993 research outputs found
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
Do broad absorption line quasars live in different environments from ordinary quasars?
We select a sample of 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 , the BAL quasar fraction is 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
, the correlation length for nonBALQs is ; for BALQs, the cross-correlation length is . Our clustering results suggest that BALQs live in similar
large-scale environments as do nonBALQs.Comment: accepted for publication in Ap
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
Cluster Alignments and Ellipticities in LCDM Cosmology
The ellipticities and alignments of clusters of galaxies, and their evolution
with redshift, are examined in the context of a Lambda-dominated cold dark
matter cosmology. We use a large-scale, high-resolution N-body simulation to
model the matter distribution in a light cone containing ~10^6 clusters out to
redshifts of z=3. Cluster ellipticities are determined as a function of mass,
radius, and redshift, both in 3D and in projection. We find strong cluster
ellipticities: the mean ellipticity increases with redshift from 0.3 at z=0 to
0.5 at z=3, for both 3D and 2D ellipticities; the evolution is well-fit by
e=0.33+0.05z. The ellipticities increase with cluster mass and with cluster
radius; the main cluster body is more elliptical than the cluster cores, but
the increase of ellipticities with redshift is preserved. Using the fitted
cluster ellipsoids, we determine the alignment of clusters as a function of
their separation. We find strong alignment of clusters for separations <100
Mpc/h; the alignment increases with decreasing separation and with increasing
redshift. The evolution of clusters from highly aligned and elongated systems
at early times to lower alignment and elongation at present reflects the
hierarchical and filamentary nature of structure formation. These measures of
cluster ellipticity and alignment will provide a new test of the current
cosmological model when compared with upcoming cluster surveys.Comment: 29 pages including 13 figures, to appear in ApJ Jan. 2005 (corrected
typos, added reference
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
Cluster Ellipticities as a Cosmological Probe
We investigate the dependence of ellipticities of clusters of galaxies on
cosmological parameters using large-scale cosmological simulations. We
determine cluster ellipticities out to redshift unity for LCDM models with
different mean densities and amplitudes of mass fluctuation
. The mean ellipticity increases monotonically with redshift for
all models. Larger values of , i.e., earlier cluster formation
time, produce lower ellipticities. The dependence of ellipticity on
is relatively weak in the range for high mass
clusters. The mean ellipticity decreases linearly with the
amplitude of fluctuations at the cluster redshift , nearly independent of
; on average, older clusters are more relaxed and are thus less
elliptical. The distribution of ellipticities about the mean is approximated by
a Gaussian, allowing a simple characterization of the evolution of ellipticity
with redshift as a function of cosmological parameters. At , the mean
ellipticity of high mass clusters is approximated by . This relation opens up the
possibility that, when compared with future observations of large cluster
samples, the mean cluster ellipticity and its evolution could be used as a new,
independent tool to constrain cosmological parameters, especially the amplitude
of mass fluctuations, .Comment: 16 pages, 4 figure
A Snapshot Survey for Gravitational Lenses Among z>=4.0 Quasars: I. The z>5.7 Sample
Over the last few years, the Sloan Digital Sky Survey (SDSS) has discovered
several hundred quasars with redshift between 4.0 and 6.4. Including the
effects of magnification bias, one expects a priori that an appreciable
fraction of these objects are gravitationally lensed. We have used the Advanced
Camera for Surveys on the Hubble Space Telescope to carry out a snapshot
imaging survey of high-redshift SDSS quasars to search for gravitationally
split lenses. This paper, the first in a series reporting the results of the
survey, describes snapshot observations of four quasars at z = 5.74, 5.82, 5.99
and 6.30, respectively. We find that none of these objects has a lensed
companion within 5 magnitudes with a separation larger than 0.3 arcseconds;
within 2.5 magnitudes, we can rule out companions within 0.1 arcseconds. Based
on the non-detection of strong lensing in these four systems, we constrain the
z~6 luminosity function to a slope of beta>-4.63 (3 sigma), assuming a break in
the quasar luminosity function at M_{1450}^*=-24.0. We discuss the implications
of this constraint on the ionizing background due to quasars in the early
universe. Given that these quasars are not highly magnified, estimates of the
masses of their central engines by the Eddington argument must be taken
seriously, possibly challenging models of black hole formation.Comment: 23 pages, 8 figures, 2 tables, submitted to A
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
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