A Lower Limit to the Universal Density of Metals at z \sim 3

Column density distribution functions of CIV with 12.05 < log (N) < 14.35 and SiIV with 11.70 < log (N) < 13.93 have been obtained using 81 CIV absorbers and 35 SiIV absorbers redward of the Ly alpha forest in the lines of sight to seven quasars with 2.518 < z(em) < 3.78. These distribution functions have been directly integrated to yield ion densities at z = 3 to 3.5 of Omega(CIV) = (2.0 \pm 0.5) x 10(-8) and Omega(SiIV) = (7.0 \pm 2.6) x 10(-9) with H0 = 65 km/s/Mpc and q0 = 0.02 (1 sigma errors). A larger sample of 11 quasar lines of sight was used to measure CII/CIV, SiIII/SiIV, and NV/CIV ratios, which suggest that CIV and SiIV are the dominant ionization stages and that corrections to Omega(Carbon) and Omega(Silicon) are no more than a factor of two. Normalizing the alpha-process elements to silicon and the Fe-coproduction elements to carbon gives a density of heavy elements in these forest clouds of Omega(metals) = (3.3 \pm 0.8) x 10(-7) (H0 = 65, q0 = 0.02). The implications for the amount of star formation and for the ionization of the IGM prior to z = 3 are discussed.Comment: 12 pages LaTeX (aaspp4.sty) with 3 encapsulated postscript figures. To be published in ApJ Letters (accepted September 3, 1997

Automorphism groups of Koras-Russell threefolds of the second kind

We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semi-direct products of two subgroups, one given by the multiplicative group and the other isomorphic to a polynomial ring in two variables with the addition law. We also show that these groups are generated by algebraic subgroups isomorphic to Gm and Ga

Cyclic covers of affine T-varieties

We consider normal affine T-varieties X endowed with an action of finite abelian group G commuting with the action of T. For such varieties we establish the existence of G-equivariant geometrico-combinatorial presentations in the sense of Altmann and Hausen. As an application, we determine explicit presentations of the Koras-Russell threefolds as bi-cyclic covers of A^3 equipped with a hyperbolic C^*-action

Equivariantly uniformly rational varieties

We introduce equivariant versions of uniform rationality: given an algebraic group G, a G-variety is called G-uniformly rational (resp. G-linearly uniformly rational) if every point has a G-invariant open neighborhood equivariantly isomorphic to a G-invariant open subset of the affine space endowed with a G-action (resp. linear G-action). We establish a criterion for Gm-uniform rationality of affine variety equipped with hyperbolic Gm-action with a unique fixed point, formulated in term of their Altmann-Hausen presentation. We prove the Gm-uniform rationality of Koras-Russel threefolds of the first kind and we also give example of non Gm-uniformly rational but smooth rational Gm-threefold associated to pairs of plane rational curves birationally non equivalent to a union of lines

Volatility regimes and liquidity co-movements in cap-based portfolios.

In contrast with prior studies focused on market-wide liquidity co-movements, we study class-wide liquidity co-movements and condition the analysis on volatility regimes using the Markov switching methodology. By defining three regimes of volatility (low, normal and high), we can investigate whether, and to what extent, liquidity co-movements in capbased portfolios are affected by volatility fluctuations. As our analysis points out, classwide shocks dominate stock-specific shocks in low volatility regimes for both large and mid caps. For small caps, cross-sectional statistical evidence of liquidity co-movements is weak in both high and low volatility regimes. Evidence indicates that failure to recognise the importance of volatility to determine class-wide variations in liquidity could significantly alter the performance and risk of size-based portfolios.

Molecular Hydrogen in a Damped Lyman-alpha System at z_abs=4.224

We present the direct detection of molecular hydrogen at the highest redshift known today (z_abs=4.224) in a Damped Lyman-alpha (DLA) system toward the quasar PSS J1443+2724. This absorber is remarkable for having one of the highest metallicities amongst DLA systems at z_abs>3, with a measured iron abundance relative to Solar of -1.12+/-0.10. We provide for the first time in this system accurate measurements of NI, MgII, SII and ArI column densities. The sulfur and nitrogen abundances relative to Solar, -0.63+/-0.10 and -1.38+/-0.10 respectively, correspond exactly to the primary nitrogen production plateau. H2 absorption lines are detected in four different rotational levels (J=0, 1, 2 and 3) of the vibrational ground-state in three velocity components with total column densities of log N(H2)=17.67, 17.97, 17.48 and 17.26 respectively. The J=4 level is tentatively detected in the strongest component with log N(H2)~14. The mean molecular fraction is log f=-2.38+/-0.13, with f=2N(H2)/(2N(H2)+N(HI)). We also measure log N(HD)/N(H2)<-4.2. The excitation temperatures T_{01} for the two main components of the system are 96 and 136 K respectively. We argue that the absorbing galaxy, whose star-formation activity must have started at least 2-5x10^8 yrs before z=4.224, is in a quiescent state at the time of observation. The density of the gas is small, n_H<=50 cm^{-3}, and the temperature is of the order of T~90-180 K. The high excitation of neutral carbon in one of the components can be explained if the temperature of the Cosmic Microwave Background Radiation has the value expected at the absorber redshift, T=14.2 K.Comment: 13 pages, 3 figures, accepted for publication in ApJ Letter

Physical conditions in broad and associated narrow absorption-line systems toward APM 08279+5255

Results of a careful analysis of the absorption systems with zabs = zem seen toward the bright, z_em ~ 3.91, gravitationally lensed quasar APM 08279+5255 are presented. Two of the narrow-line systems, at z_abs = 3.8931 and z_abs = 3.9135, show absorptions from singly ionized species with weak or no NV and O V absorptions at the same redshift. Absorption due to fine structure transitions of C II and Si II (excitation energies corresponding to, respectively, 156$\mu$m and 34$\mu$m) are detected at z_abs = 3.8931. Excitation by IR radiation is favored as the column density ratios are consistent with the shape of APM 08279+5255 IR spectrum. The low-ionization state of the system favors a picture where the cloud is closer to the IR source than to the UV source, supporting the idea that the extension of the IR source is larger than ~ 200 pc. The absence of fine structure lines at z_abs = 3.9135 suggests that the gas responsible for this system is farther away from the IR source. Abundances are ~ 0.01 and 1$Z_{\odot}$ at z_abs = 3.913 and 3.8931 and aluminum could be over-abundant with respect to silicon and carbon by at least a factor of two and five. All this suggests that whereas the \zabs = 3.8931 system is probably located within 200 pc from the QSO and ejected at a velocity larger than 1000 kms^{-1}, the \zabs = 3.9135 system is farther away and part of the host-galaxy. (abridged)Comment: 15 pages with 15 figures (psfiles), To appear in A&