Soft versus Hard X-ray emission in AGN: partial covering and warm plus cold absorber models

We analyse the ROSAT PSPC hardness ratio and the 0.5-2 keV to 2-10 keV flux ratio of 65 Active Galactic Nuclei (AGN) for which there are both ROSAT archival observations available and 2-10 keV fluxes, mostly from the HEAO-1 MC-LASS survey. We conclude that the simplest spectral model for the AGN that can accommodate the variety of X-ray colours obtained is a standard power law (with energy spectral index $\alpha\sim 0.9$) plus a $\sim 0.1$ keV black body both partially absorbed. In our sample, type 1 AGN require an absorbing column around $10^{22}\, {\rm cm}^{-2}$ with covering fractions between 20 and 100\%, while type 2 AGN display larger columns and $\sim 100\%$ coverage. This simple model also provides a good link between soft and hard AGN X-ray luminosity functions and source counts. We also consider a warm absorber as an alternative model to partial covering and find that the the presence of gas in two phases (ionized and neutral) is required.Comment: 10 pages, Latex (mn.sty), 1 table, 5 figures included (epsf), postscript version also available via anonymous ftp at ftp://astsun1.unican.es/pub/ceballos/ . Accepted for publication in MNRA

Grand Unification without Higgs Bosons

We discuss how a model for the electroweak interactions without a Higgs could be embedded into a grand unified theory. The requirement of a non-trivial fixed point in the SU(2) sector of the weak interactions together with the requirement of the numerical unification of the gauge couplings leads to a prediction for the value of the SU(2) gauge coupling in the fixed point regime. The fixed point regime must be in the TeV region to solve the unitarity problem in the elastic scattering of W bosons. We find that the unification scale is at about 10^{14} GeV. Viable grand unified theories must thus conserve baryon number. We discuss how to build such a model without using Higgs bosons.Comment: 8 pages, to be published in the proceedings devoted to the Scientific and Human Legacy of Julius Wess, initiated by the JW2011 Workshop, August 27 - 28, 2011, Donji Milanovac, Serbi

The Evolution of City Size Distributions

We review the accumulated knowledge on city size distributions and determinants of urban growth. This topic is of interest because of a number of key stylized facts, including notably Zipf’s law for cities (which states that the number of cities of size greater than S is proportional to 1/S) and the importance of urban primacy. We first review the empirical evidence on the upper tail of city size distribution. We offer a novel discussion of the important econometric issues in the characterization of the distribution. We then discuss the theories that have been advanced to explain the approximate constancy of the distribution across very different economic and social systems, emphasizing both bare-bone statistical theories and more developed economic theories. We discuss the more recent work on the determinants of urban growth and, in particular, growth regressions, economic explanations of city size distributions other than Gibrat’s law, consequences of major shocks (quasi natural experiments), and the dynamics of U.S. urban evolution.city size distribution, Gibrat’s law, Hill estimator, persistence of city size distributions, power laws, random growth, urban growth, urban hierarchy, urban primacy, Zipf regression, Zipf’s law.