Exoplanets Finding Extrasolar Planets. I Direct Searches Direct searches are difficult because stars are so bright. How Bright are Planets? Planets shine by reflected light. The amount reflected is the amount received (the solar constant) - times the area of the planet - times the albedo (fraction reflected) L = L /4πd2 x albedo x πR 2 ~ L (R /d)2 p * p * p 2 8 For the Earth, (Rp/d) ~5 x 10 2 8 For Jupiter, (Rp/d) ~10 How Bright are Planets? You gain by going to long wavelengths The Rayleigh-Jeans Tail 7 • λmax = 2.897x 10 /T Å/K 4 • For λmax >> λmax, Iλ~ A 2ckBT/λ – A: area – IJ ~ 0.002 I¤ How Far are Planets from Stars? 1 au = 1“ at 1 pc (definition of the parsec) • 1 pc (parsec) = 3.26 light years • 1“ (arcsec) = 1/3600 degree As seen from α Centauri (4.3 ly): • Earth is 0.75 arcsec from Sol • Jupiter is 4 arcsec from Sol 2 3 2 4π a /P = G (M*+MP) 2 2 1/3 θ = (G P (M*+MP)/4π D) Aside: Telescope ResoluKon • The spaal profile of the intensity of light passing through an aperture is the Fourier Transform of that aperture. 2 2 • the intensity of the light, as a funcKon of the off-axis distance θ from a slit is I = I0 sin (u)/u – u = π D sin(θ)/λ, – D is the diameter of the aperture – λ is the wavelength of the light. • I peaks at θ=0, and has nulls at sin(θ)=n λ/D, for all n not equal to 0. Telescope ResoluKon • For a circular apertures, the spaal profile of the intensity is the Fourier transform of a circle. 2 2 • The intensity of light is given by I(θ) = (π r J1(2m)/m) – r is the radius of the aperture; D is the aperture diameter – m = π r sin(θ)/λ – J1 is a Bessell funcKon of the first kind • J1(2m)/m has a maximum at m=0, and nulls at m=1.916, 3.508, 5.987, ... • For small θ, these nulls are at 1.220 λ/D, 2.233 λ/D, 3.238 λ/D, … • Point source image: central source surrounded by progressively fainter rings, call Airy rings. • An opKcal system that can produce diffracKon rings (Airy rings) is diffrac<on-limited. Chandra HRC-S at 0.277 keV (C K-α) Resolved Images Laser T Tauri (IRTF/ NSFCam) ResoluKon: Rayleigh Criterion Rayleigh's criterion for the resoluKon of a lens (or a mirror): • The peak of the second source lies in the first null of the first source, or the resoluKon R=1.220 λ/D radians. • Equal brightness sources separated by this distance will appear at two peaks, with a minimum ~74% of the peak intensity. • One can actually resolve (or separate) sources of approximately equal brightness that are closer than this. Dawes' criterion: one can resolve sources with a 3% drop between peaks; this gives a resoluKon about 80% of the Rayleigh criterion. Even closer equally bright sources will produce a non-circular central peak: equally bright sources can in principle be detected to about 1/3 of the Rayleigh distance. Complicaons: Real Telescopes • Real telescopes do not have purely circular apertures. • Central obscuraon: decreases the contrast between the central peak and the diffracKon rings. • Supports for the central obscuraon diffract light -> diffracKon spikes Aside: Seeing. I • Ideal performance requires parallel wavefronts. • Variaons in n distort wavefronts • Variaons in n are caused by temperature differences or turbulence. • Under adiabac condiKons, dn ∝ 2δT P/T2 – P: atmospheric pressure – T: atmospheric temperature • The changes in n lead to speckles, or defocussing of the image. Astronomical Seeing • Seeing at K (2.2 µm): – 0.7 sec integraons – a= 3.1 arcsec. – The slow dri is poor tracking • Shiked and co-added image: Seeing. II • Coherence length r0: the distance over which the wavefront remains coherent (the change in phase is < one radian). 1.2 0.6 • r0 ∼ λ (cos(z)) – z: zenith distance. – A telescope with an aperture smaller than r0 will be diffracKon limited. • At a good sight (laminar airflow), such as a mountaintop in the middle of the ocean, r0 ∼10 cm at 5500 Angstroms. Seeing. II • The atmosphere acts as a series of incoherent lenses of aperture r0: • λ/r0 is ~ the diameter of the seeing disk. – The rao of the seeing disk to the Rayleigh criterion at zenith is D/24 (5500A/λ)1.2 cm. – An opKcal telescope smaller than about 25 cm is diffracKon limited; larger telescopes are seeing-limited. – In the 2.2 µm K band), telescopes are diffracKon-limited up to about 3 m diameter. – In the near-IR, much of the seeing can be compensated for by using acKve or adapKve opKcs, perming diffracKon- limited imaging in the 8m VLT and 10m Keck telescopes. Telescopes in space are never seeing-limited. Seeing. III Images from SMARTS 1.3m/ Andicam. • V band; 0.369″pixels • Upper image: – σ=8.1″ – FWHM=9.5″ • Lower image: – σ=0.8″ – FWHM=1.0″ HR 8799 (A5V) AO-assisted imaging Young planets are hot and luminous dashed lines: hot start planets Fischer et al. 2014, PP VI Direct Imaging Example: HR 8799 Beta Pictoris ~9 AU from star M: ~ 7 MJ P: ~20 yrs T: ~1600K Speckle Imaging • Subaru HiCIAO Disnguishing Speckles • Locaon of speckles depends on – Wavelength – Image coordinates – Rotates with the telescope in an alt-az mount • Locaon of exoplanet is fixed relave to the star Speckle Imaging Gemini-N Altair/NIRI a) Raw image b,c) aer subtracKng Azimuthal average d) Aker summing 117 rotated images hp:// www.gemini.e du/node/256 Finding Extrasolar Planets. II Transits Transits Venus, 8 June 2004 Artist’s Conception Transits requires an edge-on orbit. 2 τ = (RP/R*) Jupiter blocks 2% of the Sun's light Earth blocks about 0.01%. How Transits Work Transit Example - Ground The Search for Earth-like Planets • 0.95m telescope • Launched March 2009 • Observe 105 square degrees of the sky • Observe ~ 100,000 stars • Observe continuously for 4.5 years -6 • Photometric accuracy: ~10 (0.1 R⊕) How to achieve µ–mag precision Kepler Field Kepler Field Kepler Timing Transit Example - Kepler Trappist 1 • A small star – about the size of Jupiter • An ultra-cool dwarf (M8) – 2560 K Trappist 1 Transit observaons Trappist 1 Inferred planetary parameters: – Density [ Mass/([4π/3]radius3) ] -> composiKon – Incident flux -> surface temperature Trappist 1 Planets in Context Trappist 1 System Star: M8V, Teff ~ 2500K, 0.08 M¤, Size of Jupiter 40 light years from Earth TransiKng Exoplanet Survey Satellite (TESS) • Launch date planned in 2018 • 2 year mission • All-sky survey, >27.4 days conKnuous coverage • >40,000 F5 – M5 stars observed at 2 min cadence • Full sky observed at 30 min cadence • Precision < 60 ppm/hr • Science: detect transits for 1.2 < RP/R⊕ < 2 Finding Extrasolar Planets. III Astrometric Wobble Astrometric Wobble 2 3 2 3 2 • 4π a1 /P = G MP / (M*+MP) Fischer et al. 2014, PP VI Finding Extrasolar Planets. IV Most planets have been found by Doppler Wobble (radial velocity variations). This selects for massive planets close to the star. First Extrasolar Planet: 51 Pegasi b Radial velocity/ Doppler Shift Reported 6 October 1995 Upsilon Andromedae Periods: 4.6, 241, 3848 days Doppler Wobble: Gliese 876 The three planets of Gl 876: masses = 2.5 MJ, 0.8 MJ, and 7.5 M⊕ High Spectra ResoluKon Orbits 2 -2/3 -1/3 K1 = 8.95/√(1-e ) Mpsin i/M⊕ [(M*+MP)/M¤] P cm/s (period in years) Green: RV detecKons Gray: Kepler Transits Source: Fischer et al. 2014, PP VI Finding Extrasolar Planets. IVa Timing The Doppler Effect applied to pulse arrival times. Applicable to pulsar planets Finding Extrasolar Planets. V Gravitational Lensing Foreground objects focus (and magnify) light because they distort space. Microlensing Theory • Einstein ring – θE = √(κMLπrel) • κ =8.18 mas/M¤ • πrel = (1au/DL) - (1au/DS) • θE ≈ 0.3 mas for ML = 0.5 M¤, DL=6 kpc, DS=8 kpc • Magnificaon – A = u2+2 / u√ (u2+4) – u = impact parameter in terms of θE • CausKc Crossings Microlensing Example Microlensing Theory Microlensing Comparison of Techniques Extrasolar Planet Detectability ProperKes of Planets • Based on ~600 good candidates in exoplanet database Red circles: radial velociKes Blue diamonds: transits Magenta hexagons: direct imaging Asterisks: microlensing Cyan squares: pulsar Kming Green triangle: Solar System Fischer et al. 2014, PP VI Extrasolar Planets Orbits Orbital Eccentricity Extrasolar Planets Orbits Extrasolar Planets Orbits Extrasolar Planets Masses Planetary Mass Distribution Extrasolar Planets Planets are preferentially found around metal-rich stars - mostly younger than the Sun. Metallicities updated Fischer et al. 2014, PP VI ½ ½ 2 1/8 Teq= (R* T*) /((2 a) (1-e ) ) • . .