Sigma

Abstract: Kinematic and photometric data have been obtained for 97 elliptical galaxies in six rich clusters. These data show that ellipticals describe a plane in three dimensions which, when viewed edge-on, projects a smaller scatter than the Faber-Jackson relationship between luminosity and velocity dispersion sigma. This plane is approximately given by L ∝ sigma8/3Sigmae-3/5, where Sigmae is the surface brightness within the effective radius Ae. The authors present a new photometric parameter Dn, the diameter which encloses an integrated surface brightness Sigma, that correlates as well with sigma as any linear combination of L and Sigma. It is shown that the Dn-sigma relation can be used to find relative distances of ellipticals with rms errors of l25% for a single galaxy and l10% for rich clusters. A poorer correlation between the line strength indicator Mg2 and Dn provides an independent, though less accurate, distance indicator. The new sigma and Mg2 distance estimators are used to determine an infall of the Local Group toward the Virgo Cluster. Associated Articles Part 1 Part 4 Part 2 Part 3 Part 5 Part 6 Part 7

Abstract: Recent X-ray observations of intense high-speed outflows in quasars suggest that supercritical accretion on to the central black hole may have an important effect on a host galaxy. I revisit some ideas of Silk and Rees, and assume such flows occur in the final stages of building up the black hole mass. It is now possible to model explicitly the interaction between the outflow and the host galaxy. This is found to resemble a momentum-driven stellar wind bubble, implying a relation M_BH = (f_g kappa/2 pi G^2) sigma^4 = 1.5 10^8 sigma_200^4 Msun between black hole mass and bulge velocity dispersion (f_g = gas fraction of total matter density, kappa = electron scattering opacity), without free parameters. This is remarkably close to the observed relation in both slope and normalization. This result suggests that the central black holes in galaxies gain most of their mass in phases of super-Eddington accretion, which are presumably obscured or at high redshift. Observed super-Eddington quasars are apparently late in growing their black hole masses.

Abstract: Bacterial sigma (sigma) factors are an essential component of RNA polymerase and determine promoter selectivity. The substitution of one sigma factor for another can redirect some or all of the RNA polymerase in a cell to activate the transcription of genes that would otherwise be silent. As a class, alternative sigma factors play key roles in coordinating gene transcription during various stress responses and during morphological development. The extracytoplasmic function (ECF) sigma factors are small regulatory proteins that are quite divergent in sequence relative to most other sigma factors. Many bacteria, particularly those with more complex genomes, contain multiple ECF sigma factors and these regulators often outnumber all other types of sigma factor combined. Examples include Bacillus subtilis (7 ECF sigma factors), Mycobacterium tuberculosis (10), Caulobacter crescentus (13), Pseudomonas aeruginosa (approximately 19), and Streptomyces coelicolor (approximately 50). The roles and mechanisms of regulation for these various ECF sigma factors are largely unknown, but significant progress has been made in selected systems. As a general trend, most ECF sigma factors are cotranscribed with one or more negative regulators. Often, these include a transmembrane protein functioning as an anti-sigma factor that binds, and inhibits, the cognate sigma factor. Upon receiving a stimulus from the environment, the sigma factor is released and can bind to RNA polymerase to stimulate transcription. In many ways, these anti-sigma:sigma pairs are analogous to the more familiar two-component regulatory systems consisting of a transmembrane histidine protein kinase and a DNA-binding response regulator. Both are mechanisms of coordinating a cytoplasmic transcriptional response to signals perceived by protein domains external to the cell membrane. Here, I review current knowledge of some of the better characterized ECF sigma factors, discuss the variety of experimental approaches that have proven productive in defining the roles of ECF sigma factors, and present some unifying themes that are beginning to emerge as more systems are studied.

Abstract: In this Letter we introduce a generalization of the Lorenz dynamical system using fractional derivatives. Thus, the system can have an effective noninteger dimension Sigma defined as a sum of the orders of all involved derivatives. We found that the system with Sigma<3 can exhibit chaotic behavior. A striking finding is that there is a critical value of the effective dimension Sigma(cr), under which the system undergoes a transition from chaotic dynamics to regular one.