Astrophysical Fractals: Interstellar Medium and Galaxies

The interstellar medium is structured as a hierachy of gas clouds, that looks self-similar over 6 orders of magnitude in scales and 9 in masses. This is one of the more extended fractal in the Universe. At even larger scales, the ensemble of galaxies looks also self-similar over a certain ranges of scales, but more limited, may be over 3-4 orders of magnitude in scales. These two fractals appear to be characterized by similar Hausdorff dimensions, between 1.6 and 2. The various interpretations of these structures are discussed, in particular formation theories based on turbulence and self-gravity. In the latter, the fractal ensembles are considered in a critical state, as in second order phase transitions, when large density fluctuations are observed, that also obey scaling laws, and look self-similar over an extended range.Comment: 30 pages, 6 figures, Proceedings of "The Chaotic Universe", Roma colloquium, 1-5 Feb 99, World Scientific Advanced Series in Astrophysics and Cosmology, ed. V. Gurzadyan, Li-Zhi Fang and Remo Ruffin

An extension of McDiarmid's inequality

We derive an extension of McDiarmid's inequality for functions $f$ with bounded differences on a high probability set ${\cal Y}$ (instead of almost surely). The behavior of $f$ outside ${\cal Y}$ may be arbitrary. The proof is short and elementary, and relies on an extension argument similar to Kirszbraun's theorem.Comment: Note (4 pages

Molecular absorptions in high-z objects

Molecular absorption lines measured along the line of sight of distant quasars are important probes of the gas evolution in galaxies as a function of redshift. A review is made of the handful of molecular absorbing systems studied so far, with the present sensitivity of mm instruments. They produce information on the chemistry of the ISM at z \sim 1, the physical state of the gas, in terms of clumpiness, density and temperature. The CMB temperature can be derived as a function of z, and also any possible variations of fundamental constants can be constrained. With the sensitivity of ALMA, many more absorbing systems can be studied, for which some predictions and perspectives are described.Comment: 8 pages, 3 figures, in "Science with ALMA: a new era for Astrophysics", ApSS, Springer (Madrid, 13-17 November 2006

Models of AGN feedback

The physical processes responsible of sweeping up the surrounding gas in the host galaxy of an AGN, and able in some circumstances to expel it from the galaxy, are not yet well known. The various mechanisms are briefly reviewed: quasar or radio modes, either momentum-conserving outflows, energy-conserving outflows, or intermediate. They are confronted to observations, to know whether they can explain the M-sigma relation, quench the star formation or whether they can also provide some positive feedback and how the black hole accretion history is related to that of star formation.Comment: 8 pages, 4 figures, Proceedings of IAU Symp-309, ed. B.L. Ziegler, F. Combes, H. Dannerbauer, M. Verdug

CMB and Molecules at High Redshift

It becomes possible now to detect cold molecules at high redshift in the millimeter domain. Since the first discovery in 1992 by Brown and van den Bout of CO lines at z=2.28 in a gravitationally lensed starburst galaxy, nearly ten objects are now known to possess large quantities of molecular gas beyond z=1 and up to z = 5, through millimeter and sub-millimeter emission lines. The continuum dust emission is the most easily detected: in the mm domain, the emission is stronger for the more redshifted objects. For the CO lines, the situation is less favorable, and the reported detections are helped by gravitational amplification. The increase of the CMB temperature T_{bg} with redshift helps the rotational line excitation (especially at high z), but not its detection. Absorption in front of quasars is a more sensitive probe of cold gas at high redshift, able to detect individual clouds of a few solar masses (instead of 10^{10} Mo for emission). From the diffuse components, one can measure the cosmic black body temperature as a function of redshift. The high column densities component allow to observe important molecules not observable from the ground, like O2, H2O and LiH for example.Comment: 8 pages, 4 figures, Proceedings of the "3K cosmology", colloquium in Roma, October 1998, ed F. Melchiorr