A Modified Magnitude System that Produces Well-Behaved Magnitudes, Colors, and Errors Even for Low Signal-to-Noise Ratio Measurements

We describe a modification of the usual definition of astronomical magnitudes, replacing the usual logarithm with an inverse hyperbolic sine function; we call these modified magnitudes `asinh magnitudes'. For objects detected at signal-to-noise ratios of greater than about five, our modified definition is essentially identical to the traditional one; for fainter objects (including those with a formally negative flux) our definition is well behaved, tending to a definite value with finite errors as the flux goes to zero. This new definition is especially useful when considering the colors of faint objects, as the difference of two `asinh' magnitudes measures the usual flux ratio for bright objects, while avoiding the problems caused by dividing two very uncertain values for faint objects. The Sloan Digital Sky Survey (SDSS) data products will use this scheme to express all magnitudes in their catalogs.Comment: 11 pages, including 3 postscript figures. Submitted to A

Anomalous hydrodynamics and "normal" fluids in rapidly rotating BECs

In rapidly rotating bose systems we show that there is a region of anomalous hydrodynamics whilst the system is still condensed, which coincides with the mean field quantum Hall regime. An immediate consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show there are kinematic constraints which connect spatial variations of density and phase, that the positions of vortices are not the simplest description of the dynamics of such a fluid (despite their utility in describing the instantaneous state of the condensate) and that the most compact description allows solution of some illuminating examples of motion. We demonstrate, inter alia, a very simple relation between vortices and surface waves. We show the surface waves can form a "normal fluid" which absorbs energy and angular momentum from vortex motion in the trap. The time scale of this process is sensitive to the initial configuration of the vortices, which can lead to long-lived vortex patches - perhaps related to those observed at JILA.Comment: 4 pages; 1 sentence and references modifie

The Damping Tail of CMB Anisotropies

By decomposing the damping tail of CMB anisotropies into a series of transfer functions representing individual physical effects, we provide ingredients that will aid in the reconstruction of the cosmological model from small-scale CMB anisotropy data. We accurately calibrate the model-independent effects of diffusion and reionization damping which provide potentially the most robust information on the background cosmology. Removing these effects, we uncover model-dependent processes such as the acoustic peak modulation and gravitational enhancement that can help distinguish between alternate models of structure formation and provide windows into the evolution of fluctuations at various stages in their growth.Comment: 24pgs, aaspp4, 10 figs. included; supporting material (e.g. color figures) at http://www.sns.ias.edu/~whu/pub.htm

Oblique ion collection in the drift-approximation: how magnetized Mach-probes really work

The anisotropic fluid equations governing a frictionless obliquely-flowing plasma around an essentially arbitrarily shaped three-dimensional ion-absorbing object in a strong magnetic field are solved analytically in the quasi-neutral drift-approximation, neglecting parallel temperature gradients. The effects of transverse displacements traversing the magnetic presheath are also quantified. It is shown that the parallel collection flux density dependence upon external Mach-number is $n_\infty c_s \exp[-1 -(M_{\parallel\infty}- M_\perp\cot\theta)]$ where $\theta$ is the angle (in the plane of field and drift velocity) of the object-surface to the magnetic-field and $M_{\parallel\infty}$ is the external parallel flow. The perpendicular drift, \M_\perp, appearing here consists of the external \E\wedge\B drift plus a weighted sum of the ion and electron electron diamagnetic drifts that depends upon the total angle of the surface to the magnetic field. It is that somewhat counter-intuitive combination that an oblique (transverse) Mach probe experiment measures.Comment: Revised version following refereeing for Physics of Plasma

QSO clustering and the AAT 2dF redshift survey

We review previous results on the clustering and environments of QSOs. We show that the correlation length for QSOs derived from existing surveys is r~5/h Mpc, similar to the observed correlation length for field galaxies at the present epoch. The galaxy environment for z<1 radio-quiet QSOs is also consistent with field galaxies. The evolution of the QSO correlation length with redshift is currently uncertain, largely due to the small numbers of QSOs (~2000) in surveys suitable for clustering analysis. We report on intial progress with the AAT 2dF QSO redshift survey, which, once completed will comprise almost 30000 QSOs. With over 1000 QSOs already observed, it is already the largest single homogeneous QSO survey. We discuss prospects for deriving limits on cosmological parameters from this survey, and on the evolution of large-scale structure in the Universe.Comment: Invited talk at RS meeting on 'Large Scale Structure in the Universe' held at the Royal Society on 25-26 March 1998 14 pages, 11 figre

A Size of ~10 Mpc for the Ionized Bubbles at the End of Cosmic Reionization

The first galaxies to appear in the universe at redshifts z>20 created ionized bubbles in the intergalactic medium of neutral hydrogen left over from the Big-Bang. It is thought that the ionized bubbles grew with time, surrounded clusters of dwarf galaxies and eventually overlapped quickly throughout the universe over a narrow redshift interval near z~6. This event signaled the end of the reionization epoch when the universe was a billion years old. Measuring the hitherto unknown size distribution of the bubbles at their final overlap phase is a focus of forthcoming observational programs aimed at highly redshifted 21cm emission from atomic hydrogen. Here we show that the combined constraints of cosmic variance and causality imply an observed bubble size at the end of the overlap epoch of ~10 physical Mpc, and a scatter in the observed redshift of overlap along different lines-of-sight of ~0.15. This scatter is consistent with observational constraints from recent spectroscopic data on the farthest known quasars. Our novel result implies that future radio experiments should be tuned to a characteristic angular scale of ~0.5 degrees and have a minimum frequency band-width of ~8 MHz for an optimal detection of 21cm flux fluctuations near the end of reionization.Comment: Accepted for publication in Nature. Press embargo until publishe

Monte Carlo study of the hull distribution for the q=1 Brauer model

We study a special case of the Brauer model in which every path of the model has weight q=1. The model has been studied before as a solvable lattice model and can be viewed as a Lorentz lattice gas. The paths of the model are also called self-avoiding trails. We consider the model in a triangle with boundary conditions such that one of the trails must cross the triangle from a corner to the opposite side. Motivated by similarities between this model, SLE(6) and critical percolation, we investigate the distribution of the hull generated by this trail (the set of points on or surrounded by the trail) up to the hitting time of the side of the triangle opposite the starting point. Our Monte Carlo results are consistent with the hypothesis that for system size tending to infinity, the hull distribution is the same as that of a Brownian motion with perpendicular reflection on the boundary.Comment: 21 pages, 9 figure

Discovery of Four Gravitationally Lensed Quasars from the Sloan Digital Sky Survey

We present the discovery of four gravitationally lensed quasars selected from the spectroscopic quasar catalog of the Sloan Digital Sky Survey. We describe imaging and spectroscopic follow-up observations that support the lensing interpretation of the following four quasars: SDSS J0832+0404 (image separation \theta=1.98", source redshift z_s=1.115, lens redshift z_l=0.659); SDSS J1216+3529 (\theta=1.49", z_s=2.012); SDSS J1322+1052 (\theta=2.00", z_s=1.716); and SDSS J1524+4409 (\theta=1.67", z_s=1.210, z_l=0.320). Each system has two lensed images. We find that the fainter image component of SDSS J0832+0404 is significantly redder than the brighter component, perhaps because of differential reddening by the lensing galaxy. The lens potential of SDSS J1216+3529 might be complicated by the presence of a secondary galaxy near the main lensing galaxy.Comment: 25 pages, 10 figures, 6 tables, accepted for publication in A

Nonlinear Bogolyubov-Valatin transformations and quaternions

In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions H. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator.Comment: 6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added; v4: few extensions, references [62], [63] added, final version to be published in J. Phys. A: Math. Gen.

High-Redshift Quasars Found in Sloan Digital Sky Survey Commissioning Data III: A Color Selected Sample at i^*<20 in the Fall Equatorial Stripe

This is the third paper in a series aimed at finding high-redshift quasars from five-color (u'g'r'i'z') imaging data taken along the Celestial Equator by the SDSS during its commissioning phase. In this paper, we first present the observations of 14 bright high-redshift quasars (3.66<z<4.77, i^*<20) discovered in the SDSS Fall Equatorial Stripe, and the SDSS photometry of two previously known high-redshift quasars in the same region of the sky. Combined with the quasars presented in previous papers, we define a color-selected flux-limited sample of 39 quasars at 3.6 < z < 5.0 and i^*<20, covering a total effective area of 182 deg^2. From this sample, we estimate the average spectral power law slope in the rest-frame ultraviolet for quasars at z~4 to be -0.79 with a standard deviation of 0.34, and the average rest-frame equivalent width of the Ly alpha+N V emission line to be 69 A with a standard deviation of 18 A. The selection completeness of this multicolor sample is determined from the model colors of high-redshift quasars, taking into account the distributions of emission line strengths, intrinsic continuum slope, the line and continuum absorption from intervening material, and the effects of photometric errors. The average completeness of this sample is about 75%. The selection function calculated in this paper will be used to correct the incompleteness of this color-selected sample and to derive the high-redshift quasar luminosity function in a subsequent paper. In the Appendix, we present the observations of an additional 18 faint quasars (3.57<z<4.80, 20.1<i^*<20.8) discovered in the region on the sky that has been imaged twice. Several quasars presented in this paper exhibit interesting properties, including a radio-loud quasar at z=4.77, and a narrow-line quasar (FWHM = 1500 km s^-1) at z=3.57.Comment: AJ accepted (Jan 2001), with minor changes; high-resolution finding charts available at http://www.sns.ias.edu/~fan/papers/q3.p