Matter distribution in
Andromeda galaxy
Elmo Tempel
Antti Tamm, Peeter Tenjes
University of Tartu
Tartu Observatory
Estonia
Novicosmo 2007
Outline
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Motivation
●
Why Andromeda galaxy?
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Modelling process
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Results
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Summary
Motivation
✔
✔
✔
✔
To study a mass distribution in galaxies, using stellar
data
Construct a visible matter distribution as accurate as
possible
Construct a dynamical model to calculate stellar
kinematics (dispersions, rotation)
What can we say about
dark matter?
Motivation
✔
✔
✔
✔
To study a mass distribution in galaxies, using stellar
data
Construct a visible matter distribution as accurate as
possible
Construct a dynamical model to calculate stellar
kinematics (dispersions, rotation)
What can we say about
dark matter?
cored or cuspy
profile?
cuspy
cored
Why Andromeda galaxy?
●
The galaxy M 31 was selected because:
Why Andromeda galaxy?
The galaxy M 31 was selected because:
●
photometrical and kinematical (rotation, dispersion) data are
known with sufficiently high resolution in order to study the bulge
region
Why Andromeda galaxy?
The galaxy M 31 was selected because:
●
●
photometrical and kinematical (rotation, dispersion) data are
known with sufficiently high resolution in order to study the bulge
region
velocity dispersions have been measured also outside the galactic
apparent major axis; in addition the kinematics of planetary
nebulae and individual RGB stars is known
Halliday et al. 2006
McElroy 1983
Merrett et al. 2006
Why Andromeda galaxy?
The galaxy M 31 was selected because:
●
●
●
photometrical and kinematical (rotation, dispersion) data are
known with sufficiently high resolution in order to study the bulge
region
velocity dispersions have been measured also outside the galactic
apparent major axis; in addition the kinematics of planetary
nebulae and individual RGB stars is known
direct measurements of stellar metallicities allow to constrain the
mass-to-light ratios of the visible matter
Why Andromeda galaxy?
The galaxy M 31 was selected because:
●
●
●
●
photometrical and kinematical (rotation, dispersion) data are
known with sufficiently high resolution in order to study the bulge
region
velocity dispersions have been measured also outside the galactic
apparent major axis; in addition the kinematics of planetary
nebulae and individual RGB stars is known
direct measurements of stellar metallicities allow to constrain the
mass-to-light ratios of the visible matter
independent estimates of the mass distribution on large scale are
available (GC, satellites, stream, kinematics of the MW + M 31)
Photometrical and Chemical
models give the visible matter
distribution (stellar component
profiles, mass-to-light ratios)
In kinematical model we add the
dark matter and calculate the
dark matter density
distribution
Photometrical model
For M 31 we use photometry in UBVRIL colours.
To have a sufficiently good fit of the data, we have chosen
five main visible compounents: a bulge, an old inner disc, a
young star-forming flat component, an extended metal poor
disc and a faint diffuse stellar halo
Sersic formula:
Chemical model
Input:
➢
Colour indexes
➢
Metallicities
➢
IMF (Scalo, Salpeter)
Output:
➢
mass-to-light ratios
➢
ages
Using five color indexes we can constrain the mass-to-light ratios
➢
Chemical model
Input:
➢
Colour indexes
➢
Metallicities
➢
IMF (Scalo, Salpeter)
Output:
➢
mass-to-light ratios
➢
ages
Using five color indexes we can constrain the mass-to-light ratios
➢
Dynamical model
●
Jeans equations in cylindrical coordinates:
The hypothesis of the model:
✔
galaxies have a axial symmetry
✔
three integrals of motion
✔
velocity ellipsoid is triaxial
✔
anisotropic velocity distribution
✔
dark matter is spherical and collision-free
Dynamical model
●
Jeans equations in cylindrical coordinates:
The hypothesis of the model:
✔
galaxies have a axial symmetry
✔
three integrals of motion
✔
velocity ellipsoid is triaxial
✔
anisotropic velocity distribution
✔
dark matter is spherical and collision-free
Dynamical model
●
●
Projection to the
line-of-sight:
Sum over subsystems (bulge, discs, stellar halo):
Dynamical model
Dark Matter distribution
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Total gravitational potential is sum of the potentials
caused by visible matter and dark matter.
In terms of circular velocities:
V2c,total = V2c,visible + V2DM
✔
Dynamical model
Dark Matter distribution
●
Total gravitational potential is sum of the potentials
caused by visible matter and dark matter.
In terms of circular velocities:
V2c,total = V2c,visible + V2DM
Usually Vgas is close to Vc
(non-circular motions are small)
✔
Dynamical model
Dark Matter distribution
●
Total gravitational potential is sum of the potentials
caused by visible matter and dark matter.
In terms of circular velocities:
V2c,total = V2c,visible + V2DM
Usually Vgas is close to Vc
(non-circular motions are small)
Star rotation can be slower
than gas
we can not ignore stellar
dispersions – especially in
central region
Dynamical model
Dark Matter distribution
●
Total gravitational potential is sum of the potentials
caused by visible matter and dark matter.
In terms of circular velocities:
V2c,total = V2c,visible + V2DM
●
Taking account the stellar dispersions:
V2c = V2 + 2R f(R)
Results – dynamical model
Results –
dark matter
Isothermal (King 1962, Einasto et al. 1974)
Burkert (Burkert 1995)
Moore (Moore 1999)
NFW (Navarro, Frenk & White 1997)
N04 (Navarro et al. 2004, Einasto et al. 1969)
Summary
We constructed a visible matter distirbution: as
accurate as possible
●
The observed stellar halo is redder than model
predicts – different IMF?
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The dark matter profile in inner regions seems to
prefer the cuspy profile...
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...but the cored profile is also possible
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References:
“Visible and dark matter in M31 – I. Properties of stellar components”
submitted to MNRAS, arXiv:0707.4375
“Visible and dark matter in M31 – II. A dynamical model and dark
matter density distribution”
submitted to MNRAS, arXiv:0707.4374