sign in sign up
<<
Home , Gliese 876, OP Andromedae

Exoplanets Finding Extrasolar Planets. I Direct Searches

Direct searches are difficult because 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 , (Rp/d) ~5 x 10

2 8 For , (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 ) • 1 pc (parsec) = 3.26 light • 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: Resoluon • 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 funcon 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 Resoluon • 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 funcon 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 opcal system that can produce diffracon rings (Airy rings) is diffracon-limited.

Chandra HRC-S at 0.277 keV (C K-α) Resolved Images

Laser

T Tauri (IRTF/ NSFCam) Resoluon: Rayleigh Criterion

Rayleigh's criterion for the resoluon of a lens (or a mirror): • The peak of the second source lies in the first null of the first source, or the resoluon 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 resoluon 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 • Real telescopes do not have purely circular apertures. • Central obscuraon: decreases the contrast between the central peak and the diffracon rings. • Supports for the central obscuraon diffract light -> diffracon spikes Aside: Seeing. I

• Ideal performance requires parallel wavefronts. • Variaons in n distort wavefronts • Variaons in n are caused by differences or turbulence.

• Under adiabac condions, 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 • Shied 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 diffracon 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 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 opcal telescope smaller than about 25 cm is diffracon limited; larger telescopes are seeing-limited. – In the 2.2 µm K band), telescopes are diffracon-limited up to about 3 m diameter. – In the near-IR, much of the seeing can be compensated for by using acve or adapve opcs, perming diffracon- 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

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 is fixed relave to the star Speckle Imaging

Gemini-N Altair/NIRI

a) Raw image b,c) aer subtracng Azimuthal average d) Aer 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 . 2 τ = (RP/R*) Jupiter blocks 2% of the '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 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 [ /([4π/3]radius3) ] -> composion – 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 Transing Exoplanet Survey (TESS) • Launch date planned in 2018 • 2 mission • All-sky survey, >27.4 days connuous 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 ( variations). This selects for massive planets close to the star.

First Extrasolar Planet: 51 Pegasi b

Radial velocity/ Doppler Shift Reported 6 October 1995

Periods: 4.6, 241, 3848 days Doppler Wobble: Gliese 876

The three planets of Gl 876:

= 2.5 MJ, 0.8 MJ, and 7.5 M⊕ High Spectra Resoluon

2 -2/3 -1/3 K1 = 8.95/√(1-e ) Mpsin i/M⊕ [(M*+MP)/M¤] P cm/s (period in years)

Green: RV detecons 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 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 • Causc Crossings Microlensing Example Microlensing Theory Microlensing Comparison of Techniques Extrasolar Planet Detectability Properes of Planets

• Based on ~600 good candidates in exoplanet database Red circles: radial velocies Blue diamonds: transits Magenta hexagons: direct imaging Asterisks: microlensing Cyan squares: pulsar ming Green triangle: Fischer et al. 2014, PP VI Extrasolar Planets Orbits 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. updated

Fischer et al. 2014, PP VI ½ ½ 2 1/8 Teq= (R* T*) /((2 a) (1-e ) )

• .