1. Scattering in Planetary Atmospheres
Svetlana Berdyugina
Kiepenheuer Institut für Sonnenphysik,
Freiburg, Germany
SPW3, Tenerife, 2002
Hot Molecules in Exoplanets and Inner Disks

2. Content Polarized scattering Model Observations Earth
Rayleigh scattering
Mie scattering
Observations
Solar system
Exoplanets
SPW3, Tenerife, 2002

3. Scattering in a stellar atmosphere
polarization depends on the scattering angle
polarization is determined by the projection of dipoles towards observer
polarization is perpendicular to the scattering plane
polarization arises because of the spatial symmetry braking
anisotropic radiation
non-spherical geometry
magnetic/electric field

4. Scattering in a planetary atmosphere
polarization depends on the scattering angle
polarization is determined by the projection of dipoles towards observer
polarization is perpendicular to the scattering plane
polarization arises because of the spatial symmetry braking
anisotropic radiation
non-spherical geometry
magnetic/electric field

5. Rayliegh Scattering: Earth
on bound electrons
Sky color and polarization 
Intensity and polarization are larger for higher
frequency (shorter wavelength) light
Hegedüs et al. (2007)

6. Can humans sense polarization?
1846, von Haidinger
Viking navigation tool

7. Earth-shine polarization
Earth shine polarized spectra: Rayleigh, O2, H2O, vegetation(?)
Sterzik et al. (2012)

8. Scattering in a stellar atmosphere
Radiative transport equation:
Scattering source function:
HotMol tools: StarPol
Chandrasekhar (1960), Fluri & Stenflo (1999), Kostogryz & Berdyugina (2014)

9. Scattering in a planetary atmosphere
Radiative transport equation for Stokes parameters:
Scattering source function:
Formal solution:
* = 0: I-(, <0, ) = stellar incident radiation from the top
* = : I+(, >0, ) = planet intrinsic radiation from the bottom
Boundary conditions
Sobolev (1956), Chandrasekhar (1960),…, Berdyugina (2017), JSQRT

10. Polarized scattering on molecules
Hot Jupiter at 0.02 AU:
single scattered stellar photons dominate planetary radiation
limb brightnening, high polarization
(Berdyugina 2017, JQSRT)
I/I0
Q/I
Source Function:
Black: thermal radiation of the planet,
Green: single scattered stellar radiation,
Magenta: multiple scattered stellar and planetary radiation,
Red dotted: the total source function
Relative opacities:
Blue dashed: total scattering
Blue solid: total absorption
Blue dashed-dotted: particle scattering

11. Polarized scattering on molecules
Hot Jupiter at 0.05 AU:
single scattered stellar photons ~ multiply scattered photons
moderate limb brightnening & polarization
(Berdyugina 2017, JQSRT)
I/I0
Q/I
Source Function:
Black: thermal radiation of the planet,
Green: single scattered stellar radiation,
Magenta: multiple scattered stellar and planetary radiation,
Red dotted: the total source function
Relative opacities:
Blue dashed: total scattering
Blue solid: total absorption
Blue dashed-dotted: particle scattering

12. Polarized scattering on molecules
Hot Jupiter at 0.1 AU:
multiply scattered photons dominate planetary radiation
low limb brightnening & polarization
(Berdyugina 2017, JQSRT)
I/I0
Q/I
Source Function:
Black: thermal radiation of the planet,
Green: single scattered stellar radiation,
Magenta: multiple scattered stellar and planetary radiation,
Red dotted: the total source function
Relative opacities:
Blue dashed: total scattering
Blue solid: total absorption
Blue dashed-dotted: particle scattering

13. Polarized scattering on molecules
H2O example
(Berdyugina 2017, JQSRT) Q I

14. Molecular polarizability
Polarization amplitudes scale with
intrinsic polarizability, W2
opacity
Rayleigh scattering: positive intrinsic polarizability with two asymptotic values
0.4 in Q branch lines
0.1 in R and P branch lines
Raman scattering: positive and negative intrinsic polarizability with asymptotic values
0.1 in RP and PR transitions
–0.2 in QP and RQ transitions
Rayleigh scattering
Raman scattering
Berdyugina et al. (2002)

15. Polarized scattering on particles
(Berdyugina 2017, JQSRT)
Scattering on droplets:
nr = 1.6 & 1.9
Forward scattering
Rayleigh limit
Geometrical optics limit
Rainbow near165-170
“Glory” near 140-150 and at 180
“Anomalous diffraction“ near 20-30
Intensity Polarization

16. Polarized scattering on particles
Hot Jupiter at 0.02 AU:
Scattering with different cloud depths:
70km km km
(Berdyugina 2017, JQSRT) I I I Q Q Q
Source Function: thermal radiation of the planet (black), single scattered stellar radiation (green),
multiple scattered stellar and planetary radiation (magenta), and the total one (red dotted line),
Relative opacities: total scattering (dashed blue) and absorption (solid blue), particle scattering (dashed-dotted blue)

17. Effects of atmosphere composition
Particles of 1m
Incident
light
Seager et al. (2000)
Molecules (1), tropospheric clouds (2), stratospheric haze (3)
Stam et al. (2004)

18. Earth
Polarized Cloudbow: POLDER
Breon & Goloub (1998)

19. Venus Polarization measurements: Lyot (1929), Dollfus (1969)
Models: Sobolev (1968), Coffeen (1968,1969), Hansen & Hovenier(1971)
Clouds: 1.05 m droplets of 75% H2SO4 + 25% H2O

20. Gas Giants I Q U Jupiter Uranus Neptune
Schmid et al. (2006), Joos & Schmid (2007)

21. Unresolved Exoplanets
Detection of reflected light  direct probe of planetary environment
Physics: scattering polarization
Polarization is perpendicular to the scattering plane
Max. polarization at 90 scattering angle
Stellar light is unpolarized (or modulated with a different period)
Polarization varies as planet orbits the star
(Fluri & Berdyugina 2010)
polarimeter

22. i=98, =270, e=0
R = 1.2RJ
a = 0.03 AU
P = 2.2 d
(Fluri & Berdyugina 2010)

23. i=98, =270, e=0
R = 1.2RJ
a = 0.03 AU
P = 2.2 d
(Fluri & Berdyugina 2010)

24. i=98, =225, e=0
R = 1.2RJ
a = 0.03 AU
P = 2.2 d
(Fluri & Berdyugina 2010)

25. i=98, =180, e=0
R = 1.2RJ
a = 0.03 AU
P = 2.2 d
(Fluri & Berdyugina 2010)

26. i=135, =270, e=0
R = 1.2RJ
a = 0.03 AU
P = 2.2 d
(Fluri & Berdyugina 2010)

27. i=180, =270, e=0
R = 1.2RJ
a = 0.03 AU
P = 2.2 d
(Fluri & Berdyugina 2010)

28. i=130, =270, e=0.5, =270 R = 1.2RJ a = 0.03 AU P = 2.2 d
(Fluri & Berdyugina 2010)

29. First Detection: HD189733b Transiting hot Jupiter
(Berdyugina et al. 2008)
Transiting hot Jupiter
mass 1.15 MJ
period 2.2 d
semimajor axis 0.03 AU
B band (440nm, DiPol, KVA60)
(Berdyugina et al. 2008)
93 nightly measurements (3h)
Errors ~510–5
UBV (360,440,550nm, TurPol)
(Berdyugina et al. 2011a)
35 nightly meas. (3-4h)
29 standard stars for calibration: ~(1-2)10–5
Errors ~110–5
Monte Carlo error analysis
Amplitude (9  1)x10–5 B
(Berdyugina et al. 2011) UB

30. HD189733b: Blue Planet Geometrical Albedo, Ag: Strong function of 
(Berdyugina et al. 2011)
Geometrical Albedo, Ag:
Strong function of 
0.60.3 at 370 nm
0.610.12 at 450 nm,
0.280.15 at 550 nm,
<0.2 at 600 nm
<0.1 at >800 nm
Similar to that of Neptune
blue: Rayleigh and Raman scattering on H2
red: absorption by molecules
P ~ scatt/abs ratio
Blue Planet

31. Model with Condensates: HD189733b
Berdyugina 2011
Polarimetry and transit data fit with one model
Semi-empirical model
Rayleigh/Mie scattering: H, H2, He, CO, H2O, CH4, e–, MgSiO3
Absorption: H, H–, H2–, H2+,He, He–, metals
Haze: High-altitude condensate layer with 20-30nm particles
R=1/RJ(U)~1.190.24  Scat
R=1/RJ(B)~1.180.10  Scat
(in agreement with Sing et al. 2011)
R=1/RJ(V)<0.750.20  Abs
R=1/RJ(RI)<  Abs
Polarization  scat/abs ()
Berdyugina et al. (2008, 2011)
Wiktorovicz (2009)
Lucas et al. (2009)
++ Pont et al. (2007), 550 nm

32. HD189733b: Blue Planet
Primary transit spectroscopy, HST (Sing et al. 2011):
Raleigh scattering – opacity increases to the blue
Additional opacity (absorption?) at nm
R(~1)
 Total opacity
= absorption+ scattering

33. HD189733b: Blue Planet
Secondary eclipse spectroscopy, HST (Evans et al. 2013):
Geometrical albedo:
Reflected flux ~ total opacity = scattering+absorption

34. What does it mean, blue planet?

35. New Trend in Hot Jupiter Art
Before:
After:

36. Blue Gas Planets Neptune geometrical albedo model
GA of a pure Rayleigh scattering atmosphere = const (white)
Raman scattering & haze absorption reduces GA in near UV
CH4 & CIA absorption reduces GA in the red
0.78
(Sromovsky 2005)

37. Blue Gas Giants Spectropolarimetry of Neptune
Methane bands are polarized
Single scattered photons avoide the absorption
Multiply scat.phot.are absorbed
Depends on scat/abs ratio
Search in blue Jupiters: identify absorption source and determine chemical composition!
100%
30%
(Joos & Schmid 2007)

38. Key Points: Polarized scattering on molecules
In planetary atmospheres polarization arises due to its anisotropic irradiation, both from the top and from the bottom.
Polarimetry is a differential technique for direct detection of exoplanets
Albedo, atmos.composition, weather, rot. periods, magnetospheres
Rayleigh scattering with the strong wavelength dependence dominates the reflected light  blue planets
Rayleigh scattering:
Polarization is sensitive to the incident stellar flux: hotter stars hosting closer-in planets are systems potentially producing larger polarization in the blue.
Limb brightening for large fluxes of single-scattered stellar photons
Molecular band polarization can be stronger than continuum
Mie scattering (nr = 1.6 & 1.9):
Forward scattering is dominant
Rainbow (near165-170)
“Glory” (near 140-150 and at 180)
“Anomalous diffraction“ (near 20-30)