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ASTRO 2233
Fall 2010
Adaptive Optics, Interferometry and Planet Detection
Lecture 16
Thursday October 21, 2010
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
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)
Adaptive Optics
Ref: Center for Adaptive Optics
Wavefront
sensor
See http://www.ucolick.org/~max/289C/ lecture 6 - Claire Max, Center for Adaptive Optics
Correcting the wavefront using tilt information from the wavefront sensor
Claire Max, Center for Adaptive Optics
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
LASER GUIDE “STARS”
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
(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).
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
Multi-conjugate adaptive optics – multiple guide stars - allows
three dimensional reconstruction of atmospheric turbulence
and wider fields of view (European Southern Observatory slide)
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
INTERFEROMETRY - Very high resolution
Angular separation of nulls in
diffraction pattern = λ/d
INTERFEROMETRY
k = 2 π/λ
VERY LARGE
ARRAY
Very Large Array, New Mexico
Cygnus A VLA Image at 5 GHz (6 cm wavelength)
Atacama Large Millimeter Array
Wavelengths 350 m to 1 cm
Best resolution ~10 mas
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
Keck 10-m optical telescopes, Hawaii.
Experimental interferometer.
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
European Southern Observatory (ESO) Very Large Telescope(S) - 4 x 8M
VLT Interferometry
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
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☼ = m p ap / m☼
- what is this telling us about the radius of the orbit
of 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
ASTROMETRY
– measuring angular deflection of the parent star about center of mass of system
Sun’s trajectory about the center-ofmass of the solar system.
As viewed from 10 parsecs (32 light
years) away.
2. Velocity of the Star measurements via Doppler Shift
Example: for circular orbits, planet-star pair, * = velocity of star
* 
2 r1
2 m2 a

p
p  m1  m2 
m2 = mass planet p is the orbit period
3 3

p  m1  m2 
G  m1  m2  2
a3  *

p
3 3
2
8 m2
4
3
*3 
* 
Maximum velocity
for elliptical orbits
2 m G
3
2
p  m1  m2 
2
1
3
1
3
 2 
m2G
 m1  m2 
 2 G 


p


1
3
2
3
p
r1 = radius of star orbit
about center-of-mass
= a m2/(m1 + m2)
a = star-planet distance
from Keppler’s 3rd law, a3  p2
For Circular Orbit
1
3
m2
 m1  m2 
Basis for discovering extrasolar planets
1
2
3
1
2 2
1  e 
http://upload.wikimedia.org/wikipedia/commons/5/59/Orbit3.gif
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
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
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