# Finding luminosity of a star with magnitude

I'm working on my assessment for Physics in the IB, and I'm planning to investigate stars in spiral galaxies and determine their ages. For this I'm going to use data from the SDSS (Sloan digital sky survey http://skyserver.sdss.org/dr13/en/tools/chart/navi.aspx).

I need to get the luminosity of a star from the absolute bolometric magnitude. However the SDSS only gives magnitude in 5 values, u g r i and z. I've tried to understand what to do with these and what they mean but I can't figure it out.

How would I get one number the absolute bolometric magnitude from 5 different values, and what do they mean?

The ugriz values are just measures of the stellar brightness taken in 5 bands from the near ultraviolet u through to the near infrared z.

You need the distance to the star to convert the apparent SDSS magnitudes to absolute magnitudes.

Then you need to find a relationship (or relationships) between bolometric correction in a particular band and the colour of the star (by colour I mean something like g-i). Possibly instead you might find relationships between bolometric correction and temperature and will need to first estimate the temperatures of the stars from their colours.

Once you have absolute magnitudes and a bolometric correction, then the absolute bolometric magnitude follows.

In principle you could try this with a number of different colours and see if the results agree. Alternatively, you would fit a library of stellar models to the spectral energy distribution defined by the 5 magnitude values.

A table of bolometric corrections for the SDSS filters was calculated by Girardi et al. (2004) and can be found here. (Other tables/formulations are available, there is no universally accepted version).

Some bolometric correction tables can be found in Schmidt et al. (2014) for very cool objects, which are more problematic.