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M. Shao, JPL/CaltechJuly 2009, Shanghai

Measuring the Orbits of Exoplanets with Direct Imaging and Astrometry

Synergy, Competition, the role of Inner working Angle

© 2008 California Institute of Technology. Government sponsorship acknowledged.

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Outline

• Discovering Earths outside our solar system- What’s an Earth? It’s more than 1 dot in a sea of speckles

- A habitable planet is 1~10 Mearth in the habitable zone (0.7~1.4AU)

• Astrometric Detection of Exo-Earths

• Direct imaging of exoplanets, - The importance of the inner working angle (IWA)

- 1st detection,

- orbit determination (the importance of multiple repeated observations)

- Multiple planets and initial false alarms

• Combining astrometry and direct detection

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Exo-Earths, Habitable Planets

• Habitable planets are between 0.5~10 Mearth, in the habitable zone, 0.7~1.4 AU, scaled to sqrt(luminosity).

HabitableTerrestrial Planetsoccupy a small fraction of the total phase space

Synthetic planet populationfrom Ida, Lin

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Most of the Year Spent in the Habitable Zone

An Exo-Earth’s orbit doesn’t have to be circular. But high eccentricity orbits can create huge temperature swings on the surface. Often, direct detection mission assume that the planet is in a circular orbit. But outside of Hot Jupiters/Neptunes there isn’t a strong preference for low eccentricity orbits.

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Finding an Earth Clone

• A major goal for space based exoplanet missions is the discovery of an Earth Clone, followed by spectroscopy of the light from the planet to identify potential signs of biological activity, (eg Oxygen in the atmosphere).- The discovery of an Earth clone that with oxygen in its atmosphere

would be a major milestone in exoplanet reasearch.• However if the discovery has a 40% or 75% probability of being a

false alarm, this would not be a major discovery.

• What’s an Earth clone- The mass of the planet is between 0.5~10 Mearth- The orbit of the planet is in the habitable zone of the stars

• Only astrometry (of the star) from space can measure the mass of the planet.

• Astrometry, and direct imaging, or both can measure the orbit of the planet.- This talk discusses how these two approaches compare (compete and

complement) each other.

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Astrometric Detection of ExoPlanets

• Measure the reflex motion of the star around the planetary system’s center of mass.

Astrometry has no sin(i) ambiguity.

Measures all 6 orbital parameters, plus mass

Solar system inner planets, 10pc(motion of star over 5 years)

Micro Arcsec

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Astrometry Looks for Periodic Motions of the Star

0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

freq cycles/yr

perio

dogr

am p

ower

periodogram of residual

One instanceEarth

Venus

1% FAP

Periodogram of astrometric data will show peaks at frequencies that correspond to1/orbital period.

In general, multiple planets with different orbital periods will produce separate, isolated peaks.

Peaks in the periodogram will appear not just from planets, but from noise in the data.

If we want the false alarm from noise to be < 1%, we must set a detection threshold equal to a planet whose astrometric signature is SNR > ~6.

SNR = amplitude_of_motion/ (1 /sqrt(N))1 is the single epoch rms errorN is the number of epochs

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Planetary Orbits from Direct Imaging

• The orbital motion of the planet around a star has 6 parameters. Measuring the motion of the planet tells us the mass of the star, but not the mass of the planet.

• The orbit can be measured with 3 images at widely separated epochs- In a multiplanet system, there could be a confusion issue (which dot in the

image is what planet), in this case 4 images, are needed to derive the orbit and confirm that all 4 images are of the same planet.

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2 3

4?

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Limitations in Direct Imaging IWA, Inner Working Angle

• When we observe a planet whose maximum star-planet separation (Rmax) is 1.4X larger than the IWA, will be observable ~1/3 of the time.

• On average 4 images of the planet will need ~12 attempts to image the planet.

• All direct detection missiosn have an IWA, closest angular separation where 10-10 contrast can be achieved. (50~70 mas for “Large” Coronagraphs and large external occulters)

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Number of Potential Targets vs IWA

Max star-planet sep > IWA*1.2

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103

100

101

102

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Inner Working Angle milliarcsec

# t

arg

et

sta

rs# target stars versus IWA < 30pc Contrast > 6e-11,

4x1.1m DAViNCI and 8m telescope with 2λ/D Coronagraph

4m telescope with 2λ/D Coronagraph

# Stars ~ IWA-3

2m telescope with 2λ/D Coronagraph

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The Number of Targets ~ IWA-3

• When IWA/Rmax ~0.9, ~20 visits are needed get 4 images of the planet.

• Changing the IWA by 20% changes the number of targets by 73%

• There is a significant difference in the number of targets for Rmax>IWA versus Rmax>1.2*IWA

• # visits needed to image a planet at 4 epochs is ~4/1st visit completeness (shown at right as a function of IWA/Rmax)

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Multiplanet Confusion

• Planet ID/orbit (important, but not widely recognized need)- An image of a exo-planetary system might show several dots. Which

planet is which?

• Planetary Identification is solid if we have the planet’s orbit.

DAViNCILooking at Earth @10pc

•A planet’s brightness can vary by a factor of 3~4 through its observable orbit.

•Two images taken a few months apart•One planet may have move inside IWA.•The planet may be 3X brighter or dimmer than before.

•Which dot is which planet is not a trivial question in a multiple planet system

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Multiplanet Confusion II

• If we only have a single image, many planets that are NOT terrestrial planets in the Habitable zone may seem to be T-HZ planets.- There are many possibilities of planets outside the HZ, or outside the mass

range of Exo-Earths, whose brightness and angular distance from the star could lead to an Initial False Positive (IFP)

- Quite often, IFP’s can’t be identified until an orbit is measured. (eg 4 images of the planet in ~12 attempts to image it.)• One might have to spend significant time, imaging the planets of stars that

don’t have Earth-Clones becaues of IFP’s• The multiplanet confusion problem is most acute for TPF mission

concepts that have a limited number targetting opportunities. (External occulters, ~120 visits)

Earth Clone

1.5 Re @1.5AU 2 Re @2AU, or 3Re @3AU …

Neptune @2AUbut near 180 phase angle “new moon”

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• Next few slides

• Combined Astrometry and Direct Imaging- What are potential advantages?

• For internal coronagraphs 70~100% more targets (1.2*IWA)

• For external coronagraphs.

- Example of a Design Ref Mission for external coronagraph.

• Assume star has 1 Earth-HZ or no planet versus # IFP is ~4 times the number of Earths.

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Combined Astrometry and Imaging

• At the limit of detection (1% FAP, SNR~6) the astrometric oribt has a 1 sigma error of- ~3% in oribtal radius, period

- ~0.2 radian in orbital phase at mid-epoch (of astrometric data set)

• ~1 radian oribtal phase error ~5 years after mid-epoch

- Mass unceratinty ~25% or 0.25 Mearth for a 1 Earth mass planet in mid-HZ

- For more massive planets , or planets with larger astrometric signatures, the orbital phase error will decrase linearly with higher SNR.

• Planets can not hid from astrometry.- If an exo-Earth exists , it will be found,.

- If no Earth-like planet is found, it doesn’t exist.

• Astrometry can tell follow on direct imaging mission “where” to look (which stars to search), but with a ~1 radian orbital phase uncertainty it only helps marginally on “When” to look.

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How Can Astrometry Help Direct Imaging?

• Summary- We start with the assumption that a “Measurement” of the orbit is a

necessary step to claiming a planet is in the habitable zone.

- For internal coronagraphs, the advantage is the ability to find planets at R_max ~ IWA instead of R_max ~1.2* IWA.

• A 20% change in IWA may seem like a small advantage, but the ability to find planets 20% closer to the star means that an increase in the number of targets by >~70%.

- For external coronagraphs, where the number of epochs a target can be observed is highly limited, astrometry can play an “enabling” role. In the presence of multiple initial false positives, astrometry is essential to limit the number of targets searched.

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Joint Astrometric/Direct Detection

• Ultimately we want a orbit of an exo-Earth with sufficient precision to pinpoint “when” a direct detection mission should image and measure the spectra of the exo-Earth.

• We compare a “direct detection only approach” to a combined astrometry + direct detection approach.

• Case 1, R_max ~1.4*IWA, 1st visit ~33% prob. of detection.- 4 images of an exo-Earth is needed to measure and verify the orbit.

- ~12 images of the star-system is needed to obtain 4 images of an exo-Earth.

• Case 1, Astrometry + Direct detection, 1st visit probability increased slightly to ~50% from 33%.- The major uncertainty in the orbit is the orbital phase. An astrometric orbit

with just 1 direct image of an exo-Earth, 5 years after the astrometric data set will reduce the orbital phase uncertainty by a factor of 10. (To account for false positives, we ideally want to to directly image an exo-Earth twice, the first to increase orbital phase precision, the 2nd to verify the 1st direct image was not a false positive. (Need images at ~4~5 epochs)

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Comparison of an Observing program different assumptions

• Two different sets of assumptions, start with 10% stars have Earth-clones.

• A star has 1 Earth or no planets

• Take 1 image of 100 target stars.

• 10% of stars have Earths, 33% of planets are observeable on 1st visit

• 3 Earths imaged

• Follow up on 3 earths to get orbits. 9 additional images for each 3 1st detections. (27 more images)

• Density of planets in/out of HZ is roughly the same, density of planets is roughly constant in log(M).

• Initial false alarms ~4X larger than exo-Earths.

• 100 images of 100 stars.

• 12 images of potential Earths, 80% false alarm

• Follow up 9 images per potential exo-Earth ~108 additional images

• If limited to ~120 visits, most likely 0 confirmed orbits

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Direct Imaging Observing Program with Astrometric Precursor

• Two different cases, internal vs external occulters

• Internal coronagraphs don’t have a hard limit on the number of visits.

• One advantage is a ~20% reduction in IWA. Expand # targets by ~70%.

• A 2nd advantage is a reduction in the number of images needed to get an orbit.

• Search 100 stars, 1200 images vs . ~50 images

• At 1 day/image 4yrs vs 2 months.

• External Coronagraphs, limited to ~120 visits.

• If astrometry identifies the 10 stars out of 100 that have Exo-Earths, and each of those 10 needs ~5 images to verify an orbit, then ~5~60 images would be needed.

• Difference is orbits of 10 exo-Earths vs 0~1 without an astrometric precursor. (followed by spectra)

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Summary• Discovery of an Earth clone outside the solar is the holy grail

of exoplanet research.- Extraordinary claims require extraordinary evidence. 80% false alarm

probability is not sufficient.

- The mass of the planet has to be measured, not “guessed” to be between 1~10 Mearth.

- The planet’s orbit has to be measured, not “guessed” to be in the habitable zone.

• A direct imaging search for exo-Earths can not ignore the problem of “Initial false positives”. - With a single image, many planets that are not terrestrial or not in the

habitable zone, can be initial false positives.

• Obtaining orbits w/o astrometry will take up to ~4 years of integration longer than with astrometry, for internal coronagraphs vs 2~3 months.

• For external coronagraphs, measuring orbits is not viable without an astrometric precursor.

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