The Sun s Internal Temperature
The Relationship between Formation and Heat Consider making a pie, mixing together cool ingredients and rolling out a crust, then putting it into a hot environment (an oven) to cook it. The heating is independent of the formation.
A Pumpkin Pie After we cook it, the heat radiates away (the pie cools off)
The Fate of the Hot Pie It cools down with no harm to itself, since its structure is supported by chemical and electrical bonds between atoms and molecules. A cool pie is still a pie! (until it gets eaten)
Very Big Objects are Different From ASTR 101: really big objects have certain special properties simply because they are so big. In particular: n planets and stars must be round (because of the enormous inward pull of their own gravity); and n stars are born incandescently hot. The very process of formation makes them hot!
Why Hot? (ASTR 101, first couple of lectures) From time to time, huge clouds of interstellar gas start to contract under the influence of gravity. As they fall inward and collect together, the atoms pick up speed and collide vigorously. They wind up in a central dense lump, jiggling about furiously in other words, the material has become hot. Stars are thus born hot!
Interrelated Effects It is the heat of stars that allows them to resist the inward pull of gravity. (Moreover, the star is filled with radiant energy in the form of energetic gamma rays. That light itself contributes to the sustaining pressure.) But it is the inward pull of gravity that made them hot in the first place! Smaller objects, like the Earth, are also heated as they from, but never got as hot as the more massive Sun, and don t depend on internal heat to hold them up. They will eventually cool off completely, yet stay intact. (The moon, a cold stone, has already done so.)
The Important Question We want to know what has kept the Sun hot over a vast span of time (billions of years). The pie and the Earth s interior gradually cool down! Why not the Sun?
Metabolism: Some Hot Bodies Maintain Their Internal Temperatures The human body is heated from within by simple metabolic processes (chemical reactions). We eat food to allow this.
Nuclear Reactions In the Sun, nuclear reactions provide energy that maintains the internal temperature. So it has a metabolism of a sort! We will explore this in detail as we progress.
How About After Death? Our bodies cool down; no more internal energy is being generated. But even then we retain our structural integrity, as a cold corpse!
Could the Sun be Like This? Alive (i.e. after a hot formation and the onset of internal nuclear reactions) it maintains a constant, steady temperature for a long time. Dead (i.e. once the nuclear fuel is used up) it loses all its internal heat and cools down. Could the sun wind up as a cold, round lump a corpse-like version of its present self?
If So we would expect stars simply to get colder with age, like campfires quietly dying away.
But NO! Paradoxically, when a star uses up its central fuel and the nuclear reactions cease, the net effect is that they get progressively hotter, and they change in structure in remarkable ways. Understanding why is the key to appreciating n the life cycles of stars, n the formation of the elements, and n how we came to be.
Self-Gravity is the Reason! The depletion of nuclear fuel and the steady loss of internal energy means that the sun (and all stars) are destined eventually to get even hotter in their innermost parts.
Back to Basic Structure: What Holds the Sun Up? How does it resist the enormous inward pull of its own gravity?
A Helpful Line of Thought How do you breathe? Why does the air in the room not fall right to the floor under the influence of gravity? It s because it is warm, and the buffeting atoms provide a sustaining pressure.
The Kinetic Theory of Gases https://www.youtube.com/watch?v=rmsqlem968y The atoms and molecules are moving around at random, bumping into one another. Notice that they have a characteristic speed (or kinetic energy), which is equivalent to a statement about the temperature of the gas. (In hotter gases, the molecules have more energy, and are moving faster!)
How Does a Thermometer Work?
The Sun Must be Hot!
No Rigid Structure The sun s enormous self-gravity overwhelms all other forces: no rigidity, no bonds between atoms, no framework of girders, can hold it up. It is supported entirely by its internal temperature. The pressure is a consequence of the rapid random motions of its constituent particles, aided by the additional pressure provided by the radiant energy flowing throughout its interior.
A Simple Calculation On straightforward physical grounds, it was known more than a century ago that the central temperature of the sun must be ~ 10-15 million Kelvin (We interpret this in terms of particle motions, characteristic radiation, etc not how it feels! )
In Cross-Section
An Amazing Implication At this very high temperature, all atoms are fully ionized. Even Uranium, for example, despite having a nucleus with 92 positively-charged protons, cannot hold onto any of its electrons. The vigour of the collisions strips them all off.
The Structure of an Atom: How Tiny is a Nucleus? Atoms and ordinary materials are almost entirely empty space even, say, a dense lump of metal.
Consequently The sun s interior consists of uncountable numbers of tiny fast-moving nuclei (mostly hydrogen and helium, but others as well) - plus a diffuse sea of free electrons.
Consider a Room Full of Beach Balls
vs B-B s
The Simplification Since the clouds of surrounding electrons are stripped off, the gaseous sun acts like a perfect (or ideal) gas. It obeys particularly simple laws no complexities like crystal structure, complex interactions between molecules, etc. In fact, we understand the interior of the sun and stars very much better than we understand the interior of the Earth.
The Perfect Gas Law Consider a police raid
Cops Breaking Down a Door The total pressure they exert on the door depends on the number of particles bombarding the target (= the number of policemen charging the locked door) the mass of each particle (= how heavy each policeman is) their speed (= how fast they run at the door)
Perfect Gas Law So, too, in the perfect gas law. The pressure exerted depends on the density of the gas (the number and mass of the particles present), and on their speeds. The speed is our indicator of temperature.
Everyday example: An average Oxygen molecule at room temperature moves at a speed of almost 500 metres a second! (Hydrogen, a lighter molecule, moves even faster)
In Sum: The sun is a huge, fantastically hot ball of completely ionized gas, with the individual particles racing and jostling around at very high speed. The interior structure is very simple. Moreover, something special happens there: thermonuclear reactions.