New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic...
Transcript of New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic...
![Page 1: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/1.jpg)
THE ROLE OF RESONANCES
IN NBODY MODELS OF BARRED GALAXIES
Daniel Ceverino & Anatoly Klypin(New Mexico State University)
![Page 2: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/2.jpg)
Realistic orbits and resonances
Natural frequencies of a general orbit:
Ω , Κ , υ
Pattern frequency: ΩP
l Κ + m1 Ω + n υ = m2 ΩP l , m i , n are integers.
RESONANCE!
Linear regime: A resonance produces a dramatic change in the evolution of the orbit.
This is not always the case.
![Page 3: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/3.jpg)
Resonances in the solar system: Trojan asteroids.
Libration around Lagrangian points L4 and L5 of the system SunJupiter.
Example of a trapping resonance. 1:1 .
L4
L5
![Page 4: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/4.jpg)
Gaps.
Gaps
Trapping resonances
![Page 5: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/5.jpg)
Searching resonances in Nbody simulations.
• Athanassoula 2003:
– Frozen potential.
– Ratio:(Ω – ΩP ) / Κ = l / m , where l and m are integers
(1:2)
(1:2)
(1:6)
(1:1)
![Page 6: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/6.jpg)
Radial frequency (K) measurements
• For every particle, we measure the frequencies during a given period of time (1-2 Gyrs) in which the pattern speed is almost constant.
– Κ: Fourier Analysis of the radial evolution.
![Page 7: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/7.jpg)
Angular frequency (Ω)
Ω: Averaged time of one angular revolution.
Time
Ang
le
Slope: Ω
![Page 8: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/8.jpg)
Face-on views of the Models using contours of equal density.
![Page 9: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/9.jpg)
weak bar (Pseudobulge) strong bar
Corotation radius.
![Page 10: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/10.jpg)
The frequency space: K vs Ω.
Commonly used in plasma physics and planetary
science. (Laskar 1990 )
Each point represents the orbit of a particle.
Straight lines with certain slopes define the main
resonances.
![Page 11: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/11.jpg)
![Page 12: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/12.jpg)
)4()( 22
2
2
2
2 Ω+Ω=∂Φ∂
=ΚdR
dR
RE ff
weak bar
ILCR
Higherorder
UH
IL
CROL
strong bar
![Page 13: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/13.jpg)
• (Ω – ΩP)/Κ = n /m
• Fraction of particles per unit bin.
• Low-order resonances (±1:m)
• Trapping resonances.
• No indications of gaps of low-order.
• 1σ statistical error.
Main resonances ( weak bar)
495m:
2
n=1 n=1
![Page 14: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/14.jpg)
Main resonances ( strong bar)
![Page 15: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/15.jpg)
A portrait of resonances for a weak bar.
![Page 16: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/16.jpg)
OL
IL 1:4
1:9
1:5 CR
![Page 17: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/17.jpg)
Inner Lindblad
IL is not
localized at a
given radius
![Page 18: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/18.jpg)
Third model: Corotation. Selected particles in corotation at 3.5 Gyr
COROTATION
Particles are trapped at corotation.
0.1 Gyr
3.5 Gyr
4.4 Gyr
![Page 19: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/19.jpg)
Instantaneous change of angular momentum.
• Torque field.
• Areas in which the angular momentum of the particles increases (positive torque) or decreases (negative torque).
Positive
Negative
![Page 20: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/20.jpg)
AM change over a longer interval• Maximum increment and
decrement in angular momentum.
• The maximum (positive) and minimum (negative) areas of AM change lie at corotation radius.
+
+
![Page 21: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/21.jpg)
A example of a orbit that circulates along corotation.
The particle is trapped at corotation radius at 1.6 Gyr.
Selected particle to be near corotation at 3.5 Gyr.
reference frame rotating with the bar.
![Page 22: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/22.jpg)
A slow orbit: Libration around a lagrangian point at corotation .
++
No net change of angular momentum+
![Page 23: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/23.jpg)
A last result: Resonances in the halo
• Similar pattern of resonances.
• We select halo particles which are close to the disk so the interaction with the bar is stronger.
![Page 24: New THE ROLE OF RESONANCESastronomy.nmsu.edu/danielcv/resonances.pdf · 2005. 3. 29. · Realistic orbits and resonances Natural frequencies of a general orbit: Ω , Κ , υ Pattern](https://reader035.fdocuments.us/reader035/viewer/2022071218/6052d3f63af9df4c8935681b/html5/thumbnails/24.jpg)
CONCLUSIONS
First time that resonances are detected in a Nbody simulation with a evolving disk in a living halo using only their trajectories.
Trapping resonances. No gaps are found.
There are no evolution after particles get trapped.
Corotation captures particles in a ring outside the bar.
Inner Lindblad is not localized at a given radius.
The halo also exhibits trapping resonances.