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

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

2. 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

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

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

5. 8kpc   Obs. G.C. (face on, from North) Microlensing Optical depth, andthe Galactic Bar structure 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1010M, axis ratio (1:0.3:0.2), ~20

6. Microlensing event rate: Ns: number of source To: duration of the survey ε(tE):detection efficiency at tE Optical depth: τ＝Γ×<tE>=Γ×(π/2)tE

7. 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) Previous measurements of optical depth, tE/(Ns) • 0.810-6, symmetric bulgemodel • <210-6, theoretical bar models

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

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

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

11. Observational fields • 50 deg.2 • ５0 Mstars • 　　1obs/１hr • 　　1obs/１０min. disk Galactic Center ~600events／yr http://www.massey.ac.nz/~iabond/alert/alert.html Each field has 80 10’x10’subfields

12. subtracted Difference Image Analysis (DIA) Observed

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

14. Timescale tE distribution abundance:~1.8 as common as stars Mass ： 〜Jupiter mass 474 events selected from 1000 candidates in 2 yrs Known objects 474events Main sequence White dwarf Brown dwarf Neutron star Planetary-mass objects Black hole TS et al. 2011, Nature, 473, 7347, 349-352

15. Fitting with Poisson Statistics 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 Original: New: Average Efficiency:

16. Simulation Put artificial events on real images • Sampling • noise • Artifacts • Nearby bright star, • Nearby variable star • Nearby high proper motion star • Differential refraction Subtracted image Art image

17. Input time scale tE,inv.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

18. Cumulative distribution of the impact parameters, u0 Simulation data

19. Detection Efficiency

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

21. tEdistribtution Efficiency corrected

22. tE/ε (~τ) distribtution

23. Event rate Γ

24. Event rate Γdeg2

25. Event rate Γ（/star/yr） 60% higher rate than the rate in WFIRST SDT report (Green et al. 2012)

26. Optical depth τ Each box: 10’x10’subfield GC Weighted average by 2D gaussian with σ=0.4deg max at low latitudes and a longitude of l ≈ 3.5◦

27. Time scale, tE GC Weighted average by 2D gaussian with σ=0.4deg max at a longitude of l ≈ 3.5◦ A reason of high optical depth at≈ 3.5◦

28. Event rate Γ（/star/yr） GC WFIRST Weighted average by 2D gaussian with σ=0.4deg max at low latitudes and a longitude of l ≈ 1◦

29. 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 previousmeasurements, 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).

31. Event rate Γdeg2（/deg2/yr） Weighted average by 2D gaussian with σ=0.4deg

32. Best fit Model Event rate Γ& Γdeg2 Γ（/star/yr） Γdeg2（/deg2/yr）

33. Fitting with Poisson Statistics

34. Optical depth

35. Event rate Γdeg2（/deg2/yr）

36. Iinv.s. Iout

37. u0,in v.s. u0,out

38. tEdistribtution

39. 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1010M, axis ratio (1:0.3:0.2) =20, (Han & Gould, 1995) Few dark matter. Exclude NFW Dark halo (Binny & Evans, 2001)

40. Is v.s. Itotal Level 6: 34/66 candidates 38% of events are blended

41. 2.Red Clump Giants • Metal-rich horizontal branch stars • Small intrinsic width in luminosity function (~0.2mag) =20-30, axis ratio 1:0.4:0.3 Stanek et al. 1997

42. Brightness of RCG & RRLyrae RCG (Sumi 2004; Collinge, Sumi & Fabrycky, 2006) RCG 2000 RRLyrae 2000 RRLyrae

43. Degeneracy in parameters Einstein crossing time：

44. 3.Streaming motions of the bar with RCGSumi (Princeton) , Eyer (Geneva Obs.) & Wozniak (Los Alamos), 2003 Sun Color Magnitude Diagram faint bright Vrot=~50km/s Sumi, Eyer & Wozniak, 2003

45. 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 Axisymmetric Galactic bulge model Kiraga & Paczynski 1994, Evans 1994 etc. Bar model with Small inclination angle. Paczynski et al.1994, Zhao et al. 1995 etc. Microlensing Optical Depth

46. DATA NRCG= 1 Million Red Clump Giant (RCG) stars as source stars

47. 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

48. Free-Floating Planet, events with timescale tE<２days M：lens mass MJ: Jupiter mass D：distance vt: velocity ~２０days for stars tE=1.2days ~Jupiter mass 1day As Many FFP as stars! Sumi et al. 2011 MOA and OGLE WFIRST can detect Earth-mass FFP

49. Luminosity Function

50. 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1010M, axis ratio (1:0.3:0.2) =20, (Han & Gould, 1995)