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HOT Big Bang
Tuesday, January 22
Hubble’s law:
Galaxies have a radial velocity (v)
proportional to their distance (d).
Hubble’s law
in mathematical form:
v  H0 d
v = radial velocity of galaxy
d = distance to galaxy
H0 = the “Hubble constant”
(same for all galaxies in all directions)
What’s the numerical value of H0?
What’s the slope
of this line? →
H0 = 70 kilometers per second per
megaparsec (million parsecs)
Or, more concisely…
H0 = 70 km / sec / Mpc
Why it’s useful to know H0:
Measure redshift of galaxy: (λ-λ0)/λ0
Compute radial velocity: v = c (λ-λ0)/λ0
Compute distance: d = v / H0
Cheap, fast way to find distance!
red
galaxy
spectra
violet
galaxy
images
With modern telescopes and
spectrographs, astronomers have
measured millions of spectra.
Kilometers per second per
megaparsec?? What bizarre units!
1 megaparsec = 3.1 × 1019 kilometers
70 km/sec/Mpc
18
H0 
 2.3 10 / sec
19
3.1  10 km/Mpc
1
H0 
17
4.4 10 sec
Why it’s intriguing to know H0:
d
Two galaxies are separated by a
distance d.
They are moving apart from each other
with speed v = H0 d.
How long has it been
since the galaxies
were touching?
distance
travel time 
speed
d
1
17
t

 4.4 10 sec
H 0d H 0
PLEASE NOTE: This length of time
(t = 1/H0) is independent of the
distance between galaxies!!
If galaxies’ speed has been constant,
then at a time 1/H0 in the past, they
were all scrunched together.
Heart of the “Big Bang” concept:
At a finite time in the past (t ≈ 1/H0), the
universe began in a very dense state.
1/H0, called the “Hubble time”,
is the approximate age of the
universe in the Big Bang Model.
1
17
t
 4.4 10 sec
H0
Since there are 3.2 × 107 seconds
per year, the Hubble time is
1/H0 = 14 billion years
Big Bang model “de-paradoxes”
Olbers’ paradox.
If age of universe ≈ 1/H0, light from
stars farther than a distance ≈ c/H0
has not had time to reach us.
Hubble time:
1/H0 = 14 billion years.
Hubble distance:
c/H0 = 14 billion light-years
= 4300 megaparsecs.
Is the universe infinitely old?
About 14 billion years have passed
since the universe started expanding
from its initial dense state.
Food for thought: what happened
before the “Big Bang” (that is, the
start of the expansion)?
Is the universe infinitely big?
We don’t know: we can see only a
region ≈ 4300 megaparsecs in
radius, with no boundary in sight.
Food for thought: if the universe is
finite, does it have a boundary?
What do I mean by a HOT Big Bang?
Hot Big Bang model: the universe starts
out very hot as well as very dense.
What do I mean by “HOT”?
90°F
212°F
9980°F
Object is hot when the atoms of which
it’s made are in rapid random motion.
Temperature:
measure of typical
speed of the atoms.
Random motions stop at
absolute zero temperature.
Kelvin = Celsius + 273
Water boils: 373 Kelvin (K)
Water freezes: 273 K
Absolute zero: 0 K
Room temperature: ~300 K
Surface of Sun: ~5800 K
Different elements respond in different
ways to changes in temperature.
Rejoice! Spectra of stars & interstellar
gas reveal they consist mostly of
hydrogen, the simplest element.
H
(as seen by astronomers)
He
Everything Else
Suppose the early universe contained
hydrogen, and no other types of atom.
1 proton:
(positive electric charge,
mass = 1.7 × 10-24 g)
1 electron:
(negative electric charge,
mass = proton/1836)
At high density & low temperature,
hydrogen is a gas of molecules.
Molecular hydrogen =
H2 = two H atoms
bonded together
At low density & low temperature,
hydrogen is a gas of atoms.
Much of the interstellar
gas in our Galaxy is
atomic hydrogen.
density ≈ 10 atoms/cm3
T ≈ 100 K
At high density & high temperature,
hydrogen is an ionized gas.
Much of the Sun’s
interior is ionized
hydrogen.
Sun’s center:
density ≈ 150 tons/m3
T ≈ 15 million K
If the temperature of the dense early
universe had been T > 3000 K, then
the hydrogen would have been ionized.
Why does this matter?
Dense ionized gases
are opaque. (You can’t
see through the Sun!)
Why does it matter whether the
early universe was opaque?
Hot, dense, opaque objects emit light!
Today, we call hot,
dense, opaque objects
that emit light “stars”.
Soon after the (Hot) Big Bang, the
entire universe was glowing.
Imagine yourself inside a star,
surrounded by a luminous, opaque
“fog”, equally bright in all directions.
Early universe was like that –
sort of monotonous, really…
The universe is NOT opaque today.
We can see galaxies millions of
parsecs away.
The universe is NOT uniformly
glowing today. The night sky is
dark, with a few glowing stars.
Gases cool as they expand.
(This accounts for the relative unpopularity
of spray deodorants. Woohoo, that’s cold!)
As the hot, dense, ionized hydrogen
expanded, it cooled.
When its temperature dropped below
3000 K, protons & electrons combined
to form neutral H atoms.
The universe became transparent.
However, light produced earlier,
when the universe was opaque,
can’t simply disappear.
It radiates freely through the
transparent universe, and should
still be visible today!
The “holy grail” of science:
an observation you can
make that will support or
disprove a theory.
For the Hot Big Bang, holy grail was
discovering the “leftover light” from the
early, opaque universe.
The “leftover light” was
discovered in the 1960s by
Bob Wilson & Arno Penzias.
Astronomers call the leftover light the
Cosmic Microwave Background.
Why microwave?
Thereby hangs a tale –
Thursday’s tale.
Thursday’s Lecture:
The Early Universe
Reading:
none