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Dark Matter in the Milky
Way - how to find it using
Gaia and other surveys
Paul McMillan
Surveys For All, 1st February 2016
Why do we care?
On the biggest scales, the ΛCDM model works
Why do we care?
On the scale of individual
galaxies, agreement is
less obvious.
Things are more
complicated, we have to
consider the baryons!
We should look at the
galaxy we can study
closest
(an individual galaxy)
Dark Matter detection
Particle physicists hope
to find dark matter as it
passes through the Earth
(and their detector).
How many particles
should they expect to
pass through per second?
Cold lump of germanium
Important piece of
information: what’s the
local dark matter density?
Thing hits other thing = Nobel prize
How can we learn
The only way we’ve detected dark matter is
through it’s gravitational effects
We can find the dark matter density by finding
the gravitational potential (and subtracting off
the baryonic bit)
Only equation in this talk
We have so many surveys of
the Milky Way’s stars
But also:
Gaia footprint
And others
So we need to learn ΦMW from
the observed stars
Measure the acceleration?
Too
small
Need to use observed positions and velocities only
How do we relate that to the potential?
We need a dynamical model: f(x,v)
given a potential
Sometimes this is just
that a given tracer is
on a (near) circular
orbit
(e.g. HI gas, masers:
Rubin 1980; Bosma
1978; Zigmanovic
2016)
HI rotation curve of M33
(possibly sign of an alien megastructure)
But generally we have to approximate that we’re not
seeing the Milky Way at a special time – that the
stellar dynamics are in equilibrium
If we just let the
stars go…
x
x
x
✓
So: the probability of a star having a given position & velocity f(x,v)
doesn’t depend on whereabouts it is on its orbit. It can only depend on
things that are constants (e.g. energy)
How do we do that?
Fortunately, we’ve
found suitable
constants (inspired by
Solar System
dynamics) – action
variables ( J ).
They’re not easy to
find in Galactic
potentials, but once
you’ve worked out
how to do that (and
we have)…
(with thanks to Spirograph™)
How do we do that?
Fortunately, we’ve
found suitable
constants (inspired by
Solar System
dynamics) – action
variables ( J ).
They’re not easy to
find in Galactic
potentials, but once
you’ve worked out
how to do that (and
we have)…
(with thanks to Spirograph™)
Finding ΦMW from stellar surveys
Find maximum likelihood on discrete data (for each star parallax,μ,vr)
Compare the best fitting f(J) in each Φ.
Fortunately we checked whether this was feasible with pseudo-data before
diving in to real data (McMillan & Binney 2013)…
Find J directly
N.B. change of scale
Orbit library
Error bars: numerical uncertainty
N.B. Orbit library (Schwarzschild modeling) is standard for external galaxies
And we already know lots about the
Milky Way
We have observations of cold gas
that is on near circular orbits in the
Milky Way
We can measure the proper motion
of (and distance to) Sgr A*
We roughly know the structure bulge, halo, disc(s) with ~known
scale lengths
There are existing constraints on
the Milky Way’s mass from other
dynamical modeling (you don’t
have to do everything yourself!)
The true ΦMW has to satisfy all of
these constraints
Putting it together
We combined these approaches to analyse RAVE survey data
1. For a given DM halo - demand
potential fits known constraints. This
Φ will have some vertical disc
density profile at the Sun
2. Fit f(J) to (binned) kinematics of
RAVE giants, which predicts a
different disc density profile.
3. Iterate until these two vertical
profiles agree with each other
4. Compare to vertical density profile
from literature (Juric et al 2008,
0.7<r-i<0.8)
(Piffl, Binney, McMillan, & RAVE 2014)
Local dark matter
We’re left with effectively two free parameters for the potential:
Local DM density & halo flattening.
For spherical halo:
ρDM, = 0.0126 M/pc3
= 0.48 GeV/cm3
Note that statistical error
bars are tiny (~0.4%)
With systematic uncertainties and
varying halo flattening
Where q is axis ratio of
DM halo, and α = 0.89
q
1
Compare to recent results (compiled by Read 2014)
Our
resul
t
Largest component of the uncertainty is the systematic uncertainty in the
distance scale (affects density profile & velocities)
We need Gaia!
Conclusions
If you want to know where the dark matter is, you
have to find the gravitational potential
To do that for the Milky Way, you need a good
model.
We have good models (using action variables),
and we’ve already used them to analyse Milky
Way data.
I can’t wait to work with Gaia data!