# Stefan-Boltzmann law, luminosity, brightness and magnitude?

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1. Apr 9, 2015

### 21joanna12

From what I understand, in the equation $P=\sigma AT^4$, P is the power output of the star which is the energy radiated per second in EM radiation of all frequencies, and I think luminosity is also defined as the energy radiated per second in EM radiation of all frequencies. Therefore luminosity is equal to power output, so the equation tells us the luminsoty.

But then I get confused trying to relate this to intensity, brightness and magnitudes. I have read than absolute magnitude is a measure of luminosity on a logarithmic scale, and apparent magnitude is a measure of intensity on a logarithmic scale, however it seems to me that both intensity and luminsoty refer to energy from all frequencies of radiation, but absolute and apparent magnitudes refer only to the energy from visible light. I am also trying to figure out how brightness fits in. Is brightness more of a qualitative term and apparent magnitude is a quantitative measure of brightness, and absolute magnitude a quantitative measure of inherent brightness? This would make more sense to me as it seems that brightness and magnitudes refer to visible light only, while lumnosity and intensity refer to EM radiation of all freqencies...

Thank you in advance for any help clearing this up :)

2. Apr 9, 2015

### Staff: Mentor

There are different luminosity scales, and even more magnitude scales.
Typically, it can also refer to the whole spectrum.
I think so.
Right.

3. Apr 9, 2015

### Ken G

Yes, the magnitude scale is a logarithmic scale, but it is limited to the luminosity in a given band. There's no easy way to convert magnitudes to luminosity, without unpacking the entire awkward magnitude concept into the much more reasonable luminosity per band, and then add up the luminosities in each band.
"Brightness" is a somewhat vague term, but it is quantitative-- it just depends on what you are using it to mean. Above you used "luminosity" and "intensity" in a way that was mainly distinguished by the fact that luminosity doesn't depend on distance while intensity falls off like distance squared. Brightness most likely is meant to also fall off like distance squared, but it might refer to a specific spectral band, presumably some visible band. The magnitude scale takes the luminosity or intensity in a given band, and converts it to a logarithmic scale, but it is intended to apply to old-time filters, which may be more narrow than the whole visible domain. Basically, in this day of CCDs it's an awkward and antiquated approach for talking about how detectable stars would be for some instrument, but it does let you use integers to talk about the detection limit of your instrument in some band. So it's still used. .