Transcript Why do the stars shine?

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 (4R3/3)
• Erad (total)=(GM/2R)(mHnH4R3/3)=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)