14,150 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
Vulnerability : a view from different disciplines
Practitioners from different disciplines use different meanings and concepts of vulnerability, which, in turn, have led to diverse methods of measuring it. This paper presents a selective review of the literature from several disciplines to examine how they define and measure vulnerability. The disciplines include economics, sociology/anthropology, disaster management, environmental science, and health/nutrition. Differences between the disciplines can be explained by their tendency to focus on different components of risk, household responses to risk and welfare outcomes. In general, they focus either on the risks (at one extreme) or the underlying conditions (or outcomes) at the other. Trade-offs exist between simple measurement schemes and rich conceptual understanding.Environmental Economics&Policies,Health Economics&Finance,Insurance&Risk Mitigation,Economic Theory&Research,Rural Poverty Reduction
The LCO/Palomar 10,000 km/sec Cluster Survey. I. Properties of the Tully-Fisher Relation
The first results from a Tully-Fisher (TF) survey of cluster galaxies are
presented. The galaxies are drawn from fifteen Abell clusters that lie in the
redshift range 9000-12,000 km/sec and are distributed uniformly around the
celestial sky. The data set consists of R-band CCD photometry and long- slit
H-alpha spectroscopy. The rotation curves (RCs) are characterized by a turnover
radius (r_t) and an asymptotic velocity v_a, while the surface brightness
profiles are characterized in terms of an effective exponential surface
brightness I_e and a scale length r_e. The TF scatter is minimized when the
rotation velocity is measured at 2.0 +/- 0.2 r_e; a significantly larger
scatter results when the rotation velocity is measured at > 3 or < 1.5 scale
lengths. This effect demonstrates that RCs do not have a universal form, as has
been suggested by Persic, Salucci, and Stel. In contrast to previous studies, a
modest but statistically significant surface-brightness dependence of the TF
relation is found, log v = const + 0.28*log L + 0.14*log I_e. This indicates a
stronger parallel between the TF relation and the FP relations of elliptical
galaxies than has previously been recognized. Future papers in this series will
consider the implications of this cluster sample for deviations from Hubble
flow on 100-200 Mpc scales.Comment: 35 pages, 8 figures, uses aaspp4.sty. Submitted to ApJ. Also
available at http://astro.stanford.edu/jeff
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 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
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
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
RXJ0142.0+2131: I. The galaxy content of an X-ray-luminous galaxy cluster at z=0.28
We present a photometric and spectroscopic study of stellar populations in
the X-ray-luminous cluster of galaxies RXJ0142.0+2131 at z=0.280. This paper
analyses the results of high signal-to-noise spectroscopy, as well as g'-, r'-,
and i'-band imaging, using the Gemini Multi-Object Spectrograph on Gemini
North. Of 43 spectroscopic targets, we find 30 cluster members over a range in
color. Central velocity dispersions and absorption-line strengths for lines in
the range 3700A < lambda_rest < 5800A are derived for cluster members, and are
compared with a low-redshift sample of cluster galaxies, and single stellar
population (SSP) models. We use a combination of these indicators to estimate
luminosity-weighted mean ages, metallicities ([M/H]), and alpha-element
abundance ratios ([alpha/Fe]).
RXJ0142.0+2131 is a relatively poor cluster and lacks galaxies with high
central velocity dispersions. Although the red sequence and the Faber-Jackson
relation are consistent with pure passive evolution of the early-type
population with a formation redshift of z_form = 2, the strengths of the 4000A
break and scaling relations between metal line indices and velocity dispersion
reject this model with high significance. By inverting SSP models for the
Hbeta_G, Mgb, and line indices, we calculate that, at a given velocity
dispersion and metallicity, galaxies in RXJ0142.0+2131 have luminosity-weighted
mean ages 0.14 +- 0.07 dex older than the low-redshift sample. We also find
that [alpha/Fe] in stellar populations in RXJ0142.0+2131 is 0.14 +- 0.03
greater than at low redshift. All scaling relations are consistent with these
estimated offsets. (abridged)Comment: AJ, accepted. 31 pages, 13 figures, uses emulateapj.cls.
High-resolution figures available on request from first autho
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
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