S - P 1 - P 2 S - A 1 - A 2 P 1 - S P 2 A 1 - S A 2 S - P 1 - A 2 S - A 1 - P 2. Periastra in the same direction. Periastra in opposite directions

Transkript

1 Periastra in opposite directions A2 A1 S P1 P2 Periastra in the same direction A P S P 2 A Periastra in the same direction S - P 1 - P 2 S - A 1 - A 2 A 1 - S - P 2 P 1 - S - A 2 Periastra in opposite directions S - P 1 - A 2 S - A 1 - P 2 P 1 - S P 2 A 1 - S A 2 Equivalent pairs, depending on the resonance

2 2.00 Stable 2/ 1 resonance m1= m2= m0= orbit Stable 2/ 1 resonance m1= m2= m0= orbit / 1 resonance m1= m2= m0= orbit y 0.00 P2 P1 S P2' y 0.00 P2(per) P1(ap) SUN P2' 0.50 y e1 = P2(per) P1(ap) SUN P2' e2 = e1 = e1 = 0.18 e2 = Initial position: Sun - periastron - periastron x e2 = x x Stable / 1 resonance m1 = m2 = m0 = orbit / 1 resonance m1= m2= m0= orbit / 1 resonance m1= m2= m0= orbit y y y 0.00 P1 P2' SUN P P2 P1 S P2' 0.00 P2 P1 S P2' e1 = 0.47 e2 = 0.57 e2 = 0.79 e1 = 0.22 e2 = 0.68 e1 = Initial position: apoastron - Sun - apoastron x Iinitial position: apoastron - apoastron- SUN x Initial position: apoastron - periastron - Sun x

3 Four Stability Reinforcement Factors for Planetary Systems with High Dynamical Regime Low order Mean Motion Resonance + Favorable relative initial orbital phases of planets + High planetary eccentricities, especially of the outer planet + Anti-aligned Apsidal Synchronous Precession = NO close approaches between planets => NO strong dynamical interactions => STABILITY over long evolutionary timescale

4 It has been recently established by a number of authors (e.g. Rivera & Lissauer 2000, Laughlin & Chambers 2001, Chiang & Murray 2002; Lee & Peale 2002, 2003; Ji et al. 2003, 2004, Zhou & Sun 2003, Bois et al. 2003) that orbits in almost all multi-planet systems (with exception of HD38529, HD168443, HD74156) are locked in so-called apsidal secular resonance, meaning that the two orbital planes precess at the same rate, i.e. the relative apsidal longitude θ 3 of two planetary orbits librates about 0 (aligned topology) or π (anti-aligned topology)., where However, this definition of the Apsidal Secular Resonance conflicts with one used over hundreds year in Celestial Mechanics. Therefore, we suggest instead the term Apsidal Synchronous Precession (ASP)

5 Resonant variables for HD160691

6 Class 1b -- Low-eccentricity near-resonant planet pairs A mean motion resonance of the planet pair is not needed to guarantee the long-term stability of the system. Therefore, the eccentricities of the planets have to be small to exclude a crossing of the orbits. As an example we state the 47Uma system, which is possibly near the 5:2 or 7:3 MMR but the orbital parameters show that a resonance is not needed for the stability of the system. Star Planet mass_p a_p e_p Period [M_Sun] [M_Jup] [AU] [days] 47Uma b (1.03) c

7 Class II -- Non-resonant planets with significant secular dynamics Planet pairs of this class can have strong gravitational interactions, where long-term variations are ascribed to secular perturbations, large variations of the eccentricities and dynamical effects like the alignment and anti-alignment for the apsidal lines. For the long-term stability of such a system, it is not necessary hat the planets are in MMR.

8 Star Planet mass_p a_p e_p Period [M_Sun] [M_Jup] [AU] [days] 55 Cnc e (1.03) b HD b (1.4) c HD37124 b (0.91) c? (Ups And, HD12661, HD160691)

9 Class III -- Hierarchical planet pairs Roughly speaking this class is for all planet pairs with a large ratio of their orbital periods -- P1/P2 > 10. Due to the large ratio of periods the gravitational interaction are not so strong like in class II and the probability of a capture in a MMR is negligible. The weaker interactions lead to stable motion in the numerical simulations, even if the orbits of the planet are not so good determined.

10 Star Planet mass_p a_p e_p Period [M_Sun] [M_Jup] [AU] [days] HD b (1.01) c HD74156 c (1.27) b HD38529 b (1.39) c

11 Class 1b -- Low-eccentricity near-resonant planet pairs A mean motion resonance of the planet pair is not needed to guarantee the long-term stability of the system. Therefore, the eccentricities of the planets have to be small to exclude a crossing of the orbits.

12 Planetensysteme ähnlich dem Sonnensystem

13 Initial Conditions and Computations Jupiter: on its orbit Saturn: a_sat = AU m_sat = xm_Sat Testplanets in the HZ: a_tp = AU Mercury 6 (J. Chambers) Integration time: 20 mio years HZ: maximum ecc.

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15 Sun Jupiter Saturn

16 Sun Jupiter Saturn

17 Influence of a third giant planet Jupiter Saturn -Uranus Jupiter -- Saturn

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24 S-Typ Planetary motion in binaries:

25 Some General Studies of planetary motion in binary systems: Dvorak R.(1984 and 1986) Rabl & Dvorak R. (1988) Dvorak R., Froeschle C. & Froeschle Ch. (1989) Holman M. & Wiegert P. (1999) Pilat-Lohinger E. & Dvorak R. (2002)

26 Stability analysis Initial Conditions: abinary =1 AU ebinary=[0,.0.9] aplanet=[0.1, 0.9] eplanet=[0, 0.9] i, Ώ,ω, = 0 M= 0,90,180,270

27 mass-ratio S-type motion e_binary Stable zone (in units of length) of S-type motion for all computed mass-ratios and eccentricities of the binary. The given size for each (mu,e_binary) pair is the lower value of the studies by Holman &Wiegert (AJ,1999) and Pilat-Lohinger &Dvorak (CMDA, 2002)

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29 Tight Binary Systems binary abinary [AU] ebinary M1 -/M2 Gliese86 ~22? g Cephei ~ HD41004 ~23? Gliese86 g Cephei HD m sin i = 4 MJ a = 0.11AU e = m sin i = 1.6 MJ a = 2.15 AU e = m sin i = 2.3 MJ a = 1.3 AU ( 1.6 or 1.7) e = /- 0.17?

30 Stability limits mass-ratio border of stable motion Gamma Cephei: AU HD41004 AB: 0.36? (e not known!) Gliese 86: 0.42 close-in planet

31 Tight Binary Systems binary abinary [AU] ebinary m1 -/m2 Gliese86 ~22? g Cephei ~ HD41004 ~23? g Cephei: m sin i = 1.6 MJ a = 2.15 AU e =

32 mass-ratio = 0.2 Stability analysis

33 gamma Cephei

34 HD41004 AB

35 Habitable Zone Zone around a star where liquid water can exist on the surface of a terrestial-like planet This zone depends on: the spectraltype, the mass, the age,. of the star the orbit of the planet the mass, the composition, the atmosphere, of the planet the parameters of other planets in this system (mass, orbit, )

36 Literaturliste Gilmour & Sephton: An introduction to Astrobiology, Cambridge Ward & Brownlee: Rare Earth (Unsere einsame Erde); Springer Goldsmith & Owen: The Search of Life in the Universe, University science books Ulmschneider: Intelligence Life in the Universe; Springer de Pater & Lissauer: Planetary Sciences; Cambridge

37 Huang (1959, 1960) führte den Begriff habitable zone Dole (1964), Shklovski & Sagan (1966) sprachen von ecosphere Region um einen Stern, wo sich auf einem Planeten Leben entwickeln kann.

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39 Sonnenentwicklung Leuchtkraft der Sonne (Lo) nimmt zu: hatte zu Beginn 0.71 von Lo wird ca. 3xLo haben am Ende der Hauptreihenphase ca. 300Lo in der Roten Riesen Phase und wächst auf 6000 Lo an in der AGB Phase

40 Sonnenentwicklung: Iben 1967 u Newman & Rood 1977 Gough 1981 Iben & Renzine 1983 Gilliland 1989

41 Änderung der Sonnenenergie -> Änderung der effektiven Temp.

42 Habitable Zone & Star Evolution CHZ = continuously habitable zone = Bereich der über mehrere Jahrmilliarden in der HZ liegt (Sternentwicklu ng!)

43 HZ im Sonnensystem (Kasting) innere Grenze: 0.95 AU (Wasserdampf bildet sich in der Stratosphäre), bzw AU (Temperaturanstieg infolge eines runaway greenhouse-effekts) äußere Grenze bei 1.37 AU (Bildung von CO2- Wolken) CHZ zwischen 0.95 und 1.15 AU

44 based on the definition given by Kasting et al. (1993). Size of the habitable zone

45 Planet ist außerhalb der HZ Planet benötigt eine interne Wärmequelle um Eis od. Permafrost zu schmelzen Planet ist näher beim Stern als HZ Wasser würde verdampfen

46 WASSER H20 Wasserstoff entstand im Gefolge des Urknalls. Unter Bedingungen, die an vielen Stellen von Galaxien herrschen (niedere Temperaturen, Existenz von interstellaren Staubteilchen - an deren Oberflächen H mit H reagiert) kam/kommt es zur Bildung von H 2. Sauerstoff wurde/wird bei 500 Mio. Grad im Inneren von Sternen erzeugt. Durch Konvektion wird ein Teil des O an Sternoberfläche transportiert und in weiterer Folge gelangt Materie auch in den interstellaren Raum (etwa bei Supernova-Explosionen). Aus ISM entstehen neue Sterne + Planeten + Monde +

47 Habitable Zone aus dynamischer Sicht Langzeitstabilität der Planetenbahnen kleine Exzentrizitäten 60% haben e > % haben e > 0.3

48 Types of Habitable Zones: (1)Hot-Jupiter type (2) Solar system type (3)+(4) giant planet type: habitable moon or trojan planet

49 Habitable Zones in the three close binaries

50 abinary=22 AU ebinary=0.7 Gliese 86

51 eb=0.2, ep = 0.2, ap=1.3 AU Zone (roter Bereich) hinter der säkularen Resonanz (blau gebogene Region) wird scheinbar geschützt. Bewegung im roten Bereich bleibt kreisförmig auch wenn eb und ep erhöht werden. ideal für habitable Planeten