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Courtney Dressing Advisor: David Charbonneau
All Souls College, Oxford July 4, 2011
Howard et al. 2011:Planet Occurrence within 0.25
AU of Solar-Type Stars from Kepler
Number of target stars: 156,453 (58,041) Number of candidates: 1,235 (438)
◦ Orbiting 997 (375) stars
Kepler February Data Release
Solar Subset:Teff = 4100-6100 K
log g = 4.0-4.9Kepmag < 15
Bright Dwarf Sample:
Teff = 3600-7100 K
Planet Candidates
Within each grid cell, calculate:◦ Number of candidates◦ “Augmented” number of candidates◦ Number of stars searched◦ Planet occurrence rate
Planet Occurrence Rate
Number of non-transiting planets with same radius and period as transiting candidates
Augmented Number of Candidates
jj a
Rp
*
pln
j jcellaugpl p
n1
,,
1
=probability of transit
where
Number of stars for which each transiting planet has SNR > 10
Number of Stars Searched
hr
tnSNR durtr
CDPP 3
# of Stars SearchedAugmented # of Planets
Planet Occurrence Rate
cellpln
j j
jcell n
pf
,
1 *,
/1
Planet Occurrence
Rate =
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
Planet Occurrence Rate
Planet Occurrence Rate
PlanetRadiu
s
10 Days
17 Days
2 REarth
2.8 REarth
Period
Dependence on Radius
RkRd
RdfR
log
kR= 2.9 +0.5/-0.4α = -1.92 ± 0.11
Dependence on Period
0/1log
PPP ePk
Pd
Dependence on Period
0/1log
PPP ePk
Pd
Larger planets have shorter cutoff periods
and sharper transitions.
Dependence on Spectral Type
Dependence on Spectral Type
K
KTeffkfTf Teff 1000
51000
f0= 0.165±0.011kT=-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
Possible Explanations for the Trend in Occurrence Rate of Small Planets with Teff
More massive planets have more H/He gas
Change at 4.5 ME?
Planet Density
Models from Fortney et al. 2007
Solar systemKeplerOther surveys
Assume planets with densities above 4 g/cm3 are primarily composed of refractory elements
Planet Density
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
Mapping Kepler Radii to Masses
Black: Kepler prediction
Red: Eta-Earth measurement
Mapping Kepler Radii to Masses
Decreasing density
Best models have ρ≳4g/cm3 for Rp≲3RE
Mapping Kepler Radii to Masses
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.
Summary
Questions?