11,003 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
The Globular Cluster Systems in the Coma Ellipticals. III: The Unique Case of IC 4051
Using archival \hst WFPC2 data, we derive the metallicity distribution,
luminosity function, and spatial structure of the globular cluster system
around IC 4051, a giant E galaxy on the outskirts of the Coma cluster core. The
metallicity distribution derived from the (V-I) colors has a mean [Fe/H] =
-0.3, a near-complete lack of metal-poor clusters, and only a small metallicity
gradient with radius; it may, however, have two roughly equal metallicity
subcomponents, centered at [Fe/H] ~ 0.0 and -1.0. The luminosity distribution
(GCLF) has the Gaussian-like form observed in all other giant E galaxies, with
a peak (turnover) at V = 27.8, consistent with a Coma distance of 100 Mpc. The
radial profiles of both the GCS and the halo light show an unusually steep
falloff which may indicate that the halo of this galaxy has been tidally
truncated. Lastly, the specific frequency of the GCS is remarkably large: we
find S_N = 11 +- 2, resembling the central cD-type galaxies even though IC 4051
is not a cD or brightest cluster elliptical. A formation model consistent with
most of the observations would be that this galaxy was subjected to removal of
a large fraction of its protogalactic gas shortly after its main phase of
globular cluster formation, probably by its first passage through the Coma
core. Since then, no significant additions due to accretions or mergers have
taken place.Comment: 24 pp. plus 13 Figures. Postscript file for the complete paper can
also be downloaded from http://www.physun.mcmaster.ca/~harris/WEHarris.html.
Astron.J., in pres
Charge exchange contribution to the decay of the ring current, measured by energetic neutral atoms (ENAs)
In this paper we calculate the contribution of charge exchange to the decay of the ring current. Past works have suggested that charge exchange of ring current protons is primarily responsible for the decay of the ring current during the late recovery phase, but there is still much debate about the fast decay of the early recovery phase. We use energetic neutral atom (ENA) measurements from Polar to calculate the total ENA energy escape. To get the total ENA escape we apply a forward modeling technique, and to estimate the total ring current energy escape we use the Dessler-Parker-Sckopke relationship. We find that during the late recovery phase of the March 10, 1998 storm ENAs with energies greater than 17.5 keV can account for 75% of the estimated energy loss from the ring current. During the fast recovery the measured ENAs can only account for a small portion of the total energy loss. We also find that the lifetime of the trapped ions is significantly shorter during the fast recovery phase than during the late recovery phase, suggesting that different processes are operating during the two phases
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
Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
By introducing Hilbert space and operators, we show how probabilities,
approximations and entropy encoding from signal and image processing allow
precise formulas and quantitative estimates. Our main results yield orthogonal
bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur
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
Composition Mixing during Blue Straggler Formation and Evolution
We use smoothed-particle hydrodynamics to examine differences between direct
collisions of single stars and binary star mergers in their roles as possible
blue straggler star formation mechanisms. We find in all cases that core helium
in the progenitor stars is largely retained in the core of the remnant, almost
independent of the type of interaction or the central concentration of the
progenitor stars.
We have also modelled the subsequent evolution of the hydrostatic remnants,
including mass loss and energy input from the hydrodynamical interaction. The
combination of the hydrodynamical and hydrostatic models enables us to predict
that little mixing will occur during the merger of two globular cluster stars
of equal mass. In contrast to the results of Proctor Sills, Bailyn, & Demarque
(1995), we find that neither completely mixed nor unmixed models can match the
absolute colors of observed blue stragglers in NGC 6397 at all luminosity
levels. We also find that the color distribution is probably the crucial test
for explanations of BSS formation - if stellar collisions or mergers are the
correct mechanisms, a large fraction of the lifetime of the straggler must be
spent away from the main sequence. This constraint appears to rule out the
possibility of completely mixed models. For NGC 6397, unmixed models predict
blue straggler lifetimes ranging from about 0.1 to 4 Gyr, while completely
mixed models predict a range from about 0.6 to 4 Gyr.Comment: AASTeX, 28 pg., accepted for ApJ, also available at
http://ucowww.ucsc.edu/~erics/bspaper.htm
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
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