Luminosity & flux equations confusion

[Flucky]

Hi folks

First off I have only just figured out that v is used as bloody frequency in loads of astrophysics equations. Not fun.

I've got monochromatic flux as:

Fv = dE / dt·dA·dv

now I'm happy with this. But now the lecture notes I'm looking at describes monochromatic luminosity as "the energy emitted by the source in unit time, per unit wavelength" but then gives the equation as:

Lv = dE / dt·dv

so surely it should be ""the energy emitted by the source in unit time, per unit frequency"

BUT monochromatic means the energy at a given wavelength doesn't it, however there is no wavelength in the equation.

Could somebody please clearly state the definition and equation, saying what each letter in the equation represents, of monochromatic/bolometric flux/luminosity as I'm really getting stressed over it and can't revise anything else until I've got my head wrapped round it.

 

[phyzguy]

I think you're right, it should be per unit frequency - the definition you have given is inconsistent between the word and the equation. And, since the relation between wavelength and frequency is inverse, they will not be the same. Different sources use different definitions, so you need to make sure the definitions you are using are consistent (as you are doing). I strongly suggest Rybicki and Lightman, "Radiative Processes in Astrophysics" - the first few chapters spell these things out in careful detail.

 

[Flucky]

I think you're right, it should be per unit frequency - the definition you have given is inconsistent between the word and the equation. And, since the relation between wavelength and frequency is inverse, they will not be the same. Different sources use different definitions, so you need to make sure the definitions you are using are consistent (as you are doing). I strongly suggest Rybicki and Lightman, "Radiative Processes in Astrophysics" - the first few chapters spell these things out in careful detail.

Hi phyzguy thanks for replying.

Seems to be going for £88 on Amazon so I might be giving that a miss.

Am I right in saying the following:

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Monochromatic Flux is the energy falling on a unit area, per unit time, at a given frequency. As no light is emitted at a single frequency instead we use how much light is emitted in an infinitesimally small range of frequency, dv.

Fv = ΔE / Δt·ΔA·Δv

Bolometric Flux is the amount of energy across all frequencies.

F^bol = ∫^∞ Fv dv


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Monochromatic Luminosity is the energy emitted by the source in unit time, per unit frequency.

Lv = ΔE / Δt·Δv

Bolometric Luminosity is the amount of energy across all frequencies.

L^bol = ∫^∞ Lv dv

 

[SteamKing]

The 'v' should be the lower case Greek letter 'nu'. What did you think it meant before you found out it was frequency?

 

[Flucky]

The 'v' should be the lower case Greek letter 'nu'. What did you think it meant before you found out it was frequency?

I didn't really think about it so automatically assumed "ah it must be velocity"

 

[phyzguy]

I think what you have is correct.