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 hotterT/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 lPoints with error bars are data (scatter with m)Red line is a fitted theoretical model

Acoustic oscillationsFluctuations 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 z1100• 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 successfulDark matter forms

dense clumpsconnected 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 rs

3 / [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 200crit

– 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