Download The Sun`s Internal Temperature

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:
 planets and stars must be round (because of the
enormous inward pull of their own gravity); and
 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



the life cycles of stars,
the formation of the elements, and
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.