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Using 3D spectroscopy with a scanning Fabry-Perot interferometer, we study the ionized gas kinematics in 59 nearby dwarf galaxies. Combining our results with data from literature, we provide a global relation between the gas velocity dispersion (sigma) and the star formation rate (SFR) and H\alpha luminosity for galaxies in a very broad range of star formation rates SFR=0.001-300 Msun/yr. We find that the SFR-sigma relation for the combined sample of dwarf galaxies, star forming, local luminous, and ultra-luminous infrared galaxies can be fitted as sigma~ SFR^(5.3+-0.2). This implies that the slope of the L-sigma relation inferred from the sample of rotation supported disc galaxies (including mergers) is similar to the L-sigma relation of individual giant HII regions. We present arguments that the velocity dispersion of the ionized gas does not reflect the virial motions in the gravitational potential of dwarf galaxies, and instead is mainly determined by the energy injected into the interstellar medium by the ongoing star formation., Comment: 15 pages, major revision of the previous version, accepted to MNRAS

Using the method of searching for arbitrary shaped voids in the distribution of volume-limited samples of galaxies from the DR5 SDSS survey, we have identified voids and investigated their characteristics and the change in these characteristics with decreasing Mlim - the upper limit on the absolute magnitude of the galaxies involved in the construction of voids. The total volume of the 50 largest voids increases with decreasing Mlim with a break near Mr* = -20.44 for SDSS galaxies. The mean density contrast in voids increases with decreasing Mlim also with a weak break near M*. The exponent of the dependence of the volume of a void on its rank increases significantly with decreasing Mlim starting from Mlim ~ -20.4 in the characteristic range of volumes, which reflects the tendency for greater clustering of brighter galaxies. The galaxies mostly tend to concentrate toward the void boundaries and to avoid the central void regions. The axial ratios of the ellipsoids equivalent to the voids are, on average, retained with changing Mlim and correspond to elongated and nonoblate void shapes, but some of the voids can change their shape significantly. The void centers show correlations reflecting the correlations of the galaxy distribution on scales (35-70)/h Mpc. The galaxy distribution in the identified voids is nonrandom - groups and filaments can be identified. We have compared the properties of the galaxies in voids and galaxies in structures identified using the minimum spanning tree. A noticeable difference is observed in the mean color indices and star formation rates per unit stellar mass of the galaxies in dense regions (structures) - as expected, the galaxies in voids are, on average, bluer and have higher log(SFR/M_star). These tendencies become stronger toward the central void regions., Comment: 26 pages, 18 figures

Current explanation of the overabundance of dark matter subhalos in the Local Group (LG) indicates that there maybe a limit on mass of a halo, which can host a galaxy. This idea can be tested using voids in the distribution of galaxies: at some level small voids should not contain any (even dwarf) galaxies. We use observational samples complete to M_B = -12 with distances less than 8 Mpc to construct the void function (VF): the distribution of sizes of voids empty of any galaxies. There are ~30 voids with sizes ranging from 1 to 5 Mpc. We then study the distribution of dark matter halos in very high resolution simulations of the LCDM model. The theoretical VF matches the observations remarkably well only if we use halos with circular velocities larger than 45 +/- 10 km/s. This agrees with the Local Group predictions. There are smaller halos in the voids, but they should not produce any luminous matter. Small voids look quite similar to their giant cousins: the density has a minimum at the center of a void and it increases as we get closer to the border. Small nonluminous halos inside the void form a web of tiny filaments. Thus, both the Local Group data and the nearby voids indicate that isolated halos below 45 +/- 10 km/s must not host galaxies and that small (few Mpc) voids are truly dark., Comment: 5 pages, 1 figure

A method for detecting voids in the galaxy distribution is presented. Using this method, we have identified 732 voids with a radius of the seed sphere Rseed > 4.0h^{-1}Mpc in a volume-limited sample of galaxies from the southern part of the 2dFGRS survey. 110 voids with Rseed > 9.0h^{-1}Mpc have a positive significance. The mean volume of such voids is 19000 h^{-3}Mpc^3. Voids with Rseed > 9.0h^{-1}Mpc occupy 55% of the sample volume. We construct a dependence of the volumes of all the identified voids on their ranks and determine parameters of the galaxy distribution. The dependence of the volume of voids on their rank is consistent with a fractal model (Zipf's power law) of the galaxy distribution with a fractal dimension D ~ 2.1 (given the uncertainty in determining the dimension using our method and the results of a correlation analysis) up to scales of 25h^{-1}Mpc with the subsequent transition to homogeneity. The directions of the greatest elongations of voids and their ellipticities (oblateness) are determined from the parameters of equivalent ellipsoids. The directions of the greatest void elongations have an enhanced concentration to the directions perpendicular to the line of sight., Comment: 14 pages, 8 figures

The apparatus of correlation gamma function (\Gamma*(r)) is used to analyze volume-limited samples from the DR4 Main Galaxy Sample of the SDSS survey with the aim of determining the characteristic scales of galaxy clustering. Up to 20 h^{-1} Mpc (H_0 = 65 km s^{-1}Mpc^{-1}), the distribution of galaxies is described by a power-law density-distance dependence, \Gamma*(r) proportional to r^{-\gamma}, with an index \gamma approximately 1.0. A change in the state of clustering (a significant deviation from the power law) was found on a scale of 20-25 h^{-1}Mpc. The distribution of SDSS galaxies becomes homogeneous (\gamma approximately 0) from a scale of ~60 h^{-1}Mpc. The dependence of \gamma on the luminosity of galaxies in volume-limited samples was obtained. The power-law index \gamma increases with decreasing absolute magnitude of sample galaxies M_abs. At M_abs ~ -21.4, which corresponds to the characteristic value Mr* of the SDSS luminosity function, this dependence exhibits a break followed by a more rapid increase in \gamma., Comment: 11 pages, 5 figures