Wei Zhu（祝伟）
I'm now an Assistant Professor in the Department of Astronomy at Tsinghua University in Beijing.
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
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Kepler's limitation #1: transiting
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Coplanar vs. mutually inclined (Kepler dichotomy or not)
-
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Kepler's limitation #2: short-period (\(P\lesssim1\) yr)
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Inner-outer correlation (in situ vs. large-scale migration)
-
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Kepler's limitation #3: relatively large planets (\(R_{\rm p}\gtrsim R_\oplus\))
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Intra-system uniformity or not
-
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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
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# 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
-
Coplanar vs. mutually inclined (Kepler dichotomy or not)
-
-
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 (\(R_{\rm p}\gtrsim R_\oplus\))
-
Intra-system uniformity or not
-
-
Summary & future prospects
Cold Jupiters
Super Earths
22 from Kepler (triangles) + 39 from RV (squares)
(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)
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1/3 of Kepler systems have cold Jupiter companions.
- >50%, if [Fe/H]>0.
(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!
(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
- 12 long-period giants in Kepler data
- 5 have inner transiting companions
- 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}
(see also Gandolfi et al. 2018)
- HD 86226 with a known RV cold Jupiter also has a transiting candidate (TOI-652.01).
- More such systems from Kepler follow-ups: Kepler-65 (Mills et al. 2019), Kepler-88 (Weiss et al. arXiv:1909.02427).
- TESS + Gaia will discover 100s more such systems.
Why inner-outer correlation matters: Kepler planet formation
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In situ
- Requires a massive disk
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Migration
- Normal disk can work
- Mean-motion resonance pile-ups
Figure from Chiang & Laughlin (2013)
Image credit: P. Armitage
Inner-outer strong correlations
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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.
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Evolution
- Compact Multi-planet Systems appear more Common around Metal-poor Hosts.
(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
Toward the intrinsic architecture
-
Kepler's limitation #1: transiting
-
Coplanar vs. mutually inclined (Kepler dichotomy or not)
-
-
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 (\(R_{\rm p}\gtrsim R_\oplus\))
-
Intra-system uniformity or not
-
-
Summary & future prospects
Intra-system uniformity
- Lissauer et al. (2011): Adjacent Kepler planets tend to have similar sizes.
- Ciardi et al. (2012): The outer planet is preferentially larger than the inner one.
- Weiss et al. (2018): Kepler multi-planet systems are like "peas in a pod."
- 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
Data from Weiss et al. (2018)
- The sample S/N cut corresponds to different radius thresholds for different stars.
CDPP CDF
From Ciardi et al. (2013)
-
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)
- He, Ford, & Ragozzine (arXiv:1907.07773) showed that the radius-clustered models did not improve the fit to the data.
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
