13,434 research outputs found
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
Mass-Selection and the Evolution of the Morphology-Density Relation from z=0.8 to z=0
We examined the morphology-density relations for galaxy samples selected by
luminosity and by mass in each of five massive X-ray clusters from z=0.023 to
0.83 for 674 spectroscopically-confirmed members. Rest-frame optical colors and
visual morphologies were obtained primarily from Hubble Space Telescope images.
Morphology-density relations (MDR) are derived in each cluster from a complete,
luminosity-selected sample of 452 galaxies with a magnitude limit M_V <
M^{*}_{V} + 1. The change in the early-type fraction with redshift matches
previous work for massive clusters of galaxies. We performed a similar
analysis, deriving MDRs for complete, mass-selected samples of 441 galaxies
with a mass-limit of 10^{10.6} M_{\sun}. Our mass limit includes faint objects,
the equivalent of =~1 mag below L^{*} for the red cluster galaxies, and
encompasses =~70% of the stellar mass in cluster galaxies. The MDRs in the
mass-selected sample at densities of Sigma > 50 galaxies Mpc^{-2} are similar
to those in the luminosity-selected sample but show larger early-type
fractions. However, the trend with redshift in the fraction of elliptical and
S0 galaxies with masses > 10^{10.6} M_{\sun} differs significantly between the
mass- and luminosity-selected samples. The clear trend seen in the early-type
fraction from z=0 to z=~ 0.8 is not found in mass-selected samples. The
early-type galaxy fraction changes much less, and is consistent with being
constant at 92% +/- 4% at \Sigma> 500 galaxies Mpc^{-2} and 83 +/- 3% at 50 <
\Sigma < 500 galaxies Mpc^{-2}. This suggests that galaxies of mass lower than
> 10^{10.6} M_{\sun} play a significant role in the evolution of the early-type
fraction in luminosity-selected samples. (Abstract abridged)Comment: 18 pages in emulate ApJ format, with 10 color figures, Accepted to
ApJ. Version updated to reflect published version, includes new references
and a correction to table
Mass-to-Light Ratios of Field Early-Type Galaxies at z~1 from Ultra-Deep Spectroscopy: Evidence for Mass-dependent Evolution
We present an analysis of the Fundamental Plane for a sample of 27 field
early-type galaxies in the redshift range 0.6<z<1.15. The galaxies in this
sample have high S/N spectra obtained at the VLT and high resolution imaging
from the ACS. We find that the mean evolution in M/L of our sample is , with a large galaxy-to-galaxy scatter. This value can
be too low by 0.3 due to selection effects, resulting in . The strong correlation between M/L and rest-frame color
indicates that the observed scatter is not due to measurement errors, but due
to intrinsic differences between the stellar populations of the galaxies. This
pace of evolution is much faster than the evolution of cluster galaxies.
However, we find that the measured M/L evolution strongly depends on galaxy
mass. For galaxies with masses , we find no significant
difference between the evolution of field and cluster galaxies: Delta ln (M/L_B) =
-1.12+/-0.06z$ for cluster galaxies. The relation between the measured M/L
evolution and mass is partially due to selection effects. However, even when
taking selection effects into account, we still find a relation between M/L
evolution and mass, which is most likely caused by a lower mean age and a
larger intrinsic scatter for low mass galaxies. Results from lensing early-type
galaxies, which are mass-selected, show a very similar trend with mass. This,
combined with our findings, provides evidence for down-sizing. Previous studies
of the rate of evolution of field early-type galaxies found a large range of
mutually exclusive values. We show that these differences are largely caused by
the differences between fitting methods. (Abridged)Comment: figures 3 and 4 available at
http://www.strw.leidenuniv.nl/~vdwel/private/FPpaper
Molecule sublimation as a tracer of protostellar accretion: Evidence for accretion bursts from high angular resolution C18O images
The accretion histories of embedded protostars are an integral part of
descriptions of their physical and chemical evolution. In particular, are the
accretion rates smoothly declining from the earlier toward later stages or in
fact characterized by variations such as intermittent bursts? We aim to
characterize the impact of possible accretion variations in a sample of
embedded protostars by measuring the size of the inner regions of their
envelopes where CO is sublimated and relate those to their temperature profiles
dictated by their current luminosities. Using observations from the
Submillimeter Array we measure the extents of the emission from the C18O
isotopologue toward 16 deeply embedded protostars. We compare these
measurements to the predicted extent of the emission given the current
luminosities of the sources through dust and line radiative transfer
calculations. Eight out of sixteen sources show more extended C18O emission
than predicted by the models. The modeling shows that the likely culprit for
these signatures is sublimation due to increases in luminosities of the sources
by about a factor five or more during the recent 10,000 years - the time it
takes for CO to freeze-out again on dust grains. For four of those sources the
increase would have had to have been a factor 10 or more. The compact emission
seen toward the other half of the sample suggests that C18O only sublimates
when the temperature exceeds 30 K - as one would expect if CO is mixed with H2O
in the grain ice-mantles. The small-number statistics from this survey suggest
that protostars undergo significant bursts about once every 20,000 years. This
also illustrates the importance of taking the physical evolutionary histories
into account for descriptions of the chemical structures of embedded
protostars.Comment: Accepted by A&A; 11 pages, 5 figure
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
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
- âŠ