Softened potentials and the multipolar expansion

When the gravitational potential is developed in a multipolar series, each multipole is well defined and corresponds to a finite sum of terms in the series. In order to use the gravitational potential in numerical simulations, however, a multipolar expansion is usually applied to a softened Newtonian potential. It turns out that the commonly used multipolar expansion in this case no longer isolates each multipole as in the former case; instead, each multipole is spilled over an infinity of terms. In this paper we show how to recover the complete multipoles. Fortunately, the overall effect of using incomplete multipoles instead of complete ones turns out to be negligible in the cases of interest, for example, in its use in treecodes.Cuando se calcula el desarrollo multipolar del potencial gravitatorio, los distintos multipolos quedan bien definidos, correspondiendo cada uno a una suma finita de términos de la serie. Sin embargo, al usar el potencial gravitatorio en simulaciones numéricas, suele desarrollarse en serie una versión suavizada del mismo. Ocurre que, en estos casos, el desarrollo multipolar estándar que suele utilizarse y a no aísla los multipolos, sino que cada uno de ellos queda distribuido en infinitos términos. En este artículo se muestra cómo recuperar los multipolos completos en estos casos. Afortunadamente, la diferencia entre usar multipolos incompletos y completos es despreciable en los casos de interés, por ejemplo, en su uso en códigos árbol.Instituto de Astrofísica de La Plat

Accretion from debris disks onto white dwarfs : Fingering (thermohaline) instability and derived accretion rates

Recent observations of a large number of DA and DB white dwarfs show evidence of debris disks, which are the remnants of old planetary systems. The infrared excess detected with \emph{Spitzer} and the lines of heavy elements observed in their atmospheres with high-resolution spectroscopy converge on the idea that planetary material accretes onto these stars. Accretion rates have been derived by several authors with the assumption of a steady state between accretion and gravitational settling. The results are unrealistically different for DA and DB white dwarfs. When heavy matter is accreted onto stars, it induces an inverse $\mu$-gradient that leads to fingering (thermohaline) convection. The aim of this letter is to study the impact of this specific process on the derived accretion rates in white dwarfs and on the difference between DA and DB. We solve the diffusion equation for the accreted heavy elements with a time-dependent method. The models we use have been obtained both with the IRAP code, which computes static models, and the La Plata code, which computes evolutionary sequences. Computations with pure gravitational settling are compared with computations that include fingering convection. The most important result is that fingering convection has very important effects on DAs but is inefficient in DBs. When only gravitational settling is taken into account, the time-dependent computations lead to a steady state, as postulated by previous authors. When fingering convection is added, this steady state occurs much later. The surprising difference found in the past for the accretion rates derived for DA and DB white dwarfs disappears. The derived accretion rates for DAs are increased when fingering convection is taken into account, whereas those for DBs are not modified. More precise and developed results will be given in a forthcoming paper

Softened potentials and the multipolar expansion

When the gravitational potential is developed in a multipolar series, eac h multipole is well defined and corresponds to a finite sum of terms in the series. In order to use the gravitational potential in numerical simulations, ho wever, a multipolar expansion is usually applied to a softene d Newtonian potential. It turns out that the commonly used multipolar expansion in this case no longer isolates eac h multipole as in the former case; instead, eac h multipole is spilled o ver an infinit y of terms. In this paper w e sho w ho w to reco ver the complete multipoles. Fortunately , the o verall effect of using incomplete multipoles instead of complete ones turnsCuando se calcula el desarrollo multipolar del potencial gravitatorio, los distintos multipolos quedan bien definidos, correspondiendo cada uno a una suma finita de términos de la serie. Sin embargo, al usar el potencial gravitatorio en simulaciones numéricas, suele desarrollarse en serie una versión suavizada del mismo. Ocurre que, en estos casos, el desarrollo multipolar est´andar que suele utilizarse y a no aísla los multipolos, sino que cada uno de ellos queda distribuido en infinitos términos. En este artículo se muestra cómo recuperar los multipolos completos en estos casos. Afortunadamente, la diferencia entre usar multipolos incompletos y completos es despreciable en los casos de interés, por ejemplo, en su uso en códigos árbol.Fil: Wachlin, Felipe Carlos. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Carpintero, Daniel Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Frequency map analysis of the orbital structure in elliptical galaxies

We present an application of the frequency map analysis to an elliptical galaxy which is represented by a generalization of a double-power-law spherical mass model. The density distribution of this model varies as r−γ close to the centre and as r−4 at large radii. We study the case with γ = 1, which is known as the ‘weak-cusp’ model and which represents well the density profile of the ‘core’ galaxies observed by the Hubble Space Telescope. The final objective of our work is to improve our understanding of the dynamics of elliptical galaxies in a similar way to Merritt & Fridman, finding the regions of stochasticity, looking for resonances that might play an important role in sustaining the triaxial morphology, and analysing the diffusion of orbits. To this end, we use the frequency map analysis of Laskar, which has been applied widely in the field of celestial mechanics but which is a relatively new technique in the area of galactic dynamics. Finally, we show some useful features of this method in understanding the global dynamical structure of the system.Facultad de Ciencias Astronómicas y Geofísica

Testing Galactic Oscillations

Recent numerical simulations using an N-body code suggest that galaxies may oscillate in a very regular and long lasting way. Here we investigate galactic oscillations using a different approach: the perturbation particle method. Our results confirm the computational results given by Miller and Smith (1994).Facultad de Ciencias Astronómicas y Geofísica

Softened potentials and the multipolar expansion

When the gravitational potential is developed in a multipolar series, each multipole is well defined and corresponds to a finite sum of terms in the series. In order to use the gravitational potential in numerical simulations, however, a multipolar expansion is usually applied to a softened Newtonian potential. It turns out that the commonly used multipolar expansion in this case no longer isolates each multipole as in the former case; instead, each multipole is spilled over an infinity of terms. In this paper we show how to recover the complete multipoles. Fortunately, the overall effect of using incomplete multipoles instead of complete ones turns out to be negligible in the cases of interest, for example, in its use in treecodes.Cuando se calcula el desarrollo multipolar del potencial gravitatorio, los distintos multipolos quedan bien definidos, correspondiendo cada uno a una suma finita de términos de la serie. Sin embargo, al usar el potencial gravitatorio en simulaciones numéricas, suele desarrollarse en serie una versión suavizada del mismo. Ocurre que, en estos casos, el desarrollo multipolar est´andar que suele utilizarse y a no aísla los multipolos, sino que cada uno de ellos queda distribuido en infinitos términos. En este artículo se muestra cómo recuperar los multipolos completos en estos casos. Afortunadamente, la diferencia entre usar multipolos incompletos y completos es despreciable en los casos de interés, por ejemplo, en su uso en códigos árbol.Instituto de Astrofísica de La Plat