S. Michael Fall

Limits on Dust in Damped Lyman-Alpha Systems and the Obscuration of Quasars

The damped Lyα systems discovered in the spectra of quasars at high red-shifts are natural places to search for dust. They have column densities greater than 1020 cm−2, contain most of the neutral hydrogen in the Universe, and may be protogalaxies or galactic disks in an early, gas-rich phase of evolution. We compare the spectra of quasars in the Wolfe et al (1986) survey that have damped Lyα with those that do not have damped Lyα to obtain statistical information about the reddening by dust. Our results are given in terms of the dimensionless dust-to-gas ratio k = 1021 (τ B /N H ) cm−2, where τ B is the optical depth in the B band in the rest frame of an absorber and N H is the column density of neutral hydrogen. Using non-parametric tests, we find, at the 95% confidence level, k ≤ 0.41 (GAL), k ≤ 0.29 (LMC) and k ≤ 0.19 (SMC), depending on whether the extinction curve is assumed to have the same shape as that in the Milky Way or the Large or Small Magellanic Clouds. Our upper limits on the dust-to-gas ratio in the damped Lyα systems are half the observed value in the Milky Way but are several times larger than the observed values in the Magellanic Clouds.

The origin of globular clusters

The purpose of this article is to review some recent attempts to understand the origin of globular clusters. To put this in perspective, it may help to recall the analogous problem of the origin of galaxies. This splits into two parts. First, given a proto-galaxy with a specified mass and radius, how does it collapse, form stars and settle into a state of dynamical equilibrium? Richard Larson explored these topics in an important series of numerical simulations in the 1970s. Progress in this area brings into sharper focus a second set of questions that really has precedence over the first. Why did proto-galaxies have properties like the initial conditions in the collapse calculations and what distinguishes galaxies from structures on much larger and much smaller scales? Similar questions face us when we consider the origin of globular clusters. First, how did stars form in a proto-cluster, what was the efficiency, the initial mass function and so forth? It is appropriate that Larson has discussed these topics in the preceding article but here we are mainly concerned with the second kind of question: What is special about objects with masses of order 105-106 MΘ and dimensions of a few tens of parsecs?

The Formation of Galactic Spheroids

The spheroidal components of galaxies, including globular clusters, are usually assumed to form during a period of rapid collapse and high luminosity. A few years ago, I developed in collaboration with Martin Rees, a theory for the origin of globular clusters (Fall and Rees 1985. 1988). We showed that realistic density or velocity perturbations in a protogalaxy would be amplified during the collapse. The result is a two-phase medium with some gas at the virial temperature, a few × 106K, and some gas at the temperture that hydrogen recombines, about 104K. The density of the hot gas can be derived from fairly general arguments, and since the two phases must be in rough pressure balance, the density and Jeans mass of the cold gas can be calculated with some confidence. We found that clouds with masses of order 106 M. would collapse gravitationally, and should therefore be identified as the progenitors of globular clusters. The condition for this mass scale to be “imprinted” is that the temperatures of the clouds remain near 104K for at least one free-fall time. Once the protogalactic gas has been enriched in heavy elements from the first generation of stars in globular clusters, cooling becomes more efficient and much smaller clouds can collapse, thereby promoting the formation of later generations of field stars. We therefore expect that on average globular clusters should have lower abundances of heavy elements and more extended space distributions than the field stars in the spheroidal components of galaxies. As the result of various selection biases, these predictions are not easy to test for the Milky Way but they are consistent with a growing body of data for other galaxies (Forte, Strom and Strom 1981, Harris 1986, 1987, Mould 1987, Mould, Oke and Nemec 1987, Elson and Walterbos 1987).

The Formation of Galactic Disks

The disk components of galaxies are usually assumed to form later than the spheroidal components but how much later is still an open question. The following argument, based on the spin-up of collapsing protogalaxies, suggests that the disk components formed recently (Fall and Efstathiou 1980, Fall 1985). Since the specific angular momentum of a disk today is likely to be nearly the same as that in the protogalaxy, the initial size can be calculated as a function of the initial rotation velocity. The initial size of the protogalaxy then determines the free-fall time and hence the maximum redshift of collapse. The initial rotation is most conveniently expressed in terms of the dimensionless spin parameter, λ ≡ J | E |1/2 G -1 M -5/2, where J, E and M are respectively the total angular momentum, energy and mass of the protogalaxy, including any dark matter it may contain. For an exponential disk with a scale length α-1 embedded in an isothermal halo with a circular velocity vc, one finds that the free-fall time is τ f f = 1.9(αv c λ)-1. The values of α-1 and v c can be derived from observation, and for all theories that invoke hierarchical clustering. the values of λ can be derived from N-body simulations. The distribution of spin parameters turns out to depend only weakly on the spectrum of perturbations at recombination and always has a median value near λ ≃ 0.05 (Barnes and Efstathiou 1987, Quinn, Salmon and Zurek 1987). I have used these results to show that the median redshift of disk formation is z d ≤ 2 for q 0 = 1/2 and z d ≤ 7 for q 0 = 0 (Fall 1987).