Introduction to exoplanetology Lesson #6: Direct exoplanet detection methods (1/2) Olivier Absil absil@astro.ulg.ac.be
Outline I. Direct detection: why and how? II. High contrast imaging from the ground III. High contrast imaging from space IV. Main results from high-contrast imaging V. Stellar interferometry
I. Direct detection Why and how?
Why direct detection? Characterization of planetary atmospheres Needs spectroscopy on actual planetary photons isolate planet from star
Why direct detection? Access non-transiting planets Opens up a wide range of separations (beyond a few 0.1 AU) Complementary with transit spectroscopy Transits mostly here
Why direct detection? Get full orbital solution 3D orbit > direct, model-independent access to the planet mass Study dynamics of planetary systems, interactions with dust disks, etc.
Challenge #1: contrast Visible: reflected light Infrared: thermal (blackbody-type) emission
Challenge #2: angular separation 1 AU @ 10 pc = 0.1 arcsec Theoretically within reach of 10-m class telescope But watch out for turbulence!
Challenge summary A firefly close to a lighthouse 1000 miles away! (note: the star never turns off)
Technique #1: imaging Diffraction in circular aperture Airy pattern Angular resolution = size of Airy disk: θ = 1.22 λ/d Rayleigh criterion λ = 2 µm, D = 10 m θ = 0.05" (50 mas) = 1 AU at 20 pc Extended pattern noise!
The Airy pattern : aperture radius θ = 1.22 λ/d
Technique #2: interferometry Two separated telescopes fringes B Angular resolution set by baseline (B): θ = 0.5 λ/b Crests of 1st packet fall on troughs of 2nd packet λ = 2 µm, B = 100 m θ = 2 mas
The fringe pattern unresolved binary resolved binary (fringe packets offset for clarity)
II. High contrast imaging from the ground
Atmospheric windows V I J H K L M N
Imaging through the Earth atmosphere Temperature variations Distorted wavefront Short exposure: speckles Long exposure: wide PSF Short exposure Long exposure
Loss of angular resolution Fried parameter r 0 : diameter of a circular area over which the rms wavefront aberration due to passage through the atmosphere is equal to 1 radian La Palma r 0 ~ 10 cm at good astronomy site Same resolution as 10 cm telescope! D = 5 cm 10 cm 60 cm 1.2 m
Atmospheric turbulence Wavelength dependence: r 0 λ 6/5 10 cm @ 500 nm 50 cm @ 2 µm 4 m @ 10 µm Seeing = FWHM of long exposure image Equal to 0.98 λ / r 0 1" seeing for r 0 = 10 cm @ 500 nm Varies slowly with wavelength (λ 1/5 )
Atmospheric turbulence Coherence time: t 0 = 0.31 r 0 / v wind Valid under Taylor s «frozen turbulence» hypothesis t 0 3 msec for r 0 = 10 cm and v wind = 10 m/s Isoplanatic angle: θ 0 = 0.31 r 0 / h θ 0 1.3" for r 0 = 10 cm and h = 5 km Stars separated by θ 0 have different short-exposure PSFs
Correction needed! Adaptive optics
Adaptive optics
Wavefront sensing Shack-Hartmann wave front sensor
Strehl ratio S = exp(iφ) 2 exp( σ φ2 ) φ = wavefront phase σ φ = rms phase on pupil Quantifies image quality peak intensity ratio wrt perfect image Perfect image S = 1 D = r 0 S = 0.36
AO correction MACAO on VLT 50% 20%
Detection in speckle noise? ESO-3.6m/ComeOn+ (1994) S=0.21 Speckles Planet
Getting rid of speckles 1. Observing strategies
Solution: PSF subtraction aka Reference-star Differential Imaging (RDI) β Pic Observe a reference star Similar to science target Scale its PSF (flux) α Pic Subtract it from science observation β Pic α Pic
Limitations of RDI No perfect reference star Should be of same magnitude, color and position as science target Time spent on reference star is «lost» (no planetary photon) Atmospheric conditions change with time Telescope/instrument aberrations also change with time Quasi-static speckles, can mimic planetary signal
Four differential solutions Keep observing the same target (no reference star) Tune an observing parameter to discriminate between stellar PSF and planet Spectral differential imaging (SDI) Spectral deconvolution (SD) Angular differential imaging (ADI) Polarimetric differential imaging (PDI)
Spectral differential imaging
SDI in practice λ1 λ2 λ3 λ1 λ2 (λ1 λ2) k(λ1 λ3)
Pros and cons of SDI + Detection down to diffraction limit (1 λ/d) Companion needs strong molecular absorption (e.g., methane) Differential aberrations between the three wavelength optical paths Narrow filters lower sensitivity
Spectral deconvolution Integral Field Spectrograph (IFS) Provides field image as function of wavelength («image cube») Diffraction and speckle pattern scale as function of wavelength Pattern moves out from star with increasing wavelength Exoplanet position is fixed Can be distinguished from speckles
SD in practice Similar principle as SDI, on much wider wavelength band Observed (x,λ) slice Rescaled (x,λ) slice
Pros and cons of SD + Works with any type of planet (no specific feature) + No differential aberrations / simultaneous observations + Does not rely on specific feature in planet spectrum + End product = spectrum of the planet! Detect and characterize planet at the same time Speckle pattern not perfectly constant over wavelength Limited inner and outer working angles (depend on wavelength range and spectral resolution)
Angular differential imaging Use field rotation while keeping telescope fixed Usually done by switching off derotator Planet moves around star as a function of parallactic angle Quasi-static speckles stay at fixed position
ADI in practice
Pros and cons of ADI + Works with any type of planet (no specific feature) + Does not require specific hardware Does not work well for stars far from zenith (small variation of the parallactic angle) Limited inner working angle (planet must move by more than 1 λ/d in the field for ADI to work) Speckle pattern evolves with time
Speckle decorrelation t0 t0 + 10 min (t0 + 10 min) t0 t0 + 100 min (t0 + 100 min) t0
Polarimetric differential imaging Reflected light from planet is partially polarized Typically 10% polarisation Star produces unpolarized light Can be exploited by polarimetric imager
PDI in practice Fig. 1. Processed images of HD 142527 (top row) and HD 161743 (bottom row) in H band. From left to right: intensity image (I) in logarithmic
Pros and cons of PDI + Speckle subtraction can be very good + No limitation in inner or outer working angle Small fraction of planet light is polarized low sensitivity Works only in reflected light (best in visible range) Requires specific, non-standard hardware
Getting rid of speckles 2. Image processing
The LOCI algorithm Locally Optimized Combination of Images Goal: make best use of a set of reference images Can be used with various observing techniques Solve a linear system to minimize residuals to be minimized pixels target PSF coefficients to be determined ref PSF individual frames
LOCI working with ADI
Practical use of LOCI To be applied locally because correlation between frames expected to depend on position Optimize LOCI coefficient on «optimization» zone Perform PSF subtraction on «subtraction» zone Optim. zone > subtr. zone to avoid planet signal subtraction
Pros and cons of LOCI Several free parameters + Can be fine tuned to any particular data set Not very straightforward to use Strong self-subtraction of planetary signal LOCI tries to remove everything bias on photometry Can be evaluated with fake companions, or mitigated by introducing even more parameters (masking) CPU intensive
Principal Component Analysis (PCA) Method to reduce the number of variables needed to describe a data set Build an orthogonal basis on which to decompose the images Truncated basis to perform PSF subtraction
How PCA works Subtract mean (M) from data set (D): A = D M Calculate covariance matrix: C = AA T Calculate eigenvectors (Q) and eigenvalues CQ = QΛ, with Λ a diagonal matrix of eigenvalues Choose first K components in Q Q K Project data onto these components F = Q K A new data set of reduced dimensions
PCA with a stack of images Use the women s face to compute orthogonal basis Project man s face on first 50 coefficients and add Describe man s face with 50 coefficient instead of thousands of pixels
Practical use of PCA
Pros and cons of PCA + Can be applied to whole image at once + CPU time can be drastically reduced! In practice, annulus-wise version is generally better Self-subtraction reduced, but still present + Reduced bias wrt LOCI, generally more linear Fake companion injection still used in most cases + Forward modeling also possible
A «real-life» example HR 8799
2008: ADI detection Contrast ~ 14 mag (~10 6 )
4 th planet with ADI+LOCI
2010: long slit spectroscopy Figure 2. Image with the HR 8799 c spectrum before extraction. The spatial direction along the star planet axis is vertical. The spectral direction is horizontal, with wavelength increasing from left to right. ANSON ET AL. Vol. 710 15% 400 s, taken nt. A plied 799 c re 1). re an on of c and his is tions. ound ation were l sky. dures ected ringe e flat Since on on to be aging speco this ectrorame on of Figure 4. into three (circles, d dash-dotte No. 1, 2010 SPECTROSCOPY OF HR 8799 c Figure 2. Image with the HR 8799 c spectrum before extraction. The spatial direction along the star planet axis is vertical. The spectral direction is horizontal, with wavelength increasing from left to right. L37 Figure 3. Upper panel: spectrum of HR 8799 c. The dashed lines and faintly shaded area (light blue in the online version) denote the errors. Lower panel: log g = detailed that non Non-equ large dif particula presence 4 µm fo Fortney (2008) t being pr behavio of whet thereby The r planet de ing purp narrowe since it models. true also in the sp 8.66 ma 9.50 ma and is ex In the
2011: HK band IFS
2013: full IFS study with SD
Getting rid of speckles 3. Hardware solutions
Coronagraphy
Coronagraphy
With central obscuration
Phase mask coronagraph Proposed by Roddier (1997) Apply 180 phase shift to PSF center Ideal mask size = 43% of 1st Airy ring Very chromatic design
Four Quadrant Phase Mask
Beyond the FQPM Quadrants octants continuous phase ramp
Vortex phase mask Continuous phase ramp from 0 to 4π Main problem: chromaticity of the phase ramp
Achromatic phase mask? Sub-wavelength gratings achromatic half wave plate Fig. 3. 4QZOG implementation: s and p are the vectorial complex Annular Groove Phase Mask (AGPM)
The AGPM performance 1000" Peak%rejec)on% 100" 10" 1" août(10" nov.(10" févr.(11" juin(11" sept.(11" déc.(11" avr.(12" juil.(12" oct.(12"
On-sky example Raw image Post-processed (ADI+PCA)
Sensitivity to planets β Pic b
Apodization «Pupil plane coronagraphy» Act on amplitude or phase of wavefront in pupil Redistribute the intensity in the focal plane to make it more compact or create a dark region
Amplitude apodization Goal: reduce PSF side lobes Degraded angular resolution
Apodized coronagraph Apodization makes PSF more compact on the focal plane mask
Shaped pupils
Microdot mask How it s done
Phase apodization Act on wavefront phase instead of amplitude Can produce asymmetric PSF APP: Apodizing Phase Plate
On-sky example
Phase-induced amplitude apodization
Other hardware solutions Low-order wavefront sensing Performed at instrument level (science camera, unexploited stellar light, etc) Corrects for non-common path errors between AO and instrument Speckle nulling Measure the complex amplitude of quasi static speckles and correct with deformable mirror
Tree of life
All steps in one picture Telescope pointed (i) (i) (i) (i)(i) AO turned on (ii) (ii) (ii) Speckle calibration Centered on mask (ii)(ii) (iii) (iii) (iii) (iii) (iii) ADI + postprocessing b" b" b"b"b" c" c" Project Project 1640 1640 Project Project Project1640 1640 1640 c"c"c" Toward Toward Exploration Exploration of Other of Other Worlds Worlds Toward Exploration of Other Worlds Toward Toward Exploration Exploration of of Other Other Worlds Worlds e" e" d" d" e"e"e" d"d"d" N" N" N" N" N" E" (iv) (iv) (iv) (iv) (iv) (v) (v) (v) (v)(v) E"E"E" 0.5 " 0.5 " 0.5 " E" 0.5 "0.5 "