A Method for Individual Source Brightness Estimation in Single- and Multi-band Data

We present a method of reliably extracting the flux of individual sources from sky maps in the presence of noise and a source population in which number counts are a steeply falling function of flux. The method is an extension of a standard Bayesian procedure in the millimeter/submillimeter literature. As in the standard method, the prior applied to source flux measurements is derived from an estimate of the source counts as a function of flux, dN/dS. The key feature of the new method is that it enables reliable extraction of properties of individual sources, which previous methods in the literature do not. We first present the method for extracting individual source fluxes from data in a single observing band, then we extend the method to multiple bands, including prior information about the spectral behavior of the source population(s). The multi-band estimation technique is particularly relevant for classifying individual sources into populations according to their spectral behavior. We find that proper treatment of the correlated prior information between observing bands is key to avoiding significant biases in estimations of multi-band fluxes and spectral behavior, biases which lead to significant numbers of misclassified sources. We test the single- and multi-band versions of the method using simulated observations with observing parameters similar to that of the South Pole Telescope data used in Vieira, et al. (2010).Comment: 11 emulateapj pages, 3 figures, revised to match published versio

The Power of General Relativity

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to $R^{1+\delta}$. This scale-free extension reduces to general relativity when $\delta \to 0$. In order to constrain generalisations of general relativity of this power class we analyse the behaviour of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires $\delta >0$ or $\delta <-1/4$. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound $-0.017<\delta <0.0012.$ We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter--radiation equality will be shifted by $\sim 1$ for a value of $\delta \sim 0.0005.$ We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound $\delta =2.7\pm 4.5\times 10^{-19}$ assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound $0\leq \delta <7.2\times 10^{-19}$ on theories of this type.Comment: 26 pages and 5 figures. Published versio

The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments

In 2002 a measurement of the effect of solar gravity upon the phase of coherent microwave beams passing near the Sun has been carried out with the Cassini mission, allowing a very accurate measurement of the PPN parameter $\gamma$. The data have been analyzed with NASA's Orbit Determination Program (ODP) in the Barycentric Celestial Reference System, in which the Sun moves around the centre of mass of the solar system with a velocity $v_\odot$ of about 10 m/sec; the question arises, what correction this implies for the predicted phase shift. After a review of the way the ODP works, we set the problem in the framework of Lorentz (and Galilean) transformations and evaluate the correction; it is several orders of magnitude below our experimental accuracy. We also discuss a recent paper \cite{kopeikin07}, which claims wrong and much larger corrections, and clarify the reasons for the discrepancy.Comment: Final version accepted by Classical and Quantum Gravity (8 Jan. 2008

On the Weyl - Eddington - Einstein affine gravity in the context of modern cosmology

We propose new models of an `affine' theory of gravity in $D$-dimensional space-times with symmetric connections. They are based on ideas of Weyl, Eddington and Einstein and, in particular, on Einstein's proposal to specify the space - time geometry by use of the Hamilton principle. More specifically, the connection coefficients are derived by varying a `geometric' Lagrangian that is supposed to be an arbitrary function of the generalized (non-symmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. In addition to the standard Einstein gravity, such a theory predicts dark energy (the cosmological constant, in the first approximation), a neutral massive (or, tachyonic) vector field, and massive (or, tachyonic) scalar fields. These fields couple only to gravity and may generate dark matter and/or inflation. The masses (real or imaginary) have geometric origin and one cannot avoid their appearance in any concrete model. Further details of the theory - such as the nature of the vector and scalar fields that can describe massive particles, tachyons, or even `phantoms' - depend on the concrete choice of the geometric Lagrangian. In `natural' geometric theories, which are discussed here, dark energy is also unavoidable. Main parameters - mass, cosmological constant, possible dimensionless constants - cannot be predicted, but, in the framework of modern `multiverse' ideology, this is rather a virtue than a drawback of the theory. To better understand possible applications of the theory we discuss some further extensions of the affine models and analyze in more detail approximate (`physical') Lagrangians that can be applied to cosmology of the early Universe.Comment: 15 pages; a few misprints corrected, one footnote removed and two added, the formulae and results unchanged but the text somewhat edited, esp. in Sections 4,5; the reference to the RFBR grant corrected

Covariant conservation of energy momentum in modified gravities

An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy-momentum is built-in to the field equations. This crucial result, called the generalized Bianchi identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, we demonstrate that in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories. In the light of our interpretation of the independent connection as an auxiliary variable we can also reconsider some criticisms of the Palatini formulation originally raised by Buchdahl.Comment: 8 pages. v2: more discussio

Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics

In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a collisionless self-gravitating gas, we develop a framework to include systematically the first general relativistic corrections to the matter distribution and gravitational potentials for general stationary systems. Then, we use our method to obtain particular solutions for the case of the Morgan & Morgan disks. The models obtained are fully analytical and correspond to the post-Newtonian generalizations of classical ones. We explore some properties of the models in order to estimate the importance of post-Newtonian corrections and we find that, contrary to the expectations, the main modifications appear far from the galaxy cores. As a by-product of this investigation we derive the corrected version of the tensor virial theorem. For stationary systems we recover the same result as in the Newtonian theory. However, for time dependent backgrounds we find that there is an extra piece that contributes to the variation of the inertia tensor.Comment: 30 pages, 8 figures. v2: Minor corrections and references added. Conclusions unchanged. v3: Version published in PR

The Einstein static universe in Loop Quantum Cosmology

Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Lambda is unstable to homogeneous perturbations. We show that LQC modifications can lead to a centre of stability for a large enough positive value of Lambda.Comment: 12 pages, 7 figures; v2: minor changes to match published version in Classical and Quantum Gravit

Exploring Halo Substructure with Giant Stars. VI. Extended Distributions of Giant Stars Around the Carina Dwarf Spheroidal Galaxy -- How Reliable Are They?

The question of the existence of active tidal disruption around various dSph galaxies remains controversial. That debate often centers on the nature (bound vs. unbound) of extended populations of stars. However, the more fundamental issue of the very existence of the extended populations is still contentious. We present an evaluation of the debate centering on one particular dSph, Carina, for which claims both for and against the existence of stars beyond the King radius have been made. Our review includes an examination of all previous studies bearing on the Carina radial profile and shows that the survey method which achieves the highest detected dSph signal-to-background in the outer parts of the galaxy is the Washington M, T2 + DDO51 (MTD) filter approach from Paper II in this series. We then address statistical methods used to evaluate the reliability of MTD surveys in the presence of photometric errors and for which a new, a posteriori statistical analysis methodology is provided. Finally, these statistical methods are tested by new spectroscopy of stars in the MTD-selected Carina candidate sample. Of 74 candidate giants with follow-up spectroscopy, the MTD technique identified 61 new Carina members, including 8 stars outside the King radius. From a sample of 29 stars not initially identified as candidate Carina giants but that lie just outside of our selection criteria, 12 have radial velocities consistent with membership, including 5 extratidal stars. Carina is shown to have an extended population of giant stars extending to a major axis radius of 40' (1.44x the nominal King radius).Comment: 56 pages, 10 figures. Submitted to the Astronomical Journal, 2004 Sep 2

Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential

We consider a system of particles interacting via a screened Newtonian potential and study phase transitions between homogeneous and inhomogeneous states in the microcanonical and canonical ensembles. Like for other systems with long-range interactions, we obtain a great diversity of microcanonical and canonical phase transitions depending on the dimension of space and on the importance of the screening length. We also consider a system of particles in Newtonian interaction in the presence of a ``neutralizing background''. By a proper interpretation of the parameters, our study describes (i) self-gravitating systems in a cosmological setting, and (ii) chemotaxis of bacterial populations in the original Keller-Segel model

Forces between electric charges in motion: Rutherford scattering, circular Keplerian orbits, action-at-a-distance and Newton's third law in relativistic classical electrodynamics

Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous inter-charge force. Problems discussed include small angle Rutherford scattering, Jackson's recent `torque paradox' and circular Keplerian orbits. Results consistent with special relativity are obtained only with an instantaneous interaction. The impossiblity of stable circular motion with retarded fields in either classical electromagnetism or Newtonian gravitation is demonstrated.Comment: 26 pages, 5 figures. QED and special relativity forbid retarded electromagnetic forces. See also physics/0501130. V2 has typos corrected, minor text modifications and updated references. V3 has further typos removed and added text and reference