Chi-squared test for planetary orbits after the impact of a single flyby and multiple stellar flybys

Abstract

Aims. In this work, I present the cumulative effects of passing stars on planetary disks and I explore the orbital modification of their components as a consequence of multiple stellar encounters. I analyze the effects of masses of the passing stars and look for differences between the effects of four encounters with low masses of 0.1 M⊙, as well as a single 0.4 M⊙ stellar encounter on a 100 a.u. planetary disk. Methods. I applied the chi-squared (χ2) test to estimate the correlation between the resulting parameters of orbits after single and multiple impacts. I found that the χ2 value is equal to 0.666 and the probability index is equal to 0.955. Results. This first approach suggests that three or four low-mass multiple encounters can produce comparable orbits of planets as produced by a single massive encounter.