Courtney Dressing
Advisor: David Charbonneau
All Souls College, Oxford
July 4, 2011


Number of target stars: 156,453 (58,041)
Number of candidates: 1,235 (438)
◦ Orbiting 997 (375) stars
Solar Subset:
Teff = 4100-6100 K
log g = 4.0-4.9
Kepmag < 15
Bright Dwarf
Sample:
Teff = 3600-7100 K

Within each grid cell, calculate:
◦
◦
◦
◦
Number of candidates
“Augmented” number of candidates
Number of stars searched
Planet occurrence rate

Number of non-transiting planets with same
radius and period as transiting candidates
n pl
n pl ,aug ,cell  
j 1
1
pj
where
 R* 
p j 

 a j
=probability of transit

Number of stars for which each transiting
planet has SNR > 10
SNR 

n tr t dur
 CDPP
3 hr
Planet
Occurrence =
Rate
Augmented # of Planets
# of Stars Searched
n p l , cell
f cell 

j 1
1/ p j
n *, j


Periods <50 days
Radii: 2-32 REarth
Radius
Range
Occurrence
Rate
2-4
0.130±0.008
4-8
0.023±0.003
8-32
0.013±0.002
2.8 REarth
Planet
Radius
2 REarth
10 Days
Period
17 Days
df  R 
d log R
kRR

kR= 2.9 +0.5/-0.4
α = -1.92 ± 0.11
df  P 
d log P


 k P P 1 e

  P / P0 

df  P 
d log P


 k P P 1 e

  P / P0 
Larger planets have
shorter cutoff periods
and sharper transitions.

 Teff  5100 K 
f T eff  f 0  k T 

 1000 K

f0= 0.165±0.011
kT=-0.081±0.011

Random errors?
◦ Trend preserved for Teff = 4100-6100 K
◦ Trend preserved after Monte Carlo applying
gaussian random deviates to Teff and log g

Systematic stellar radius bias?
◦ Would require log g error of 1.6 dex
◦ Errors in KIC are ~0.25 dex

Systematic metallicity bias?
◦ Errors on [Fe/H] in KIC are ≳0.2 dex (rms)
◦ Cannot be ruled out


More massive
planets have more
H/He gas
Change at 4.5 ME?
Models from Fortney et al. 2007
Solar system
Kepler
Other surveys

Assume planets
with densities
above 4 g/cm3
are primarily
composed of
refractory
elements

Toy density models
◦ Constant density
◦ Piece-wise constant density

Compared to Eta-Earth Survey
◦
◦
◦
◦
Volume-limited survey of 166 GK dwarfs
35 planets detected around 24 stars
Keck-HIRES
See Howard et al. 2010


Black: Kepler
prediction
Red: Eta-Earth
measurement
Decreasing density

Best models
have ρ≳4g/cm3
for Rp≲3RE




Planet occurrence increases with decreasing
radius and increasing orbital period
Smaller planets (2-4 RE) are more common
around cooler stars (metallicity effect?)
Larger planets have steeper cutoffs at shorter
periods than smaller planets
There is a ridge of high planet occurrence
from 3 days and 2 RE to 50 days and 4 RE.