Testing dark matter
with Gaia
O. Bienaymé
Strasbourg Observatory
Gaia – Revue des Exigences préliminaires
1
Dark matter within our Galaxy
Flat rotation curve
=> missing luminous mass
=>dark matter halo
Gaia / DM
2
Dark matter within our Galaxy
Vertical motion of stars (Kaptein, Oort 1920’)
=>total mass density in the solar neigbourhood
Gaia / DM
3
Dark matter within our Galaxy
Vertical motion of stars (Kaptein, Oort 1920’)
=>total mass density in the solar neigbourhood (Hipparcos sat.)
versus : seen mass (stars+gas)
=>dark halo cannot be extremely flattened (Crézé et al 1998).
=>dark disk is not massive, if any ….
Gaia / DM
4
Dark matter within our Galaxy
Halo shape
Local stellar 3D kinematics with Hipparcos satellite
(about ten thousand stars)
=> vertical force perpendicular to the disk
=> (u,v,w) 3D velocity coupling
=> (u,w) tilt with RAVE and SDSS
they give local constrain on the shape of the potential
that is nearly spherical
Gaia / DM
5
Dark matter within our Galaxy
Halo shape
Local stellar kinematics with Hipparcos satellite
=> vertical force perpendicular to the disk
=> (u,v,w) 3D velocity coupling
=> (u,w) tilt with RAVE and SDSS
they give local constrain on the shape of the potential
that is nearly spherical
Gaia / DM
6
Siebert et al 2008; RAVE
500 red clump stars
velocity ellpsoid tilt
Tilt=6deg at z=1kpc
Potential nearly spherical
Dark matter within our Galaxy
Halo stars velocity distribution (radial velocities)
(but no proper motions i.e. tangential motion)
=> flat rotation curve at large R
High velocity star D.F. in the solar neigbourhood
 Galactic escape velocity
 total galaxy mass & flat rotation curve (model dependent)
Globular clusters, dwarf galaxy satellites
Gaia / DM
8
Galactic escape velocity
33 stars
Gaia / DM
9
Halo stars: velocity distribution
552 Vrad
Gaia / DM
10
Dark matter within our Galaxy
Halo shape
Sagittarius tails
precession of the orbit measures the shape of the potential
Other streams
Gaia / DM
11
Dark matter within our Galaxy
Halo shape
Correnti 2010
Sagittarius tails
precession of the orbit measures the shape of the potential
Other streams
Gaia / DM
12
Dark matter within our Galaxy
Gaia / DM
13
Dark matter within our Galaxy
Need for distances (parallaxes), proper motions
tangential velocities , radial velocities and very
large samples,
to constrain accurately the 3D shape of the
galactic potential
Gaia / DM
14
Gaia: a unique experiment
The next cornerstone of the ESA Science
Programme
Unique characteristics
 Unprecedented astrometric accuracy (7-200 as)
 Simultaneous astrophysical characterisation +
radial velocity of observed objects
 Survey down to V = 20
 109 objects observed all over the sky
 Launch 2012, Soyouz from Kourou
Gaia / DM
15
The third dimension: further and further
Solar neighbourhood
Up to ~ 30 pc
Ground-based, Hubble
Precision: 3-5 mas
Solar neighbourhood
Up to ~ 200 pc
Hipparcos 1989-1993(-2007)
Accuracy: (0.1) - 0.2-1 mas
All over the Galaxy
Up to ~ 10 000 pc
Gaia (2012-2018)
Accuracy: 8-20 as
In the bulge of the Galaxy
Up to ~ 10 000 pc
Jasmine (?)
Precision: 10 as
In the Galaxy and the Local Group
Up to ~ 30 000 pc
SIM (?)
Precision: 3 as
Gaia / DM
16
Performances for a G2 V star
Astrometry:
Magnitude
< 10
15
20
6
20
240
Accuracy [as]
Photometry: accuracy on G magnitude
V=15
V=20
Per observation [mag]
0.002
0.03
End of mission [mag]
0.0002
0.003
Spectroscopy
Magnitude
RV accuracy [km/s]
Gaia / DM
V=12.5
V=16.5
<1
15
17
Gaia / DM
APC, 9 June 2010
18
Gavitational Potential with GAIA
Measure the total mass distribution
from the gravitational potential
Measure the baryonic mass
(mainly stars, mainly the disk)
Deduce the ‘exact’ shape
of the D.M. distribution
Hayashi, Navarro … 2007
Gaia / DM
APC, 9 June 2010
19
disk structure
Disk warp and flare, relation with Monoceros stream?
At 15 kpc:
disk rotation ~ 6 mas/yr
For a 1 kpc high warp:
~90 as/yr in latitude
~600 as/yr in longitude
easily measurable by Gaia
Gaia / DM
20
Streams
Intégrale du mouvement
Streams
in the
Galactic Halo
Amina’s figures
Gaia / DM
APC, 9 June 2010
21
Streams in the Galactic Halo
Simulation of the accretion of 100 satellites galaxies (A. Helmi)
Position space
Velocity space
Again here, 3D kinematics at the faint end of the Gaia survey (V>16-17) would be
a plus…or would even be crucial to identify sub-structures of the phase space
Gaia / DM
22
Streams in the Galactic Halo
Integrals of motion space
Gaia / DM
APC, 9 June 2010
23
Constrains on the Clumpiness of the dark matter halo
Gaia / DM
APC, 9 June 2010
24
Gaia: long-term objective
Choose potential, write Hamiltonian, write closest integrable
Hamiltonian, find distribution function F(J), adjust
potential…
On shorter term: can we answer the crucial question of the
existence of galactic dark matter by confirming/excluding (or
at least constraining) a modified gravity approach?
Gaia / DM
MOND within our Galaxy
Stellar Disk within MOND
a newtonian astronomer observes
a spherical dark halo
and a dark disk (Milgrom, 86)
Gaia / DM
Testing Newtonian gravity on galactic scales
Modified gravity is only one version of MOND
Only the relation between the potential and the matter
source is altered, so one can constrain the potential in
the usual way
Crucially depends on our knowledge of the baryonic
distribution
Depends on the exact choice for 
Then, the theory makes a unique and falsifiable prediction
for the galactic potential
=> as an example let us use (x)=x/(1+x) and the
Besançon model based on the synthesis approach
Gaia / DM
The « dark disk » from the Besançon
Galactic model in MOND
With (x)=x/(1+x), at the solar position one has eff = 78 Mpc-2 within z=1.1 kpc
to compare with present constraints dyn = 74+-6 Mpc-2 (TEST 1)
The effective radial density distribution in the disk has a scale-length enhanced by 25%
[deep MOND => 50%]
2.5kpc3.1kpc
CountsKz force
Bienaymé, Famaey et al.
2009, A&A
=> measuring dynamically the disk surface density as a function of R with GAIA (but
problem of extinction, maybe JASMINE too) should allow to constrain  or even exclude
MOND as modified gravity (TEST 2)
=> quick way to exploit GAIA data
Gaia / DM
The vertical tilt of the velocity ellipsoid
Angle = arctg[22UW /(2U - 2W) ]/2 is linked to the disk scale-legnth and dark halo
flattening (Bienaymé 2009)
=>
compute orbits in axisymmetric Besançon model to measure the tilt as a
function of z at solar position
TEST 3
Newton+DM
MOND
6°
RAVE data
10°<14° Siebert et al. 2008
(z=1kpc)= 7.3°+-1.8°
Gaia / DM
Conclusion
We presented 3 quick tests to test MOND as modified
gravity in the Milky Way with GAIA-like quality data
This should allow to constrain  or even exclude MOND as
modified gravity
Testing gravity crucially depends on our knowledge of the
baryonic distribution (even more than when determining
the DM distribution) => importance of :
- star counts, stellar population synthesis
- gaseous content (including molecular gas)
- inhomogeneities (clusters, gas clouds)
Test other alternative theory
Gaia / DM