The Microlensing Event Rate and Optical Depth Toward the Galactic Bulge from MOA-II

Takahiro Sumi (Osaka University)

Galactic Bar

de Vaucouleur,1964, gas kinematicsBlitz&Spergel,1991, 2.4μm IR luminosity asymmetryWeiland et al.,1994, COBE-DIRBE,confirmed the asymmetry.Nakada et al.,1991, 　 distribution of IRAS bulge starsWhitelock&Catchpole, 1992, distribution of MiraKiraga &Paczynski,1994 Microlening Optical depth

8kpc

COBE-DIRBE Weiland et al.,1994, confirmed the asymmetry.

3030 l

all extinction correct disk subtracted

1010 b

RCG by IR (Babusiaux & Gilmore, 2005)

Deep survery by Cambridge IR survery instrument (CIRSI)

=225.5

Microlensing Optical depth, and the Galactic Bar structure

(face on, from North)

8kpc

G.C.Obs.

Microlensing Optical depth, (Alcock et al. 2000; Afonso et al.2003; Sumi et al. 2003;Popowski et al. 2004; Hamadache et al. 2006;Sumi et al. 2006)

M=1.61010M,

axis ratio (1:0.3:0.2),

~20

Optical depth: τ ＝ Γ×<tE>=Γ×(π/2)tE

Microlensing event rate:

Ns: number of sourceTo: duration of the surveyε(tE) 　 : detection efficiency at tE

Previous measurements of optical depth, tE/(Ns)

High [use All stars as source]• 3.310-6, OGLE (Udalski et al.

1994)• 3.910-6, MACHO, (Alcock et

al. 1997)• 2.43(3.23)10-6, MACHO,

(Alcock et al. 2000)• 2.59(3.36)10-6, MOA, (Sumi et al. 2003)

Low [use Red Clump Giant (RCG)]• 2.010-6, MACHO, (Popowski

et al. 2001)• 0.9410-6, EROS, (Afonso et

al. 2003)• 2.1710-6, MACHO, (Popowski

et al. 2004)• =2.5510-6,OGLE-II, (Sumi et

al. 2006)

• 0.810-6, symmetric bulge model • <210-6, theoretical bar models

Test Optical depth with unblended fit

50% more events, 30% higher efficiency, 21% underestimate tE,

=2.00.410-6,

=2.5510-6, with blending fit

OGLE-II, (Sumi et al. 2006)

MOA (since 1995)

（ Microlensing Observation in Astrophysics ）（ New Zealand/Mt. John Observatory, Latitude ： 44S, Alt: 1029m ）

MOA-II 1.8m telescope

First light: 　　 2005/3Survey start: 　 2006/4

Mirror : 1.8mCCD : 80M pix. FOV : 2.2 deg.2

Observational fields

•50 deg.2

•５ 0 Mstars

　　 1obs/ １ hr

　　 1obs/ １０min.

~600events ／ yrhttp://www.massey.ac.nz/~iabond/alert/alert.html

Galactic Centerdisk

Each field has 80 10’x10’subfields

Difference Image Analysis (DIA)

Observed subtracted

All source & RCG SampleExtended RCG region

All source: I <20 mag

10’x10’subfield

Timescale tE distribution

TS et al. 2011, Nature, 473, 7347, 349-352

474events

Planetary-massobjects

Known objects

Black hole

Neutron star

White dwarf

Main sequence

Brown dwarf

abundance 　 :~1.8 as common as starsMass ： 〜 Jupiter mass

474 events selected from 1000 candidates in 2 yrs

Original:

New:

Average Efficiency:

Not Poisson -> need bootstrapOnly the detection efficiency of the detected events in the subfield in question are used.

Poisson statistic

Can use larger area for Average EfficiencyEven if there is a few events in the subfield

Fitting with Poisson Statistics

Simulation

Subtracted image

Art image

Put artificial events on real images• Sampling• noise• Artifacts• Nearby bright star, • Nearby variable star• Nearby high proper motion star• Differential refraction

Input time scale tE,in v.s. output tE,out

tE,in = tE,out

mean of tE,in(tE,out)

~5% smaller

90% interval

Bias is only ~5% in all range

Cumulative distribution of the impact parameters, u0

Simulationdata

Detection Efficiency

Optical depth

All source result is middle of previous all and RCG source results.RCG is 30% lower than all source

tE distribtutionEfficiency corrected

tE /ε (~τ) distribtution

Event rate Γ

Event rate Γdeg2

Event rate Γ （ /star/yr ）

60% higher rate thanthe rate in WFIRST SDT report(Green et al. 2012)

Optical depth τ

max at low latitudes and a longitude of l ≈ 3.5◦

Each box: 10’x10’subfield

Weighted average by 2D gaussian with σ=0.4deg

GC

Time scale, tE

max at a longitude of l ≈ 3.5◦A reason of high optical depth at≈ 3.5◦

Weighted average by 2D gaussian with σ=0.4deg

GC

Event rate Γ （ /star/yr ）

max at low latitudes and a longitude of l ≈ 1◦

Weighted average by 2D gaussian with σ=0.4deg

WFIRSTGC

Summary By using 474 events from 2 years of MOA-II data, we found:• τ200 = [2.35 ± 0.18]exp[0.51±0.07](3−|b|) × 10−6

• Γ = [2.39 ± 1.1]exp[0.60±0.05](3−|b|) × 10−5 star−1 yr−1

• Event rate is maximized at low latitudes and a longitude of l ≈ 1◦.

• All source and RCG are consistent in Γ• Our optical depth are consistent with previous measurements,

somewhat lower than previous all-source measurements and slightly higher than previous RCG measurements. This suggests that the previously observed difference between all-source and RCG samples may be largely due to statistical fluctuations or due to how to hand the blending.

• 60% higher event rate than assumed in the report of the WFIRST SDT (Green et al. 2012).

Event rate Γdeg2 （ /deg2/yr ）

Weighted average by 2D gaussian with σ=0.4deg

Best fit Model Event rate Γ & Γdeg

2Γ（ /star/yr）

Γdeg2（ /deg2/yr）

Fitting with Poisson Statistics

Optical depth

Event rate Γdeg

2 （ /deg2/yr ）

Iin v.s. Iout

u0,in v.s. u0,out

tE distribtution

Optical depth,

• =2.550.4510-6, at (l,b)=(1.2,-2.8)

• Consistent with measurements with RCGs by Afonso et al (2003) and Popowski et al. (2004)

• Consistent with the bar model with

M=1.61010M, axis ratio (1:0.3:0.2) =20, (Han & Gould, 1995)

Few dark matter. Exclude NFWDark halo (Binny & Evans, 2001)

Is v.s. Itotal Level 6: 34/66 candidates

38% of events are blended

2.Red Clump Giants• Metal-rich horizontal branch stars• Small intrinsic width in luminosity function

(~0.2mag)

Stanek et al. 1997

=20-30, axis ratio 1:0.4:0.3

Brightness of RCG & RRLyrae

RCG

2000 RRLyrae

2000 RRLyrae

RCG

(Sumi 2004; Collinge, Sumi & Fabrycky, 2006)

Degeneracy in parameters

Einstein crossing time ：

3.Streaming motions of the bar with RCG

Sumi (Princeton) , Eyer (Geneva Obs.) & Wozniak (Los Alamos), 2003

Sun

faint

Vrot=~50km/s

Color Magnitude Diagram

Sumi, Eyer & Wozniak, 2003

bright

Microlensing Optical Depth

28

)(N i Ei

Ei

obs t

t

T ｓ２

611.181.0

663.060.0

62.19.0

62.12.1

1036.3

1025.3

109.3

103.3

bg DoPHOT 9 events. Udalski et al. 1994

DoPHOT 13 events Alcock et al. 1998

DIA 99 events Alcock et al. 2000

DIA 28 events Sumi et al. 2002

period obs.:

number source:

obs

s

T

N

6105.2~0.1model Bar model with Small inclination angle.

Paczynski et al.1994, Zhao et al. 1995 etc.

6102.1~4.0model Axisymmetric Galactic bulge model

Kiraga & Paczynski 1994, Evans 1994 etc.

DATARed Clump Giant (RCG) stars as source stars

NRCG= 1 Million

Pieces of information

• Microlensing Optical depth, and Event Timescale, tE=RE/Vt, (Sumi et al. 2006)

• Brightness of Red Clump Giant (RCG) and RRLyrae stars, (Stanek et al. 1997, Sumi 2004;

Collinge, Sumi & Fabrycky, 2006)

• Proper motions of RCG, (Sumi, Eyer & Wozniak, 2003; Sumi et al. 2004), Proper motion of 5M stars, I<18 mag,

~1mas/yr

Free-Floating Planet, events with timescale tE< ２ days

tE=1.2days ~Jupiter mass

1day

M ： lens massMJ: Jupiter massD ： distancevt: velocity~ ２０ days for stars

WFIRST can detect Earth-mass FFPSumi et al. 2011MOA and OGLE

As Many FFP as stars!

Luminosity Function

Optical depth, • =2.550.4510-6,

at (l,b)=(1.2,-2.8)

• Consistent with measurements with RCGs by Afonso et al (2003) and Popowski et al. (2004)

• Consistent with the bar model with

M=1.61010M,

axis ratio (1:0.3:0.2) =20, (Han & Gould, 1995)