| MadSci Network: Astronomy |
Some astronomers believe that hypernovae are produced by stars that have masses greater than 20 or 25 solar masses. The hypernova is really a sudden outburst of energy produced by the star. To date there is no agreement among astronomers on the mechanism that produces the outburst. One problem that compounds the disagreement is that there are no stars with this mass in our Galaxy and the reason is that they do not live long enough to be observed. In fact it is not clear that they exist at all, but if they do, they may cause the most energetic explosions in the Universe. At least most astronomers tend to agree that the collapse of a massive star is needed to produce the hypernova outburst. A star collapses when it runs out of nuclear fuel. When nuclear fuel is exhausted, the star cannot support itself against gravitational collapse, and the collapse either produces an explosion or a black hole. Therefore in order to know the time that a star lives before it collapses, we need to know how long its nuclear fuel lasts.
The current theory of stellar evolution says that a star converts hydrogen to helium at its center, which is about 1/10 of its total mass. The conversion of hydrogen into helium is a type of nuclear reaction. In this reaction four hydrogen atoms produce a helium atom plus a small amount of energy equal to 0.0067 of the original mass of the four hydrogen atoms. Remember that in a nuclear reaction mass can be converted into energy according to Einstein's formula: energy=mc2 where c is the speed of light, about 3X1010cm/s and m is the mass converted into energy. That energy produces all the light from the star. Therefore we can calculate how long does the hydrogen lasts at the center if we know the total light that the star emits in time. That light is called the luminosity. The luminosity is the total light emitted in one second. If the star shines with luminosity L during a time t, the total energy emitted during that time is Lt, and this energy must equal the total energy produced by the conversion of hydrogen into helium. If 1/10 of the mass of the star will be converted into helium, and 0.0067 of that mass will produce the luminous energy of the star, then the total energy produced by converting the mass into energy is 0.0067 X 1/10 X Mc2= 0.00067Mc2=6X1017M where M is the mass of the star. We have then Lt= 6X1017M or t=6X1017M /L. Let's check this for our Sun, which has about M= 2X1033 grams and L= 4X1033erg/s. We get t=3X1017seconds=1010 years = 10 billion years.This is about right as far as astronomers can tell.
If we want to apply the above formula to a star of 20 solar masses, we run into a problem. We do not know their luminosity because we have not observed one yet (before it explodes, that is)! Current theory of stars says that the luminosity of a star is proportional to the fourth power of its mass if that mass is bigger than 3 solar masses. If, and this is a big if, this relation between luminosity and mass holds for stars bigger than 20 solar masses, we can guess the luminosity of a the star by a rule of three: L/Lo= M 4/M 4o where Lo and Mo are the Sun luminosity and mass respectively. Thus for M=20Mo I get L=204Lo and the hydrogen burns for about t=1 million years. This may seem like a long time, but it is short compared with cosmic times.You can work out the time for stars of bigger mass. t should be shorter.
When the star turns all its hydrogen into helium at the core, it starts a series of quick stages in which helium is converted into carbon. These stages are much shorter than the hydrogen-into-helium stage, therefore we can take the t=1 million years as the life span of a star that will somehow produce a hypernova. The carbon stage is the explosive point according to some astronomers like Umeda et al. (Astrophysical Journal Letters, Vol. 633, p. L17 [2005]). Some astronomers doubt that a hypernova is actually an exploding star. Instead there are theories that say that hypernovae are produced by beams of material ejected from a black hole into a surrounding disk (Joss and Becker, Astronomical Society of the Pacific Conference Series, Vol 367, p. 517, [2007]). In this case we still need a massive star to collapse and produce the black hole, and this collapse happens when the nuclear fuel runs out.
Vladimir Escalante Ramírez
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