Stellar life expectancy

[Aphex_Twin]

Hi there.

I'm new to the field of astrophysics so if my questions are a bit silly, don't mind saying it.

1. What is the relation between the luminosity/colour or a star and it's mass?

2. What is the relation between luminosity/colour and life expectancy (I know brighter stars die young, but HOW young)?

3. How much energy is released by a supernova explosion, knowing only the stellar mass?

I'm interested in something accurate, prefferably a formula or a table plot of observations.

Thank you ;)

[Chronos]

For discussion of mass luminosity relationships and stellar life expectancy, see
http://www.pd.astro.it/E-MOSTRA/NEW/A3003EVO.HTM
For discussion of the energy output of supernovae, see
http://en.wikipedia.org/wiki/Supernova

Being overweight is just as hazardous to the health of a star as it is to ordinary people.

[Aphex_Twin]

Is there a way to tell the supernova energy output as a function of mass?

[Chronos]

There is a relationship between mass and brightness of different types of supernova. For example, type Ia supernova [the brightest, most energetic of all supernova] are attributed to white dwarfs that have siphoned off mass from a red giant companion star until their own mass exceeds the Chandrasekhar limit [~1.4 solar masses]. For this reason, their masses are very nearly the same and they achieve very nearly the same absolute luminosity when they detonate. For this reason, type Ia supernova are used as 'standard candles' to estimate distances to the regions of the universe in which they occur.

Type II supernova are formed when the core of very massive [>12 solar masses] stars collapse. The masses of these stars, as well as their absolute luminosity, widely vary. Certain types of type II supernova are very similar in mass and absolute luminosity, hence can also be used as standard candles. Spectral analysis is used to determine the specific classification of all types of supernova

In the case of extremely massive stars, this collapse can hypothetically result in a hypernova. A hypernova can be even more energetic than a type Ia supernova, but only for a very brief period of time and most of that energy is in the form of gamma rays, so they are not visibly more brighter than type Ia supernova. Hypernova are believed to be responsible for gamma bursts. Fortunately, stars capable of going hypernova are very scarce in 'old' galaxies like ours [most detonated in the distant past]. A hypernova releases such intense gamma radiation it could destroy all life forms [at least any similar to our own] within a few thousand light years. The only known hypernova candidate near earth is Eta Carinae, which weighs in at a hefty 100-120 solar masses. It is possibly the most massive star in our galaxy. Fortunately, it is 7500 light years away.

[Aphex_Twin]

Interesting. So if a star is between 1.4 and 12 solar masses, the ensuing supernova explosion would be weaker(?) than a 1.4 solar masses.

But I was looking for something more accurate (if it exists), be it in the form of a table of data or mathematical formula (I am not afraid of Maths). I would also settle for a link or a set of starting data to derive that information from.

[Chronos]

Interesting. So if a star is between 1.4 and 12 solar masses, the ensuing supernova explosion would be weaker(?) than a 1.4 solar masses.Stars in that range are usually not massive enough to become type II supernova [there are some exceptions]. The 1.4 solar mass limit applies to white dwarf stars that gravitationally siphon material off companion stars that have entered their red giant phase. The composition of the white dwarf star determines whether it goes nova or supernova. Supernova is a one shot deal that destroys the star. A white dwarf star may, however, go nova multiple times [eg, RS Ophiuchi].But I was looking for something more accurate (if it exists), be it in the form of a table of data or mathematical formula (I am not afraid of Maths). I would also settle for a link or a set of starting data to derive that information from.It's complicated. Mass is but one factor, metallicity is anotherm along with some other, less well understood characteristics. Try this paper for an overview.
http://arxiv.org/PS_cache/astro-ph/pdf/0409/0409350.pdf

[meteor]

type Ia supernova are used as 'standard candles' to estimate distances to the regions of the universe in which they occur.

However, is an error to classify the whole population of SN Ia like standard candles. There are some individuals that can be problematic. See:
http://arxiv.org/abs/astro-ph/0211219

This is not to say that SN Ia are standard candles. In fact, even after excluding a number of extreme events or outliers (e.g. SN 1991bg or 1991T), spectroscopic and photometric differences among SN Ia do remain.

[Chronos]

I entirely agree with you, meteor. Those are among the many reasons there is no simple answer to the question Aphex posed. I was merely trying to frame it. Remind me to nominate, you know your stuff.

[Aphex_Twin]

Thanks, I think I can get heads to tails to those links.

[Labguy]

If nothing else, the chart here will help with masses - ages - numbers (propensity):

http://anzwers.org/free/universe/startype.html