Stability criteria for wide binaries stars harboring Oort Clouds

CALANDRA, M. F.; CORREA-OTTO, J. A.; GIL-HUTTON, R. A.

ASTRONOMY AND ASTROPHYSICS

EDP SCIENCES S A

Año: 2018 vol. 611 p. 1 - 8

0004-6361

Context. In recent years, several numerical works were done in the field of the stability limit.Altough, many of them included the analysis of asteroids or planets, is not possible to find inthe literature any work that study how the presence of a binary star could affect other possibleconfigurations in a three body problem. In order to analize this subject of study we consider otherstructures like Oort Clouds in wide binary systems. Regarding to the existence of Oort Clouds inextrasolar systems there are recent works such as, Nordlander et al. (2017) and Black (2010) thatdoes not reject its possible existence.Aims. The aim of this work is to obtain the stability limit for Oort Cloud objects consideringdifferent masses of the secondary star and zero and non-zero inclinations of the particles. Weimprove our numerical treatment getting a mathematical fit that allow us to find the limit andcompare our results with other previous works in the field.Methods. We use a symplectic integrator to integrate binary systems where the primary star ism 1 = 1 M and the secondary, m 2 , takes 0.25 M and 0.66 M in two sets of simulations S 1 andS 2 . The orbital parameters of the secondary star were varied to see different scenarios. We alsoused two different integration times (one shorter than the other) and included the presence of 1000to 10000 massless particles in circular orbits to form the Oort Cloud. The particles were disposedin four different inclination planes, to investigate how the presence of the binary companion couldaffect the stability limit.Results. Using the Maximum Eccentricity Method, e max , together with the critical semimajor axisa crit (Holman & Wiegert 1999), we found that the e max criteria could reduce the integration timesto find the limit. For those cases where the particles were in inclined orbits we found that there are particle groups that survive the integration time with a high eccentricity. This particle groups arefound for our two sets of simulations, meaning that there are independent of the secondary mass.We also find in agreement with other authors such as, Morais & Giuppone (2012) and Gayon& Bois (2008) that the numerical value of the stability limit for retrograde orbits is higher thanthose found for prograde orbits when the particles are in the same plane that the binary. Finally,the results obtained in this work allow us to build a numerical expression depending of μ, e b andi p .