Spin rate distribution of small asteroids shaped by YORP effect* Petr Pravec 1Astronomical Institute AS CR, Czech Republic Presented at the 40th annual meeting of the Division for Planetary Sciences of the AAS 2008 October 14 *Published in Pravec, Harris, Vokrouhlický, and 28 colleagues, Icarus 197, 497, 2008

Asteroid f-distribution Large asteroids: collisionally evolved Maxwellian distribution Broadening of the distribution with decreasing size. At D = 10 km, the transition from Maxwellian appears to be completed.

Small asteroids, spin rate distribution Data obtained within the BinAstPhotSurvey for 268 main belt/Mars crossing asteroids (selection effects suppressed for all but lowest amplitude asteroids with A < 0.08 mag). Small asteroids D = 3 to 15 km have uniform distribution from f = 1 to 9.5 d-1 and there is an excess of slow rotators with f < 1 d-1.

YORP flattens the spin rate distribution (1) The YORP theory (e.g., Čapek and Vokrouhlický 2004) predicts that df/dt produced by the YORP effect is independent of f, as long as it is in a range of frequencies where damping timescales of excited rotation are short in comparison with YORP spin up/spin down timescales. Any concentration in the original f-distribution is therefore dispersed and the resulting distribution is flattened, i.e., it is more uniform than the original distribution.

YORP flattens the spin rate distribution (2) Model: df/dt independent of f at all values of f up to the spin barrier and asteroids “bounce” back at f = 0 and fmax. After time 3 <td> (mean YORP doubling/halting time), the spin rate distribution is uniform. T = 0 T = <td> T = 3 <td>

YORP flattens the spin rate distribution (3) YORP spin rate evolution timescale: Čapek and Vokrouhlický (2008) estimated td ~ 12 Myr for an asteroid with D = 2 km, ρ = 2.5 g/cm3, a = 2.5 AU, f(td) = 4 d-1 , and є = 0/180°. Scaling it to the median D = 6.5 km and a = 2.26 AU of our sample, we get |df/dt| ~ 0.022 d-1/Myr, i.e., td ~ 180 Myr for asteroid with f(td) = 4 d-1 and a general initial spin orientation. So, if the asteroids in the MBA/MCs sample are at least 500 Myr old, then the model predicts their spin rate distribution is uniform. Collisional lifetimes of the asteroids: Most asteroids in our sample have lifetimes of 2 Gyr or longer (Bottke et al. 2005). Only five asteroids in the sample that are members of two recent families (Baptistina and Massalia) are estimated to be 150-200 Myr old (Bottke et al. 2007, Vokrouhlický et al. 2006). Most asteroids in the sample have probable ages 10-20 times longer than their estimated YORP doubling/halting time td.

Slow rotators excess – a generalized YORP (1) We propose that the excess of slow rotators is caused by a generalized YORP effect that causes that slowed down asteroids spend longer times in the range f < 1 d-1 than in intervals of same width outside of that range. The generalized YORP effect: At low f values where damping timescales of excited rotations are comparable to YORP timescales, the YORP evolution becomes chaotic, causing asteroids to spend prolonged times there (see Vokrouhlický et al. 2007).

Slow rotators excess – a generalized YORP (2) Model modified: df/dt in the range f < 1 d-1 half that in the range f = 1 to fmax. The excess of slow rotators is reproduced. T = 0 T = <td> T = 3 <td>

Slow rotators excess – time of residence Time of residence of an asteroid in the slow rotators excess – estimated from the relative height of the excess: tsre ~ 110 Myr for median D = 6.5 km

Conclusions Small main belt/Mars crossing asteroids with D = 3 to 15 km have uniform distribution from f = 1 to 9.5 d-1 and there is an excess of slow rotators with f < 1 d-1. We propose that both features are a result of the YORP effect on spins of the small asteroids. In the range f = 1 to 9.5 d-1, the distribution has been flattened by YORP that has timescales 10-20 times shorter than probable ages for most asteroids in the sample. In the range f < 1 d-1, slowed down asteroids appear to spend a prolonged time, and we propose that it is a result of the generalized YORP effect for slow, non-principal axis rotators.