Exoplanet & Brown Dwarf Atmospheres Lecture 2: A few loose ends, Opacities, clouds credit J. Fortney, C. Morley, P. Gao for some slides Post-processing 1D Models • High resolution spectra • Modified Feutrier (Saumon internal) • DISORT (open source) • Transit spectra • Fortney (in house) • Exo-Transmit (open source) • Transmission spectra are much more forgiving of the 1D model • Geometric albedo spectra • McKay/Marley/Cahoy model, moving it to open source Some Terminology: Albedos The Various Albedos • Bond Albedo • Reflected Power/Incident Power • Don’t care what direction scattered light goes to • Always depends on scattering/absorption of the planet’s atmosphere AND the stellar spectrum • Same planet around 2 different stars (G and M) would have different Bond Albedos • Energy Balance: The Various Albedos • Geometric Albedo • Almost always at a particular wavelength or a particular bandpass • Planet must be viewed a full illumination (full phase) • Does not depend on stellar spectrum • Apparent reflectivity of the planet seen at full phase The Various Albedos • Lambert Sphere • A white billiard ball at all wavelengths • Bond albedo = 1 • Geometric albedo = 2/3 • Semi-Infinite Rayleigh Scattering atmosphere • Rayleigh scattering is conservative (“single scattering albedo” = 1) • Bond albedo = 1 • Geometric albedo = 3/4 The Various Albedos • Single scattering albedo • Ratio of scattering to extinction by a single particle • Qscat / (Qscat + Qabs) • =1 for Rayleigh Opacities 2 3 4 5 6 7 Wavelength (um) “Raw” Opacity Files • From combination of laboratory and theory • Gives intensities as a function of wavelength • “Molecular line list” • Temperature validity range important Theory Tennyson & Yurchenko (2012) Lab NH3 (296K) Actual CH4 ‘Line List’ (HiTRAN) Gives molecule/isotope id: the wavenumber, line strength, Einstein A, line widths, lower energy level and some info on the states involved in the transition CaH (UCL) Convert from Lines to Monochromatic Opacity Specific P, T Partition function Line shape Broadening Foreign broadening (often only N2 available, estimate H2) Tabulate Wavenumber -> Convert from Lines to Monochromatic Opacity Specific P, T Partition function Line shape Broadening Foreign broadening (often only N2 available, estimate H2) Tabulate Wavenumber -> R/T Opacity Methods • Line by line (too many) • Sampling (choose ~10,000s) • Mean opacities • Rosseland, Planck • Double means • Binning • k-coefficients (statistical means within bins) Correlated κ Distribution • Definition: Probability distribution of monochromatic absorption coefficients in finite spectral interval at a given P, T • Do a very large number of monochromatic calculations to describe the opacity • at STP the line width is ~0.1 cm-1 • if bin width 100 cm-1 need ~10(pts/ half width) x 100 / 0.1 ~ 104 points for 1 bin One bin ) Correlated κ Distribution κ n(κ) g(κ) Probability distribution f( Probability Absorption Coefficient (cm2) cumulative distribution Absorption Coefficient (cm2) ) 2 cient (cm κ(g) ffi Absorption Coe Cumulative Probability Basic Assumptions • Exact wavenumber position is not important since source functions (sunlight, thermal radiation) vary slowly with wavelength • Use finite number of spectral bins • Each wavelength bin has the same distribution of κν at various levels in the atmosphere (always true as number of bins becomes very large) vs. wavelength -> Absorption Coefficient (cm2) Cumulative Probability 0 n =4 Absorption Coefficient (cm2) Cumulative Probability 0 n =8 Absorption Coefficient (cm2) Cumulative Probability 0 n =14 • Solve radiative transfer for N spectral bins, each of which has n Gauss points corresponding to n mean opacities in each bin, so n × N times (8×200=1600 times for our models). n N • flux in i’th bin Fi = ∑wjFi,j and the total flux F = ∑Fi j=1 i=1 • Compare to sampling methods which compute intensities at thousands of points, but lose information from other wavelengths. Sampling has trouble at low Teff. • K-coeff excellent for conserving flux, important for finding radiative equilibrium • True line by line would be hundreds of millions of points (Pro Detail: How to Mix Gasses?) • Compute molecular opacities at finite number of P, T combinations • Mix opacities according to chemistry, compute k- coefs or • Keep track of individual k-coefs for each molecule & combine on the fly Output is very low resolution spectrum. Post-process with Feutrier solver & monochromatic opacity tables to get final spectrum Output is very low resolution spectrum. Post-process with Feutrier solver & monochromatic opacity tables to get final spectrum Clouds Brown dwarfs and giant planets are self-luminous and cool over time. 3500 M M (K) 75 M J f e T young planets older brown dwarfs L T 500 Y 13 MJ -3 1 1 Myr 10 Myr log Age100 Myr (Gyr) 1 Gyr 10 Gyr Age Burrows et al. 1997 Monday, January 30, 12 6 Brown Dwarfs, which are heated from below, rather than above, have much steeper P-T profiles than Sing et al. (2016) irradiated planets Different cloud behavior (transitions at different Teff values) and behavior with Teff P ERSPECTIVES outflow from it: It contains many forbidden Space Telescope (launched in August 2003) 4. A. Boss, Astrophys. J. 551, L167 (2001). emission lines (15, 16), which are usually as- and millimeter observations with ground- 5. B. Reipurth, C. Clarke, Astron. J. 122, 432 (2001). sociated with young stars in which a fraction based radio telescopes may reveal the sizes 6. M. R. Bate, I. A. Bonnell, V. Bromm, Mon. Not. R. Astron. Soc. 332, L65 (2002). of the inflowing material is ejected perpen- and masses of brown dwarf disks, allowing 7. A. A. Muench et al., Astrophys. J. 558,L51 (2001). dicular to the disk. If confirmed through fu- us to determine whether most disks are 8. A. Natta et al., Astron. Astrophys. 393, 597 ture observations, this finding would further truncated. Better statistics of the frequency (2002). 9. R. Jayawardhana et al., Astron. J. 126, 1515 (2003). strengthen the analogy between nascent of binary brown dwarfs could provide an- 10. M. Liu et al., Astrophys. J. 585, 372 (2003). brown dwarfs and their stellar counterparts. other observational test. Infrared studies of 11. R. Jayawardhana, S. Mohanty, G. Basri, Astrophys. J. The mounting evidence thus points to a even younger “proto-brown dwarfs,” which 578,L141 (2002). similar infancy for Sun-like stars and brown are still embedded in a dusty womb, may 12. R. Jayawardhana, S. Mohanty, G. Basri, Astrophys. J. 592, 282 (2003). dwarfs. Does this mean that the two kinds also provide clues to their origin. 13. J. Muzerolle et al., Astrophys. J. 592, 266 (2003). of objects are born in the same way? Many 14. S. Mohanty, R. Jayawardhana, D. Barrado y Navascués, observers tend to think so (7–12), but it References Astrophys. J. 593, L109 (2003). may be too early to rule out the ejection 1. G. Basri, Mercury 32, 27 (2003). 15. M. Fernández, F. Comerón, Astron. Astrophys. 380, 2. K. Lodders, Science 303, 323 (2004). 264 (2001). scenario for at least some brown dwarfs. 3. C. Low, D. Lynden-Bell, Mon. Not. R. Astron. Soc. 176, 16. D. Barrado y Navascués, S. Mohanty, R. Jayawardhana, Far-infrared observations with the Spitzer 367 (1976). Astrophys. J., in press. ASTRONOMY lish a firm reference frame for the spectral classification of L and T dwarfs. Brown Dwarfs—Faint at Heart, Such observations represent major progress, because small sizes (roughly the radius of Jupiter) and low masses hamper Rich in Chemistry the detection of brown dwarfs. Their mass- es only reach up to ~7% that of the Sun (for Katharina Lodders comparison, Jupiter’s mass is ~0.1%), not enough to initiate and sustain the hydrogen decade ago, brown dwarfs were not to those of giant planets, but are much burning that powers real stars. Brown on June 8, 2009 much more than a theoretical curios- more massive. Brown dwarfs are further dwarfs may burn deuterium if they exceed Aity in astronomy textbooks. It was divided into subtypes from zero for the 13 Jupiter masses. However, the energy re- unclear whether such objects, with masses hottest (L0, T0) to eight for the coolest (L8, leased by this deuterium burning is a small and temperatures between the giant planets T8), depending on whether certain spectral fire compared to the inferno of hydrogen and the coolest known dwarf stars, even features assumed to be a proxy of temper- burning in stars and lasts less than 100 mil- existed. Today, the problem is how to tell ature are present. Today, ~250 L dwarfs lion years for the most massive brown all the different low-mass objects apart. In and ~50 T dwarfs are known (9). dwarfs. In contrast, hydrogen can burn for a recent paper in Astrophysical Journal, Initially, subtyping of L dwarfs was several billion years in dwarf stars (10). McLean et al. (1) propose a unified classi- based on red optical spectra, whereas T Much of the energy released by a brown www.sciencemag.org fication scheme for brown dwarfs on the dwarfs were sorted by near-infrared spectralBand depthdwarf over depends its lifetime on is fromgas gravitation- column basis of near-infrared spectra. The scheme features (5–8). McLean et al. (1) have now aboveal energy cloud gained +during abundance its formation and also provides insights into the chemistry of advanced a unified classification scheme contraction. A brown dwarf’s main fate is these cool, dense objects. [For a discussion for L and T dwarfs based on ~50 objects an- to sit and cool inNon-condensing space. of brown dwarf origins, see (2).] alyzed with the Keck II Near-Infrared Deprived of a nuclear engine, brown The first brown dwarf, prosaically Spectrometer. They have used the high- dwarfs never exceed ~3000 K near their sur- called Gl229 B, was discovered in 1995 (3, quality near-infrared spectra to categorize faces.