2,091 research outputs found
A new Q-matrix in the Eight-Vertex Model
We construct a -matrix for the eight-vertex model at roots of unity for
crossing parameter with odd , a case for which the existing
constructions do not work. The new -matrix \Q depends as usual on the
spectral parameter and also on a free parameter . For \Q has the
standard properties. For , however, it does not commute with the
operator and not with itself for different values of the spectral
parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published
versio
The Dynamical Fingerprint of Core Scouring in Massive Elliptical Galaxies
The most massive elliptical galaxies have low-density centers or cores that
differ dramatically from the high-density centers of less massive ellipticals
and bulges of disk galaxies. These cores have been interpreted as the result of
mergers of supermassive black hole binaries, which depopulate galaxy centers by
gravitationally slingshotting central stars toward large radii. Such binaries
naturally form in mergers of luminous galaxies. Here, we analyze the population
of central stellar orbits in 11 massive elliptical galaxies that we observed
with the integral field spectrograph SINFONI at the European Southern
Observatory Very Large Telescope. Our dynamical analysis is orbit-based and
includes the effects of a central black hole, the mass distribution of the
stars, and a dark matter halo. We show that the use of integral field
kinematics and the inclusion of dark matter is important to conclude upon the
distribution of stellar orbits in galaxy centers. Six of our galaxies are core
galaxies. In these six galaxies, but not in the galaxies without cores, we
detect a coherent lack of stars on radial orbits in the core region and a
uniform excess of radial orbits outside of it: when scaled by the core radius,
the radial profiles of the classical anisotropy parameter beta are nearly
identical in core galaxies. Moreover, they match quantitatively the predictions
of black hole binary simulations, providing the first convincing dynamical
evidence for core scouring in the most massive elliptical galaxies.Comment: 8 pages, 3 figures, accepted by Ap
The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity for odd N
Following Baxter's method of producing Q_{72}-operator, we construct the
Q-operator of the root-of-unity eight-vertex model for the crossing parameter
with odd where Q_{72} does not exist. We use this
new Q-operator to study the functional relations in the Fabricius-McCoy
comparison between the root-of-unity eight-vertex model and the superintegrable
N-state chiral Potts model. By the compatibility of the constructed Q-operator
with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we
verify the set of functional relations of the root-of-unity eight-vertex model
using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation,
References added and updated-Journal versio
The stellar populations of the central region of M31
We continue the analysis of the dataset of our spectroscopic observation
campaign of M31, by deriving simple stellar population properties (age
metallicity and alpha-elements overabundance) from the measurement of Lick/IDS
absorption line indices. We describe their two-dimensional maps taking into
account the dust distribution in M31. 80\% of the values of our age
measurements are larger than 10 Gyr. The central 100 arcsec of M31 are
dominated by the stars of the classical bulge of M31. They are old (11-13 Gyr),
metal-rich (as high as [Z/H]~0.35 dex) at the center with a negative gradient
outwards and enhanced in alpha-elements ([alpha/Fe]~ 0.28+- 0.01 dex). The bar
stands out in the metallicity map, where an almost solar value of [Z/H]
(~0.02+-0.01 dex) with no gradient is observed along the bar position angle
(55.7 deg) out to 600 arcsec from the center. In contrast, no signature of the
bar is seen in the age and [alpha/Fe] maps, that are approximately
axisymmetric, delivering a mean age and overabundance for the bar and the
boxy-peanut bulge of 10-13 Gyr and 0.25-0.27 dex, respectively. The
boxy/peanut-bulge has almost solar metallicity (-0.04+- 0.01 dex). The
mass-to-light ratio of the three components is approximately constant at M/LV ~
4.4-4.7 Msol/Lsol. The disk component at larger distances is made of a mixture
of stars, as young as 3-4 Gyr, with solar metallicity and smaller M/LV (~3+-0.1
Msol/Lsol). We propose a two-phase formation scenario for the inner region of
M31, where most of the stars of the classical bulge come into place together
with a proto-disk, where a bar develops and quickly transforms it into a
boxy-peanut bulge. Star formation continues in the bulge region, producing
stars younger than 10 Gyr, in particular along the bar, enhancing its
metallicity. The disk component appears to build up on longer time-scales.Comment: Language-edited version, Accepted for publication in A&
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
We construct the explicit -operator incorporated with the
-loop-algebra symmetry of the six-vertex model at roots of unity. The
functional relations involving the -operator, the six-vertex transfer matrix
and fusion matrices are derived from the Bethe equation, parallel to the
Onsager-algebra-symmetry discussion in the superintegrable -state chiral
Potts model. We show that the whole set of functional equations is valid for
the -operator. Direct calculations in certain cases are also given here for
clearer illustration about the nature of the -operator in the symmetry study
of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations
added for clearer presentation, References updated-Journal version with
modified labelling of sections and formula
Depleted Galaxy Cores and Dynamical Black Hole Masses
Shallow cores in bright, massive galaxies are commonly thought to be the
result of scouring of stars by mergers of binary supermassive black holes. Past
investigations have suggested correlations between the central black hole mass
and the stellar light or mass deficit in the core, using proxy measurements of
or stellar mass-to-light ratios (). Drawing on a wealth
of dynamical models which provide both and , we identify
cores in 23 galaxies, of which 20 have direct, reliable measurements of and dynamical stellar mass-to-light ratios ().
These cores are identified and measured using Core-S\'ersic model fits to
surface brightness profiles which extend out to large radii (typically more
than the effective radius of the galaxy); for approximately one fourth of the
galaxies, the best fit includes an outer (\sersic) envelope component. We find
that the core radius is most strongly correlated with the black hole mass and
that it correlates better with total galaxy luminosity than it does with
velocity dispersion. The strong core-size-- correlation enables
estimation of black hole masses (in core galaxies) with an accuracy comparable
to the -- relation (rms scatter of 0.30 dex in ), without the need for spectroscopy. The light and mass deficits correlate
more strongly with galaxy velocity dispersion than they do with black hole
mass. Stellar mass deficits span a range of 0.2--39 \mbh, with almost all (87%)
being ; the median value is 2.2 .Comment: Proof-corrected version, AJ, 146, 160,
http://stacks.iop.org/1538-3881/146/16
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Measuring Dark Matter Profiles Non-Parametrically In Dwarf Spheroidals: An Application To Draco
We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Our non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 = 20 pc is well fit by a power law with slope alpha = -1.0 +/- 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.NSF-0908639Astronom
An elliptic current operator for the 8 vertex model
We compute the operator which creates the missing degenerate states in the
algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to
the concept of an elliptic current operator. We find that in sharp contrast
with the corresponding formalism in the six-vertex model at roots of unity the
current operator is not nilpotent with the consequence that in the construction
of degenerate eigenstates of the transfer matrix an arbitrary number of exact
strings can be added to the set of regular Bethe roots. Thus the original set
of free parameters {s,t} of an eigenvector of T is enlarged to become
{s,t,\lambda_{c,1}, ..., \lambda_{c,n}\} with arbitrary string centers
\lambda_{c,j} and arbitrary n.Comment: 16 pages, Latex typographic errors corrected, text added, reference
added, accepted by Journal of Physics A,Mathematical and Genera
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