## DDA 2015 – Stochastic YORP On Real Asteroid Shapes

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.

Jay W. McMahon (UC Boulder)

#### Abstract

Since its theoretical foundation and subsequent observational verification, the YORP effect has been understood to be a fundamental process that controls the evolution of small asteroids in the inner solar system. In particular, the coupling of the YORP and Yarkovsky effects are hypothesized to be largely responsible for the transport of asteroids from the main belt to the inner solar system populations. Furthermore, the YORP effect is thought to lead to rotational fission of small asteroids, which leads to the creation of multiple asteroid systems, contact binary asteroids, and asteroid pairs. However recent studies have called into question the ability of YORP to produce these results. In particular, the high sensitivity of the YORP coefficients to variations in the shape of an asteroid, combined with the possibility of a changing shape due to YORP accelerated spin rates can combine to create a stochastic YORP coefficient which can arrest or change the evolution of a small asteroid’s spin state. In this talk, initial results are presented from new simulations which comprehensively model the stochastic YORP process. Shape change is governed by the surface slopes on radar based asteroid shape models, where the highest slope regions change first. The investigation of the modification of YORP coefficients and subsequent spin state evolution as a result of this dynamically influenced shape change is presented and discussed.

#### Notes

• Background
• YORP controls small asteroid spin evolution
• YORP highly sensitive to location of features on surface (Statler 2009)
• “stochastic YORP” (Cotto-Figueroa 2013)
• “stochastic YORP” $\rightarrow$ evolution of asteroid families (Bottke et al. 2015)
• Motivation
• Do shapes change as spin increases?
• How does shape evolution map to YORP coefficients?
• Shape evolution
• Regolith will flow “downhill”
• Body will reshape to relax to some slope limit (Scheeres 2015)
• This study: use actual radar-derived asteroid shapes instead of idealized sphere/ellipsoid
• Use (101955)Bennu
• Apollo asteroid
• OSIRIS-REx sample return target
• Results
• 5-m boulder (as spin limitis approached):
• effect on obliquity very small
• larger effects on spin rate
• shape of boulder matters
• Much future work to do

## DDA 2015 – Contact Binary Asteroids

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.

Samantha Rieger (UC Boulder)

#### Abstract

Recent observations have found that some contact binaries are oriented such that the secondary impacts with the primary at a high inclination. This research investigates the evolution of how such contact binaries came to exist. This process begins with an asteroid pair, where the secondary lies on the Laplace plane. The Laplace plane is a plane normal to the axis about which the pole of a satellite’s orbit precesses, causing a near constant inclination for such an orbit. For the study of the classical Laplace plane, the secondary asteroid is in circular orbit around an oblate primary with axial tilt. This system is also orbiting the Sun. Thus, there are two perturbations on the secondary’s orbit: J2 and third body Sun perturbations. The Laplace surface is defined as the group of orbits that lie on the Laplace plane at varying distances from the primary. If the secondary is very close to the primary, the inclination of the Laplace plane will be near the equator of the asteroid, while further from the primary the inclination will be similar to the asteroid-Sun plane. The secondary will lie on the Laplace plane because near the asteroid the Laplace plane is stable to large deviations in motion, causing the asteroid to come to rest in this orbit. Assuming the secondary is asymmetrical in shape and the body’s rotation is synchronous with its orbit, the secondary will experience the BYORP effect. BYORP can cause secular motion such as the semi-major axis of the secondary expanding or contracting. Assuming the secondary expands due to BYORP, the secondary will eventually reach the unstable region of the Laplace plane. The unstable region exists if the primary has an obliquity of 68.875 degrees or greater. The unstable region exists at 0.9 Laplace radius to 1.25 Laplace radius, where the Laplace radius is defined as the distance from the central body where the inclination of the Laplace plane orbit is half the obliquity. In the unstable region, the eccentricity of the orbit increases. Once the eccentricity becomes very large or approaching 1, the orbit of the secondary intersects with the primary and will eventually collide and becomes a contact binary.

#### Notes

• Motivation
• contact binaries exist with high obliquity, ~90 deg
• Does Laplace plane have a role?
• Resonances between binary orbit and solar perturbations?
• Laplace plane
• $\omega_2 \sin 2 \phi + \omega_s \sin 2(\phi – \epsilon) = 0$
• $\phi$ = incl. orbit relative to equator
• Near asteroid, orbit lies close to equator. Further, orbit lies near orbit plane.
• LP unstable in $e$ for obliquity above 68.875 deg and $a$ between 0.9 and 1.25 Laplace radii (Tremaine et al. 2009)
• Evolution of contact binary
• Fission occurs. Jacobson & Scheeres 2011
• Dissipation $\rightarrow$ stable circ. orbit in LP
• Model: simple model — secular expansion of $a$ from BYORP and tides
• Const. accel. perp. to radial vector
• Use first Fourier coefficient for BYORP accel.
• Results
• Verify instability region
• Unstable region: eccentric instability causes deviation from LP, collision
• New (eccentricity) instability mode
• cf Cuk & Nesvorny 2010
• reimpact
• regardless of obliquity
• $\rightarrow$ contact binary
• Evection resonance could also play a role

## DDA 2015 – The Evolution of the Grand Tack’s Main Belt through the Solar System’s Age

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.

Rogerio Deienno (National Institute for Space Research)

#### Abstract

The Asteroid Belt is marked by the mixture of physical properties among its members, as well as its peculiar distribution of orbital eccentricities and inclinations. Formation models of the Asteroid Belt show that its formation is strongly linked to the process of terrestrial planet formation. The Grand Tack model presents a possible solution to the conundrum of reconciling the small mass of Mars with the properties of the Asteroid Belt, providing also a scenario for understanding the mixture of physical properties of the Belt objects. Regarding the orbital distribution of these objects, the Grand Tack model achieved good agreement with the observed inclination distribution, but failed in relation to the eccentricities, which are systematically skewed towards too large values at the end of the dynamical phase described by the Grand Tack model. Here, we evaluate the evolution of the orbital characteristics of the Asteroid Belt from the end of the phase described by the Grand Tack model, throughout the subsequent evolution of the Solar System. Our results show the concrete possibility that the eccentricity distribution after the Grand Tack phase is consistent with the current distribution. Finally, favorable and unfavorable issues faced by the Grand Tack model will be discussed, together with the influence of the primordial eccentricities of Jupiter and Saturn. Acknowledgement: FAPESP.

#### Notes

• Asteroid belt:
• formation process halted before formation of a planet due to Jupiter
• so-called “Grand Tack” model
• Walsh et al. 2011
• Jup &  Sat migrate inwards, Saturn faster
• inward stops, outward begins
• but fails to explain a lot
• current MB structure different from Grand Tack predictions
• especially dist. in $e$, also $a$ ($i$ not bad)
• This work
• Num int 5 planets & 10,000 test particles, 4.5 Gyr
• ICs: Grand Tack
• Mercury integrator, 10-day time step — expensive
• E-belt (Bottke et al. 2012) results @ 0.4 Gyr (planetary instability)
• at 0.4 Gyr, reset planets to their current orbits
• $\rightarrow$ asteroid belt of today — almost
• much better match to observed $a$-$e$-$i$ distributions
• lost somewhat more asteroids than observed
• Influence of primordial eccentricities ofJup & Saturn
• destabilizes MMRs
• $\rightarrow$ constraints on primordial eccentricities