The Microlensing Event Rate and Optical Depth Toward the Galactic Bulge from MOA-II Takahiro Sumi (Osaka University)

Galactic Bar de Vaucouleur,1964, gas kinematics Blitz&Spergel,1991, 2.4μm IR luminosity asymmetry Weiland et al.,1994, COBE-DIRBE,confirmed the asymmetry. Nakada et al.,1991, distribution of IRAS bulge stars Whitelock&Catchpole, 1992, distribution of Mira Kiraga &Paczynski,1994 Microlening Optical depth  8kpc

COBE-DIRBE Weiland et al.,1994, confirmed the asymmetry. all extinction correct disk subtracted

RCG by IR (Babusiaux & Gilmore, 2005) Deep survery by Cambridge IR survery instrument (CIRSI)  =22  5.5 

Microlensing Optical depth,  and 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=1.6  M , axis ratio (1:0.3:0.2),  ~20  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=1.6  M , axis ratio (1:0.3:0.2),  ~20 

Optical depth: τ ＝ Γ× =Γ×(π/2)t E Microlensing event rate: N s : number of source T o : duration of the survey ε(t E ) : detection efficiency at t E

Previous measurements of optical depth,  t E /(N s  ) High   [use All stars as source] 3.3  10 -6, OGLE (Udalski et al. 1994) 3.9  10 -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)] 2.0  10 -6, MACHO, (Popowski et al. 2001) 0.94  10 -6, EROS, (Afonso et al. 2003) 2.17  10 -6, MACHO, (Popowski et al. 2004)  =2.55  10 -6,OGLE-II, (Sumi et al. 2006) 0.8  10 -6, symmetric bulge model <2  10 -6, theoretical bar models

Test Optical depth with unblended fit 50% more events,  30% higher efficiency,  21% underestimate t E,   =2.0  0.4  10 -6,  =2.55  10 -6, with blending fit OGLE-II, (Sumi et al. 2006)

MOA (since 1995) （ Microlensing Observation in Astrophysics ） （ New Zealand/Mt. John Observatory, Latitude ： 44  S, Alt: 1029m ）

MOA-II 1.8m telescope First light: 2005/3 Survey start: 2006/4 Mirror : 1.8m CCD : 80M pix. FOV : 2.2 deg. 2 Mirror : 1.8m CCD : 80M pix. FOV : 2.2 deg. 2

Observational fields 50 deg. 2 ５ 0 Mstars 1obs/ １ hr 1obs/ １０ min. 50 deg. 2 ５ 0 Mstars 1obs/ １ hr 1obs/ １０ min.  ~600events ／ yr Galactic Center disk Each field has 80 10’x10’subfields

Difference Image Analysis (DIA) ObservedObservedsubtractedsubtracted

All source & RCG Sample Extended RCG region All source: I <20 mag 10’x10’subfield

Timescale t E distribution TS et al. 2011, Nature, 473, 7347, events Planetary-mass objects Known objects Black hole Neutron star White dwarf Main sequence Brown dwarf abundance :~1.8 as common as stars Mass ： 〜 Jupiter mass 474 events selected from 1000 candidates in 2 yrs

Original: New: Average Efficiency: Not Poisson -> need bootstrap Only the detection efficiency of the detected events in the subfield in question are used. Poisson statistic Can use larger area for Average Efficiency Even 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 t E,in v.s. output t E,out t E,in = t E,out mean of t E,in (t E,out ) 5% smaller ~5% smaller 90% interval Bias is only ~5% in all range

Cumulative distribution of the impact parameters, u 0 Simulation data

Detection Efficiency

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

t E distribtution Efficiency corrected

t E /ε (~τ) distribtution

Event rate Γ

Event rate Γ deg 2

Event rate Γ （ /star/yr ） 60% higher rate than the 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, t E 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 WFIRST GC

Summary By using 474 events from 2 years of MOA-II data, we found: τ 200 = [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 Γ deg 2 （ /deg 2 /yr ） Weighted average by 2D gaussian with σ=0.4deg

Best fit Model Event rate Γ & Γ deg 2 Γ （ /star/yr ） Γ deg 2 （ /deg 2 /yr ）

Fitting with Poisson Statistics

Optical depth

Event rate Γ deg 2 （ /deg 2 /yr ）

I in v.s. I out

u 0,in v.s. u 0,out

t E distribtution

Optical depth,   =2.55  0.45  10 -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=1.6  M , axis ratio (1:0.3:0.2)  =20 , (Han & Gould, 1995) Few dark matter. Exclude NFW Dark halo (Binny & Evans, 2001)

I s v.s. I total 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  =20-30 , axis ratio 1:0.4:0.3

Brightness of RCG & RRLyrae RCG 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 V rot =~50km/s Color Magnitude Diagram Sumi, Eyer & Wozniak, 2003 bright

Microlensing Optical Depth DoPHOT 9 events. Udalski et al DoPHOT 13 events Alcock et al DIA 99 events Alcock et al DIA 28 events Sumi et al Bar model with Small inclination angle. Paczynski et al.1994, Zhao et al etc. Axisymmetric Galactic bulge model Kiraga & Paczynski 1994, Evans 1994 etc.

DATA Red Clump Giant (RCG) stars as source stars N RCG = 1 Million

Pieces of information Microlensing Optical depth,  and Event Timescale, t E =R E /V t, (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 Microlensing Optical depth,  and Event Timescale, t E =R E /V t, (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 t E < ２ days t E =1.2days ~Jupiter mass 1day M ： lens mass M J : Jupiter mass D ： distance v t : velocity ~ ２０ days for stars WFIRST can detect Earth-mass FFP Sumi et al MOA and OGLE As Many FFP as stars!

Luminosity Function

Optical depth,   =2.55  0.45  10 -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=1.6  M , axis ratio (1:0.3:0.2)  =20 , (Han & Gould, 1995)