Anisotropic distribution of orbit poles of small binary asteroids

P. Pravec, P. Scheirich, D. Vokrouhlický, A. W. Harris, P. Kušnirák, K. Hornoch, D. P. Pray, D. Higgins, A. Galád, J. Világi, Š. Gajdoš, L. Kornoš, J. Oey, M. Husárik,

W. R. Cooney, J. Gross, D. Terrell, R. Durkee, J. Pollock, D. Reichart, K. Ivarsen, J. Haislip, A. LaCluyze, Yu. N. Krugly, N. Gaftonyuk, R. D. Stephens, R. Dyvig, V. Reddy,

V. Chiorny, O. Vaduvescu, P. Longa-Pena, A. Tudorica, B. D. Warner, G. Masi, J. Brinsfield, R. Goncalves, P. Brown, Z. Krzeminski, O. Gerashchenko, V. Shevchenko,

I. Molotov, F. Marchis

Presented on the EPSC-DPS Joint Meeting 2011 in Nantes, France2011 October 6

Small, inner main-belt binariesObservations: More than 500 inner main-belt asteroids (ahel = 1.9 - 2.5 AU, D < 10 km) surveyed with the

photometric method for binarity during 2005-2011.Found 45 binaries (with asynchronous primary), re-observed 18 of them in their return

apparitions (up to May 2011).A key observation: 15 of the 18 having positively re-observed mutual events in the

second, return apparition. This is a strikingly high number; our simulations of the binary survey show that we would see eclipses in only ~1/3 binaries in their return if their orbits were oriented randomly.

Observed binary orbit pole distribution

Estimated binary orbit poles (for 10 of the 18 binaries observed in 2-3 apparitions):

A selection effect of the photometric binary detection method is present – the observed pole distribution is biased.

Bias on an orbit pole distribution

An example of the original isotropic and resulting biasedorbit pole distributions:

Modified by the mutual events occurrence probability function (shown here for three values of the binary critical inclination angle):

Simulations of the binary survey

Direct de-biasing of the observed pole distribution is complicated by•models of the observed binaries gave incomplete, uncertain or multiple estimates for the orbit poles.•The pcov probability of covering the mutual events is usually < 1 for discovery (survey) observations of a previously unknown binary where the orbit period is not known a priori and thus a distribution of the observations cannot be matched to the orbit period.

Simulations of the re-detections of the binaries in their second, return apparitions are much more feasible•they have got pcov = 1 as the planned re-observations were matched to the already known orbit periods and it’s irrelevant that we have not got accurate or unique pole position estimates for all the binaries.

Probability of binary detection

Prob. of mutual events occurrence

Prob. of covering the eventProb. of resolving event

Simulations of the binary survey - modelNumerical model of the binary survey (analogous to that we used for simulations of our survey for NEA binary asteroids in Pravec et al. 2006)

•accounts for actual asteroid-Earth and asteroid-Sun geometry of the observations•accounts for pres = 0 for partial events with attenuation depth < 4% (“grazing eclipses”)•allows to test various orbit pole distributions

Model assumptions and approximations:

Simulations of the binary survey - results

The null hypothesis: An isotropic distribution of binary orbit poles.Rejected at a confidence level > 99.99%.The expected number of positive re-detections is 6 ± 3 (95% probability interval).

Estimated probability density for a number of positive re-observations of the 18 binaries in the return apparitions.

The probabilities become ≥ 5% for orbit poles concentrated within 30° of the ecliptic poles (concentration in ecliptic latitude) or within 40° of binary heliocentric orbit poles (concentration in obliquity).

Interpretation

Three considered hypotheses:

The binary orbit poles oriented preferentially up/down-right are due to

1.the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism), or

2.the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism), or

3.elimination of binaries with poles close to the ecliptic plane by dynamical instability (such as the effect of the Kozai resonance due to the solar tide perturbations).

We have checked that 3. does not apply, a few details follow.

Model of binary’s short-term evolutionEffects that have been included in the model:(i)gravitational interaction between the binary components (with primary’s gravitational field up to zonal quadrupole term and secondary’s field in monopole representation only),(ii)solar gravitational tide effects modeled in the center-of-mass system of the binary (solar orbit obtained with an independent numerical integration and included in our model with Fourier series representation of the non-singular eccentricity and inclination vectors),(iii)primary’s spin direction subject to gravitational torque due to the secondary component and the Sun,

Major simplifying assumptions:(i) point-mass representation of the secondary,(ii) an axisymmetric representation of the primary and its principal axis rotation,(iii) no long-term effects included (such as tides or radiation forces and torques).

Our model thus represents the binary dynamicsover a ~105 yr timescale or so.

Equations (A.1) and (A.2) are numerically propagated using a Burlish-Stoer scheme with variable time-step complying to a chosen accuracy level.

Short-term evolution of binary orbits

4029 Bridges (ih = 5.4°)

1453 Fennia (ih = 23.7°, Hungaria)

2044 Wirt (ih = 24.0°, Phocaea)

Clones of a few binaries with initial ecliptic latitudes from -80° to +80° with a step of 20° integrated for 250 kyr.

Low-inclination main-belt binaries (such as Bridges) – all orbits stable with only small oscillations in ecliptic latitude of their pole.

High-inclination Hungaria and Phocaea binaries – a non-trivial evolution due to secular resonances between the heliocentric orbit precession and the coupled spin evolution of the binary (Cassini dynamics), but no evidence for larger stability at higher latitudes vs low latitudes.

Conclusions

Orbit poles of small asteroid binaries concentrate near the ecliptic poles or their heliocentric orbit poles.

We propose that the binary orbit poles oriented preferentially up/down-right are due to the YORP tilt of spin axes of their parent bodies or the primaries toward the asymptotic states near obliquities 0 and 180°.

The alternative process of dynamical elimination of binaries with poles closer to the ecliptic (e.g., by the Kozai effects of gravitational perturbations from the Sun) does not explain the observed orbit pole concentration. Basically, the gravitational effects of primary’s non-sphericity (J2 perturbation and on) make always the argument of pericenter of secondary’s orbit to precess very fast and inhibit Kozai instability (the case of “frozen orbits” for the secondary at high inclination with respect to primary’s equator was not explored, but we do not consider such situation representative).

Additional slides for discussion

Selection effect of the photometric binary detection method

The probability of the photometric detection of a binary asteroid:

where pme is a probability of occurrence of a mutual event pcov is a probability of covering the mutual event with a given set of observations pres is a probability of resolving the mutual event with a given set of observations

An analytical formula for pme for the special case of a system with spherical components, zero eccentricity and observed at zero solar phase: