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 $(q,t)$-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 $T$-systems for the $(q,t)$-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 $(q, t)$-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 $\lesssim$ 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