Stellar Interiors Astronomy 315 Professor Lee Carkner Lecture 10

What is Inside?   Why does a given star have a given T, R, M and L? How are T, R, M and L related?  Must be due to what is going on in the star

The Insider   Can only see the very outer layers directly   Our best information comes from the Sun

Energy   However, the energy must somehow get to the surface and pass through the regions along the way  We want to determine 2 things:   How is energy transported?

Equations of Stellar Structure   Weight of each layer of a star is balanced by the pressure of the layers beneath it   A star is a sphere and as you move out from the center you enclose more and more mass (no gaps)   Relationship between pressure, temperature and density

Hydrostatic Equilibrium   Star wants to contract   Star wants to expand  Star must be in a state where gravity and thermal pressure balance

Basic Hydrostatic Equilibrium

Cross Section of H.E.

Central T and P  We can use the equations to stellar structure to find things like the pressure and temperature   We know mass from binary stars   P C = 3 X 10 9 atmospheres for Sun   T C = 1.5 X 10 7 K for Sun

Stellar Models   Requires large computing power   Temperature, pressure and density are strongest near the core and fall off toward the surface

Model of the Sun’s Interior

Why Does the Sun Shine?   What could power the Sun for this length of time?  Chemical energy (burning) --  Kelvin-Helmholtz contraction (gravitational energy) --  Nuclear Fusion Reactions --

Fusion  Hydrogen fusion requires the atoms to be moving fast (high T) and to be packed tightly together (high P)   Each reaction converts 4 H to 1 He and some mass to energy (E=mc 2 )   Rate of reactions depends on the temperature and pressure 

Hydrogen Fusion

Scientific Notation  The numbers is astronomy are often too large to represent with words or even by writing out all digits   Example: number of seconds in a year   Move decimal point seven places to the left, so our exponent is 7   To put into calculator use “EE” key in place of “X10”   However, you should always write out the “X10”, don’t write “EE” in what you hand in  “There are X 10 7 seconds in one year.”

The Main Sequence Explained  Why is there a main sequence?   The stronger the pressure the higher the temperature and the more reactions   High mass stars produce more energy in their cores and thus have a larger temperature and luminosity 

Energy Transport  In general energy is transported in 3 ways:  Conduction --  Radiation --  Convection --  Star have no conduction   Radiation and convection both very important

Solar Granulation

Convection in Granules

Opacity  Opacity determines whether energy is transported by radiation or convection  Opacity --  High opacity -- very little radiation can penetrate   Low opacity -- radiation penetrates easily 

Ionization  Atoms can only absorb photons if they have electrons   High ionization means low opacity   At high temperatures it is easy for photons to move freely through a gas

M < 0.4 M sun  Completely Convective   Low temperatures mean atoms are not ionized and can absorb radiation better 

0.4 M sun < M < 4 M sun  Inner Radiative Zone   Free electrons and protons don’t absorb light very well so the primary means of energy transport is radiative  Outer Convective Zone   The atoms absorb the radiation and heat up 

Interior of a 1 M sun Star

Energy Transport M > 4M sun  Inner convective zone   Even though the opacity is low, there are so many photons that enough get absorbed to produce convection  Outer radiative zone 

Energy Transport Down the Main Sequence

What is a Star?  A big sphere of gas (mostly hydrogen)  Powered by fusion reactions in the core   Energy gets out via radiation or convection depending on the opacity 

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