zwicky in the 1930s. A recent observed discrepancy in effects of gravity-assist maneuvers of space probes may help resolve the matter.
Questions from Users:
*** Space and Dark Matter
Next Stop: (S-5) Waves and Photons
Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 9 December 2006