What we learn from multi-planet systems

Wei Zhu (祝伟)

Canadian Institute for Theoretical Astrophysics

\(\longrightarrow\) Tsinghua University (2021 March)

Exoplanet Demographics, 2020-11-11

  • Since April of 2019.
  • Exoplanet@Tsinghua:
    • Xuening Bai (白雪宁), disk physics, planet formation;
    • Shude Mao (毛淑德), gravitational (micro-)lensing, planet search;
    • Chris Ormel, planet formation, protoplanetary disks;
    • Sharon Wang (王雪凇), exoplanet detection & characterization;
    • Wei Zhu (祝伟), exoplanet statistics & architecture, microlensing.
  • Other fields of focus: high-energy astrophysics, cosmology and galaxy formation.
  • We are hiring! At both faculty & post-doc levels.

http://astro.tsinghua.edu.cn/

Solar system as an example

  • Planets have diverse properties (\(\sim10^2\) in separation and \(\sim10^4\) in mass).
  • Planets have small but substantial orbital eccentricities (\(\lesssim0.2\)) and mutual inclinations (\(\lesssim 6^\circ\)).
  • Solar system was once dynamically active, and may become chaotic again in \(\sim\) Gyr timescale.

Image credit: iLectureOnline

Solar system as an example

\(\Delta I = 5.7^\circ \quad \quad \quad 2.1^\circ  \quad \quad \quad~~ 1.3^\circ \quad \quad \quad \quad 0.5^\circ ~~ \quad \quad \quad - \quad \quad \quad \quad 2.1^\circ \quad \quad \quad \quad 0.5^\circ \quad \quad \quad \quad 0.5^\circ \)

\(e = 0.21 \quad \quad \quad 0.01      \quad \quad       0.02      \quad \quad 0.06       ~~\quad \quad       0.05       \quad \quad \quad      0.06        \quad \quad       0.05          \quad \quad0.01 \)

  • Planets have diverse properties (\(\sim10^2\) in separation and \(\sim10^4\) in mass).
  • Planets have small but substantial orbital eccentricities and mutual inclinations.
  • Solar system was once dynamically active, and may become chaotic again in \(\sim\) Gyr timescale.

w/ known companions

w/o known companions

Transit (ground)

Transit (space)

RV

Microlensing

Imaging

Based on data from NASA Exoplanet Archive.

Are multi-planet systems flat?

  • The weighted transit duration ratio (Steffen et al. 2010).
  • Mutual inclination disperson \( \sigma_i\sim 3^\circ \) (e.g., Fang & Margot 2012, Fabrycky et al. 2014).
    • A lower limit.

\( \xi \equiv \frac{\rm (Transit~chord~length)_{in}}{\rm (Transit~chord~length)_{\rm out}} = \frac{T_{\rm in} P_{\rm in}^{-1/3}}{T_{\rm out} P_{\rm out}^{-1/3}} = \sqrt{\frac{1-b_{\rm in}^2}{1-b_{\rm out}^2}} \)

Coplanarity \(\longrightarrow\) Kepler dichotomy?

Figure from Ballard & Johnson (2016)

  • With a fixed mutual inclination distribution, at least two different populations of planetary systems are needed.
    • Regardless of the intrinsic multiplicity distribution (e.g., Lissauer et al. 2011, Johansen et al. 2012, He et al. 2019).
  • Transit method cannot constrain the mutual inclination because of the degeneracy with intrinsic multiplicity.
    • Transit + RV (Tremaine & Dong 2012, Figueira et al. 2012).
    • Transit + TTV (Zhu et al. 2018).

Mutual inclination depends on multiplicity

Transit doubles

Transit triples

Transit quadruples

\( \xi = \frac{T_{\rm in} P_{\rm in}^{-1/3}}{T_{\rm out} P_{\rm out}^{-1/3}} = \sqrt{\frac{1-b_{\rm in}^2}{1-b_{\rm out}^2}} \)

  • Weighted transit duration ratio
  • Systems with more planets have smaller mutual inclinations and are dynamically colder.
    • E.g., Zhu et al. (2018), He et al. (2020).

Orbital eccentricity also depends multiplicity

  • The transit duration method $$ \frac{T}{T_0} = \sqrt{1-b^2} \frac{\sqrt{1-e^2}}{1+e\sin{\omega}} $$ where \( T_0 \propto P^{1/3} \rho_\star^{-1/3} \).
    • Transit singles have \(\sigma_e\approx0.3\), whereas transit multis have \(\sigma_e\approx0.05\) (Van Eylen et al. 2015, 2019, Xie et al. 2016, Mills et al. 2019).
  • Systems with more planets have smaller eccentricities and are dynamically colder.
    • RV planets show a similar behaviour (e.g., Limbach & Turner 2015, Zinzi & Turrini 2017).

Transit singles

Transit doubles

Transit triples

Transit quadruples

Based on DR25 MCMC parameters and Berger et al. (2020) stellar parameters.

  • Fewer-planet systems are dynamically hotter.
  • Each system has on average 3 planets.
  • Our solar systems fits "well" in this picture.
  • Dynamical evolution may have reshaped the architecture.

Zhu et al., 2018

(see also He et al. 2020)

Kepler system intrinsic architecture

\( \sigma_i,~\sigma_e \propto k^\zeta \)

  • Fewer-planet systems are dynamically hotter.
  • Each system has on average 3 planets.
  • Our solar systems fits "well" in this picture.
  • Dynamical evolution may have reshaped the architecture.
\sigma_i,~\sigma_e \propto k^\alpha

Zhu et al., 2018

(see also He et al. 2020)

Orbital eccentricity

Kepler system intrinsic architecture

{\rm \#~of~planetary~systems} = \frac{\rm \#~of~detected~systems}{\rm detectability~of~individual~system}

Planet-planet mutual inclinations affect the frequency of planetary systems

Coplanarity \(\longrightarrow\)>50% of Sun-like stars have Kepler-like planets (e.g., Fressin et al. 2013, Petigura et al. 2013).

mutual inclination

{\rm \#~of~planetary~systems} = \frac{\rm \#~of~detected~systems}{\rm detectability~of~individual~system}

Planet-planet mutual inclinations affect the frequency of planetary systems

  • Fraction of Sun-like stars with Kepler-like planets is ~30% (Zhu et al. 2018).
  • Fraction of Sun-like stars with planets in an extended parameter space may be higher (e.g., Mulders et al. 2018, He et al. 2020).
    • Or not, if planet occurrences are strongly correlated.

(Colors mean different multiplicities.)

  • No strong preference for mean-motion resonances (e.g., Lissauer et al. 2011, Fabrycky et al. 2014).
  • Spacing depends on multiplicity.
  • ~80-90% of Kepler planet pairs do not allow intermediate planets (e.g., Fang & Margot 2013).
  • Kepler systems are dynamically packed (e.g., Pu & Wu 2015). However, interior/exterior planets remain allowed.

Spacing in mutual Hill radii

On the intra-system variation

See Zhu (2020) and Murchikova & Tremaine (2020).

Figure adapted from Penny et al. (2019)

  • Solar system planets have very diverse properties.
  • In a (super-)Kepler's view, Solar system planets (Venus & Earth) have very similar properties.

Kepler system vs. Solar system

Figure adapted from Penny et al. (2019)

  • Kepler systems are massive.
    • Inside 1 AU: 3 super Earths (~5 \(M_\oplus\)) vs. ~2 \(M_\oplus\).

Cold Jupiters

Super Earths

22 from Kepler (triangles) + 39 from RV (squares)

  • Super Earths preferentially have cold Jupiter companions $$ P({\rm CJ}|{\rm SE}) \approx33\% $$
    • \( P({\rm CJ})=10\%\) (Cumming et al. 2008).
    • \(P({\rm CJ}|{\rm SE})>50\%\), if [Fe/H]>0.
  • Cold Jupiters almost always have inner super Earth companions $$ P({\rm SE}|{\rm CJ})=\frac{P({\rm CJ}|{\rm SE}) \cdot P({\rm SE})}{P({\rm CJ})} \approx100\% $$

Zhu & Wu (2018), Bryan et al. (2019)

Inner-outer correlation

Independent confirmations

  • Long-period (\(>2\,\)yr) transiting planets frequently have inner transiting companions.
    • Herman, Zhu & Wu (2019); Masuda, Winn, & Kawahara (2020).
  • TESS detections of super Earths in RV cold Jupiter systems.
    • pi Mensae (Huang et al. 2018, Gandolfi et al. 2018), HD 86226 (Teske et al. 2020)
  • TESS + Gaia.

2 yr

Figure from Herman, Zhu & Wu (2019)

Strong inner-outer correlation challenging formation models of Kepler planets

  • Migration models typically expect anti- or no correlations:
    • Formation-and-migration (e.g., Bern model, Schlecker et al. 2020).
    • Migration-then-assembly (e.g., pebble accretion, Izidoro et al. 2015, Bitsch et al. 2019).
  • In situ?

Pebbles (\(\sim\) cm)

Pebble isolation mass (\(\sim10\,M_\oplus\))

On the Poisson process assumption

  • Fraction of stars with Kepler-like planets ~30%.
  • Fraction of stars with cold giants ~10%.
  • Fraction of stars with planets in the joint parameter space?
    • 37% [\(=1-(1-30\%)\times(1-10\%)\)] under the Poisson assumption.
    • ~30%, because of the strong correlation.

Figure adapted from Penny et al. (2019)

(Un)Popularity of Solar system-like architecture

Figure from Zhu & Wu (2018)

  • Systems with inner small planets and outer giant planets are a popular kind.
  • Systems very similar to ours are very rare.
    • Solar system has no super Earth (~70%).
    • Solar system has a cold Jupiter (~10%).

What we learn from multi-planet systems?

  • Orbital eccentricities, mutual inclinations, and spacings all depend on the multiplicity, suggesting that the dynamical evolution may have reshaped the system architecture.
    • Systems with more planets are dynamically colder.
  • The inner (<1 AU) and the outer (~1-10 AU) planetary systems are strongly correlated, indicating that planet formation is a global behavior.
    • This inner-outer correlation unexpected in theories of Kepler planet formation.
    • Implications to Solar system-like architecture.
  • Future prospects:
    • Young multi-planet systems.
    • Combining different detection techniques (e.g., transit, RV, astrometry, microlensing).

What we learn from multi-planet systems?

  • Orbital eccentricities, mutual inclinations, and spacings all depend on the multiplicity, suggesting that the dynamical evolution may have reshaped the system architecture.
    • Systems with more planets are dynamically colder.
  • The inner (<1 AU) and the outer (~1-10 AU) planetary systems are strongly correlated. This inner-outer correlation unexpected in theories of Kepler planet formation.
    • Implications to Solar system-like architecture.
  • Future prospects:
    • TESS+Gaia to study the architecture of hundreds of multi-planet systems (e.g., pi Mensae, Xuan & Wyatt 2020, Damasso et al. 2020, De Rosa et al. 2020).
    • Young multi-planet systems.
    • Linking to cold Neptunes via microlensing surveys (e.g., Roman microlensing).
  • Nearly half of Kepler planets found in systems w/ one transiting planets.
    • E.g., Thompson et al. (2018), Xie et al. (2016), Berger et al. (2018, 2020).
  • Transit singles & transit multis have statistical similar properties.
    • E.g., Xie et al. (2016), Munoz Romero & Kempton (2018), Zhu et al. (2018), Weiss et al. (2018).

(Kepler planets around Sun-like stars, based on Kepler DR25 & Gaia parameters)

Talk outline

  • Introduction, job ad, & outline (3 slides)
  • Inner multiplicity
    • Mutual inclination distribution and the "Kepler dichotomy" (3 slides & refer to He talk).
      • what it means, the issue, the solution (and possibly others).
    • Kepler planets are dynamically compact and the eccentricity distribution (3 slides).
      • period ratio distribution, dynamical spacing, interpretation.
    • On the apparent correlation in planetary sizes (3 slides).
      • the observation, the potential issues (two-fold).
  • Global multiplicity
    • Hot Jupiters are lonely & friends of hot Jupiters (3 slides).
      • HJ & SE, HJ & CJ, the interpretation.
    • Super Earth-cold Jupiter correlation (3 slides).
      • Observations (RV & transit), the theoretical implication.
    • Microlensing FFPs are probably dynamically ejected planets from multi-planet systems (1-2 slides & refer to Mroz talk).
  • Future prospects
    • Gaia+TESS (or other transit surveys) enabling further architecture studies (1-2 slides).
    • Multi-planet systems around younger stars to study how the dynamical evolution works. Briefly mention about direct imaging (1 slide).
    • Roman microlensing survey as a link to the cold Neptune population (1 slide & refer to several other ulensing talks).

0.4 \(R_\oplus\)

0.9 \(R_\oplus\)

1.0 \(R_\oplus\)

0.5 \(R_\oplus\)

11 \(R_\oplus\)

9 \(R_\oplus\)

4.0 \(R_\oplus\)

3.9 \(R_\oplus\)

On the intra-system variation: Do Solar system planets show size (or mass) similarity?

  • No, if knowing all planets

 

 

 

 

 

 

 

  • Giant planets are not observable: orbital period too long
  • Mercury & Mars undetectable: too small
  • Yes, if only Venus & Earth are seen

See Zhu (2020) and Murchikova & Tremaine (2020).

A review on multi-planet systems

By Wei Zhu

A review on multi-planet systems

A review talk on multi-planet systems at the Exoplanet Demographics Conference.

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