The absorption spectrum of the QSO PKS 2126-158 (z_em = 3.27) at high resolution

Spectra of the z_em = 3.268 quasar PKS 2126-158 have been obtained in the range lambda lambda 4300-6620 A with a resolution R = 27000 and an average signal-to-noise ratio s/n = 25 per resolution element. The list of the identified absorption lines is given together with their fitted column densities and Doppler widths. The modal value of the Doppler parameter distribution for the Ly-alpha lines is = 25 km/s. The column density distribution can be described by a power-law dn/dN \propto N^{-beta} with beta = 1.5. 12 metal systems have been identified, two of which were previously unknown. In order to make the column densities of the intervening systems compatible with realistic assumptions about the cloud sizes and the silicon to carbon overabundance, it is necessary to assume a jump beyond the He II edge in the spectrum of the UV ionizing background at z = 3 a factor 10 larger than the standard predictions for the integrated quasar contribution. An enlarged sample of C IV absorptions (71 doublets) has been used to analyze the statistical properties of this class of absorbers strictly related to galaxies. The column density distribution is well described by a single power-law, with beta=1.64 and the Doppler parameter distribution shows a modal value b = 14 km/s. The two point correlation function has been computed in the velocity space for the individual components of C IV features. A significant signal is obtained for scales smaller than 200-300 km/s, xi(30< Delta v < 90 km/s) = 32.71 +- 2.89. A trend of decreasing clustering amplitude with decreasing column density is apparent, analogously to what has been observed for Ly-alpha lines.Comment: 16 pages, LaTeX (l-aa.sty), 13 ps figures, included in text with epsf, Fig. 1 can be retrieved at http://www.sissa.it/~dodorico/paper.html, accepted by Astronomy and Astrophysic

Inhomogeneous metal enrichment at z \sim 1.9: the Lyman limit systems in the spectrum of the HDF-S quasar

We present a detailed analysis of three metal absorption systems observed in the spectrum of the HDF-South quasar J2233-606 (z_em = 2.238), taking advantage of new VLT-UVES high resolution data (R=45000, S/N = 40-60, \lambda\lambda 3050-10000 \AA). Three main components, spanning about 300 km/s, can be individuated in the Lyman limit system at z~1.92. They show a surprisingly large variation in metallicities, respectively ~1/500, 1/8 and 1/100 solar. The large value found for the second component at z=1.9259, suggests that the line of sight crosses a star-forming region. In addition, there is a definite correlation between velocity position and ionisation state in this component, which we interpret as a possible signature of an expanding H II region. The systems at z~1.94 and z~1.87 have also high metallicity, ~1/4 and 1/3 solar. We find that photoionisation and collisional ionisation are equal alternatives to explain the high excitation phase revealed by O VI absorption, seen in these two systems. From the width of the Si IV, C IV, Si III and C III lines in the system at z~1.87, we can estimate the temperature of the gas to be log T ~ 4.7, excluding collisional ionisation. Finally, we compute the Si IV/C IV ratio for all Voigt profile components in a sample of log N(C IV) > 14 systems at z < 2. The values show a dispersion of more than an order of magnitude and most of them are much larger than what is observed for weaker systems. This is probably an indication that high column density systems preferably originate in galactic halos and are mostly influenced by local ionising sources.Comment: 11 pages, 11 figures, accepted by A&A main journa

Functional and Local Renormalization Groups

We discuss the relation between functional renormalization group (FRG) and local renormalization group (LRG), focussing on the two dimensional case as an example. We show that away from criticality the Wess-Zumino action is described by a derivative expansion with coefficients naturally related to RG quantities. We then demonstrate that the Weyl consistency conditions derived in the LRG approach are equivalent to the RG equation for the $c$-function available in the FRG scheme. This allows us to give an explicit FRG representation of the Zamolodchikov-Osborn metric, which in principle can be used for computations.Comment: 19 pages, 1 figur

Asymptotic freedom in Horava-Lifshitz gravity

We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The RG flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Horava-Lifshitz gravity is perturbatively renormalizable. Notably, the fundamental fixed point action does not obey detailed balance.Comment: 4 pages, 2 figure