HR diagram: magnitude - luminosity relation

[stargazer3]

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?

 

[RobinSky]

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.

 

[cepheid]

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.

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).

 

[RobinSky]

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).

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.

 

[pmacias]

Hi there,

The HR diagram, or Hertzsprung-Russell diagram, is a plot of stars' luminosity (brightness) against their spectral class (temperature). It is a useful tool for astronomers to understand the life cycle and evolution of stars.

To determine the luminosity of a star, we need to measure its distance and apparent magnitude (brightness as seen from Earth). Using the distance, we can calculate the absolute magnitude, which is the brightness the star would have if it were 10 parsecs away (a standard distance used in astronomy). The difference between the apparent and absolute magnitudes gives us the distance modulus, which is used to determine the star's luminosity.

As for your question about integrating the photon count to determine luminosity, this method is not accurate. It does not take into account the effects of atmospheric absorption, as you mentioned, and it also does not consider the different wavelengths of light emitted by the star. Instead, astronomers use a combination of photometric and spectroscopic measurements to determine a star's luminosity.

I hope this helps clarify the construction of the HR diagram and the determination of luminosity. Keep exploring and asking questions - that's what science is all about!