Survey Statistics (Planet Occurrence)

Andrew Howard UC Berkeley → IfA/Hawaii

Sagan Summer Workshop - July 23-27, 2012

Monday, July 23, 2012 2003 Michelson Interferometry Summer School

Monday, July 23, 2012 2003 Michelson Interferometry Summer School

Monday, July 23, 2012 Outline

Planet Occurrence - what can we measure?

Planet-Metallicity Correlation

Doppler Surveys - Eta-Earth Survey

Transit Survey Completeness

Kepler Planet Occurrence

Monday, July 23, 2012 Outline

Planet Occurrence - what can we measure?

Planet-Metallicity Correlation

Doppler Surveys - Eta-Earth Survey

Transit Survey Completeness

Kepler Planet Occurrence

Monday, July 23, 2012 Planet Occurrence

Apparently simple measurement:

Number of Planets Occurrence = Number of

Monday, July 23, 2012 Driven by Science Questions

High planet occurrence → planets of particular types commonly form and evolve under particular conditions

Monday, July 23, 2012 Driven by Science Questions

High planet occurrence → mass / radius / temp planets of particular types orbital characteristics { degree of multiplicity } commonly form and evolve under particular conditions

Monday, July 23, 2012 Driven by Science Questions

High planet occurrence → planets of particular types commonly form and evolve under particular conditions initial conditions: evolutionary conditions: stellar mass planetary dynamics stellar metallicity planet/disk dynamics stellar multiplicity /planet interactions { implied disk properties } { stellar evolution } Monday, July 23, 2012 Driven by Science Questions

High planet occurrence → planets of particular types difficult to disentangle commonly formation and evolution form and evolve under particular conditions

Monday, July 23, 2012 Planet Distribution - Msini-Period

Exoplanet.eu: ● all planets

“RV+Astrometry”

Monday, July 23, 2012 Planet Distribution - Msini-Period

Exoplanet.eu: ● all planets

“RV+Astrometry”

Monday, July 23, 2012 Inferring Planet Formation Mechanisms from Planet Population Statistics

Measurements Models

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: ● all planets RV+Transit

Exoplanet.eu: clearinghouse of planet claims

Exoplanets.org: curated orbit database

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: ● RV-detected ● Transit-detected

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: ● RV-detected

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: RV-detected and: ● Mstar > 0.6 Msun ● Mstar < 0.6 Msun (M dwarfs)

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: RV-detected and: ● Mstar > 0.6 Msun

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: RV-detected, Mstar > 0.6 Msun and: ● Mstar < 1.2 Msun ● Mstar > 1.2 Msun (F dwarfs, subgiants, giants)

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: RV-detected and: ● Mstar =0.6-1.2 Msun

Monday, July 23, 2012 Exoplanet Distribution - Msini-Period

Exoplanets.org: RV-detected and: ● Mstar =0.6-1.2 Msun

How do you compute?

# of Planets # of Stars

Monday, July 23, 2012 Planet Occurrence Apparently simple measurement requires careful treatment of numerator and denominator:

Number of Planets Occurrence = Number of Stars

Monday, July 23, 2012 Planet Occurrence Apparently simple measurement requires careful treatment of numerator and denominator: • Define planet parameters of measurement (M, R, P, e, etc.) • Set planet detection threshold • Incompleteness — correct for missed planets

Number of Planets Occurrence = Number of Stars

Monday, July 23, 2012 Planet Occurrence Apparently simple measurement requires careful treatment of numerator and denominator:

Number of Planets Occurrence = Number of Stars

• Define stellar parameters of measurement (M, R, Fe/H, Teff, logg, etc.)

Monday, July 23, 2012 • Define planet parameters of measurement (M, R, P, e, etc.) • Set planet detection threshold • Incompleteness — correct for missed planets

Number of Planets Occurrence = Number of Stars

• Define stellar parameters of measurement (M, R, Fe/H, Teff, logg, etc.)

Monday, July 23, 2012 Pause ...... questions so far?

• Define planet parameters of measurement (M, R, P, e, etc.) • Set planet detection threshold • Incompleteness — correct for missed planets

Number of Planets Occurrence = Number of Stars

• Define stellar parameters of measurement (M, R, Fe/H, Teff, logg, etc.)

Monday, July 23, 2012 Outline

Planet Occurrence - what can we measure?

Planet-Metallicity Correlation

Doppler Surveys - Eta-Earth Survey

Transit Survey Completeness

Kepler Planet Occurrence

Monday, July 23, 2012 Planet-Metallicity Correlation Early Observation: 4/4 Jupiter host stars are iron-rich (Gonzalez et al. 1997)

Monday, July 23, 2012 Planet-Metallicity Correlation Early Observation: 4/4 Jupiter host stars are iron-rich (Gonzalez et al. 1997)

Science Question: Are jovian planets formed by core accretion, which depends critically on quickly accreting a ~10 Earth-mass core out of metals from the protoplanetary disk?

Monday, July 23, 2012 Planet-Metallicity Correlation Early Observation: 4/4 Jupiter host stars are iron-rich (Gonzalez et al. 1997)

Science Question: Are jovian planets formed by core accretion, which depends critically on quickly accreting a ~10 Earth-mass core out of metals from the protoplanetary disk? Core Accretion

Monday, July 23, 2012 Planet-Metallicity Correlation Early Observation: 4/4 Jupiter host stars are iron-rich (Gonzalez et al. 1997)

Science Question: Are jovian planets formed by core accretion, which depends critically on quickly accreting a ~10 Earth-mass core out of metals from the protoplanetary disk?

Statistical Question: Are jovian planets more commonly found orbiting metal- rich stars? What is the occurrence of jovian planets as a function of stellar metallicity?

Monday, July 23, 2012 Planet-Metallicity Correlation Early Observation: 4/4 Jupiter host stars are iron-rich (Gonzalez et al. 1997)

Science Question: Are jovian planets formed by core accretion, which depends critically on quickly accreting a ~10 Earth-mass core out of metals from the protoplanetary disk?

Statistical Question: Are jovian planets more commonly found orbiting metal- rich stars? What is the occurrence of jovian planets as a function of stellar metallicity?

Many responses: Focus on Fischer & Valenti (2005)

Monday, July 23, 2012 Measure [Fe/H] using Spectroscopy Made Easy (SME)

Valenti & Fischer (2005) — measure stellar parameters (SME) Fischer & Valenti (2005) — planet-metallicity correlation

Monday, July 23, 2012 Define the Sample

1040 nearby dwarfs and subgiants in planet search programs at Keck/Lick/AAT — nearly unbiased sample

Monday, July 23, 2012 Compute Planet Occurrence

• Define planet parameters of measurement (M, R, P, e, etc.) • Set planet detection threshold • Incompleteness — correct for missed planets

Number of Planets Occurrence = Number of Stars

• FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos)

Monday, July 23, 2012 Compute Planet Occurrence

• Define planet parameters of measurement (M, R, P, e, etc.) • Set planet detection threshold • Incompleteness — correct for missed planets

Number of Planets Occurrence = Number of Stars

• FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 Compute Planet Occurrence

• Period < 4 years, ~Jovian mass (depending on period) • K > 30 m/s • Assume 100% planet detection completeness (reasonable)

Number of Planets Occurrence = Number of Stars

• FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 Monday, July 23, 2012 Monday, July 23, 2012 Planet-Metallicity Correlation

Monday, July 23, 2012 Fit to Model

Monday, July 23, 2012 Fit to Model

Poisson errors ∝ sqrt(Npl)

Monday, July 23, 2012 Fit to Model

Poisson errors ∝ sqrt(Npl)

Fit to Power Law Model

Free params

Monday, July 23, 2012 Planet-Metallicity Correlation

Statistical Question: Are jovian planets more commonly found orbiting metal-rich stars? What is the occurrence of jovian planets as a function of stellar metallicity? Answer: Yes, metal-rich stars are more commonly planet hosts. Jovian planet occurrence scales as the square of the number of iron atoms Science Question: Are jovian planets formed by core accretion, which depends critically on quickly accreting a ~10 Earth-mass core out of metals from the protoplanetary disk? Answer: The planet-metallicity correlation supports the core accretion mechanism, both qualitatively and quantitatively.

Monday, July 23, 2012 • Period < 4 years, ~Jovian mass (depending on period) • K > 30 m/s • Assume 100% planet detection completeness (reasonable)

Number of Planets Occurrence = Number of Stars

• FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 • Period < 4 years, ~Jovian mass (depending on period) • K > 30 m/s • Assume 100% planet detection completeness (reasonable) No incompleteness Number of Planets Occurrence = Number of Stars

• FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 • Period < 4 years, ~Jovian mass (depending on period) • K > 30 m/s • Assume 100% planet detection completeness (reasonable) No incompleteness Number of Planets Occurrence = Number of Stars Well-defined sample • FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 • Period < 4 years, ~Jovian mass (depending on period) • K > 30 m/s • Assume 100% planet detection completeness (reasonable) No incompleteness Number of Planets Occurrence = Number of Stars Well-defined sample Uniform [Fe/H] Catalog • FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 Pause ...... questions so far?

• Period < 4 years, ~Jovian mass (depending on period) • K > 30 m/s • Assume 100% planet detection completeness (reasonable) No incompleteness Number of Planets Occurrence = Number of Stars Well-defined sample Uniform [Fe/H] Catalog • FGK dwarfs and subgiants — nearby; nearly unbiased (Hipparcos) • [Fe/H] and other stellar params measured uniformly by SME

Monday, July 23, 2012 Outline

Planet Occurrence - what can we measure?

Planet-Metallicity Correlation

Doppler Surveys - Eta-Earth Survey

Transit Survey Completeness

Kepler Planet Occurrence

Monday, July 23, 2012 NASA-UC Eta-Earth Program

• RV survey of 238 nearby GKM dwarfs

• Search for low-mass planets (Msini = 3-30 MEarth) • Constrain population of low-mass planets and planet formation theory

39% G stars 33% K stars 28% M stars

Statistically unbiased (nearly) stellar population:

Eta-Earth stars • V < 11 Hipparcos (d < 50 pc) • distance < 25 pc • log R’HK < -4.7 (inactive)

Monday, July 23, 2012 NASA-UC Eta-Earth Program

• RV survey of 238 nearby GKM dwarfs

• Search for low-mass planets (Msini = 3-30 MEarth) • Constrain population of low-mass planets and planet formation theory

G stars 39% G stars 33% K stars 28% M stars

Statistically unbiased (nearly) stellar population:

Eta-Earth stars • V < 11 Hipparcos (d < 50 pc) • distance < 25 pc • log R’HK < -4.7 (inactive)

Monday, July 23, 2012 NASA-UC Eta-Earth Program

• RV survey of 238 nearby GKM dwarfs

• Search for low-mass planets (Msini = 3-30 MEarth) • Constrain population of low-mass planets and planet formation theory

G stars K stars 39% G stars 33% K stars 28% M stars

Statistically unbiased (nearly) stellar population:

Eta-Earth stars • V < 11 Hipparcos (d < 50 pc) • distance < 25 pc • log R’HK < -4.7 (inactive)

Monday, July 23, 2012 NASA-UC Eta-Earth Program

• RV survey of 238 nearby GKM dwarfs

• Search for low-mass planets (Msini = 3-30 MEarth) • Constrain population of low-mass planets and planet formation theory

G stars K stars M stars 39% G stars 33% K stars 28% M stars

Statistically unbiased (nearly) stellar population:

Eta-Earth stars • V < 11 Hipparcos (d < 50 pc) • distance < 25 pc • log R’HK < -4.7 (inactive)

Monday, July 23, 2012 Stellar Mass Distribution G & K dwarfs

30

20 Number 10

0 0.4 0.6 0.8 1.0 1.2 1.4 Mstar (MSun)

Monday, July 23, 2012 Stellar Mass Distribution G & K dwarfs

30

HIRES Echelle Spectrum 20 Number 10

0 0.4 0.6 0.8 1.0 1.2 1.4 Mstar (MSun)

Monday, July 23, 2012 Stellar Mass Distribution G & K dwarfs

30

HIRES Echelle Spectrum Iodine Absorption Cell 20 Number 10

0 0.4 0.6 0.8 1.0 1.2 1.4 Mstar (MSun)

Monday, July 23, 2012 Stellar Masses G & K : All have parallaxes & Stellar evolution Tracks

Number of RVs per Star Median: 35 Keck RVs per star

All have high cadence run during 10 Keck nights

Monday, July 23, 2012 Stellar Metallicities 40 Unbiased Metallicity: 30 Volume-limited survey median [Fe/H] = -0.04 20 Number

10

0 ï0.6 ï0.4 ï0.2 ï0.0 0.2 0.4 0.6 [Fe/H]

Stellar Activity - logR’HK 50

40 Activity: logR’HK < -4.7 30

Number 20

10

0 ï5.2 ï5.1 ï5.0 ï4.9 ï4.8 ï4.7 ï4.6 log RvHK

Monday, July 23, 2012 166 GK Stars in Eta-Earth Survey

Monday, July 23, 2012 Standard Stars

The best standards have an RMS of 1.5-2.0 m/s.

These are almost always late G / early K dwarfs.

We do not explicitly average over P-modes; Texp ~ 1-5 min

Monday, July 23, 2012 Standard Stars

The best standards have an RMS of 1.5-2.0 m/s.

These are almost always late G / early K dwarfs.

We do not explicitly average over P-modes; Texp ~ 1-5 min

Monday, July 23, 2012 Minimum RV Observations for Eta-Earth Star

HD 191785 ) 1 −

s 5

m (

y t i

c 0 o l e V

−5 RMS = 2.42 ms−1 2005 2006 2007 2008 2009 Time (Years)

Monday, July 23, 2012 Minimum RV Observations for Eta-Earth Star

HD 191785 ) 1 −

s 5

m (

y t i

c 0 o l e V

−5 RMS = 2.42 ms−1 2005 2006 2007 2008 2009 Time (Years)

Monday, July 23, 2012 Minimum RV Observations for Eta-Earth Star

HD 191785 ) 1 −

s 5

m (

y t i

c 0 o l e V

−5 RMS = 2.42 ms−1 2005 2006 2007 2008 2009 Time (Years)

20+ observations over 4 years Monday, July 23, 2012 Minimum RV Observations for Eta-Earth Star

HD 191785

1 high-cadence run ) 1 −

s 5

m (

y t i

c 0 o l e V

−5 RMS = 2.42 ms−1 2005 2006 2007 2008 2009 Time (Years)

20+ observations over 4 years Monday, July 23, 2012 Precision of Eta-Earth Observaons

Velocity RMS of Eta-Earth stars Limited by: Stellar jitter Guiding Inst. Stability Photon Noise

Monday, July 23, 2012 HD 156668 - Discovery RVs

2005 Time (Yr) 2010

1 10 100 1000

Period (d) Howard et al. 2011

Monday, July 23, 2012 HD 156668 - High-pass Filtered RVs

2005 Time (Yr) 2010

1 10 100 1000

Period (d) Howard et al. 2011

Monday, July 23, 2012 HD 156668 - Residual RVs

2005 Time (Yr) 2010

1 10 100 1000

Period (d) Howard et al. 2011

Monday, July 23, 2012 HD 156668b - Detected Super-Earth!

Star: HD 156668 (K3V) distance = 24 pc V = 8.3 [Fe/H] = 0.05 quiet

Planet: M sin i = 4.15 ME P = 4.6455 d e = 0 (fixed)

Howard et al. 2011

Monday, July 23, 2012 HD 7924 b HD 156668 b

Mass = 4.15 ME /sin i P = 4.6455 d K = 1.89 m s⌧1 5 e = 0.0 )

1

s

m (

y t 0 i

c

o l

e

V

⌧5

⌧1 RMS = 1.74 m s ri = 0.97 0.0 0.5 1.0 Orbital Phase

HD 97658 b Gl 785 b

Mass = 8.17 ME /sin i P = 9.494 d Mass = 21.6 ME /sin i P = 74.39 d K = 2.75 m s⌧1 K = 4.07 m s⌧1 10 e = 0.0 10 e = 0.30

) ) 1 1 ⌧ ⌧ s 5 s 5 m m ( (

y t y i t 0 i c c 0 o l o l e e V V ⌧5 ⌧5

⌧1 ⌧10 RMS = 2.78 m s = 1.59 ⌧1 ri RMS = 2.06 m s = 1.17 ⌧10 ri 0.0 0.5 1.0 0.0 0.5 1.0 Orbital Phase Howard et al. 2009, 2011a,b, ApJ Orbital Phase Monday, July 23, 2012 HD 7924 b 33 Detected Planets in the Survey

• Some found by others; confirmed here • Firm Period, Msini • All published

Monday, July 23, 2012 Limits on Non-detecons of Planets

15 HD 185144

10 Nobs = 131 RMS = 2.0 m/s

5

0 RV (m/s) ï5

ï10 Best Observed ï15 2004 2005 2006 2007 2008 2009 2010 2011 Date

Monday, July 23, 2012 Limits on Non-detecons of Planets

15 HD 84737

10 Nobs = 22 RMS = 3.0 m/s

5

0 RV (m/s) ï5

ï10 Worst Observed ï15 2004 2005 2006 2007 2008 2009 2010 2011 Date

15 HD 185144

10 Nobs = 131 RMS = 2.0 m/s

5

0 RV (m/s) ï5

ï10 Best Observed ï15 2004 2005 2006 2007 2008 2009 2010 2011 Date

Monday, July 23, 2012 Limits on Non-detecons of Planets

15 HD 84737

10 Nobs = 22 RMS = 3.0 m/s

5

0 RV (m/s) ï5

ï10 Worst Observed ï15 2004 2005 2006 2007 2008 2009 2010 2011 Date

15 HD 185144 HD 185144 1000 10 Nobs = 131 RMS = 2.0 m/s ) 50 days E 5 100 0 RV (m/s) ï5 10 Maximum Msini (M ï10 Best Observed 1 ï15 2004 2005 2006 2007 2008 2009 2010 2011 1 10 100 1000 Date Period (d)

Monday, July 23, 2012 Limits on Non-detecons of Planets

15 HD 84737 HD 84737 1000 10 Nobs = 22 RMS = 3.0 m/s ) 50 days E 5 100 0 RV (m/s) ï5 10 Maximum Msini (M ï10 Worst Observed 1 ï15 2004 2005 2006 2007 2008 2009 2010 2011 1 10 100 1000 Date Period (d) 15 HD 185144 HD 185144 1000 10 Nobs = 131 RMS = 2.0 m/s ) 50 days E 5 100 0 RV (m/s) ï5 10 Maximum Msini (M ï10 Best Observed 1 ï15 2004 2005 2006 2007 2008 2009 2010 2011 1 10 100 1000 Date Period (d)

Monday, July 23, 2012 Completeness

HD 84737 1000 ) 50 days E

100

10 Maximum Msini (M

1

1 10 100 1000 Period (d)

HD 185144 1000 ) 50 days E

100

10 Maximum Msini (M

1

1 10 100 1000 Period (d)

Monday, July 23, 2012 Detected planets Candidate planets (FAPs ~ 1-5%)

Candidate planets included in counting planets.

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Detected planets Candidate planets (FAPs ~ 1-5%) = 1 planet 100% Complete Candidate planets included in counting planets.

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Detected planets Candidate planets (FAPs ~ 1-5%) = 1 planet 100% Complete Candidate planets included in counting planets. 2 planets ≈ 50% Complete ≈

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Detected planets Candidate planets (FAPs ~ 1-5%) = 1 planet 100% Complete Candidate planets included in counting planets. 2 planets ≈ 50% Complete ≈ 3 planets ≈ 30% Complete

≈ Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Msini = 300-1000 ME 2 Detected planets 0 Candidate planets

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Msini = 100-300 ME 2 Detected planets 0 Candidate planets

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Msini = 30-100 ME 2 Detected planets 0 Candidate planets

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Msini = 10-30 ME 4 Detected planets 1 Candidate planets

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Msini = 3-10 ME 6 Detected planets 2 Candidate planets

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Howard et al. 2010, Science, 330, 653 Monday, July 23, 2012 Key Result: Power-law Mass Distribuon

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 0.05

Msini = 30ï100 M 0.04 Earth

Key Result: Power-law Mass DistribuonMsini = 10ï30 MEarth

Msini = 3ï10 MEarth 0.03 Compute Errors assume binomial statistics 0.02 scale missed planets w/det + cand Probability Density 0.01

0.00 0.00 0.05 0.10 0.15 0.20 0.0 0.12 Occurrence 0.24 Rate

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 0.05

Msini = 30ï100 M 0.04 Earth

Key Result: Power-law Mass DistribuonMsini = 10ï30 MEarth

Msini = 3ï10 MEarth 0.03 Compute Errors assume binomial statistics 0.02 scale missed planets w/det + cand Probability Density 0.01

0.00 0.00 0.05 0.10 0.15 0.20 0.0 0.12 Occurrence 0.24 Rate

0.2

0.0

ï0.2 α df/dlogM = kM ï0.4 +0.27 _ k = 0.39 -0.16 ï0.6 +0.12 α = -0.48 -0.14 ï0.8 ï1.0

ï1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Howard et al. 2010, Science, 330, 653 k Monday, July 23, 2012 Key Result: Occurrence rate of Super-Earths + Neptunes

Occurrence rate of super-Earths & Neptunes:

+5 15 -4% occurrence Msini = 3-30 ME, P < 50 days

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Key Result: Earth-mass Planets Common

Extrapolaon of Power Law Model:

+16 ηEarth = 23 -10% for Msini = 0.5-2.0 ME, P < 50 days

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 Credit: NASA/JPL-Caltech/UC Berkeley

Monday, July 23, 2012 Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 1. Hot Neptunes rare Msini=10-100 ME, P < 20 days Rare Hot Neptunes

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 1. Hot Neptunes rare Msini=10-100 ME, P < 20 days

2. Highest planet occurrence rate: ● Msini=10-30 ME, P > ∼20 days ● Msini=3-10 ME, P > ∼5 days Rare Hot Neptunes

Highest Planet ? ? Occurrence Rate

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 1. Hot Neptunes rare Msini=10-100 ME, P < 20 days

2. Highest planet occurrence rate: ● Msini=10-30 ME, P > ∼20 days ● Msini=3-10 ME, P > ∼5 days

3. Low-mass planets: No short-period pileup Rare Hot Neptunes

Highest Planet ? ? Occurrence Rate

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 1. Hot Neptunes rare Msini=10-100 ME, P < 20 days

2. Highest planet occurrence rate: ● Msini=10-30 ME, P > ∼20 days ● Msini=3-10 ME, P > ∼5 days

3. Low-mass planets: No short-period pileup

4. Low-mass planets:

Rare Multi-planet systems common Hot Neptunes

Highest Planet ? ? Occurrence Rate

Howard et al. 2010, Science, 330, 653

Monday, July 23, 2012 • Period < 50 days, Msini ≥ 3 Earth-masses • Msini and period well-measured by Doppler signal • Correct incompleteness with star-by-star analysis

Number of Planets Occurrence = Number of Stars

• GK dwarfs — nearby; nearly unbiased (Hipparcos)

Monday, July 23, 2012 • Period < 50 days, Msini ≥ 3 Earth-masses • Msini and period well-measured by Doppler signal • Correct incompleteness with star-by-star analysis

Significant incompleteness Number of Planets Occurrence = Number of Stars

• GK dwarfs — nearby; nearly unbiased (Hipparcos)

Monday, July 23, 2012 • Period < 50 days, Msini ≥ 3 Earth-masses • Msini and period well-measured by Doppler signal • Correct incompleteness with star-by-star analysis

Significant incompleteness Number of Planets Occurrence = Number of Stars Well-defined sample • GK dwarfs — nearby; nearly unbiased (Hipparcos)

Monday, July 23, 2012 Break ...... questions?

• Period < 50 days, Msini ≥ 3 Earth-masses • Msini and period well-measured by Doppler signal • Correct incompleteness with star-by-star analysis

Significant incompleteness Number of Planets Occurrence = Number of Stars Well-defined sample • GK dwarfs — nearby; nearly unbiased (Hipparcos)

Monday, July 23, 2012