Supernova: The Heavenly Wizardry of Light!

Supernova! I wonder who came up with this term at first. The term signifies the death of a high mass¹ star. Historically nova was the name used for an apparently new star! What an irony. The death of a star has been given the name whose last part signifies the birth of a star. If you give it another look it is not that ironic though! The death of a star as supernova may actually trigger the birth of another star, but that is another story. Lets just talk about supernovae.

High mass stars end their life in a cataclysmic event, we now cal supernova. During this phase the star releases more energy than it has released in its entire life span by the nuclear fusion reactions. Also, since elements having atomic number greater than that of Iron cannot be manufactured in the stellar core (as they are endothermic) , the huge amount of energy heat during this time assists in synthesizing all the heavier elements that we see today in the process called necleosynthesis!

The amount of energy released during this period is really enormous. To get a feel of that lets have a look at the magnitude of the numbers involved.

Let us consider a typical heavy mass star of mass (M_S) = 10M_ʘ ²

The luminosity of the sun is L_ʘ= 3.85x1026 J/sec

Now, the relation between luminosity and mass is

Also the relation between the life time of a star and its mass is

Thus, comparing with solar values, we get

Here, we have assumed that the life time of the sun is 10 billion years, which comes from a different set of calculations.

Hence the total amount of energy liberated by a 10M_ʘ star over its entire life time by the nuclear process is

Now, as the star goes supernova, lets see what happens to the outer layers of the star and how much is the energy liberated in the process!

That is, we consider the energy budget of the star. Clearly, the energy source of a supernova explosion is gravitational: the collapse of a core of mass M_C= 1.5M_ʘ from an initial white dwarf radius R_C (0.01Rʘ) to the final radius R_nc ~ 20 km (<<R_C) of the neutron core releases an amount of gravitational energy of the order of

                             

This the amount of energy released! From our calculations done above, it is clear that the energy produced by a star during its life time is not even 1% of this value.

The energy absorbed in nuclear processes amounts to

about one tenth of
  



There remains ample energy for ejecting all the material outside the core, for imparting it enormous velocities and for producing the huge luminosities observed. The radiated energy may be estimated by assuming a typical luminosity L_SN ~10³⁷ J/sec for a typical period Tsn of on year:

This is clearly an overestimate, since most of the supernova remains that bright only for a short interval of time of the order of hours or days or at max of the order of week. Still it is only few percent of the released energy. A similar amount would be required for the ejection of the loosely bound envelope,

assuming total stellar mass M ~ 10M_ʘ, and a comparable amount would suffice for supplying the high expansion velocities of the ejecta:

adopting v_exp ~10,000 km/sec, as derived from observations.

When we combine all the mechanisms of energy dissipation, two questions immediately arise: first, if such a small fraction of released energy is sufficient for powering a supernova explosion, where does the bulk of the energy go? Second- the question that has puzzled astrophysicists for decades- what is the mechanism that deposits the required energy in the envelope? The answers to these questions are linked and involve one of the major factors affecting the entire supernova process. These are the neutrinos, which take part in any weak interaction so that the lepton number is conserved! But that is another story and shall be addressed somewhere else.

The purpose of this article was to give the readers a feel of the huge numbers involved in a supernova explosion and the enormity of the scale at which they occur. I hope I succeeded in that!

1: Stars having core mass greater than 1.46 M_ʘ are considered to be high mass stars.

2: The symbol ʘ stands for solar values, for example M_{ʘ ­}represents the sun’s mass and so on.

Reference: An introduction to the Theory of Stellar Structure and Evolution by Dina Prialnik

By Ahmad Ryan

Ahmad Ryan is a feature writer for the blog who is currently in his4th year, B-Tech, Physical Sciences
Indian Institute of Space science and Technology
Trivandrum.