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

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

1. Core formation

2. Hydrostatic gas accretion

3. Runaway gas accretion

Jupiter (~300\(M_\oplus\))

Saturn (~100\(M_\oplus\))

Uranus & Neptune (~15 \(M_\oplus\))

Terrestrial planets & giant impacts

(disk lifetime)

Image credit: C. Mordasini

(~1,000 km)

Terrestrial planets formed after the gaseous disk is gone, also called second-generation planets.

Planetesimal formation, gas physics

A brief summary of

solar system formation

Snow line

If theory is correct, then extra-solar systems should look like ours.

But they do not.

How does solar system look like from outside?

'Pale Blue Dot' by Voyager 1 from 40 AU

Solar system seen from alpha centauri (1.3 pc)

Earth: R_Earth, 300 K

100xR_Earth, 6000 K

10xR_Earth, 150 K

L \propto R^2 T^4
\frac{L_{\rm Jupiter}}{L_{\rm Sun}} = 4 \times 10^{-9} \\ \frac{L_{\rm Earth}}{L_{\rm Sun}} = 6 \times 10^{-10}

(In addition, planets are very close to the star.)

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?

https://www.dcsc.tudelft.nl/~mverhaegen/n4ci/gallery.htm

So far, <10 detections

b

c

d

e

  • Radial velocity

How to detect planets indirectly?

  • Transit
  • Astrometry
  • Microlensing

First detection: 1989/1995

# of detections: ~700

First detection: 2000

# of detections: >4000

# of detections: 0

(Gaia ~2024)

First detection: 2003

# of detections: ~50

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

Warm Jupiters

Sub-Saturns

(1%)

(10%)

(30%)

(tens of %)

(~3%)

(~5%)

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

Dynamical channel

Possible solutions

Disk migration

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

The success of core accretion model

Fischer & Valenti (2005)

f \propto Z^2 \propto N_{\rm Fe}^2
  • Giant planet-metallicity correlation

Pollack et al. (1996)

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

Pollack et al. (1996)

Suzuki et al. (2016)

(see Herman, Zhu, & Wu 2019 for the radius distribtuion)

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

{\rm transit~depth} = \frac{R_{\rm p}^2}{R_\star^2} \\ {\rm duration} = \frac{2R_\star}{v_{\rm p}}
a \cdot \sin{i} < R_\star \rightarrow \sin{i} < R_\star/a \sim 3\%
  • 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?

0 Earth-like planets, but 1000s of exoplanets!

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)

Owen (2019)

(see also Owen & Wu, 2013, 2017)

Image credit: NASA

Mean-motion resonances

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

\( x\)

\( y \)

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

Jupiter's satellites

MMRs prevent close encounters

Disk-driven migration leading to mean-motion resonances

Lee & Peale (2002)

Evolution of GJ 876 system

Image credit: P. Armitage

MMRs in observed planet pairs

Figures from Winn & Fabrycky (2015)

  • 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

Wide-Field InfaRed Survey Telescope (WFIRST, ~2025)

Brightness

Image credit: Penny et al. (2019)

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

Future directions:

Better characterization of close-in planets

James Webb Space Telescope (~2021)

TESS: Transiting Exoplanet Survey Satellite (2018-now)

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.

SURP-2020: Exoplanets

By Wei Zhu(祝伟)

SURP-2020: Exoplanets

A lecture given to 2020 UofT SURP students.

  • 351
Loading comments...

More from Wei Zhu(祝伟)