# HR diagram: magnitude - luminosity relation

1. ### stargazer3

44
Hey PF,

I'm just being stupid today, because I can't figure out the way HR diagram is constructed, hope you guys can help. So suppose that you complete an observation in several different filters, and you need to work out the luminosity and temperature for each object in your field of view.

Now for the temperature you could just plot an instrumental magnitude against filter wavelength and fit a black-body profile to it, the peak of the curve showing the effective temperature of the star.

But what about the luminosity? Is it reasonable to take an area of one pixel and, knowing average photon count rate, integrate it over 4π steradians? Then, after multiplying by a typical photon energy (assuming the filters are quite narrow), I'd get a luminosity from a particular source? Something seems wrong here, but I can't figure out what. Is it because the atmospheric absorption is not considered? If so, how to do it properly?

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3. ### RobinSky

112
Luckily for us there is a relation between the apparent magnitude m & luminosity L for a star.

L=4πmd2

And the apparent magnitude is easily measured with or without a CCD/DSLR etc. This is commonly done by people who observer variable stars.

Last edited: Mar 25, 2013
4. ### cepheid

5,194
Staff Emeritus
This is not actually true (at all). The relation is between luminosity and FLUX (or irradiance, if you prefer), which I'll call F. F is basically the rate at which light energy arrives, per unit area, in watts per square metre. The relation is:

L = (4πd2) F

It's true that a CCD measures flux, but it's not true that flux and apparent magnitude are the same thing. They are related though:

m = -2.5*log(F/F0).

where F0 is an arbitrary reference flux (the flux of a source that you define to have magnitude 0 in whatever magnitude scale you're using).

5. ### RobinSky

112
I'm very well aware that magnitude and flux is not equal. Yet, thank you for your correction. I'm sorry I didn't know that the relationship held true between luminosity and flux, and not between luminosity and magnitude as I thought before.
I also see on Wikipedia the relationship you mentioned

http://en.m.wikipedia.org/wiki/Luminosity#section_1

At luminosity formulas. Thanks! :-)

Regards,
Robin.