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)