A simple analytical formulation for periodic orbits in binary stars

An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based on calculations known from classical mechanics, but with the addition of certain terms necessary to give a reasonably good approximation. The results are compared with simulations. The derived simple set of analytical expressions gives periodic orbits on the discs of binary systems without the need to solve the equations of motion by numerical integratio

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

On the Galactic Spiral Patterns: Stellar and Gaseous

The gas response to a proposed spiral stellar pattern for our Galaxy is presented here as calculated via 2D hydrodynamic calculations utilizing the ZEUS code in the disk plane. The locus is that found by Drimmel (2000) from emission profiles in the K band and at 240 $\mu m$. The self-consistency of the stellar spiral pattern was studied in previous work (see Martos et al. 2004). It is a sensitive function of the pattern rotation speed, $\Omega_p$, among other parameters which include the mass in the spiral and its pitch angle. Here we further discuss the complex gaseous response found there for plausible values of $\Omega_p$ in our Galaxy, and argue that its value must be close to $20 km s^{-1} kpc^{-1}$ from the strong self-consistency criterion and other recent, independent studies which depend on such parameter. However, other values of $\Omega_p$ that have been used in the literature are explored to study the gas response to the stellar (K band) 2-armed pattern. For our best fit values, the gaseous response to the 2-armed pattern displayed in the K band is a four-armed pattern with complex features in the interarm regions. This response resembles the optical arms observed in the Milky Way and other galaxies with the smooth underlying two-armed pattern of the old stellar disk populations in our interpretation.Comment: Accepted for Publication in the Journal of the Korean Astronomical Society, expanded from the proceedings of the 2004 Mexico-Korea meetin

A Simple Analytical Formulation for Periodic Orbits in Binary Stars

An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary terms to give a fairly good approximation that we compare with simulations, resulting in a simple set of analytical expressions that solve periodic orbits on discs of binary systems without the need of solving the motion equations by numerical integrations.Comment: Accepted on MNRAS. 29 pages including 6 Figures and 4 table

Geometrical and physical properties of circumbinary discs in eccentric stellar binaries

In a previous work, we studied stable configurations for circumstellar discs in eccentric binary systems. We searched for ‘invariant loops': closed curves (analogous to stable periodic orbits in time-independent potentials) that change shape with the binary orbital phase, as test particles in them move under the influence of the binary potential. This approach allows us to identify stable configurations when pressure forces are unimportant, and dissipation acts only to prevent gas clouds from colliding with one another. We now extend this work to study the main geometrical properties of circumbinary discs. We have studied more than 100 cases with a range in eccentricity 0 ≤e≤ 0.9 and mass ratio 0.1 ≤q≤ 0.9. Although gas dynamics may impose further restrictions, our study sets lower stable bounds for the size of the central hole in a simple and computationally cheap way, with a relation that depends on the eccentricity and mass ratio of the central binary. We extend our previous studies and focus on an important component of these systems: circumbinary discs. The radii for stable orbits that can host gas in circumbinary discs are sharply constrained as a function of the binary's eccentricity. The circumbinary disc configurations are almost circular, with eccentricity ed < 0.15, but if the mass ratio is unequal the disc is offset from the centre of mass of the system. We compare our results with other models, and with observations of specific systems like GG Tauri A, UY Aurigae, HD 98800 B, and Fomalhaut, restricting the plausible parameters for the binar