Rick's Cosmology Tutorial: Chapter 12 Abstract

Characteristic Stellar Timescales and Energies

The gravitational energy due to collapse of a large, stellar mass, diffuse gas cloud down to stellar dimensions is calculated. It is sufficient to sustain solar luminosities only for the order of tens of millions of years. This was noted by Kelvin in 1862, just a few years after the publication of the Origin of Species. For more than 40 years, the physics community regarded tens of millions of years as setting an upper bound for the lifetime of stars. This was despite strong opposition from both Darwin and the geologists. The possibility of an energy source compatible with stellar lifetimes of tens of billions of years did not exist within known physics until 1905 and the advent of E = mc^2. Apparently it was not until 1920 that the physics community, in the form of Eddington, predicted that the stars' source of energy was 'atomic', although the geologist T.C.Chamberlin had made the suggestion already in 1899. It would not be until about 1930 that the matter was settled - in favour of Darwin and the geologists.

It is shown that a low density gas cloud of typical stellar mass will easily attain temperatures sufficient to initiate nuclear fusion of hydrogen due to gravitational collapse down to (say) solar size.

It is shown that the energy available from nuclear fusion is sufficient to power the sun at its current luminosity for the order of 10 Byrs, involving fusing only ~10% of the stellar material.

If the sun were to undergo gravitational collapse as free-fall, i.e. unresisted by any pressure, the time taken to collapse to a point (or black hole) would be roughly half an hour.

The sun is not transparent. If it were we would be bathed in hard gamma rays originating from the nuclear reactions in the ~14 million K core. Even more importantly, the sun would loose energy so quickly its nuclear fire would go out. In fact, the stellar medium is ionised, and also very dense near the core. It is therefore highly opaque to radiation. The rate of heat transport away from the core is thereby severely throttled, allowing the high temperatures to be maintained. Whilst it is fun to tell nuclear-phobes that the sun is an entirely unshielded nuclear reactor, it is completely untrue. It is shielded by 700,000 kilometres of ionised gas. Hence, whilst the light transit time in vacuo from the centre would be a mere 2.3 seconds, it actually takes a photon about 50,000 years to diffuse from the centre to the photosphere - not that it is the same photon as set out on the journey, of course. A photon will undergo around 10^23 interactions before escaping the star, it's mean free path being only about 1 mm.

Read Chapter 12(pdf): Stellar Timescales and Energies

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"Mountains of Creation" (W5/IC1848 in Cassiopeia) This stellar nursery is ~70 light-years in size. The image was made using the infrared Spitzer Space Telescope (Lori Allen, Harvard-Smithsonian CfA)