Reflected Light FromExtra Solar Planets

Modeling light curves of planets

with highly elliptical orbits

Daniel Bayliss, Summer Student, RSAA, ANU

Ulyana Dyudina, RSAA, ANU

Penny Sackett, RSAA, ANU

Introduction

• 119 extra solar planets detected.

– 118 found by precise radial velocity measurements.

– 1 by found by transit photometry.

• No reflected light from extra solar planets detected to date, however the albedo of τ Boo constrained by lack of signal (Charbonneau et al.,1999, ApJ, 522, L145).

Reflected light

• Amount of reflected light given by:

p=albedo d=planet-star separation

=phase function Rp=planet radius

Space Photometry

• Current photometric precision limited by atmosphere to around LP/L* ~50 x 10-6.

• Canadian micro satellite MOST target list includes 3 stars

with planets (close-in, circular).

• NASA’s Kepler satellite (2007) with 100,000+ target stars.

• Predicted to achieve precision of LP/L*< 10 x 10-6.

MOST

Kepler

Elliptical Orbits

Semi-major axis

Apocentre Pericentre

Eccentricities of Extra Solar PlanetsE

ccen

tric

ity

Semi-major axis (AU)

Inclination: i=0° (face on)

Orientation of the orbital plane - Inclination

Inclination: i=10°

Inclination: i=45°

Inclination: i~90° (edge on)

Argument of pericentre: ω=0°

To observer

Orientation of the orbital plane - Argument of Pericentre

To observer

Argument of pericentre: ω=90°

To observer

Argument of pericentre: ω=-90°

Model

• Reflective properties of planets based on Pioneer data of Jupiter.

• Planetary radius assumed to be 1 Jupiter radius.

• Example light curve properties:

– Semi-major axis = 0.1 AU

– Argument of pericentre = 60°

– Eccentricity = 0.5

TimeP days

8 x 10-6

0

Example Light Curve

i=90o (Edge on)

LP

/ L

*

Pericentre Apocentre

Time

8 x 10-6

i=75o

0

LP

/ L

*

P days

Time

8 x 10-6

i=60o

0

LP

/ L

*

P days

Time

8 x 10-6

i=45o

0

LP

/ L

*

P days

Time

8 x 10-6

i=30o

0

LP

/ L

*

P days

Time

8 x 10-6

i=15o

0

LP

/ L

*

P days

Time

8 x 10-6

i=0o (Face on)

0

LP

/ L

*

P days

Example - HD 108147b

• Extra solar planet discovered by Pepe, Mayor, et al (2002, A&A , 388, 632).

• Properties:

– Semi-major axis = 0.104 AU

– Period = 10.9 days

– Eccentricity = 0.498

– Argument of pericentre = -41°

– Inclination = ?

Time10.9 days

40 x 10-6

HD 108147b

0

LP

/ L

*

Time10.9 days

10 x 10-6

Contrast

contrast

0

LP

/ L

*

Contrast for e=0In

clin

atio

n (i

)

90

0-90

Scale at 0.1 AU (x10-6)

100

10

1

0.1

Argument of pericentre (ω)

090

Kepler

Contrast for e=0.6In

clin

atio

n (i

)

90

0-90

Scale at 0.1 AU (x10-6)

Argument of pericentre (ω)

090

100

10

1

0.1

Contrast for various e

Argument of pericentre (ω)

Scale at 0.1 AU (x10-6)

Incl

inat

ion

(i)

e=0.6 e=0.7 e=0.8

e=0 e=0.1 e=0.2

e=0.3 e=0.4 e=0.5

100

10

1

0.1

Conclusions

1. A low inclination (face on) orientation can show strong contrast if it has a high eccentricity orbit.

2. Light curves from elliptical orbits may help constrain a systems inclination.

3. Favourable pericentric orientation can dramatically increase the contrast.