Interferometric Imaging
With contributions from Image Credit: Michael Ireland, Stefan Kraus, LkCa 15 A+b: K. Teramura (UH/IfA) 2014 Sagan FrantzWorkshop, MartinachePasadena, CA, 2014, Ming July 22 Zhao Interferometric Imaging
Angular Resolution
D ⇥ ⇠ D Diffraction-limit
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Angular Resolution
D
B ⇥ ⇠ B Diffraction-limit
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Angular Resolution D
B ⇥ ⇠ B Diffraction-limit
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Optical View of Interferometry
D B Fringe Frequency 2 ⇥ = |E | B Primary Beam λ Δθ ≈ D ⌧ delay 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Van-Cittert-Zernike Theorem
Bproj Response for < E~1 E~2 > cos 2⇡ source · / at position δ
Response for arbitrary Bproj brightness ˜ = I ( ) cos(2⇡ )d distribution Iλ V Z B B FT(I( )) = ˜( proj )= I ( ) cos(2⇡ proj )d V Z Complex Visibility One Fourier Component of the Image
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
An Optical Fourier Transformer
Basics • The amplitude of fringe corresponds to Fourier amplitude of a single Fourier component of brightness distribution • The phase corresponds to the Fourier phase • You need amplitudes & phases for imaging Collect them all to win!
Normalized Visibility V Lipman Thesis 1998 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Examples of Visibilities: Binaries
Equal Brightness
Brightness Ratio 5:1
Increasing Binary Separation From the Michelson2014 Sagan Summer Workshop, Pasadena, School CA, 2014Notes July 22 2000 Interferometric Imaging
Star + Dust Shell
Fraction of Flux from dust shell
Size of (debris) disk
Fraction of Flux from Star
Baseline/wavelength Dullemond & Monnier 2010 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
The Atmosphere is a Problem
A Keck-sized patch of atmosphere during typical good seeing
Each contour is one radian of phase delay of 2-micron light
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Problem: Atmosphere Corrupts the Phase
??
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
The “Closure Phase” is Not Corrupted
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Important Properties of Closure Phases
• More robust to calibration error – Atmospheric turbulence generally does not bias measurement (unlike Visibility^2) – Reasonable hope of measurement error reducing as root N (unlike Visibility^2) – There can be biases due to chromatic effects (just like Visibility^2) and wavefront curvature over an aperture • Sensitive to asymmetries in brightness distribution
– Bispectrum REAL for point-symmetry (ΦCP = 0 or 180 degs) – Must resolve object to have significant signal (not photocenter!) – Critical for validating Vis^2 modeling – Necessary for imaging (if no phase referencing)
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Aperture Masking: Examples
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Aperture Masking: Examples
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Keck-I Telescope: 10-m Segmented Primary
“non-redundant” pattern
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Short Exposures and Power Spectra FFT
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Closure Phase is a Good Observable
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Basics of Interferometric Imaging • How much data do you need? – The number of filled pixels ~> number of independent visibility measurements (degrees of freedom argument) • Dynamic Range expected to be 1000:1 to 100:1 – From calibration errors mainly • What range of baselines? – Longest baselines set your highest resolution – Diffraction-limit of individual telescope (or shortest baseline) usually sets the maximum field-of-view of the interferometer • How can you get enough data with only a few telescopes? – Not usually problem for aperture masking – Not usually problem for simple objects, like star + planet
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Image Reconstruction using a “forward transform” with Regularization
“Imaging” can be thought as model-fitting to a grid of pixels values. With finite (u,v) coverage and with noisy data, there are an infinite number of images which will fit the data. So how do we choose? (use a forward transform method) Find “smoothest” image consistent with data (χ2~1) MEM uses the “entropy” S to parameterize the “smoothness.”
Fraction of flux in pixel i
Skilling & Bryan (1984) Entropy Image prior
Sum over all pixels
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Image Reconstruction using a “forward transform” with Regularization
“Imaging” can be thought as model-fitting to a grid of pixels values. With finite (u,v) coverage and with noisy data, there are an infinite number of images which will fit the data. So how do we choose? (use a forward transform method) Find “smoothest” image consistent with data (χ2~1) MEM uses the “entropy” S to parameterize the “smoothness.”
Fraction of flux in pixel i
Skilling & Bryan (1984) Entropy Image prior
Sum over all pixels
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Example from aperture masking data: WR 104
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
WR 104 MEM Reconstruction
Iterations 1 to 30
WR 104 (2.2 microns)
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
CHARA Georgia State University
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Infrared Imaging with CHARA
pre-eclipsepre-eclipse (<1 milliarcsecond resolution)EpsilonEpsilon AurigaeAurigae EclipseEclipse (CHARA-MIRC)(CHARA-MIRC) surfacesurface brightnessbrightness ε Aur Eclipse of 2009-20111.51.5 125%125% (CHARA/MIRC) 2008,2008, Pre-EclipsePre-Eclipse UT2009Nov03UT2009Nov03 UT2009Dec03UT2009Dec03 UT2010Feb18UT2010Feb18 1.01.0 100%100% 0.50.5 75%75%
0.00.0 50%50% -0.5-0.5 25%25% Milliarcseconds Milliarcseconds -1.0-1.0 0.250.25 AUAU -1.5-1.5 0%0% Kemp 1980 3 milliarcseconds 1.51.51.01.00.5Kloppenborg0.50.00.0-0.5-0.5 et al. 2010, Nature -1.0-1.0-1.5-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.5 2014MilliarcsecondsMilliarcseconds Sagan Workshop, Pasadena, CA, 2014 July 22 MilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcseconds Interferometric Imaging
Infrared Imaging with CHARA
pre-eclipse pre-eclipsepre-eclipse (<1 milliarcsecondEpsilon resolution)AurigaeEpsilonEpsilon Eclipse AurigaeAurigae (CHARA-MIRC) EclipseEclipse (CHARA-MIRC)(CHARA-MIRC)surface surfacesurface brightness brightnessbrightness 1.5 ε Aur Eclipse of 2009-20111.51.5 125% 125%125% 2008,(CHARA/MIRC) Pre-Eclipse 2008,UT2009Nov032008, Pre-EclipsePre-Eclipse UT2009Nov03UT2009Dec03UT2009Nov03 UT2009Dec03UT2010Feb18UT2009Dec03 UT2010Feb18UT2010Feb18 1.0 1.01.0 100% 100%100% 0.5 0.50.5 75% 75%75%
0.0 0.00.0 50% 50%50% -0.5 -0.5-0.5 25% 25%25% Milliarcseconds -1.0 0.25 AU Milliarcseconds Milliarcseconds -1.0-1.0 0.250.25 AUAU -1.5 -1.5-1.5 0% 0%0% Kemp 1980 3 milliarcseconds 1.51.00.50.0-0.5-1.0-1.51.51.51.01.00.50.5Kloppenborg0.00.0-0.5-0.5-0.5 et al. 2010, Nature -1.0-1.0-1.5-1.5-1.51.51.51.51.01.01.00.50.50.50.00.00.0-0.5-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.51.01.01.00.50.50.50.00.00.0-0.5-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.5 Milliarcseconds 2014MilliarcsecondsMilliarcseconds Sagan Workshop, Pasadena, CA, 2014 July 22 MilliarcsecondsMilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcseconds Interferometric Imaging
Infrared Imaging with CHARA
pre-eclipse pre-eclipse pre-eclipsepre-eclipse Epsilon Aurigae(<1 milliarcsecondEpsilon Eclipse resolution)Aurigae (CHARA-MIRC)EpsilonEpsilon Eclipse AurigaeAurigae (CHARA-MIRC) EclipseEclipsesurface (CHARA-MIRC)(CHARA-MIRC)surface surfacesurface brightness brightness brightnessbrightness 1.5 1.5 ε Aur Eclipse of 2009-20111.51.5 125% 125% 125%125% 2008, Pre-Eclipse UT2009Nov032008,(CHARA/MIRC) Pre-Eclipse 2008,UT2009Dec03UT2009Nov032008, Pre-EclipsePre-Eclipse UT2009Nov03UT2010Feb18UT2009Dec03UT2009Nov03 UT2009Dec03UT2010Feb18UT2009Dec03 UT2010Feb18UT2010Feb18 1.0 1.0 1.01.0 100% 100% 100%100% 0.5 0.5 0.50.5 75% 75% 75%75%
0.0 0.0 0.00.0 50% 50% 50%50% -0.5 -0.5 -0.5-0.5 25% 25% 25%25% Milliarcseconds -1.0 0.25 AU Milliarcseconds -1.0 0.25 AU Milliarcseconds Milliarcseconds -1.0-1.0 0.250.25 AUAU -1.5 -1.5 -1.5-1.5 0% 0% 0%0% Kemp 1980 3 milliarcseconds 1.51.00.50.0-0.5-1.0-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.51.51.51.51.01.01.00.50.50.5Kloppenborg0.00.00.0-0.5-0.5-0.5 et al. 2010, Nature -1.0-1.0-1.0-1.5-1.5-1.5-1.51.51.51.51.01.01.01.00.50.50.50.50.00.00.0-0.5-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.51.01.01.00.50.50.50.00.00.0-0.5-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.5 Milliarcseconds MilliarcsecondsMilliarcseconds 2014MilliarcsecondsMilliarcsecondsMilliarcseconds Sagan Workshop, Pasadena, CA, 2014 July 22 MilliarcsecondsMilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcseconds Interferometric Imaging
Infrared Imaging with CHARA
pre-eclipse pre-eclipse pre-eclipse pre-eclipsepre-eclipse Epsilon AurigaeEpsilon Eclipse Aurigae(<1 (CHARA-MIRC) milliarcsecondEpsilon Eclipse resolution)Aurigae (CHARA-MIRC)EpsilonEpsilon Eclipse surfaceAurigaeAurigae (CHARA-MIRC) EclipseEclipsesurface (CHARA-MIRC)(CHARA-MIRC)surface surfacesurface brightness brightness brightness brightnessbrightness 1.5 1.5 1.5 ε Aur Eclipse of 2009-20111.51.5 125% 125% 125% 125%125% 2008, Pre-Eclipse UT2009Nov032008, Pre-Eclipse UT2009Dec03UT2009Nov032008,(CHARA/MIRC) Pre-Eclipse 2008,UT2010Feb18UT2009Dec03UT2009Nov032008, Pre-EclipsePre-Eclipse UT2009Nov03UT2010Feb18UT2009Dec03UT2009Nov03 UT2009Dec03UT2010Feb18UT2009Dec03 UT2010Feb18UT2010Feb18 1.0 1.0 1.0 1.01.0 100% 100% 100% 100%100% 0.5 0.5 0.5 0.50.5 75% 75% 75% 75%75%
0.0 0.0 0.0 0.00.0 50% 50% 50% 50%50% -0.5 -0.5 -0.5 -0.5-0.5 25% 25% 25% 25%25% Milliarcseconds -1.0 0.25 AU Milliarcseconds -1.0 0.25 AU Milliarcseconds -1.0 0.25 AU Milliarcseconds Milliarcseconds -1.0-1.0 0.250.25 AUAU -1.5 -1.5 -1.5 -1.5-1.5 0% 0% 0% 0%0% Kemp 1980 3 milliarcseconds 1.51.00.50.0-0.5-1.0-1.51.51.00.50.0-0.5-1.0-1.51.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.51.01.01.01.00.50.50.50.5Kloppenborg0.00.00.0-0.5-0.5-0.5-0.5 et al. 2010, Nature -1.0-1.0-1.0-1.5-1.5-1.5-1.51.51.51.51.01.01.01.00.50.50.50.50.00.00.0-0.5-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.51.01.01.00.50.50.50.00.00.0-0.5-0.5-0.5-1.0-1.0-1.0-1.5-1.5-1.51.51.51.01.00.50.50.00.0-0.5-0.5-1.0-1.0-1.5-1.5 Milliarcseconds Milliarcseconds MilliarcsecondsMilliarcseconds 2014MilliarcsecondsMilliarcsecondsMilliarcseconds Sagan Workshop, Pasadena, CA, 2014 July 22 MilliarcsecondsMilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcsecondsMilliarcseconds MilliarcsecondsMilliarcseconds Interferometric Imaging
Facilities Overview • Non-redundant aperture masking (not complete!) – Keck (NIRC2, segment tilting) – Subaru – VLT (NACO, VIZIR) – Magellan (MagAO) – Gemini (TRECS, GPI) – Palomar (PHARO) – LBT/I – JWST • Long-baseline optical/IR interferometry – Recently shutdown: Keck, IOTA, GI2T, ISI, Palomar Testbed – CHARA (visible/NIR) – VLTI (NIR/MIR) – NPOI (visible) – SUSI (visible) 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Non-Redundant Aperture Masking Directly Detecting Planets Around Sun-like Stars Wide companions: Latest results (Ireland et al 2011, Kraus et al in prep) show Contrast = ~7 mags 1RXS1609 b that these >100AU low- or 500:1 mass companions are much more common than wide brown dwarfs.
Disk Fragmentation Product? Really Planets? Lafreniere et al (2008,2010) 30 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Resolution is Key • Young planets are relatively bright, but unfortunately very few young stars closer than ~150pc:
• 10 AU = 70 mas at 140 pc. ~1 M¤ ~ R=12 • Probing these key separations requires the biggest telescope and the highest angular resolution, highest contrast technique.
Credit: M. Bessell 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
AO images taken with same settings have subtle AO Imaging differences
Example: Contrast Curves for Gemini Planet Imager (1 minute exposures, H band)
~30AU at Taurus/140pc
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Aperture Mask Interferometry
Placing an aperture mask in the pupil plane filters atmospheric turbulence on scales larger than the subapertures Adaptive optics system still used to allow long integrations 100:1 brightness contrast requires 1/100 radian precision è 0.6 degs (example here: Palomar/PHARO) PHARO data from Lloyd/Ireland 2014 Sagan Workshop, Pasadena, CA, 2014 July 22
Interferometric Imaging
Aperture-Masking Target LkCa15
• LkCa 15 has a mass of 1.03 +/- 0.05 M¤ from CO line dynamics (mm interferometry). • Taurus star-forming region. Well-studied at 2-3 Myr age.
• d~150 pc; M*=1 M¤; Mdisk=55 Mjup • A transition disk with an imaged hole in scattered and emitted light… Kraus & Ireland 2012
34 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Multicolor Image Reconstruction Submm; Andrews et al. in prep
(.Deprojected radius ~20 AU)
Andrews et al. (2011) Reconstructed Multicolor Image SMA, Sub-mm Image Blue=K’, Red=L’ Dusty Outer Disk Planet + Co-orbital material? Kraus & Ireland 2012 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Closure Phase signal can be ambiguous
Interpretation of marginally-resolved, low-SNR structures can be difficult
Case of T Cha (Olofsson et al 2013; Huelamo et al. 2011)
Companion model Disk model
Olofsson et al. 2013; Huelamo et al. 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 2011 Interferometric Imaging
Multi-wavelength data sometimes indicates complexity! V1247 Ori
H band
K band
➜ Not consistent with companion scenario nor symmetric disk L band ➜ Complex density structures in the gap region, possibly due to dynamical interaction with gap-opening planets Kraus et al. 2013 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Better than closure phases? The Kernel Phase Martinache 2010 Ireland 2013
non- Φj = Φ0j + 1 Δφ redundant
Φ = ΦO + A.φ
full jΣi Δφi aperture Φj = Φ0j + Arg(e )
with good AO system, Φ = Φ0 + A × φ the phase can be linearized… measured unknown known unknown 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Better than closure phases? The Kernel Phase Martinache 2010 Ireland 2013
non- New Method not generally Φj = Φ0j + 1 Δφ redundant applicable yet: Successfully applied to Φ = ΦO + A.φ archival HST/NICMOS data: full jΣi Δφi aperture Pope et al, 2013Φ j = Φ0j + Arg(e )
with good AO system, Φ = Φ0 + A × φ the phase can be linearized… measured unknown known unknown 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
NRM or Kernel Phases??
Poor Strehls: Aperture-Masking Wins
NGAO or L/M bands: Kernel-phase wins Credit: Ireland 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Credit: NASA 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Best Candidates for CHARA/MIRC
• υ And b Models from Burrows et al. 2005 – H=2.96 – K=2.86 • τ Boo b – H=3.55 – K=3.51 • 51 Peg b – H=4.23 – K=3.91
flux ratio < 10e-4 : 1 Precision requirement: < 0.04o in general Zhao et al. 2011 More difficult than NRM detections to date 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
AfterDrifts az /elseen corrections… in Raw data
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Upper limits of υ And b
Ratio ~ 6x10e-4
Contrast: ~ 1700:1
(90% confidence level)
Zhao et al. 2011 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
VLTI/AMBER Study of β Pictoris
- A5V-type star
- a 9 MJ planet at 300mas
First modest experiment: Ratio ~3.5x 10e-3 Contrast limit ~ 300:1
Absil et al. 2010 2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
Potential targets H<7mag if method can be perfected…
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging
PrecisionO. Absil et al.: Circumstellar material Visibilities in the Vega inner system 239
Absil et al 2006,2013
Fig. 1. Fit of a uniform stellar disk model to the E2–W2 data. The qual- Fig. 2. The data obtained with the S1–S2 baseline ( 34 m) are displayed ity of the• fit is satisfactoryNear-IR (reduced χdebris2 of 1.29), with small disks residuals that discoveredas a function of the projected using baseline’s positionspecial angle∼ together with the do not display any obvious trend except for a small underestimation of best UD fit computed over the whole data set (3.217 mas). The data the actual data for baselines between 140 and 150 m. points are significantly below the best UD fit, with a mean visibility combiners using single-modedeficit ∆V2 2%. Thefibers addition of a uniform diffuse source of emission in the FLUOR# field-of-view reconciles the best fit with the data (dotted between all calibrators and stable night after night to line). Note that there is no obvious dependence of the data points with around 85%. Data– 13 that share of a42 calibrator target are affected with by a com-~1%respect K-band to position angle,excess.. which would beOdd.. indicative of an asymmetric mon systematic error due to the uncertainty of the a priori an- extended emission. gular diameter• Mid-IR of this calibrator. nulling In order to interpretfor exozodiacal our data dust properly, we used a specific formalism (Perrin 2003) tailored to propagate these correlations into the model fitting process. All observed in the residuals of the fit obtained with a simple limb- diameters are derived– Keck-I from the visibility (Millan-Gabet data points using a fullet al.darkened 2013) disk (LD) and stellar model.LBTI (see later talk model of the FLUOR instrument including the spectral band- Note that fitting an LD stellar model to our data would only width effects (Kervellaby etDenis al. 2003). Defrere) marginally2014 improve Sagan the Workshop, fit (see TablePasadena, 3), asCA, the 2014 shape July of22 the first-lobe visibility curve is not very sensitive to limb darken- ing. Moreover, the actual limb-darkening parameter may be sig- 3. Data analysis nificantly larger than standard tabulated values because Vega is 3.1. Stellar diameter suspected to be a fast rotating star viewed nearly pole-on and the equatorial darkening may bias the limb profile (Gulliver et al. The measurements obtained with the long E2–W2 baseline 1994; Peterson et al. 2004). Complementary observations to our are particularly appropriate foraprecisediameterdetermina- data set, obtained by Aufdenberg et al. (2006) at 250 m base- tion, because they provide good spatial frequency coverage of lines, confirm this fact and lead to an accurate estimation∼ of the the end of the first lobe of the visibility curve (see Fig. 1). K-band limb profile, which mostly affects visibilities beyond the Previous interferometric measurements obtained in the visible first null and will not be discussed here. by Hanbury Brown et al. (1974) and Mozurkewich et al. (2003) were used to derive uniform disk (UD) diameters θ = 3.08 UD ± 0.07 (λ = 440 nm) and θUD = 3.15 0.03 (λ = 800 nm) re- 3.2. Visibility deficit at short baselines spectively. In the K band, where the limb-darkening± effect is not With this precise diameter estimation, we can now have a look at as strong, Ciardi et al. (2001) estimated the UD diameter to be the short-baseline data. In fact, these points do not significantly θ = 3.24 0.01 mas. We have fitted a uniform stellar disk UD contribute to the UD fit because of the low spatial frequencies model to our± E2–W2 data, assuming that Vega’s photospheric they sample. Including all the data points in the fitting procedure intensity I(φ, λ)equalsthePlanckfunctionwithaneffective tem- gives a best-fit diameter θ = 3.217 0.013 mas, but with perature of 9550 K for all angles φ.Thebest-fitdiameterisθ = UD UD apoorχ2 = 3.36. We show the reason for± this poor reduced χ2 3.218 0.005 mas for an effective wavelength of 2.118 µm, r in Fig. 2, where the S1–S2 data points are plotted as a function which± significantly revises the previously obtained estimates1. of position angle together with the best UD fit (solid line). The The quality of the fit is quite good (χ2 = 1.29). Unlike in the r observations are consistently below the fit, with a ∆V2 = 1.88 PTI data of Ciardi et al. (2001), we do not see any obvioustrend 0.34%. ± in the residuals of the fit, except for three points at projected baselines between 140 and 150 m which are slightly above the Systematic errors in the estimation of the calibrator diam- fit (by 1.5σ). In fact, Fig. 3 not only shows a significant dis- eters or limb-darkened profiles are possible sources of bias in crepancy∼ between the CHARA/FLUOR and the PTI data, but interferometric observations. In order to explain the measured also between the 1999 and 2000 PTI data. Our observations do visibility deficit in the S1–S2 data, the diameters of the three not support the scenario of Ciardi et al. (2001), who proposed short-baseline calibrators (Table 2) should have been underes- auniformdustringwitha3 6% integrated flux relative to the timated by 0.26, 0.35 and 0.33 mas respectively, which repre- Vega photosphere in K band− to account for the trend that they sent about 10 times the estimated error on their diameters. We have made sure that such improbable errors were not present 1 The K-band diameter proposed by Ciardi et al. (2001) was com- in our calibration procedure by cross-calibrating the three cali- puted with the assumption of a flat spectrum for the Vega intensity. This brators. No significant departure from the expected LD diame- explains a large part of the discrepancy with our new value. ters was measured, and the calibrated visibilities of Vega do not Interferometric Imaging
Precision Astrometry for Exoplanets detection
Sun Motion as seen from 10 pc
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Colavita 2005 (MSS)
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 No. 6, 2010 THE PHASES DIFFERENTIAL ASTROMETRY DATA ARCHIVE. V. 1661
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Recent astrometry successes 10 10
0 0 10 100 1000 10000 10 100 1000 10000 Period (days) Period (days) Figure 1. Periodograms of the F statistic comparing models with and without tertiary companions to HD 176051 (HR 7162) in astrometric-only models. The left § Hubble Fine Guidance Sensors figure is for analysis only using the PHASES data, while the right is for combined analysis of PHASES and non-PHASES astrometric measurements. For HD 176051 the 1% FAP isCandidate at z 8.37 for the PHASES-only substellar analysis, and z 11.33 for the combined analysis, as indicated by horizontal lines. -- interferometer measures companion= for HD176051= Table 4 Orbit Model for HD 176051 motion at sub-milliarcsecond 0.4 Parameter Value Uncertainty
PA B (days) 22430 15 precision (Benedict et al) − TA B (MHJD) 41384 23 − eA B 0.2667 0.0022 0.2 − aA B (arcsec) 1.2756 0.0023 − iA B (deg) 114.159 0.078 − ωA B (deg) 281.71 0.26 § PHASES experiment on Palomar − ΩA B (deg) 48.846 0.093 0 − PBa Bb (days) 1016 40 − Testbed Interferometer TBa Bb (MHJD) 53583 39 − eBa Bb 0 (Fixed) − -- Limited to binary stars aCOL (µas) 241 41 -0.2 iBa Bb (deg) 115.8 8.2 − 167 Degree Projection (mas) ωBa Bb (deg) 0 (Fixed) − <0.5” (Muterspaugh et al) ΩBa Bb,1 (deg) 69 11 χ 2 and− dof 1015.3 772 -0.4 See Monnier poster this meeting Note. Best-fit orbital elements in the Campbell basis for HD 176051, with 1σ uncertainties. for proposed A-star (exoplanet survey 52925 53290 53655 54020 54385 54750 t (MJD) Using CHARA/MIRC one of the easiest and most reliable PHASES targets to observe. Figure 2. TimeMuterspaugh series of PHASES observations et al. of HD2010abcd 176051 (HR 7162) As a result, 98 PHASES measurements were successfully taken for the 1016 day subsystem orbital solution, measured along an axis at angle of HD 221673. Despite there being large amounts of data 167◦ from2014 increasing Sagan differential Workshop, right ascensionPasadena, through CA, increasing 2014 July differential 22 declination; it was along this axis that the PHASES measurements are typically available, single Keplerian orbit fitting was frustrated from most sensitive. For clarity, only measurements with uncertainties along this axis the early beginnings—the data show much more scatter than of 100 µas along this axis are shown. predicted by the measurement uncertainties. The initial PHASES-only search for companions found a most significant peak of z 32.9ataperiodof1276days possibly containing a variable star based on the scatter in the dif- (k 9) with FAP 0.0%. This= low value inspired a revised search ferential magnitude measurements by various observers. How- including= both the PHASES and lower-precision non-PHASES ever, Hipparcos photometry shows a scatter of only 6 mmag. astrometric observations to investigate whether the detection The revised Hipparcos-based parallax is 5.94 0.45 mas (van continued to be valid. The revised search finds a most significant Leeuwen 2007). This parallax and the best-fit± single Keplerian peak of z 95.9 at a period of 1435 days (k 8, within one model predict an average stellar mass of 2 M .Itslongorbital sample of= the peak value for the PHASES-only= search) with period ( 800 years) implies a large range of" orbits in which FAP 0.0%. The periodograms are plotted in Figure 3. companions∼ can be stable—up to 47 years according to the cri- Afewsingle-componentRVmeasurementsof72Peghave teria of HW99. Thus, binary dynamics are expected to have a been published by Tokovinin & Smekhov (2002)andAbtetal. smaller impact on planet formation in this system than others. (1980). However, the relatively small number and short time HD 221673 is extremely bright at infrared wavelengths coverage of each RV data set reduces any impact they have on (K 1.76), is observable for long stretches during the late constraining either the binary orbit or confirming the existence summer= /fall months of best weather at Palomar, and served as of additional components (especially low-mass, long-period Interferometric Imaging What’s next? Non-redundant Masking (& Kernel Phase) • Transitional disks w/ GPI & SPHERE. Contrast limits 10x deeper • Faint companion search for high-mass stars. RV surveys say that 3-5 Msun stars can host 5-20 MJup planets! • SM fiber pupil remapping. See poster FIRST instrument (E. Huby) • JWST for all young stars. Contrasts of >10 mags at M band, yielding true Jupiter-mass planets in the nearest star-forming regions.
Source: Lafreniere and JWST Aperture Masking Team
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging What’s next? Long-baseline (IR) interferometery • Hot Jupiter detections. New instruments on CHARA/VLTI • Debris and Zodical Dust. LBTI nulling experiment (see Defrere talk) • YSO disks. Not discussed here.. EARLIEST stages of planet formation. Much progress in NIR, MIR: CHARA, VLTI/PIONIER, VLTI/ MATISSE.. Complex structures seen… • Astrometry. Major progress now possible for binary systems • Planning for future facility…. Big leap is needed to image young giant planets in nearby star-forming regions at sub- AU scale
2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Interferometric Imaging Planet Formation Imager Concept planetformationimager.org
Thermal IR imaging interferometer 2 au with <1 milliarcsecond resolution to 14 mas resolve giant planet formation processes down to the scale of circumplanetary accretion disks
0.3 au 2 mas 10 au Credit: Kraus et al. 2014, simulations from 70 mas Ayliffe, Bate, Dong, Whitney & Zhu2014 Sagan Workshop, Pasadena, CA, 2014 July 22 Figure 3. Mosaic of hydrodynamics simulations of a protoplanetary disk with four embedded planets (background), the gap that is opened by one of the planets (top-left panel), and of the circumplanetary accretion disk (bottom-left panel), illustrating the need to probe a wide range of spatial scales in order to study the mechanisms that are at work during planet formation. The background image is the 10 µm model image of the four-planet simulation by Dong, Whitney & Zhu described in Sect. 4.2, while the insets show surface density profiles from simulations by Ayli↵e&Bate.? Besides the physical scales (in au) we give the angular scale on the sky for a distance of 140pc (in mas), which corresponds to the distance of the most nearby star forming regions (e.g. Taurus).
4.4 Exoplanetary System Architecture Planet population synthesis models aim to reproduce the observed exoplanet system populations by linking planet formation models with models about the dynamical processes of planet-disk interaction, planet-planet interaction, dust evolution, and accretion physics. These models depend on a proper knowledge of the relevant processes and on the adjustment of a large number of free parameters, which introduces major uncertainties. PFI will change the situation fundamentally, both by providing robust information about the initial conditions of planet formation and by probing the protoplanet distribution during the evolutionary phase that is most critical for shaping the architecture of exoplanetary systems, namely the first 100 Myr. Observing planetary systems during this time interval will allow PFI to determine where in the disk planets⇠ form and how they migrate through interaction with the gas-rich disk, providing insights into the mechanisms that halt migration, for instance at deadzones, disk truncation points, or during the disk dissipation phase (typically at 10 Myr). ⇠ Achieving this goal will require detecting planets in a statistically meaningful sample of systems at di↵erent evolutionary phases, e.g. of the order of 100 systems in the classical T Tauri/Herbig Ae/Be phase ( 0.5Myr), transitional disk ( 5 Myr), and early debris disk phase ( 50 Myr). These observations will allow us to⇠ construct planet population⇠ diagrams for these di↵erent evolutionary⇠ phases and to compare them with the population diagrams for mature exoplanet systems. Based on state-of-the-art population synthesis models we expect dra- matic changes during these phases, such as the inward-migration of the Hot Jupiters during the first 1-2 Myr and the ejection of planets due to dynamical instabilities (e.g. Raymond et al.?). Another important objective of PFI will be to determine the location of the “snow line” for important molecules like water (H2O), marking the location where these molecules condense to form ice grains. At the Interferometric Imaging
Summary • Interferometry comes in handy when you need: – High Angular Resolution – Precision Calibration / High Dynamic Range • In general, one sacrifices sensitivity for these advantages • NRM (w/ AO) is superior to adaptive optics alone for finding faint “companions” within a few L/D <~ 200mas – Requires sophisticated error analysis – Kernel phase w/extreme AO will increase sensitivity soon • Long-baseline interferometry challenging, but some successes: – Hot Jupiter “near-”detections – Near-IR debris disk & mid-IR Zodiacal dust detections – Exoplanet discovery via astrometry (for close binaries) 2014 Sagan Workshop, Pasadena, CA, 2014 July 22