ASTRO 2233

Extra-Solar Planets

Fall 2010

Lecture 14 – Telescopes and Adaptive Optics

Thursday October 14 2010

Keppler discovery of three orbiting planets with the outer two in a 2:1 resonance about Kepler-9, a solar type star a bit more active than the Sun

Mass estimates from RV measurements with Keck: 0.25 Mj for 9b and 0.17 Mj for 9c

Holman et al, Science, 330, 51-54, Oct 1 2010

Ionospheric absorption

Interstellar absorption Atmospheric absorption

Wavelength – will use micro-meters (10-6 m) (designated by µm) for optical and infra-red wavelengths)

Celes%al  coordinates  

   -­‐  Right  ascension  and  declina%on  

PRECESSION?  

Suppose  we  have  two  stars  with    apparent  magnitudes  m1  and  m2.    We  can  calculate  the  ra%o  of  their    brightnesses  b1  and  b2  by  the  formula:  

m1  -­‐  m2  =  -­‐2.5  log  (b1  /  b2)    

Let's  compare  Sirius,  the  brightest  star    visible  in  the  night  sky,  to  the  Sun.  

(-­‐1.5)  -­‐  (-­‐26.8)  =  -­‐2.5  log  bSirius  /  bSun  log  bSirius  /  bSun  =  -­‐10.1  bSirius  /  bSun  =  10

-­‐10.1  =  7.9  x  10-­‐11  bSirius  /  bSun  =  1/13,200,000,000.  Sirius  appears  13,200,000,000  %mes    fainter  than  the  Sun.  But  Sirius  is  actually  more  luminous  than    the  Sun.  It  is  just  much  more  distant.    

Apparent  magnitudes  of  some  familiar  objects  For  the  apparent  brightness,  we  usually  use  the  apparent  magnitude,  conven%onally  wriZen  as  m.    

5  magnitudes  =  100  

ABSOLUTE MAGNITUDE = APPARENT MAGNITUDE IF OBJECT WAS AT A DISTANCE OF 10 PARSECS

ONE PARSEC = DISTANCE AT WHICH 1 AU SUBTENDS AN ANGLE OF 1.0 ARCSEC

= 2 105 AU

AU - THE ASTRONOMICAL UNIT – IS THE MEAN DISTANCE OF THE EARTH FROM THE SUN

1.0 AU = 1.5 108 km ~ 500 light secs

1 PARSEC ~ 3.26 LIGHT YEARS

DOPPLER  SHIFT  

Non-­‐rela%vis%c  Doppler  shi^  (v  <<  c):  

                                                       ν    =    νo  +  Δν    =    νo  [1  -­‐    v/c]                      ν  =  frequency    

                                                       λ    =    λo  +  Δλ    =    λo  [1  +  v/c]                      λ  =  wavelength    

                                                                                                                                                                       v  =  radial  vel.  

Velocity distribution across rotating Sun

Rotation period of Sun = ~30 days = ~3 x 106 sec

Radius of Sun = 7 x 108 m

Vel of limb = ~1,500 m/sec = 1.5 km/sec

Vel range across the Sun 3 km/sec

Radial velocity measurement precision 1 m/s

Requires measurement precision of 1 part in 3,000 The spectrum of the Sun showing Fraunhofer absorption lines, primarily from hydrogen

Angular Resolution and Contrast Discrimination Requirements:

Direct Imaging of Planets:

Resolution:

At 10 pc (30 light years) Sun – Jupiter distance (5 AU) subtends 0.5 arcsec

HST resolution in the visible = ~0.04 arcsec so no problem?

Glare from star:

At visible wavelengths Sun – Jupiter L / LJ 108 to 109

At infrared wavelengths Better but L / LJ 103 to 104 but lower resolution

For Sun – Earth at 10 pc angular separation = 0.1 arcsec - a problem

For Sun – Earth at visible wavelengths L / LE 109 to 1010

at near infrared 105 to 106

NEED BETTER RESOLUTION AND HIGH CONTRAST IMAGING – Coronagraphs, adaptive optics, interferometry

For small angles sinθ = θ; First Null is at θ = λ/a radians

Plane wave incident on a slit Fraunhofer Diffraction Pattern

I(θ) = I0 [sin (πaθ/λ)/ (πaθ/λ)]2

HOW DO TELESCOPES WORK?

Intensity at the focal point as telescope scans a “point” source of light

Telescope resolution ~ λ/D radians

For circular apertures first null is at 1.22 λ/a

RESOLUTION = λ/D radians 1 rad = 2 105 arcsec

At optical wavelengths 10 cm diameter gives ~ 1 arcsec resolution

Hubble Space Telescope: 2.4 m aperture => 0.04 arcsec at 0.6 µm

Earth based telescopes: Atmospheric turbulence limits resolution to, at the very best “seeing”, about 0.25 arcsec, more normal good seeing about 0.5 arcsec.

Adaptive optics a partial solution

Achromatic lenses invented by Fraunhofer ~1815 – solved the problem

Lenses produce chromatic aberration: light of different wavelengths comes to focus at different points.

OPTICAL TELESCOPES

FUERTES OBSERVATORY

12 inch diameter refractor http://www.astro.cornell.edu/facilities/fuertes/index.php

Joseph van Fraunhofer 1787 - 1824

Fraunhofer Diffraction Patterns

Fraunhofer lines in the solar spectrum

Fraunhofer achromatic lenses

Resolution: The minimum angle at which two point sources of light (or radio waves) can be distinguished. Very close to λ/D

Field of View: Solid angle over which a telescope can focus an incoming plane wave – dependent on ratio of focal length to diameter – F/D ratio

Number of independent pixels over the field of view ≈ FOV x D2/λ2

e.g. FOV = 1 square degree; resolution = 1 arcsec

Number of pixels ≈ 107 ≈ # of pixels in a digital camera.

200 inch PALOMAR TELESCOPE

Equatorial mount

Japanese 8 m Subaru telescope on Mauna Kea, Hawaii showing Nasmyth focus

8 m diameter => 15 mas optical resolution no atmosphere

Gemini North 8 m telescope on Mauna Kea showing the Cassegrain focus.

Elevation – azimuth mount

8 m diameter => 15 mas optical resolution

no atmosphere

SEEING!

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

HUBBLE SPACE TELESCOPE

D = 2.4 m => resolution = 0.04 arcsec at λ = 0.5 µm

JAMES WEBB SPACE TELESCOPE

D = 6.5 m

Infra red

Optimized

0.6 to 28 m

Launch – 2014?

Planned Large Optical/IR Telescopes Expected 2015 to 2020

ELA – European Extremely Large Telescope 40 m diameter

Thirty meter telescope (TMT) Caltech/California/?? project

Large Synoptic Survey Telescope (LSST) 8.4 m diameter; 9.6 sq deg FOV

3,200 megapixel camera

PanSTARRS 1.8 m telescope

WIDE FIELD TELESCOPES

SPITZER INFRARED TELESCOPE

Diameter 0.85 m Camera at 3.6 µm, 4.5 µm, 5.8 µm and 8 µm Spectrometer at 5.3-14 µm (low resolution), 10-19.5 µm (high resolution), 14-40 µm (low resolution), and 19-37 µm (high resolution) Photometers at 24 µm, 70 µm, and 160 µm

RESOLUTION = λ/D radians 1 rad = 2 105 arcsec

At optical wavelengths 10 cm diameter gives ~ 1 arcsec resolution

Hubble Space Telescope: 2.4 m aperture => 0.04 arcsec at 0.5 µm

JWST (James Webb Space Telescope): 6 m aperture, Near - IR

at = 1 m, Resolution = 30 mas

30 meter telescope (ground based) => ~4 mas at 0.6 µm (ignoring atmos.)

DIRECT DETECTION need high resolution and very high contrast imaging

=> large telescopes + adaptive optics for telescopes on Earth

ASTROMETRY need as resolution => interferometry, probably space

Problem:

Earth’s Atmosphere:

Turbulent “blobs” of different refractive index (n ~ 1.0003 for air)

=> Different propagation velocities ( c/n )

=> Non-planar wavefronts at the telescope

i.e. The phase of the electromagnetic wave (light) across the telescope’s aperture is distorted destroying the diffraction pattern.

=> Resolution limit of ~0.5 arcsec independent of telescope size (and atmospheric conditions - seeing)

0.5 arcsec => blob (isoplanetic patch) size of about 20 cm at visible wavelengths => < 20 cm diameter telescope is “Diffraction Limited”.

Better at infra-red wavelengths: at 2 m isoplanetic patch size ~1 m so at 2 m a 1 m telescope is diffraction limited – i.e. can achieve resolution of /D

Effects of Atmospheric Turbulence on “Seeing” – i.e. telescope effective resolution

SOLUTION – ADAPTIVE OPTICS (AO)

Adaptive Optics Ref: Center for Adaptive Optics Wavefront

sensor

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”