Resonant Origins for Plutos High Inclination Curran D. Muhlberger - - PowerPoint PPT Presentation

Background Techniques Results Conclusions

Resonant Origins for Pluto’s High Inclination

Curran D. Muhlberger

University of Maryland, College Park

April 7, 2008

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Introduction Planetary Migration Orbital Resonances

Goals

Explain Pluto’s high eccentricity (e = 0.24) and high inclination (i = 17° ) using resonances Three candidates

1

6:4 mean motion resonance

2

1:1 secular resonance

3

2:1 secular resonance

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Introduction Planetary Migration Orbital Resonances

Planetary Migration by Scattering Planetesimals

Planets other than Jupiter preferentially scattered planetesimals inward, migrated

• utward

Migrations move locations of resonances, catching Pluto If migration rate is slow enough, characteristic effect on resonances is rate-independent

8 5 1

• 0.2

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Introduction Planetary Migration Orbital Resonances

Orbital Elements & Symmetries

Longitude of ascending node Argument of periapsis True anomaly Inclination Ascending node Reference direction Celestial body Plane of reference O r b i t

Ω ω ν i ☊ ♈

Orbital Elements: a, e, i, Ω, ϖ = Ω+ω, λ (˙ λ ≈ n) Secular Variables h = esin(ϖ) k = ecos(ϖ) p = sin(i/2)sin(Ω) q = sin(i/2)cos(Ω) Eigenfrequencies: f, g

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Introduction Planetary Migration Orbital Resonances

Resonant Behavior

Mean Motion Resonance Simple ratio of orbital periods (dependent on λ, n) Secular Resonance Simple ratio of precession periods (averaged orbits) Form resonant arguments subject to symmetries

Good: 6λP −4λN −2ΩP, 2ΩP −ΩN −ΩJ Bad: 3λP −2λN −ΩN, 2ΩP −ΩN

Capture Jump

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Numerical Methods

Simulation and Analysis

Both of pre-existing and new software used throughout project. Used HNBody and HNDrag to simulate Solar System over billions of years (> 24GB of data generated) To determine secular eigenfrequencies, wrote code to perform FFT on orbital elements Features of PowerSpectrumEstimator:

Data windowing to reduce spectral leakage Overlapping data segments to minimize variance Automatic peak finding with inverse quadratic interpolation Removal of aliased peaks Orthogonality of total angular momentum

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Numerical Methods

Example: Outer Solar System p Spectra

Matches g6 to better than 1%; matches g7 to within 7%; matches g8 to within 25%; g5 is effectively 0

Frequency [cycles/day] Spectra of 'p' for the Outer Solar System Jupiter Saturn Uranus Neptune 3.390916e-11 5.609270e-08 6.727809e-09 1.818169e-09 2e-08 4e-08 6e-08 8e-08 1e-07 Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Candidate #1 – 6:4 Mean Motion Resonance

Pluto is currently trapped in a 3:2 eccentricity resonance (3nP −2nN − ˙ ϖP) and a Kozai resonance ( ˙ ΩP − ˙ ϖP). Together, these imply a 6:4 inclination resonance (6nP −2nN −2 ˙ ΩP). Initially, these were split (no Kozai resonance) Being first-order, eccentricity resonance is stronger Simulations rule out capturing in inclination resonance first What about afterwards?

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Examples of Mean Motion Resonances

a [AU] Orbital Elements for Pluto 32.99 32.992 32.994 32.996 32.998 33 33.002 33.004 e 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 t [yr] 9.9e-05 9.95e-05 0.0001 0.0001005 0.000101 0.0001015 0.000102 5e+07 1e+08 1.5e+08 2e+08 a [AU] Orbital Elements for Pluto 32.94 32.96 32.98 33 33.02 33.04 33.06 33.08 33.1 33.12 e 0.005 0.01 0.015 0.02 0.025 0.03 0.035 i [deg] t [yr] 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1e+09 2e+09 3e+09 4e+09 5e+09 6e+09 7e+09 8e+09

Migration rates too slow, inclination rise too small

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Candidate #2 – 1:1 Secular Resonance

A 1:1 resonance ( ˙ ΩP − ˙ ΩN) should be easier to find and more powerful than a 2:1 resonance. Studied an idealized Jupiter+Neptune+Pluto system May have been present at Solar System formation Could capture into 3:2 mean motion resonance at just the right time, maintain high inclination

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Example of 1:1 Secular Resonance

Plot and Spectrum of Pluto's 'p' aP = 33 AU Pluto Neptune 5e-07 1e-06 1.5e-06 2e-06 Time [yr]

• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2 0.25 2e+07 4e+07 6e+07 8e+07 1e+08 1.2e+08 a [AU] Orbital Elements for Pluto 32.9 33 33.1 33.2 33.3 33.4 33.5 33.6 e 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 i [deg] Time [yr] 5 10 15 20 25 30 2e+07 4e+07 6e+07 8e+07 1e+08 1.2e+08

Static inclination resonance extremely broad and powerful (3 AU, 25° )

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Secular Resonances in the Solar System

In full Solar System, 1:1 resonance is not as broad or powerful. Still, migrating across makes jump or capture possible. Inclination jump of 10°observed near initial conditions Capture raises more questions: when/how did it break out? Leaves observed 2:1 resonance a coincidence Early proximity to 1:1 indicates that 2:1 was not active prior to capture in eccentricity resonance.

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Candidate #3 – 2:1 Secular Resonance

By raising MU → 1.8MU, we could create conditions where 2p1 ≈ g8. By dragging Pluto directly, we could study strength of jump and capture. Raising MU ⇐ ⇒ increasing Uranus’s initial position Jump is too weak (2° ) to explain current inclination What about capture?

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Example of 2:1 Capture

Spectra of 'p' for the Outer Solar System: Initial Jupiter Saturn Uranus Neptune Pluto 7.669366e-07 3.874448e-07 Frequency / 2π [rad/yr] Spectra of 'p' for the Outer Solar System: Resonance (2e7 yr) Jupiter Saturn Uranus Neptune Pluto 7.669416e-07 4.129240e-07 5e-07 1e-06 1.5e-06 2e-06 2.5e-06 3e-06 3.5e-06 4e-06 i [deg] t [yr] 2 4 6 8 10 12 14 16 2e+07 4e+07 6e+07 8e+07 1e+08 1.2e+08 1.4e+08 1.6e+08 1.8e+08 e 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.23 0.235 0.24 a [AU] Orbital Elements for Pluto 37.4 37.5 37.6 37.7 37.8 37.9 38 38.1 38.2 38.3

Capture is possible! Yields i → 16° +

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions Mean Motion Resonances Secular Resonances (1:1) Secular Resonances (2:1)

Active Resonances in 2:1 Capture

3λP - 2λN - ϖP 50 100 150 200 250 300 350 2ΩP - ΩN - 0 50 100 150 200 250 300 350 6λP - 4λN - 2ΩP 50 100 150 200 250 300 350 2ΩP - 2ϖP 50 100 150 200 250 300 350

Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination

Background Techniques Results Conclusions

Summary

Currently, no overwhelmingly likely explanation. However, some can be ruled out while others can be constrained.

Resonance Grade Pros Cons Mean Motion D

Currently active Could not capture Too weak

Secular 1:1 B

Strong enough Possibly active in early solar system Not active today Large jump instead of capture

Secular 2:1 B+

Possibly active today Capable of capture MU → 1.8MU Dragging Pluto, not Neptune Curran D. Muhlberger Resonant Origins for Pluto’s High Inclination