# DDA 2015 – Cross Sections for Planetary Systems Interacting with Passing Stars and Binaries

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Fred C. Adams (U. Michigan)

#### Abstract

Numerous spectroscopic and photometric studies have provided strong evidence of the presence of multiple stellar populations in globular clusters and raised many fundamental questions concerning the formation and dynamical evolution of these stellar systems. After a brief review of the main observational studies, I will present the results of theoretical investigations exploring a number of aspects of the internal dynamics of multiple-population clusters and their formation history. Most planetary systems are formed within stellar clusters, and these environments can shape their properties. This talk considers scattering encounters between solar systems and passing cluster members, and calculates the corresponding interaction cross sections. The target solar systems are generally assumed to have four giant planets, with a variety of starting states, including circular orbits with the semimajor axes of our planets, a more compact configuration, an ultracompact state with multiple mean motion resonances, and systems with massive planets. We then consider the effects of varying the cluster velocity dispersion, the relative importance of binaries versus single stars, different stellar host masses, and finite starting eccentricities of the planetary orbits. For each state of the initial system, we perform an ensemble of numerical scaRering experiments and determine the cross sections for eccentricity increase, inclination angle increase, planet ejection, and capture. This talk reports results from over 2 million individual scattering simulations. Using supporting analytic considerations, and fibng functions to the numerical results, we find a universal formula that gives the cross sections as a function of stellar host mass, cluster velocity dispersion, starting planetary orbital radius, and final eccentricity. The resulting cross sections can be used in a wide variety of applications. As one example, we revisit constraints on the birth aggregate of our Solar System due to dynamical scattering and find N < 10,000 (consistent with previous estimates).

#### Notes

• Most stars form in clusters
• particle fluxes
• dynamical interactions
• need to know cross sections and rates at which things fly by
• closest approach distribution = power law
• Simulationstodetermine cross sections
• many Monte Carlo simulations
• 2 million runs
• many parameters + chaotic behavior
• do planetary eccentricities get pumped up?
• yes
• Results:
• by and large, $\sigma \gg A$
• $\dfrac{\sigma}{a} = A v^{-\frac{7}{5}} \exp\left[b(1-e)\right]$
• $\sigma = \sigma_0 \exp\left[b(1-\sin \Delta i)\right]$
• $\Delta i \propto \Delta e$
• size of birth cluster constrained to $< 10^4$ stars
• G. Li & Adams 2015 (MNRAS 448:344)