Correlation between exoplanet heavy­element content and host star metallicity (?)

Steve Desch Astrophysics Seminar September 11, 2009

Outline

Reviewing Guillot et al. (2006):

Exoplanets are smaller and therefore more metals­rich than expected; correlates with host star's metallicity.

•Observations­­­what can we measure about exoplanets? •Planetary Models­­­what can we infer about exoplanets? •Analysis of Guillot et al. (2006), who found a correlation of planetary metals content with host star metallicity. •Models for giant planet formation ­­­ where did these exoplanets come from? •Conclusions •??? •Pr ofit! Observations of Exoplanets Up until 1980s astronomers traditionally searched for planets using astrometric techniques.

Over decades, the Sun will shift ~ 1010 cm ~ 0.001 AU (in ecliptic plane). Sensitive to distant ­­­ and slowly orbiting ­­­ planets. As seen from 10 pc, amounts to 0.001". Too small to be measured by ground­based telescopes.

Cr edit: http://planetquest.jpl.nasa.gov Observations of Exoplanets First planets outside the solar system were discovered in 1992 by Wolszczan et al. ... around a pulsar! PSR B1257+12 Timing of pulsar signals revealed changing distance of pulsar from Earth, due to tugging of the star by planets.

Credit: http://en.wikipedia.org/wiki/ PSR_B1257%2B12 Observations of Exoplanets First planets around Sunlike stars found in 1995, from radial velocity searches.

Credit: http://planet quest.jpl.na sa.gov Observations of Exoplanets Doppler shifts detected in sharp atomic lines.

Vr = VSTAR sin i = (VP) x (MP / MSTAR) sin i

1/3 VP  (2 G MSTAR / P)

MP sin i  MSTAR / VP Only gives knowledge

of MP sin i (i.e., a i lower limit) To Earth

Vr

Observations of Exoplanets First exoplanets around main sequence stars were a surprise.

­1 ­3 Expected Vr = (VJ) x (MJ/M) ~ (12 km s ) x (10 ) ~ 12 m/s. High­precision data collection for decades presumed. California / Carnegie planet search prepared for the long haul. First exoplanet was around 51 Pegasi (51 Peg b), discovered by Mayor & Queloz in October 1995, scooping California!

V ~ 60 m/s !! P = 4.23 days!! a = 0.053 AU T ~ 1300 K

M sin i = 0.472  0.039 MJ Observations of Exoplanets This caused Marcy & Butler of the California search to look at their data early. They quickly confirmed 51 Peg b and announced 47 UMa b and 70 Vir b in 1996.

Observations of Exoplanets

First transiting exoplanet discovered was HD 209458 b

(Cha rbonneau et al. 2000; Henry et al. 2000). Observations of Exoplanets

If radius of star is known, we automatically get radius of the planet, because

2 ­0.4m (RP / RSTAR) = 1 ­ 10 We also can observe the spectrum of the background star in and out of transit, and learn about the absorbing characteristics of the exoplanet's atmosphere. This is how Na vapor was discovered in HD 209458 b (Charbonneau et al. 2002) and HD189773b (Redfield et al 2008), and water vapor in HD 189773b (Tinetti et al. 2007), or maybe not (Grillmair et al. 2007; Ehrenreich et al. 2007)?

Observations of Exoplanets Best strategy is to combine radial velocity and transit measurements.

•From the photometric dimming during eclipse, we know RP.

•From the radial velocity measurements, we know MP sin i.

•From the fact that it transits, we know sin i  1. Possible to get both mass and radius simultaneously.

This is the point of the Kepler mission, launched March 2009: discover a boatload of planets by photometry, then follow up with the (more difficult) radial velocity observations.

Observations of Exoplanets

Will sample 100,000 stars every 30 minutes. Expected to find ~ 500 planetary systems. Observations of Exoplanets

New r esults! (August 2009) Observations of Exoplanets

Kalas et al. (2008)

Direct imaging of planets came in 2008, with this object  around Fomalhaut ( PsA), orb iting just inside a dusty ring. Observations of Exoplanets Transit Micro­ There are now 373 RV known exoplanets. lensing 10 http://planetquest.jpl .nasa.gov 1 5 m/s

1 m/s 0.1 Each discovery technique has its 0.01 own selection

effects. M / MJ 5% 0.1% 0.01 0.1 1 10 100 a / AU Observations of Exoplanets

To Earth

dL dS

Star's gravity can deflect light of background star through Einstein angle E ~ 0.001" If angular separation of source and lens is  and u =  / E, background star's light am plified by factor A(u): Observations of Exoplanets

Normal lensing event (OGLE2005­BLG­006). Angular separation between lens and source varies Einstein angle over months. Observations of Exoplanets

To Earth

dL dS

Planet's gravity can also deflect light of background star. Planet's Einstein angle smaller; planet moves 1 Einstein angle in matter of hours.

Observations of Exoplanets

Combined star­planet gravitational potential can lead to complicated lensing patterns.

Detailed modeling provides MP / MSTAR and (P ­ STAR) / E Follow­up radial­velocity and/or transit observations can

provide m ore information. Observations of Exoplanets Ground­based Optical Gravitational Lensing Experiment (Udalski et al.) surveys the Galactic bulge for chance alignments. Follow­up observations revealed 18+ transits (Bouchy et al. 2005). These are primarily the dataset used by Guillot et al. (2006).

Along with planetary properties (MP, RP), stellar properties are also recorded (age, [Fe/H], Teff).

NB: OGLE­TR­10b has two different radius determinations by two groups (Bouchy et al. 2005 and Holman et al. 2005),

Planetary Interior Models The analysis of Guillot et al. (2006) draws on the planetary models of Guillot (2005), AREPS 33, 493

Assumes a three­layer model: •convective envelope of molecular

H2, He •convective mantle of liquid metallic hydrogen •core of rock and ice

Solves equations of hydrostatic equilibrium, including equation of state of H / He mixtures, and includes cont ractional luminosity. Planetary Interior Models

Guillot ( 2005) Planetary Interior Models Guillot (2005)

Planets shrink as they age

Luminosity initially due to Kelvin­Helmholtz contraction; after electr on degeneracy sets in, is du e to simple cooling. Planetary Interior Models Simple model for giant planets supposes they are basically polytropes, with isentropic gas such that P = K .

Lane­Emden equation of stellar structure Planetary Interior Models Once n is fixed, solutions for () exist, allow us to find other variables:

n is fixed once equation of state is determined (may depend on mass)

Mass­Radius Relation Planetary Interior Models

Equation of state softens Guillot (2005) with increasing mass. At low M, rocky core dominates EOS, is near incompressible, =∞, n=0 At high M, metallic H dominates; electrons become degenerate, approaches =5/3, n=3/2.

For M = 0.1 MJ, n = 0.6

For M = 1 MJ, n = 1.0 For M = 10 M , n = 1.3 in J 80% of planet. Planetary Interior Models Radius varies with mass:

+0.16 For M = 0.1 MJ, n = 0.6, R ~ M

0 For M = 1.0 MJ, n=1.0, R ~ M From polytropic models  ­0.18 with P =K  For M = 10 MJ, n=1.3, R ~ M

Maximum radius at M ~ few MJ Radius swells with stellar heating: Irradiation increases surface temperature and therefore K, entropy of interior.

+0.25 For M = 0.1 MJ, n = 0.6, R ~ K

+0.50 For M = 1.0 MJ, n=1.0, R ~ K

+0.76 For M = 10 MJ, n=1.3, R ~ K Incr easing K always increases rad ius. Planetary Interior Models Note: These planets heavily irradiated.

Rocky planets are Guillot ( 2005) simply denser Analysis of Guillot et al (2006)

Extra­large planets (HD209458b, OGLE­TR­10b) hard to account for. Why the extra entropy?

Difference between observed exo­ planet radii and radii predicted based on standard evolutionary model, assuming solar metallicity. [Fe/H] = log10[ (Fe/H) / (Fe/H) ] Analysis of Guillot et al (2006)

Models used to calculate the mass of metals (mass of core?) in the planet.

Negative MZ just means their model is missing physics, can't explain why solar metallicity plane t is too large. Analysis of Guillot et al (2006)

Guillot et al. added an extra term to their planetary models. First idea: HD209458b and OGLE­TR­10b differ from other exoplanets: maybe non­zero orbital inclination, tidal dissipation act in these bodies only. Can't model, but could exclude those two exoplanets. A second idea: key physics missing from all models, e.g., EOS is wrong? Opacities wrong? Too hard. Where to start? A third idea: extra term is slowing contraction: Tidal effects generate kinetic energy that is transported downward by convection (Guillot & Showman 2002; Showman & Guillot 2002).

The y arbitarily put 0.5% of incident stellar heating into interior. Analysis of Guillot et al (2006)

Core masses updated with this new model.

OGLE­TR­10b ­­­ with two different radius determinations ­­­ is the oddball. solar metallicity

Analysis of Guillot et al (2006)

Inferred metals mass ­ ([Fe/H]­0.8) metallicity correlation: MZ = (60 ME) x 10

Note: higher MZ in atmosphere would increase opacity, increase

Teff, increase R Conclusions

Inferred metals mass ­ ([Fe/H]­0.8) metallicity correlation: MZ = (60 ME) x 10 Correlation is with metallicity only: •Guillot et al. found no correlation with stellar age. •No correlation with stellar mass •No correlation with stellar effective temperature •No correlation with UV flux received from star ­­­ this is not due to photoevaporation.

Conclusions

Inferred metals mass ­ ([Fe/H]­0.8) metallicity correlation: MZ = (60 ME) x 10 "Large cores don't form if [Fe/H] < ­0.1" (?!) Several implications: •If Jupiters require large (P < 4 years) cores to form, then Jupiters should be rare / not exist around low­metallicity stars •Resembles survey results of Fischer & Valenti (2005)

2 Prob = 3% x [(Fe/H) / (Fe/H)]

Conclusions Several implications: •It appears Jupiters do need large cores to form; distinguishes between formation mechanisms. •Mechanism 1 is "disk instability" (Boss 2000): entire regions of the protoplanetary disk become unstable simultaneously and collapse to form planet.

1 •Predicts MZ / MP  (Fe/H) , (no lower limit on metallicity), not observed.

Conclusions Several implications: •Mechanism 2 is "core accretion" (e.g., Pollack et al. 1996).

First a 10 ME core forms, which can then capture H, He gas

2 •If core mass inhibited by growth times, MZ (Fe/H) (e.g., Ida 1 & Lin 2004) If inhibited by available mass, MZ (Fe/H) . MP = mass of gas, independent (?) of MZ. •Sousa et al. (2008) recently concluded that low­metallicity stars preferentially form "Neptunes" while high­metallicity stars form "Jupiters". Implication is that Jupiters form early enough to accrete gas. Supports core accretion models in which growth times are bottleneck, explains Fischer & Valenti (2005) observations. ...

Conclusions Caveats / Points of Discussion: •Guillot's planetary models remarkably sensitive to "minor" variations in physics (at the level to which they are put to use). How can they be trusted? •Why is downward­transported heat equal to 0.5% of the incident starlight? Seems like an ad hoc kludge. •OGLE­TR­10b is singled out as unsusual because it has two disparate measured radii. But Guillot et al. used the value of Bouchy et al., from which the other radii were derived. Seems logically inconsistent. •Small number statistics. Obviously more data are needed. •Conclusions are probably correct but premature.