The Sun and other starsThe Sun and other stars

The physics of starsThe physics of stars

A star begins simply as a roughly spherical ball of (mostly) hydrogen gas, responding only to gravity and it’s own pressure.

To understand how this simple system behaves, however, requires an understanding of:1. Fluid mechanics2. Electromagnetism3. Thermodynamics4. Special relativity5. Chemistry6. Nuclear physics7. Quantum mechanics

X-ray ultraviolet infrared radio

The SunThe Sun

•The Solar luminosity is 3.8x1026 W•The surface temperature is about 5700 K

•From Wein’s Law: K m 00290.0max T

Most of the luminosity comes out at about 509 nm (green light)

The nature of starsThe nature of stars

• Stars have a variety of brightnesses and colours

• Betelgeuse is a red giant, and one of the largest stars known

• Rigel is one of the brightest stars in the sky; blue-white in colour

Betelgeuse

Rigel

The Hertzsprung-Russell diagramThe Hertzsprung-Russell diagram

• The colours and luminosities of stars are strongly correlated• The Hertzsprung-Russel (1914) diagram proved to be the key that unlocked the secrets of stellar evolution• Principle feature is the main sequence• The brighter stars are known as giants

BLUE Colour RED

Lu

min

os

ity

Types of StarsTypes of Stars

Assuming stars are approximately blackbodies:

K m 00290.0max T424 TRL

Means bluer stars are hotter

Means brighter stars are larger

Betelgeuse is cool and very, very large

White Dwarfs are hot and tiny

Types of starsTypes of stars

Intrinsically faint stars are more common than luminous stars

Hydrostatic equilibriumHydrostatic equilibrium

The force of gravity is always directed toward the centre of the star. Why does it not collapse?

The opposing force is the gas pressure. As the star collapses, the pressure increases, pushing the gas back out.

• How must pressure vary with depth to remain in equilibrium?

Hydrostatic equilibriumHydrostatic equilibrium

Consider a small cylinder at distance r from the centre of a spherical star.

Pressure acts on both the top and bottom of the cylinder.

By symmetry the pressure on the sides cancels out

drA

dm

FP,b

FP,t

2r

GM

dr

dP r

• It is the pressure gradient that supports the star against gravity

• The derivative is always negative. Pressure must get stronger toward the centre

Stellar Structure EquationsStellar Structure Equations

2r

GM

dr

dP r

24 rdr

dM r

Hm

kTP

Hydrostatic equilibrium:

Mass conservation:

Equation of state:

5.15

11

nA

ZYXi 2

1

4

32

1

• These equations can be combined to determine the pressure or density as a function of radius, if the temperature gradient is known This depends on how energy is generated and transported

through the star.

Stellar structureStellar structure

•Making the very unrealistic assumption of a constant density star, solve the stellar structure equations.

2r

GM

dr

dP r

24 rdr

dM r

Hm

kTP

The solar interiorThe solar interior

•Observationally, one way to get a good “look” into the interior is using helioseismology

Vibrations on the surface result from sound waves propagating through the interior

The solar interiorThe solar interior

•Another way to test our models of the solar interior are to look at the Solar neutrinos

BreakBreak

Stellar luminosityStellar luminosity

Where does this energy come from? Possibilities:

• Gravitational potential energy (energy is released as star contracts)

• Chemical energy (energy released when atoms combine)

• Nuclear energy (energy released when atoms form)

Gravitational potentialGravitational potential

So: how much energy can we get out of gravity?

Assume the Sun was originally much larger than it is today, and contracted. This releases gravitational potential energy on the Kelvin-Helmholtz timescale

.

Binding energyBinding energy

There is a binding energy associated with the nucleons themselves. Making a larger nucleus out of smaller ones is a process known as fusion.

For example:

remnants mass low HeHHHH

~0.7% of the H mass is converted into energy, releasing 26.71 MeV.

E.g. Assume the Sun was originally 100% hydrogen, and converted the central 10% of H into helium. How much energy would it produce in its lifetime?