Cosmology and Dark Matter III: The Formation of Galaxies

1. Cosmology and Dark Matter III: The Formation of Galaxies Jerry Sellwood

2. 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

3. 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

4. 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!

5. 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

6. 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!)

7. 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

9. 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

10. 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

11. 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

12. 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

13. Kravtsov et al • Expansion is not shown – positions are in co-moving coordinates

14. 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

15. 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

16. Dark Matter halos • Dark matter clumps are called halos • Every halo has many sub-halos • Examine the mass profiles of the halos

17. “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”

18. 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

19. 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.

20. More simulation needed • Governato et al • Dark matter + gas + stars • Promising disk + bulge • embedded in a DM halo