ASTRO 2233 Fall 2010 Adaptive Optics, Interferometry and Planet Detection Lecture 16 Thursday...
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ASTRO 2233
Fall 2010
Adaptive Optics, Interferometry and Planet Detection
Lecture 16
Thursday October 21, 2010
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Projects:
Everyone has submitted an outline.
After reading the Astro2010 reports and additional class discussions you can change topics if you wish but discuss it with me.
Next Tuesday: Phil Muirhead
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Effects of Atmospheric Turbulence on “Seeing” – i.e. telescope effective resolution
SOLUTION – ADAPTIVE OPTICS (AO) Refractive index of atmosphere at 0.5 m
n = 1 + 79 x 10-6 P / T ; P (ressure) in millibars T(emperature) in Kelvin = 1.0003 for P = 1,000 mBar; T = 300K
Variations due to small fluctuations in T (and P)
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Adaptive OpticsRef: Center for Adaptive Optics Wavefront
sensor
See http://www.ucolick.org/~max/289C/ lecture 6 - Claire Max, Center for Adaptive Optics
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Correcting the wavefront using tilt information from the wavefront sensor
Claire Max, Center for Adaptive Optics
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How often do you need to correct wavefront?
How fast does the atmosphere change? - depends on wind speed at turbulent layer
Time constant for an isoplanetic patch size of 20 cm
= 0.31 20/Vavg Vavg is average wind speed
For Vavg = 20 m/s (70 km/hr)
Time constant = 3 ms - need to correct wavefront every 1 ms
In the near infra-red where patch size is ~1 m
Time constant ~ 15 ms - need to correct wavefront ~100 times/sec
Much easier in the near infra-red - slower correction - fewer actuators due to larger patch size
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(a) Astronomers using Keck’s adaptive optics have obtained the best pictures yet of the planet Neptune. The images show bands encircling the planet and what appear to be fast-moving storms of haze. (b) The same image without adaptive optics (I. de Pater).
Path of laser on Gemini North. The laser is located at the bottom of the yellow/orange beam near the right middle of the image. Note that the laser's light is directed by "relay optics" that direct the light to a "launch telescope" located behind the secondary mirror at the top/center of the telescope. Illustration based on Gemini computer animation.
Laser reflects off sodium layer at ~80 km altitude
LASER GUIDE “STARS”
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Measure of Performance – STREHL RATIO
Measure of the optical quality of a telescope including “seeing” problems due to atmospheric turbulence
Strehl Ratio = Ratio of the amplitude of the point spread function (PSF) – the diffraction pattern - with and without the atmosphere assuming a perfect telescope.
Point spread function for no atmosphere – Strehl ratio = 1.0
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Multi-conjugate adaptive optics – multiple guide stars - allows three dimensional reconstruction of atmospheric turbulence and wider fields of view (European Southern Observatory slide)
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Extreme adaptive optics – high resolution and high contrast imaging
• Multiple guide stars• Thousands of actuators on deformable mirror• Very high precision for setting deformable mirror - a few nm• Very high speed in setting deformable mirror – several kHz
Center for Adaptive Optics image
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Angular separation of nulls in diffraction pattern = λ/d
INTERFEROMETRY - Very high resolution
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k = 2 π/λ
INTERFEROMETRY
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VERY LARGE ARRAY
Very Large Array, New Mexico
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Cygnus A VLA Image at 5 GHz (6 cm wavelength)
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Atacama Large Millimeter Array
Wavelengths 350 m to 1 cm
Best resolution ~10 mas
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RESOLUTION = λ/D
VLA (A array) at 3.5 cm: Resolution ~ 0.2 arcsec
Atacama mm array: Resolution ~ 0.02 arcsec at 1 mm wavelength
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Keck 10-m optical telescopes, Hawaii.
Experimental interferometer.
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LARGE BINOCULAR TELESCOPE
Mt Graham, Arizona
Two 8.4 m mirrors spaced 14.4 m apart
8.4 m => ~14 mas resolution (no atmosphere)
14.4 m => 8 mas fringe spacing as interferometer
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European Southern Observatory (ESO) Very Large Telescope(S) - 4 x 8M
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VLT Interferometry
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Space Interferometry Mission - SIM
What: Interferometer – 10m baseline
Positional Accuracy – 4 μarcsec
(1 μarcsec relative over 1 deg field)
Distance measurements: 1% accuracy to several thousand parsecs
10% over whole galaxy
CALIBRATE CEPHEID and RR LYRA VARIABLE STARS
Planet search – astrometric search
nulling interferometer tests
dynamic range of 104
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Detection of Angular Motion of the Parent Star about the Center-of-Mass of System
No periodic motion means no planet – or planet to small/distant from star
1.Astrometry – measuring the positional motion of the star
Remember for two bodies in a circular orbit about each other – i.e. about the CM:
m1 r1 = m2 r2
For a planet about a star
a☼ = mp ap / m☼ - what is this telling us about the radius of the orbitof a planet that would make it easiest to
detect where a☼ = radius of star orbit via periodic positional changes of the star? ap = radius of planet orbit – large is good => bigger star orbit radius
The angular shift in the star’s position is :
θ = a☼ / R radians where R is the distance to the star from Earth
= {mp ap / m☼} / R arc sec if ap is in AU and R is in parsecs
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Sun’s trajectory about the center-of-mass of the solar system.
As viewed from 10 parsecs (32 light years) away.
ASTROMETRY – measuring angular deflection of the parent star about center of mass of system
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Example: for circular orbits, planet-star pair, * = velocity of star
1 2* 2
1 2
33 3* 1 2 1 23 2
3 3 22
33 2* 2
1 2
1133
2* 12
331 2
1
32
2 123 2
1 2
2 2 = mass planet
8 4
2
2
2 1
1
r m am
p p m m
p m m G m ma p
m
m G
p m m
m G
m m p
G m
p m m e
For Circular Orbit
Maximum velocity for elliptical orbits
r1 = radius of star orbit about center-of-mass
= a m2/(m1 + m2)
a = star-planet distance
Basis for discovering extra-solar planets
http://upload.wikimedia.org/wikipedia/commons/5/59/Orbit3.gif
2. Velocity of the Star measurements via Doppler Shift
from Keppler’s 3rd law, a3 p2
p is the orbit period
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For a star in a circular orbit and assuming that mp << m☼ then:
The measured maximum velocity is given by
vmax = 28.4 p-1/3 {mp Sin i / MJ} m☼-2/3 m sec-1
Where p is the orbit period in years, Sin i is the sine of the orbit inclination relative to the line-of-sight from Earth, MJ is the mass of Jupiter and m☼ is the mass of the star in solar masses.
For an elliptical orbit:
vmax = {2 G / p}1/3 {mp Sin i / (mp + m☼)2/3} {1 / (1 – e2)1/2} m sec-1
Jupiter orbiting the Sun:
vmax = 12.5 m sec-1, where p = 11.9 years
For Earth orbiting the Sun
vmax = 0.1 m sec-1 - very difficult to measure
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The measured maximum velocity is given by
vmax = 28.4 p-1/3 {mp Sin i / MJ} m☼-2/3 m sec-1
Where p is the orbit period in years, Sin i is the sine of the orbit inclination relative to the line-of-sight from Earth, MJ is the mass of Jupiter and m☼ is the mass of the star in solar masses.
Gliese 281 g:
m☼ = 0.3 solar masses
P = 36.5 days = 0.1 years
Sin i = 1
mp = 3 Earth masses = 0.01 mass of Jupiter
Velocity = 1.36 m/sec
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Astrometry:
Advantages: Direct measurement of mass of the planet – assumes we know star’s mass from stellar type – i.e. spectral class
Sensitive to large planets a long way from the star
Disadvantages: θ 1 / Distance to the star => nearby stars only
[θmax for Sun – Jupiter from 10 light years 1.6 milli arc sec]
Velocity measurements:
Advantages: Sensitive to large planets close to the star
Not directly dependent on distance to the star – just need sensitivity
Disadvantages: mp Sin i - lower limit on the mass
Not sensitive to planets at large distances from the star
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