1. PHYS1142 25 The Solar Atmosphere Photosphere: visible “surface” of the Sun, about 500 km thick. Moving outwards temperature falls from 8000 K to 4500 K and density of gas rapidly decreases. Granulation of surface indicates large scale movement of gas - convection currents transfer heat. Chromosphere: outside photosphere, about 1500 km thick, temperature rises from 4500 K to 6000 K. Visible as red flash during solar eclipse. Corona: starts about 2000 km from the solar surface, rapid temperature rise to 500,000 K then slower rise to well over one million K. Probably heated by electric currents due to changing magnetic fields. Total energy in corona is small despite the high temperatures since the gas is very tenuous. Becomes the solar wind.

2. PHYS1142 26 Meeting the Energy Budget 1370 Watts of solar energy per second hit every square metre at the distance of the Earth’s orbit. Figs. Z13.4 & K11-4 This covers 4  x (Sun to Earth distance) 2 square metres of area = 2.81 x 10 23 m 2 (or ~ 550 million times Earth’s surface area) Hence Sun’s total radiative energy output = 3.85 x 10 26 Watts (or ~ ten thousand million million power stations) Source of energy cannot be chemical since Sun is too small - it would only burn for a few thousand years. Can convert a little mass to a lot of energy: e = m  c 2 (where c 2 = 90,000,000,000,000,000) Source is nuclear energy.

3. PHYS1142 27 Luminosity (energy output) of a Star Need energy reaching Earth and distance from Earth, just as for Sun. Parallax (triangulation using Earth’s orbit as a baseline) gives distance. Surface temperature of a star - measure spectrum and fit a black body curve. Plot luminosity against temperature - the Hertzsprung-Russell (H-R) Diagram Figs. Z14.17 & K12-17 Weighing Stars - binary systems Visual binaries : Figs. Z14.22 & K12-23 need to see the orbits and measure the distance to Earth; gives the mass. Spectroscopic binaries : Figs. Z14.24 & K12-27 Doppler shift gives velocities and orbital period which can be used to find the mass.

4. PHYS1142 28 Eclipsing binaries: measure orbital motion from variation of apparent brightness. Plot luminosity against mass (scale Sun = 1) Figs. Z14.27 & K12-34 Now have a mass-luminosity diagram for Main Sequence stars. This tells us that the heavier they are, the greater is their energy output rate i.e. Luminosity  (mass  mass  mass  mass) but Total energy available  mass Therefore, low mass stars live longer. So where does all this energy come from? n.b.  means “is proportional to”

5. PHYS1142 29 Star Birth Giant molecular gas cloud condenses. Gas looses gravitational energy and gains heat energy. Cloud increases in density and mass, attracts more gas and warms up more - a protostar. Eventually the temperature at the centre of reaches 8,000,000 K and hydrogen “burning” begins - a star is born. Figs. Z16.9 & K13-13 Proton-proton chain: fusion of hydrogen to form helium. Figs. Z13.15 & K11-7 Each p-p chain provides so little energy that 140 thousand million million kilogrammes of matter must be converted per year to keep the Sun shining (equivalent to the mass of our Moon every 500 thousand years). Hydrogen is converted to helium in the core.

6. PHYS1142 30 The Proton-Proton Chain For the Sun, hydrogen in core lasts about 10 billion (10 thousand million) years; we have just over 5 billion years to go. hydrogen nucleus positron neutrino gamma ray helium nucleus deuterium nucleus

7. The Inverse Square Law: if we double our distance from a star then we receive one quarter of the amount of heat and light - try stretching your hand out to a light bulb and gradually backing away; the temperature drops quickly.

8. The Hertsprung-Russell Diagram: our Sun is a very average star. Stars above it are brighter and stars to the left of it are hotter.