Chapter 6 – Transit PHY6795O – Chapitres Choisis en Astrophysique Naines Brunes et Exoplanètes

Chapter 6 – Transit

PHY6795O – Chapitres Choisis en Astrophysique

Naines Brunes et Exoplanètes

6. Transit 2

Contents

6.1 Introduction 6.2 Transit searches 6.3 Noise limits 6.4 Transit light curves 6.5 Transmission and emission spectroscopy 6.6 Properties of transiting planets 6.7 Future projects 6.8 Summary

PHY6795O – Naines brunes et Exoplanètes

3

6.1 Introduction Principle

Photometric method consisting of measuring the host star flux variation due to the planet primary and secondary eclipses.

Most prolific detection method. Provide an estimate of the planet radius/temperature through

primary/secondary eclipse. Powerful technique for atmosphere characterization. For a solar type star, transit depth ΔF/F is ~10-2 (10 mmag) for

a Jupiter, ~10-4 for an Earth. Detection much easier on small (M) stars (R★~0.1-0.5 R)

PHY6795O – Naines brunes et Exoplanètes 6. Transit

6. Transit 4

Contents

6.1 Introduction 6.2 Transit searches 6.3 Noise limits 6.4 Transit Light curves 6.5 Transmission and emission spectroscopy 6.6 Properties of transiting planets 6.7 Future projects 6.8 Summary


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Kreidberg et al. 2014

6.2 Transit searches (1) Ground-based surveys can easily reveal giants but space is

generally required for detecting Earths and super-Earths. First mention of this technique (along with radial velocity) by

Struve (1952). Observing strategy is to monitor tens of thousands of

relatively brights stars (V<13) over weeks or months if not years (e.g. Kepler) Transit probability is typically 1%.

Data processing Automatic field recognition matches to reference catalogues (e.g. 2 MASS),

providing an astrometric solution to a few arcsec. Differential aperture photometry + ‘’detrending’’, i.e. correction of non-

Gaussian noise (e.g. ramp effect on HST).


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6.2 Transit searches (2) Candidate identification

Searches typically adopt a box-least squares algortithm (Kovacs et al. 2002) with coarse search grid to identify epoch, depth and duration of strongest signals.

Search refined using analytical transit profile models. False positives

• Eclipsing binaries w/o background stars. Equal mass grazing binaries. Binaries including giant stars are excluded based on their reduced proper motion H which is correlated with the absolute magnitude.

Given an estimate of the stellar mass and radius, planet radius and impact parameter are then derived from light curve models.

Candidate confirmation Most promissing candidates subjected to radial velocity follow-up measurements

• Small RV amplitude combined with transit signature imply i~90 °• A few RV measurements required to exclude double- and single-lined

binaries.• A few tens of RV measurements typically required to confirm a single planet.


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6.2 Transit searches (3) Host star parameters determined from RV observations,

more generally from high resolution spectroscopy. Teff and log g derived from diagnostic lines such as Hα, Na I D and

Mg I Then M★ and R★ from stellar evolutionary models.

Planet parameters estimated combined χ2 fit to the light curve and RV measurements. Details depend on eccentricity and adopted limb darkening model.

Exoplanet transit data bases NASA/IPAC/NExScI Star and Exoplanet Database

• www.nsted.ipac.caltech.edu Exoplanet Transit Database of the Czech Astronomical Society

(ETD)• www.var.astro.cz/ETD

Amateur Exoplanet Archive (AXA)• www.brucegary.net/AXA/x.htm


http://www.var.astro.cz/ETD

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6.2 Transit searches (4) Large-field searches from the ground

The Hungarian Automated Telescope (HAT/HATNet) Hat north is six Cannon 11 cm cameras, 2kx2k CCD, all controlled and

automated with a single Linux computer. Precision of 3-10 mmag at I~8-11 29 discoveries as of March 2015.

OGLE (Optical Gravitational Lensing Experiment) 1.3m telescope also used for micro-lensing. 8 detections by the transit method so far out of 17.

Trans-Atlantic Exoplanet Survey (TrES) Three 0.1m wide-field (6°) telescopes. Emphasis on bright stars. Five planets discovered so far.

Wide-Angle Search for Planets (WASP/SuperWASP) Two-wide field cameras: La Palma (Canary Islands) and Sutherland (S.

Africa) Each telescope uses 8 2kx2k CCDs with FOV of 15°x20° (RA, Dec) 65 planets discovered so far.


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XO Two 0.1m telescopes on Haleakala (Maui; Hawaii). Equipment similar to TrES. Drift scan mode. 5 discoveries so far.

MEarth Eight 0.4m automated telescopes at Mt Hopkins. In operation since January

2008. Sample of 2000 nearby M dwarfs with masses between 0.1 and 0.35 M. Sensitive to Earth-size planets. One (spectacular) detection of a super-Earth: a 6.5 ME around GJ1214 (13 pc;

Charbonneau et al. 2009).

Radial velocity discoveries Planets first discovered by RV then detected in transit. Ex: HD189733b (P=2.219 d, MP=1.15 MJ) with large transit depth (3%). Prime

target for atmospheric studies. Long-period planets found by small telescopes and amateur participation. Ex:

111d period of HD80606b (MP=4 MJ, e=0.93). First transit detected through secondary eclipse from SPITZER at 8 μm. (Laughlin et al 2009). Prediction of primary eclipse on 14 February 2009 confirmed by three independent groups.


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Searches in open clusters Advantage of sampling host stars of known age. Disadvantage: relatively few bright stars available. No detection so far.

Globular clusters Central core of 47 Tuc surveyed in a 8-d observation by HST. No candidate

found. Ground-based observations of outer region of 47 Tuc (22 000 stars over 33

nights) and for ω Cen (31 000 over 25 nights). No detection. Based on known planet frequency, more than 20 might have been detected

in the combined (core and halo) surveys of 47 Tuc. Planets in dense core with a=1 AU should survive disruptions by stellar

encounters. Should be stable despite several close stellar encounters. Null results likely suggest that planet formation has a significant

dependency on metallicity.


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6.2 Transit searches (7) Large-field searches from space

Space avoids limitations imposed by variable atmospheric extinction (~0.1%) and scintillation (0.01%).

Enable long uninterrupted observations. CoRoT

Led by CNES (France). Launched on 2006 December 27th. Two science missions: transit and asteroseismology. 0.27m telescope on polar orbit, 4 2kx2k CCDs. Long (150 d)

continuous observations towards Galactic center and anti-center. 12 000 target stars in transit mode. Photometric precision of ~700 ppm at R=15 28 detections so far including the super-Earth CoRoT-7b (P=0.853

d, MP= 4.8 ME)• Follow-up RV measurements have enveilled another (non-transiting) planets.


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6.2 Transit searches (7) Large-field searches from space

Kepler Launched on 2009 March 6 on Earth-trailing heliocentric orbit. 0.95 Schmidt telescope, 42 2kx1k CCD , 115 sq degrees. 150 000 main sequence stars (8-15) in Cygnus region, monitored

continuously over 3.5 years, four measurements per hour.• Mission lasted nearly six years.

All stars with K<14.5 were characterized before launch. Main mission was to determine ηEarth , the fraction of stars with a planet

in the habitable zone. Goal partly achieved. Very successful mission:

• 1000 confirmed planets• 3600 candidates• 2165 eclipsing binaries• Most typical planets are super-Earths

K2 (Kepler extension) Mission extension with two reaction wheels + Sun radiation pressure. Enables a 83d continuous monitoring on the ecliptic.


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6.2 Transit searches (8) Kepler FOV and photometric accuracy


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6.2 Transit searches (9)


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6.2 Transit searches (10) Follow-up observations from space

Hubble Space Telescope Observations mostly in spectroscopic mode Recent observations with WFC3 enables spectroscopy at R~70

between 1.4 an 1.7 μm with an accuracy of 20-30 ppm in spatial scanning mode, performance very close to the photon noise limit (as good as it can get).

• e.g. transit spectroscopy of GJ1214b (Kreidberg et al. 2014).

Spitzer Space Telescope 0.85 IR telescope launched in 2003 Three instruments: the IRAC camera operating at 3.6, 4.5, 5.8 and 8 μm, the IRS

spectrograph (5.3-37μm) and the MIPS camera (24, 70 and 160 μm). First detection of light from an exoplanet: HD208458b (Deming et al. 2005). Exoplanet studies is a significant scientific legacy of Spitzer even though the

mission was not designed for such science programs!

Hipparcos ~100 photometric measurements between 1990-93 for 118 000 stars Enabled posteriori measurements of known transits, e.g. to improved the orbital

period (e.g. HD209458b and HD189733).


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6.2 Transit searches (11) Follow-up observations from space

MOST (Microvariability and Oscillations of Stars) Canadian-built. 0.15m telescope launched in 2003. Allows 60d continuous observations between dec of -19 and +36. Asterosesimology main science mission. Important upper limits on the albedo of HD209458b. Detection of a few transiting systems (e.g. 55 Cancri e)


6. Transit 17

Contents

6.1 Introduction 6.2 Transit searches 6.3 Noise limits 6.4 Transit light curves 6.5 Transmission and emission spectroscopy 6.6 Properties of transiting planets6.7 Future projects 6.8 Summary


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6.3 Noise limits (1) Limitations from space

Stellar surface structures (star spots, plages, granulation and non-radial oscillations)

• Strong functions of spectral type.• Same limitations for RV and astrometry.

For Kepler, at V=12, 10 min sampling, smallest detectable planetary radii for 4.5 Gyr old G2, K0 and K5 stars, given a total of 3 or 4 transits, were found to: 1.5, 1.0 and 0.8 RE.

Limitations from the ground For nearby, relatively bright stars and moderate telescope apertures,

contribution from photon noise is generally negligible. Main limitations are:

• Atmospheric transparency variations• Atmospheric scintillation noise• Detector “granularity” (intra-pixel sensitivity).

– Can be corrected with high-precision autoguiding and/or defocussing the telescope to spread light over several pixels.

Accuracy limited to a few mmag over relevant integration times.• Ground-based telescopes limited to transit depths up to about 1%.


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6.3 Noise limits (2) Conjugate-plane photometry to improve scintillation noise

(Osborn et al. 2011)


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6.3 Noise limits (3) Conjugate-plane photometry to improve scintillation noise

(Osborn et al. 2011)


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6.3 Noise limits (4) Reduction of scintillation noise by a factor of ten possible with

conjugate-plane photometry to improve scintillation noise


6. Transit 22

Contents

6.1 Introduction 6.2 Transit searches 6.3 Noise limits 6.4 Transit light curves 6.5 Transmission and emission spectroscopy 6.6 Properties of transiting planets6.7 Future projects 6.8 Summary


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6.4 Transit light curves (1) There are four observables that characterize the

duration and profile of the primary transit: the period P, the transit depth ΔF, the time interval between 1st and 4th contact tT , and the time interval between 2nd and 3rd contact tF..


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6.4 Transit light curves (2) Three geometrical equations describing the light curve

Transit probability


(6.5)

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6.4 Transit light curves (3) Simplified expression for tT (circular orbit)


(6.4)

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6.4 Transit light curves (4) Theoretical light curves - limb darkening

Limb darkening refers to the drop of intensity in a stellar image moving from the centre to its limb. Intensity is represented by functions of μ=cos θ, where θ is the angle between the normal to the stellar surface and the line of sight to the observer.

Limb darkening depends on spectral type and wavelength (weak in the red)

Limb darkening law

The linear (c1=c3=c4=0) or

the quadratic (c1=c3=0) form is

usually a good approximation.


(6.6)

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6.4 Transit light curves (5) Theoretical light curves - limb darkening


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6.4 Transit light curves (6) Light curve fitting

Light curve equation (for small RP)

Three parameters to fit (e.g. MCMC methods) : RP/R★

a/R★

b=a cos i/R★ (impact parameter)


(6.9)

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6.4 Transit light curves (7) Physical parameters derived from the light curve

Assumption of circular orbit, no limb darkening and no contamination from background (blended) sources. Equations 6.1-6.3 can be rewritten as


(6.13)

(6.14)

(6.15)

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Invoking Kepler’s third law

an expression for the stellar density ρ★ star can be derived from equation 6.15, assuming MP<<M★,

A unique solution can be imposed on the dimensionless ratios by invoking the stellar mass-radius relation


(6.16)

(6.17)

(6.18)

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where k is a constant, distinct for main sequence or giants, and x is the corresponding power law. The five physical parameters R★, M★, i, a and RP can be derived,


(6.19)

(6.23)

(6.20)

(6.21)

(6.22)

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Physical parameters derived from the light curve

Estimate of the stellar density allows a discrimination between dwarfs (ρ★~1 g/cm3) and giants (ρ★~0.1-0.01 g/cm3).

If M★ and R★ are assumed known from the spectral type, then the problem is over-constrained, and Equation 6.26 can be re-arranged to give an expression of the orbital period, even if only a single transit is observed.

P can be derived this way to 15-20% if δt < 5 min and photometric accuracy is < 0.0025 mag.

6.4 Transit light curves (10)


(6.26)

(6.27)

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Reflected light A planet of radius RP at distance a from the star intercepts a fraction

(RP /2a)2 of the stellar luminosity. For RP << R★ << a, the planet/star flux ratio, ε, can be written

where p(λ) is the geometrical albedo, the ratio of brightness at zero phase (seen from the star) to that of a fully reflecting, diffusively scattering (Lambertian) flat disk with the same cross-section. For a Lambert sphere, p(λ)=2/3. The phase function g(α) is

where α is the angle between star and observer subtended at the planet, i the orbit inclination and ϕ is the orbital phase, with ϕ=0 at the time of radial velocity maximum.



(6.38)

(6.39)

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Secondary eclipse Total light just before the time of the secondary eclipse is the sum

of the stellar flux and that of the planet. The difference corresponds to the flux of the planet’s day-side region. During the secondary eclipse, the total light is that of the star alone.

Infrared photometry of the secondary eclipse provides an estimate of the planetary temperature. In the Rayleigh-Jeans limit ( ), the depth of the secondary eclipse is

For RP=1 RJ, R★ =1 R and planet/star planet temperatures of 1500 K and 6000 K, .

Probability of an observable secondary eclipse depends on the orbital parameters, and particular eccentricity and argument of pericenter.



(6.41)

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Rossiter-McLaughlin effect As the planet transits, the radial velocity signal is slightly altered

as a small positive or negative anomaly in the radial velocity curve, caused by the progressive occultation of the rotating stellar disk.

Provides information on the star’s spin axis orientation with respect to the planet’s orbital plane.



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Rossiter-McLaughlin effect The maximum amplitude of the anomaly is

where v sin i★ is the projected stellar equatorial rotation velocity. For a Sun-like star, v sin i★ ~ 2 km/s, and the maximum size of the effect is around 20 m/s for a Jupiter-like planet, and around 0.2 m/s for an Earth.

Spectroscopic monitoring of ΔV tracks the planet’s trajectory referred to the sky-projected stellar rotation axis.

Relevance to formation and migration. Close-in giants explained by migration. Disk migration acting alone

may largely preserve the initial spin-orbit alignment. Planet-planet scattering or Kozai migration would produce at least

occasionally large misalignments.



(6.42)

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Rossiter-McLaughlin effect6.4 Transit light curves (15)


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Transit timing variations The time of the transit event and its duration can be affected

by several factors: gravitational bodies, including other planets and/or satellites Tidal forces Relativistic precession Apparent effects due to changes in geometrical projection (proper

motion and parallax) as viewed by the observer.



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Transit timing variations – Kepler 9b/9c



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Transit timing variations - satellite For a circular satellite orbit, the displacement of the

planet with respect to the planet-satellite barycentre is

where as and Ms are the satellite’s semi-major axis and mass. For circular co-planar orbits, the peak-to-peak difference between the mid-transit point for the planet and system barycentre is then

Ex: a 1 ME orbiting HD209458b at a maximum distance of the Hill radius, RH, the amplitude of the timing excursion about the mean orbital phase is 13s, comparable to the present standard error on the central time of a single transit with Kepler. PESTO @ OMM will have a timing resolution of ~0.1s !



(6.54)

(6.55)

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Transit timing variations – parallax and space motion For an exoplanet orbit coplanar with that of the Earth-Sun

system, observers at the two extremes of the Earth’s orbit would register a given transit event displaced in time by

Am: mean orbital radius (1 AU)

P: orbital period of the Earthd★: distance to the star

P=400d, d★= 10 pc, Δt~5 sec.



(6.57)

6. Transit 42

Contents



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Introduction Both transit and secondary eclipse probe an exoplanet’s atmosphere. In both situations, observations are made in the combined light of the

star-planet system. Conditions in the planetary atmosphere are deduced from the

differences in flux as the planet moves in front/behind the star. Both measurements at the limit of what can be achieved from the

ground.

6.5 Transmission and emission spectroscopy (1)


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Introduction The planet-star contrast varies significantly from the optical

(10-5-10-6) to the mid-infrared (10-3-10-4). Optical-mid-infrared features several molecular bands of H20,

CO, CO2 and CH4.



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Transmission spectroscopy Transmission spectroscopy probes the other regions of the

atmosphere. The area of the planetary atmosphere intercepted is

approximately an annulus of radial dimension ~5H where H is the scale height

with μm is the mean molecular weight, T the atmosphere temperature, gp the planet surface gravity, and k the Boltzman’s constant.



(6.58)

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Transmission spectroscopy The fractional contribution of the transmission signal, δ, is given by

the ratio of the annular to stellar areas

δ depends on wavelength through the mean molecular weight, related to the chemical composition of the atmosphere.

It it relatively difficult to detect atmosheric features characterized by a high mean molecular weight.

δ can also be written in terms of the planet density ρp:

with



(6.59)

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Expected transmission signal for various exoplanets



Host NameTp

(K)ρ

(g/cm3)R ★

(R)δ

(ppm)

H2-richm=2

H2O-richm=18

Earthm=29

Hot Jupiters/NeptunesG0V HD209458b 1130 0.37 1.14 700 - -M3V GJ436b 700 1.5 0.42 800 - -

Super EarthsM4V GJ1214b 600 2 0.2 2300 250 160

K1V HD97658b 800 3.4 0.7 150 20 10

EarthsM3V TESS-xxx 600 5.5 0.2 - 95 60M3V TESS-xxx 300 5.5 0.2 - 50 30

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Emission spectroscopy – secondary eclipse Provides a measure of the planet’s thermal emission and associated

spectral features. Emission spectrum contains information about the atmosphere’s

temperature and gradient. Absorption lines indicate a temperature profile decreasing with height. An isothermal profile would produce a featureless emission spectrum.



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Emission spectroscopy – secondary eclipse The equilibrium temperature of the planet is related to the star

temperature by

where T★ is the stellar effective temperature, R★ the stellar radius, a the semi-major axis of the planet and AB is the Bond albedo. AB is the fraction of bolometric flux (integrated over all wavelengths) scattered by the planet. Typical albedos (geometric and Bond) for Jupiter and gas giants: 0.3-0.5. Appears to be very small for Hot Jupiters. Ex: HD209458b; AB < 4%.

The factor f describes the effectiveness of atmospheric circulation, and the degree to which the energy absorbed is transferred from the planet’s day to night sides. f=1 means a perfect heat redistribution (uniform temperature between

night and day sides). f=2 means no circulation. Night-side remains cold.



(6.60)

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Observations – HD209458b

Host star: V=7.7, G0V (M★=1.01 M) at 47 pc.

Planet’s properties: MP=0.69 MJ, RP=1.35 RJ, P=3.5d. Most intensively observed transiting planets Large transit depth (2%). Density, surface gravity and escape velocity (43 km/s) indicate

that the planet is stable against disruption by tidal forces, thermal evaporation or mass stripping by the stellar wind.

Na, CO, H2O, VO, TiO and CH4 detected it its atmosphere. Evidence for clouds. Temperature inversion resulting from high-altitude absorbers.



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Observations – HD189733b Host star: V=7.7, K0V (M★=0.8 M) at 19 pc.

Planet’s properties: MP=1.13 MJ, RP=1.14 RJ, P=2.2d Another intensively observed transiting planet. Large transit depth (2.5%). Day-side temperature mapped by Spitzer



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Observations – Wasp-43b (Stevenson et al. 2014)



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Observations – Wasp-43b (Stevenson et al. 2014)



6. Transit 58

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Mass-Radius relation (as of 2010)

6.6 Properties of transiting planets (1)


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Mass-Radius relation (as of 2015)



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Mass-Radius relation for stars and planet



n ~3 for low-mass stars with large radiative cores.

n=3/2 for fully convective stars (<0.4 M)

Objects below H-burning minimum mass supported by electron degeneray

n~1 for M~ MJ

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Kepler’s results



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Kepler’s results



6. Transit 64

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6.7 Future projects – TESS


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6.7 Future projects – JWST


2018

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NIRCam FGS/NIRISS

MIRI NIRSpec

Four science instrument all with observing capabilities to perform transit spectroscopy

2018

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JWST for transit/eclipse spectroscopy



HST

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FGS/NIRSS overview

2018

Two instruments in one box provided by CSA FGS (Fine Guidance Sensor)

Provides fine guiding to the observatory 0.6-5 μm IR camera. No filters, single optical train with

two redundant detectors each with a FOV of 2.3’x2.3’• Noise equivalent angle (one axis): 4 milliarcsec• 95% sky coverage down to JAB=19.5

NIRISS (Near-Infrared Imager and Slitless Spectrograph)

0.6-5 μm IR camera.Four observing modes Main science drivers

• First Light: high-z galaxies• Exoplanet detection and characterization

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NIRISS Single Object Slitless Spectroscopy (SOSS) mode

2018

Specifically optimized for transit spectroscopy Broad simultaneous wavelength range: 0.6-2.8 um Spectral resolution: 700 @ 1.2 um Grism with built-in defocussing weak lens to increase

dynamic range and minimize systematic ‘’red noise’’ due to undersampling and flatfield errors. Similar capability to HST’s scanning mode

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Harware implementation

2018

20 pixels

Monochromatic PSF measured in the lab

λ

Kreidberg et al, 2014

HST data. ~30 ppm noise level, within ~10% of the photon noise limit !

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NIRISS will miss very few Earth/Super-Earths found by TESS

2018

Figure courtesy of George Ricker (TESS PI)

NIRISS Saturation limit

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NIRISS transit spectroscopy simulations – Hot Jupiter

2018

Noise level: 25 – 100 ppm Model courtesy of J. Fortney

JWST/NIRISS, HD189733 (K1V) J=6.0, 2.7 hrs (1 transit)Efficiency: 33%

HST

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NIRISS simulations – Water rich super-Earth

2018

Noise level: 25 – 100 ppm Model courtesy of J. Fortney

JWST/NIRISS, GJ1214 (M4.5V) J=9.8, 8.4 hrs (3 transits)Efficiency: 83%

HST

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NIRISS simulations – Earth size HZ water-world + M3V

2018

Noise level: 10 – 20 ppm

JWST/NIRISS, Earth + M3V, 13 pc J=8, 27 hrs (15 transits; 350 days )Efficiency: 33%

6. Transit 82

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Most prolific detection method (~1000 known objects), most from Kepler

Powerful technique for exoplanet atmosphere characterization but has to be done from space (HST, Spitzer, JWST)

Transit depth

Secondary eclipse depth

Transit probability

Physical parameters R★, M★, i, a and RP can be derived from the transit light curve given a mass-radius relation.

6.8 Summary (1)


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Atmospheric signal from transit spectroscopy

Equilibrium temperature derived from secondary eclipse observations

Future projects: K2, TESS, PLATO & JWST

6.8 Summary (2)


Documents

Chapter 6 – Transit PHY6795O – Chapitres Choisis en Astrophysique Naines Brunes et Exoplanètes