Eddington-Malmquist bias in a cosmological context

In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars "in space" or gathered "from the sky". Malmquist (1920) derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work. We derived the Malmquist relation within a general cosmological framework, including Friedmann's model, analogously to the way Malmquist showed in 1936 that his formula is also valid in the presence of extinction in Euclidean space. We also discuss some conceptual aspects that explain the wide scope of the bias relation. The Malmquist formula for the intrinsic difference _m - M_0 = - sigma_M^2 dlna(m)/dm is also valid for observations made in an expanding Friedmann universe. This is holds true for bolometric and finite-band magnitudes when a(m) refers to the distribution of observed (uncorrected for K-effect or z-dependent extinction) apparent magnitudes.Comment: 5 pages, 3 figures, A&A (in press

Revisiting the optical depth of spiral galaxies using the Tully-Fisher B relation

Aims. We attempt to determine the optical depth of spiral galaxy disks by a statistical study of new Tully-Fisher data from the ongoing KLUN+ survey, and to clarify the difference between the true and apparent behavior of optical depth. Methods. By utilizing so-called normalized distances, a subsample of the data is identified to be as free from selection effects as possible. For these galaxies, a set of apparent quantities are calculated for face-on positions using the Tully-Fisher diameter and magnitude relations. These values are compared with direct observations to determine the mean value of the parameter C describing the optical depth. Results. The present study suggests that spiral galaxy disks are relatively optically thin tauB = 0.1, at least in the outermost regions, while they appear in general to be optically thick tauB > 1 when the apparent magnitude and average surface brightness are studied statistically.Comment: 9 pages, 13 figures, accepted for publication in Astronomy & Astrophysic

A graph of dark energy significance on different spatial and mass scales

The current cosmological paradigm sees the formation and evolution of the cosmic large-scale structure as governed by the gravitational attraction of the Dark Matter (DM) and the repulsion of the Dark Energy (DE). We characterize the relative importance of uniform and constant dark energy, as given by the Lambda term in the standard LCDM cosmology, in galaxy systems of different scales, from groups to superclusters. An instructive "Lambda significance graph" is introduced where the matter-DE density ratio /rho_Lambda for different galaxy systems is plotted against the radius R. This presents gravitation and DE dominated regions and shows directly the zero velocity radius, the zero-gravity radius, and the Einstein-Straus radius for any fixed value of mass. Example galaxy groups and clusters from the local universe illustrate the use of the Lambda significance graph. These are generally located deep in the gravity-dominated region /rho_Lambda > 2, being virialized. Extended clusters and main bodies of superclusters can reach down near the border line between gravity-dominated and DE dominated regions /rho_Lambda = 2. The scale--mass relation from the standard 2-point correlation function intersects this balance line near the correlation lenght. The log /rho_Lambda vs. log R diagram is a useful and versatile way to characterize the dynamical state of systems of galaxies within the Lambda dominated expanding universe.Comment: 4 pages, 2 figure