Please pick up your corrected problem set and midterm.

Problem Set #4: median score = 85

Midterm Exam: median score = 72

Recap: Recap: The Story So Far…The Story So Far…

Monday, November 3 Next planetarium show: Thu, Nov 6, 6 pm.

History of cosmology:

Version 1.0: “Superdome” model

Version 2.0: Geocentric model

spherical Earth at center

Version 3.0: Heliocentric model

Sun at center

v. 3.1: InfiniteInfinite heliocentric model

v. 4.0: Big Bang model

v. 4.1: Big Bang model with space-time curvaturespace-time curvature.

Mass & energy cause space to curve. This curvature causes an observedobserved

bending of the path of light.

Curvature on large scales:

PositivePositive curvaturecurvature: gravitational lensing makes distant objects loom large.

NegativeNegative curvaturecurvature: gravitational lensing makes distant objects appear tiny.

Measured curvature on large scales:

Observed angular sizes of distant galaxies: consistent

with flatflat space.

If space is curved, its radius of curvature is bigger than bigger than the observable universethe observable universe.

Expansion on large scales:

As light travels through space, its wavelength expands along with

the expansion of space.

Galaxy with the highest known redshifthighest known redshift:

Name: IOK-1IOK-1

Redshift: z = 7z = 7

Redshift z=7. What does this mean?

Hydrogen has an emission line at λ0 = 122 nm. In this galaxy, the line is seen at λ = 8 × 122 nm

= 976 nm.

1 nm = 1 nanometer = 10-9 meters

7nm 122

nm 122 - nm 976 - z

0

0

Redshift z=7. What does this mean?

Light emitted with wavelength λ0 = 122 nm122 nm has been stretched to λ = 8 × 122 nm8 × 122 nm = 976

nm.Universe has expanded from a scale factor a = 1/8a = 1/8 (when light was emitted) to

a = 1a = 1 (when light is observed).

If we observe a distant galaxy with

redshift z, the scale factor a at the time the galaxy’s light was emitted was:

z1

1 a

Example: z = 1 implies a=1/(1+1) = ½. Lengths (including wavelengths of light) have doubled since light was emitted.

Photons from distant galaxies aren’t stamped

with “born on” dates.

However, they are stamped with the amount by which the universe has expanded since they were “born”. z1

1 a

(measurable) redshift

scale factor

When was the light we observe from this galaxy emitted?

A convenient aspect of a “Big Bang” universe: the start of expansion gives

an “absolute zero” for time.

Different calendars have a different “zero point” (birth of Christ, hijra to Medina, etc.)

For a cosmic time time scale, there’s also a logical “absolute zero”: the instant at

which expansion began.

For a temperature temperature scale, there’s a logical absolute zero: the temperature

at which random motions stop.

t = 0 (start of expansion, alias “The Big Bang”)

t ≈ 14 billion years (now)

t ≈ ??? (first galaxies)

When was the light we observe from this galaxy emitted?

t ≈ 750 million years (when the universe was only 5% of its present age).

How far away is this galaxy?

The galaxy’s light took about 13 billion years to reach us.

If the universe weren’t expanding, we could say “it’s about 13 billion light-years away”.

But the universe ISIS expanding!!!

How far away is this galaxy?

Farther away than it used to be!

te = time light was emitted to = time now

de = distance when light was emitted do = distance now

te < to

de < do

When the light we observe now was emitted:

de = 1700 megaparsecs

Now, when we observe the light:

do = 8 × de = 8 ×1700 = 13,600 megaparsecs

= 5.5 billion light-years

= 44 billion light-years

Point to ponder:

5.5 billion light-years (initial distance) is less than

13 billion light-years (distance if static) is less than

44 billion light-years (current distance)

Point to ponder:

Current distance to z=7 galaxy = 44 billion light-years = 13,600 megaparsecs

= more than 3= more than 3× Hubble distance!× Hubble distance!

As z → infinity, current distance → 3.2 × Hubble distance

The most distant object we can see (in theory) is one that emitted a photon at t=0.

We will see this photon with a hugehuge redshift z, since the universe has

expanded hugely since the “Big Bang”.

Photons emitted at t=0 come to us from the cosmological horizon.

The cosmological horizon is at a distance of 3.2 × the Hubble distance (about 14,000 megaparsecs, or

46 billion light-years).

Longer than the Hubble distance because of universal expansion.

Wednesday’s Lecture:

Reading:

Chapter 8

Photons & ElectronsProblem Set #5 handed out.