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.
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.
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.