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

Pdf

Dependence on Period

0/1log

PPP ePk

Pd

Pdf

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?