Model of the Solar Interior The theoretical data presented here is the basis of the Two–Layer Model of Stars: Core & Envelope

Traditional models of the Solar Interior present three regions: The Core, The Radiative Zone and the Convective Zone

I will present evidence that suggests that a Two-Layer Model of the Sun may be more useful for us in understanding how stars operate.

The page reproduced to the left is just for cosmetics. You do not need to read it. It is a visual reminder that if an astronomer understands the reactions that go on within the Sun and the pressure and temperature conditions that control those reactions, they can calculate the properties of the interior of the Sun with great precision even though they have never “seen” into the solar interior directly.

The Sun’s internal structure is displayed in the following four slides that show how the luminosity, mass, temperature, and density vary with the distance from the Sun’s center. These internal structure (L, M, T and ρ) parameters are from the Standard Solar Model. A solar radius (the distance from the Sun’s center to the photosphere) equals 696,000 km.

This graph displays the cumulative luminosity as a function of solar radius. Notice how the luminosity climbs toward 1 Solar Luminosity as the fractional radius increases. The region shaded in red represents that portion of the Sun located within 0.2 solar radii or 1/5’th the solar radius. Notice that about 95% of the entire solar luminosity is generated within 0.2 solar radii of the center. We shall call this region the core. Almost all the energy produced by the Sun occurs in the core. How big is the core? Since it is about 1/5’th the solar radius, the volume of the core is 1/5’th cubed the volume of the Sun or, equivalently less than 1% the volume of the Sun. Let me emphasize this result. The core of the Sun that produces almost all the energy occupies only 1% of the Sun’s volume. What does the other 99% of the Sun do? We will call the volume of the Sun beyond 0.2 solar radii the envelope. The envelope produces no energy (almost) and occupies 99% of the Sun’s volume. Isn’t this interesting? 99% of the Sun’s volume has nothing to do with energy production – or does it? In fact, the envelope is essential for energy production because its weight on the core maintains the core pressures so that fusion can continue. Without the envelope that core would explode! 95% COREENVELOPE Energy production is the basis of the Two-Layer model of the Sun. One layer – the core- produces energy and by its thermal pressure supports the envelope against further collapse. Without the core the envelope would collapse. The second layer is the envelope that produces no energy but is required to maintain core fusion conditions. Lets examine some other properties of the core and envelope.

How much of the Sun’s mass is contained within the core? About 33% or 1/3 of the Sun’s mass is in the core. 2/3’rds of the Sun’s mass are in the envelope. Let’s think about this. 1/3 of the Sun’s mass is squeezed into 1% of the Sun’s volume. The core must be very dense! 33%

COREENVELOPE What is a characteristic density of the core?How about 100 g/cm 3 ! Remember that iron has a density of about 8 g/cm 3. So the core of the Sun is over 10 times as dense as iron. How about the envelope?Halfway through the envelope the density is down to about 1 gm/cm 3 or equivalent to the density of water! Thus, the core of the Sun is extremely high in density while the envelope is low in density. 100 g/cm 3 Imagine that you had an iron bar the size of a loaf of ordinary white bread and just like white bread you could squeeze that iron bar down to a ball of about the size of a tennis ball, just like you could do to white bread. That squished iron bar would still not be as dense as the core of the Sun. Pressures are so great in the cores of stars that material we think of as sturdy can be squished like white bread! 1 g/cm 3

COREENVELOPE What is a characteristic temperature in the core?How about a bit over 10 Million Kelvins.What is a characteristic temperature in the Envelope?How about a few Million Kelvins.The Sun is cool only at its very outer surface. We conclude that the core is very hot (10’s Million K) while the envelope is much cooler (Millions of K). 15 Million K 3 Million K

Let’s compare the Sun to a Weight Lifter. The Weights represent the envelope of the Sun pushing down on the core represented by the Weight Lifter. Envelope Core Currently the Sun, like our Weight Lifter, is “happy” because a balance exists between the downward weight of the “envelope” and the upward force from the “core”. This balanced will be maintained throughout the Main Sequence lifetime of the Sun. However, this balance must eventually give way, as it must with our Weight Lifter, as the Sun runs out of energy in its core. Just as the Weight Lifter will eventually tire, so the Sun will eventually run out of fuel to sustain core hydrogen burning. Then the inevitable will happen.

The Sun, just like our Weight Lifter, will be crushed by the weight of the envelope. Gravity never gets tired! Sooner or later all stars meet the same fate – to be crushed by their envelopes. The details of what happens to stars as their cores are crushed is described in Units 64 & 66. We will explore next how the crushing of a star’s core can cause the envelope to swell creating a Giant star.

The Sun can be functionally divided into two layers. Please keep this Two-layer Model in mind as you study the life cycle of stars. The core –Produces almost all the energy –Supports the weight of the envelope preventing further collapse –Contains 1/3 the mass of the Sun –Has a density of near 100 g/cm 3 –Has temperatures is excess of 10 million K The Envelope –Produces essentially no energy –Restrains the core against blowing up and maintains conditions for fusion –Contains 2/3’rds the solar mass –Has a density of around 1 g/cm 3 –Has a temperature in the millions of K