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 = 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!

violet red galaxy images galaxy spectra

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

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?

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.

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)?

Food for thought: if the universe is finite, does it have a boundary? 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

Temperature: measure of typical speed of the atoms. 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.

Water boils: 373 Kelvin (K) 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.

(as seen by astronomers) H He Everything Else (as seen by astronomers)

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

Dense ionized gases are opaque. (You can’t see through the Sun!) 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 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.

Astronomers call the leftover light the Cosmic Microwave Background. 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