The Polarization Signature of Extrasolar Planets Transiting Cool Dwarfs

1
The Polarization Signature of Extrasolar Planets
Transiting Cool Dwarfs

• Antonio Mário Magalhães
• Alex C. Carciofi
• IAG
• Universidade de São Paulo, Brazil

2
Collaborators

• Polarimetry Group at IAG-USP
• Alex Carciofi (Posdoc)
• Antonio Pereyra (Pos-doc)
• Rodolfo Valentim (MSc student)
• Flaviane Benedito, Viviana Gabriel, Fábio Godoy,
  Cássio Alves, Reinaldo Caraça, Suryendrani
  Batista (Undergrads)
• Cláudia Rodrigues (INPE/DAS)
• Acknowledgements
• FAPESP - São Paulo State Funding Agency
• CNPq, CAPES - Federal agencies

3
Summary

• Motivation
• Analytical Results
• Approximation formulae
• Numerical Results
• Monte Carlo code
• G dwarfs
• K, M T dwarfs
• Conclusions Perspectives

4
Motivation

• Venus transit, 2004 June

Magalhães
5
Motivation

• Venus transit, 2004 June
• Break in spherical symmetry!

Magalhães
6
Motivation

• Visible Sun
• (mostly) spherical

7
Motivation

• Visible Sun
• (mostly) spherical
• P ? 105 in V band
• Kemp 1987

8
Motivation

• Visible Sun
• (mostly) spherical
• P ? 105 in V band
• Kemp 1987
• Sun has Limb Polarization
• centrosymmetric
• increases towards the limb

9
Motivation

• Visible Sun
• (mostly) spherical
• P ? 105 in V band
• Kemp 1987
• Sun has Limb Polarization
• centrosymmetric
• increases towards the limb

• _at_ 6000A

Leroy 72
10
Motivation

• Visible Sun
• (mostly) spherical
• P ? 105 in V band
• Kemp 1987
• Sun has Limb Polarization
• centrosymmetric
• increases towards the limb

Leroy 00
11
Motivation

• An occultation will break the spherical symmetry
• ? polarization signal!
• Potential probe to
• stellar atmosphere
• orbital parameters
• Observable?

12
Analytical Results

• Flux from star
• Net flux
• Stokes Parameters
• P(?) limb polarization
• f(?) limb darkening

Carciofi Magalhães 05, ApJ Dec
13
Analytical Results

• Analytical approximations
• The maximum Occultation Polarization (OP) is
• 
  where
• The maximum OP depends on
• larger ? larger OP

14
Analytical Results

• Analytical approximations
• The maximum Occultation Polarization (OP) is
• 
  where
• The maximum OP depends on
• larger ? larger OP
• larger Rp, smaller ? smaller OP

15
Numerical Results
Carciofi Magalhães 05

• Monte Carlo simulations
• Limb Darkening
• Sun Claret 00
• Limb Polarization
• Sun Fluri Stenflo 99
• for other Sp Types
• explore Pl value at limb

Red Giant
k0
1
5
50
Sun
16
Numerical Results

• Monte Carlo simulations
• Limb Darkening
• Limb Polarization
• Planet radii 0.09 2 RJup
• a 0.04 UA (Silva Cruz 05)
• Transit geometries for
• 1 Rjup 2 Rjup in front of Sun
• .5 Rjup 1 Rjup in front of M2V
• .2 Rjup .4 Rjup in front of TV

17
Numerical Results

• Results for Sunlike star
• Flux
• Limit of detectability
• Hough Lucas 03

• (_at_ 4600A)
• Polarization

Carciofi Magalhães 05
2 RJup
1 RJup
2 RJup
1 RJup
18
Numerical Results

• Results for Sunlike star
• Flux

• (_at_ 4600A)
• Polarization

2 RJup
1 RJup
2 RJup
1 RJup
19
Numerical Results

• Results for Sunlike star
• Flux

• CaI 4226A (Pl from Bianda et al. 99)
• Polarization
• ? Much higher P than _at_ continuum!

Carciofi Magalhães 05
2 RJup
1 RJup
2 RJup
2 RJup
1 RJup
1 RJup
20
Numerical Results

• Results for M5 dwarf 1 RJup
• We define
• ? efficiency of starplanet system
• For detection of polarization
• Ex if Pl1? ? gt 104 for detectability of P

• Central occultation, _at_4600A

k0
1
5
50
Carciofi Magalhães 05
21
Numerical Results

• Results for M5 dwarf 1 RJup
• We define
• ? efficiency of starplanet system
• For detection of polarization
• Ex if Pl1 ? ? gt 104 for detectability of P

• _at_4600A

Carciofi Magalhães 05
22
Numerical Results

• Results for a T dwarf 1 RJup

Carciofi Magalhães 05
k0
k0
1
1
5
5
50
50
23
Numerical Results

• Summary of expected Occultation Polarization
• ?
• Nonsymmetrical OP curves
• ? eccentricity!
• (eg., from CoRoT sample)
• ?P106 can be obtained in 1h for V9 4m
  telescope
• CoRoT will likely detect longer transits as well,
  and
• higher P values expected

• Note Detectability 106 104
• Hough Lucas 03

Carciofi Magalhães 05
24
Summary of Occultation Polarization (OP)

• For G dwarfs
• OP is generally large enough for 1 RJup
• resonant lines favored
• For K, M, Tdwarfs
• least favourable cases
• 1 RJup, 1 RNep possible
• more favourable cases
• 1 REarth possible for M, T types
• OP)max during occultation independent of incl.
  angle
• Obtaining orbital eccentricity possible