10,887 research outputs found
Isomorphisms among quantum Grothendieck rings and cluster algebras
We establish a cluster theoretical interpretation of the isomorphisms of
[F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of
representations of quantum loop algebras. Consequently, we obtain a
quantization of the monoidal categorification theorem of
[Kashiwara-Kim-Oh-Park, arXiv:2103.10067]. We establish applications of these
new ingredients. First we solve long-standing problems for any non-simply-laced
quantum loop algebras: the positivity of -characters of all simple
modules, and the analog of Kazhdan-Lusztig conjecture for all reachable modules
(in the cluster monoidal categorification). We also establish the conjectural
quantum -systems for the -characters of Kirillov-Reshetikhin modules.
Eventually, we show that our isomorphisms arise from explicit birational
transformations of variables, which we call substitution formulas. This reveals
new non-trivial relations among -characters of simple modules.Comment: 60 page
The Shearing HI Spiral Pattern of NGC 1365
The Tremaine-Weinberg equations are solved for a pattern speed that is
allowed to vary with radius. The solution method transforms an integral
equation for the pattern speed to a least squares problem with well established
procedures for statistical analysis. The method applied to the HI spiral
pattern of the barred, grand-design galaxy NGC 1365 produced convincing
evidence for a radial dependence in the pattern speed. The pattern speed
behaves approximately as 1/r, and is very similar to the material speed. There
are no clear indications of corotation or Lindblad resonances. Tests show that
the results are not selection biased, and that the method is not measuring the
material speed. Other methods of solving the Tremaine-Weinberg equations for
shearing patterns were found to produce results in agreement with those
obtained using the current method. Previous estimates that relied on the
assumptions of the density-wave interpretation of spiral structure are
inconsistent with the results obtained using the current method. The results
are consistent with spiral structure theories that allow for shearing patterns,
and contradict fundamental assumptions in the density-wave interpretation that
are often used for finding spiral arm pattern speeds. The spiral pattern is
winding on a characteristic timescale of ~ 500 Myrs.Comment: Accepted for publication in The Astrophysical Journa
Does the Fornax dwarf spheroidal have a central cusp or core?
The dark matter dominated Fornax dwarf spheroidal has five globular clusters
orbiting at ~1 kpc from its centre. In a cuspy CDM halo the globulars would
sink to the centre from their current positions within a few Gyrs, presenting a
puzzle as to why they survive undigested at the present epoch. We show that a
solution to this timing problem is to adopt a cored dark matter halo. We use
numerical simulations and analytic calculations to show that, under these
conditions, the sinking time becomes many Hubble times; the globulars
effectively stall at the dark matter core radius. We conclude that the Fornax
dwarf spheroidal has a shallow inner density profile with a core radius
constrained by the observed positions of its globular clusters. If the phase
space density of the core is primordial then it implies a warm dark matter
particle and gives an upper limit to its mass of ~0.5 keV, consistent with that
required to significantly alleviate the substructure problem.Comment: 6 pages, 5 figures, accepted for publication in MNRAS, high
resolution simulations include
An extensive study of dynamical friction in dwarf galaxies: the role of stars, dark matter, halo profiles and MOND
We investigate the in-spiraling timescales of globular clusters in dwarf
spheroidal (dSph) and dwarf elliptical (dE) galaxies, due to dynamical
friction. We address the problem of these timescales having been variously
estimated in the literature as much shorter than a Hubble time. Using
self-consistent two-component (dark matter and stars) models, we explore
mechanisms which may yield extended dynamical friction timescales in such
systems in order to explain why dwarf galaxies often show globular cluster
systems. As a general rule, dark matter and stars both give a comparable
contribution to the dynamical drag. By exploring various possibilities for
their gravitational make-up, it is shown that these studies help constrain the
parameters of the dark matter haloes in these galaxies, as well as to test
alternatives to dark matter. Under the assumption of a dark haloes having a
constant density core, dynamical friction timescales are naturally extended
upwards of a Hubble time. Cuspy dark haloes yield timescales 4.5
Gyr, for any dark halo parameters in accordance with observations of stellar
line-of-sight velocity dispersion in dwarf spheroidal galaxies. We find that
under the hypothesis of MOND dynamics, due to the enhanced dynamical drag of
the stars, the dynamical friction timescales would be extremely short. Taking
the well-measured structural parameters of the Fornax dSph and its globular
cluster system as a case study, we conclude that requiring dynamical friction
timescales comparable to the Hubble time strongly favours dark haloes with a
central core.Comment: 18 pages, four figures, final version, accepted in MNRA
Formation and evolution of dwarf galaxies in the CDM Universe
We first review the results of the tidal stirring model for the
transformation of gas-rich dwarf irregulars into dwarf spheroidals, which turns
rotationally supported stellar systems into pressure supported ones. We
emphasize the importance of the combined effect of ram pressure stripping and
heating from the cosmic ultraviolet background in removing the gas and
converting the object into a gas poor system as dSphs. We discuss how the
timing of infall of dwarfs into the primary halo determines the final
mass-to-light ratio and star formation history. Secondly we review the results
of recent cosmological simulations of the formation of gas-rich dwarfs. These
simulations are finally capable to produce a realistic object with no bulge, an
exponential profile and a slowly rising rotation curve. The result owes to the
inclusion of an inhomogeneous ISM and a star formation scheme based on regions
having the typical density of molecular cloud complexes. Supernovae-driven
winds become more effective in such mode, driving low angular momentum baryons
outside the virial radius at high redshift and turning the dark matter cusp
into a core. Finally we show the first tidal stirring experiments adopting
dwarfs formed in cosmological simulations as initial conditions. The latter are
gas dominated and have have turbulent thick gaseous and stellar disks disks
that cannot develop strong bars, yet they are efficiently heated into spheroids
by tidal shocks.Comment: 14 pages, 4 Figures, o appear in the proceedings of the CRAL
conference, Lyon, June 2010, "A Universe of Dwarf Galaxies", eds. Philippe
Prugniel & Mina Koleva; EDP Sciences in the European Astronomical Society
Publications Series. (invited talk
G(2) Holonomy Spaces from Invariant Three-Forms
We construct several new G(2) holonomy metrics that play an important role in
recent studies of geometrical transitions in compactifications of M-theory to
four dimensions. In type IIA string theory these metrics correspond to D6
branes wrapped on the three-cycle of the deformed conifold and the resolved
conifold with two-form RR flux on the blown-up two-sphere, which are related by
a conifold transition. We also study a G(2) metric that is related in type IIA
to the line bundle over S^2 x S^2 with RR two-form flux. Our approach exploits
systematically the definition of torsion-free G(2) structures in terms of
three-forms which are closed and co-closed. Besides being an elegant formalism
this turns out to be a practical tool to construct G(2) holonomy metrics.Comment: 29 pages, LaTeX2e, corrected some typo
Resolving the M2-brane
We construct deformed, T^2 wrapped, rotating M2-branes on a resolved cone
over Q^{1,1,1} and Q^{1,1,1}/Z_2, as well as on a product of two Eguchi-Hanson
instantons. All worldvolume directions of these supersymmetric and regular
solutions are fibred over the transverse space. These constitute gravity duals
of D=3, N=2 gauge theories. In particular, the deformed M2-brane on a resolved
cone over Q^{1,1,1} and the S^1 wrapped M2-brane on a resolved cone over
Q^{1,1,1}/Z_2 provide explicit realizations of holographic renormalization
group flows in M-theory for which both conformal and Lorentz symmetries are
broken in the IR region and restored in the UV limit. These solutions can be
dualized to supersymmetric type IIB pp-waves, which are rendered non-singular
either by additional flux or a twisted time-like direction.Comment: Latex, 23 pages, references adde
Dust Formation in Very Massive Primordial Supernovae
At redshift z>5 Type II supernovae (SNII) are the only known dust sources
with evolutionary timescales shorter than the Hubble time. We extend the model
of dust formation in the ejecta of SNII by Todini & Ferrara (2001) to
investigate the same process in pair-instability supernovae (PISN), which are
though to arise from the explosion of the first, metal free, very massive
(140-260 Msun) cosmic stars. We find that 15%-30% of the PISN progenitor mass
is converted into dust, a value >10 times higher than for SNII; PISN dust
depletion factors (fraction of produced metals locked into dust grains) range
between 0.3 and 0.7. These conclusions depend very weakly on the mass of the
PISN stellar progenitor, which instead affects considerably the composition and
size distribution. For the assumed temperature evolution, grain condensation
starts 150-200 days after the explosion; the dominant compounds for all
progenitor masses are SiO2 and Mg2SiO4 while the contribution of amorphous
carbon and magnetite grains grows with progenitor mass; typical grain sizes
range between 0.001 and a few 0.1 micron and are always smaller than 1 micron.
We give a brief discussion of the implications of dust formation for the IMF
evolution of the first stars, cosmic reionization and the intergalactic medium.Comment: 10 pages, 8 figures, accepted for publication in MNRA
Corrective effect of many-body interactions in dynamical friction
Dynamical friction is a fundamental and important phenomenon in astrophysics.
The Chandrasekhar formula is a well-known analytical estimation of the effect.
However, current astrophysicists have realized that the formula is not correct
in some cases because of several approximations dared in the formulation and/or
complex non-linearities in the real universe. For example, it has been
indicated that the dynamical friction doesn't work in cored density profiles
(constant density in the central region) despite that the Chandrasekhar formula
predicts drag force even in the constant densities. In the former half of this
paper, I discuss by N-body simulations that many-body interactions are also
important in actual dynamical friction though derivation of the Chandrasekhar
formula is based on the assumption of two-body interaction. In the simulation,
the many-body interactions are caused by a very small number of field particles
co-rotating with a perturber. However, the contribution from the many-body
interactions accounts for a non-negligible fraction of the actual dynamical
friction. In the latter half, I discuss why the cored profiles suppress the
dynamical friction. One possible explanation is that corrective effect of the
many-body interactions drive orbital motion of the perturber. The cessation of
dynamical friction by this corrective effect would be feasible even in shallow
cusp density profiles although the shallow cusp may evolve into a constant
density.Comment: 11 pages, 17 figures, accepted for publication in MNRA
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