DETECTION OF THE YORP EFFECT FOR SMALL ASTEROIDS IN THE KARIN CLUSTER

The Karin cluster is a young asteroid family thought to have formed only $\simeq 5.75$~My ago. The young age can be demonstrated by numerically integrating the orbits of Karin cluster members backward in time and showing the convergence of the perihelion and nodal longitudes (as well as other orbital elements). Previous work has pointed out that the convergence is not ideal if the backward integration only accounts for the gravitational perturbations from the Solar System planets. It improves when the thermal radiation force known as the Yarkovsky effect it is accounted for. This argument can be used to estimate the spin obliquities of the Karin cluster members. Here we take advantage of the fast growing membership of the Karin cluster and show that the obliquity distribution of diameter $D\simeq 1-2$ km Karin asteroids is bimodal, as expected if the YORP effect acted to move obliquities toward the extreme values ($0^\circ$ or $180^\circ$). The measured magnitude of the effect is consistent with the standard YORP model. The surface thermal conductivity is inferred to be $0.07$-0.2 W m$^{-1}$ K$^{-1}$ (thermal inertia $\simeq 300-500$ J m$^{-2}$ K$^{-1}$s$^{-1/2}$). We find that the strength of the YORP effect is roughly $\simeq 0.7$ of the nominal strength obtained for a collection of random Gaussian spheroids. These results are consistent with a surface composed of rough, rocky regolith. The obliquity values predicted here for 480 members of the Karin cluster can be validated by the light-curve inversion method.

[1]  A. Morbidelli,et al.  Constraining the cometary flux through the asteroid belt during the late heavy bombardment , 2013, 1301.6221.

[2]  Z. Ivezic,et al.  Solar system objects observed in the Sloan Digital Sky Survey commissioning data , 2001 .

[3]  D. Vokrouhlický,et al.  Secular spin dynamics of inner main-belt asteroids , 2006 .

[4]  D. Vokrouhlický,et al.  The YORP effect with finite thermal conductivity , 2004 .

[5]  M. Granvik,et al.  The Gaia Mission: Expected Applications to Asteroid Science , 2007 .

[6]  Alessandro Morbidelli,et al.  Yarkovsky/YORP chronology of asteroid families , 2006 .

[7]  Derek C. Richardson,et al.  Karin cluster formation by asteroid impact , 2006 .

[8]  Francesca DeMeo,et al.  The taxonomic distribution of asteroids from multi-filter all-sky photometric surveys , 2013, 1307.2424.

[9]  Stefano Mottola,et al.  Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect , 2007, 0704.1915.

[10]  D. Vokrouhlický,et al.  Spin rate distribution of small asteroids , 2008 .

[11]  P. N. Smith,et al.  The Properties of Fragments from Catastrophic Disruption Events , 1998 .

[12]  A. Harris,et al.  A survey of Karin cluster asteroids with the Spitzer Space Telescope , 2009 .

[13]  R. C. Domingos,et al.  Chaotic diffusion caused by close encounters with several massive asteroids - II. The regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne , 2013 .

[14]  D. Rubincam,et al.  Radiative Spin-up and Spin-down of Small Asteroids , 2000 .

[15]  William F. Bottke,et al.  THE YARKOVSKY AND YORP EFFECTS: Implications for Asteroid Dynamics , 2006 .

[16]  David Vokrouhlický,et al.  The vector alignments of asteroid spins by thermal torques , 2003, Nature.

[17]  Richard P. Binzel,et al.  Phase II of the Small Main-Belt Asteroid Spectroscopic Survey: The Observations , 2002 .

[18]  D. Vokrouhlický,et al.  In search of the source of asteroid (101955) Bennu: Applications of the stochastic YORP model , 2015 .

[19]  Richard P. Binzel,et al.  Small main-belt asteroid spectroscopic survey: Initial results , 1995 .

[20]  Andrea Milani,et al.  Asteroid Proper Elements and the Dynamical Structure of the Asteroid Main Belt , 1994 .

[21]  Harold F. Levison,et al.  The recent breakup of an asteroid in the main-belt region , 2002, Nature.

[22]  The influence of rough surface thermal-infrared beaming on the Yarkovsky and YORP effects , 2012, 1203.1464.

[23]  D. Nesvorn'y,et al.  Dynamical evolution of the Cybele asteroids , 2015, 1505.03745.

[24]  S. Slivan,et al.  Spin vectors in the Koronis family: III. (832) Karin , 2012 .

[25]  A study of asteroid pole-latitude distribution based on an extended set of shape models derived by the lightcurve inversion method , 2011 .

[26]  Richard P. Binzel,et al.  Phase II of the Small Main-Belt Asteroid Spectroscopic Survey: A Feature-Based Taxonomy , 2002 .

[27]  A. Cellino,et al.  P/2006 VW139: a main-belt comet born in an asteroid collision? , 2012, 1205.4949.

[28]  D. Oszkiewicz,et al.  Asteroid models from the Lowell photometric database , 2016, 1601.02909.

[29]  D. J. Tholen,et al.  The Eight-Color Asteroid Survey: Results for 589 Minor Planets , 1985 .

[30]  W. Bottke,et al.  Detection of the Yarkovsky effect for main-belt asteroids , 2004 .

[31]  R. Duffard,et al.  S3OS2: the visible spectroscopic survey of 820 asteroids , 2004 .

[32]  C. Murray,et al.  Solar System Dynamics: Expansion of the Disturbing Function , 1999 .

[33]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[34]  C. Maurel,et al.  ASTEROID SECULAR DYNAMICS: CERES’ FINGERPRINT IDENTIFIED , 2015, 1506.01586.

[35]  J. Masiero,et al.  REVISING THE AGE FOR THE BAPTISTINA ASTEROID FAMILY USING WISE/NEOWISE DATA , 2012, 1209.1430.

[36]  Harold F. Levison,et al.  The Long-Term Dynamical Behavior of Short-Period Comets , 1993 .