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Původ Trojanů Jupitera
Thesis title in Czech: Původ Trojanů Jupitera
Thesis title in English: The origin of Jupiter Trojans
Key words: sluneční soustava, planetky, Trojané, Jupiter
English key words: solar system, asteroids, Trojans, Jupiter
Academic year of topic announcement: 2018/2019
Type of assignment: diploma thesis
Thesis language:
Department: Astronomical Institute of Charles University (32-AUUK)
Supervisor: doc. Mgr. Miroslav Brož, Ph.D.
Author:
Guidelines
Úkolem studenta je porovnat dvě teorie původu Trojanů Jupitera, zejména s ohledem
na pozorované rozdělení sklonů (až 30 stupňů) a také početní asymetrii mezi Trojany
v okolí Lagrangeových bodů L4 a L5 (Szabó etal. 2007).

Jednotlivé úlohy jsou následující:

- shrnutí dosavadních observačních a teoretických znalostí o Trojanech;

- provedení N-částicových orbitálních simulací pomocí integrátoru Swift
s předepsanou migrací planet pro určení stability primordiálních Trojanů
a zachycení Trojanů ve fázi planetesimálního disku (cf. Nesvorný etal. 2013);

- hydrodynamická simulace protoplanetárního disku pomocí kódu Fargo-Thorin
(Chrenko etal. 2017) popisující vznik planety Jupiter a související zachycení
Trojanů již ve fázi plynného disku;

Diskuze získaných výsledků a rozdílů mezi teoriemi má potenciál rozhodnout,
kdy Trojanská tělesa vznikla a zda muselo docházet k pozdním nestabilitám
planetárního systému (a velkému pozdnímu bombardování), či nikoli. Zásadním
rozdílem oproti předchozím modelům je skutečnost, že jádra obřích planet se
v plynném disku pohybují po excentrických dráhách.
References
Brož M., Rozehnal J., 2011, Eurybates - the only asteroid family among Trojans? Mon. Not. R. Ast. Soc., 414, 565.

Chrenko O., Brož M., Lambrechts M., 2017, Eccentricity excitation and merging of planetary embryos heated by pebble accretion. Astron. Astrophys., 606, 114.

Lyra W., Johansen A., Klahr H., Piskunov N., 2009, Standing on the shoulders of giants. Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids. Astron. Astrophys., 493, 1125.

Masset F., 2000, FARGO: A fast eulerian transport algorithm for differentially rotating disks. Astron. Astrophys. Suppl. Ser., 141, 165.

Nesvorný D., Vokrouhlický D., Morbidelli A., 2013, Capture of Trojans by jumping Jupiter. Astron. J., 768, 45.

Szabó G.M., Ž. Ivezić, M. Jurić, R. Lupton, 2007, The properties of Jovian Trojan asteroids listed in SDSS Moving Object Catalogue 3. Mon. Not. R. Astron. Soc., 377, 1393.

Preliminary scope of work
TBD
Preliminary scope of work in English
The origin of the Trojan asteroids Jupiter located in the vicinity of the
L4 and L5 Lagrange points of the Sun-Jupiter-asteroid system is a topic
of active research. Trojans are also targets for in-situ exploration by
the Lucy mission (Levison etal. 2017).

There are two intriguing properties of Trojans: large spread of inclinations
(up to 30 degrees) and an asymmetry between the L4/L5 populations,
the L4 being more populated than L5 (Szabo et al. 2007). The former observation
excludes a possibility that Trojans were captured during the accretion
of the Jupiter's core because most of large planetesimals in the
protoplanetary disk should have almost zero inclinations (Weidenschilling
2000). The latter is strange too since the Lagrange points should be symmetric
from the point of purely gravitational interaction.

The inclination problem was addressed by Morbidelli et al. (2005) who explained
Trojans as objects captured from a cometary disk (which may have large spread
of inclinations) during a brief period of time when Jupiter and Saturn were
close to the 1:2 mean-motion resonance which causes an instability of the
Trojan region by secondary resonances. On the other hand, the L4/L5 asymmetry
may be explained as a result of gas drag which affects the capture of Trojans
by growing proto-Jupiter (Marzari & Scholl 1998).

The problem is that the two explanations are not compatible with each other
because the instability of the Trojan region destroys the primordial population
and the capture from the cometary disk should be symmetric. So these scenarios
are not viable in the framework of the Morbidelli et al (2005) 'Nice model'.

An alternative hypothesis was also tested: a relatively recent disruption of a
large (DPB =~ 300 km) parent body which creates a lot of fragments (O'Brien &
Morbidelli 2008). There are two problems, however, namely the very low
likelihood of such disruption and no observed Trojan family of the required
size (Brož & Rozehnal 2011).

Moreover, a re-analysis of the Trojan dynamics in the framework of newer models
(Morbidelli et al. 2007, Nesvorný et al. 2013) suggests the instability
was triggered a bit earlier by the 3:5 Jupiter-Saturn resonance,
or driven by close encounters between giant planets. The latter may
potentially explain the L4/L5 asymmetry.

Finally, let us mention the study of Levison et al. (2009) on the implantation
of D-type bodies in the Main Asteroid Belt. Their model suggests that
a lot of Trojans might have been captured from the cometary disk but they
were subsequently destroyed by mutual collisions. However, these results do not
seem entirely convincing since they had to assume a special scaling law to
obtain a reasonable fit of the size-frequency distribution of Trojans.
 
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