High-resolution spectroscopy for exoplanet characterisation Matteo Brogi University of Warwick @MattBrogi Evry Schatzman School, Aussois, France - 23 September 2019 www.mattbrogi.com Basic concepts Spectral resolution and spectrographs Exoplanets and their orbits Low-resolution spectroscopy of transiting exoplanets Basic concepts in spectroscopy: resolution Spectral resolution (∆λ) versus resolving power (λ/∆λ) Spectrographs are characterised by a ~constant resolving power R=λ/∆λ This translates into a variable spectral resolution ∆λ according to wavelength λ How close can two spectral lines be to be considered “spectrally resolved”? Saddle point ∂ƒ/∂λ = 0 ∂2ƒ/∂λ2 = 0 1 FWHM separation Line intensity Wavelength Wavelength Throughout these lectures we’ll adopt the Houston criterion We’ll assume that spectrographs turn a delta function into a Gaussian with FWHM=λ/R #3 Linking resolution to velocity Objects in motion absorb/emit at shifted wavelengths λ’ due to Doppler effect We will use the non-relativistic Doppler formula v v λ′# = λ 1 + Δλ ≡ (λ′# − λ) = λ ( c ) c λ c R = = Δλ v The minimum velocity shift v that can be fully resolved is related to R via c v = R R = 500 (low-res) ⇒ ∆v = 600 km s–1 Generally insufficient for most astrophysical sources R = 5,000 (intermediate-res) ⇒ ∆v = 60 km s–1 OK for the broadest spectral lines R = 50,000 (high-res) ⇒ $v = 6 km s–1 OK for most of spectral lines, and exoplanet orbital motion too! #4 Using spectroscopy to find exoplanets Periodic shift of spectral lines due to reflex motion around the centre of mass 51 Pegasi b: ~50 m/s (Mayor et Quéloz 1995) ESO Proxima Cen b: ~1.4 m/s Period of the orbit Eccentricity of the orbit Only lower limit on planet mass (orbital inclination unknown) 10 cm/s required to do Earth-Sun systems current limits are 30 cm/s (instrumental) and ~1 m/s (stellar) (Anglada-Escudé et al. 2016) #5 Where are the high-resolution spectrographs? Calar Alto 3.5m:CARMENES (R=80k) Mount Hopkins MMT:ARIES (R=60k) La Palma TNG:HARPS-N (R=112k) TNG:GIANO (R=70k) Mauna Kea Keck:NIRSPEC (R=50k) Subaru:HDS (R=160k) Subaru:IRD (R=75k) CHFT: SPIRou (R=70k) Cerro Paranal VLT:CRIRES+ (R=100k) VLT:UVES (R=80-110k) VLT:ESPRESSO (R=190k) La Silla 3.6m:HARPS (R=112k) 3.6m:NIRPS (R=70k) #6 Using spectroscopy to characterise exoplanets CRIRES at the Very Large Telescope In operation between June 2006 and August 2014 R = 50,000-100,000 Spectral coverage 1.0-5.3 µm (non simultaneous!) ⇒ JHKLM bands Typical simultaneous coverage: 0.07 µm @ 2.3 µm NIRSPEC at Keck Telescope GIANO (R=50k, YHJK simultaneous) CARMENES (visible & YJH R=25,000 JHKLM and HARPS (R=112k, visible) at TNG simultaneous) at Calar Alto 3.5m Nomenclature for orbital phases � of exoplanets � = 0.5: superior conjunction � = 0.25: quadrature � = 0: inferior conjunction = 0.75: quadrature � = 0.5: (secondary) eclipse � � = 0: (primary) transit #8 Orbital radial velocity of an exoplanet i ≈ 90° i = 0° i = 45° edge-on orbit face-on orbit 2πa Planet orbital velocity (circular): v = orb P Maximum planet radial velocity: KP = vorb sin(i) Planet radial velocity at each orbital phase In the reference frame RV = v sin(i) sin(2πφ) ≡ K sin(2πφ) P orb P of the exoplanet system Additional velocity terms are needed to compute the RV as measured by the observer (day 2) #9 Light curves of transiting exoplanets Dimming of starlight due to transit or eclipse of planetary body ESO E. de Mooij Period of the orbit Radius of the planet relative to the star Orbital inclination Measuring the stellar light accurately is a challenging task from the ground due to instability of the instrument (flexure, pointing, etc.) and of the Earth’s atmosphere (transparency, water vapour, etc.) #10 Light curves of transiting exoplanets from the ground Expectations… …versus reality! Flux Time E. de Mooij WASP-39b, Nikolov+ 2017 The flux of the target is divided through a reference star If the atmosphere behaves exactly the same the correction is perfect Requires stars of similar brightness, spectral type, and spatially close on the sky! #11 Transmission spectroscopy of exoplanets RP = RP(λ) If the opacity increases the planet appears bigger Transmission spectroscopy WASP-39b, Wakeford+ 2017 Transit Missing stellar light due to opaque planet disk #12 The information in exoplanet transmission spectra UV Optical Near-Infrared H2O H2O H2O Na K Depth Wavelength Optical wavelengths Dominated by lines of alkali metals (Na / K doublets), Rayleigh scattering from H2, some (weak) H2O For very hot giants there can be TiO / VO in gas phase Infrared wavelengths Dominated by molecular absorption, mostly H2O and possibly CH4, CO, CO2, etc. #13 A first-order estimate of transmission signals Transit depth Change in transit depth ∆D 2 D = (RP/R⋆) due to atmospheric opacity Jupiter-Sun ~ 1% ∆D ≈ Aring / Astar Earth-Sun ~ 0.008% Aring = area outer radius - area inner radius Outer radius = RP + δ Inner radius = RP 2 2 Aring = π(RP + δ) − πRP 2 2 2 = π(RP + 2δRP + δ − RP) R⋆ RP = πδ(2RP + δ) ≈ πδRP Aring δR ΔD = = P 2 A⋆ R⋆ What is δ ? A first-order estimate of transmission signals Transit depth Change in transit depth ∆D 2 D = (RP/R⋆) due to atmospheric opacity ∆D(λ) ≈ nHR /(R )2 Jupiter-Sun ~ 1% P ★ Earth-Sun ~ 0.008% Change in planet opacity κ(λ) Also dependent on abundance For strong absorbers: Planet scale height H n ≈ log(∆κ) ~ 2-5 Dependent on temperature (Teq), gravity (g) and mean molecular weight (µ) H = kBTeq / (gµ) R⋆ RP An atmosphere dominated by H-He (µ=2.2) will have atmospheric features 8× stronger than a water-dominated atmosphere (µ=18) A first-order estimate of transmission signals Transit depth Change in transit depth ∆D 2 D = (RP/R⋆) due to atmospheric opacity ∆D ≈ nHR /(R )2 Jupiter-Sun ~ 1% P ★ Earth-Sun ~ 0.008% Planet scale height H H = kBTeq / (gµ) Change in planet opacity κ n ≈ log(∆κ) ~ 2-5 R⋆ RP hot-giant planet (1,500K, µ=2.2) ∆D ~ 0.01% = 100 ppm water-world (2.5 RE, 10ME, 800K, µ=18) ∆D ~ 4 ppm The information in exoplanet transmission spectra Effect of hazes Photochemically-produced particles Increased opacity at all wavelengths Rayleigh-scattering in the optical #17 The information in exoplanet transmission spectra Effect of clouds Particles produced by condensation Increased opacity at all wavelengths Heavily-muted spectral features #18 The information in exoplanet transmission spectra Effect of metallicity Increasing the mean molecular weight Reduces scale height Reduced amplitude of features (overall) #19 Example: the “cloudiness” levels of hot Jupiters Key comparative study by Sing et al., Nature (2016) 10 exoplanets high-quality optical-NIR data (HST STIS & WFC3) Weak IR water features are either due to low water abundance, or to muting effects of clouds Scale heights Answer is still not definitive Ongoing research Large HST proposals (100s hours) to increase the sample and complete the 0.8-1.3 µm region Wavelength (µm) Reflected light starlight from exoplanets At visible wavelength, secondary eclipse depth = missing reflected starlight Very challenging measurements, especially spectrally-resolved Evans+2013 Hot Jupiters are not reflective at visible wavelengths (Na and K lines absorb radiation) Eclipse Missing reflected starlight Some “contamination” from the tail of thermal emission is possible in the red optical #21 A first-order estimate of reflected-light signals 2 2 4 Stellar flux at planet: F⋆,pl = L⋆/(4πa ) L⋆ = 4πσR⋆Teff Luminosity: energy / s ⇒ [W s–1] Flux: energy / s / unit area ⇒ [W s–1 m–2] The stellar luminosity is distributed on a sphere of surface 4πa2 R⋆ RP A first-order estimate of reflected-light signals 2 2 4 Stellar flux at planet: F⋆,pl = L⋆/(4πa ) L⋆ = 4πσR⋆Teff 2 Energy reflected / s: Erefl = AπRPF⋆,pl The planet is a disk of area π(RP)2 An average reflectivity (albedo) A is assumed R⋆ RP A first-order estimate of reflected-light signals 2 2 4 Stellar flux at planet: F⋆,pl = L⋆/(4πa ) L⋆ = 4πσR⋆Teff 2 Energy reflected / s: Erefl = AπRPF⋆,pl Flux ratio at the observer (distance D) 2 2 2 FP,refl AπRPF⋆,pl 4πD R = = A P 2 F⋆ 4πD L⋆ ( 2a ) R⋆ RP A first-order estimate of reflected-light signals 2 2 4 Stellar flux at planet: F⋆,pl = L⋆/(4πa ) L⋆ = 4πσR⋆Teff 2 Energy reflected / s: Erefl = AπRPF⋆,pl Flux ratio at the observer (distance D) 2 2 2 FP,refl AπRPF⋆,pl 4πD R = = A P 2 F⋆ 4πD L⋆ ( 2a ) R⋆ RP WASP-33b (0.025au, A=0.1, 1.6RJup) 2×10–5 = 20 ppm Hot-giant planet (0.04au, A=0.1, 1.15RJup) 5×10–6 = 5 ppm Earth around the Sun (1au, A=0.35, 0.09RJup) 1.6×10–10 = 0.16 ppb Emission spectroscopy of exoplanets At infrared wavelength, secondary eclipse depth = missing planet thermal emission HD 209458 b, Swain+ 2009 5 FP = FP(λ) If the opacity increases 4 1000 we probe higher altitudes × 3 Dayside spectroscopy 2 Planet-to-starflux 1 2 3 4 6 8 10 Wavelength (µm) Eclipse Missing planet flux (reflected or thermal) #26 A first-order estimate of emission signals Approximating the star and the planet as black bodies Stellar flux at planet: 2 2 4 F⋆ = L⋆/(4πa ) L⋆ = 4πσR⋆Teff Let’s make it wavelength dependent B(Teff, λ) is the Planck function for black-body radiation 2hc2 1 B(T, λ) = λ5 exp[hc/(λkT)] − 1 It has units of [W s–1 m–2 m–1 sr–1] (energy / time / area / wavelength / solid angle) R⋆ RP Radiation is isotropic so for the flux F(T, λ) = πB(T, λ) 2 2 L⋆(λ) = 4π R⋆B(Teff, λ) A first-order estimate of emission signals Approximating the star and the planet as black bodies Stellar flux at planet: 2 2 F⋆(λ) = L⋆(λ)/(4πa ) L⋆(λ) = 4πR⋆B(Teff, λ) Energy absorbed / time: 2 Eabs(λ) = (1 − A)πRPF⋆(λ) Energy absorbed = Energy re-emitted (over all wavelengths) Eabs = Eout 4πσR2T4 (1 − A)πR2