Lecture 24: Galaxy Evolution and the Big Bang

Scaling Relations of GalaxiesFundamental Plane (ellipticals)Faber-Jackson (ellipticals)Tully-Fisher (spirals)

Faber-Jackson (Ellipticals)

Fundamental Plane (Ellipticals)

Three Uses of Scaling Relations

1) distance estimates

2) observational constraint on theory

3) basic understanding

Big Bang Cosmology: What is It?expansion of the universe

nucleosynthesis

microwave background

growth of large scale structure

velo

city

(red

shift

)

distance

H_0: slope of relation, Hubble constant, recession velocity/distance

Cosmological (Copernican) Principlewe do not live in a special place

thus, universe expanding from everyone’s viewpoint

don’t think of redshifts as “velocities”

don’t think of Big Bang as explosion

homogenous: same at all locations

isotropic: same in all directions

every observer sees “recession”more distant objects “recede” faster

redshift from stretching of wavelength

logical conclusion: universe was very tiny

before now

measures change of scale with time

Big Bang: all matter and energy interchangeable, in equilibrium, em+weak+strong forces unified

Inflation: nuclear force splits off, universe expands exponentially, grows 10^50x in 10^-33s!, cools, photons,

quarks, neutrinos, electrons, then protons, neutrons condense out

Big Freeze Out: in 100s, He, deuterium, some lithium

two limiting factors: temperature dropping,free N decaying

no other way toproduce as much Heas observed

Penzias & Wilson

describe brightness distribution on sphere

superpositions of terms

what scales have power?

Measuring Spacetime

define a metric

for a plane

Robertson-Walker metric

homogeneous-isotropic flat universe

scale factor a(t), cosmic time t (time measured by observer in uniformly expanding universe)

are co-moving coordinates (remain constant in t)

d�2 = dx2 + dy2 + dz2

d�2 = −c2dt2 + a(t)2[dr2 + r2(dθ2 + sin2θdφ2)]

(r, θ,φ)

proper distance (can’t measure this!)

Friedmann Equation�a

a

�2

=8πG

3c2u(t)− κc2

r2c,0a(t)2+

Λ

3

from energy conservation for expanding sphere, but relativistically correct

relativistic particles like photons contribute energy density too

kappa tells us if universe positively or negatively curved

cosmological constant is new energy density term arising from vacuum energy (virtual particles, anti-particles)

often rewritten....

u_r = radiation density (energy density from relativistic particles like photons), u_m = matter density (energy density from non-relativistic particles such as protons, neutrons, electrons, WIMPs? ), u_Lambda = constant energy density from vacuum

for flat universe, kappa = 0, so

�a

a

�2

=8πG

3c2[ur(t) + um(t) + uΛ]−

κc2

r2c,0a(t)2

3H(t)2c2

8πG= ur(t) + um(t) + uΛ (at t_0, H_0, and we know this!)

Cosmographydifferent “distances”

comoving distance (proper distance today)

angular diameter distance

luminosity distance

proper motion distance

light travel distance (lookback time)

Inflation

flatness problem

horizon problem

magnetic monopole problem

early, tremendous growth phase solves these problems...and generates fluctuations that can grow

Perturbation Theory