Optimal Monetary Policy in a Channel System of Interest-Rate Control

This paper studies optimal interest-rate policies when the central bank operates a channel system of interest-rate control. We conduct our analysis in a dynamic general equilibrium model with infinitely-lived agents who are subject to idiosyncratic trading shocks which generate random liquidity needs. In response to these shocks agents either borrow against collateral or deposit money at the central bank at the specified rates. We show that it is optimal to have a strictly positive interest-rate corridor if the opportunity cost of holding collateral is strictly positive and that the optimal corridor is strictly decreasing in the collateral's real returnOptimal Monetary Policy, Channel System, Interest Rate Rule, Essential Money

Bars in Cuspy Dark Halos

We examine the bar instability in models with an exponential disk and a cuspy NFW-like dark matter (DM) halo inspired by cosmological simulations. Bar evolution is studied as a function of numerical resolution in a sequence of models spanning 10K to 100M DM particles - including a multi-mass model with an effective resolution of 10G. The goal is to find convergence in dynamical behaviour. We characterize the bar growth, the buckling instability, pattern speed decay through resonant transfer of angular momentum, and possible destruction of the DM halo cusp. Overall, most characteristics converge in behaviour in detail for halos containing more than 10M particles. Notably, the formation of the bar does not destroy the density cusp in this case. These higher resolution simulations clearly illustrate the importance of discrete resonances in transporting angular momentum from the bar to the halo.Comment: 6 pages, 5 figures, IAU Symposium 254 submission. The animations referenced by the paper can be found at http://www.cita.utoronto.ca/~dubinski/IAU25

Gas Feedback on Stellar Bar Evolution

We analyze evolution of live disk-halo systems in the presence of various gas fractions, f_gas less than 8% in the disk. We addressed the issue of angular momentum (J) transfer from the gas to the bar and its effect on the bar evolution. We find that the weakening of the bar, reported in the literature, is not related to the J-exchange with the gas, but is caused by the vertical buckling instability in the gas-poor disks and by a steep heating of a stellar velocity dispersion by the central mass concentration (CMC) in the gas-rich disks. The gas has a profound effect on the onset of the buckling -- larger f_gas brings it forth due to the more massive CMCs. The former process leads to the well-known formation of the peanut-shaped bulges, while the latter results in the formation of progressively more elliptical bulges, for larger f_gas. The subsequent (secular) evolution of the bar differs -- the gas-poor models exhibit a growing bar while gas-rich models show a declining bar whose vertical swelling is driven by a secular resonance heating. The border line between the gas-poor and -rich models lies at f_gas ~ 3% in our models, but is model-dependent and will be affected by additional processes, like star formation and feedback from stellar evolution. The overall effect of the gas on the evolution of the bar is not in a direct J transfer to the stars, but in the loss of J by the gas and its influx to the center that increases the CMC. The more massive CMC damps the vertical buckling instability and depopulates orbits responsible for the appearance of peanut-shaped bulges. The action of resonant and non-resonant processes in gas-poor and gas-rich disks leads to a converging evolution in the vertical extent of the bar and its stellar dispersion velocities, and to a diverging evolution in the bulge properties.Comment: 12 pages, 12 figures, accepted for publication by the Astrophysical Journal. Minor corrections following the referee repor

Merger of Massive Black Holes using N-Body Simulations with Post-Newtonian Corrections

We present preliminary results from self-consistent, high resolution direct {\it N}-body simulations of massive black hole binaries in mergers of galactic nuclei. The dynamics of the black hole binary includes the full Post-Newtonian corrections (up to 2.5PN) to its equations of motion. We show that massive black holes starting at separations of 100 pc can evolve down to gravitational-wave-induced coalescence in less than a Hubble time. The binaries, in our models, often form with very high eccentricity and, as a result, reach separations of 50 Schwarzschild radius with eccentricities which are clearly distinct from zero -- even though gravitational wave emission damps the eccentricity during the inspiral. These deviations from exact circular orbits, at such small separations, may have important consequences for LISA data analysis.Comment: 8 pages, 6 figures, proceedings to the 7th LISA Symposium, Barcelona, 16-20 June 2008. Submitted to Journal of Physics: Conference Serie

Star cluster evolution in barred disc galaxies. I. Planar periodic orbits

The dynamical evolution of stellar clusters is driven to a large extent by their environment. Several studies so far have considered the effect of tidal fields and their variations, such as, e.g., from giant molecular clouds, galactic discs, or spiral arms. In this paper we will concentrate on a tidal field whose effects on star clusters have not yet been studied, namely that of bars. We present a set of direct N-body simulations of star clusters moving in an analytic potential representing a barred galaxy. We compare the evolution of the clusters moving both on different planar periodic orbits in the barred potential and on circular orbits in a potential obtained by axisymmetrising its mass distribution. We show that both the shape of the underlying orbit and its stability have strong impact on the cluster evolution as well as the morphology and orientation of the tidal tails and the sub-structures therein. We find that the dissolution time-scale of the cluster in our simulations is mainly determined by the tidal forcing along the orbit and, for a given tidal forcing, only very little by the exact shape of the gravitational potential in which the cluster is moving.Comment: 15 pages, 17 figures, 5 tables; accepted for publication in MNRAS. Complementary movies can be be found at this http URL http://lam.oamp.fr/research/dynamique-des-galaxies/scientific-results/star-cluster-evolution

The regeneration of stellar bars by tidal interactions. Numerical simulations of fly-by encounters

We study the regeneration of stellar bars triggered by a tidal interaction, using numerical simulations of either purely stellar or stellar+gas disc galaxies. We find that interactions which are sufficiently strong to regenerate the bar in the purely stellar models do not lead to a regeneration in the dissipative models, owing to the induced gas inflow in those models. In models in which the bar can be regenerated, we find a tight correlation between the strength and the pattern speed of the induced bar. This relation can be explained by a significant radial redistribution of angular momentum in the disc due to the interaction, similar to the processes and correlations found for isolated barred spirals. We furthermore show that the regenerated bars show the same dynamical properties as their isolated counterparts.Comment: 18 pages, 26 figures, accepted for publication in MNRA