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Why do the stars shine? Lecture 8 CAPSTONE 07/14/2010 07.14.2010 PS119a Sunshine 07.14.2010 1 Age of the Sun • Consider a cloud of mass M, full of hydrogen atoms, of radius R. Over time, each atom leads to a total radiation -U/2 for each atom (the mass interior to the radial distance of each particle is always acting as the total mass, M, at the center). • Total energy radiated is energy lost per particle times the no. of particles, which is particle density times volume. • Erad(total) =-Utot/2= (sum of individual U/2 for each atom)=(GMmH/2R) x nH x (4R3/3) • Erad (total)=(GM/2R)(mHnH4R3/3)=GM2/2R. 07.14.2010 PS119a Sunshine 07.14.2010 2 • Note: R is now the radius of the star. The potential energy gain is U(initial)-U(final), but U(initial)=0 since the cloud radius is so much larger than the final star. • Assume the Sun has shown at constant luminosity for t years. Total energy radiated = L0x t=4x1033 ergs/sec x t. • (We know today that main sequence stars do not change luminosity over the life of mankind.) • Lt=GM2/2R, t=GM2/2RL • t = 15 million years • This is the ~Kelvin Helmholtz timescale and assumes that all the energy emitted by the Sun comes from gravitational energy (in the form of radiation). • But, the Sun has to be as old as the Earth, or 5 billion years. (radioactivity, Darwin). • There must be some other source of energy. 07.14.2010 PS119a Sunshine 07.14.2010 3 Nuclear reactions • Note that the mass of He nucleus is less than the mass of 4 nucleons (2p, 2n) by 2.87% • Energy equivalent is 0.0287 x mH x c2 for each H. • = 4.288x10-5 ergs x 1/(1.6 x 10-12 erg/ev)=6.86 Mev/H • Or 28.72 Mev per He nucleus • 1 H atom is 109 ev, so =0.007 per H atom. • (28.72 x 106ev) / [(4 nucleons per He)x(109ev/nucleon)]=0.007 • (origin of Agent 007, who is always stopping A bombs from going off) 07.14.2010 PS119a Sunshine 07.14.2010 4 How much energy in the Sun? • • • • Total no. of H atoms x energy per atom? (M0/mH) x mHc2 x 0.007= 1.3 x 1052 ergs How long can the Sun shine? t=(1.3 x 1052 ergs)/4 x 1033 ergs/sec = 3.2 x 1018 sec x (1 yr./3.1 x 107 sec) • Or 1011 years (only ~10% of H needs to be burned) • 20 times the apparent age of Earth! • So, nuclear reactions could explain the above discrepancy. 07.14.2010 PS119a Sunshine 07.14.2010 5 But, is their any proof it does? • Postulate nuclear reactions, ==>neutrinos should come from Sun. (very ephemeral) • 2002 Nobel Prize given to Ray Davis and Masatoshi Koshiba for detection. • Were found to be well below expected rate ( a problem for 25 years) • Led to discovery important in neutrino physics, but problem is resolved. • 60 years between postulate of nuclear energy and proof. (Recall parallax, age of Earth, etc. that all took time to get big dilemmas 07.14.2010 PS119a Sunshine 07.14.2010 6 resolved)