88 In-class activity (1) CHAPTER 4. RADIATION FROM PLANETS Density structure. Very similar equations apply for the density structure and one We just talkedobtains about for basic an homogeneous, atmospheric isothermal properties. atmosphere a densityLooking structure at the equivalent table tobelow, the how come that µ variespressure: so strongly for Solar System planets? Can you explain the µ=2.3 z/H⇢ kT ⇢(z)=⇢ e with H = . (4.19) for the Gas and Ice Giants? If you think0 of the different⇢ gµ types of extrasolar planets we came across in the lecture, which of these have the largest scale heights? where H⇢ is the density scale height and ⇢0 the density at the reference point z0 = 0. In Discuss in teamsthe simple and case share described your here ideas the pressure with andthe density class. scale heights are identical:

HP = H⇢ = H.

Table 4.3: Basic atmospheric parameters for planets with atmospheres and Titan.

object Tground Pground Te↵ µ/µH g H dT/dz ad vesc 2 | 1 [bar] [m s ] [km] [K/km] [km s ] 14 Mercury 10 448 K 3.7 4.4 Venus 730 K 92 328 K 44 8.9 6.9 10.4 Earth 288 K 1.01 263 K 28 9.8 8.4 11.2 Mars 215 K 0.006 227 K 44 3.7 11. 5.0 Jupiter 124 K 2.3 23.1 19. 1.9 59.5 Saturn 95 K 2.3 9.0 38. 0.84 35.5 Uranus 59 K 2.3 8.7 24. 0.85 21.3 Neptune 59 K 2.3 11.0 19. 0.86 23.5 Titan 93 K 1.46 80 K 28 1.4 17. 2.6

Scale heights for planets. The equation for the scale height indicate the following relationships: – The scale height depends on the atmospheric properties. For a planet with given radius Rp and bulk density⇢ ¯ (or mass) the scale height is proportional to the at- mospheric temperature H T and inverse proportional to the mean particle mass / H 1/µ, / – The scale height depends for given atmospheric temperature and composition on the planet properties. The scale height is inverse proportional to the surface gravity H 1/g = R2 /GM 1/R ⇢¯. / P P / p The scale height can be particularly large for hot planets, with a hydrogen atmosphere and a small gravitational acceleration (large radius and low mean density). For solar system planets the scale heights are given in Table 4.3. H was calculated with the indicated Te↵ and mean particle mass µ/µH. The scale heights are in a narrow range of 5 – 40 km. From the composition, one would expect much smaller scale heights for the terrestrial planets when compared to giant planets because of the much larger particle mass ( 30 in terrestrial planets but only 2.3 in giant planets). But this e↵ect is ⇡ compensated by the higher atmosphere temperature and lower gravity for the terrestrial planets. 4.4. ATMOSPHERES OF SOLAR SYSTEM PLANETS 89

Column density. The column density ⌃(z0) gives the total density of gas per unit area above a certain height z0 (e.g. defined as z0 = 0). ⌃(z0) is an important quantity for the calculation of the optical depth. Since the density drop-o↵ with height is exponential ⌃(z0) for is proportional to the density at ⇢(z0)=⇢0

1 z/H z/H ⌃(z )=⇢ e dz = ⇢ He 1 = ⇢ H. 0 0 0 |0 0 Z0 This can be directly linked to the pressure µP P ⌃(P )= 0 H = 0 . (4.20) 0 kT g All solar system planets have a gravitational acceleration at the surface of the order g 2 ⇡ 10 m s . Thus for order of magnitude estimates one can use a surface density of ⌃(1bar) 2 ⇡ 1kg cm .

Chemical composition for atmospheres of solar system planets An important input parameter for the analysis of atmospheres is their composition which is given in Table 4.4. We will discuss later the interpretation of these abundances.

Table 4.4: Abundances by mass of the most important chemical spezies for solar system objects. object dominant secondary minor molecule constituents constituents

Venus 96.5 % CO2 3.5 % N2 0.01 % SO2 Earth 78.1 % N2 20.1 % O2 0.93 % Ar, 0.03 % CO2

Mars 95.3 % CO2 2.7 % N2 1.6~2% %Ar Ar,, ~2% N 0.272 % N2 Jupiter 85 % H2 15 % He 0.24 % CH4 Saturn 94 % H2 6 % He 0.3 % CH4 Uranus 85 % H2 15 % He 1 % CH4 Neptune 85 % H2 15 % He 1 % CH4

Titan 92 % N2 4 % CH4, 4 % Ar Temperature – Pressure profiles for solar system planets Temperature – Pressure profiles for hot jupiters

LETTER RESEARCH

–6 140

Ca-Ti HAT-P-12b HD 209458b 130 WASP-6b WASP-31b Al-C 120 –4 WASP-39b WASP-17b HD 189733b WASP-19b a 110 HAT-P-1b WASP-12b Clear WASP-19b solar abundance 100 ×10 WASP-17b –2 90 ×0.1 80 Cr MgSi Fe HAT-P-1b log[Pressure (bar)] 0 70 ×0.01 Na O O amplitude (%) ×100 HD 189733b 3 Mg 2 2 S Mn S 2 Si H 60 KCl O ×1 4 m μ 50 Sub-solar 2 ×0.001 Zn 1.4- ×1,000 WASP-12b S 40 HD 209458b

500 1,000 1,500 2,000 2,500 3,000 30 Hazy WASP-31b Temperature (K) ×10 20 Cloudy HAT-P-12b Figure 2 | Pressure–temperature profiles and condensation curves. 10 Profiles are calculated for each planet from one-dimensional non-grey ×100 17 0 radiative transfer models , which assume planet-wide average conditions –3 –2 –1 0 1 2 3

in chemical equilibrium at solar abundances, and clear atmospheres. Near-to-mid-infrared altitude difference (ΔZJ – LM/Heq) Profiles take into account incident stellar fluxes as well as the planetary interior fluxes that are appropriate given each planet’s known mass and Figure 3 | Transmission spectral index diagram of ∆ZJ − LM versus radius. Dashed and dotted lines are calculations of condensation curves H2O amplitude. Black points show the altitude difference between the ∆ of chemical species expected to condense in planetary and brown dwarf near-infrared and the mid-infrared spectral features ( ZJ − LM) versus the µ atmospheres25. The thicker portions of the pressure–temperature profiles amplitude of the 1.4- m H2O feature for eight of ten targets (see Table 1). σ indicate the pressures probed in transmission. Error bars represent the 1 measurement uncertainties. Purple and grey lines show model trends for hazy and cloud atmospheres, respectively, Sing et al. 2015 (Nature) with increasing Rayleigh scattering haze and grey cloud deck opacity during its inward orbital migration, avoided accretion and dissolution corresponding to 10×, 100× and 1,000× the solar value. We also show of icy planetesimals as well as the subsequent accretion of an appreci- clear-atmosphere models with sub-solar abundances of 0.1×, 0.01× able amount of H2O-rich gas. Such scenarios have been proposed for and 0.001× the solar value (red line). WASP-6b and WASP-39b are not 20,21 22 Jupiter based on Galileo probe measurements that indicate it to included because there are currently no HST WFC3 data for these two be a water-poor gas giant, although the measurements were affected planets. by local meteorology22. However, it is possible that these weak water absorption bands of molecular absorption, which is strongest at mid-infrared (3–5 µ m) could be attributed to cloud opacity, which have yielded featureless wavelengths and dominated by H2O, CO and CH4. We also define 23,24 transmission spectra for a number of transiting exoplanets . For ∆ ZJ − LM to measure the relative strength between the near-infrared simplicity, we define a cloud as a grey opacity source, and a haze continuum (1.22–1.33 µ m, located between strong H2O absorption as one that yields a Rayleigh-scattering-like opacity, which could be bandheads) and the mid-infrared molecular absorption. Lastly, we due to small (sub-micrometre size) particles. Silicate or higher-tem- quantify the amplitude of the H2O absorption feature seen in the WFC3 perature cloud condensates are expected to dominate the hotter data, calculating the ratio of the observed feature to that of radiative atmospheres, like those observed for brown dwarfs, while in cooler transfer models17 assuming clear atmospheres and solar abundances. atmospheres sulfur-bearing compounds are expected to play an Comparisons between these indices (Fig. 3, Extended Data Figs 1 and 2) important part in the condensation chemistry25,26. In Fig. 2, we plot show trends between cloudy and cloud-free planets. When comparing model atmospheric pressure–temperature profiles for the planets in the ∆ ZJ − LM index to the H2O amplitude (Fig. 3), the hot-Jupiter trans- our comparative study and compare them to the condensation curves mission spectra strongly favour models in which the H2O amplitude is for the expected cloud-forming molecules. The base, or bottom, of a lower owing to obscuration by hazes and clouds, rather than to lower condensate cloud is expected to form where the planetary pressure– abundances (5.9σ significance). Contaminating effects of persistent temperature profiles cross the condensation curve; in this case, Cr, unocculted star spots5 and plages28 have been proposed in order to MnS, MgSiO3, Mg2SiO4 and Fe are possible condensates. For exam- mimic the optical haze-scattering signature of hot Jupiters (particularly ple, the spectra of WASP-31b shows clouds4, which probably form HD 189733b, which orbits an active star; see Methods). However, our at pressures of about 10 mbar and can be explained by Fe or MgSiO4 survey sample is sufficiently varied in stellar activity, such that we find condensates. However, the curves alone cannot explain cloudy ver- no correlation between stellar activity and the strength of the optical sus cloud-free planets, because hazy planets such as HAT-P-12b and scattering slope (as measured by the ∆ ZUB − LM index) for planets in our WASP-12b do not cross condensation curves at observable pressures. sample (Extended Data Fig. 3). One of the main distinguishing features Therefore, atmospheric circulation must also play a part, as vertical between hazy atmospheres and those that are clear and have sub-solar mixing allows for particles to be lofted and maintained at pressures abundances resides in the near-infrared continuum, measured with the probed in transmission at the terminators. Additionally, equatorial WFC3 spectra. The presence of haze raises the level of the near-infrared eastward superrotation arising from day–night temperature variations continuum relative to the mid-infrared continuum, leading to high can allow clouds that form on the nightside to be transported to the ∆ ZJ − LM index values with low near-infrared H2O amplitudes terminator27. (Extended Data Fig. 4). In clear-atmosphere models, where the abun- We compare spectral features from our large survey to both ana- dances are lower, the continuum level drops at both near- and mid- lytic4,26 and radiative-transfer models assuming varying degrees of infrared wavelengths, accompanied by a reduction in the amplitude of 17,18 clouds and hazes . In order to evaluate the spectral behaviour of absorption features, resulting in ∆ ZJ − LM index values that are too low the sample as a whole, we define and measure three broadband spectral to explain the data (Fig. 3). indices, which can then be compared to both the observational data The hot-Jupiter transmission spectra ordered by the ∆ ZUB − LM spec- and the theoretical models (see Table 1 and Methods). We first define tral index reveals a continuum from clear atmospheres to atmospheres an index ∆ ZUB − LM that compares the relative strength of scattering, with strong clouds and hazes (Fig. 1 and Table 1). The presence of which is strongest at blue-optical (0.3–0.57 µ m) wavelengths, to that clouds has also been inferred for brown dwarf atmospheres, which

7 JANUARY 2016 | VOL 529 | NAT URE | 61 © 2016 Macmillan Publishers Limited. All rights reserved In-class activity (2) Having a second look at the basic principles of atmospheric escape, do you see any connection to the composition / existence of atmospheres in Solar System planets? What types of exoplanets are most likely to lose their atmospheres? Why? As usual...discuss in teams and share your thoughts with the class… RESEARCH LETTER

a 2.0

H I Lyα blue wing 14.4 5 )

–1 1.5 s 14.0 log[Column density (cm –2 ) erg cm 1.0 R 13.6 –14 0 10 × 13.2

0.5 ( Distance Flux ( –2

12.8 )]

0 –5 12.4 b 5 12.0 H I Ly red wing α –10 –5 0 5 4 Distance (R ) ) –1

s Figure 3 | Particle simulation showing the comet-like exospheric cloud –2 transiting the star, as seen from Earth. GJ 436b is the small black dot 3 represented at mid-transit at 0.8521Rw (ref. 26) from the centre of the star,

erg cm which is represented by the largest black circle. The dotted circle around the

–14 planet represents its equivalent Roche radius. The colour of simulation particles 2 10

× denotes the logarithm of the column density of the cloud. The transit of this simulated cloud gives rise to absorption over the blue wing of the Lyman-a line

Flux ( as shown spectrally in Extended Data Fig. 2 and by the synthetic light curve 1 in Fig. 2a.

0 21 Hydrogen escaping–4 –2 the 0 2warm 4 29.5 Neptune-mass 30.5 planet escape velocity (,26 km exoplanet s at the planet surface), consistent GJ 436b RESEARCH LETTER Time from mid-transit (h) with gas escaping from the planet. The acceleration mechanism of hydrogen atoms escaping from highly irradiated hot Jupiters is Figure 2 | Lyman-a transit light curves of GJ 436b. a, b, Data are from visit 1 debated: after escaping the planets with initial velocities dominated a 2.0 (circles), visit 2 (stars), visit 3 (squares) and visit 0 (triangles). All uncertainties by the orbital velocity (,100 km s21 for GJ 436b in the host star are 1s. a, The Lyman-a (Lya) line is integrated over [2120,240] km s21 reference frame), atoms are submitted to the stellar radiation pressure, and shows mean absorption signalsH I Lyα with blue respect wing to the out-of-transit flux of interact with the stellar wind and are14.4 eventually ionized by stellar 17.6 6 5.2% (pre-transit), 56.2 6 3.6% (in-transit) and 47.2 654.1% (post- ) 21 –1 1.5 transit). b, The line is integrated over [130,1200] km s and shows no extreme ultraviolet (EUV; 10–91.2 nm) radiation. For strong lines such s 14.0 log[Column density (cm –2 notable absorption signals: 0.7 6 3.6% (pre-transit), 1.7 6 3.5% (in-transit) and as Lyman-a, radiation pressure can overcome the stellar gravity, repel- 8.0 6 3.1% (post-transit). With a depth of 0.69%, the optical transit (thin black ling the escaping atoms towards the observer and producing a blue- lines in a and b) is barely seen at this scale between its contact) points (dotted shifted signature. In one hot Jupiter (HD 189733b), the absorption erg cm 1.0 R 13.6 lines in a and b). A synthetic light curve (green) calculated from the three- –14 dimensional numerical simulation20 is overplotted on the data in0 a. 10 × 13.2

0.5 ( Distance Flux ( visits 2 and 3, whereas it is missing in visit 1. By contrast, the flux –2

remains stable over the whole red-shifted wing of the line (Fig. 2b). 12.8 )] The decrease of the red-wing flux seen6 during the post-transit phases 20 0 of visit 1 is not reproduced during visits 2 and 3. The mean–5 post-transit 12.4 0 Doppler velocity (km s red-shifted signal is compatible with no detection at the 3s level. b 5 –20 Our combined analysis of X-ray and ultraviolet data (see Methods) )

R 12.0 H I Lyα red wing shows that stellar magnetic activity cannot explain the–10 observed –5–4 0 5 –40 4 decrease at Lyman-a. We propose that the asymmetric absorption is Distance (R ) )

–1 caused by the passage of a huge hydrogen cloud, surrounding and –6 –60 s

Figure 3 | Particle simulation( Distance showing the comet-like exospheric cloud –2 trailing the planet (Fig. 3). The planetary atmosphere is an obvious transiting the star, as seen from Earth. GJ 436b is the small black dot –80 3 source for this hydrogen. To produce this extinction signature, we –8 –1 represented at mid-transit at 0.8521Rw (ref. 26) from the centre of the star, )

erg cm estimate that an ellipsoidal, optically thick cloud ofwhich neutral is represented hydrogen by the largest black circle. The dotted circle around the –100

–14 should have a projected extension in the plan of theplanet sky of represents,12 stellar its equivalent–10 Roche radius. The colour of simulation particles 2 10 –120 × radii (Rw < 0.44R[) along the orbital path of the planetdenotes and the,2.5 logarithmRw in of the column density of the cloud. The transit of this simulated cloud gives rise to–12 absorption over the blue wing of the Lyman-a line the cross direction, well beyond the planet Roche lobe radius (0.37Rw). –14 –12 –10 –8 –6 –4 –2 024 Flux ( as shown spectrally in Extended Data Fig. 2 and by the synthetic light curve 1 Since GJ 436b grazes the stellar disk during transit, we surmise that Distance (R ) a central transit would have totally eclipsed thein star. Fig. 2a. This could happen in the case of other red dwarfs exhibiting central transits from Figure 4 | Polar view of three-dimensional simulation representing a slice of the comet-like cloud coplanar with the line of sight. Hydrogen atom 0 planets similar to GJ 436b. Future ultraviolet observationsplanet escape of systems velocity ( 26 km s21 at the planet surface), consistent –4 –2 0 2 4 29.5 30.5 velocity, and direction in the rest frame of the star are represented by arrows. similarTime to from GJ 436 mid-transit could potentially(h) reveal total Lyman-witha gaseclipses. escaping fromParticles the planet.are colour-coded The acceleration as a function mechanism of their projected of velocities on the line The radial velocity interval of the absorption signalhydrogen constrains atoms the escapingof sight (the from dashed highly vertical irradiated line). Inset, hot zoom Jupiters out of this is image to the full spatial Figure 2 | Lyman-a transitdynamics light curves of the of hydrogen GJ 436b. a atoms, b, Data and arethe from three-dimensional visit 1 debated: structureafter escapingextent the of planets the exospheric with initial cloud velocities (in blue). The dominated planet orbit is shown to scale (circles), visit 2 (stars), visitof the 3 (squares) exospheric and visit cloud. 0 (triangles). The whole All uncertaintiesvelocity rangeby is in the excess orbital of thevelocitywith (, the100 green km ellipse s21 for and GJ the 436b star is in represented the host with star the yellow circle. are 1s. a, The Lyman-a (Lya) line is integrated over [2120,240] km s21 reference frame), atoms are submitted to the stellar radiation pressure, and shows mean absorption signals with respect to the out-of-transit flux of 460 | NATURE | VOL 522 | 25 JUNE 2015 interact with the stellar wind and are eventually ionized by stellar 17.6 6 5.2% (pre-transit), 56.2 6 3.6% (in-transit) and 47.2 6 4.1% (post-G2015 Macmillan Publishers Limited. All rights reserved transit). b, The line is integrated over [130,1200] km s21 and shows no extreme ultraviolet (EUV; 10–91.2 nm) radiation. For strong lines such notable absorption signals: 0.7 6 3.6% (pre-transit), 1.7 6 3.5% (in-transit) and as Lyman-a, radiation pressure can overcome the stellar gravity, repel- 8.0 6 3.1% (post-transit). With a depth of 0.69%, the optical transit (thin black ling the escaping atoms towards the observer and producing a blue- lines in a and b) is barely seen at this scale between its contact points (dotted shifted signature. In one hot Jupiter (HD 189733b), the absorption lines in a and b). A synthetic light curve (green) calculated from the three- dimensional numerical simulation20 is overplotted on the data in a. Ehrenreich et al. (2015), Nature

visits 2 and 3, whereas it is missing in visit 1. By contrast, the flux remains stable over the whole red-shifted wing of the line (Fig. 2b). The decrease of the red-wing flux seen6 during the post-transit phases 20 of visit 1 is not reproduced during visits 2 and 3. The mean post-transit 0 Doppler velocity (km s red-shifted signal is compatible with no detection at the 3s level. –20 Our combined analysis of X-ray and ultraviolet data (see Methods) ) R shows that stellar magnetic activity cannot explain the observed –4 –40 decrease at Lyman-a. We propose that the asymmetric absorption is caused by the passage of a huge hydrogen cloud, surrounding and –6 –60 trailing the planet (Fig. 3). The planetary atmosphere is an obvious ( Distance –80 source for this hydrogen. To produce this extinction signature, we –8 –1 ) estimate that an ellipsoidal, optically thick cloud of neutral hydrogen –100 should have a projected extension in the plan of the sky of ,12 stellar –10 –120 radii (Rw < 0.44R[) along the orbital path of the planet and ,2.5Rw in –12 the cross direction, well beyond the planet Roche lobe radius (0.37Rw). –14 –12 –10 –8 –6 –4 –2 024 Since GJ 436b grazes the stellar disk during transit, we surmise that Distance (R ) a central transit would have totally eclipsed the star. This could happen in the case of other red dwarfs exhibiting central transits from Figure 4 | Polar view of three-dimensional simulation representing a slice planets similar to GJ 436b. Future ultraviolet observations of systems of the comet-like cloud coplanar with the line of sight. Hydrogen atom velocity and direction in the rest frame of the star are represented by arrows. similar to GJ 436 could potentially reveal total Lyman-a eclipses. Particles are colour-coded as a function of their projected velocities on the line The radial velocity interval of the absorption signal constrains the of sight (the dashed vertical line). Inset, zoom out of this image to the full spatial dynamics of the hydrogen atoms and the three-dimensional structure extent of the exospheric cloud (in blue). The planet orbit is shown to scale of the exospheric cloud. The whole velocity range is in excess of the with the green ellipse and the star is represented with the yellow circle.

460 | NATURE | VOL 522 | 25 JUNE 2015 G2015 Macmillan Publishers Limited. All rights reserved Red spectra of low mass stars and substellar objects IR spectra of low mass stars and substellar objects MPIA/V. Joergens - First published in "Joergens, Viki, 50 Years of Brown Dwarfs - From Prediction to Discovery to Forefront of Research, Astrophysics and Space Science Library 401, Springer, ISBN 978-3-319-01162-2." Comparison of sizes and effective temperatures of planets, brown dwarfs, and stars. Displayed are the Sun, the red dwarf star Gliese 229A, the young brown dwarf Teide 1, the old brown dwarf Gliese 229B, the very cool brown dwarf WISE 1828+2650, and the planet Jupiter. Graphic after American Scientist/Linda Huff using NASA satellite images (Sun, Jupiter) and NASA artist work (Gliese 229A + B, Teide 1, WISE1828+2650). Luminosity tracks of sub-stellar objects

Burrows et al. (1997)