Galacticus: A Semi-Analytic Model of Galaxy Formation

We describe a new, free and open source semi-analytic model of galaxy formation, Galacticus. The Galacticus model was designed to be highly modular to facilitate expansion and the exploration of alternative descriptions of key physical ingredients. We detail the Galacticus engine for evolving galaxies through a merging hierarchy of dark matter halos and give details of the specific implementations of physics currently available in Galacticus. Finally, we show results from an example model that is in reasonably good agreement with several observational datasets. We use this model to explore numerical convergence and to demonstrate the types of information which can be extracted from Galacticus.Comment: 35 pages, submitted to New Astronom

Self-Consistent Theory of Halo Mergers - II: CDM Power Spectra

We place additional constraints on the three parameters of the dark matter halo merger rate function recently proposed by Parkinson, Cole & Helly by utilizing Smoluchowski's coagulation equation, which must be obeyed by any binary merging process which conserves mass. We find that the constraints from Smoluchowski's equation are degenerate, limiting to a thin plane in the three dimensional parameter space. This constraint is consistent with those obtained from fitting to N-body measures of progenitor mass functions, and provides a better match to the evolution of the overall dark matter halo mass function, particularly for the most massive halos. We demonstrate that the proposed merger rate function does not permit an exact solution of Smoluchowski's equation and, therefore, the choice of parameters must reflect a compromise between fitting various parts of the mass function. The techniques described herein are applicable to more general merger rate functions, which may permit a more accurate solution of Smoluchowski's equation. The current merger rate solutions are most probably sufficiently accurate for the vast majority of applications.Comment: 11 pages, submitted to MNRA

Entropy Injection as a Global Feedback Mechanism

Both preheating of the intergalactic medium and radiative cooling of low entropy gas have been proposed to explain the deviation from self-similarity in the cluster L_x-T_x relation and the observed entropy floor in these systems. However, severe overcooling of gas in groups is necessary for radiative cooling alone to explain the observations. Non-gravitational entropy injection must therefore still be important in these systems. We point out that on scales of groups and below, gas heated to the required entropy floor cannot cool in a Hubble time, regardless of its subsequent adiabatic compression. Preheating therefore shuts off the gas supply to galaxies, and should be an important global feedback mechanism for galaxy formation. Constraints on global gas cooling can be placed from the joint evolution of the comoving star formation rate and neutral gas density. Preheating at high redshift can be ruled out; however the data does not rule out passive gas consumption without inflow since z~2. Since for preheated gas t_cool > t_dyn, we speculate that preheating could play a role in determining the Hubble sequence: at a given mass scale, high sigma peaks in the density field collapse early to form ellipticals, while low sigma peaks collapse late and quiescently accrete preheated gas to form spirals. The entropy produced by large scale shock-heating of the intergalatic medium is significant only at late times, z<1, and cannot produce these effects.Comment: 10 pages, submitted to MNRA

Integrality in the Steinberg module and the top-dimensional cohomology of SL_n(O_K)

We prove a new structural result for the spherical Tits building attached to SL_n(K) for many number fields K, and more generally for the fraction fields of many Dedekind domains O: the Steinberg module St_n(K) is generated by integral apartments if and only if the ideal class group cl(O) is trivial. We deduce this integrality by proving that the complex of partial bases of O^n is Cohen-Macaulay. We apply this to prove new vanishing and nonvanishing results for H^{vcd}(SL_n(O_K); Q), where O_K is the ring of integers in a number field and vcd is the virtual cohomological dimension of SL_n(O_K). The (non)vanishing depends on the (non)triviality of the class group of O_K. We also obtain a vanishing theorem for the cohomology H^{vcd}(SL_n(O_K); V) with twisted coefficients V.Comment: 36 pages; final version; to appear in Amer. J. Mat

A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n)

In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).Comment: 18 pages. v2: final version, to appear in Algebraic Topology: Applications and New Directions, AMS Contemporary Mathematics Serie