Wei Zhu
I'm now an Assistant Professor in the Department of Astronomy at Tsinghua University in Beijing.
Cornell Planetary Lunch
2019-11-18
Images credit: NASA/Kepler
Image credit: iLectureOnline
Figure adapted from Penny et al. (2019)
Kepler only detects transiting planets
Multi-planet systems are co-planar?
Kepler only detects relatively large planets (\(R_{\rm p}\gtrsim R_\oplus\))
Planets around the same host have similar sizes/masses, regular spacings?
Kepler only detects short-period planets (\(P\lesssim1\) yr)
Kepler systems formed in a different way?
\( T_{\rm dur} \propto \frac{R_*}{v_{\rm orb}} \propto a^{1/2} \propto P^{1/3} \) \(\longrightarrow\) \( \xi \equiv \frac{T_{\rm dur, in}/P_{\rm in}^{1/3}}{T_{\rm dur, out}/P_{\rm out}^{1/3}} = \frac{\sqrt{1-b_{\rm in}^2}}{\sqrt{1-b_{\rm out}^2}} \)
If exactly coplanar: \( \frac{b_{\rm in}}{b_{\rm out}} = \frac{a_{\rm in}}{a_{\rm out}} = \left(\frac{P_{\rm in}}{P_{\rm out}}\right)^{2/3} \)
Tremaine & Dong (2012): Transit provides no constraints on mutual inclination.
Zhu, Petrovich, Wu 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 singles
Transit multis
(see also Van Eylen et al. 2018)
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
mutual inclination
\( N_{\red{j}} = N_* \sum_{\blue{k}} f_{\blue{k}} \cdot g_{\red{j}\blue{k}} \)
\( N_{\red{1}} = N_* \sum_{\blue{k}} f_{\blue{k}} \cdot g_{\red{1}\blue{k}} \)
\( \sum_{\red{j}} N_{\red{j}} = N_* \sum_{\blue{k}} f_{\blue{k}} \cdot\sum_{\red{j}} g_{\red{j}\blue{k}} \)
\( N_{\red{1}} + \sum_{\red{j}} N_{\red{j}} = N_* \sum_{\blue{k}} f_{\blue{k}} \cdot \left( g_{\red{1}\blue{k}} + \sum_{\red{j}} g_{\red{j}\blue{k}} \right) \)
\(\red{j}\) (\(\geq1\)): # of tranets
\(\blue{k}\) (\(\geq1\)): # of planets
With very few assumptions, we have:
Multi-planet systems are not always coplanar
Fewer-planet systems are dynamically hotter (Zhu et al. 2018).
Kepler only detects relatively large planets (\(R_{\rm p}\gtrsim R_\oplus\))
Planets around the same host have similar sizes/masses, regular spacings?
Kepler only detects short-period planets (\(P\lesssim1\) yr)
Kepler systems formed in a different way?
Image from Lissauer et al. (2011)
Outer-to-inner radius ratio
Outer planet larger
Inner planet larger
Data
Radius bootstrap
Noisy sample
Quiet sample
Data from Weiss et al. (2018)
Stellar noise (ppm)
From Ciardi et al. (2013)
Kepler detections pile up toward the
detection threshold (defined by signal-to-noise ratio, S/N).
CDF
Detection threshold
Systems around
Radius of inner Kepler planet
Radius of outer Kepler planet
Systems around
Radius of inner Kepler planet
Radius of outer Kepler planet
Multi-planet systems are not always coplanar
Fewer-planet systems are dynamically hotter (Zhu et al. 2018).
Kepler multi-planet systems do not show intra-system uniformity
It is hard to infer their formation conditions based on current properties (Zhu arXiv:1907.02074)
Kepler only detects short-period planets (\(P\lesssim1\) yr)
Kepler systems formed in a different way?
Figure adapted from Penny et al. (2019)
Cold Jupiters
Super Earths
22 from Kepler (triangles) + 39 from RV (squares)
(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)
Cold Jupiters
Super Earths
22 from Kepler (triangles) + 39 from RV (squares)
(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)
Cold Jupiters
Super Earths
22 from Kepler (triangles) + 39 from RV (squares)
(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)
Cold Jupiters
Super Earths
22 from Kepler (triangles) + 39 from RV (squares)
(see also Bryan et al. 2019, Herman, Zhu, & Wu 2019)
Zhu & Wu, 2018, AJ, 156, 92
1 yr
Inner and outer regions correlate in occurrence rate & dynamical states
(see also Gandolfi et al. 2018)
Figure adapted from Penny et al. (2019)
Minimum-mass solar/extra-solar nebula:
Weidenschilling (1977); Hayashi (1981)
The outer region dominates the mass and angular momentum budget
Mimimum mass extra-solar nebula
Mimimum mass solar nebula
Chiang & Laughlin (2013)
(see also Schlichting 2014)
Figure from Penny et al. (2019)
(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
Period ratio of inner pair
Period ratio of outer pair
Stability boundary
Radius of inner Kepler planet
Radius of outer Kepler planet
Sensitivity limit
Noisy stars
Intermediate stars
Quiet stars
Brightness
Pollack et al. (1996)
Suzuki et al. (2016)
(see Herman, Zhu, & Wu 2019 for the radius distribtuion)
OB120026L:
x
y
Planet 1
Planet 2
Star
Planet 2
Planet 1
Sabrina Madsen
A pair of planets likely in mean-motion resonance from gravitational microlensing
Light curve from Han et al. (2013)
Image credit: KASI
By Wei Zhu