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 OpticsRef: 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

(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”

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

Angular separation of nulls in diffraction pattern = λ/d

INTERFEROMETRY - Very high resolution

k = 2 π/λ

INTERFEROMETRY

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☼ = 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

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

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

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