No. 1, 2010 ALBEDO COLORS OF EXOPLANETS 191 Jupiter 1 AU Neptune 1 AU Jupiter 2 AU Neptune 2 AU Jupiter 5 AU Neptune 5 AU 350 nm 350 Theoretical Albedo Spectra of Exoplanet Direct Imaging Targets No. 1, 2010 ALBEDO COLORS OF EXOPLANETS 193 R = 5 R = 15 0.7 0.7 Jupiter Saturn 0.6 0.6 Uranus Neptune 0.5 Titan 0.5 0.4 0.4 Albedo 0.3 Albedo 0.3 0.2 0.2 0.1 0.1 550 nm 0 0 300 400 500 600 700 800 900 1000 300 400 500 600 700 800 900 1000 Wavelength (nm) Wavelength (nm) Figure 2. Low-resolution albedo spectra of the outer planets in our solar system. Original high-resolution data from Karkoschka (1994). Left: R λ/∆λ 5; right: R 15. = = = From Cahoy et al. (2010) (A color version of this figure is available in the online journal.) in general for exoplanets and how the phase at which they are Aplanet’sphaseangleα is the angle between the incident ray observed affects the colors. from the star to the planet and the reflected ray from the planet As we discuss in more detail in Sections 2.2 and 4, coarse to the observer. The scattering angle Θ is related to the phase Nikole K. Lewis, Saganspectra can beFellow, used in combination withMIT/EAPS atmospheric models angle via α π Θ. to constrain the temperature, composition, the presence or In this work,= we− use the term geometric albedo to refer to the absence of clouds in an exoplanet’s atmosphere, and the albedo spectra at full phase. We use the term albedo spectra to Mark Marley,exoplanet’s NASA radius (Marley etAmes al. 1999, 2007;Marley&McKay refer to spectra observed at different orbital phases. 1999;Fortneyetal.2008b, 2008a). Color–color comparisons In order to reduce confusion in later discussions of planet of exoplanets can be made (Traub 2003; Sudarsky et al. phase functions and particle scattering functions, we use the 2005;Fortneyetal.2008b), and understanding how system notation Ag(λ)forgeometricalbedohereinsteadofusingthe Jonathan Fortney,geometry and exoplanet UCSC composition relate to variability in other common notation for geometric albedo, p.Asnotedin the observations is important for interpreting these color–color Sobolev (1975), for a perfectly reflecting Lambert sphere, the comparisons. geometric albedo is 2/3, and for a semi-infinite purely Rayleigh scattering atmosphere, it is 3/4(Dlugach&Yanovitskij1974). 2.2. Albedos Flux measurements at different planet phase angles can be used to define the phase function Φ(λ, α): The definition and relationships between geometric albedo Ag, phase α, the phase integral q, spherical albedo As, and 2 Fp(λ, α) Rp Bond albedo AB,andadditionalparametersofinterestsuch Ag(λ) Φ(λ, α). (3) F (λ) = d as planetary effective temperature are important to understand ⊙ ! " in the context of interpreting direct imaging observations. As noted for Equation (2), Ag(λ)isdefinedatα 0◦, Fp(λ, α) Although this material is not new, we review it since the is the monochromatic planet flux, F (λ)isthemonochromatic= distinctions between the various types of albedos are important ⊙ stellar flux, Rp is the planet’s radius, d is the planet–star to emphasize. Note that while Marley et al. (1999) presented separation, and Φ(λ, α)istheplanet’sphasefunctionatangle 750 nm geometric albedo spectra and tables of Bond albedos for α.Thephasefunctionisnormalizedtobe1.0atfullphase. exoplanets in systems with varying stellar types, our focus The scattering phase function of the particles in the exoplanet’s here is more closely on the combined effects of separation, atmosphere, p(Θ), contributes to the disk-integrated phase composition, and planet phase on model gas and ice giant function. The observed phase function allows calculation of spectra. We do tabulate Bond albedos for our exoplanet models, the phase integral, q: but only for a solar analog parent star. Measurements of the planet’s brightness at a given wave- π q(λ) 2 Φ(λ, α)sinαdα. (4) length and full phase yield the planet’s monochromatic geomet- = ric albedo: #0 Fp(λ, α 0◦) The spherical albedo, Ag(λ) = . (2) = F ,L(λ) Simulated direct images of Jupiters and Neptunes around a solar analog at⊙ 10 pc, as a functionAs (λ) q(λ)Ag(λ)(5) of planet–star separation (1 AU, 2 AU, and 5 AU) and λ Figure 1. = Geometric albedo Ag(λ)istheratioofthereflectedflux Fp(λ, α 0 )ofanobjectatfullphase(α 0 )totheflux is the fraction of incident light reflected toward all angles. = ◦ = ◦ from a perfect Lambert disk, F ,L of the same radius Rp under The planet’s Bond albedo, an incident flux-weighted ⊙ the same incident flux F at the same distance d from the star. and wavelength-integrated function of As (λ)andΦ(λ, α), (350 nm, 550 nm, and 750 nm, each with 100 nm bandwidth). The simulation is for a⊙ D 4 m space telescope with a phase-induced amplitude apodization (PIAA) coronagraph (Guyon et al. 2005). The PIAA coronagraph has an IWA 2λ/D. The integration= time is 10 hr and effects from photon noise and 1 zodi of both local ∼ 1 and exozodiacal dust are included (system inclination is 60◦). Note the scale with λ in these 256 256 pixel images: 350 nm 2.8 mas pixel− ,550nm 4.4 mas pixel 1,and750nm 6.0 mas pixel 1 (Cahoy et al. 2009). × ∼ ∼ − ∼ − Section 3,wedescribehowwegenerateaseriesofexoplanet cal of a 1 MJ EGP using a similar approach but with a different model atmospheres over a range of planet–star separations model and implementation than that used in this work. While and metallicities using a one-dimensional radiative–convective our 1 MJ results that include clouds tend to be less red at full model that was previously tailored for use with EGPs (Marley phase and less blue at new compared with those in Sudarsky 1997;Fortneyetal.2005, 2006;Marleyetal.2007;Fortney& et al. (2005), we generally agree with their cloud-free result and Marley 2007;Fortneyetal.2008b, 2008a)andbrowndwarfs extend their approach to include different compositions, Nep- (Marley et al. 1996;Burrowsetal.1997;Marley1997;Marley tune analogs, and comparisons with observed spectra and colors et al. 2002;Saumonetal.2006, 2007). The model was originally of solar system planets. used for solar system planetary bodies such as Titan and Uranus (Toon et al. 1977, 1989;McKayetal.1989; Marley & McKay 2. BACKGROUND 1999). These global mean one-dimensional exoplanet models are then used as input to a high-resolution albedo spectra model. This section provides some background on exoplanet direct We describe our updates to the albedo model that allow us imaging methods and the scientific value of albedo spectra to calculate emergent intensities and thus albedo spectra as a constructed from observations made in the optical. We briefly function of phase. review common direct imaging terminology and techniques in In Section 4,wepresentresults:albedospectrafrom0.35µm Section 2.1 and then formally define geometric albedo and to 1 µm as a function of planet type, planet–star separation, illustrate how albedo spectra of exoplanets relate to exoplanet metallicity, and phase. Because of the practical constraints in- science goals in Section 2.2.Wealsobrieflydiscussthe herent in spacecraft flybys of solar system giant planets, there challenges and current limitations that affect direct imaging is relatively little data in the literature reporting planet-averaged efforts. Consideration of both the instrumentation constraints phase functions; we do compare Voyager 1 data of Uranus and for direct imaging and exoplanet science goals helps to define Neptune from Pollack et al. (1986)withourmodelphasefunc- and justify the planet–star separations and atmospheric model tions. We also compare the model albedo spectra with obser- types used in this work. vations of solar system giant planets from Karkoschka (1994). 2.1. Direct Imaging Since early exoplanet direct imaging observations will have limited resolution, in Section 5 we consider lower-resolution, To give the reader an idea of the challenges inherent in coarse spectra derived from our high-resolution results. For the coronagraphic detection and characterization of gas- or ice-giant lower resolution cases, we consider R λ/∆λ 5and15,and exoplanets, Figure 1 shows simulated direct images of Jupiter = = we also consider how changes in albedo spectra might present and Neptune analogs observed in three different 100 nm wide themselves in terms of color–color comparisons using standard bands around a solar analog at a distance of 10 pc from the filters in the optical. This helps us to evaluate features that might observer (Cahoy et al. 2009). The simulations are performed be detectable using a combination of different wide (or narrow) for a 4 m diameter space telescope, where the light from the filter bands. parent star has been suppressed by a phase-induced amplitude Color–color diagrams were suggested as a comparative an- apodization (PIAA) coronagraph (Guyon et al. 2005), and stellar alytic tool for direct imaging of exoplanets in an example leakage is included as one of several background sources. that considered the color diversity of solar system planets in Importantly, for this figure only, we assume a gray albedo Traub (2003). Recently, Fortney et al. (2008b)presentedde- spectrum with a geometric albedo that is a constant 0.3 with tailed color–color comparisons of hot young Jupiters in the wavelength and thus the same for each planet in each bandpass. infrared. Earlier, Sudarsky et al. (2005)modeledreflected-light The simulations are described in greater detail in Cahoy et al. albedo spectra and performed color–color analyses in the opti- (2009). WFIRST-AFTA Brings Humanity WFIRST-AFTACloser to Characterizing Brings Humanity Earths Closer to Characterizing