Dynamics of High Perihelion Tnos

Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms

Dynamics of High Perihelion TNOs

Tabaré Gallardo

Departamento de Astronomía, Facultad de Ciencias, Uruguay

December 1, 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Motivation: orbital scattering in the TNR

50 2013 JD64 e>0.2

Eris 40

30 2014 FC72 2012 VP113 2014 FZ71 inclination 20

90377 Sedna 10

0 40 45 50 55 60 65 70 75 80 85 q (au)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Why scattered orbits decoupled from Neptune?

non discovered planets? stellar companion? passing stars? what about long term dynamics?

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Why scattered orbits decoupled from Neptune?

non discovered planets? stellar companion? passing stars? what about long term dynamics?

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Secular resonances?

There are no linear secular resonances for a > 50 au.

Knezevic et al. 1991

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Diffusion at low inclinations (i < 20◦)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Diffusion at high inclinations (i > 20◦)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Resonant Kozai Dynamics Other mechanisms Topics

Kozai dynamics outside MMRs Kozai dynamics inside MMRs other mechanisms: dynamical implantation of objects from Oort cloud planet nine

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

Non Resonant Kozai Dynamics

K = constant a = constant p H = 1 − e2 cos i = constant

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Kozai-Lidov secular dynamics

Kozai model: coplanar circular non-perturbed orbits for the planets. Hamiltonian K(λ, ω, Ω, L, G, H) −→ K(−, ω, −, L, G, H) −→ L, H constants √ a and H = 1 − e2 cos i constants

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model √ Other mechanisms Oscillating perihelion H = 1 − e2 cos i

50 2013 JD64

Eris 40

30 2014 FC72 2014 FZ71 2012 VP113 20 inclination (degrees) inclination

90377 Sedna 10

0 10 20 30 40 50 60 70 80 90 100 q (au)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

√ H = 1 − e2 cos i is constant, but... not all range in (e, i) is allowed limits in (e, i) are deﬁned by energy level curves K = constant

µ K(ω, q, a, H) = − − R 2a sec

We need Rsec

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Lidov and Kozai

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

History: looking for Rsec

Lidov 1961-1962: satellite perturbed by Moon, analytical Rsec.

Kozai 1962: asteroids perturbed by Jupiter, analytical Rsec as series expansions in aaster/aJ Bailey et al. 1992: comet (sungrazer) perturbed by Jupiter, numerical Rsec. Thomas & Morbidelli 1996: TNOs perturbed by JSUN, numerical Rsec. Kozai 2004: analytical version for transneptunians. Gallardo et al. 2012: analytical model (rings) and numerical survey. Saillenfest et al. 2016: complete numerical survey.

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

Numerical method by Bailey et al. (1992) and Thomas & Morbidelli (1996):

1 Z 2π Z 2π Rsec = 2 R(λpla, λ) dλpla dλ 4π 0 0

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 (a) H=0.1, a=50 AU (e) H=0.1, a=100 AU 84.2 60 83.7 45 40 50 35 40 30 i 25 i 30

q (AU) 20 q (AU) 20 15 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model 10 Other mechanisms Oscillating perihelion 10 5 Kozai maps: K(ω, q) = constant 69.1 44.9 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(b) H=0.3, a=50 AU (f) H=0.3, a=100 AU 72.5 60 70.9 45 40 50 35 40 30 i i 25 30 q (AU) 20 q (AU) 15 20 10 10 5 28.4 16.1 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(c) H=0.5, a=50 AU (g) H=0.5, a=100 AU 60 60 56.9 45 Tabaré Gallardo High Perihelion TNOs - CBDO 2016 55 40 50 35 45 30 40 i i 25 35 q (AU) q (AU) 30 20 25 15 20 10 11.5 15 18.3 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(d) H=0.7, a=50 AU (h) H=0.7, a=100 AU 45.6 60 40.2 45 55 40 50 35 i i 45 30 q (AU) q (AU) 40 25 35 20

15 11.4 30 11.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω (a) H=0.1, a=50 AU (e) H=0.1, a=100 AU 84.2 60 83.7 45 40 50 35 40 30 i 25 i 30

q (AU) 20 q (AU) 20 15 10 10 5 69.1 44.9 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(b) H=0.3, a=50 AU (f) H=0.3, a=100 AU 72.5 60 70.9 45 40 50 35 40 30 i i 25 30 q (AU) 20 q (AU) 15 Non resonant Kozai dynamics Rsec and Kozai Maps 20 Resonant Kozai Dynamics Rings model 10 Other mechanisms Oscillating perihelion 10 5 K = constant 28.4 16.1 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(c) H=0.5, a=50 AU (g) H=0.5, a=100 AU 60 60 56.9 45 55 40 50 35 45 30 40 i i 25 35 q (AU) q (AU) 30 20 25 15 20 10 11.5 15 18.3 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(d) H=0.7, a=50 AU (h) H=0.7, a=100 AU 45.6 60 40.2 45 Tabaré Gallardo High Perihelion TNOs - CBDO 2016 55 40 50 35 i i 45 30 q (AU) q (AU) 40 25 35 20

15 11.4 30 11.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω (a) H=0.1, a=200 AU (e) H=0.1, a=300 AU 60 82 50 79.6 45 50 40 40 35 30 i 30 i 25 q (AU) q (AU) 20 20 Non resonant Kozai dynamics Rsec and Kozai Maps 15 Resonant Kozai Dynamics Rings model 10 Other mechanisms Oscillating perihelion 10 ω = ◦ i ∼ ◦ 44.9 5 57 Equilibrium point0 30 at 60 90 90, 12063 150 180 0 30 60 90 120 150 180 ω ω

(b) H=0.3, a=200 AU (f) H=0.3, a=300 AU 60 65.2 90 65.2 80 50 70 40 60 i

50 i

q (AU) 30 q (AU) 40 20 30 20 10 16.1 16.1 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

55 Tabaré Gallardo High Perihelion TNOs - CBDO 2016 110 100 50 90

45 i 80 i

q (AU) 40 q (AU) 70 35 60

30 50 4.8 7.8 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(d) H=0.7, a=200 AU (h) H=0.7, a=300 AU 80 29 200 42.1

180 75

160

70 i

140 i q (AU) q (AU) 65 120

60 100 6.3 11.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω H=0.49, a=36 AU H=0.48, a=41 AU 36 60.7 61.3 40 35

34 38 33 36 32 i i

q (AU) 31 q (AU) 34 30 32 29 28 59.8 30 60.1 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

H=0.46, a=50 AU H=0.46, a=52 AU 40 62.0 40 61.8 39 38 39 37 Non resonant Kozai dynamics 38Rsec and Kozai Maps 36 i Resonant Kozai Dynamics Rings model i 35

q (AU) Other mechanisms q (AU) 37Oscillating perihelion 34

33 36 Metamorphosis 32 from a = 54 to a = 500 AU 31 60.2 35 60.9 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

H=0.46, a=54 AU H=0.46, a=80 AU 48 62.4 80 62.6 46 75 44

42 70 i 40 i

q (AU) 38 q (AU) 65 36 60 34 32 59.8 55 61.0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

H=0.36, a=100 AU H=0.2, a=500 AU 50 65.4 70 66.9 45 65 40 60 35 55

30 i 50 i

q (AU) 25 q (AU) 45 20 40 15 35 10 34.3 30 54.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion 2 Survey of Saillenfest et al. 2016 (CK = H )

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Some conclusions up to now

For non resonant orbits There is a family of equilibrium points at i ∼ 63◦ and ω = 90◦ (and 270◦). it generates the largest ∆q ∼ 16,4 au Sedna? ... no way!

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Sedna

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model √ Other mechanisms Oscillating perihelion H = 1 − e2 cos i

50 2013 JD64

Eris 40

30 2014 FC72 2014 FZ71 2012 VP113 20 inclination (degrees) inclination

90377 Sedna 10

0 10 20 30 40 50 60 70 80 90 100 q (au)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Our model: spherical Sun + circular rings of matter

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

Kozai Maps using analytical Rsec

66 97.4

64 81.3 L L AU H degrees q H i

62 69.2

60 60.0

0 30 60 90 120 150 180 Ω

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Equation for $ = Ω + ω

d$ 3Ck = (3 − 4 cos i + 5 cos 2i) + ... dt 16a7/2(1 − e2)2 d$ = 0 −→ i ∼ 46◦ dt

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

65 dω/dt=0

2005 NU 55 125

2004 XR190 dϖ/dt=0

inclination 45 2004 DF77 Eris

40 2007 TC434

35 2006 QR180 30 40 60 80 100 120 140 a (UA)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion

136199 Eris 360 270

Ω 180 90

270

ω 180 90

44 i 43

ϖ 80 75 70 0 50 100 150 200 time (Myr)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Eris by 200 Myr:

http://youtu.be/CA1XPj_DklY

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Rsec and Kozai Maps Resonant Kozai Dynamics Rings model Other mechanisms Oscillating perihelion Some other conclusions

$˙ ∼ 0 at i ∼ 46◦. Eris is the only known TNO with oscillating $

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms

Resonant Kozai Dynamics

Resonant condition:

σ = (p + q)λN − pλ − q$

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Gallardo 2006: atlas of resonances

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Gallardo 2006

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Numerical Methods

How to take into account the resonant condition?

Kozai 1985: imposing σ = σ0 Gomes et al. 2005 and Gallardo et al. 2012: sinusoidal evolution of σ with constant centre, frequency and amplitude Brasil et al. 2014: different secular levels according the actual evolution of σ Saillenfest et al. 2016: adiabatic invariants

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms

Kozai method, σ = σ0

1 Z 2π Z 2π Rsec = 2 R(λJ, λ) dλJ dλ 4π 0 0

1 Z 2π Rsec = R(λJ, λ(σ0 , λJ, )) dλJ 2π 0

pλ = (p + q)λJ − σ0 − q$

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Gomes et al. 2005 method

1 Z 2πp 1 Z 2π Rsec = dλN R(λN, λ[λN, σ(α)]) dα 2πp 0 2π 0

σ(α) = σ0 + ∆σ sin(α)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Gomes et al. 2005

Non resonant resonant

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 (a) res 5:11, H=0.1, a=50.95 AU (e) res 1:6, H=0.1, a=99.45 AU 50 84.3 80 84.1 45 70 40 60 35 30 50

25 i 40 i

q (AU) 20 q (AU) 30 15 20 10 5 10 76.8 68.9 0 0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(b) res 5:11, H=0.3, a=50.95 AU (f) res 1:6, H=0.3, a=99.45 AU 50 72.5 80 72.2 45 70 40 60 35 30 50

25 Non resonant Kozai dynamicsi 40 i Handling the critical angle q (AU) 20 Resonant Kozai Dynamics q (AU) 30Adiabatic invariants 15 Other mechanisms65.7 62.6 20 10 59.7 10 5 39.4 23.8 Gallardo 0 et al. 2012 0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

45 70 40 60 57 35

30 i 50

25 40 i q (AU) q (AU) 20 30 15 45.1 10 32.8 20 33.8 5 10 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(d) res 5:11, H=0.7, a=50.95 AU (h) res 1:6, H=0.7, a=99.45 AU 50 45.6 80 44.5

45 70 40 60 35

50 i

30 i q (AU) q (AU) 40 29.4 25 15.2 20 28.2 30

15 8.9 20 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 (a) res 5:11, H=0.1, a=50.95 AU (e) res 1:6, H=0.1, a=99.45 AU 50 84.3 80 84.1 45 70 40 60 35 30 50

25 i 40 i q (AU) 20 q (AU) 30 15 20 10 5 10 76.8 68.9 0 0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

(b) res 5:11, H=0.3, a=50.95 AU (f) res 1:6, H=0.3, a=99.45 AU 50 72.5 80 72.2 45 70 40 60 35 30 50

25 i 40 i q (AU) 20 q (AU) 30 15 65.7 62.6 20 10 59.7 10 5 39.4 23.8 0 0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

45 70 40 60 57 35

30 i 50

25 40 i q (AU) q (AU) 20 30 15 45.1 Non resonant Kozai dynamics Handling the critical angle 20 Resonant Kozai Dynamics 33.8 Adiabatic invariants 10 32.8 Other mechanisms 5 10 0 30 60 90 120 150 180Asymmetric 0 resonances 30 60 1:N 90 120 150 180 ω ω

(d) res 5:11, H=0.7, a=50.95 AU (h) res 1:6, H=0.7, a=99.45 AU 50 45.6 80 44.5

45 70 40 60 35

50 i

30 i q (AU) q (AU) 40 29.4 25 15.2 20 28.2 30

15 8.9 20 0 30 60 90 120 150 180 0 30 60 90 120 150 180 ω ω

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Brasil et al. 2014

energy K is constant but level curves change:

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Saillenfest et al. 2016

K(σ, ω, Ω, Σ, U, V) = K(σ, ω, −, Σ, U, V) wide separation between the two time scales for σ and ω allows reduction to an integrable approximation: adiabatic invariant approximation.

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Adiabatic invariants

Suppose that in K(σ, ω, Σ, U) variables (ω, U) can be considered constants or with very slow variation: K(σ, Σ) will have action angle variables (θ, J) J is conserved providing the timescale for (ω, U) is well larger than for (σ, Σ). Libration center and amplitude can change but J is preserved. J is taken as the conserved quantity representing the librational motion.

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms the meaning of J

1 I J = Σdσ 2π

σ libration: area enclosed σ circulation: area below

Lemaitre 2010

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms resonance 2:37

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Separatrix crossing

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Separatrix crossing

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Asymmetric level curves for resonances 1:N

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms evolution resonance 1:11

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms Generating large q

Kozai mechanism inside MMRs generates very large orbital changes: capture in MMR with Neptune Kozai makes q to grow and e diminishes separatrix is crossed and the resonance’s strength drops hibernation in large q it is expected that resonances 1:N are depleted at low q

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms

Real objects (η0 = H)

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Handling the critical angle Resonant Kozai Dynamics Adiabatic invariants Other mechanisms More conclusions (resonant orbits)

reservoir with increasing population at 100 < a < 300 au (region where MMRs are efﬁcient) 50 < q < 70 au (region where librations broke) 30 < i < 50 (corresponding region due to H = constant) a migrating Neptune helps to capture in MMR and then to break the MMR we cannot explain (still...) the orbits of 2012 VP113 and Sedna

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms

Other Mechanisms

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Dynamical implantation of Oort cloud comets

From de Oort cloud (a ∼ 10,000 au): galactic tides drive q ∼ 30 au planetary perturbations make a decrease (hundreds au) eventually is captured in MMR 1:N ends up in the reservoir

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms

Saillenfest et al. 2016, from simulations by Fouchard et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Dynamical implantation of Oort cloud comets

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Dynamical implantation of Oort cloud comets

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Dynamical implantation of Oort cloud comets

Saillenfest et al. 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Dynamical implantation of Oort cloud comets

Sedna and 2012 VP113 could be implanted objects from Oort cloud

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Planet Nine

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Evidence: non uniform distribution of Ω

360

270

180 longitude node longitude

0 0 50 100 150 200 250 300 350 400 450 500 a (au)

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Eccentric Kozai curves

Batygin and Brown 2016

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Without planet Nine

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms With planet Nine

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Effects on Neptune

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Non resonant Kozai dynamics Dynamical implantation Resonant Kozai Dynamics Planet Nine Other mechanisms Conclusions

large (q, i) observed in TNOs can be explained by Kozai inside MMRs in particular 1:N resonances Sedna and 2012 VP113 can be implanted from Oort cloud a problem with Ω: an eccentric perturber?

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 References

Brasil et al. 2014, AA 564, A44. Gallardo et al. 2012, Icarus 220, 392-403. Gomes et al. 2005, CMDA 91, 109129. Saillenfest et al. 2016, CMDA, 126 (4), 369403 and DOI 10.1007/s10569-016-9735-7 www.ﬁsica.edu.uy/∼gallardo

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Muito obrigado!

Tabaré Gallardo High Perihelion TNOs - CBDO 2016 Abstract submission deadline extended to December 11

Tabaré Gallardo High Perihelion TNOs - CBDO 2016