Supernovae Equations
Volume of a Supernova Remnant
V = volume (meters cubed)
R = the radius of the supernova at the moment of measurement (meters)
V = (4/3)·π·R
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This equation determines the total volume of an SNR at any given moment. It is used by scientists to predict how large the supernova was, SNRs released, how far it is to other things relatively nearby and is often also another variable in other equations.
Mass of a Supernova Remnant
M = Mass (kg)
E = the volume that which the remnant has expanded (meters cubed)
I = the average density of interstellar medium (kg/metre cubed)
M = E · I
This equation is used to get an estimate size of the supernova and the amount of supernova remnants produced. However, it can also be rearranged to find how much the supernova has expanded by.
The Age of a Supernova
A = age (years)
M = mass of the supernova (kg)
R = the rate of expansion (meters/second)
A = M/R
This equation is used to find how old a supernova is only applied if the supernova is expanding at a constant rate. This information can tell us more about a supernovae souroundings and how it is influenced by the supernova itself. This equation can also be rearranged to calculate the mass a supernova and its rate of expansion.
Nuclear decay equation and half-life of type Ia supernova
1) 56/28Ni → 56/27Co + 0/-1e
2) 56/27Co → 56/26Fe +0/-1e
These equations show the energy released from type Ia supernovae. We can see that they involve beta decay, because the element changes, but the mass stays the same. The equation determines absolute brightness during an explosion, revealing a consistent peak luminosity for all type Ia supernovae. We can use this knowledge to measure cosmological distances.
The first beta decay reaction has a half-life of 6.1 days. This is relatively short as most nickel decays during the initial period of brightening. The resulting Cobalt-56 is unstable therefore, another reaction takes place. The Second beta decay reaction has a half-life of 77.7 days. This is a dominant energy source for a few days after peak intensity. The number of cobalt-56 per unit of time must be proportional to the number of cobalt-56 atoms present. The unstable cobalt-56 decays into Iron-56.