Transcript Photometric Survey of Binary Near

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, France
2011 October 6
Small, inner main-belt binaries
Observations:
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 biased
orbit 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.
•
Probability of binary detection
Prob. of mutual events occurrence
Prob. of resolving event
Prob. of covering the event
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.
Simulations of the binary survey - model
Numerical model of the binary survey
(analogous to that we used for simulations of our survey for NEA binary asteroids in Pravec et al. 2006)
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•
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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).
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).
Estimated probability density for a number of positive re-observations of the 18 binaries in the return apparitions.
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 evolution
Effects 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 nonsingular 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 dynamics
over 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
Clones of a few binaries with initial ecliptic
latitudes from -80° to +80° with a step of 20°
integrated for 250 kyr.
4029 Bridges (ih = 5.4°)
1453 Fennia (ih = 23.7°, Hungaria)
2044 Wirt (ih = 24.0°, Phocaea)
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: