Wei Zhu（祝伟）
I'm now an Assistant Professor in the Department of Astronomy at Tsinghua University in Beijing.
Intra-System Planet Size Hierarchy
(or not)
Wei Zhu (祝伟)
2019 May 9, Group Meeting
Solar system as the best known example
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 \(R \oplus\)
Mars' low mass places challenges on solar system formation theories \( \rightarrow \) grand tack model (Walsh et al. 2011)
Image credit: Lunine et al. (2009)
Planetesimal formation
Run-away
growth
Pebble
accretion
Oligarchic
growth
Giant impact
phase
Solar system formation (theory)
If formation stops after oligarchic growth (i.e., at isolation mass), then planets should have similar sizes and regular spacings.
Terrestrial
planet form
Our solar system did not stop at isolation mass, but what about others?
- Lissauer et al. (2011) first noticed that adjacent Kepler planets tend to have similar sizes.
- Ciardi et al. (2012) pointed out that the outer one is preferentially larger than the inner one.
- Based on better measured stellar parameters, Weiss et al. (2018) claimed that Kepler multi-planet systems are like "peas in a pod."
Image credit: Lissauer et al. (2011)
HATNet
Keck
KMTNet
Kepler
See also Millholland, Wang, & Laughlin (2017) for the claim of mass similarity
Intra-system size uniformity?
Peas in a Pod: Planets in a Kepler Multi-planet System Are Similar in Size and Regularly Spaced
Quantifying the detection significance
Data
One bootstrap trial
Weiss et al. (2018)
Statistical distribution
Radius of inner planet
Radius of outer planet
Radius of inner planet
Radius of outer planet
Spacing uniformity
Data
One bootstrap trial
Weiss et al. (2018)
Statistical distribution
Inner period ratio
Outer period ratio
Inner period ratio
Outer period ratio
Image credit: Lunine et al. (2009)
Planetesimal formation
Run-away
growth
Pebble
accretion
Oligarchic
growth
Giant impact
phase
Peas in a pod \( \rightarrow \) Extra-solar system has no giant impact phase?
If formation stops after oligarchic growth (i.e., at isolation mass), then planets should have similar sizes and regular spacings.
Terrestrial
planet form
Issue 1: Planet radius is not a fundamental parameter in transit detection
{\rm Transit ~ S/N} = \frac{(R_{\rm p}/R_\star)^2 \cdot \sqrt{\rm \# ~ of ~ transit ~ events}}{\rm photometric ~ noise ~ per ~ transit}
Stellar photometric noise over 6-hr integration (\( {\rm CDPP}_{\rm 6hr}\))
Kepler
K2
{\rm Transit ~ S/N} = \frac{(R_{\rm p}/R_\star)^2 \cdot \sqrt{\rm \# ~ of ~ transit ~ events}}{\rm photometric ~ noise ~ per ~ transit}
Issue 1: Planet radius is not a fundamental parameter in transit detection
Issue 1: Planet radius is not a fundamental parameter in transit detection
{\rm S/N} = \frac{(R_{\rm p}/R_\star)^2 \cdot \sqrt{\rm \# ~ of ~ transit ~ events}}{\rm photometric ~ noise ~ per ~ transit}
Issue 2: Not all planets transit
Issue 3: Kepler systems preferentially have outer giant planets
Do planets show intra-system size uniformity?
- Select most significant transit detections (S/N>100);
- Find the most weakest detection in the same system;
- Compare the S/N distribution of these weakest detections with the overall S/N distribution.
Conclusion:
- No intra-system size uniformity;
- The detection of weak signals is unaffected by the presence of strong signals.
System-wide size hierarchy?
Strong (weak) detection \(\approx\) large (small) planet
\[ \downarrow \]
Large planets should almost always have small companions
On the spacing uniformity claim
- Arbitrary cut at Period ratio=4.
- Detection bias & dynamical stability.
Data used in Weiss et al. (2018)
All planet triplets
Image credit: Lunine et al. (2009)
Planetesimal formation
Run-away
growth
Pebble
accretion
Oligarchic
growth
Giant impact
phase
Kepler planet systems do not show
"peas in a pod" pattern
If formation stops after oligarchic growth (i.e., at isolation mass), then planets should have similar sizes and regular spacings.
Terrestrial
planet form
Evidences of Kepler planetary systems having violent past
- Intra-system size diversity
- Nearly random period ratio distribution
- Large eccentricity (\(e \approx 0.3\)) & mutual inclination (\( \Delta i \approx 20^\circ \))
Structure growth in planet formation
Image credit: Lunine et al. (2009)
Planetesimal formation
Run-away
growth
Pebble
accretion
Oligarchic
growth
Giant impact
phase
Terrestrial
planet form
Given an initial mass contrast, what is the final?
(too big to fail in planet formation?)
HATNet
Keck
KMTNet
Kepler
Hot Jupiters
(~1%)
Cold Jupiters
(~10%)
Cold Neptunes
Super Earths
(30%)
Data from NASA Exoplanet Archive
Inter-system diversity
Intra-system size hierarchy
By Wei Zhu（祝伟）
Intra-system size hierarchy
Presentation at Norm Murray group meeting
