Exact Solutions of Integrable 2D Contour Dynamics

A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding tau-functions are determined and the emergence of cusps is studied.Comment: 13 pages, 3 figure

Genus-zero Whitham hierarchies in conformal-map dynamics

A scheme for solving quasiclassical string equations is developped to prove that genus-zero Whitham hierarchies describe the deformations of planar domains determined by rational conformal maps. This property is applied in normal matrix models to show that deformations of simply-connected supports of eigenvalues under changes of coupling constants are governed by genus-zero Whitham hierarchies.Comment: 12 pages, 3 figure

Scalar Field Dark Matter mass model and evolution of rotation curves for Lsb galaxies

We study the evolution of gas rotation curves within the scalar field dark matter (SFDM) model. In this model the galactic haloes are astronomical Bose-Einstein Condensate drops of scalar field. These haloes are characterized by a constant-density core and are consistent with observed rotation curves of dark matter dominated galaxies, a missing feature in CDM haloes resulting from DM-only simulations. We add the baryonic component to the SFDM haloes and simulate the evolution of the dark matter tracer in a set of grid-based hydrodynamic simulations aimed to analyse the evolution of the rotation curves and the gas density distribution in the case of dark matter dominated galaxies. Previous works had found that when considering an exact analytic solution for a static SF configuration, the free parameters of the model allows for good fits to the rotation curves, we confirm that in our simulations but now taking into account the evolution of the baryonic component in a static dark matter and stellar disk potential. Including live gas is a step forward from the previous work using SFDM, as for example, the rotation velocity of the gas is not always exactly equal to the circular velocity of a test particle on a circular orbit. Contrasting with the data the cored mass model presented here is preferred instead of a cuspy one.Comment: 8 pages, 8 figures. Accepted for publication in MNRA

Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies

We present a method to study phase transitions in the large N limit of matrix models using matched solutions of Whitham hierarchies. The endpoints of the eigenvalue spectrum as functions of the temperature are characterized both as solutions of hodograph equations and as solutions of a system of ordinary differential equations. In particular we show that the free energy of the matrix model is the quasiclassical tau-function of the associated hierarchy, and that critical processes in which the number of cuts changes in one unit are third-order phase transitions described by C1 matched solutions of Whitham hierarchies. The method is illustrated with the Bleher-Eynard model for the merging of two cuts. We show that this model involves also a birth of a cut

New insights in the origin and evolution of the old, metal-rich open cluster NGC 6791

NGC 6791 is one of the most studied open clusters, it is massive ($\sim5000\,M_{\odot}$), located at the solar circle, old ($~8\,$Gyr) and yet the most metal-rich cluster (${\rm [Fe/H]}\simeq0.4$) known in the Milky Way. By performing an orbital analysis within a Galactic model including spiral arms and a bar, we found that it is plausible that NGC 6791 formed in the inner thin disc or in the bulge, and later displaced by radial migration to its current orbit. We apply different tools to simulate NGC 6791, including direct $N$-body summation in time-varying potentials, to test its survivability when going through different Galactic environments. In order to survive the 8 Gyr journey moving on a migrating orbit, NGC 6791 must have been more massive, $M_0 \geq 5\times10^4 M_{\odot}$, when formed. We find independent confirmation of this initial mass in the stellar mass function, which is observed to be flat; this can only be explained if the average tidal field strength experienced by the cluster is stronger than what it is at its current orbit. Therefore, the birth place and journeys of NGC 6791 are imprinted in its chemical composition, in its mass loss, and in its flat stellar mass function, supporting its origin in the inner thin disc or in the bulge.Comment: 14 pages, 10 Figures, 3 Tables. Accepted for publication in MNRA