Exoplanets:

Theories vs. Observations

Wei Zhu (祝伟)

Astro 101 Lecture

2020-05-27

Outline

• Solar system formation theory
• Exoplanet discoveries & theory developments
• Future directions
• Summary

Planet formation in one picture

Minimum Mass Solar Nebula

• MMSN: A disk model that gives the minimum mass of solid material to build the solar system.

Weidenschilling (1977); Hayashi (1981)

(see here for a step-by-step construction of MMSN)

Murcury

Mars

Asteroid

belt

$$ \Sigma(r) \propto r^{-3/2} $$

planet #1

planet #2

planet #3

Region of dominance

Pollack et al. (1996)

Giant planets & core accretion model

\({\rm M}_{\rm env}\)

Terrestrial planets & giant impacts

(disk lifetime)

Image credit: C. Mordasini

(~1,000 km)

Image from  Maruyama & Ebisuzaki (2017)

A brief summary of

solar system formation

Snow line

How does solar system look like from outside?

'Pale Blue Dot' by Voyager 1 from 40 AU

Can we see planets directly?

• Yes, but only hot (young) and distant planets
• Star light must be suppressed
  • atmosphere turbulence \( \rightarrow \) Adaptive optics (AO)

HR 8799: planet brightness ~\(10^{-5}\) star

Can we see planets directly?

So far, <10 detections

b

c

d

e

• Radial velocity

How to detect planets indirectly?

• Transit

• Astrometry

• Microlensing

Exoplanet detections

The use of CCDs and computers in astronomical observations significantly improved the efficiency and precision.

Ground-based transit

Radial velocity survey

Global microlensing survey

Kepler

Mayor & Queloz (1995)

Charbonneau et al. (2000)

Gillon et al. (2017)

Bond et al. (2003)

Hot Jupiters

Cold Jupiters

Cold Neptunes

Super Earths

Data from NASA Exoplanet Archive

(1%)

(10%)

(30%)

(tens of %)

51 Peg b & Nobel prize

Didier Queloz

Michel Mayor

"for the discovery of an exoplanet orbiting a solar-type star."

• Hot Jupiters: \( m_{\rm p}> M_{\rm Sat} \), \(P < 10 \) days (or \(a < 0.1\) au)
• Minimum-mass solar nebula: $$ \Sigma(r) \propto r^{-3/2} $$
• More mass in the outer region: $$ \frac{d M}{d\log{r}} \propto \Sigma \cdot r^2 \propto r^{1/2} $$

Weidenschilling (1977); Hayashi (1981)

Hot Jupiter puzzle

Murcury

Mars

Asteroid

belt

Figure from Dawson & Johnson (2018)

Possible solutions

• Ex situ formation + migration:
  • Dynamical process & tidal interaction;
  • Disk migration (Planet-disk interaction).
• In situ formation

The success of core accretion model

• Giant planet-metallicity correlation

Pollack et al. (1996)

• Core accretion model is sensitive to the amount of available solid material.

Pollack et al. (1996)

The failure of core accretion model

• Runaway gas accretion would yield bimodal mass distribution.

• Observations show a rather smooth mass (and radius) distribution.

• Light curve shape: depth & duration

• Transit condition:

Transit method

• Earth: depth=\(10^{-4}\), duration=12 hr (vs. period=1 yr).
• Jupiter: depth=1%, duration=1 d (vs. period=11 yr).

Kepler mission (2009-2013)

K2 mission (2014-2019)

\(10^5\) target stars & 4-yr observations, how many Earth-like planets do we expect to detect?

Kepler discoveries

• Planets are ubiquitous in the Galaxy:
  • ~30% of Sun-like stars have Kepler-like planets;
  • Each system has on average 3 planets within 1 au;
  • \(\lesssim10\%\) have Earth-like planets.
• More small planets than big ones.
• Small planets have ~1-10% mass in atmosphere (first-generation planets?)
• Photo-evaporation valley.

Saturn

Neptune

Earth

Photo-evaporation valley

Fulton et al. (2017)

Image credit: NASA

Mean-motion resonances

Image credit: M. Rex (left), Fabrycky & Murray-Clay (right)

• Mean motion \( n \equiv \frac{2\pi}{P} \)
• MMRs: \( \frac{n_1}{n_2} \approx \frac{p+q}{p} \)

Jupiter's satellites

Disk-driven migration leading to mean-motion resonances

Image credit: P. Armitage

MMRs in observed planet pairs

• RV planet pairs: ~1/3 of well characterized pairs are close to MMRs (Wright et al. 2011).

• Kepler planet pairs:
  1. Weak preference for MMRs;
  2. Asymmetry around MMRs.

Kepler planets: in situ or migration?

Mimimum mass extra-solar nebula

Mimimum mass solar nebula

Chiang & Laughlin (2013)

• Why in situ:
  • No strong preference for MMRs;
  • Kepler planets preferentially have outer companions;
  • ...
• Why migration:
  • Somewhat inevitable;
  • Mass budget;
  • ...

Where we are now...

• Key processes in planet formation:
  • Planetesimal formation, core formation, gas accretion, giant impacts.
• Exoplanet observations
  • RV & giant planets: the success & failure of core-accretion model;
  • Kepler planets:
    • Small planets with significant atmosphere are common;
    • Photo-evaporation valley;
    • Mean-motion resonances, in situ vs. migration.

Future directions:

Probing the cold planet population

Brightness

• Planet mass-radius relation \(\rightarrow\) constraint on composition;
• Exoplanet atmosphere observations.

Future directions:

Better characterization of close-in planets

Future directions:

Observing planet formation

Figures from Andrews (2020)

Atacama Large Millimeter/submillimeter Array (ALMA)

Summary

• Key processes in planet formation:
  • Planetesimal formation, core formation, gas accretion, giant impacts.
• Exoplanet observations
  • RV & giant planets: the success & failure of core-accretion model;
  • Kepler planets:
    • Small planets with significant atmosphere are common;
    • Photo-evaporation valley;
    • Mean-motion resonances, in situ vs. migration.
• Future directions:
  • Cold planet population, better characterization of close-in planets, observational planet formation, etc.