The Role of Stellar Feedback and Dark Matter in the Evolution of Dwarf Galaxies

Supernova and multiple supernova events regulate several structural properties of dwarf galaxies. In particular, they govern the metal enrichment and the energy budget of the ISM; they might induce partial (blowout) or total (blowaway) gas removal from the galaxy; the morphology of the galactic gaseous body. Significant amounts of dark matter may play an equally important role: the dark matter gravitational potential tends to concentrate baryons towards the center, thus enhancing both the star formation rate and metal production. Also, the dynamical properties of the ISM, and the occurrence of a blowout or blowaway are shown to be determined by the dark matter content. We present detailed analytical/numerical models describing the evolution of dwarf Irregular galaxies including the above and other effects. The main results are: (i) dwarfs with total masses M\simlt 5\times 10^6 M_\odot are blown away; those with gas masses up to $\simeq 10^9 M_\odot$ lose mass in an outflow; (ii) metallicities are found to correlate tightly with dark matter content and are consistent with a range of dark-to-visible mass ratios $\phi\approx 0-30$ with about 65% of the dwarfs in the sample having $\phi\approx 0-10$; (iii) we predict a lower limit to the oxygen abundance in dIs of $12+log(O/H)\approx 7.2$; (iv) outflows are not particularly important for the metallicity evolution of dwarf galaxies and certainly less than star formation for gas consumption; however, dwarfs with gas masses few $\times 10^8 M_\odot$ are shown to be the major pollutants of the IGM; (v) the ISM HI velocity dispersion correlates with metallicity and, indepentently of dark matter, scales as $Z^{3.5}$. (Abridged)Comment: 56 pages, aasms4.sty, LaTeX, 12 figures. MNRAS, submitte

Gauss decomposition of trigonometric R-matrices

The general formula for the universal R-matrix for quantized nontwisted affine algebras by Khoroshkin and Tolstoy is applied for zero central charge highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonomitric R-matrix in tensor product of these modules. Explicit calculations for the simplest case of $A_1^{(1)}$ are presented. As a consequence new formulas for the trigonometric R-matrix with a parameter in tensor product of $U_q(sl_2)$-Verma modules are obtained.Comment: 14 page

Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting

We employ new calculational technique and present complete list of classical $r$-matrices for $D=4$ complex homogeneous orthogonal Lie algebra $\mathfrak{o}(4;\mathbb{C})$, the rotational symmetry of four-dimensional complex space-time. Further applying reality conditions we obtain the classical $r$-matrices for all possible real forms of $\mathfrak{o}(4;\mathbb{C})$: Euclidean $\mathfrak{o}(4)$, Lorentz $\mathfrak{o}(3,1)$, Kleinian $\mathfrak{o}(2,2)$ and quaternionic $\mathfrak{o}^{\star}(4)$ Lie algebras. For $\mathfrak{o}(3,1)$ we get known four classical $D=4$ Lorentz $r$-matrices, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) we provide new results and mention some applications.Comment: 13 pages; typos corrected. v3 matches version published in PL

Quantum deformations of D=4D=4 Euclidean, Lorentz, Kleinian and quaternionic o⋆(4)\mathfrak{o}^{\star}(4) symmetries in unified o(4;C)\mathfrak{o}(4;\mathbb{C}) setting -- Addendum

In our previous paper we obtained a full classification of nonequivalent quasitriangular quantum deformations for the complex $D=4$ Euclidean Lie symmetry $\mathfrak{o}(4;\mathbb{C})$. The result was presented in the form of a list consisting of three three-parameter, one two-parameter and one one-parameter nonisomorphic classical $r$-matrices which provide 'directions' of the nonequivalent quantizations of $\mathfrak{o}(4;\mathbb{C})$. Applying reality conditions to the complex $\mathfrak{o}(4;\mathbb{C})$ $r$-matrices we obtained the nonisomorphic classical $r$-matrices for all possible real forms of $\mathfrak{o}(4;\mathbb{C})$: Euclidean $\mathfrak{o}(4)$, Lorentz $\mathfrak{o}(3,1)$, Kleinian $\mathfrak{o}(2,2)$ and quaternionic $\mathfrak{o}^{\star}(4)$ Lie algebras. In the case of $\mathfrak{o}(4)$ and $\mathfrak{o}(3,1)$ real symmetries these $r$-matrices give the full classifications of the inequivalent quasitriangular quantum deformations, however for $\mathfrak{o}(2,2)$ and $\mathfrak{o}^{\star}(4)$ the classifications are not full. In this paper we complete these classifications by adding three new three-parameter $\mathfrak{o}(2,2)$-real $r$-matrices and one new three-parameter $\mathfrak{o}^{\star}(4)$-real $r$-matrix. All nonisomorphic classical $r$-matrices for all real forms of $\mathfrak{o}(4;\mathbb{C})$ are presented in the explicite form what is convenient for providing the quantizations. We will mention also some applications of our results to the deformations of space-time symmetries and string $\sigma$-models.Comment: 10 pages. We supplement results of our previous paper by adding new $\mathfrak{o}(2,2)$ and $\mathfrak{o}^{\star}(4)$ $r$-matrices needed for the complete classification of real classical $r$-matrices for all four real forms of $\mathfrak{o}(4;\mathbb{C})

Ca II triplet spectroscopy of RGB stars in NGC 6822: kinematics and metallicities

We present a detailed analysis of the chemistry and kinematics of red giants in the dwarf irregular galaxy NGC 6822. Spectroscopy at 8500 Angstroms was acquired for 72 red giant stars across two fields using FORS2 at the VLT. Line of sight extinction was individually estimated for each target star to accommodate the variable reddening across NGC 6822. The mean radial velocity was found to be v_helio = (52.8 +/- 2.2) km/s with dispersion rms = 24.1 km/s, in agreement with other studies. Ca II triplet equivalent widths were converted into [Fe/H] metallicities using a V magnitude proxy for surface gravity. The average metallicity was [Fe/H] = (-0.84 +/- 0.04) with dispersion rms = 0.31 dex and interquartile range 0.48. Our assignment of individual reddening values makes our analysis more sensitive to spatial variations in metallicity than previous studies. We divide our sample into metal-rich and metal-poor stars; the former are found to cluster towards small radii with the metal-poor stars more evenly distributed across the galaxy. The velocity dispersion of the metal-poor stars is higher than that of the metal-rich stars; combined with the age-metallicity relation this indicates that older populations have either been dynamically heated or were born in a less disclike distribution. The low ratio (v_rot/v_rms) suggests that within the inner 10', NGC 6822's stars are dynamically decoupled from the HI gas, possibly in a thick disc or spheroid.Comment: 15 pages, 12 figures, includes tabular dat

Extremal projectors for contragredient Lie (super)symmetries (short review)

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.Comment: 21 pages, LaTeX; typos corrected, references adde