Toward the intrinsic architecture of planetary systems

Wei Zhu (祝伟)

Canadian Institute for Theoretical Astrophysics

Ringberg Castle Workshop

2019-09-10, Germany

Kepler (2009-2013) & K2 (2014-2019)

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

Image credit: NASA/Kepler, Batalha (2014)

Kepler's limitations

  • Kepler detects transiting planets with \(P\lesssim1\) yr and \( R_{\rm p} \gtrsim R_\oplus\)

Image credit: iLectureOnline

Figure adapted from Penny et al. (2019)

Toward the intrinsic architecture

  • Kepler's limitation #1: transiting

  • Kepler's limitation #2: short-period (\(P\lesssim1\) yr)

    • Inner-outer correlation (in situ vs. large-scale migration)

  • Kepler's limitation #3: relatively large planets (\(R_{\rm p}\gtrsim R_\oplus\))

  • Summary & future prospects

Kepler dichotomy?

Ballard & Johnson (2016)

(See also Lissauer et al. 2011, Johansen et al. 2012)

  • Half of transiting planets (tranets) are found in single-tranet systems.
  • If assuming small (and fixed) mutual inclinations, two populations are needed:
    • Compact systems
    • 1-planet systems (or 2-planet with large mutual inclinations)

No sign for Kepler dichotomy

Zhu et al. (2018)

(See also Xie et al. 2016, Munoz Romero et al. 2018, Weiss et al. 2018)

One-tranet hosts

Multi-tranet hosts

Transit + Transit Timing Varitation (TTV)

  • # of systems with k transiting planets
    • ~50% in transit singles
  • # of systems with k transiting planets AND at least one showing TTV signals (Holczer++16)
    • ~50% in transit singles
  • Majority of transit singles are actually multi-planet systems with large mutual inclinations

 

Zhu, Petrovich, Wu et al., 2018

Transit singles

Transit multis

Transit Timing Variation (TTV)

  • No interaction

 

 

 

  • Interaction with additional planet

Holman & Murray (2005); Agol et al. (2005)

Dynamics coupled with multiplicity

{\rm inclination~dispersion~of~} k{\rm -planet~system} \propto k^\alpha

Zhu, Petrovich, Wu et al., 2018

  • Low-multiples: dynamically hot.
  • High-multiples: dynamically cold.
{\rm \#~of~planetary~systems} = \frac{\rm \#~of~detected~systems}{\rm detectability~of~individual~system}

Planet-planet mutual inclinations affect the occurrence rate of planetary systems

mutual inclination

Planet-planet mutual inclinations affect the occurrence rate of planetary systems

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

Fraction of Sun-like stars with Kepler-like planets

  • >50% (Fressin et al. 2013; Petigura et al. 2013; Winn & Fabrycky 2015)

 

  • 30% (Zhu, Petrovich, Wu et al. 2018)
  • 30% of Sun-like stars have Kepler planets
  • Fewer-planet systems are dynamically hotter
  • Each system has on average 3 planets
  • Our solar systems fits "well" in this picture
i,~e \propto k^\alpha

Zhu, Petrovich, Wu et al., 2018

(See Xie et al. 2016, Van Eylen et al. 2018, Mills et al. 2019 for eccentricity constraints)

Orbital eccentricity

Kepler multi system intrinsic architecture

Toward the intrinsic architecture

  • Kepler's limitation #1: transiting

  • Kepler's limitation #2: short-period (\(P\lesssim1\) yr)

    • Inner-outer correlation (in situ vs. large-scale migration)

  • Kepler's limitation #3: relatively large planets (\(R_{\rm p}\gtrsim R_\oplus\))

  • Summary & future prospects

Cold Jupiters

Super Earths

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

Zhu & Wu, 2018, AJ, 156, 92

(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)

Super Earth-cold Jupiter correlations

Cold Jupiters

Super Earths

P({\rm CJ}|{\rm SE}) \approx 33\% {\rm ~vs.~} P({\rm CJ})=10\%

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

  • 1/3 of Kepler systems have cold Jupiter companions.
    • >50%, if [Fe/H]>0.

Zhu & Wu, 2018, AJ, 156, 92

(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)

Super Earth-cold Jupiter correlations

Cold Jupiters

Super Earths

P({\rm CJ}|{\rm SE}) \approx 33\% {\rm ~vs.~} P({\rm CJ})=10\%

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

P({\rm SE}) = 30\%
P({\rm SE}|{\rm CJ}) = \frac{P({\rm SE})}{P({\rm CJ})} P({\rm CJ}|{\rm SE}) \approx 100\%
  • 1/3 of Kepler systems have cold Jupiter companions.
    • >50%, if [Fe/H]>0.
  • Cold Jupiters (almost) always have inner super Earth companions!

Zhu & Wu, 2018, AJ, 156, 92

(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)

Super Earth-cold Jupiter correlations

Inner-outer correlation

P({\rm SE}|{\rm CJ}) = 100\% \left( \frac{N_{\rm in,out}/N_{\rm out}}{5/12} \right) \left( \frac{R_\star/a_{\rm in}}{0.03} \right)^{-1} \left( \frac{i_0}{4^\circ} \right)
i_0 \propto k^{-2}

1 yr

  1. 12 long-period giants in Kepler data
  2. 5 have inner transiting companions
  3. 1 has five inner planets:

Inner and outer regions correlate in occurrence rate & dynamical states

TESS discovers a super Earth in

\(\pi\) Mensae system

10 M_{\rm J}\\ 3~{\rm AU}\\ e=0.6
5 M_\oplus\\ 6~{\rm d}

Huang et al., (2018)

(see also Gandolfi et al. 2018)

  • HD 86226 with a known RV cold Jupiter also has a transiting candidate (TOI-652.01).
  • TESS + Gaia will discover 100s more such systems.

Why inner-outer correlation matters: Kepler planet formation

  • In situ
    • Requires a massive disk
  • Migration
    • Normal disk can work
    • Mean-motion resonance pile-ups

Figure from Chiang & Laughlin (2013)

Image credit: P. Armitage

Inner-outer strong correlations

  • In situ formation is preferred
    • They do not compete for building blocks (cf., inside-out formation).
    • Cold Jupiters do not prohibit super Earths' formation (cf., Izidoro et al. 2015).
    • Cold Jupiters require more stringent formation conditions.
  • Evolution
    • Compact Multi-planet Systems appear more Common around Metal-poor Hosts.

Zhu & Wu, 2018, AJ, 156, 92

(see also Zhu, 2019, ApJ, 873, 8; Brewer et al., 2018, ApJL, 867, 3)

HATNet

Keck

Cold Jupiters

(~10%)

Cold Neptunes

 

  • Most Kepler-like planetary systems have outer giant planets.
  • Almost all cold giant planets have inner small planets.
  • Inner-outer correlation constrains planet formation and evolution.

Kepler-like systems frequently have

outer giant companions

Kepler

planets

(30%)

(Zhu et al. 2018)

Toward the intrinsic architecture

  • Kepler's limitation #1: transiting

  • Kepler's limitation #2: short-period (\(P\lesssim1\) yr)

    • Inner-outer correlation (in situ vs. large-scale migration)

  • Kepler's limitation #3: relatively large planets (\(R_{\rm p}\gtrsim R_\oplus\))

  • Summary & future prospects

Intra-system uniformity

  1. Lissauer et al. (2011): Adjacent Kepler planets tend to have similar sizes.
  2. Ciardi et al. (2012): The outer planet is preferentially larger than the inner one.
  3. Weiss et al. (2018): Kepler multi-planet systems are like "peas in a pod."
  4. Millholland et al. (2017): Planets in the same system should also have similar masses.

Image from Lissauer et al. (2011)

Outer-to-inner radius ratio

Outer planet larger

Inner planet larger

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 \(R_\oplus\)

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

Does dynamical stability allow for undetectable small planets?

  • Yes, even for high-multiples (\(\geq 4\)).
  • Even less an issue for 2-tranet & 3-tranet systems, which contribute >80% of Kepler multi systems.

From Weiss et al. (2018)

{\rm Transit ~ S/N} = \frac{(R_{\rm p}/R_\star)^2 \cdot \sqrt{\rm \# ~ of ~ transit ~ events}}{\rm photometric ~ noise ~ per ~ transit}

Sign for smaller undetectable planets

Noisy sample

Quiet sample

Zhu, arXiv:1907.02074

Data from Weiss et al. (2018)

  • The sample S/N cut corresponds to different radius thresholds for different stars.

CDPP              CDF

  • Kepler detections pile up toward the

    detection threshold.

{\rm S/N} = \frac{(R_{\rm p}/R_\star)^2 \cdot \sqrt{\rm \# ~ of ~ transit ~ events}}{\rm photometric ~ noise ~ per ~ transit}

On the apparently similar sizes

Forward modeling

(short-cut)

Bootstrap

Full forward modeling confirming

no radius clustering

(Even though the authors stated the opposite)

Non-clustered model

Clustered periods & sizes model

Transit depth ratio

Transit depth ratio

Transit depth ratio

Transit depth ratio

What we learn about planet formation and evolution from no intra-system similarity?

  • (Unlikely) Planet formation does not care about initial conditions (e.g., stellar properties).

 

  • Dynamical evolution has erased most of their memory of initial conditions:
    • Dynamically compact;
    • Compositional diversity;
    • Large eccentricities and mutual inclinations;
    • No (strong) preference for mean-motion resonances.

Summary & Future directions

  • Kepler is both revolutionary and limited.
  • Multi-planet systems can have large (\(\gtrsim 10^\circ\)) mutual inclinations, but there is no dichotomous feature.
  • Most inner planets have outer giant companions, disfavoring disk migration.
  • Planets do not show intra-system uniformity.
  • We need to understand the cold planets better \(\rightarrow\) Microlensing!

(Figure from Penny et al., 2019, ApJS, 241, 3)

planet intrinsic architecture (Ringberg)

By Wei Zhu(祝伟)

planet intrinsic architecture (Ringberg)

Presentation at Ringberg Castle Workshop in Germany

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