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)

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%).