Okay gang, let's roll!

And welcome back to analyzing the universe.

Today, I want to talk to you about some of the

incredible things that we can tell from looking at the stars.

It is truly astonishing that the feeble light from objects apparently so

very dim, can illuminate so brightly our knowledge of the heavens in so many ways.

The story begins over 100 years ago when the world of physics was truly

shaken to its roots by the discoveries of the quantum world.

Several key surprises had fundamental implications for the study of astronomy.

The first surprise was the requirement of specific

orbits for electrons as they traveled about the nucleus.

Unlike planets, for example, that could orbit

their stars at any distance, quantum mechanics

forbade all but a very specific set of distances for the electrons to reside in.

Indeed, this understanding became a triumph, as it explained with incredible

accuracy, the heretofore mysterious occurrence of the dark lines

in stellar spectra. So the idea is that in the case of planets

for instance, you have a sun, and you have planets going around the sun.

But those planets could inhabit any region external to the Sun.

There was nothing to prevent Mercury,

for instance, fundamentally from being in a slightly different position relative to

the Sun than it is today. That is not the case with atoms.

In atoms, there are very specific, discreet

levels that allow the electrons to reside in.

And those discrete levels give rise to discrete energies,

corresponding to the change in those levels within the atom.

What you see on the screen right now, is

the light output of over a dozen different stars.

In the visible part of the spectrum,

from red, the low energy photons, to blue, the

high energy photons. You can see many, many dark

lines which correspond to unique energies in the

spectrum. These energies correspond to an electron

in a particular atomic element, or compound, jumping from

one discrete level to another. Thus, these lines give us

valuable hints as to the chemical composition of the stars.

The way this mechanism works is as follows.

Radiation comes from the center of the stars in all wavelengths.

And they pass by an electron. The electron ignores all

those photons. Except the ones corresponding

to the energy necessary to jump to a higher orbit.

So the situation might be that the blue photon continues on its

merry way, the red photon continues

on its merry way. But the yellow photon can be absorbed

by the electron, which then jumps up to

a higher energy orbit. So this would correspond on our little

energy diagram here, to an electron say, in the ground state,

going into say, the second excited state,

and that energy difference has to correspond

exactly to the photon that has been absorbed

by the electron. What happens next is that the

electron usually, almost immediately, falls back

to the lower energy state and re-emits the photon.

So the electron can go back to this energy level.

And re-emit the photon, but here's the kicker.

The direction of this re-emitted photon is

random, and usually different from the incident direction.

Electron comes down, re-emits the photon. In a different direction.

And this is shown in the following animation.

Furthermore, the electron may retrace its steps differently, and re-emit

different wavelength light altogether. In other words, the

electron can instead of jumping immediately down to the ground state,

can come down here, re-emitting

a different

Energy photon, and then come back down to the ground

state re-emitting yet another energy photon.

And that would be the same as going

like this in our energy level

diagram. In either event, the net result

is that light of a specific wavelength is subtracted from the

overall output, hence the dark lines in our spectrum.

Now let's look at those spectra again carefully.

Notice that not only are the lines different, but

the overall output or color is different as well.

The sample stars near the top have distinctly

more blue light than those at the bottom.

Where it is clear that the red light predominates and this, in fact,

is indignative of the different colored stars that we see in the sky.

Which brings us to the second part of

our story, which was the discovery by Max Planck

of the radiation law that governs how stars emit light, the

so-called Blackbody Radiation Law. What we

see here is that as the temperature goes up, not only

does the total energy output per surface area element go up,

but also the maximum of the radiation shifts

towards the blue. The hotter stars around 10,000 kelvin

are much bluer than the cooler stars around 3,000 kelvin.

Incidentally the kelvin is just another temperature unit based on the fact that

zero kelvin corresponds to the absolute minimum possible level of atomic activity.

But where are the dark lines?

It turns out that these are departures from black body radiation.

A true black body would have only continuous radiation.

But when you put it all together, black

body plus lines, you get something like this.

Which is the solar energy spectrum.

It is very close to a black body, with lots

of dark lines superimposed on it. And

so now, we get to our final chapter of our little story,

which is what our understanding of what a star's radius is.

In the late 1800s, Joseph Stefan deduced from experimental data,

what the total radiation output must be for objects close to a black body.

It turns out to be the following expression.

Sigma t to the 4th. Sigma is a

constant, based on thermodynamic considerations.

And t is the temperature raised to the fourth power.

Now remember that our black body spectrum was the energy

output for each surface area element of the object.

Well in order to find out the total then, we must take

our expression here, and multiply by the whole surface of the star.

Where R is the radius of our star. That

is the luminosity, or total energy output

of any black body radiator that is spherical in shape.

And the units on this luminosity, depend on what units we measure

for sigma, and what units we measure for the

radius. T is always going to be in Kelvin.

So for instance, if this was in CGS units,

we would have ergs per second here,

and R would be measured in centimeters.

Now you can see the effects of the high power that luminosity has on temperature.

A mere factor of 10 in temperature corresponds

to a factor of 10,000 in luminosity.

But if all we can see is the apparent brightness of the star

in the sky, how can we find out the luminosity, or

total energy output that the star has. Only if we can find the

luminosity can we deduce what the radius of the star is.

Clearly we need to determine the distances to the stars.

Only with distances in hand can we

deduce the actual parameters related to our observations

of these faint pinpoints of light in the sky.

And that is the subject of our next lecture.

Lecture 4 Atomic Spectra, the Fingerprints of the Stars

Analyzing the Universe

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