NOT ENOUGH MACHOS IN THE GALACTIC HALO Éric AUBOURG EROS, CEA-Saclay Experimental results 1- Galactic disk 2- Small masses (LMC/SMC) 10-7 10-2 M o 3- SMC 4- LMC
GRAVITATIONAL MICROLENSING (Paczynski, 1986) light rays trajectory Image 1 in plane of deflector Observer O Déflecteur D Source star S u Image 2 Einstein radius : R E = 4GM c 2 D OS x (1-x) where x = D OD D OS Angular separation of the images : 2 R ~ E ~ 10 D -3 arcsec OD a single image observed but amplified (A ~ 1/u) Typical duration : t E = R E v t = 90 M/M o days
surveys : follow-up : EROS 2, MACHO, OGLE 2 PLANET, GMAN Milky Way compact objects Sun flux - Symmetric - Achromatic - Unique t 52 kpc Dark Halo 63 kpc Large Magellanic Cloud Small Magellanic Cloud
EROS 1 candidate #1 Blue magnitude 18 18.5 19 19.5 20 20.5 17.5 8150 8200 8250 8300 8550 8600 8650 8700 8900 8950 9000 9050 Red magnitude 18 18.5 19 19.5 20 8150 8200 8250 8300 8550 8600 8650 8700 8900 8950 9000 9050 Time (JD- 2.440.000) A 0 = 2.5 t E = 23 days
BLENDING 2.5 log(flux) 6.2 6 5.8 5.6 reconstructed magnification real magnification 5.4 5.2 5 4.8 Total base flux (F 1 +F 2 ) 4.6 4.4 Base flux of magnified star (F 1 ) -4-2 0 2 4 time F tot = A(t) F 1 + F 2
TRIPLE DEGENERACY velocity distribution model flux t E A 0 = u 0 2 + 2 u 0 u 0 2 + 2 t 0 t u 0, t 0 : randomly distributed (statistical tests of consistency on all events) t E : mass function (Dirac) 4 G m defl. D t E = = c 2 OS x (1-x) R E v t v t dark matter distribution model in halo (or Clouds)
EROS 2 : OPTICAL SET-UP - 1m primary mirror - 2 x 8 CCD's covering 1 square degree - dichroic cube => red and blue simultaneously - automatic pointing and guiding system Secondary 1m Primary Guiding camera & optics Blue camera Red camera
Backgrounds unknown DATA ANALYSIS Images Star catalogue Selection criteria based on microlensing properties Find significant variation Select variations compatible with microlensing Rejection of variable stars Efficiency through Monte Carlo simulation on light curve Estimate blending effect through simulated images
EROS FIELDS TOWARDS THE GALACTIC SPIRAL ARMS -10 0 10 10 Norma-Cygne Sun D = 7kpc 10 0 Persee GC 0 βsct -10 θmus Sagittaire-Carene Ecu-Croix -10 γ Nor γ Sct -10 0 10 (in kpc)
Recent Results towards the Galactic Spiral Arms (EROS experiment) All fields : 7 events (~ as expected) Excess towards γ Sct (5 observed vs. 1.6 expected) Mostly short durations bulge events τ x 10 6 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 Total Disk Bulge Halo θ Mus a = 1.5 kpc a = 3.0 kpc γ Nor γ Sct β Sct at b = -2.5 0.0 300 310 320 330 340 350 0 10 20 30 40 50 60 Galactic longitude (in degrees)
MICROLENSING : PRESENT STATUS 1993 : EROS 1, MACHO, OGLE First microlensing events 1996 : EROS 1 2 candidates towards LMC t E ~ 25 days exclusion contour 1997 : MACHO 6-8 candidates towards LMC t E ~ 40 days positive detection, M = 0.5 M 20-100% of standard halo 1996-1998 : EROS 1 + MACHO No short duration event (t E < 15 days) No dark objects 10-7 M < M < 10-2 M
EXCLUSION CONTOUR Halo mass fraction (%) 100 80 60 excluded at 95% CL by EROS ( ) or by MACHO ( ) or by combined analysis EROS + MACHO ( ) 40 20 0 10-8 MACHO allowed area 95% CL 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 Deflector mass (M o ) => Objects with mass in range [10-7 - 0.02] M o - make up at most 20% of standard halo - M TOT < 1 x 10 11 M o (~ model-independant)
MICROLENSING : PRESENT STATUS 1993 : EROS 1, MACHO, OGLE First microlensing events 1996 : EROS 1 2 candidates towards LMC t E ~ 25 days exclusion contour 1997 : MACHO 6-8 candidates towards LMC t E ~ 40 days positive detection, M = 0.5 M 20-100% of standard halo 1996-1998 : EROS 1 + MACHO No short duration event (t E < 15 days) No dark objects 10-7 M < M < 10-2 M 1998 : EROS 2, MACHO First SMC candidate First self-lensing hint t E ~ 130 days 1999 : EROS 2 (SMC Data) One candidate on two years of date (11.10 6 star.years) Exclusion contour (extended towards M ~ 0.1 M )
Afonso C. et al. (EROS) 1999, A&A 344, L63 EROS 2 SMC ANALYSIS 2 years have been analysed and published 8.6 deg 2 spread over 10 fields 5.3 million stars Sampling : 1 measurement/2-4 days One event (SMC-97-1)
(Alcock et al., 1995, ApJ 454, L125) DETECTION OF PARALLAX EFFECT Deflector Source Earth Sun - events with large t E - simultaneous observation with a satellite in orbit around the Sun A
flux R time (days) FIRST SMC CANDIDATE u 0 = 0.42 t E = 129 days flux B time (days) χ 2 = 261 / 279 (once modulation included) Intrinsic variable star P = 5.1 days 5% peak-to-peak
PARALLAX ANALYSIS ON CANDIDATE LIGHT CURVE no detectable effect at 95% CL : M. x > 0.7 Mo (1-x) where x = D OD D OS Deflector mass 10 2 10 1 D(SMC) = 65 kpc most probable mass for a halo deflector 1σ 10-1 brown dwarfs 10-2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 D(deflector) / D(source) 2 possible interpretations : deflector in the halo : x<2/3 and M > 0.6 Mo deflector in the SMC : x~9/10 and M ~ 0.1 Mo
EXCLUSION CONTOUR Halo mass fraction (%) 100 80 60 excluded at 95% CL by EROS 1 ( ) and EROS 2 SMC ( ) 40 20 0 10-8 permitted by MACHO at 95% CL 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 Mass of the deflectors (M o )
MICROLENSING : PRESENT STATUS 1993 : EROS 1, MACHO, OGLE First microlensing events 1996 : EROS 1 2 candidates towards LMC t E ~ 25 days exclusion contour 1997 : MACHO 6-8 candidates towards LMC t E ~ 40 days positive detection, M = 0.5 M 20-100% of standard halo 1996-1998 : EROS 1 + MACHO No short duration event (t E < 15 days) No dark objects 10-7 M < M < 10-2 M 1998 : EROS 2, MACHO First SMC candidate First self-lensing hint t E ~ 130 days 1999 : EROS 2 (SMC Data) One candidate on two years of date (11.10 6 star.years) Exclusion contour (extended towards M ~ 0.1 M ) 1999 : EROS 2, MACHO, OGLE, PLANET, MPS Binary lens event towards SMC New self-lensing hint 1999 : EROS 2 (LMC Data) LMC data, on 25 square degrees and 2 years of data 2 candidates, new combined exclusion plot
BINARY LENSES α z ζ dζ = J dz O D S amp = 1 det J thus amp = if det J = 0 caustic curve in source plane m 1 m 2 2 Log(amplification) 1.5 1 0.5 0-3 -2-1 0 1 2 3 t/t E light curve : u 0, t 0, t E q = m 1 / m 2, a, θ
EVENT 98-SMC-1 Amplification 160 140 Amplification 160 140 120 120 100 100 80 80 60 40 CTIO EROS MACHO MPS OGLE PLANET 60 40 20 20 0 2330 2335 2340 2345 2350 2355 2360 2365 2370 2375 2380 Time (days since 1 jan 1990) 0 2358 2358.2 2358.4 2358.6 2358.8 2359 2359.2 2359.4 2359.6 2359.8 2360 Time (days since 1 jan 1990)
Amplification 160 140 120 100 80 60 40 20 0 2358 2358.2 2358.4 2358.6 2358.8 2359 2359.2 2359.4 2359.6 2359.8 2360 Time (days since 1 jan 1990)
Lasserre T. (EROS), 1999, astro-ph/9909505 Lasserre T. el al. (EROS), 2000, A&A accepted, astro-ph/0002253 EROS 2 LMC ANALYSIS 2 years have been analysed 25 deg 2 spread over 43 fields 17.5 million stars Sampling : 1 measurement/4-6 days Two events
LMC : BUMPER BACKGROUND Bumpers Monte-Carlo Cut on accumulation in HR diagram (bright blue stars) + Amplification and chromatism A < 1.6 (A R -1)/(A B -1) > 1.2
LMC : UNEXPECTED BACKGROUND Consistent with binary lens (with parallax or xarallap) Low main sequence star, achromatic Previous variation in 1995 (MACHO)
LMC : EVENT # 1 u 0 = 0.20(0.01) t E = 106(3) days χ2 / dof = 400/150 Bad χ2 but passes all selection criteria Accepted as candidate
LMC : EVENT # 2 u 0 = 0.23(0.01) t E = 39(3) days χ2 / dof = 183/135 Chromatic event, 72(7)% of base flux in amplified
EXCLUSION CONTOUR Halo mass fraction (%) 100 80 60 excluded at 95% CL by EROS 1 ( ) and EROS 2 LMC ( ) 40 20 0 10-8 permitted by MACHO at 95% CL 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 Mass of the deflectors (M o )
BACK TO EROS 1 EROS 1 # 2 was a variable star, compatible with microlensing. New variation 8 years later. Confirmed on MACHO data. EROS 1 # 2 is no longer a microlensing candidate EROS 1 upper limited should be revised downward
One single experiment with 3-4 events EROS COMBINED LIMIT Lasserre T. el al. (EROS), 2000, A&A accepted, astro-ph/0002253 EROS 1 CCD (1991-95) 0 candidate EROS 1 Plates (1990-93) 1 candidate EROS 2 SMC (1996-98) 0-1 candidate EROS 2 LMC (1996-98) 2 candidates Considered as
Lasserre T. el al. (EROS), 2000, A&A accepted, astro-ph/0002253 EROS COMBINED LIMIT Halo mass fraction (%) 100 80 60 Excluded at 95% CL by EROS1 1990-95 and EROS2 1996-98 with 3 candidates with 4 candidates 40 20 Permitted by MACHO at 95% CL 0 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 1 10 Mass of the deflectors (M o )
EROS COMBINED LIMIT Halo mass fraction (%) 100 80 60 Excluded at 95% CL by EROS1 1990-95 and EROS2 1996-98 with 3 candidates with 4 candidates 40 EROS 1 (plates) 1 cand EROS 2 SMC 0-1 cand EROS2 LMC 2 cand 20 Permitted by MACHO 6yr at 95% CL 0 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 1 10 Mass of the deflectors (M o )
CONCLUSIONS? Galactic structure - Galactic Spiral Arms : 7 events constraints on structure: extension of the bar SMC results - 1 event with very long t E (129 days) most probably in SMC - 1 binary event with best time coverage ever most probably in SMC LMC results - no halo (<10%) compact objects in mass range 10-7 M o 0.02 M o - only 1 event left for EROS1-2 events for EROS 2 EROS 1+2 SMC+LMC combined result - less than in mass range 100% of standard halo 10-7 M o 3 M o 40% of standard halo 10-7 M o 1 M o 20% of standard halo 10-7 M o 0.1 M o