Physics Today

Physics Today The Dynamical Evidence for Dark Matter Scott Tremaine Citation: Physics Today 45(2), 28 (1992); doi: 10.1063/1.881329 View online: http://dx.doi.org/10.1063/1.881329 View Table of Contents: http://scitation.aip.org/content/aip/magazine/physicstoday/45/2?ver=pdfcov Published by the AIP Publishing This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.112.203.62 On: Mon, 25 Aug 2014 15:15:09 THE DYNAMICAL EVIDENCE FOR DARK MATTER 'The Starry Night/ by Vincent van Gogh. The 1889 oil painting suggests how the night sky might look if all of the mass in the universe were luminous. Observations of galaxy dynamics and modern theories of galaxy formation imply that the visible components of galaxies, composed mostly of stars, lie at the centers of vast halos of dark matter that may be 30 or more times larger than the visible galaxy. In most models of galaxy formation, the halos are comparable in size to the distance between galaxies. The halos form as a result of the gravitational instability of small density fluctuations in the early universe; the star-forming gas collects at the minima of the halo potential wells. Infall of outlying material into existing halos and mergers of small halos with larger ones continue at the present time. If the halos were visible to the naked eye, there would be well over 1000 nearby galaxies with halo diameters larger than the full Moon. Figure 1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded 2 8 PHYSICS TODAY FEBRUARY 1992to IP: 128.112.203.62 On: Mon, 25 Aug 2014 15:15:09 Studies of the dynamics of galaxies show that at least 90% of the mass in the universe is in some invisible, unknown form. Scott Tremaine Almost all of our information about the universe beyond enough compared with the size of the Galaxy that the bulk Earth comes from photons—visible photons from stars, x- properties of the stellar distribution are constant within it. ray photons from hot plasmas, radio photons from the 21- The distance of the nearest star to the Sun is 1.3 cm hyperfine transition in hydrogen, microwave photons parsecs (1 pc is 3.086 x l O 13 km). About the smallest from the cosmic background radiation and so forth. volume containing a statistically useful sample of stars is a It would be folly to assume that all the matter in the Sun-centered sphere of radius 10 pc, in which there are universe emits detectable photons. Thus we should not be 300 known stars.2 An instructive exercise is to divide surprised if the mass of a galaxy or other astronomical these into an inner sample of 61 stars within 5 pc and an system, as measured by its gravitational field, exceeds the outer sample of 239 stars between 5 and 10 pc from the sum of the masses of those of its components that shine Sun. The corresponding densities are 0.12 and 0.065 stars brightly enough to be detected in our telescopes. The per cubic parsec. Since the density ought to be constant difference between this "luminous mass" and the total over such small distances, the drop in density by a factor of mass is ascribed to "dark matter"—matter whose exis- two from the inner to the outer sample implies that the tence is inferred solely from its gravitation.1 outer sample is seriously incomplete. Thus even at the An early example of this reasoning was the prediction smallest interstellar distances, many of the stars are so in 1846 of the existence and location of Neptune from faint that they have yet to be discovered, which is a hint unexplained residuals in the motion of Uranus. Another that substantial dark mass might lurk in faint stars. example from the solar system was the anomalous Most stars are in a state of thermal equilibrium, in precession of Mercury's perihelion. A hypothetical planet which energy generated by hydrogen fusion is balanced by ("Vulcan"), or else a ring of material, inside Mercury's heat lost through thermal radiation. However, below a orbit was invoked to explain this anomaly, but Einstein transition mass Mc of 0.08 times the mass MQ of the Sun, showed in 1916 that it was a consequence of general stars cannot fuse hydrogen, as their electrons become relativity rather than of dark matter. This is a cautionary degenerate before they are dense and hot enough for reminder that dark matter may sometimes be explained fusion to proceed. The luminosity of stars with M<MC, away by revisions to the accepted laws of physics. usually called "brown dwarfs," is supplied by slow At present there is no significant dynamical evidence gravitational contraction rather than by fusion3 and hence for dark matter in the solar system. On larger scales, is much smaller than the luminosity of hydrogen-burning however, the story is quite different. There is convincing stars. (The luminosity drops by more than two orders of evidence not just that dark matter is present but that most magnitude between 0.10AfQ and 0.07MQ.) Brown dwarfs of the mass in galaxies is dark. The visible parts of are so faint that they would be very difficult to detect even galaxies, composed mainly of stars, are surrounded by if they were much more numerous than the brighter, extended halos of dark matter that may be a factor of 30 or hydrogen-burning stars. Hence they are a natural candi- more larger in both mass and size. Van Gogh's famous date for dark mass. painting "The Starry Night" (figure 1) provides a surpris- We can attempt to estimate the number density of ingly accurate view of what the dark halos might look like brown dwarfs by extrapolating the number density of if they were visible. The average mass density of the dark brighter stars. The plausible assumption in this extrapo- matter could exceed the critical value needed to close the lation is that the transition mass Mc plays no special role universe. in the physics of star formation: Since the transition mass An equally remarkable conclusion, based on nucleo- involves nuclear physics and star formation probably does synthesis arguments, is that most of the dark matter—and not, the rates of formation of stars above and below Mc hence most of the mass in the universe—is not composed of should be similar. The luminosity L(M) of a star of mass M protons or neutrons. Thus the material that makes up the can be computed from stellar structure theory and stars that we see and the everyday world that we know is checked by observations of binary star orbits. Let 4>(L) &L only a minor pollutant in a sea of invisible material of be the number density of stars with luminosity in the unknown nature. range [L, L + dL], as determined from star catalogs. Then The solar neighborhood The first natural place beyond the solar system to look for dark matter is the solar neighborhood—an imaginary Scott Tremaine is director of the Canadian Institute for volume centered on the Sun that is large enough to Theoretical Astrophysics and is a professor of physics and contain plenty of stars for statistical analyses but small astronomy at the University of Toronto. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.112.203.62 On: Mon, 25 Aug 2014 15:15:09PHYSICS TODAY FEBRUARY 1992 29 the number density n(M) AM of stars with mass in the density along a trajectory:4 range [M, M + AM] is given by dUM) (1) n(M) = AM dt Figure 2 shows the number density derived in this way. Here Vx and Vv denote gradients with respect to position The density becomes quite uncertain as we approach the and velocity. Assuming slab symmetry and a stationary transition mass Mc, both because AL/AM becomes very distribution (that is, no dependence on x, y or t), we large and because measurement of <f>(L) becomes harder multiply the equation by v2 and integrate over velocity to and harder at low luminosities. The figure suggests that get n{M) is relatively flat for masses below Mc, which would AU imply that brown dwarfs contain a negligible fraction of d (2) the mass in the solar neighborhood. A sharp upturn in — —- Az Az n(M) below about 0.15MQ is not excluded by the data, although there is no reason to suppose that it is present. where v(z) = j/(z,v)dv is the number density of stars and 2 2 Fortunately there is a dynamical method of measur- az (z) = iv2 f(z,\)A\/v(z) is their mean-square velocity in ing the total mass density in this region. The stars in the the z direction. Thus measurements of the number solar neighborhood belong to the Galactic disk, which has density and velocity dispersion of any given type of star as a radius of about 10 kpc but a thickness of only a few a function of height above the Galactic midplane deter- hundred parsecs. Because the disk is so thin, it can be ap- mine the potential U(z) through equation 2 and the mass proximated as an infinite slab.

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