NOT ENOUGH MACHOS IN THE GALACTIC HALO. Éric AUBOURG EROS, CEA-Saclay

Transcription

1 NOT ENOUGH MACHOS IN THE GALACTIC HALO Éric AUBOURG EROS, CEA-Saclay Experimental results 1- Galactic disk 2- Small masses (LMC/SMC) M o 3- SMC 4- LMC

2 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

3 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

4 EROS 1 candidate #1 Blue magnitude Red magnitude Time (JD ) A 0 = 2.5 t E = 23 days

5 BLENDING 2.5 log(flux) reconstructed magnification real magnification Total base flux (F 1 +F 2 ) Base flux of magnified star (F 1 ) time F tot = A(t) F 1 + F 2

6 TRIPLE DEGENERACY velocity distribution model flux t E A 0 = u u 0 u 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)

7 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

8 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

9 EROS FIELDS TOWARDS THE GALACTIC SPIRAL ARMS Norma-Cygne Sun D = 7kpc 10 0 Persee GC 0 βsct -10 θmus Sagittaire-Carene Ecu-Croix -10 γ Nor γ Sct (in kpc)

10 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 Total Disk Bulge Halo θ Mus a = 1.5 kpc a = 3.0 kpc γ Nor γ Sct β Sct at b = Galactic longitude (in degrees)

11 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 % of standard halo : EROS 1 + MACHO No short duration event (t E < 15 days) No dark objects 10-7 M < M < 10-2 M

12 EXCLUSION CONTOUR Halo mass fraction (%) excluded at 95% CL by EROS ( ) or by MACHO ( ) or by combined analysis EROS + MACHO ( ) MACHO allowed area 95% CL Deflector mass (M o ) => Objects with mass in range [ ] M o - make up at most 20% of standard halo - M TOT < 1 x M o (~ model-independant)

13 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 % of standard halo : 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 ( star.years) Exclusion contour (extended towards M ~ 0.1 M )

14 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)

15 (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

16 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

17 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 D(SMC) = 65 kpc most probable mass for a halo deflector 1σ 10-1 brown dwarfs 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

18 EXCLUSION CONTOUR Halo mass fraction (%) excluded at 95% CL by EROS 1 ( ) and EROS 2 SMC ( ) permitted by MACHO at 95% CL Mass of the deflectors (M o )

19 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 % of standard halo : 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 ( 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

20 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) t/t E light curve : u 0, t 0, t E q = m 1 / m 2, a, θ

21 EVENT 98-SMC-1 Amplification Amplification CTIO EROS MACHO MPS OGLE PLANET Time (days since 1 jan 1990) Time (days since 1 jan 1990)

22 Amplification Time (days since 1 jan 1990)

23 Lasserre T. (EROS), 1999, astro-ph/ Lasserre T. el al. (EROS), 2000, A&A accepted, astro-ph/ 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

24 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

25 LMC : UNEXPECTED BACKGROUND Consistent with binary lens (with parallax or xarallap) Low main sequence star, achromatic Previous variation in 1995 (MACHO)

26 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

27 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

28 EXCLUSION CONTOUR Halo mass fraction (%) excluded at 95% CL by EROS 1 ( ) and EROS 2 LMC ( ) permitted by MACHO at 95% CL Mass of the deflectors (M o )

29 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

30 One single experiment with 3-4 events EROS COMBINED LIMIT Lasserre T. el al. (EROS), 2000, A&A accepted, astro-ph/ EROS 1 CCD ( ) 0 candidate EROS 1 Plates ( ) 1 candidate EROS 2 SMC ( ) 0-1 candidate EROS 2 LMC ( ) 2 candidates Considered as

31 Lasserre T. el al. (EROS), 2000, A&A accepted, astro-ph/ EROS COMBINED LIMIT Halo mass fraction (%) Excluded at 95% CL by EROS and EROS with 3 candidates with 4 candidates Permitted by MACHO at 95% CL Mass of the deflectors (M o )

32 EROS COMBINED LIMIT Halo mass fraction (%) Excluded at 95% CL by EROS and EROS 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 Mass of the deflectors (M o )

33 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