A pair of planets likely in mean-motion resonance from gravitational microlensing

Wei Zhu (祝伟)

Astrophysical Dynamics, Shanghai

(Based on Madsen & Zhu, 2019, ApJL, 878, 29)

Sabrina Madsen

Microlensing probes the cold planet population

Mao & Paczynski (1991); Gould & Loeb (1992); Gaudi (2012)

For typical disk surface density profile (\( \Sigma \propto r^{-1} \) or \( \propto r^{-3/2} \) ), there is more mass in the outer region

Microlensing commonly probes projected configuration

Orbital period: years

planetary perturbation: days

Mao & Paczynski (1991); Gould & Loeb (1992); Gaudi (2012)

How to probe orbital configuration of microlensing planets

  • Light curve modeling (e.g., Gaudi++2008; Ryu++2018)
  • Radial velocity follow-up (e.g., Yee++2016 for a binary)
  • Dynamical stability

OGLE-2006-BLG-109

  • Direct imaging system HR 8799:
    • Likely double 2:1 mean-motion resonances (b & c, c & d)

Fabrycky & Murray-Clay (2010)

(see also Wang et al. 2018)

b

c

d

Long-term stability constrains orbital configuration of multi-planet systems

Marois et al. (2008)

Two-planet system OB120026L

planet 2

planet 1

Han et al. (2013)

(see also Beaulieu et al. 2016)

Both planets inside Einstein ring

Both planets outside Einstein ring

\red{q_1\sim 1\times 10^{-4},~s_1=0.96 {~\rm or~} 1.03} \\ \blue{q_2\sim 8\times 10^{-4},~s_2=0.81{~\rm or~} 1.25}

Madsen & Zhu, 2019, ApJL, 878, 29

Effect of orbital orientations

planet 2

planet 1

Dynamical stability

planet 2

planet 1

  • Randomize e vector
  • N-body integration
  • Reject unstable orbits

Madsen & Zhu, 2019, ApJL, 878, 29

Hadden & Lithwick (2018)

Pluto & Neptune

Mean-motion resonances

Eccentric orbits

Eccentric orbits & in MMRs

 

 

 

Nearly circular orbits & out of MMRs

Madsen & Zhu, 2019, ApJL, 878, 29

Compare with similar planet pairs

from RV

MMR

non-MMR (probably)

Madsen & Zhu, 2019, ApJL, 878, 29

Orbital evolution prefers

mean-motion resonances

Lee & Peale (2002)

Evolution of GJ 876 system

MMR

non-MMR (probably)

A pair of microlensing planets likely in

mean-motion resonance

  • Microlensing can also probe the detailed dynamical state of multi-planet systems
    1. Two planets close to each other;
    2. Azimuthal offset;
    3. Stability & evolution history --> MMRs
  • More similar systems from microlensing

planet 2

planet 1

Madsen & Zhu, 2019, ApJL, 878, 29

Pollack et al. (1996)

Suzuki et al. (2016)

(see Herman, Zhu, & Wu 2019 for the radius distribtuion)

30-100 \(M_\oplus\) planets not predicted by core accretion theory

OB120026L:

How often do cold Jupiters have cold Neptune companions?

  • A single detection out of ~20 microlensing systems with Sun-like hosts
  • Low detection efficiency for Neptunes (~5%, Zhu et al. 2014).
  • Perhaps all cold Jupiter systems also have cold Neptunes: P(CN|CJ)~100%.
    • Mean-motion resonances may also be common.

HATNet

Keck

Multi-planet systems from microlensing: Connection to the overall exoplanet demographics

Hot Jupiters

(~1%)

Cold Jupiters

(~10%)

Cold Neptunes

(?)

Super Earths

(30%)

(Zhu et al. 2018)

Hot Jupiters have distant companions

(Knutson et al. 2014)

Hot Jupiters are lonely (Steffen et al. 2010)

Super Earths & cold Jupiters tend to co-exist

(Zhu & Wu 2018)

  • Why is the mass function so smooth? Is it related to multiplicity?
  • How many Neptunes per system?
  • Do cold Jupiters frequently have cold Neptune companions?
  • ...

Data from NASA Exoplanet Archive

Back-Ups

Orbital motion in microlensing

& RV follow-ups

Skowron et al. (2011); Yee et al. (2016)

(OGLE-2006-BLG-109, Gaudi et al. 2008, Bennett et al. 2010;

OGLE-2016-BLG-1190, Ryu et al. 2018;

Gaia16aye, Wyrzykowski et al. 2019)

OB120026: Sun-like host with a cold Jupiter & a cold Neptune

Beaulieu et al. (2016)

Orbital solution of microlensing system

OGLE-2006-BLG-109: A Jupiter/Saturn analog

Gaudi et al. (2008); Bennett et al. (2010)

MMR in Microlensing (Shanghai)

By Wei Zhu(祝伟)

MMR in Microlensing (Shanghai)

Talk at the Astrophysical Dynamics Conference in Shanghai

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