Southern Sky Redshift Survey: Clustering of Local Galaxies

We use the two-point correlation function to calculate the clustering properties of the recently completed SSRS2 survey. The redshift space correlation function for the magnitude-limited SSRS2 is given by xi(s)=(s/5.85 h-1 Mpc)^{-1.60} for separations between 2 < s < 11 h-1 Mpc, while our best estimate for the real space correlation function is xi(r) = (r/5.36 h-1 Mpc)^{-1.86}. Both are comparable to previous measurements using surveys of optical galaxies over much larger and independent volumes. By comparing the correlation function calculated in redshift and real space we find that the redshift distortion on intermediate scales is small. This result implies that the observed redshift-space distribution of galaxies is close to that in real space, and that beta = Omega^{0.6}/b < 1, where Omega is the cosmological density parameter and b is the linear biasing factor for optical galaxies. We also use the SSRS2 to study the dependence of xi on the internal properties of galaxies. We confirm earlier results that luminous galaxies (L>L*) are more clustered than sub-L* galaxies and that the luminosity segregation is scale-independent. We find that early types are more clustered than late types, but that in the absence of rich clusters, the relative bias between early and late types in real space, is not as strong as previously estimated. Furthermore, both morphologies present a luminosity-dependent bias, with the early types showing a slightly stronger dependence on luminosity. We also find that red galaxies are significantly more clustered than blue ones, with a mean relative bias stronger than that seen for morphology. Finally, we find that the relative bias between optical and iras galaxies in real space is b_o/b_I $\sim$ 1.4.Comment: 43 pages, uses AASTeX 4.0 macros. Includes 8 tables and 16 Postscript figures, updated reference

MeV Right-handed Neutrinos and Dark Matter

We consider the possibility of having a MeV right-handed neutrino as a dark matter constituent. The initial reason for this study was the 511 keV spectral line observed by the satellite experiment INTEGRAL: could it be due to an interaction between dark matter and baryons? Independently of this, we find a number of constraints on the assumed right-handed interactions. They arise in particular from the measurements by solar neutrino experiments. We come to the conclusion that such particles interactions are possible, and could reproduce the peculiar angular distribution, but not the rate of the INTEGRAL signal. However, we stress that solar neutrino experiments are susceptible to provide further constraints in the future.Comment: 7 pages, figure 1 changed, added reference

Luminosity dependent clustering of star-forming BzK galaxies at redshift 2

We use the BzK color selection proposed by Daddi et al. (2004) to obtain a sample of 1092 faint star-forming galaxies (hereafter sBzKs) from 180 arcmin^2 in the Subaru Deep Field. This sample represents star-forming galaxies at 1.4 < z < 2.5 down to K(AB)=23.2, which roughly corresponds to a stellar-mass limit of ~ 1 x 10^{10} Msun. We measure the angular correlation function (ACF) of these sBzKs to be w(theta) = (0.58 +- 0.13) x theta["]^{-0.8} and translate the amplitude into the correlation length assuming a reasonable redshift distribution. The resulting value, r0 = 3.2^{+0.6}_{-0.7} h^{-1} Mpc, suggests that our sBzKs reside in haloes with a typical mass of 2.8 x 10^{11} Msun. Combining this halo mass estimate with those for brighter samples of Kong et al. (2006), we find that the mass of dark haloes largely increases with K brightness, a measure of the stellar mass. Comparison with other galaxy populations suggests that faint sBzKs (K(AB)<23.2) and Lyman Break Galaxies at z ~ 2 are similar populations hosted by relatively low-mass haloes, while bright sBzKs (K(AB)<21) reside in haloes comparable to or more massive than those of Distant Red Galaxies and Extremely Red Objects. Using the extended Press-Schechter formalism, we predict that present-day descendants of haloes hosting sBzKs span a wide mass range depending on K brightness, from lower than that of the Milky Way up to those of richest clusters.Comment: 14 pages, 9 figures, accepted for publication in Ap

Statistical Tests for CHDM and \LambdaCDM Cosmologies

We apply several statistical estimators to high-resolution N-body simulations of two currently viable cosmological models: a mixed dark matter model, having $\Omega_\nu=0.2$ contributed by two massive neutrinos (C+2\nuDM), and a Cold Dark Matter model with Cosmological Constant (\LambdaCDM) with $\Omega_0=0.3$ and h=0.7. Our aim is to compare simulated galaxy samples with the Perseus-Pisces redshift survey (PPS). We consider the n-point correlation functions (n=2-4), the N-count probability functions P_N, including the void probability function P_0, and the underdensity probability function U_\epsilon (where \epsilon fixes the underdensity threshold in percentage of the average). We find that P_0 (for which PPS and CfA2 data agree) and P_1 distinguish efficiently between the models, while U_\epsilon is only marginally discriminatory. On the contrary, the reduced skewness and kurtosis are, respectively, S_3\simeq 2.2 and S_4\simeq 6-7 in all cases, quite independent of the scale, in agreement with hierarchical scaling predictions and estimates based on redshift surveys. Among our results, we emphasize the remarkable agreement between PPS data and C+2\nuDM in all the tests performed. In contrast, the above \LambdaCDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.Comment: 12 pages, 10 figures, LaTeX (aaspp4 macro), in press on ApJ, Vol. 479, April 199

Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory

We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski signature (-+++). The condition of SO(4)-invariance imposed on gauge fields yields a bosonic matrix model which is a consistent truncation of the plane wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills equations are reduced to the equation of a particle moving in the double-well potential. The classical solution is a bounce, i.e. a particle which begins at the saddle point \phi=0 of the potential, bounces off the potential wall and returns to \phi=0. The gauge field tensor components parametrized by \phi are smooth and for finite time both electric and magnetic fields are nonvanishing. The energy density of this non-Abelian dyon configuration does not depend on coordinates of R^1\times S^3 and the total energy is proportional to the inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N) Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy is proportional to the square of the inverse radius of S^2. From the viewpoint of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian (dyonic) flux tubes extended along the x^3-axis.Comment: 11 pages; v2: one formula added, some coefficients correcte

Clustering of i-dropout galaxies at z=6 in GOODS and the UDF

We measured the angular clustering at z~6 from a large sample of i-dropout galaxies (293 with z<27.5 from GOODS and 95 with z<29.0 from the UDF). Our largest and most complete subsample (having L>0.5L*) shows the presence of clustering at 94% significance. For this sample we derive a (co-moving) correlation length of r_0=4.5^{+2.1}_{-3.2} h_{72}^{-1} Mpc and bias b=4.1^{+1.5}_{-2.6}, using an accurate model for the redshift distribution. No clustering could be detected in the much deeper but significantly smaller UDF, yielding b<4.4 (1 sigma). We compare our findings to Lyman break galaxies at z=3-5 at a fixed luminosity. Our best estimate of the bias parameter implies that i-dropouts are hosted by dark matter halos having masses of ~10^11 M_sun, similar to that of V-dropouts at z~5. We evaluate a recent claim that at z>5 star formation might have occurred more efficiently compared to that at z=3-4. This may provide an explanation for the very mild evolution observed in the UV luminosity density between z=6 and z=3. Although our results are consistent with such a scenario, the errors are too large to find conclusive evidence for this.Comment: minor changes to match published versio

Redshift-Space Distortions and the Real-Space Clustering of Different Galaxy Types

We study the distortions induced by peculiar velocities on the redshift-space correlation function of galaxies of different morphological types in the Pisces-Perseus redshift survey. Redshift-space distortions affect early- and late-type galaxies in different ways. In particular, at small separations, the dominant effect comes from virialized cluster cores, where ellipticals are the dominant population. The net result is that a meaningful comparison of the clustering strength of different morphological types can be performed only in real space, i.e., after projecting out the redshift distortions on the two-point correlation function xi(r_p,pi). A power-law fit to the projected function w_p(r_p) on scales smaller than 10/h Mpc gives r_o = 8.35_{-0.76}^{+0.75} /h Mpc, \gamma = 2.05_{-0.08}^{+0.10} for the early-type population, and r_o = 5.55_{-0.45}^{+0.40} /h Mpc, \gamma = 1.73_{-0.08}^{+0.07} for spirals and irregulars. These values are derived for a sample luminosity brighter than M_{Zw} = -19.5. We detect a 25% increase of r_o with luminosity for all types combined, from M_{Zw} = -19 to -20. In the framework of a simple stable-clustering model for the mean streaming of pairs, we estimate sigma_12(1), the one-dimensional pairwise velocity dispersion between 0 and 1 /h Mpc, to be 865^{+250}_{-165} km/s for early-type galaxies and 345^{+95}_{-65} km/s for late types. This latter value should be a fair estimate of the pairwise dispersion for ``field'' galaxies; it is stable with respect to the presence or absence of clusters in the sample, and is consistent with the values found for non-cluster galaxies and IRAS galaxies at similar separations.Comment: 17 LaTeX pages including 3 tables, plus 11 PS figures. Uses AASTeX macro package (aaspp4.sty) and epsf.sty. To appear on ApJ, 489, Nov 199

The Subaru/XMM-Newton Deep Survey (SXDS) -VII. Clustering Segregation with Ultraviolet and Optical Luminosities of Lyman-Break Galaxies at z~3

We investigate clustering properties of Lyman-break galaxies (LBGs) at z~3 based on deep multi-waveband imaging data from optical to near-infrared wavelengths in the Subaru/XMM-Newton Deep Field. The LBGs are selected by U-V and V-z' colors in one contiguous area of 561 arcmin^2 down to z'=25.5. We study the dependence of the clustering strength on rest-frame UV and optical magnitudes, which can be indicators of star formation rate and stellar mass, respectively. The correlation length is found to be a strong function of both UV and optical magnitudes with brighter galaxies being more clustered than faint ones in both cases. Furthermore, the correlation length is dependent on a combination of UV and optical magnitudes in the sense that galaxies bright in optical magnitude have large correlation lengths irrespective of UV magnitude, while galaxies faint in optical magnitude have correlation lengths decreasing with decreasing UV brightness. These results suggest that galaxies with large stellar masses always belong to massive halos in which they can have various star formation rates, while galaxies with small stellar masses reside in less massive halos only if they have low star formation rates. There appears to be an upper limit to the stellar mass and the star formation rate which is determined by the mass of hosting dark halos.Comment: 16 pages, 15 figures, accepted for publication in Ap

Membranes for Topological M-Theory

We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological A-model (a by-product of this reduction is a Green-Schwarz formulation of topological strings). We conclude that the action is BRST-exact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.Comment: 22 pp, plain tex. v2: refs. adde

Spectrum of Sizes for Perfect Deletion-Correcting Codes

One peculiarity with deletion-correcting codes is that perfect $t$-deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius $t$ with respect to the Levenshte\u{\i}n distance may be of different sizes. There is interest, therefore, in determining all possible sizes of a perfect $t$-deletion-correcting code, given the length $n$ and the alphabet size~$q$. In this paper, we determine completely the spectrum of possible sizes for perfect $q$-ary 1-deletion-correcting codes of length three for all $q$, and perfect $q$-ary 2-deletion-correcting codes of length four for almost all $q$, leaving only a small finite number of cases in doubt.Comment: 23 page