Presentation: fusion

In a previous presentation we looked at the outer layers of the sun, but now we can turn our focus to its energy source in the core--fusion--which is the energy source for all other types of stars. (Sadly, this Ford Fusion contains no fusion.)

So we'll need to talk about cheerleaders, in order to explain why certain stars undergo slower or faster fusion rates. We have to talk about cheerleaders.

In our discussion of fusion we'll go over the requirements for fusion, as well as how fusion differs in main-sequence stars, and other stars.

First, fusion, and its requirements.

Fusion is accomplished in the core of a star like our sun by means of a proton-proton chain.

Don't worry about the specific steps involved in the proton-proton chain, the essential point is that hydrogen is squished together in a series of processes in order to form helium, releasing energy as a result. (There is a different fusion process in massive stars, but essentially still taking hydrogen and making helium as an end-product.)

A hydrogen nucleus is just a proton, and since all protons hate each other (because they are positively charged, and like charges repel), it is not easy to get hydrogen to fuse. Under low pressures and temperatures, hydrogen does not get squeezed very much, and moves too slowly, they won't collide with each other very much, or not at all (if repulsion is not overcome). Not much squeezing, not much energy produced (if at all).

Under sufficiently high pressures and temperatures, hydrogen gets squeezed a lot, and moves very quickly, such that they will collide with each other very often, fusing and releasing energy. Lots of squeezing, lots of energy produced.

So why fusion only in the core of a star like our sun? Consider a wedge section of the sun, where the outer layers rest on the layers below. Since the structure of the sun is stable, then the weight of the outermost layer must be supported by pressure from the layer below it. Then the layer below will have a greater weight from the outermost layer and itself, which must be supported by greater pressure from the layer below it, and so on. This means that the core of the sun will experience immense pressures, so fusion (which requires sufficiently higher pressures and temperatures) will take place there.

Try this next time you go swimming in a pool--as you go deeper and deeper in order to retrieve something from the bottom, the pressure increases because of the weight of all the layers above you pressing downwards. This is the idea of hydrostatic equilibrium, but it applies to any type of stable fluid subject to gravity.

Consider this cheerleader model of a low-mass star, where the top cheerleader presses down on the "core" cheerleader at the bottom. Not a lot of squeezing, so not a lot of pressure (and temperature), and not a lot of fusion. Thus a low-mass star will not produce a lot of energy, and not be very bright.

Now consider this cheerleader model of a massive star, where the top cheerleaders press down on the cheerleaders below them, which press down on the hapless "core" cheerleader at the bottom. A lot of squeezing, so lots of pressure (and temperature), and a lot of fusion. Thus a massive star will produce a lot of energy, and be very bright.

Second, main-sequence stars, which obey the cheerleader model. (Go main-sequence stars! Yay!)

Compared to a medium-mass star like our sun, the low-mass "red dwarf" star does not have a lot of squeezing in its core, so it will be dimmer and cooler. Likewise the massive star will have a lot of squeezing in its core, so it will be brighter and hotter.

Let's put in the masses of main-sequence stars on the H-R diagram from the Midterm 2 cover sheet. In units of solar masses, our sun has a mass of...exactly 1 M_Sun. The low-mass stars are the dimmest and coolest, starting in the lower right-hand corner with a mass of 0.08 M_Sun to 0.8 M_Sun. Medium-mass stars like our sun are hotter and brighter, ranging from 0.8 M_Sun to 8 M_Sun. The massive stars are the hottest and brightest, from 8 M_Sun up to 50 M_Sun (or ever higher). Don't worry about memorizing the values of these masses, just get an appreciation of the pattern of low-mass to medium-mass to massive stars on the main-sequence.

Third, other stars, which do not obey the cheerleader model.

These are located off the main-sequence on the H-R diagram, and there is no correlation between mass and luminosity between these types of stars, or even within each type of star.

On the H-R diagram, plotting the masses for giants shows that while there is a range of values from 2 M_Sun to 10 M_Sun, you can find any value of mass in this range anywhere inside this "pocket" (which have been arbitrarily placed on this diagram). There isn't much of a pattern to these mass patterns, unlike the main-sequence stars.

Likewise for supergiant masses, which range from 5 M_Sun to 20 M_Sun; again you can find any value of mass in this range anywhere inside this "pocket." No clear pattern here as well.

And for white dwarfs, too, which range from 0.1 M_Sun to 2.0 M_Sun; again any value of mass in this range can be found anywhere in this "pocket," with no clear pattern.

In the subsequent in-class activity you will be comparing the luminosities and fusion lifetimes (until they convert all the hydrogen in their cores into helium) for main-sequence stars.