Transcript Mass Models for Spiral Galaxies

Cosmology and Dark Matter III:
The Formation of Galaxies
Jerry Sellwood
The story so far
• Four serious problems with the hot big bang
model were solved in one attractive stroke
• What caused inflation? How does it work?
– Questions still without clear answers
– But the idea is very appealing
• We can test two key predictions:
– universe really should be flat – i.e.  = 1
– power spectrum of density fluctuations
Is the universe flat?
• Astronomers could not find enough matter
• Expressed as fractions of crit, we find
– stars in galaxies 0.5%
– all normal atoms 4% (from BBN)
– dark matter: not more than 20% – 30%
• Increasing confidence that the mass density
was less than critical
• Crisis for inflation
Accelerating Universe
• Gravity attracts and slows expansion of the
universe
• Should see more rapid expansion in the past
– i.e. at large distances or high redshift
• Type Ia supernovae seem to be “standard
candles” – more distant ones are fainter
• Slowing expansion: apparent brightness
should decrease less rapidly with redshift
• data showed the opposite!
Dark Energy
• Supernovae data alone not all that convincing
(e.g. possible systematic errors)
• But CMB measurements (and theoretical
prejudice) suggest universe is in fact flat
• Can save inflation if 70% of the critical density
is a new component: Dark Energy
• Gravitationally repulsive to cause acceleration
• We have resurrected Einstein’s cosmological
constant with = 0.7 so M +  = 1
Cosmic microwave background
• NASA’s WMAP measured temperature
differences in CMB from point to point
• Blue is cooler than mean, red is hotter
• T/T  10-5 (i.e. measurements aren’t easy!)
Origin of fluctuations
• Curvature fluctuations laid down during
inflation
• Slight density differences affect the
expansion rate relative to the mean
• Differences amplify since they were created
– Overdense regions are slightly warmer
– Underdense regions are slightly cooler
• Two-thirds counteracted by gravitational
redshift
Fluctuation power spectrum
• Want to quantify the fluctuations on
different angular scales
• Expand in surface harmonics, Ylm (or
multipoles)
• Compute the total power at each l
Points with error bars are data (scatter with m)
Red line is a fitted theoretical model
Acoustic oscillations
Fluctuations are
superpositions of
many waves of
different scales
Each wave begins to
oscillate once  is
inside the horizon
We get peaks in the
power at max
compression and
rarefaction
Standard ruler
• For the first peak at about 1, we know
– the oscillation period and thus the time since
waves entered the horizon
– the expansion rate, and can therefore calculate
the linear scale of these waves
• We also measure the angular scale
• So we can determine the curvature of the
universe!
• Find that it must be flat – within the errors
Growth of structure
• The universe was very smooth at z1100
• Not today – stars & planets, galaxies, and
clusters of galaxies formed somehow
• Computer simulations needed
– start from “reasonable” initial conditions
– treat baryons and dark matter in same way as a 1st
approximation
– choose a box size and make it periodic
– fill it with particles – almost uniformly
– compute forces on particles and step forward in time
• Kravtsov et al
• Expansion is not shown – positions are in
co-moving coordinates
Appear successful
Dark matter forms
dense clumps
connected by a
“cosmic web” of
filaments
Resembles observed
galaxy distribution
Comparison requires
a rule to assign
galaxies within
mass clumps
Power specturm
• Data points with
error bars are from
2dFGRS
• Line is the average
power spectrum from
35 simulations with a
(physically
reasonable) rule for
assigning galaxies
• Agreement is
impressive
Dark Matter
halos
• Dark matter clumps
are called halos
• Every halo has many
sub-halos
• Examine the mass
profiles of the halos
“Universal” halo density profile
• Spherically averaged density of dark matter seems
to approximate the form:
(r) = s rs3 / [r(r+rs)3-]
• i.e. a broken power law, with 1 <  < 1.5
•  = 1 
is “NFW”
Concentration
• The cosmology papers do
not use s directly, but
define a new parameter c
• They define , r200, within
which the average density
is 200crit
– halo approximately settled
• and then set c = r200/rs
• Furthermore, c correlates
mass – halos are predicted
to be a 1-parameter family
Clear and testable predictions
• If only we could measure DM halos directly
• we see only baryons, which are distributed
differently
• Gas cools in DM halos
• Settles into a rotationally supported disk
• Compresses the halo as it cools
• Forms stars etc.
More simulation needed
• Governato et al
• Dark matter +
gas + stars
• Promising disk
+ bulge
• embedded in a
DM halo