Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source file, no figur

Bias and Hierarchical Clustering

It is now well established that galaxies are biased tracers of the distribution of matter, although it is still not known what form this bias takes. In local bias models the propensity for a galaxy to form at a point depends only on the overall density of matter at that point. Hierarchical scaling arguments allow one to build a fully-specified model of the underlying distribution of matter and to explore the effects of local bias in the regime of strong clustering. Using a generating-function method developed by Bernardeau & Schaeffer (1992), we show that hierarchical models lead one directly to the conclusion that a local bias does not alter the shape of the galaxy correlation function relative to the matter correlation function on large scales. This provides an elegant extension of a result first obtained by Coles (1993) for Gaussian underlying fields and confirms the conclusions of Scherrer & Weinberg (1998) obtained using a different approach. We also argue that particularly dense regions in a hierarchical density field display a form of bias that is different from that obtained by selecting such peaks in Gaussian fields: they are themselves hierarchically distributed with scaling parameters $S_p=p^{(p-2)}$. This kind of bias is also factorizable, thus in principle furnishing a simple test of this class of models.Comment: Latex, accepted for publication in ApJL; moderate revision

Modeling the impact of iron and phosphorus limitations on nitrogen fixation in the Atlantic Ocean

International audienceThe overarching goal of this study is to simulate subsurface N* (sensu, Gruber and Sarmiento, 1997) anomaly patterns in the North Atlantic Ocean and determine the basin wide rates of N2 fixation that are required to do so. We present results from an Atlantic implementation of a coupled physical-biogeochemical model that includes an explicit, dynamic representation of N2 fixation with light, nitrogen, phosphorus and iron limitations, and variable stoichiometric ratios. The model is able to reproduce nitrogen, phosphorus and iron concentration variability to first order. The latter is achieved by incorporating iron deposition directly into the model's detritus compartment which allows the model to reproduce sharp near surface gradients in dissolved iron concentration off the west coast of Africa and deep dissolved iron concentrations that have been observed in recent observational studies. The model can reproduce the large scale N* anomaly patterns but requires relatively high rates of surface nitrogen fixation to do so (1.8×1012 moles N yr?1 from 10° N?30° N, 3.4×1012 moles N y

Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions

We have studied the spin ordering of a dilute classical Heisenberg model with spin concentration $x$, and with ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic next-nearest-neighbor interaction $J_2$. Magnetic phases at absolute zero temperature $T = 0$ are determined examining the stiffness of the ground state, and those at finite temperatures $T \neq 0$ are determined calculating the Binder parameter $g_L$ and the spin correlation length $\xi_L$. Three ordered phases appear in the $x-T$ phase diagram: (i) the ferromagnetic (FM) phase; (ii) the spin glass (SG) phase; and (iii) the mixed (M) phase of the FM and the SG. Near below the ferromagnetic threshold $x_{\rm F}$, a reentrant SG transition occurs. That is, as the temperature is decreased from a high temperature, the FM phase, the M phase and the SG phase appear successively. The magnetization which grows in the FM phase disappears in the SG phase. The SG phase is suggested to be characterized by ferromagnetic clusters. We conclude, hence, that this model could reproduce experimental phase diagrams of dilute ferromagnets Fe$_x$Au$_{1-x}$ and Eu$_x$Sr$_{1-x}$S.Comment: 9 pages, 23 figure

Theory of Parabolic Arcs in Interstellar Scintillation Spectra

Our theory relates the secondary spectrum, the 2D power spectrum of the radio dynamic spectrum, to the scattered pulsar image in a thin scattering screen geometry. Recently discovered parabolic arcs in secondary spectra are generic features for media that scatter radiation at angles much larger than the rms scattering angle. Each point in the secondary spectrum maps particular values of differential arrival-time delay and fringe rate (or differential Doppler frequency) between pairs of components in the scattered image. Arcs correspond to a parabolic relation between these quantities through their common dependence on the angle of arrival of scattered components. Arcs appear even without consideration of the dispersive nature of the plasma. Arcs are more prominent in media with negligible inner scale and with shallow wavenumber spectra, such as the Kolmogorov spectrum, and when the scattered image is elongated along the velocity direction. The arc phenomenon can be used, therefore, to constrain the inner scale and the anisotropy of scattering irregularities for directions to nearby pulsars. Arcs are truncated by finite source size and thus provide sub micro arc sec resolution for probing emission regions in pulsars and compact active galactic nuclei. Multiple arcs sometimes seen signify two or more discrete scattering screens along the propagation path, and small arclets oriented oppositely to the main arc persisting for long durations indicate the occurrence of long-term multiple images from the scattering screen.Comment: 22 pages, 11 figures, submitted to the Astrophysical Journa

Nonlinear stochastic biasing from the formation epoch distribution of dark halos

We propose a physical model for nonlinear stochastic biasing of one-point statistics resulting from the formation epoch distribution of dark halos. In contrast to previous works on the basis of extensive numerical simulations, our model provides for the first time an analytic expression for the joint probability function. Specifically we derive the joint probability function of halo and mass density contrasts from the extended Press-Schechter theory. Since this function is derived in the framework of the standard gravitational instability theory assuming the random-Gaussianity of the primordial density field alone, we expect that the basic features of the nonlinear and stochastic biasing predicted from our model are fairly generic. As representative examples, we compute the various biasing parameters in cold dark matter models as a function of a redshift and a smoothing length. Our major findings are (1) the biasing of the variance evolves strongly as redshift while its scale-dependence is generally weak and a simple linear biasing model provides a reasonable approximation roughly at R\simgt 2(1+z)\himpc, and (2) the stochasticity exhibits moderate scale-dependence especially on R\simlt 20\himpc, but is almost independent of $z$. Comparison with the previous numerical simulations shows good agreement with the above behavior, indicating that the nonlinear and stochastic nature of the halo biasing is essentially understood by taking account of the distribution of the halo mass and the formation epoch.Comment: 34 pages, 11 figures, ApJ (2000) in pres

Computational Study of Turbulent-Laminar Patterns in Couette Flow

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.Comment: 4 pages, 5 figure

A Counts-in-Cells Analysis of Lyman-break Galaxies at z~3

We have measured the counts-in-cells fluctuations of 268 Lyman-break galaxies with spectroscopic redshifts in six 9 arcmin by 9 arcmin fields at z~3. The variance of galaxy counts in cubes of comoving side length 7.7, 11.9, 11.4 h^{-1} Mpc is \sigma_{gal}^2 ~ 1.3\pm0.4 for \Omega_M=1, 0.2 open, 0.3 flat, implying a bias on these scales of \sigma_{gal} / \sigma_{mass} = 6.0\pm1.1, 1.9\pm0.4, 4.0\pm0.7. The bias and abundance of Lyman-break galaxies are surprisingly consistent with a simple model of structure formation which assumes only that galaxies form within dark matter halos, that Lyman-break galaxies' rest-UV luminosities are tightly correlated with their dark masses, and that matter fluctuations are Gaussian and have a linear power-spectrum shape at z~3 similar to that determined locally (\Gamma~0.2). This conclusion is largely independent of cosmology or spectral normalization \sigma_8. A measurement of the masses of Lyman-break galaxies would in principle distinguish between different cosmological scenarios.Comment: Accepted for publication in ApJ, 16 pages including 4 figure

Testing Gaussian random hypothesis with the cosmic microwave background temperature anisotropies in the three-year WMAP data

We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using de-biased internal linear combination (DILC) map produced from the 3-year WMAP data. We test the phases for spherical harmonic modes with l <= 10 (which should be the cleanest) for their uniformity, randomness, and correlation with those of the foreground templates. The phases themselves are consistent with a uniform distribution, but not for l <= 5, and the differences between phases are not consistent with uniformity. For l=3 and l=6, the phases of the CMB maps cross-correlate with the foregrounds, suggestion the presence of residual contamination in the DLC map even on these large scales. We also use a one-dimensional Fourier representation to assemble a_lm into the \Delta T_l(\phi) for each l mode, and test the positions of the resulting maxima and minima for consistency with uniformity randomness on the unit circle. The results show significant departures at the 0.5% level, with the one-dimensional peaks being concentrated around \phi=180 degs. This strongly significant alignment with the Galactic meridian, together with the cross-correlation of DILC phases with the foreground maps, strongly suggests that even the lowest spherical harmonic modes in the map are significantly contaminated with foreground radiation.Comment: submitted to ApJL, one paragraph is added in Section 3 and some more in the Referenc