Giant Planet Occurrence Rate as a Function of Mass

Sabine ReffertLandessternwarte Heidelberg, Germany

in collaboration with

Christoph Bergmann LSW; Univ. Canterbury (NZ)

Trifon Trifonov LSW; Univ. Hong Kong

Andreas Künstler LSW; AIP Potsdam

Andreas Quirrenbach LSW

Our Lick Survey

• Doppler survey of 376 G and K giants at Lick Observatory

• Hamilton Spectrograph (R~60 000), 60cm CAT Telescope, Iodine Cell

• ongoing since 1999 (86 K giants), added stars in 2000 (76 K giants) and in 2004 (174 G and K giants), ended in 2012

• most stars have between 20 and 100 observations, though there are outliers in both directions

• radial velocity precision 5-8 m/s

• RV jitter of K giants typically at least 20 m/s (due to pulsations on short timescales)

Hertzsprung-Russell Diagram

K0 M0K3G5

masses are derived from comparison with evolutionary tracks (Girardi et al. 2000)

Masses of 373 G and K Giants in Lick Sample

• stellar masses range from 0.9 to 7.8 MSun

• but most masses are between 1 and 3 MSun

1 - 3 MSun

Planets in Lick Sample

• identified 17 secure planets and 26 planet candidates (total: 43)

• in altogether 35 systems

• on top of that, there are 2 linear trends in the systems which could be indicative of planets/brown dwarfs in wide orbits

• 2 planets and 4 planet candidates are found in spectroscopic binaries

• 2 planet candidates have masses larger than 40 MJup (not shown in diagram)

• periods are in the range from 0.5 to 2.3 years

1 - 3 MSun

• note: no distinction between planets and brown dwarfs here

• mass distribution between planets and brown dwarfs is continuous; most massive secure substellar object has mass of 25 MJup

Distribution of Planets as a Function of Metallicity and Mass

K0 M0K3G5

planet fraction highest for largest metallicity and smallest mass bin

Planet Occurrence as a Function of Mass and Metallicity

K0 M0K3G5

heavily smoothed map

• planet occurrence rate strong function of both metallicity and stellar mass

• planet occurrence rate varies between 0% and about 40% across diagram

Planet Metallicity Correlation

K0 M0K3G5

f([Fe/H]) / 10�[Fe/H] � = 1.7+0.3�0.4

Comparison of Planet-Metallicity Correlation with Others

K0 M0G5

f([Fe/H]) / 10�[Fe/H]

� = 1.7+0.3�0.4Lick Giant Star Sample 1-5 MSun, giants

Fischer & Valenti (2005) 0.7-1.5 MSun

Udry & Santos (2007) 0.7-1.4 MSun

Johnson et al. (2010) 0.2-2.0 MSun, MS + subgiants

Pasquini et al. (2007) 1-3 MSun, giants

Takeda et al. (2008) 1.5-5 MSun, giants

� = 2.0� = 2.0� = 2.0

� = 2.04

� = 1.2± 0.2

� ⇡ 0

� ⇡ 0

in sharp contrast to other giant star investigations, we find the same planet-metallicity correlation as known for main-sequence stars

Planet Occurrence Rate as a Function of Mass

• strong dependence on mass

• best fitted with gaussian

• maximum at about 1.9 MSun

• for M★ > 2.7 MSun planet rate < 1.6% (1σ)

Fitting Planet Occurrence Rate as a Function of Mass

• fitted planet occurrence rate as a function of mass with gaussian, power law with cutoff, simple power law and with a flat distribution

• gaussian works best, whereas a flat distribution does not work (Bayesian evidence against it is ‘strong’)

• (maximum), (width)

• result consistent with Johnson et al. (2010), who derived a rising planet occurrence rate for masses up to 2 MSun based on subgiants

• although there are 113 stars in the mass bin between 2.7 and 5 MSun, we do not find a single planet among them

• this gives a giant planet occurrence rate of <1.6% (1σ) in this mass range

• mass and metallicity are not correlated

µ = 1.9+0.1�0.5M� � = 0.5+0.5

�0.2M�

Why Giant Planets might not form around Massive Stars…

• snow line is located further out for more massive stars: asnow ~ M★

α with α = 1 (Ida & Lin 2005) or α = 2 (Kennedy & Kenyon 2008)

• further out, gas densities and Kepler velocities are smaller, which slows down the growth rate

• migration time scale is also longer, τmig ~ M★1.5 (Kennedy & Kenyon 2008)

➡ thus, slower growth rate, longer migration time scale and faster disk dispersal of the protostellar disk together might prevent the formation of giant planets which would be observable at a few AU today

Effect of Stellar Evolution?

• significant orbital evolution takes place once a star leaves the main-sequence due to stellar evolution

• most important effects are due to mass loss (which will make the orbit wider) and tidal effects (which shrink the orbit)

• results depend strongly on detailed modelling of stellar mass loss

time [Gyr]

stel

lar

radi

us/

plan

et s

emi-m

ajor

axi

s [A

U]

stellar radius

size of planet orbit

→ tip of red giant branchReference: Villaver & Livio 2009, ApJ 705, L81

biggest changes in orbits occur around the tip of the red giant branch, when the stellar radius is largest

→ stellar mass dependent critical semi-major axes for planet survival

Effect of Stellar Evolution?

• the observed semi-major axes of planets around giant stars are 0.5 AU and up, considerably larger than the critical semi-major axis for survival; a large parameter space is not populated, especially for stars with masses larger than 2 MSun

• Kunitomo et al. (2011) conclude that other effects than stellar evolution must shape the observed planet population (such as the planet formation process)

• on the other hand, significant changes (planets being enguled for kicked out) to the orbits of planets in our Lick sample might have occurred already: 41% of Lick giants are on the RGB, 56% on the HB (3% unknown); however, 80% of our planet-bearing giants are on the HB!

• yet, most likely the observed paucity of planets around the more massive giant stars is not a result of stellar evolution, but rather due to those planets not being formed initially

Summary

1. There is a strong planet-metallicity correlation present in our sample, with β = 1.7 very similar to what is found for main-sequence stars.

2. Giant planet occurrence rate and stellar mass are tightly correlated, with a peak around 1.9 MSun and a sharp decline for higher masses.

3. Analysis of a sample with uniform planet detection capability yields the same result.

4. There is no planet-metallicity correlation for the candidate planets; some of them might indeed not be real planets.

5. The absence of giant planets at the high mass end of the Lick sample might be explained by a smaller growth rate and a longer migration time scale coupled with a shorter lifetime of the protostellar disk.

6. The absence of giant planets at the high mass end is most likely not due to stellar evolution.

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