Optical Turbulence Measurements and Models for Mount John University Observatory

Site measurements were collected at Mount John University Observatory in 2005 and 2007 using a purpose-built scintillation detection and ranging system. $C_n^2(h)$ profiling indicates a weak layer located at 12 - 14 km above sea level and strong low altitude turbulence extending up to 5 km. During calm weather conditions, an additional layer was detected at 6 - 8 km above sea level. $V(h)$ profiling suggests that tropopause layer velocities are nominally 12 - 30 m/s, and near-ground velocities range between 2 -- 20 m/s, dependent on weather. Little seasonal variation was detected in either $C_n^2(h)$ and $V(h)$ profiles. The average coherence length, $r_0$, was found to be $7 \pm 1$ cm for the full profile at a wavelength of 589 nm. The average isoplanatic angle, $\theta_0$, was $1.0 \pm 0.1$ arcsec. The mean turbulence altitude, $\bar{h_0}$, was found to be $2.0\pm0.7$ km above sea level. No average in the Greenwood frequency, $f_G$, could be established due to the gaps present in the \vw\s profiles obtained. A modified Hufnagel-Valley model was developed to describe the $C_n^2(h)$ profiles at Mount John, which estimates $r_0$ at 6 cm and $\theta_0$ at 0.9 arcsec. A series of $V(h)$ models were developed, based on the Greenwood wind model with an additional peak located at low altitudes. Using the $C_n^2(h)$ model and the suggested $V(h)$ model for moderate ground wind speeds, $f_G$ is estimated at 79 Hz.Comment: 14 pages; accepted for publication in PAS

Calculation of Hydrogenic Bethe Logarithms for Rydberg States

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n <= 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at quant-ph/0504002.Comment: 10 pages, RevTe

The Effects of Clumping and Substructure on ICM Mass Measurements

We examine an ensemble of 48 simulated clusters to determine the effects of small-scale density fluctuations and large-scale substructure on X-ray measurements of the intracluster medium (ICM) mass. We measure RMS density fluctuations in the ICM which can be characterized by a mean mass-weighted clumping factor C = /^2 between 1.3 and 1.4 within a density contrast of 500 times the critical density. These fluctuations arise from the cluster history of accretion shocks and major mergers, and their presence enhances the cluster's luminosity relative to the smooth case. We expect, therefore, that ICM mass measurements utilizing models which assume uniform density at a given radius carry a bias of order sqrt(C) = 1.16. We verify this result by performing ICM mass measurements on X-ray images of the simulations and finding the expected level of bias. The varied cluster morphologies in our ensemble also allow us to investigate the effects of departures from spherical symmetry on our measurements. We find that the presence of large-scale substructure does not further bias the resulting gas mass unless it is pronounced enough to produce a second peak in the image of at least 1% the maximum surface brightness. We analyze the subset of images with no secondary peaks and find a bias of 9% and a Gaussian random error of 4% in the derived mass.Comment: To appear in ApJ