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4. Direct imaging of extrasolar planetsReminder: Direct imaging is challenging:• The proximity to its host star: 1 AU at 1” for alpha Cen 0.15” for the 10th most nearby solar-type star• The low ratio of planet to star light. Jupiter is 20 mag fainter than the Sun• The ratio in the near-infrared is better: A hot Jupiter has an effective T of 1000-1500 K, making it 103-4 fainter

4.1 Expected properties of extrasolar planets

1. Sizes of gas giants, brown dwarfs & stars2. Thermal evolution3. Reflective light from gas giants

4. Polarized light

Sizes of gas giants, brown dwarfs& low-mass stars

The sizes of Jupiter-mass planets, brown dwarfs and the latestM dwarfs are very similar, while they span a factor 100 in mass

The virial theorem: EG = - 2EK. stars thermal energy brown dwarfs electron degeneracy planets Coulomb pressure

Sizes of low mass stars

• Mickey Mouse model: star is a sphere with a constant density:

The virial theorem gives us:

Since the nuclear T will be near ignition T of hydrogen:

EK=

Sizes of Brown dwarfs

• The central T is too low for H-ignition• They burn Deuterium but run out of fuel quickly. This

means they can shrink further until balanced byelectron degeneracy pressure:

Ek∝ therefore,

and

Larger mass smaller object (like White Dwarfs)

A size of a Brown dwarf has yet to be measured

Sizes of gas-giant planets

• Assuming ‘low pressure regime’ Coulomb Force planet is incompressible

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The gas pressure - gravity equilibriumchanges over 3 regimes

From Jupiters to M-dwarf stars all similar sizes

Zero temperature sizeThe zero-T size of a sphere of hydrogen is a function of

mass that peaks at 0.3 Mjup.

Msaturn = 0.3 Mjup Rsaturn = 0.8 Mjup

If Rplanet(M) < Rzero-T(M) Rocky core

If Rplanet(M) > Rzero-T(M) heat source?

Thermal evolutionYoung gas giants and brown dwarfs will contain primordial

heat from formation and contract / release EG / coolYoung BD will also burn D extra heat source

Reflected light from extrasolar planets

A planet illuminated by a star reflects part of this energy backinto space

Monochromatic albedo: ratio between reflected and incident light at a certain wavelength

Bond albedo: ratio between reflected and incident light integrated over frequency

Geometric Albedo

Ratio of planet to star-light

p(λ)= λ-dependent geometric albedo, ψ(α)=phase function, with α = angle star-planet-Earth

α

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Phase functionFor a diffusely scattering Lambert sphere

One can also assume a measured phase function from Venus,Showing more backward scattering. Rocky object generally show strong backward scattering (“the opposition effect”)

Reflective spectra of planetswavelength dependence of albedo

Important factors are Raleigh scattering, molecularabsorption, atmospheric condensates (clouds)

Jupiter: 1. In cool planets, NH4, SH, NH3 and CH4 form clouds. 2. The optical reflection spectrum is dominated by absorption bands of CH4. 3. Upper cloud decks of NH4, SH, NH3 scatter incident radiation

Jupiter is bright between the methane bands.

Hot Jupiters: 1. At T>1100 K MgSi3 condenses, albedo depends strongly on height of this cloud deck. 2. Low cloud deck (high Gsurf planets), strong absorption through pressure broadened Na and K lines. 3. High cloud deck (low Gsurf planets), reduces Na/K absorption significantly

Hot Jupiter (low cloud)

Hot Jupiter (high cloud)

Jupiter

Polarized reflected light

Reflected star light is scattered by atmospheric particlesThis will generally be polarized, while direct star light not

Fractional polarization of a star P=10-4-5 due to Oblateness, magnetic field, star spots...

Observing exoplanets in polarized light can increase the contrast by 10,000-100,000

Polarization of the Sun near the Limb.

• P of the planetary light contains info about structure and composition of the atmosphere such as presence and height of cloud deck

• The degree of polarization is also a strong function of the planetary phase. At opposition (straight back- scattering), P drops to zero

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4.2 Instrumental Challenges

Rayleigh criterion: The diffraction limited resolution ofa telescope with circular aperture (diameter = D) is

For D=10m, this is 0.01” at V 0.1 AU at 10 pc1st and higher orders still contain significant amount of flux

this is only theoretically, a limit which is not reached in practice

seeingSeeing significantly degrades the angular resolution of a ground-based telescope, to the order of 1” in the optical

this corresponds to 10 AU at 10 pc

Imaging efforts are directed at:1) Reducing the angular size of the stellar image2) Suppressing the stellar light3) Minimizing the effects of atmospheric turbulence4) Enhancing the planet/star contrast by observing in IR

Adaptive opticsCompensate for seeing across the telescope by1) Measuring the wavefront at 1 kHz2) Compensate it using a deformable mirrorThe more actuators and faster the correction - the better

Strehl ratio

Ratio between the obtained peak brightness and thatexpected theoretically from diffraction

Coronograph

A coronograph is a device that suppresses the lightfrom a centrally bright star. This enables low contrast

objects close to the star to be studied.

It consists of a small focal plane mask +Undersized aperture mask (Lyot stop), suppressing scatteredlight

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Nulling interferometry

A nulling interferometer combines signals from two or more telescopes that are phase shifted in such way that thesignals cancel each other out for a certain region of sky

InterferencePattern for

2 telescopes

InterferometryFrom spaceTPF (NASA)Darwin (ESA)

Imaging polarimetry

Aims to image the full Stokes parameters

Challenges: rapidly changing atmospheric conditions on time scales of a fraction of a second. How can we reach 10-4-5?

ZIMPOL: part of SPHERE, Future instrument on VLT.

Important NL contribution viaWaters, Stam (UvA), Keller (UU)

ZIMPOL

1. Modulates incoming signal at 1-50 kHz frequency,rotating pol signal by 90 deg

2. Polarizer passes through only one linear pol (soswitching L/R at 1-50 kHz

3. Semi-masked CCD array is moved up and down at thesame rate

4.3 Current searches for optical reflected lightSpectroscopic method:• Light from the planet is not spatially resolved from the star,but• The planet signal varies in Doppler shift relative to the star (due to orbital motion)• The planet signal varies in amplitude

Only upper limits have been found so far:hot Jupiters are darker than Jupiter

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Observed fake

Ups and b

Collier Cameron et al.

Canadian MOST satelliteVery small space telescope

(15cm aperture) monitors hot Jupiters. It could observe the

amplitude variation of theplanet+star system.

So far only upper limits havebeen reached.

4.4 First detections of IR-thermal lightYoung planets: Two promising results with the AO

assisted NACO camera on the VLT have detected two young, still warm, planets (BD?) at >>AU

T-Tauri star GQ Lupi at 100 AUBrown dwarf 2M1207 at 55 AU

Other detections: Free floating planets!?In particular surveys of the Orion nebula (2 Myr) show

the presence of a dozen low mass young brown dwarfs that could be planets (>8 Mjup), which do not orbit a star.

• They could have been ejected from a star system?• Very low-mass tail end of the stellar mass function?

The transit method• 90% of the planets so far have been discovered

using the radial velocity technique• No proper planet has yet been imaged

Much information about planetary orbits and statisticsNo information about the individual planets themselves

The transit method, in combination with RV, deliversMass, Radius, mean density (composition), and

Many follow-up opportunities

Principle of methodIf the inclination of the orbit is near 90o an exoplanet cancross the star, causing a dip in the star’s light curve.

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Geometric probability of a transit

For a planet with radius rp to transit its host starof radius rs, the inclination must be

Where a is the radius of the orbit. The geometric transit probability is

Probabilities are small. Also - planets in our own solar systemare mis-aligned

Hot Jupiters10% chance

Hot jupiters have 10-15% probability to transit Duration of the transitThe frequency of the transit event is simply once every period

The duration of the transit is

sackett

Depth and shape of the transit

Several parameters influence the shape and depth of the transitIf the period is known from multiple transits

1. The planet/star size ratio2. The stellar limb darkening3. The impact parameter of the transit acos(i)/rs4. The mean density of the star (rsMs-1/3)

Simple transit shape analysis

1. Ignore limb darkening2. Assume star is on the main sequence ρ∝Rs

-2

3. Depth of transit = (Rp/Rs)2

4. Fractional duration of the transit

D/P = 0.0756 P(days)-2/3 ρ(solar)-1/3 .

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HD 209458b: A hot Jupiter blocks ~1% of the lightFor ~2-3 hours

You can observe with an amateur telescope in the back garden!

Limb darkening

At the outer edge, the star is less bright, making thetransit at that point more shallow