% dda2008.tex
% DDA 2008 presentation.
% Miroslav Broz (miroslav.broz@email.cz), Oct 12th 2006

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\conference{DDA 2008, Boulder, CO, April 28--May 1}

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\titlefn
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Asteroid Clusters
\medskip
\titlefnb
in Major Mean Motion Resonances
\medskip
with Jupiter
}}
\pagetitle{\box0}

\authors{%
M.~Bro�\anot{1},
D.~Vokrouhlick�\anot{1}
%W.F.~Bottke\anot{2},
%A.~Morbidelli\anot{3},
%D.~Nesvorn�\anot{2}%
}

\begingroup
\baselineskip=\smallbaselineskip
\smallfonts

\affilation{1}{Charles University, Prague}
%\affilation{2}{Southwest Research Institute, Boulder}
%\affilation{3}{Observatoire de la C�te d'Azur, Nice}
   
%\correspondence{5}{mira@sirrah.troja.mff.cuni.cz}

\endgroup
\endtitle

%\vfill

\pagenumbers{Asteroids clusters in resonances\dots}

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%\abstract
%???

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\ul{Table of contents}

(PART 1)~update of the resonant populations

(PART 2)~observed clusters of resonant asteroids

(PART 3)~impact events and subsequent evolution

\eject

%\noindent
%\epsfxsize=\hsize
%\epsfbox{figs/ae0_nea_koronis2.eps}

%\eject

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\ul{Update of resonant populations {\rm (Aug 2007)}}

\medskip
\noindent
\epsfxsize=\hsize
\epsfbox{figs/ae_resonant.eps}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J2/1 --- dynamical lifetimes}

\noindent
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r21_obs_loglftime4.eps}}

\li{median of 10 orbits within uncertainty ellipsoid}
\li{2/3 of the population {\setred long-lived\setblack} $>100\,{\rm My}$}
\li{(the rest unstable $\leftarrow$ Yarkovsky origin (Bro�~\etal~2005))}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J2/1 --- absolute magnitude distribution}

\medskip
\noindent
\epsfxsize=.7\hsize
\centerline{\epsfbox{figs/r21-absmag_distribution.eps}}

\li{almost all sub-populations similar!}
\li{short-lived steep $\Leftarrow$ Yarkovsky driven transport $\propto {1/D}$}
\li{long-lived also steeper than adjacent Main Belt $\Leftarrow$ ?}
%\break$\Leftarrow$ different collisional evolution?}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J2/1 --- pseudo-proper elements vs sizes}

\noindent
\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/r21_arer_sizes_BIG_BODIES.eps}}

\li{pseudo-proper elements --- surfaces of sections, averaging}
\li{no prominent clusters, {\setred big bodies\setblack} far from each other and `isolated' $\Rightarrow$ not a single collisional event?}
\li{impact-generated clusters would spread within $\sim$1\,Gyr}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\uldot{J2/1 --- Yarkovsky effect vs long-lived?}

\medskip
\noindent
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r21_zgy_loglftime_radii.eps}}

\li{NO! semimajor axis drift only relevant for $\lesssim 0.1$--0.5\,km}
\li{preferential orientation of the spin axes for the small sizes}

\eject

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\uldot{J2/1 --- planetary migration?}

\medskip
\noindent
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r21-js_loglftime_DIFFERENT_LINES.eps}}

\li{a `static' test --- Saturn at exact resonance with Jupiter}
\li{Zhongguos and Griquas {\setred partially unstable\setblack} wrt. 1:2, 4:9,\break
and the Great Inequality resonance}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J3/2 resonance}

\medskip
\noindent
\epsfxsize=\hsize
\epsfbox{figs/ae_resonant1.eps}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J3/2 --- dynamical lifetimes}

\noindent
\epsfxsize=\hsize
\epsfbox{figs/r32-lft_ae_escape.eps}%

\li{{\setred 20\,\%\setblack} of Hildas escape within 4\,Gyr\break
(large amplitude of libration, secondary resonances)}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J3/2 --- pseudo-proper elements}

\epsfxsize=\hsize
\centerline{\epsfbox{figs/r32_arir_sizes_hilda_schubart.eps}}

\li{a distinct collisional {\setred Schubart cluster\setblack} (Schubart 1991);\break
$v_{\rm cutoff} \simeq 60\,{\rm m}/{\rm s}$,
$\sim 100$\,km parent body,
LF/PB $\simeq$ 0.25}

\li{{\setblue Hilda cluster\setblack} at higher inclinations; $\sim 200$\,km PB}
%$v_{\rm cutoff} \simeq 150\,{\rm m}/{\rm s}$,
%LF/PB $\simeq$ 0.5}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Schubart cluster --- colours}

\medskip
\noindent
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r32_wo_schubart.astorb.sloan_pc1_lt0.1_hist.eps}}

\li{SLOAN colours of J3/2 bimodal (C/X- and D-types)}
\li{Schubart cluster only C/X-type $\Rightarrow$ collisional origin}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Schubart cluster --- SFD}

\medskip
\noindent
\epsfxsize=.85\hsize
\centerline{\epsfbox{figs/r32_schubart_absmag_distribution.eps}}

\li{Schubart cluster significantly {\setred steeper\setblack} than the rest of J3/2
$\Rightarrow$ collisional origin (but not as steep as MB families)}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Simulated impact in J3/2}

\noindent
\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/r32-impact2_ae_inicond.eps}}

\li{a disruption of a 100\,km PB; isotropic velocity field with
$v_{\rm mean\/} = 50\,{\rm m}/{\rm s}$, $f = 0$, $\omega + f = 180^\circ$}
\li{`mapping' of the osculating elements into pseudo-proper}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Impact in J3/2 --- evolution over 4 Gyr}

\medskip
\noindent
\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/r32-impact2_ae_4Gyr_DIFFUSION.eps}}

\li{$N$-body simulation, SWIFT integrator, 4 planets only}
\li{the shape of the swarm is well {\setred preserved\setblack} for 4\,Gyr}
\li{problem: observed {\setblue Schubart cluster\setblack} has larger spread in~$e$}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Impact in J3/2 --- Yarkovsky effect}

\medskip
\noindent
\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/r32-impye2_ae_1Gyr_DIFFUSION_ARROW.eps}}

\li{the Yarkovsky enhances the {\setred diffusion in eccentricity\setblack}\break
$\rightarrow$ different mechanism than for Main Belt families!}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J3/2 --- planetary migration}

\medskip
\noindent
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r32-js_loglftime_DIFFERENT_LINES.eps}}

\li{Hildas {\setred strongly unstable\setblack} wrt. 2:1 Jupiter--Saturn MMR
(and partially also to 3:7)}
\li{talk 12.05 by H. Levison on capture of D-type Hildas}

\eject

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\ul{J4/3 resonance}

\medskip
\noindent
\epsfxsize=\hsize
\epsfbox{figs/ae_resonant2.eps}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J4/3 --- 2001 QG$_{207}$ and 2006 UB$_{219}$}

\medskip
\noindent
\tmpdim=.4\hsize
\centerline{%
\vbox{%
\hbox{%
\epsfxsize=\tmpdim\epsfbox{figs/r43-astorb200712b_follow_esigma_0007_LABELS.eps}%
\epsfxsize=\tmpdim\epsfbox{figs/r43-astorb200712b_follow_esigma_0011.eps}%
}\hbox{%
\epsfxsize=\tmpdim\epsfbox{figs/r43-astorb200712b_filter_sigma_0007.eps}%
\epsfxsize=\tmpdim\epsfbox{figs/r43-astorb200712b_filter_sigma_0011.eps}%
}%
}}

\li{2 new objects $\Rightarrow$ a real Thule {\it group}}
\li{libration about pericentric branch of the J4/3}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J4/3 --- absolute magnitude distribution}

\medskip
\noindent
\epsfxsize=.8\hsize
\centerline{\epsfbox{figs/r21_librating_absmag_distribution.eps}}

\li{J4/3: strongly {\it depleted\/} (even though stable orbits exist)}
%\li{J2/1: {\setred steeper\setblack} SFD than J3/2 and Dohnanyi ($-0.5$)}
%\li{J3/2 population {\setblue shallower\setblack} than Dohnanyi ($-0.5$)}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{J4/3 --- dynamical lifetimes}

\medskip
\noindent
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r43-lft_at.eps}}

\li{(279) Thule orbit stable over 4\,Gyr}
\li{2001 QG$_{207}$, 2006 UB$_{219}$: 45\,\% and 60\,\% of clones {\setred escape\setblack}}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Conclusions}

\li{J2/1 population almost doubled}
\li{two collisional families in the J3/2 resonance\break (probably old, different from MB families)}
\li{two more asteroids in the J4/3}
\li{constrains for planetary migration models}

\ul{Future work}

\li{stability wrt. analytical planetary migration}
\li{influence of close encounters with massive asteroids}

\eject

\end


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\ul{J3/2 --- a stalactite diagram}

\epsfxsize=\hsize
\centerline{\epsfbox{figs/r32-hcm_stalactite_diagram_min5.eps}}

\li{standard HCM metric $d_1$; only clusters $>5$~bodies}
\li{both clusters are statistically significant}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Schubart cluster --- parent body size}

\medskip
\noindent
\centerline{%
\epsfxsize=.5\hsize
\epsfbox{figs/schubart_parent_body_volume_D_complete.eps}%
\epsfxsize=.5\hsize
\epsfbox{figs/hilda_parent_body_volume_D_complete.eps}%
}

\li{Schubart: approx.~110\,km parent body}
\li{Hilda: approx.~190\,km}

\eject

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\ul{J2/1 --- Yarkovsky effect 2}

\medskip
\noindent
\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/r21_zgy_loglftime_obliq_0.01.eps}}

\li{preferential orientation of the spin axes for small sizes}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end









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\ul{Impact clusters in J2/1 and J3/2}

\li{example: a disruption of a 30-km body in the J2/1}

\medskip
\epsfxsize=\hsize
\centerline{\epsfbox{figs/r21-impye_aei_00001005.eps}}

\eject

\ul{Impact clusters (cont.)}

\epsfxsize=\hsize
\centerline{\epsfbox{figs/r21-impye_aei_00100005.eps}}

\li{are stable on a 100\,My timescale, but\dots}

\eject

\ul{Impact clusters (cont.)}

\epsfxsize=\hsize
\centerline{\epsfbox{figs/r21-impye_aei_00999005.eps}}

\li{\dots disperse in 1\,Gy due to chaotic diffusion and the Yarkovsky effect
\kern 4.5cm\raise.3cm\hbox{$\uparrow$} {\smallfonts {\setred J3/2\setblack} is more stable}}

% ??? which is more important?

\eject







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Origin of resonant populations}

\li{migration of planets due to planetesimal disc 30--50\,$M_\oplus$
similar to the `Nice model' (Morbidelli \etal, 2005)}

\epsfxsize=\hsize
\centerline{\epsfbox{figs/j32_pdisc_50ME_cold_I00j_at_planets.eps}}

\eject

\ul{Origin of Hildas $\leftarrow$ captured}

\medskip

\halign{%
\hfil #\hfil &
\hfil #\hfil \cr
original population & final population \cr
%
\epsfxsize=.5\hsize
\epsfbox{figs/j32_pdisc_50ME_cold_I00j_aet_00000000.eps}
&
\epsfxsize=.5\hsize
\epsfbox{figs/j32_pdisc_50ME_cold_I00j_aet_00001900.eps}
\cr
}

\li{almost no J3/2 bodies remain $\Rightarrow$ must had been captured during
the 1:2 crossing event (by chaotic capture)\break or after (by resonance sweeping)}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Origin of J2/1 asteroids $\leftarrow$ primordial}

\medskip

\halign{%
\hfil #\hfil &
\hfil #\hfil \cr
original population & final population \cr
%
\epsfxsize=.5\hsize
\epsfbox{figs/j21_pdisc_50ME_cold_I00j_aet_00000000.eps}
&
\epsfxsize=.5\hsize
\epsfbox{figs/j21_pdisc_50ME_cold_I00j_aet_00003000.eps}
\cr
}

\li{$\sim$~half of J2/1 orbits survive $\Rightarrow$ might be primordial}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Summary}

\medskip

%\begingroup
%\smallfonts

\halign{%
\hfil #\hfil &
\hfil #\hfil &
\hfil #\hfil &
\hfil #\hfil \cr
{\bf time} & {\bf J2/1} & {\bf J3/2} & {\bf J4/3} \cr
{\smallfonts before present} \cr
%
4.56\,Gy \cr
& \multispan{3}{\hfil LARGE PRIMORDIAL POPULATION\hfil} \cr
%
4.5\,Gy \cr
& {\smallfonts excitation, 90\,\% depletion} & 100\,\% & 100\,\% \cr
& {\smallfonts by embedded embryos} \cr
%
3.9\,Gy \cr
{\smallfonts LHB} & $\sim$50\,\% depletion & chaotic & low-probable \cr
& some captures & capture & ch.~capture \cr
3.8\,Gy \cr
& $\sim$50\,\% depletion & & \cr
& (G.~I. resonance) & & \cr
3.5\,Gy \cr
& several collisions & $1+$~large & no collisions \cr
& & disruptions & \cr
500\,My \cr
& & {\smallfonts Schubart cluster} & \cr
present \cr
& Zhongguos, Griquas & Hildas & Thule and \cr
& & & 2001~QG$_{207}$ \cr
}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ul{Origin of resonant populations}

\li{migration of planets due to planetesimal disc 30--50\,$M_\oplus$
similar to the `Nice model' (Morbidelli \etal, 2005)}

\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/j21_pdisc_50ME_cold_I00_xyt_00000000.eps}}

\eject

\ul{Jupiter and Saturn 1:2 MMR}

\li{the resonance occurs 3.8~Gy ago, after 700\,My of slow migration
$\Rightarrow$ secular perturbations exerted on Uranus}

\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/j21_pdisc_50ME_cold_I00_xyt_00002900.eps}}

\eject

\ul{Jupiter and Saturn 1:2 MMR (cont.)}

\li{Neptune enters the planetesimal disc $\Rightarrow$ fast migration}

\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/j21_pdisc_50ME_cold_I00_xyt_00004000.eps}}

\eject

\ul{Jupiter and Saturn 1:2 MMR (cont.)}

\li{the disc slowly disperses, the planeteary orbits damp down}

\epsfxsize=.9\hsize
\centerline{\epsfbox{figs/j21_pdisc_50ME_cold_I00_xyt_00009080.eps}}

\eject


\end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

??? a capture from {\em hot} MB orbits

??? a capture from the outer planetesimal disc

both are possible!

a spectroscopic signature for some D-type asteroids (Roig et al. 2006)

final orbits of D-type planetesimals in the MB might reside in resonances (Morbidelli et al. 2006)

??? Yarkovsky evolution, removal of small bodies

??? collisional evolution?

??? steep SFD of Zhongguos!

??? J4/3 notes

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\ul{Conclusions}

\li{steep SFD of Zhongguos must persist for 4\,Gy! How?}
\li{???}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\eject
\end













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\ul{Zhongguos and Griquas in the J2/1}

\noindent
\epsfxsize=\hsize
\epsfbox{figs/distmap33.eps}

\eject

\ul{Hildas in the J3/2 resonance}

\noindent
\epsfxsize=\hsize
\epsfbox{figs/r32_arer_sizes_schubart.eps}

\eject

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\li{`static' tests with Jupiter and Saturn in exact resonances}

\epsfxsize=\hsize
\centerline{\epsfbox{figs/r32-js_loglftime.eps}}

\li{J3/2 is very sensitive to the 1:2 MMR, J2/1 not so much}



