• Does the large scale structure of galaxy clustering continue (in space, in size)?

• And if so, to what scales? (sizes, distances, masses)

• How do we measure this structure?

• In other words, how do we measure distances?

1. Revisit the distance ladder

(i) After parallax . . .

. . . all methods of determining distances involve ``standard candles''

(ii) Distances are then estimated via measuring apparent brightness and inferring luminosity

(distance is inferred via the inverse-square law)

So what makes an ideal ``standard candle?''

(a) should be ``standard,'' i.e. well-defined luminosity

(b) should be bright (see it to large distances)

Cepheids are ok, Super Novae are very good, but . . .

. . . galaxies are even brighter, and:

rotation speed (V) and the luminosity (L) of a galaxy are well correlated.

The Tully-Fisher relation

Why does this relation exist?

Both V and L are measures of mass.

2. Universal Expansion and Hubble's Law

The Universe is expanding:

On average, galaxies are all moving away from each other.

The Hubble flow:

The farther away galaxies are the faster they move away from each other
(to be demonstrated).

The cosmological redshift, z:

Recession speed is measured as a Doppler shift of a known spectral feature:

z = recession speed (v) / c

Hubble diagrams :

recession speed vs. distance

Crucial: Distance must be inferred from some standard candle!

Slope of the relation in the Hubble diagram gives Hubble's constant :

H₀ = 75 (km/s)/Mpc   (73 km/s/Mpc is current best estimate)

The cosmological redshift, z, is another ``distance indicator:''

Measure recession speed, infer a distance (d):

d = v / H₀

Assumptions:

Expansion and the Universe are

smooth,

uniform,

and appear the same to every observer.

3. Large Scale Structure Revisited

Wide-angle surveys: shallow but broad

vs.

``pencil-beam'' surveys: narrow but deep

Observed: lack of homogeneity in the galaxy distribution

Homogeneous means: the same everywhere

Non-isotropic ?

Isotropic means: looks the same in every direction

Do observations `fly in the face' of Universal Expansion?

The Universe on very large scales is:

neither smooth nor uniform

- large voids (40-100 Mpc)

- clusters and super-clusters (1-40 Mpc)

- The Great Wall

- Structures up to 200 Mpc across!

Compare to total size of observable universe: 4000 Mpc

Large scale structures on scales 5% of this size!

Perhaps only on the largest scales, the Universe looks the same in every direction.

But examine these:

2dF Redshift Survey
Sloan Digital Sky Survey (SDSS)
Cosmic microwave background (from WMAP)

What do you think?

(a) All galaxies are moving with our galaxy through the Universe.

(b) All galaxies are moving at the same speed.

(c) The speed of light is finite.

(d) The Hubble diagram relates rotation speed to luminosity.

(e) On average, all galaxies move away from each other.

(a) The ``Hubble flow'' is observed only for small scale structures.

(b) The Universe can't expand if structures are too large.

(c) Large scale structures imply large scale inhomogeneities.

(d) Large scale structures call into question the reality of any expansion.

(e) Uniformity can't occur if there is expansion.