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The Search for Earth-like Planets: Yes We Can Robert J. Vanderbei 2008 November 11 Princeton Alumni Association of Canada Toronto Chapter http://www.princeton.edu/∼rvdb The Big Questions: Then and Now Jan 1, 2000 Jan 1, 20?? Are We Alone? Indirect Detection Methods More than 300 planets found so far Wobble Methods Radial Velocity. For edge-on systems. Measure periodic doppler shift. Astrometry. Best for face-on systems. Measure circular wobble against background stars. First Discovery: 51 Pegasi b • Mayor and Queloz (1995) • Mag. 5.5 main sequence star • Detected by radial velocity method • Velocity difference: 70 m/s = 160 mph • Period: 4.2 days • Separation: 0.05 AU • Angular separation: 0.0035 arcseconds • Mass: > 0.47MJ • Hot Jupiter Notable Recent Discovery: Gliese 581c Possibly Terrestrial • Mag. 10.5 red dwarf • Detected by radial velocity method • Period: 13 days • Separation: 0.07 AU • Angular Separation: 0.012 arcseconds • Mass: > 5ME Transit Method • HD209458b confirmed both via RV and transit. • Period: 3.5 days • Separation: 0.045 AU (0.001 arcsecs) • Radius: 1.3RJ • Intensity Dip: ∼ 1.7% • Venus Dip = 0.01%, Jupiter Dip: 1% • Kepler and Corot Venus Transit (R.J. Vanderbei) Direct Detection Why It’s Hard Premise: If there is intelligent life “out there”, it probably is similar to life as we know it on Earth. • Bright Star/Faint Planet: In visible light, our Sun is ten billion times brighter than Earth. • Close to Each Other: A planet at 1 AU from a star at 33 light-years can appear at most 0.1 arcseconds in separation. (The full moon is 1800 arcseconds in diameter.) • Far from Us: There are less than 100 Sunlike stars within 10 parsecs. Can Ground-Based Telescopes Do It? • Atmospheric distortion limits resolution to about 1 arcsec. Note: Resolution refers to equally bright objects. If one is much brighter than the other, then it is more difficult. • Large aperture with adaptive optics. • Interferometry. No they can’t! Can Hubble Do It? Planet No it can’t! The problem is diffraction The Problem is Diffraction Requires an telescope with a mirror measured in kilometers to mitigate diffraction effects. Pupil Mask Image (PSF) linear -0.5 -20 -10 0 0 10 0.5 -0.5 0 0 0.5 Image (PSF) Cross Section 0 10 20 -20 -2 10 -10 -4 10 0 -6 10 10 -8 -20 -10 Image (PSF) log 10 10 20 -20 -10 0 10 20 20 -20 -10 0 10 20 Diffraction Control via Shaped Pupils Consider a telescope. Light enters the front of the telescope—the pupil plane. The telescope focuses the light passing through the pupil plane from a given direction at a certain point on the focal plane, say (0, 0). Focal plane Light cone Pupil plane However, a point source produces not a point image but an Airy pattern consisting of an Airy disk surrounded by a system of diffraction rings. These diffraction rings are too bright. The rings would completely hide the planet. By placing a mask over the pupil, one can control the shape and strength of the diffraction rings. The problem is to find an optimal shape so as to put a very deep null very close to the Airy disk. Diffraction Control via Shaped Pupils Consider a telescope. Light enters the front of the telescope—the pupil plane. The telescope focuses the light passing through the pupil plane from a given direction at a certain point on the focal plane, say (0, 0). Focal plane Light cone Pupil plane However, a point source produces not a point image but an Airy pattern consisting of an Airy disk surrounded by a system of diffraction rings. These diffraction rings are too bright. The rings would completely hide the planet. By placing a mask over the pupil, one can control the shape and strength of the diffraction rings. The problem is to find an optimal shape so as to put a very deep null very close to the Airy disk. The Spergel-Kasdin-Vanderbei Pupil Pupil Mask Image (PSF) linear -0.5 -20 -10 0 0 10 0.5 -0.5 0 0.5 20 -20 Image (PSF) Cross Section 0 -10 0 10 20 Image (PSF) log 10 -20 -10 -5 10 0 -10 10 10 -15 10 -20 -10 0 10 20 20 -20 -10 0 10 20 Shaped Pupil Coronagraph (TPF-C) 20 petals 150 petals Maybe We Can! Apodized Pupil Coronagraph (Unmanufacturable) Apodized pupil 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Image plane 0 -20 -40 -60 -80 -100 -120 -140 -160 -180 -60 -40 -20 0 20 40 60 Pupil Mapping (TPF-C) All above methods require optics of extraordinary quality: 1/10, 000 wave precision. Space-based Occulter (TPF-O) Telescope Aperture: 4m, Occulter Diameter: 50m, Occulter Distance: 72, 000km Plain External Occulter (Doesn’t Work!) -40 -30 -20 y in meters -10 0 10 20 30 40 -40 -30 -20 -10 0 x in meters 10 20 30 40 -30 -20 -10 0 x in meters 10 20 30 40 -40 -30 -20 y in meters -10 0 10 20 30 40 -40 Shaped Occulter -40 -30 -20 y in meters -10 0 10 20 30 40 -40 -30 -20 -10 0 x in meters 10 20 30 40 -30 -20 -10 0 x in meters 10 20 30 40 -40 -30 -20 y in meters -10 0 10 20 30 40 -40