OGLE-2012-BLG-0026Lb,c likely in Mean-Motion Resonance

Wei Zhu (祝伟)

Canadian Institute for Theoretical Astrophysics

Microlensing 23, NYC

(Based on Madsen & Zhu, arXiv:1901.04495)

Sabrina Madsen

Microlensing commonly probes projected configuration

  • Orbital period of microlensing planet ~ years
  • Microlensing timescale ~ months
  • Planetary perturbation ~ days

Gaudi (2012)

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)

  • 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 event OGLE-2012-BLG-0026

planet 2

planet 1

Han et al. (2013)

(see Beaulieu et al. 2016 for AO observations)

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}
q11×104, s1=0.96 or 1.03q28×104, s2=0.81 or 1.25\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 (arXiv:1901.04495)

Face-on                               Edge-on

Effect of orbital orientations

planet 2

planet 1

Eccentric orbits

Madsen & Zhu (arXiv:1901.04495)

planet 2

planet 1

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

Pluto & Neptune

Mean-motion resonances

Madsen & Zhu (arXiv:1901.04495)

Eccentric orbits

Eccentric orbits & in MMRs

 

 

 

Nearly circular orbits & out of MMRs

Compare with similar planet pairs

from RV

Madsen & Zhu (arXiv:1901.04495)

Orbital evolution prefers

mean-motion resonances

Lee & Peale (2002)

Evolution of GJ 876 system

Two planets in OB120026L likely in

mean-motion resonance

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

planet 2

planet 1

HATNet

Keck

Multi-planet systems from microlensing: connection to the general exoplanetary demography

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

1. Two planets in OGLE-2012-BLG-0026 are

almost certainly closely spaced

planet 2

planet 1

Einstein ring

\red{q_1 = 1.3\times 10^{-4},~s_1=0.96 {~\rm or~} 1.03} \\ \blue{q_2 = 7.9\times 10^{-4},~s_2=0.81{~\rm or~} 1.25}
q1=1.3×104, s1=0.96 or 1.03q2=7.9×104, s2=0.81 or 1.25\red{q_1 = 1.3\times 10^{-4},~s_1=0.96 {~\rm or~} 1.03} \\ \blue{q_2 = 7.9\times 10^{-4},~s_2=0.81{~\rm or~} 1.25}

planet 2

planet 1

Probability distribution

2. Closely spaced, massive planet pairs from radial velocity are often found in mean-motion resonances

Madsen & Zhu (arXiv:1901.04495)

Madsen & Zhu (arXiv:1901.04495)

Face-on                               Edge-on

Effect of orbital orientations

Two planets in OB120026L likely in

mean-motion resonance

  • 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.
50~M_\oplus~{\rm planet~not~predicted}\\ {\rm by~core~accretion~theory}
50 M planet not predictedby core accretion theory50~M_\oplus~{\rm planet~not~predicted}\\ {\rm by~core~accretion~theory}

Pollack et al. (1996)

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)

Orbital solution of microlensing system

Ryu (incl. Zhu) et al. (2018)

OGLE-2016-BLG-1190

MMR in Microlensing (New York)

By Wei Zhu(祝伟)

MMR in Microlensing (New York)

Talk at the 23rd microlensing conference in NYC

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