Planet hunting through

gravitational microlensingShude Mao

25/09/2013 @ Tsinghua

Collaborators: Yingyi Song, Wei Zhu, Matthew Penny,

Andy Gould, Doug Lin

Outline• Basics of microlensing• Current status• Discovery of extrasolar

planets• Multiple planets and

degeneracy• Future directions

What is near-field microlensing?

Standard light curve is (Paczynski 1986)

symmetric, achromatic & non-repeating

Image credit: NASA/ESA

Image separation is too small to resolve individual images, we can only observe magnification effects.

DS lens source

Basic scales in microlensing

• Einstein radius rE~ M1/2 ，~few AU, coincident with the size of the solar system!

• Einstein radius crossing time tE ~ rE/V, degeneracy!

• Angular size ~ mas (difficult to resolve)!

Einstein Ring

PHYS40691 - FRONTIERS OF ASTROPHYSICS:Gravitational Microlensing in GalaxiesNOAO/AURA/NSF Image/Eamonn Kerins

Mostly herehereand here

Galactic bulge

SmallMagellanicCloud

LargeMagellanicCloud

Current surveys monitor the brightness of order ~ several hundred million stars nightly and in real time since 1990’s.

Where are we looking?

What do we see?

Credit: OGLEChallenges: probability~10-6, event

rate ~ 10 events per year per 106

stars.

Examples: a high magnification standard light curve

tE~42 days, typicalmax ~3000fs=0.04

Obs. max ~36

OGLE-2004-BLG-343

Examples: A short standard event：

tE=1.25 day,Free-floating planets? Statistically!

8 years of data

OGLE-2008-BLG-365

Black hole microlensing candidate

• M~few Msun, and dark - a stellar mass black hole?

• Several other BH candidates have been proposed

(Mao et al. 2003)

4 years

OGLE-1999-BUL-32 • Subtle parallax

signature • duration~ 640

days; longest event ever

Microlensing data sets: • Two decades of observations by

OGLE, MOA, MACHO etc. assembled time series for hundreds of millions of stars toward GC, LMC, SMC, etc.

• To date ~ 12,000 events have been detected– The vast majority of events are

detected towards the Galactic bulge

– Duration: a few hours to 4 years, peak magnification: 1 to ~few thousand

– Current event rate by OGLE ~2000/yr, real-time

Microlensing applications

Reference image, R Target image, T

• Dark matter: MACHOS?• Galactic structure/dynamics

- Color-magnitude diagrams- Microlensing optical depth maps- Proper motions (kinematics)- Extinction maps

• High magnification events/caustic crossing events• Stellar atmosphere (limb-

darkening)• metallicity, surface gravity of

stars• Black holes? • Extrasolar planets

DS lens source

Principles of extrasolar planet detection with

microlensing

• Einstein radius rE~ M1/2 ， few AU, coincident with the size of the solar system!

• Einstein radius crossing time tE ~ rE/V, degeneracy!

• Angular size ~ mas (difficult to resolve)!

Einstein Ring

lens

source

• The presence of the planet perturbs the image positions and magnifications

• In fact it can create one or three extra images!

Negative parity

Positive parity

Principle of planet detection

Microlensing planet: OGLE-2005-BLG-390

(Beaulieu et al 2006)

Principle was discussed in Mao & Paczynski (1991) and Gould & Loeb (1992)

Family Album of Microlensing Planets

~5.5 MEarth Apeak ~ 3

~14 MEarth Apeak~ 8

~22 MEarth Apeak ~ 12

Apeak ~ 8~830 MEarth

Apeak ~ 290~86 MEarth

~1000 MEarth Apeak ~ 14

Beaulieu et al 2006

Sumi et al. 2010

Bond et al 2004

Gaudi et al 2008 Muraki et al., 2011

Batista et al., 2011

~1200 MEarthApeak ~ 40

Udalski et al 2005; Dong et al 2009

~13 MEarth Apeak ~ 800

Gould et al 2006

Apeak ~ 500~50 MEarth

Dong et al in prep

Exoplanet discovery space

(Mao 2012)

• Between 0.5-10 AU - 17% have Jupiters, 50% Neptune and Super-Earths Cassan et al. (2012); Gould (2006, 2010)

• Free-floating planets may be common: ~ 1.8 per star

Sumi et al. (2011), Nature

keplermicrolensing

RV

Testing core accretion theories

• Microlensing can be particularly useful for testing the core accretion planet formation theory.

Ida & Lin (2008, 2010)

Simulated planetary events

• Microlensing detection efficiency:– 3% show planetary signatures, of which

8% show multiple planets! (cf. radial velocity and transit ~30%)

• However, with planetary events in high proportions in high magnification events!

Zhu, Mao et al. (2013)

Earth

Saturn

Jupiter

Separation/rE

semi-major axis (AU)

First: OGLE-2006-BLG-019L

• q1 = 1.35 × 10-3, d1 ~2.3 AU • q2 = 4.86 × 10-4, d2 ~ 4.6 AU

A Saturn and Jupiter analog!

Gaudi et al. (2008)

Second: OGLE-2012-BLG-0026

• q1 = (1.30 ± 0.01) × 10-4, d1 = 1.034 ± 0.001

• q2 = (7.84 ± 0.21) × 10-4, d2 = 1.304 ± 0.006

• tE = 93.92 ± 0.58 days

Close/wide degeneracy!

Han et al. (2013)

OGLE-2005-BLG-071Binary model:• q = (7.1 ± 0.3)

× 10-3

• d = 1.294 ± 0.002

• tE = 70.9 ± 3.3 days

residuals?Udalski et al. (2005)

？？？

OGLE-2005-BLG-071Wide+ of MCMC

A:• q = (7.5 ±

0.2) × 10-3

• d~1.306 • tE ~ 71.1

+2.3/-2.4 days• With orbital

motion and parallax!

• Other perturbations?

Dong et al. (2008)

double-lens to triple-lens degeneracy

• q1 = 2.49 × 10-3, d1 = 1.303, q2 = 4.99 × 10-3, d2 = 1.304

• φ = 3 degree (a range is allowed)!

Song, Mao & An (2013)

double-lens/triple-lens degeneracy

• Double and triple lenses can be shown to be mathematically degenerate to second order

• If unaccounted for, it may bias the multiple fraction to be lower than the true value

• We give detailed recipes how this degeneracy can be explored

Song, Mao & An (2013)

Current mode of discoveryCurrent mode of discovery:

Survey (MOA and OGLE collaborations) + follow-up (microFun/PLANET collaborations) around the globe

MicroFun - 24 hour relay

Future• Near-future

– Survey much areas of sky, more fields (OGLE-IV: 233 fields, 330 square degrees)

– Part-time pure survey mode• Microlensing in five years

– KMTnet: pure survey mode• Microlensing in ten years?

– Space satellites (Euclid/WFIRST)

Microlensing in ~5 years

• KMTNet–Three 1.6m

telescope with ~4 deg2 FoV

–Thousands of events with ~15min cadence per year

– will find ~40 ηEarth and 1-2 orders of mag more Neptunes and Jupiters in a 5-yr survey

Chile

South Africa

Australia

Microlensing in ~10 years (?)

OGLE image Hubble ACS HRC

• Space allows to observe in IR, and study fainter, smaller stars to discover very low-mass planets

• Can partially/completely remove the degeneracies

Microlensing from space: Euclid

A simulated event at baseline and peak

baseline

peak

0.3/pixel 0.1/pixel

Euclid (2020) focus on weak lensing and BAO, but may have a microlensing component

A simulated Earth-mass event

Deviation around 6 hours; can be discovered in space.

Sensitivities and yields

• Default MF: 1/3 per log m per log a, flat log mass dependence

• total detections (-1.5<log M/Me<3): ~400, 6 Earths (range: 6-100 in different models)

• Sensitivity to free floating planets

5 year mission,

two-month per year

Kepler

Summary• Microlensing has diverse

applications• Current real-time event rate to

~2000 events/yr– More subtle effects can be seen – Multiple planets; there is some

degeneracy in modelling; triple lensing remains a challenge!

• Exoplanet microlensing will remain exciting from the ground (and space!) in the next decade!– Will complement other methods and

test planet formation theory– Chinese contribution from Dome-A?

Exotic microlensing events

EROS-BLG-2000-5An et al (2002)

OGLE-1999-BUL-19

Smith, Mao et al. (2002)

Alcock et al. (1997)

• Standard light curve assumes single lens and point source with linear motions!

• Extra features in the light curve give additional constraints to break the microlens degeneracy

parallax finite source size

binary lens

Parameters of triple lens system

Degeneracies in triple gravitational microlensing

The double-triple lens degeneracy

Euclid's sensitivityTotal detections (-1.5<log(M/Me)<3): Default: 390 RV: 307 uL: 438 uL saturated: 267

Expected yields for different assumed mass functions

Expected measurement of planet mass fn

Mp-a plane sensitivity

Penny et al., MNRAS, 2012. In prep.

Exoplanet discovery space

Microlensing proving to be best for planets like those in our Solar system!

From space

Every Image is like HST!

OGLE image with 0.5” seeing

Hubble ACS HRC

Microlensing as a Nature telescope

• EROS-2004-BLG-254 shows strong broadening of magnification peak due to finite source smearing

• UVES spectra of source obtained whilst still being microlensed indicated source is a K3 III Bulge 10.5 kpc away

• Lens angular Einstein radius θE = 0.114 mas determined from light-curve modeling and from V, V-I photometry of source

• Lens proper motion relative to source given by μ = θE/tE = 3.1 mas/yr

• Can be used to obtain limb-darkening profiles.

(Cassan et al 2006)

Orbital motion in microlensing events

Extinction maps

• Observed red clump giants are redder and fainter than expected due to extinction (Stanek et al. 1997, Sumi 2004)!

• We can use to obtain maps of extinction; many anomalous in reference to the standard extinction law!

l=0b=-2

Baade Window: l=1b=-3.9

Limb darkening profile

Finite source events observed to date are proving a stern test ofstellar atmosphere models for ~10 events observed so far!

Limb-darkened stellar disk intensity profile is:

where parameter a is a parameter computed from stellar atmosphere models

Table from Cassan et al (2006)

Essential numbers

• Lens mass degeneracy! • Partial or complete removal

possible with exotic events (parallax, finite source size).

• Optical depth

– independent of the mass function of lenses

– can be used to infer the overall mass distribution of our Galaxy

• Event rate and duration distribution

– Event rate ~10 events/million stars/year, very low!

– The analysis of event time scale distribution offers a method to determine the lens mass function, independent of light.

Statistical measures of microlensing

Effects of rotationCan cause caustics to change shape

Or to rotate

~5% predicted~20% observed

Selection effects?

Penny, Mao & Kerins (2011)

• 1. Distribution of all planets;• 2. Distribution of detected planets;• 3. Microlensing detection

efficiency:•     All planetary events/all

microlensing events = 155/5000;•     Multiple-planetary events/all

planetary events = 12/155;• 4. Distribution of impact

parameters.

• Best wishes,• Wei

First: OGLE-2006-BLG-019L(Gaudi et al. 2008)

• q1 = 1.35 × 10^-3, d1 = 2.3 AU = 1.04• q2 = 4.86 × 10^-4, d2 = 4.6 AU = 2.07

Second: OGLE-2012-BLG-0026(Han et al. 2013)

Second: OGLE-2012-BLG-0026(Han et al. 2013)

Second: OGLE-2012-BLG-0026(Han et al. 2013)

Model D:• q1 = (1.30 ± 0.01) × 10^-4, d1 =

1.034 ± 0.001• q2 = (7.84 ± 0.21) × 10^-4, d2 =

1.304 ± 0.006• tE = 93.92 ± 0.58 days

OGLE-2005-BLG-071 (Udalski et al. 2005)

Wide model:• q = (7.1 ±

0.3) × 10^-3• d = 1.294 ±

0.002• tE = 70.9 ±

3.3 days

OGLE-2005-BLG-071 (Dong et al. 2008)

Wide+ of MCMC A:

• q = (7.5 ± 0.2) × 10^-3

• d = 1.306 +0.002/-0.004

• tE = 71.1 +2.3/-2.4 days

OGLE-2005-BLG-071: from double-lens to triple-lens (contours of parameters)

OGLE-2005-BLG-071: from double-lens to triple-lens (one example)

• q1 = 2.49 × 10^-3, d1 = 1.303• q2 = 4.99 × 10^-3, d2 = 1.304• φ = 3 degree (there is a range!)

Upgraded Microlensing Experiments

• OGLE IV is running in full power since 2011: 1.4 Deg2

camera

• MOA-II has been online:

1.8m telescope2.2 Deg2 camera

Detections

Earth mass

Mars mass

<Mercury mass

0.75 degree

77 arcsec

Penny et al. (2012)