4. Direct imaging of extrasolar planets. 4.1 Expected properties of extrasolar planets. Sizes of gas giants, brown dwarfs & low-mass stars

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1 4. Direct imaging of extrasolar planets Reminder: 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 K, making it fainter 4.1 Expected properties of extrasolar planets 1. Sizes of gas giants, brown dwarfs & stars 2. Thermal evolution 3. 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 latest M dwarfs are very similar, while they span a factor 100 in mass Sizes of low mass stars Mickey Mouse model: star is a sphere with a constant density: E K = The virial theorem gives us: Since the nuclear T will be near ignition T of hydrogen: The virial theorem: E G = - 2E K. stars thermal energy brown dwarfs electron degeneracy planets Coulomb pressure 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 by electron degeneracy pressure: E k therefore, Sizes of gas-giant planets Assuming low pressure regime Coulomb Force planet is incompressible and Larger mass smaller object (like White Dwarfs) A size of a Brown dwarf has yet to be measured 1

2 The gas pressure - gravity equilibrium changes over 3 regimes Zero temperature size The zero-t size of a sphere of hydrogen is a function of mass that peaks at 0.3 M jup. From Jupiters to M-dwarf stars all similar sizes M saturn = 0.3 M jup R saturn = 0.8 M jup If R planet (M) < R zero-t (M) Rocky core Thermal evolution Young gas giants and brown dwarfs will contain primordial heat from formation and contract / release E G / cool Young BD will also burn D extra heat source If R planet (M) > R zero-t (M) heat source? Reflected light from extrasolar planets A planet illuminated by a star reflects part of this energy back into space Monochromatic albedo: ratio between reflected and incident light at a certain wavelength Bond albedo: ratio between reflected and incident light integrated over frequency Ratio of planet to star-light Geometric Albedo p(λ)= λ-dependent geometric albedo, ψ(α)=phase function, with α = angle star-planet-earth α 2

3 Phase function For 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 planets wavelength dependence of albedo Important factors are Raleigh scattering, molecular absorption, atmospheric condensates (clouds) Jupiter 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 (high cloud) Hot Jupiter (low cloud) Polarized reflected light Reflected star light is scattered by atmospheric particles This will generally be polarized, while direct star light not Fractional polarization of a star P= due to Oblateness, magnetic field, star spots... 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 Polarization of the Sun near the Limb. Observing exoplanets in polarized light can increase the contrast by 10, ,000 3

4 4.2 Instrumental Challenges Rayleigh criterion: The diffraction limited resolution of a telescope with circular aperture (diameter = D) is seeing Seeing 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 For D=10m, this is 0.01 at V 0.1 AU at 10 pc 1st and higher orders still contain significant amount of flux this is only theoretically, a limit which is not reached in practice Imaging efforts are directed at: 1) Reducing the angular size of the stellar image 2) Suppressing the stellar light 3) Minimizing the effects of atmospheric turbulence 4) Enhancing the planet/star contrast by observing in IR Adaptive optics Compensate for seeing across the telescope by 1) Measuring the wavefront at 1 khz 2) Compensate it using a deformable mirror The more actuators and faster the correction - the better Strehl ratio Ratio between the obtained peak brightness and that expected theoretically from diffraction Coronograph A coronograph is a device that suppresses the light from 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 scattered light 4

5 Nulling interferometry A nulling interferometer combines signals from two or more telescopes that are phase shifted in such way that the signals cancel each other out for a certain region of sky Interferometry From space TPF (NASA) Darwin (ESA) Interference Pattern for 2 telescopes 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 ? ZIMPOL: part of SPHERE, Future instrument on VLT. Important NL contribution via Waters, Stam (UvA), Keller (UU) ZIMPOL Modulates incoming signal at 1-50 khz frequency, rotating pol signal by 90 deg Polarizer passes through only one linear pol (so switching L/R at 1-50 khz Semi-masked CCD array is moved up and down at the same rate 4.3 Current searches for optical reflected light Spectroscopic 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 5

6 Ups and b Canadian MOST satellite Very small space telescope (15cm aperture) monitors hot Jupiters. It could observe the amplitude variation of the planet+star system. So far only upper limits have been reached. Observed fake Collier Cameron et al. 4.4 First detections of IR-thermal light Young planets: Two promising results with the AO assisted NACO camera on the VLT have detected two young, still warm, planets (BD?) at >>AU Brown dwarf 2M1207 at 55 AU T-Tauri star GQ Lupi at 100 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 Principle of method If the inclination of the orbit is near 90 o an exoplanet can cross the star, causing a dip in the star s light curve. Much information about planetary orbits and statistics No information about the individual planets themselves The transit method, in combination with RV, delivers Mass, Radius, mean density (composition), and Many follow-up opportunities 6

7 Geometric probability of a transit For a planet with radius rp to transit its host star of radius rs, the inclination must be Probabilities are small. Also - planets in our own solar system are mis-aligned Where a is the radius of the orbit. The geometric transit probability is Hot jupiters have 10-15% probability to transit Duration of the transit The frequency of the transit event is simply once every period The duration of the transit is Hot Jupiters 10% chance sackett Depth and shape of the transit Several parameters influence the shape and depth of the transit If the period is known from multiple transits 1. The planet/star size ratio 2. The stellar limb darkening 3. The impact parameter of the transit acos(i)/rs 4. The mean density of the star (rsms -1/3 ) Simple transit shape analysis 1. Ignore limb darkening 2. Assume star is on the main sequence ρ R s Depth of transit = (Rp/Rs) 2 4. Fractional duration of the transit D/P = P(days) -2/3 ρ(solar) -1/3. 7

8 HD b: A hot Jupiter blocks ~1% of the light For ~2-3 hours Limb darkening At the outer edge, the star is less bright, making the transit at that point more shallow You can observe with an amateur telescope in the back garden! 8

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