Explicit Analytical Expression for a Lanchester Attrition-Rate Coefficient for Bonder and Farrell’s m-Period Target-Engagement Policy

Working Paper #5, DTRA Project, July 9, 2001The purpose of this working paper is to give an explicit analytical expression for a Lanche s- ter-type attrition-rate coefficient for direct-fire combat in a heterogeneous-target environment with serial acquisition of targets for Bonder and Farrell’s m-period target-acquisition policy1. It develops this result (its main result) from Taylor’s [2001d] new important general result (that does not depend on the target-engagement policy of a firer type or even on the particulars of the target-acquisition process) for a Lanchester attrition-rate coefficient for serial acquisition by developing explicit ana- lytical expressions for the two key intermediate quantities on which the coefficient depends: namely, (1) expected time to acquire a target that will be engaged, (2) next-target-type-to-be-engaged probability. An analytical expression for the former quantity (the expect value) was recently developed by one of the authors (Taylor [2001e]), while the paper at hand develops such an expression for the latter probability. These two new important intermediate results have allowed us to develop the explicit analytical expression for a Lanchester attrition-rate coefficient for Bonder and Farrell’s target- acquisition policy via Taylor’s general expression for direct-fire combat in a heterogeneous-target environment with serial acquisition of targets. These analytical results are then verified against simulation results

Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200

Do broad absorption line quasars live in different environments from ordinary quasars?

We select a sample of $\sim 4200$ traditionally defined broad absorption line quasars (BALQs) from the Fifth Data Release quasar catalog of the Sloan Digital Sky Survey. For a statistically homogeneous quasar sample with $1.7\le z\le 4.2$, the BAL quasar fraction is $\sim 14$ and is almost constant with redshift. We measure the auto-correlation of non-BAL quasars (nonBALQs) and the cross-correlation of BALQs with nonBALQs using this statistically homogeneous sample, both in redshift space and using the projected correlation function. We find no significant difference between the clustering strengths of BALQs and nonBALQs. Assuming a power-law model for the real space correlation function $\xi(r)=(r/r_0)^{-1.8}$, the correlation length for nonBALQs is $r_0=7.6\pm 0.8 h^{-1}{\rm Mpc}$; for BALQs, the cross-correlation length is $r_0=7.4\pm 1.1 h^{-1}{\rm Mpc}$. Our clustering results suggest that BALQs live in similar large-scale environments as do nonBALQs.Comment: accepted for publication in Ap

Dynamical Confirmation of SDSS Weak Lensing Scaling Laws

Galaxy masses can be estimated by a variety of methods; each applicable in different circumstances, and each suffering from different systematic uncertainties. Confirmation of results obtained by one technique with analysis by another is particularly important. Recent SDSS weak lensing measurements of the projected-mass correlation function reveal a linear relation between galaxy luminosities and the depth of their dark matter halos (measured on 260 \hinv kpc scales). In this work we use an entirely independent dynamical method to confirm these results. We begin by assembling a sample of 618 relatively isolated host galaxies, surrounded by a total of 1225 substantially fainter satellites. We observe the mean dynamical effect of these hosts on the motions of their satellites by assembling velocity difference histograms. Dividing the sample by host properties, we find significant variations in satellite velocity dispersion with host luminosity. We quantify these variations using a simple dynamical model, measuring \mtsd a dynamical mass within 260 \hinv kpc. The appropriateness of this mass reconstruction is checked by conducting a similar analysis within an N-body simulation. Comparison between the dynamical and lensing mass-to-light scalings shows reasonable agreement, providing some quantitative confirmation for the lensing results.Comment: 7 pages, 3 figures, accepted for publication in ApJ Letter

A Map of the Universe

We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper belt objects in the Solar system, to the galaxies and quasars from the Sloan Digital Sky Survey. This map projection, based on the logarithm map of the complex plane, preserves shapes locally, and yet is able to display the entire range of astronomical scales from the Earth's neighborhood to the cosmic microwave background. The conformal nature of the projection, preserving shapes locally, may be of particular use for analyzing large scale structure. Prominent in the map is a Sloan Great Wall of galaxies 1.37 billion light years long, 80% longer than the Great Wall discovered by Geller and Huchra and therefore the largest observed structure in the universe.Comment: Figure 8, and additional material accessible on the web at: http://www.astro.princeton.edu/~mjuric/universe

Exploratory Chandra Observations of the Three Highest Redshift Quasars Known

We report on exploratory Chandra observations of the three highest redshift quasars known (z = 5.82, 5.99, and 6.28), all found in the Sloan Digital Sky Survey. These data, combined with a previous XMM-Newton observation of a z = 5.74 quasar, form a complete set of color-selected, z > 5.7 quasars. X-ray emission is detected from all of the quasars at levels that indicate that the X-ray to optical flux ratios of z ~ 6 optically selected quasars are similar to those of lower redshift quasars. The observations demonstrate that it will be feasible to obtain quality X-ray spectra of z ~ 6 quasars with current and future X-ray missions.Comment: 15 pages, ApJL, in press; small revisions to address referee Comment

The overdensities of galaxy environments as a function of luminosity and color

We study the mean environments of galaxies in the Sloan Digital Sky Survey as a function of rest-frame luminosity and color. Overdensities in galaxy number are estimated in $8 h^{-1} \mathrm{Mpc}$ and $1 h^{-1} \mathrm{Mpc}$ spheres centered on $125,000$ galaxies taken from the SDSS spectroscopic sample. We find that, at constant color, overdensity is independent of luminosity for galaxies with the blue colors of spirals. This suggests that, at fixed star-formation history, spiral-galaxy mass is a very weak function of environment. Overdensity does depend on luminosity for galaxies with the red colors of early types; both low-luminosity and high-luminosity red galaxies are found to be in highly overdense regions.Comment: submitted to ApJ

The Linear Theory Power Spectrum from the Lyman-alpha Forest in the Sloan Digital Sky Survey

We analyze the SDSS Ly-alpha forest P_F(k,z) measurement to determine the linear theory power spectrum. Our analysis is based on fully hydrodynamic simulations, extended using hydro-PM simulations. We account for the effect of absorbers with damping wings, which leads to an increase in the slope of the linear power spectrum. We break the degeneracy between the mean level of absorption and the linear power spectrum without significant use of external constraints. We infer linear theory power spectrum amplitude Delta^2_L(k_p=0.009s/km,z_p=3.0)=0.452_{-0.057-0.116}^{+0.069+0.141} and slope n_eff=-2.321_{-0.047-0.102}^{+0.055+0.131} (possible systematic errors are included through nuisance parameters in the fit - a factor >~5 smaller errors would be obtained on both parameters if we ignored modeling uncertainties). The errors are correlated and not perfectly Gaussian, so we provide a chi^2 table to accurately describe the results. The result corresponds to sigma_8=0.85, n=0.94, for a LCDM model with Omega_m=0.3, Omega_b=0.04, and h=0.7, but is most useful in a combined fit with the CMB. The inferred curvature of the linear power spectrum and the evolution of its amplitude and slope with redshift are consistent with expectations for LCDM models, with the evolution of the slope, in particular, being tightly constrained. We use this information to constrain systematic contamination, e.g., fluctuations in the UV background. This paper should serve as a starting point for more work to refine the analysis, including technical improvements such as increasing the size and number of the hydrodynamic simulations, and improvements in the treatment of the various forms of feedback from galaxies and quasars.Comment: Improved presentation, including fit results for (z). Simple code to produce LyaF chi^2 given linear power spectrum available at: http://www.cita.utoronto.ca/~pmcdonal/code.htm