Exocomets of $β$ Pictoris II: Two dynamical families of exocomets simulated with REBOUND

Abstract

We investigate the dynamical evolution of particles in the $β$ Pic system to determine likely formation pathways to the present-day observed exocomet populations. We aim to relate these results to similar studies recently carried out since the discovery of the inner planet $β$ Pic c. We simulate the $β$ Pic system using the non-symplectic adaptive N-body integrator IAS15 in REBOUND. We seed the system with over 100,000 mass-less test particles that evolve for 25 Myr, and adopt initial conditions and a particle distribution that closely matches similar simulations in recent literature. Using IAS15, REBOUND resolves close-encounters between test particles and the two gas giants in the system, which is crucial for understanding aspects of the dynamical evolution. Planet-disk interactions rapidly clear most of the system within 35 AU apart from a region within the orbit of $β$ Pic c, and a region between 20 and 25 AU. After 10 Myr, exocomets can be sourced continuously from these regions, as well as from the inner edge of the region beyond ~35 AU where particles are stable on longer timescales. From the region interior to $β$ Pic c, the exocomets are formed by excitation via mean-motion resonance with $β$ Pic c, obtaining a narrow distribution of radial velocities, consistent with spectroscopic observations. Particles initialized in the outer system may enter onto stargrazing orbits due to disruption by the two gas giants, causing a wider radial velocity distribution, and we propose that this population corresponds to a second dynamical family previously observed via spectroscopy. These particles typically undergo chaotic dynamical evolution for $10^2$ to $10^3$ years after passing the water sublimation limit at ~8 AU until reaching the sublimation distance of calcium near 0.4 AU, implying that the two families of exocomets may have different volatile contents.

Figures (10)

• Figure 1: Example of the orbit of a simulated test particle initiated with $a = 25.73$ AU. The gray points show the orbit computed during the low-resolution simulation. The particle initially undergoes interactions with $\beta$ Pic b, and reaches a periastron distance less than 3 AU at some moment in the simulation. Then the resolution of the simulation is increased, resulting in the orbit shown in green. This high-resolution simulation ends when the periastron distance becomes less than 0.4 AU (marked with the green dot).
• Figure 2: Branching ratios of the entire initial particle population, up to 35 AU after running the simulation (see Methods) for 25 million years. Throughout the system, the majority of particles are ejected (blue) up to a distance of $\sim$ 35 AU, beyond which particles are stable over the system's lifetime. Particles ejected without attaining an orbit that passes within the 3 AU limit and thus only ever simulated using the lower resolution time-step before being ejected are presented in dark blue. However, many particles from the outer system pass within the 3 AU boundary and are also simulated using the high-resolution time-step before being ejected (light blue). All particles initiated on orbital distance smaller than 3 AU are always simulated in high-resolution and therefore also in light blue. A significant number of particles approach the star to within 0.4 AU, which we classify as stargrazers (green). A small number of particles collides with either of the planets. This figure is comparable with the simulation output of RodetLai2024 (Fig. 19).
• Figure 3: Time-dependency of the evolution of test-particles. The two leftmost panels show the survival times of particles that get ejected (leftmost) or are stargrazing (middle), as a function of the initial semi-major axis at which the particles are seeded. The percentage of all simulated particles that is removed from the simulation is indicated with the colorbar. The rightmost panel shows particles that become classified as stargrazing after 10 million years. We call these "late stargrazers" and investigate them in further detail in section \ref{['sec:formation_of_exocomets_at_late_times']}. Note that there seem to be two different sources of late stargrazers, in the inner and outer parts of the system respectively. Orbital resonance with $\beta$ Pic b are also indicated such as in Fig. \ref{['fig:branchingratio']}, clearly showing that stargrazers are not expected to be produced from low-order resonances (e.g. 1:3 and 1:4), because these have been cleared earlier in the life of the system.
• Figure 4: The fraction of particles stargrazing at simulation times greater than 10 million years, normalized by the total number of late stargrazers from each respective stable region. The rate of stargrazers from both regions is decreasing over time at a similar rate.
• Figure 5: Orbital alignment of the two exocomet populations. The leftmost panel shows the difference between the argument of periastron of the test particle $\omega$ and the argument of periastron of $\beta$ Pic c $\omega_c$. The two panels to the right show the orbits of stargrazing test particles originating from the inner and outer exocomet reservoirs respectively. The dashed line indicates the direction of the line of sight, and the plane of the sky is parallel to the horizontal axis. Note that in this projection of the coordinate system, particles generally orbit in a counter clock-wise direction.