Formation of the First Stars and Quasars

We review observable signatures of the first generation of stars and low-luminosity quasars, including the metal enrichment, radiation background, and dust opacity/emission that they produce. We compute the formation history of collapsed baryonic halos based on an extension of the Press-Schechter formalism, incorporating the effects of pressure and H2-dissociation, and calibrate this history to observational data at redshifts z<5. To be consistent with the lack of faint point-sources in the Hubble Deep Field, we introduce a lower limit of 75 km/s for the circular velocities of halos harboring central black holes. Based on our models, we predict that future satellite instruments such as MAP, Planck, and NGST will be able to detect the signatures small star clusters and low-luminosity quasars at redshifts exceeding z=10.Comment: 10 pages, 5 figures included. Invited talk at the 32nd COSPAR Scientific Assemby, 15-17 July, 1998, Nagoya, Japan; to appear in Adv. of Space Researc

Vanishing theorems and character formulas for the Hilbert scheme of points in the plane

Earlier we showed that the Hilbert scheme of $n$ points in the plane can be identified with the Hilbert scheme of regular $S_n$ orbits on $C^{2n}$. Using this result, together with a recent theorem of Bridgeland, King and Reid on the generalized McKay correspondence, we prove vanishing theorems for tensor powers of tautological bundles on the Hilbert scheme. We apply the vanishing theorems to establish (among other things) the character formula for diagonal harmonics conjectured by Garsia and the author. In particular we prove that the dimension of the space of diagonal harmonics is equal to $(n+1)^{n-1}$.Comment: 33 page

`First Light' in the Universe; What Ended the "Dark Age"?

The universe would have been completely dark between the epoch of recombination and the development of the first non-linear structure. But at redshifts beyond 5 -- perhaps even beyond 20 -- stars formed within `subgalaxies' and created the first heavy elements; these same systems (together perhaps with `miniquasars') generated the UV radiation that ionized the IGM, and maybe also the first significant magnetic fields. Although we can already probe back to $z \simeq 5$, these very first objects may be so faint that their detection must await next-generation optical and infrared telescopes. Observations in other wavebands may offer indirect clues to when reionization occurred. Despite the rapid improvements in numerical simulations, the processes of star formation and feedback are likely to remain a challenge for the next decade.Comment: For ``Physics Reports'' special issue in memory of D.N. Schram

Models for High-Redshift Lyman Alpha Emitters

We present models for dusty high-redshift Lyman alpha emitting galaxies by combining the Press-Schechter formalism with a treatment of inhomogeneous dust distribution inside galaxies. These models reproduce the surface density of emitters inferred from recent observations, and also agree with previous non-detections. Although a detailed determination of the individual model parameters is precluded by uncertainties, we find that (i) the dust content of primordial galaxies builds up in no more than 5x10^8 years, (ii) the galactic HII regions are inhomogeneous with a cloud covering factor of order unity, and (iii) the overall star formation efficiency is at least 5 percent. Future observations should be able to detect Lyman alpha galaxies upto redshifts of about z=8. If the universe is reionized at z(reion)<8, the corresponding decline in the number of Lyman alpha emitters at z>z(reion) could prove to be a useful probe of the reionization epoch.Comment: 4 pages, poster contribution to Proc. of 9th Annual October Astrophysics Conference in Maryland, "After the Dark Ages: When Galaxies Were Young (the Universe at 2 < z < 5", College Park, October 199