Collision outcome maps of planetary embryo - planetesimal disks in inclined binary stars

1. Introduction

To date already 711 of the 4469 (∼15%) discovered exoplanet systems are part of a binary or multiple star system. Most studies of the terrestrial planet formation in binary star systems focused on planar binary configurations (e.g. [1], or [5]). However, for binary star systems with separations a_b>30-40 au the alignment is highly likely randomly distributed [2]. [4] have shown that in the intermediate phase planetesimal decouple from the gas due to the forced inclination of the secondary star, which may result in more destructive collisions. Thus, in the final phase of terrestrial planet formation in binary stars, the planet forming disk may still contain a large fraction of planetesimals. In the last stage all gravitational interactions of the disk objects have to be taken into account. To handle the N² gravitational interactions in the N-body problem a parallelized GPU N-body code has to be used (e.g. [6]).

Usually, the so-called perfect merging approach is used to handle collisions in N-body simulations. This might be feasible for low velocity encounters. On the other hand, [3] derived scaling laws to predict collision outcomes.

 

2. Methods and Setup

We investigated the post gas phase, thus we only considered gravitational interactions. Known, that the complexity of the N-body problem scales with O(N²), we applied our self-developed GPU parallelized N-body code GANBISS [6], which allows the simulation of some thousand interacting objects. For the two-body collisions of disk objects we assumed the perfect merging scenario.
Different binary star configurations were simulated where the separation a_b and the eccentricity e_b of the solar mass binary stars were fixed to a_b=60 au and e_b=0.2, respectively. We varied the inclination of the secondary star between i_b=0, 20, and 45°. The planetesimal - planetary embryo disks were placed between 1-4 au around the primary star with initially 2000 planetesimals (each has a mass of 0.00118 M_⊕) and 25 planetary embryos (mass range: 0.0582 - 0.152 M_⊕). Each configuration was simulated for 10 Myr.

For all collisions that occurred during the N-body simulation, the collision parameters -- impact velocity and impact angle -- were stored and subsequently analyzed using the analytic model of [3] (LS12) and thus assigned different classes of collision outcomes which mainly depend on the impact velocity, the impact angle, and the mass fraction of the colliding bodies. The different collision outcomes of LS12 can be summarized in three main categories:

• accretive collisions: perfect merging, graze and merge, and partial accretion
• destructive collisions: partial erosion, and super catastrophic
• hit-and-run events

3. Results

Figure 1 shows the post-processed analysis of the recorded collisions following the model of LS12 for the configuration a_b=60 au, e_b=0.2, and i_b=20°. In total 193 perfect merging events occurred, only 16 graze and merge and 229 partial accretions, which are summarized as accretive collisions. Destructive collisions consist of partial erosion (137) and super catastrophic collisions (176), which occurred show less frequently than the accretive collisions. The largest fraction are the hit-and-run collisions (1255). 

Table 1 shows the number of the different collision categories for each computed binary star configuration. The fraction of the three different collision categories differs strongly for the various binary configurations. In the planar configuration the accretive collisions dominate, followed by the hit-and-run collisions. The destructive collisions are very rare. The misalignment of the secondary star results in possible large mutual inclinations of the disk objects [4], which leads to larger impact velocities, and consequently to more destructive collisions. Thus, the numbers of destructive collisions for the configurations i20 and i45 (short for a60-e02-i20/i45) are significantly higher compared to the planar configuration. However, in the i20 configuration the fraction of accretive collisions is larger than the fraction of destructive collisions. The opposite can be seen with the i45 configuration. However, the largest fraction of collisions in the inclined configurations are the hit-and-run collisions.

Table 1: The table shows the number of different collision outcomes according to the analytic model of LS12 for our three different computed binary star configurations. The different outcomes are summarized in accretive (N_accr), destructive (N_destr) and hit-and-run (N_hr) collisions.

Configuration	Ncoll	Naccr	Ndestr	Nhr
a60-e02-i00	2013	1319	3	691
a60-e02-i20	2006	438	313	1255
a60-e02-i45	1982	232	634	1116

 

 

4. Summary and Conclusions

We simulated the late stage of terrestrial planet formation in binary star systems for various configurations. Using our GPU parallelized N-body code GANBISS we were able to simulate the gravitational interactions of the disk objects and the binary stars. For the analysis of the collisions occurred in the N-body simulations, we applied the model from LS12 in a post process. A misalignment of the secondary star with respect to the disk results in more diverse collision outcomes compared to a planar configuration. Especially, more destructive and hit-and-run collisions occurred. This suggests that the perfect merging approach is even less suitable for inclined binary star systems than for planar systems - and should be investigated further.

 

Acknowledgements

M.Z.~and E.P-L want to acknowledge the support by the Austrian Science Fund FWF - projects PAT3059124 and P33351-N. The computational results presented have been achieved using the Vienna Scientific Cluster (projects 71637, 71686, 70320).

 

References

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