The mass function

We present the mass functions for different mass estimators for a range of cosmological models. We pay particular attention to how universal the mass function is, and how it depends on the cosmology, halo identification and mass estimator chosen. We investigate quantitatively how well we can relate observed masses to theoretical mass functions.Comment: 14 pages, 12 figures, to appear in ApJ

Patchy He II reionization and the physical state of the IGM

We present a Monte-Carlo model of He II reionization by QSOs and its effect on the thermal state of the clumpy intergalactic medium (IGM). The model assumes that patchy reionization develops as a result of the discrete distribution of QSOs. It includes various recipes for the propagation of the ionizing photons, and treats photo-heating self-consistently. The model provides the fraction of He III, the mean temperature in the IGM, and the He II mean optical depth -- all as a function of redshift. It also predicts the evolution of the local temperature versus density relation during reionization. Our findings are as follows: The fraction of He III increases gradually until it becomes close to unity at $z\sim 2.8-3.0$. The He II mean optical depth decreases from $\tau\sim 10$ at $z\geq 3.5$ to $\tau\leq 0.5$ at $z\leq 2.5$. The mean temperature rises gradually between $z\sim 4$ and $z\sim 3$ and declines slowly at lower redshifts. The model predicts a flattening of the temperature-density relation with significant increase in the scatter during reionization at $z\sim 3$. Towards the end of reionization the scatter is reduced and a tight relation is re-established. This scatter should be incorporated in the analysis of the Ly$\alpha$ forest at $z\leq 3$. Comparison with observational results of the optical depth and the mean temperature at moderate redshifts constrains several key physical parameters.Comment: 18 pages, 9 figures; Changed content. Accepted for publication in MNRA

Properties and use of CMB power spectrum likelihoods

Fast robust methods for calculating likelihoods from CMB observations on small scales generally rely on approximations based on a set of power spectrum estimators and their covariances. We investigate the optimality of these approximation, how accurate the covariance needs to be, and how to estimate the covariance from simulations. For a simple case with azimuthal symmetry we compare optimality of hybrid pseudo-C_l CMB power spectrum estimators with the exact result, indicating that the loss of information is not negligible, but neither is it enough to have a large effect on standard parameter constraints. We then discuss the number of samples required to estimate the covariance from simulations, with and without a good analytic approximation, and assess the use of shrinkage estimators. Finally we discuss how to combine an approximate high-ell likelihood with a more exact low-ell harmonic-space likelihood as a practical method for accurate likelihood calculation on all scales.Comment: 15 pages, 11 figures; updated to match version accepted by PR

An Isocurvature CDM Cosmogony. I. A Worked Example of Evolution Through Inflation

I present a specific worked example of evolution through inflation to the initial conditions for an isocurvature CDM model for structure formation. The model invokes three scalar fields, one that drives power law inflation, one that survives to become the present-day CDM, and one that gives the CDM field a mass that slowly decreases during inflation and so ``tilts'' the primeval mass fluctuation spectrum of the CDM. The functional forms for the potentials and the parameter values that lead to an observationally acceptable model for structure formation do not seem to be out of line with current ideas about the physics of the very early universe. I argue in an accompanying paper that the model offers an acceptable fit to main observational constraints.Comment: 11 pages, 3 postscript figures, uses aas2pp4.st

557 GHz Observations of Water Vapor Outflows from VY CMa and W Hydrae

We report the first detection of thermal water vapor emission in the 557 GHz, $1_{10} - 1_{01}$ ground state transition of ortho-H$_2$O toward VY Canis Majoris. In observations obtained with the Submillimeter Wave Astronomy Satellite (SWAS), we measured a flux of $\sim 450$Jy, in a spectrally resolved line centered on a velocity $v_{LSR} = 25$km s$^{-1}$ with a full width half maximum of $\sim 35$ km s$^{-1}$, somewhat dependent on the assumed line shape. We analyze the line shape in the context of three different radial outflow models for which we provide analytical expressions. We also detected a weaker 557 GHz emission line from W Hydrae. We find that these and other H$_2$O emission line strengths scale as suggested by Zubko and Elitzur (2000).Comment: Astrophysical Journal Letters, accepte

Formation of early-type galaxies from cosmological initial conditions

We describe high resolution Smoothed Particle Hydrodynamics (SPH) simulations of three approximately $M_*$ field galaxies starting from \LCDM initial conditions. The simulations are made intentionally simple, and include photoionization, cooling of the intergalactic medium, and star formation but not feedback from AGN or supernovae. All of the galaxies undergo an initial burst of star formation at $z \approx 5$, accompanied by the formation of a bubble of heated gas. Two out of three galaxies show early-type properties at present whereas only one of them experienced a major merger. Heating from shocks and -PdV work dominates over cooling so that for most of the gas the temperature is an increasing function of time. By $z \approx 1$ a significant fraction of the final stellar mass is in place and the spectral energy distribution resembles those of observed massive red galaxies. The galaxies have grown from $z=1 \to 0$ on average by 25% in mass and in size by gas poor (dry) stellar mergers. By the present day, the simulated galaxies are old ($\approx 10 {\rm Gyrs}$), kinematically hot stellar systems surrounded by hot gaseous haloes. Stars dominate the mass of the galaxies up to $\approx 4$ effective radii ($\approx 10$ kpc). Kinematic and most photometric properties are in good agreement with those of observed elliptical galaxies. The galaxy with a major merger develops a counter-rotating core. Our simulations show that realistic intermediate mass giant elliptical galaxies with plausible formation histories can be formed from \LCDM initial conditions even without requiring recent major mergers or feedback from supernovae or AGN.Comment: accepted for publication in Ap

AGN Obscuring Tori Supported by Infrared Radiation Pressure

Explicit 2-d axisymmetric solutions are found to the hydrostatic equilibrium, energy balance, and photon diffusion equations within obscuring tori around active galactic nuclei. These solutions demonstrate that infrared radiation pressure can support geometrically thick structures in AGN environments subject to certain constraints: the bolometric luminosity must be roughly 0.03--1 times the Eddington luminosity; and the Compton optical depth of matter in the equatorial plane should be order unity, with a tolerance of about an order of magnitude up or down. Both of these constraints are at least roughly consistent with observations. In addition, angular momentum must be redistributed so that the fractional rotational support against gravity rises from the inner edge of the torus to the outer in a manner specific to the detailed shape of the gravitational potential. This model also predicts that the column densities observed in obscured AGN should range from about 10^{22} to about 10^{24} cm^{-2}.Comment: ApJ, in pres

Starburst and AGN activity in ultraluminous infrared galaxies

(Abridged) We examine the power source of 41 local Ultraluminous Infrared Galaxies using archival infrared and optical photometry. We fit the observed Spectral Energy Distributions (SEDs) with starburst and AGN components; each component being drawn from a family of templates. We find all of the sample require a starburst, whereas only half require an AGN. In 90% of the sample the starburst provides over half the IR emission, with a mean fractional luminosity of 82%. When combined with other galaxy samples we find that starburst and AGN luminosities correlate over 6 decades in IR luminosity suggesting that a common factor governs both luminosities, plausibly the gas masses in the nuclear regions. We find that the mid-IR 7.7 micron line-continuum ratio is no indication of the starburst luminosity, or the fractional AGN luminosity, and therefore that this ratio is not a reliable diagnostic of the power source in ULIRGs. We propose that the scatter in the radio-IR correlation in ULIRGs is due to a skewed starburst IMF and/or relic relativistic electrons from a previous starburst, rather than contamination from an obscured AGN. We show that most ULIRGs undergo multiple starbursts during their lifetime, and by inference that mergers between more than two galaxies may be common amongst ULIRGs. Our results support the evolutionary model for ULIRGs proposed by Farrah et al 2001, where they can follow many different evolutionary paths of starburst and AGN activity in transforming merging spiral galaxies into elliptical galaxies, but that most do not go through an optical QSO phase. The lower level of AGN activity in our local sample than in z~1 HLIRGs implies that the two samples are distinct populations. We postulate that different galaxy formation processes at high-z are responsible for this difference.Comment: 24 pages, 8 figures. Accepted for publication in MNRA

Proton beam therapy and localised prostate cancer: current status and controversies

Proton therapy is a promising, but costly, treatment for prostate cancer. Theoretical physical advantages exist; yet to date, it has been shown only to be comparably safe and effective when compared with the alternatives and not necessarily superior. If clinically meaningful benefits do exist for patients, more rigorous study will be needed to detect them and society will require this to justify the investment of time and money. New technical advances in proton beam delivery coupled with shortened overall treatment times and declining device costs have the potential to make this a more cost-effective therapy in the years ahead