系外行星普查统计和微引力透镜

Exoplanet Statistics & Gravitational Microlensing

Wei Zhu (祝伟)

2021年全国行星科学大会,苏州

2021-06-20

(Slides accessible here)

Solar System

  • Planets have diverse properties (\(\sim10^2\) in separation and \(\sim10^4\) in mass).
  • Planets have small but substantial orbital eccentricities (\(\lesssim0.2\)) and mutual inclinations (\(\lesssim 6^\circ\)).
  • Solar system was once dynamically active, and may become chaotic again in \(\sim\) Gyr timescale.

Image credit: iLectureOnline

Solar System formation in one picture

Giant planet formation (\(\lesssim\) 10 Myr)

Terrestrial planet formation (\(\sim\) 100 Myr)

Transit (ground)

Transit (space)

Radial velocity

Microlensing

Imaging

Hot Jupiters

Cold Jupiters

Super Earths

Cold Neptunes

What You See Is Not What You Get!

Based on data from NASA Exoplanet Archive.

发生率(Occurrence Rates)

  • 行星的发生率(Occurrence rate of planets)$$ \bar{n}_{\rm p} \equiv \frac{\rm \#~of~planets}{\rm \#~of~stars} $$
  • 行星系统的发生率(Occurrence rate of planetary systems) $$ F_{\rm p} \equiv \frac{\rm \#~of~planetary~systems}{\rm \#~of~stars} $$
  • 行星系统的多重性(Multiplicity) $$ \bar{m}_{\rm p} \equiv \frac{\rm \#~of~planets}{\rm \#~of~planetary~systems} = \frac{\bar{n}_{\rm p}}{F_{\rm p}} $$

行星发生率(Occurrence rate of planets)

  • Extreme planets (hot Jupiters, hot Neptunes, ultra-short-period planets) are rare (~%).
  • Every Sun-like star has \(\bar{n}_{\rm p}=1.23\pm0.06\) planets with \(P<400\) d and \(1-20\,R_\oplus\).
  • Habitable zone planets are not well constrained.

Zhu & Dong (2021, ARAA)

(see also Fressin et al. 2013, Petigura et al. 2018, Hsu et al. 2019, etc)

  • Fraction of Sun-like stars with Kepler-like planets is ~30% (Zhu et al. 2018).
  • Fraction of Sun-like stars with planets in an extended parameter space may be higher (e.g., Mulders et al. 2018, He et al. 2020).

(Colors mean different observed multiplicities.)

行星系统的发生率(Occurrence rate of planetary systems)

Architecture of exoplanetary systems

(How are planets in the same system distributed?)

  • Planets are not locked in mean-motion resonances (see 王素's talk).
    • Spacings are close to random except for rare cases (see 姜朝峰's talk).
  • Systems with more planets are dynamically colder.
    • Planets have smaller mutual inclinations and orbital eccentricities (see 谢基伟's talk).

Figures from Winn & Fabrycky (2015) and Zhu & Dong (2021)

1. Planets are ubiquitous

  • Many (or majority) of them reside in multi-planet systems.

  • Dynamical interactions between planets may have largely reshaped the system architecture.

外行星系统

(Outer planetary system)

  • ~10% Sun-like stars have cold Jupiters (e.g., Cumming+2008, Fulton+2021).
    • ~6% for Jupiter analogs (Wittenmyer+2016).
    • Many Kepler long period planets show TTVs, indicating the existence of additional planets (Wang+2016).

Cold Jupiters

Cold Jupiters

Super Earths

22 from Kepler (triangles) + 39 from RV (squares)

  • 1/3 of Kepler systems have cold Jupiter companions.
    • >50%, if [Fe/H]>0.

Inner-outer correlation

  • Cold Jupiters (almost) always have inner super Earth companions!

\( P({\rm SE}|{\rm CJ}) \cdot P({\rm CJ}) = P({\rm CJ}|{\rm SE}) \cdot P({\rm SE}) \) \( \rightarrow P({\rm SE}|{\rm CJ})=100\% \)

\(P({\rm CJ}|{\rm SE}) \approx 33\% {\rm ~vs.~} P({\rm CJ})=10\%\)

(Un)Popularity of Solar system-like architecture

  • Solar system has no super Earth (70%).
  • Solar system has a cold Jupiter (10%).
  • A pathway toward finding another Solar System?

外行星系统

(Outer planetary system)

  • ~10% Sun-like stars have cold Jupiters (e.g., Cumming+2008, Fulton+2021).
    • ~6% for Jupiter analogs (Wittenmyer+2016).
    • Many Kepler long period planets show TTVs, indicating the existence of additional planets (Wang+2016).
  • Low-mass planets at wide separations are a few times more abundant (e.g., Suzuki+2016; Herman+2019).
    • See talks by 臧伟呈 and 杨弘靖.

Cold Jupiters

Cold Neptunes

微引力透镜 (Gravitational microlensing)

Paczynski (1986); Mao & Paczynski (1991)

\(t_{\rm E} \sim 30{\rm days} \left(\frac{M_{\rm L}}{M_\odot}\right)^{1/2} \)

\( t_q \sim 40{\rm min} \left(\frac{q}{10^{-6}}\right)^{1/2} \left( \frac{t_{\rm E}}{30 \rm days}\right) \)

背景恒星亮度

背景恒星

”透镜“星体

\( t_{\rm E} \)

\( t_q \)

Microlensing from ground: KMTNet

  • 3x1.6m telescopes with wide FoV;
  • ~10\(^8\) stars observed once every >20 min;
  • Every year ~3000 microlensing events discovered, with ~30 planet detections;
  • Current limit: planet-to-star mass ratio \(q\sim10^{-5}\).
    • ref: Earth/Sun \(q=3\times10^{-6}\).

银河系中心

1 deg

Microlensing from ground: KMTNet

  • 3x1.6m telescopes with wide FoV;
  • ~10\(^8\) stars observed once every >20 min;
  • Every year ~3000 microlensing events discovered, with ~30 planet detections;
  • Current limit: planet-to-star mass ratio \(q\sim10^{-5}\).
    • ref: Earth/Sun \(q=3\times10^{-6}\).

银河系中心

1 deg

Microlensing reveals the distribution of cold planets

Neptune

Jupiter

臧伟呈

杨弘靖

流浪行星(Free floating planets)

  • 透镜质量\(M_{\rm L} \sim 300 M_\oplus \left(\frac{t_{\rm E}}{1~\rm day}\right)^2 \)
  • “流浪” = 距离主星距离超过~15 AU

  • 银河系中可能存在与恒星数目相当的流浪行星 (KMTNet+OGLE约1例/年)

Mroz et al. (2017, 2021)

a Mars-mass FFP!

From ground to space

  • Higher resolution:Individual stars resolved.
  • Deeper observations
    • More stars \(\rightarrow\) More microlensing events
    • Smaller stars \(\rightarrow\) Lower-mass planets

3'

9"

Images from Pietrukowicz et al. (2019)

Figure from Mao (2012)

Small-size stars

Intermediate-size stars

Large-size stars

Time in event unit

Magnification in brightness (log)

Space-based microlensing surveys (e.g., CSST and ET)

Figure from Penny et al. (2019)

See talk on ET by 张辉

1. Planets are ubiquitous (\(\gtrsim30\%\)) in the inner ~1 AU.

  • Many (or majority) of them reside in multi-planet systems.

  • Dynamical interactions between planets may have largely reshaped the system architecture.

2. Cold (~1-10 AU) planets are also abundant (\(\gtrsim10\%\)).

  • They tend to co-exist with inner planets.
  • Cold planets remain less understood, and microlensing will help probe the low-mass regime.

Summary

(Slides accessible here)

Standing on the shoulders of Kepler

Kepler mission (2009-2018):

  • Kepler detected transiting planets with \(P\lesssim1\) yr and \( R_{\rm p} \gtrsim R_\oplus\).
  • Multi-planet systems can be dynamically hot (large \(e\) & \(i\)).
  • Kepler planets are only the tip of the icerberg.
  • Strong correlation between inner (\(\lesssim1\) au) and outer (\(\gtrsim1\) au) planetary systems.

Ongoing/Future transit missions:

  • Spectroscopic survey.
  • Secular effect.

Gaia astrometry:

  • Massive planets.
  • multi-planet systems.
  • Inner-outer correlation.

Microlensing:

  • Cold planet statistics.
  • Planet multiplicity.
  • Parallax \(\rightarrow\) lens mass function.

EarthTwo?

TESS

Cheops

2009

2025

2020

2018

2015

2012

Kepler

Gaia

LAMOST

KMTNet

Dedicated RV telescope?

WFIRST

(+CSST)

Orbital eccentricities of exoplanets

(\frac{P^2}{4\pi^2} = \frac{a^3}{GM_\star} = \frac{3(a/R_\star)^3}{4\pi G\rho_\star})
\rightarrow T_0 \propto P^{1/3} \rho_\star^{-1/3}
T_0 = \frac{2R_\star}{2\pi a /P}

Transit singles have \(\sigma_e\approx0.3\), whereas transit multis have \(\sigma_e\approx0.05\) (Van Eylen et al. 2015, 2019, Xie et al. 2016, Mills et al. 2019).

  • See Ji-Wei Xie's talk.

Transit duration \(T\)

Zhu & Dong (2021)

Systems with more planets have smaller eccentricities and are dynamically colder.

  • RV planets show a similar behaviour (e.g., Limbach & Turner 2015, Zinzi & Turrini 2017).
  • More compact systems also have smaller mutual inclinations (Zhu et al. 2018, He et al. 2020).

Transit singles

Transit doubles

Transit triples

Transit quadruples

Orbital eccentricities of exoplanets

  • No strong preference for mean-motion resonances (e.g., Lissauer et al. 2011, Fabrycky et al. 2014).
  • Spacing depends on multiplicity.
  • ~80-90% of Kepler planet pairs do not allow intermediate planets (e.g., Fang & Margot 2013).
  • Kepler systems are dynamically packed (e.g., Pu & Wu 2015). However, interior/exterior planets remain allowed.

Spacing in mutual Hill radii

Exoplanet statistics and microlensing

By Wei Zhu(祝伟)

Exoplanet statistics and microlensing

A presentation in the 2021 National Conference on Planetary Science in Suzhou.

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