HOT Big BangHOT Big Bang

Tuesday, January 22

Hubble’s law:Hubble’s law: Galaxies have a radial velocity (v) proportional to their distance (d).

Hubble’s law Hubble’s law in mathematical form:in mathematical form:

dH v 0v = 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)

H0 = 70 km / sec / Mpc

Or, more concisely…

Why it’s usefuluseful 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!

violetred

galaxy spectra

galaxy images

With modern telescopes and spectrographs, astronomers have

measured millions of spectra.

Kilometers per second per megaparsec?? What bizarrebizarre units!

1 megaparsec = 3.1 × 1019 kilometers

sec/103.2km/Mpc10 3.1

km/sec/Mpc 70H 18190

sec10 4.41H 170

Why it’s intriguingintriguing to know H0:

Two galaxies are separated by a distance d.

They are moving apart from each other with speed v = H0 d.

d

sec104.4H1

dHdt 17

00

How long has it been since the galaxies

were touching?

speeddistance timetravel

PLEASE NOTE:PLEASE NOTE: This length of time (t = 1/H0) is independent ofindependent of the

distance between galaxies!!

If galaxies’ speed has been constant, then at a time 1/H0 in the past, they

were allall scrunched together.

PLEASE NOTE:PLEASE NOTE:

1/H0, called the “HubbleHubble timetime”, is the approximate age of the

universe in the Big Bang Model.

Heart of the “Big Bang” concept:

At a finite time in the past (t ≈ 1/H0), the universe began in a very dense state.

sec104.4H1t 17

0

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:Hubble time: 1/H0 = 14 billion years.

Hubble distance:Hubble distance: c/H0 = 14 billion light-years

= 4300 megaparsecs.

Is the universe infinitely old?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?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 HOTHOT Big Bang?

Hot Big Bang model: the universe starts out very hothot as well as very dense.

What do I mean by ““HOT”HOT”?

90°F 9980°F212°F

Object is hothot when the atoms of which it’s made are in rapid random motion.

TemperatureTemperature: measure of typical

speed of the atoms.

Random motions stop at absolute zeroabsolute zero temperature.

Kelvin = Celsius + 273Water 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 hydrogenhydrogen, the simplest element.

H He

Everything Else

(as seen by astronomers)

Suppose the early universe contained hydrogenhydrogen, 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 ionizedionized gas.

Much of the Sun’s interior is ionized

hydrogen.

Sun’s center: density ≈ 150 tons/m3

T ≈ 15 million K

IfIf the temperature of the dense early universe had been T > 3000 K, thenthen

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 “starsstars”.

Soon after the (Hot) Big Bang, the entire universe entire universe was glowing.

Imagine yourself insideinside 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 The universe is NOTNOT opaque today. opaque today. We can see galaxies millions of We can see galaxies millions of

parsecs away.parsecs away.

The universe is The universe is NOTNOT uniformly uniformly glowing today. The night sky is glowing today. The night sky is dark, with a few glowing stars.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 todaystill 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 BackgroundCosmic Microwave Background.

Why microwavemicrowave? Thereby hangs a tale –

Thursday’s tale.

Thursday’s Lecture:

Reading:

none

The Early Universe