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Final results on galactic dark matter from the
EROS-2 microlensing survey
Astro-ph/0607207
Patrick Tisserand
Mount Stromlo Obs., Australia
EROS-2
Expérience de Recherche d’Objets Sombres
Observation : 1996-2003 at La Silla (Chile)
CEA/DAPNIA/SPP-Saclay
~ 850 000 images processed -
Large Magellanic Cloud (LMC)
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55 million stars monitored
Microlensing formalism
History and the EROS-2 experiment
Situation before this analysis
Microlensing Background
Analysis and Candidates status
Final Result of EROS-2
Discussions
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Small Magellanic Cloud (SMC)
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Rotation velocity (km.sec-1)
Surface luminosity (mag/arcsec2)
Problem : Galaxy rotation curve
A large amount of dark
matter exists at the
galaxy’s scale
Machos
« Massive Astronomical
Compact Halo Objects »
_ Planets
_ Brown dwarfs
_ Stellar remnants
_ Unknown compact matter
Halo
Characteristics:
Disc
- spherical isothermal distribution
- Radius between 50 and 200 kpc
- Mass : M(r) α r
- Total Mass ~ 1012 M
- Density : (r) α 1/r2
Van Albada et al., 1985
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One hypothesis:
A halo full of machos...
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Tool : lensing effect
• Lensing effect :
• For
Indirect detection
1 M :
Image Separation ~ 0.2 milli arcsec
Σ
Exp:
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EROS
MACHO
OGLE
~ milli arcsec
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~ arcsec
3
1986ApJ...304....1P, B.Paczyński
Microlensing effect :
½
tE ~ 70 ( M ) days
M
tE  tE (M, Dd, Vt )
Degeneracy !
Light curve characteristics:
 Symmetric
 Achromatic
 Unique
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( ~1 evt / 106)
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Some microlensing events observed :
Appeared in 1993
MACHO – LMC#1
tE = 17 days, Amplification ~ 7.5
EROS2-LMC#8
OGLE2-99-LMC#1
Increase by
3.5 magnitudes !
Appeared in 2000 tE ~10 days
Alert 1999
tE ~66 days, Amplification ~ 50
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Event rate predictions
from «standard» isothermal halo model

Probability (τ=Optical Depth) :
τ = Probability that,
a given time, a source star is inside
one Einstein disk
(Amplification > 1.34)
τ depends mainly on the halo density
Independent of machos velocity and mass
Virialised System:
 ~ ( v / c )2
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Typical Value
(in the case of a
dark halo
100% machos)
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LMC  0.45 10-6
-6
SMC  0.65 10
6
Events rate comparison :
Lensing Galactic-Galactic
stars:
gal-gal  2.0 10-6
Lensing LMC-Galactic stars:
LMC-gal  0.01 10-6
Full Macho Halo:
LMC  0.45 10-6
SMC  0.65 10-6
(MACHO  0.12 10-6)
Self lensing:
LMC-LMC  0.005 - 0.05 10-6
SMC-SMC  0.04 10-6
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History :
1986
:
1990-92 :
1993
:
1994-95 :
B. Paczyński propose microlensing effect to probe the halo.
EROS1/MACHO/OGLE start the adventure.
 First candidates !
First alert system by MACHO & OGLE
 Detection of exotic events (binary lenses)
1994-98 :
EROS1/MACHO : No short timescale events discovered (10-7M<M<10-3M)
1996
Start of EROS-2.
:
jan 2000 : End of the MACHO experiment.
2000
:
EROS2/MACHO : First result up to Mass=10M
~ 2002
:
Start of the SuperMACHO experiment + 3rd OGLE phase.
feb 2003 : End of the EROS-2 observations.
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EROS-2 : Expérience de Recherche d’Objets Sombres

Second Phase : July 1996 - February 2003

Dedicated telescope 1m Ø (Marly),
at La Silla (Chile)

2 cameras : test for achromaticity

2×8 CCDs : wide field (~1deg²)
Red filter
Blue filter
BEros ~ between V and R
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&
REros ~ I
Collaboration:
CEA/DAPNIA, LAL-IN2P3, IAP-INSU,
Observatoire de Marseille, Collège de
France (PCC), OHP
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Status before
this analysis
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Toward the Galactic center ….
Hundreds of
microlensing effect
have been observed
EROS2 : 120
MACHO : 62
OGLE : 33
Galactic latitude (deg)
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Only Clump giant stars
have been used !!
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Halo constraints in 2003:
Microlensing halo candidates:
EROS1 : 1 LMC
EROS2 : 4 LMC + 3 SMC
Exclusion diagram at 95% C.L.
MACHO : 13 LMC
Excluded at
95% C.L.
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Physical Microlensing
Background
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known physical background :
(discovered by MACHO)
« BLUE BUMPER »
Bright stars of the upper
main sequence
Amplification < 2
+ Chromatic Variation
Easy to reject !
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Candidates follow-up :
longer baseline ( + 3 yrs)
3 candidates show a new bump a few years later !!
 Variable Stars = Background
Withdrawn !
 EROS 1 – LMC#1 :
~ 1992
~ 1998
 MACHO – LMC#23 :
~ 1995
~ 2001
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(Probable) New
ZOOM on the background:
2nd fluctuation:
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Be type Stars.
EROS1-LMC#1
source star have
emission features.
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Supernovae :
~ 590 Supernovae detectable
If :  Appeared close to a cataloged
star.
 or SN cataloged.
 26 Supernovae detected at low S/N .
(Similar rate for MACHO)
== Serious background !
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Supernovae elimination :
• Galaxies seen on reference images
• Fit of an “asymmetric” microlensing light curve :
and / or
Elimination if |S| > 0.3
• Elimination of the 3 remaining EROS-2 LMC candidates (#5, #6 et #7) :
Better Photometry!
EROS2-LMC#5 : S = 0.5
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EROS2-LMC#7 : S = 0.62
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Halo microlensing candidates status
MACHO
EROS
EROS1-LMC#1
EROS2-LMC#3
EROS2-LMC#5
EROS2-LMC#6
EROS2-LMC#7
EROS2-SMC#1
EROS2-SMC#2
EROS2-SMC#3
EROS2-SMC#4
:
:
:
:
:
Variable star
Variable star
Supernovae
Supernovae
Supernovae
: Long Period Variable
: Long Period Variable
: Long Period Variable
MACHO-A-LMC#1
MACHO-A-LMC#4
MACHO-A-LMC#5 : galactic red dwarf lens
MACHO-A-LMC#6
MACHO-A-LMC#7
MACHO-A-LMC#8
MACHO-A-LMC#13
MACHO-A-LMC#14 : self-lensing
MACHO-A-LMC#15
MACHO-A-LMC#18
MACHO-A-LMC#21
MACHO-A-LMC#23 : Variable star
MACHO-A-LMC#25
Only 1 on 9 candidates remain
10 on 13 could be considered as
halo candidates
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Data Analysis
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Principe
of the
analysis:
Detection efficiency controlled by a MONTE-CARLO simulation:
=> False microlensing effects added on real light curve (~ 99% stable)
They passed the same selection cuts!
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Blending problem
Star cataloged
and surveyed
Fainter star located
in the seeing disk
(less than 2”)
Optical depth
estimate :
MACHO : estimate an additional 30%
error due to blending
under-estimated
Using bright star, we considerably
reduce that problem
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EROS2 : With HST LMC luminosity
function weighted with the probability
to generate an observable event.
→ ~1%
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Crowded field:
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Bright Star Sample
Better resolution → better rejection of variable stars
Statistics still excellent due to a better <efficiency>
Largely reduce the Blending problem
First time
in LMC !
On our 33.4 Million stars
sample, we retained :
LMC : ~6 Million
SMC : ~0.9 Million
Remember galactic center !
Efficiency
LMC
Magnitude cut different for each field:
CLUMP
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Mag  [16-Rmax] with Rmax [18.2-19.7]
Homogeneous sample : ~uniform photometric resolution (~7%)
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Number of events expected
in the case of a
dark halo
100% machos
τ
τ
~ 0.45 10-6
-6
SMC ~ 0.65 10
× Efficiency
LMC
For 6.9 million bright stars
monitored during 6.7 years
Macho
mass
Duration tE
Number Magellanic
events (full halo)
effi. = 100%
Real effi.
10-3 M
~ 2.2 days
~ 2500
~63
10-2 M
~ 7 days
~ 785
~173
1 M
~ 70 days
~ 78
~35
10 M
~7.4 months
~ 25
~9
100 M
~ 2 years
~8
~0.4
M
½
tE ~ 70 ( M ) days

We need ~13 events to
confirm the positive
signal of MACHO at 20%
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No new microlensing event detected
1 candidate in the SMC still selected
EROS2-SMC#1
Known since 1997 (EROS+MACHO)
→ Probably due to SMC lens
(for a halo lens, earth motion would distort the
light curve visibly)
tE = 120 days
Duration expected for SMC
self-lensing
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Final EROS combined limit (1990-2003)
_3% at 10-2 M
Domain
excluded from
all EROS data
_7% at 0.4 M
_10% at 1 M
ZOOM
LMC data set / No event
LMC + SMC data set with 1 SMC halo candidate
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Comparison : EROS-2/MACHO
LMC
2 different strategies : 2 different data sets
EROS2: ~ 7 Million Bright stars in
sparse wide field
(~84 deg2 LMC + ~10deg2 SMC)
MACHO: ~ 11 Million faint and bright
stars in dense field
(~13.4 deg2, LMC bar)
~2 Million bright stars in common !
MACHO field
EROS2 field
Our Measurement is mainly based on a less crowded area
Photometry easier and result less affected by blending
Remark : A positive result must be seen everywhere, not be concentrated in a special area
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Discussion of the EROS2 result

Our analysis is conservative :
- Use only bright-well measured sub-sample of Magellanic stars (~20% total)
- Largely reduce the blending effect

Measurement obtained mainly with stars in the outer part of the LMC (sparse field)

Machos in the mass range 10-7 M< M < 5 M are ruled out as the primary occupants of the
Milky Way Halo.

Result compatible with the Optical depth expected from the known star distribution (selflensing + galactic disk stars)

2 different Monte-Carlo have been computed to estimate our detection efficiency:
_ simulated microlensing effect on true light curve
_ fake images that pass all the photometric chain with simulated microlensed star
► they are in excellent agreement for the bright star sample.

An all star sample analysis (33.4 millions) has been done with stricter cuts. Only 5
microlensing candidates have been selected : for one, the lens is a galactic red dwarf star
located at about 300pc. (result also compatible with self-lensing)

Serious background : Supernovae & Variable stars
Many former candidates died for these reasons (ex: EROS2-LMC#1 and MACHO-LMC#23)
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Difference between MACHO/EROS2

2 completely different data sets :
_Most of the MACHO stars are considered too faint for us : ~9 millions.
_MACHO observation concentrated in the LMC bar : crowded region

Blending effect : MACHO suggest an additional 30% systematic error on the result.

Our limit is at f<7% for 0.4 M , about 13 events would have been necessary to
confirm the MACHO signal.

The higher MACHO optical depth may be due, in part, to self-lensing in central part
of the LMC. But this would contradict LMC models (Mancini et al., 2004) which suggest that only 12 MACHO candidates should be expected to be due to self-lensing (#9 and #14 are already known to
be self-lensing).

5 MACHO candidates are really convincing : #1, #5, #9, #14 and #21.
3 are explained by LMC self-lensing or due to a galactic lens.
Possible confirmation : _ OGLE III and SuperMACHO
_ AGAPE, MEGA and WeCaPP (toward M31)
_ Photometric follow-up of candidates
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