MadSci Network: Astronomy

Re: Destructive force of a supernova & critical mass calculations

Date: Thu Nov 30 23:20:52 2000
Posted By: Vladimir Escalante-Ramírez, Faculty, Institute of Astronomy, National University of Mexico
Area of science: Astronomy
ID: 974612373.As

There are two types of supernovae. Type I yields about 10^42 joules of 
energy and type II yields about 10^43 joules. Here 10^42 means 10 to the 
42th power, or a 1 followed by 42 zeros. One ton of TNT is 
equal to 4.18 X 10^9 joules so you see that a type I supernova 
is about 2 X 10^32 tons of TNT and a type II is 10 times that. 

The destructive force of an explosion is hard to measure. 
It depends a lot on what is being destroyed. For instance, 
to vaporize a piece of ice of, say, ten tons you need about 
4.2 X 10^9 joules which is one ton of TNT. Destroying a harder 
material may take much more than that. A type II supernova 
can sweep up about 1000 solar masses. A solar mass is 2 X 10^30 
kilograms. Another way to look at this is by looking at 
Hiroshima after Aug. 6, 1945, when it received a bomb of 
14 kilotons. One kiloton is 1000 tons of TNT. Nagasaki 
received 22 or 23 kilotons three days later. Today's fusion 
bombs have yields of the order of megatons, that is, millions of 
tons of TNT. 

I don't know what you mean by "critical mass". Nuclear 
weapons explode by a chain reaction in a fissile material like 
uranium 235 or plutonium 239. To produce the fission of 
most of the material, it is necessary to have a certain 
amount of the material concentrated on a block 
so that the number of neutrons needed to produce the reaction 
grow with time. When that happens we say that the amount of fissile 
material is above "critical mass". The critical mass depends on the 
shape of the block of fissile material, so there is no simple 
way to calculate the mass. Generally speaking the lower the surface of 
the block the lower the critical mass because less neutrons will 
escape the block through the surface. 

With respect to supernovae, the situation is completely different. 
A supernova explodes for a very different reason. Fissile elements 
like uranium or plutonium are very scarce in the universe. Normally, a star 
supports itself against its own gravity by the energy it generates from 
fusion.  However, it is not possible to fuse iron nuclei together.  If a star 
is massive enough, it will create iron in its core after several million 
years.  At this point, it has no way to produce the energy it needs to support 
itself against gravity.  So its core collapses to become a “neutron star,” 
composed entirely of neutrons.  The outer regions of the star collapse until 
they hit the neutron star, at which point they bounce (literally) back into 
space.  This is what we call a Type II supernova.  The star needs a mass 
of about 10 times the Sun's mass for this to happen. 

It is even less clear how type I supernova go off. Apparently a star 
with a mass around one solar mass can go supernova, type I version, 
if it evolves into a white dwarf and then gets more 
mass from somewhere else. White dwarfs are stars that exhaust 
their fuel and collapse to the point where electrons and 
atomic nuclei are at their maximum degree of compression. 
If the white dwarf mass is increased beyond a limit of 
1.4 solar masses, called the Chandrasekhar limit, it 
collapses very fast by forcing electrons and protons to 
combine and produce a very high amount of neutrons and 
neutrinos. Neutrons stay and form a neutron star, but 
neutrinos fly away and can blow out the outer part of 
the star producing the supernova event. There are many 
uncertainties with this picture because we do not understand 
the physics involved very well. White dwarfs 
can get this extra mass if they are part of a binary system, 
and their companion star expands and starts passing mass 
to them. 

Vladimir Escalante Ramirez

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