12,254 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
Ages, metallicities and -element enhancement for galaxies in Hickson compact groups
Central velocity dispersions and eight line-strength Lick indices have been
determined from 1.3 resolution long-slit spectra of 16 elliptical
galaxies in Hickson compact groups. These data were used to determine galaxy
properties (ages, metallicities and -element enhancements) and allowed
a comparison with the parameters determined for a sample of galaxies in lower
density environments, studied by Gonz\'alez (1993). The stellar population
parameters were derived by comparison to single stellar population models of
Thomas et al. (2003) and to a new set of SSP models for the indices Mg,
Fe5270 and Fe5335 based on synthetic spetra. These models, based on an update
version of the fitting functions presented in Barbuy et al. (2003), are fully
described here. Our main results are: (1) the two samples have similar mean
values for the metallicities and [/Fe] ratios, (2) the majority of the
galaxies in compact groups seem to be old (median age of 14 Gyr for eight
galaxies for which ages could be derived), in agreement with recent work by
Proctor et al. (2004). These findings support two possible scenarios: compact
groups are either young systems whose members have recently assembled and had
not enough time to experience any merging yet or, instead, they are old systems
that have avoided merging since their time of formation.Comment: Accepted for publication in A
The Universality of the Fundamental Plane of E and S0 Galaxies. Spectroscopic data
We present here central velocity dispersion measurements for 325 early-type
galaxies in eight clusters and groups of galaxies, including new observations
for 212 galaxies. The clusters and groups are the A262, A1367, Coma (A1656),
A2634, Cancer and Pegasus clusters, and the NGC 383 and NGC 507 groups. The new
measurements were derived from medium dispersion spectra, that cover 600 A
centered on the Mg Ib triplet at lambda ~ 5175. Velocity dispersions were
measured using the Tonry & Davis cross-correlation method, with a typical
accuracy of 6%. A detailed comparison with other data sources is made.Comment: 12 pages, 5 tables, 3 figures, to appear in AJ. Note that tables 2
and 3 are in separate files, as they should be printed in landscape forma
Tuning of magnetic and electronic states by control of oxygen content in lanthanum strontium cobaltites
We report on the magnetic, resistive, and structural studies of perovskite
LaSrCoO. By using the relation of synthesis
temperature and oxygen partial pressure to oxygen stoichiometry obtained from
thermogravimetric analysis, we have synthesized a series of samples with
precisely controlled . These samples show three structural
phases at , , , and two-phase
behavior for other oxygen contents. The stoichiometric material with
is a cubic ferromagnetic metal with the Curie temperature K. The increase of to 0.15 is followed by a linear decrease of
to 160 K and a metal-insulator transition near the
boundary of the cubic structure range. Further increase of results in
formation of a tetragonal phase for
and a brownmillerite phase for . At low
temperatures, these are weak ferromagnetic insulators (canted antiferromagnets)
with magnetic transitions at and 120 K, respectively. At
higher temperatures, the phase is -type
antiferromagnetic between 230 K and 360 K. Low temperature magnetic
properties of this system for can be described in terms of a
mixture of Co ions in the low-spin state and Co ions in the
intermediate-spin state and a possible spin transition of Co to the
intermediate-spin state above . For , there appears to
be a combination of Co and Co ions, both in the high-spin state
with dominating antiferromagnetic interactions.Comment: RevTeX, 9 pages, 7 figures, to be published in Physical Review
First energetic neutral atom images from Polar
Energetic neutral atoms are created when energetic magnetospheric ions undergo charge exchange with cold neutral atoms in the Earth\u27s tenuous extended atmosphere (the geocorona). Since they are unaffected by the Earth\u27s magnetic field, these energetic neutrals travel away in straight line trajectories from the points of charge exchange. The remote detection of these particles provides a powerful means through which the global distribution and properties of the geocorona and ring current can be inferred. Due to its 2 Ă 9 RE polar orbit, the Polar spacecraft provides an excellent platform from which to observe ENAs because it spends much of its time in the polar caps which are usually free from the contaminating energetic charged particles that make observations of ENAs more difficult. In this brief report, we present the first ENA imaging results from Polar. Storm-time ENA images are presented for a northern polar cap apogee pass on August 29, 1996 and for a southern polar cap perigee pass on October 23, 1996. As well, we show with a third event (July 31, 1996) that ENA emissions can also be detected in association with individual substorm
The Fundamental Plane in RX J0142.0+2131: a galaxy cluster merger at z=0.28
We present the Fundamental Plane (FP) in the z = 0.28 cluster of galaxies RX
J0142.0+2131. There is no evidence for a difference in the slope of the FP when
compared with the Coma cluster, although the internal scatter is larger. On
average, stellar populations in RX J0142.0+2131 have rest-frame V-band
mass-to-light ratios (M/L_V) 0.29+-0.03 dex lower than in Coma. This is
significantly lower than expected for a passively-evolving cluster formed at
z_f=2. Lenticular galaxies have lower average M/L_V and a distribution of M/L_V
with larger scatter than ellipticals. Lower mass-to-light ratios are not due to
recent star formation: our previous spectroscopic observations of RX
J0142.0+2131 E/S0 galaxies showed no evidence for significant star-formation
within the past ~4 Gyr. However, cluster members have enhanced alpha-element
abundance ratios, which may act to decrease M/L_V. The increased scatter in the
RX J0142.0+2131 FP reflects a large scatter in M/L_V implying that galaxies
have undergone bursts of star formation over a range of epochs. The seven
easternmost cluster galaxies, including the second brightest member, have M/L_V
consistent with passive evolution and z_f = 2. We speculate that RX
J0142.0+2131 is a cluster-cluster merger where the galaxies to the east are yet
to fall into the main cluster body or have not experienced star formation as a
result of the merger.Comment: 4 pages, 2 figures, accepted for publication in ApJ Letter
The Possible z=0.83 Precursors of z=0 M* Early-type Cluster Galaxies
We examine the distribution of stellar masses of galaxies in MS 1054-03 and
RX J0152.7-1357, two X-ray selected clusters of galaxies at z=0.83. Our stellar
mass estimates, from spectral energy distribution fitting, reproduce the
dynamical masses as measured from velocity dispersions and half-light radii
with a scatter of 0.2 dex in the mass for early-type galaxies. When we restrict
our sample of members to high stellar masses, > 1e11.1 Msun (M* in the
Schechter mass function for cluster galaxies), we find that the fraction of
early-type galaxies is 79 +/- 6% at z=0.83 and 87 +/- 6% at z=0.023 for the
Coma cluster, consistent with no evolution. Previous work with
luminosity-selected samples finds that the early-type fraction in rich clusters
declines from =~80% at z=0 to =~60% at z=0.8. The observed evolution in the
early-type fraction from luminosity-selected samples must predominately occur
among sub-M* galaxies. As M* for field and group galaxies, especially
late-types, is below M* for clusters galaxies, infall could explain most of the
recent early-type fraction growth. Future surveys could determine the
morphological distributions of lower mass systems which will confirm or refute
this explanation.Comment: 5 pages in emulate ApJ format with three color figures. Accepted for
publication in ApJ Letters, v642n2. Updated to correct grammatical and
typographic errors found by the journa
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
The Fundamental Plane of Gravitational Lens Galaxies and The Evolution of Early-Type Galaxies in Low Density Environments
Most gravitational lenses are early-type galaxies in relatively low density
environments -- a ``field'' rather than a ``cluster'' population. We show that
field early-type galaxies with 0 < z < 1, as represented by the lens galaxies,
lie on the same fundamental plane as those in rich clusters at similar
redshifts. We then use the fundamental plane to measure the combined
evolutionary and K-corrections for early-type galaxies in the V, I and H bands.
Only for passively evolving stellar populations formed at z > 2 (H_0=65 km/s
Mpc, Omega_0=0.3, Lambda_0=0.7) can the lens galaxies be matched to the local
fundamental plane. The high formation epoch and the lack of significant
differences between the field and cluster populations contradict many current
models of the formation history of early-type galaxies. Lens galaxy colors and
the fundamental plane provide good photometric redshift estimates with an
empirical accuracy of -0.03 +/- 0.11 for the 17 lenses with known redshifts. A
mass model dominated by dark matter is more consistent with the data than
either an isotropic or radially anisotropic constant M/L mass model, and a
radially anisotropic model is better than an isotropic model.Comment: 36 pages, 9 figures, 6 tables. ApJ in press. Final version contains
more observational dat
The Star Formation Epoch of the Most Massive Early-Type Galaxies
We present new Keck spectroscopy of early-type galaxies in three galaxy
clusters at z~0.5. We focus on the fundamental plane (FP) relation, and combine
the kinematics with structural parameters determined from HST images. The
galaxies obey clear FP relations, which are offset from the FP of the nearby
Coma cluster due to passive evolution of the stellar populations. The z~0.5
data are combined with published data for 11 additional clusters at
0.18<z<1.28, to determine the evolution of the mean M/L(B) ratio of cluster
galaxies with masses M>10^11 M_sun, as implied by the FP. We find
dlog(M/L(B))/dz = -0.555+-0.042, stronger evolution than was previously
inferred from smaller samples. The observed evolution depends on the
luminosity-weighted mean age of the stars in the galaxies, the initial mass
function (IMF), selection effects due to progenitor bias, and other parameters.
Assuming a normal IMF but allowing for various other sources of uncertainty we
find z* = 2.01+-0.20 for the luminosity-weighted mean star formation epoch. The
main uncertainty is the slope of the IMF in the range 1-2 Solar masses: we find
z* = 4.0 for a top-heavy IMF with slope x=0. The M/L(B) ratios of the cluster
galaxies are compared to those of recently published samples of field
early-type galaxies at 0.32<z<1.14. Assuming that progenitor bias and the IMF
do not depend on environment we find that the present-day age of stars in
massive field galaxies is 4.1 +- 2.0 % (~0.4 Gyr) less than that of stars in
massive cluster galaxies, consistent with most, but not all, previous studies
of local and distant early-type galaxies. This relatively small age difference
is surprising in the context of expectations from ``standard'' hierarchical
galaxy formation models. [ABRIDGED]Comment: Accepted for publication in ApJ. Minor corrections to match published
versio
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