11,492 research outputs found
Construction of Parseval wavelets from redundant filter systems
We consider wavelets in L^2(R^d) which have generalized multiresolutions.
This means that the initial resolution subspace V_0 in L^2(R^d) is not singly
generated. As a result, the representation of the integer lattice Z^d
restricted to V_0 has a nontrivial multiplicity function. We show how the
corresponding analysis and synthesis for these wavelets can be understood in
terms of unitary-matrix-valued functions on a torus acting on a certain vector
bundle. Specifically, we show how the wavelet functions on R^d can be
constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos
in Sections 1 and 4, v3 adds a number of references on GMRA theory and
wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and
two more reference
External Shear in Quadruply Imaged Lens Systems
We use publicly available N-body simulations and semi-analytic models of
galaxy formation to estimate the levels of external shear due to structure near
the lens in gravitational lens systems. We also describe two selection effects,
specific to four-image systems, that enhance the probability of observing
systems to have higher external shear. Ignoring additional contributions from
"cosmic shear" and assuming that lens galaxies are not significantly flattened,
we find that the mean shear at the position of a quadruple lens galaxy is 0.11,
the rms shear is roughly 0.15, and there is roughly a 45% likelihood of
external shear greater than 0.1. This is much larger than previous estimates
and in good agreement with typical measured external shear. The higher shear
primarily stems from the tendency of early-type galaxies, which are the
majority of lenses, to reside in overdense regions.Comment: 5 pages, 2 figures, ApJ in press, minor revision
Harmonic analysis of iterated function systems with overlap
In this paper we extend previous work on IFSs without overlap. Our method
involves systems of operators generalizing the more familiar Cuntz relations
from operator algebra theory, and from subband filter operators in signal
processing.Comment: 37 page
Exploring Cluster Ellipticals as Cosmological Standard Rods
We explore the possibility to calibrate massive cluster ellipticals as
cosmological standard rods using the Fundamental Plane relation combined with a
correction for luminosity evolution. Though cluster ellipticals certainly
formed in a complex way, their passive evolution out to redshifts of about 1
indicates that basically all major merging and accretion events took place at
higher redshifts. Therefore, a calibration of their luminosity evolution can be
attempted. We propose to use the Mg relation for that purpose because
it is independent of distance and cosmology. We discuss a variety of possible
caveats, ranging from dynamical evolution to uncertainties in stellar
population models and evolution corrections to the presence of age spread.
Sources of major random and systematic errors are analysed as well. We apply
the described procedure to nine elliptical galaxies in two clusters at
and derive constraints on the cosmological model. For the best
fitting -free cosmological model we obtain: , with
90% confidence limits being (the lower limit being due to the
presence of matter in the Universe). If the inflationary scenario applies (i.e.
the Universe has flat geometry), then, for the best fitting model, matter and
contribute about equally to the critical cosmic density (i.e.
). With 90% confidence
should be smaller than 0.9.Comment: 21 pages, including 5 eps-figures, Latex, uses aasms4.sty, accepted
by ApJ main journa
The Fundamental Plane at z=1.27: First Calibration of the Mass Scale of Red Galaxies at Redshifts z>1
We present results on the Fundamental Plane (FP) of early-type galaxies in
the cluster RDCS J0848+4453 at z=1.27. Internal velocity dispersions of three
K-selected early-type galaxies are determined from deep Keck spectra.
Structural parameters are determined from HST NICMOS images. The galaxies show
substantial offsets from the FP of the nearby Coma cluster, as expected from
passive evolution of their stellar populations. The offsets from the FP can be
expressed as offsets in M/L ratio. The M/L ratios of the two most massive
galaxies are consistent with an extrapolation of results obtained at
z=0.02-0.83. The evolution of early-type galaxies with masses >10^11 M_sun is
well described by ln M/L(B) = (-1.06 +- 0.09) z, corresponding to passive
evolution of -1.50 +- 0.13 mag at z=1.3. Ignoring selection effects, the best
fitting stellar formation redshift is z*=2.6, corresponding to a luminosity
weighted age at the epoch of observation of ~2 Gyr. The M/L ratios of these two
galaxies are also in excellent agreement with predictions from models that
include progenitor bias. The third galaxy is a factor ~10 less massive than the
other two, shows strong Balmer absorption lines in its spectrum, and is offset
from the Coma Fundamental Plane by 2.9 mag in rest-frame B. Despite their large
range in M/L ratios, all three galaxies fall in the ``Extremely Red Object''
(ERO) class with I-H>3 and R-K>5, and our results show that it is hazardous to
use simple models for converting luminosity to mass for these objects.
Measurements of M/L ratios at high redshift can be considered first steps to
empirically disentangle luminosity and mass evolution at the high mass end of
the galaxy population, lifting an important degeneracy in the interpretation of
evolution of the luminosity function. [SHORTENED]Comment: Accepted for publication in the Astrophysical Journa
The Sloan-Lens ACS Survey II: stellar populations and internal structure of early-type lens galaxies
We derive Fundamental Plane parameters of 15 early-type lens galaxies
identified by the Sloan Lens ACS (SLACS) Survey. The size of the sample allows
us to investigate for the first time the distribution of lens galaxies in the
FP space. After correcting for evolution, we find that lens galaxies occupy a
subset of the local FP. The edge-on projection (approximately M vs M/L) is
indistinguishable from that of normal early-type galaxies. However -- within
the fundamental plane -- the lens galaxies appear to concentrate at the edge of
the region populated by normal early-type galaxies. We show that this is a
result of our selection procedure (approximately velocity dispersion
sigma>240km/s). We conclude that SLACS lenses are a fair sample of high
velocity dispersion early-type galaxies. By comparing the central stellar
velocity dispersion that of the best fit lens model, we find
== =1.01+-0.02 with 0.065 rms scatter. We conclude that
within the Einstein radii the SLACS lenses are very well approximated by
isothermal ellipsoids, requiring a fine tuning of the stellar and dark matter
distribution (bulge-halo ``conspiracy''). Interpreting the offset from the
local FP in terms of evolution of the stellar mass-to-light ratio, we find for
the SLACS lenses d log M/L_B/dz=-0.69+-0.08 (rms 0.11) consistent with the rate
found for field early-type galaxies and with a scenario where most of the stars
were formed at high redshift (>2) with secondary episodes of star formation
providing less than ~10% of the stellar mass below z=1. We discuss star
formation history and structural homogeneity in the context of formation
mechanisms such as collisionless (``dry'') mergers. [Abridged]Comment: 2006, ApJ, 604, 622; 13 pages, 7 figures, 2 tables. Replaced Table 2,
since the previous version was incorrectly sorted. Updated references. No
changes in plots or content. More info available at SLACS website
www.slacs.or
Redshift-distance Survey of Early-type Galaxies: The D_n-sigma Relation
In this paper R-band photometric and velocity dispersion measurements for a
sample of 452 elliptical and S0 galaxies in 28 clusters are used to construct a
template D_n-sigma relation. This template relation is constructed by combining
the data from the 28 clusters, under the assumption that galaxies in different
clusters have similar properties. The photometric and spectroscopic data used
consist of new as well as published measurements, converted to a common system,
as presented in a accompanying paper. The resulting direct relation, corrected
for incompleteness bias, is log{D_n} =1.203 log{sigma} + 1.406; the zero-point
has been defined by requiring distant clusters to be at rest relative to the
CMB. This zero-point is consistent with the value obtained by using the
distance to Virgo as determined by the Cepheid period-luminosity relation. This
new D_n-sigma relation leads to a peculiar velocity of -72 (\pm 189) km/s for
the Coma cluster. The scatter in the distance relation corresponds to a
distance error of about 20%, comparable to the values obtained for the
Fundamental Plane relation. Correlations between the scatter and residuals of
the D_n-sigma relation with other parameters that characterize the cluster
and/or the galaxy stellar population are also analyzed. The direct and inverse
relations presented here have been used in recent studies of the peculiar
velocity field mapped by the ENEAR all-sky sample.Comment: 46 pages, 20 figures, and 7 tables. To appear in AJ, vol. 123, no. 5,
May 200
Black Hole Masses and Host Galaxy Evolution of Radio-loud Active Galactic Nuclei
We report stellar velocity dispersion measurements for a sample of 28 AGN
host galaxies including our previous work. Using the mass-dispersion
() and the fundamental plane relations, we estimate the
black hole mass for a sample of 66 BL Lac objects and investigate the role of
black hole mass in the energetics of BL Lac objects. The black hole mass range
for different BL Lac spectral types is similar, . Neither X-ray nor radio luminosity correlates with black hole
mass. Low-frequency-peaked BL Lac objects have higher Eddington ratios on
average, because of either more beaming or higher intrinsic power. For the
black hole mass range , the radio
luminosity of BL Lac objects and flat-spectrum radio quasars spans over 4
orders of magnitude, with BL Lac objects being low-power AGNs. We also
investigate the evolution of host galaxies for 39 AGNs out to
with measuredstellar velocity dispersions. Comparing the mass-to-light ratio
evolution in the observed frame with population synthesis models, we find that
single burst star formation models with are
consistent with the observations. From our model, we estimated
the intrinsic mass-to-light ratio evolution in the Cousins band, , consistent with that of normal early
type galaxies.Comment: ApJ accepted, 22 pages, 11 figure
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