# Luminosity & flux equations confusion

• Flucky
In summary: The 'v' should be the lower case Greek letter 'nu'. What did you think it meant before you found out it was frequency?In summary, the lecture notes say monochromatic flux is the energy emitted by the source in unit time, per unit wavelength, while bolometric flux is the amount of energy across all frequencies.
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.

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.

phyzguy said:
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.

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

Am I right in saying the following:

---------------------------------------

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.

Fbol = ∫ Fv dv

---------------------------------------

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.

Lbol = ∫ Lv dv

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

SteamKing said:
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"

I think what you have is correct.

## 1. What is luminosity and how is it different from flux?

Luminosity is a measure of the total amount of energy that a star or other celestial object emits per unit time. It is an intrinsic property of the object and is independent of distance. Flux, on the other hand, is a measure of the amount of energy that reaches a given area per unit time. It is dependent on both the luminosity of the object and the distance from the object.

## 2. What is the equation for calculating luminosity?

The equation for calculating luminosity is L = 4πR2σT4, where L is luminosity, R is the radius of the object, σ is the Stefan-Boltzmann constant, and T is the temperature of the object in Kelvin.

## 3. How is flux related to luminosity?

Flux is directly proportional to luminosity and inversely proportional to the square of the distance from the object. This means that as the luminosity of an object increases, the flux also increases. However, as the distance from the object increases, the flux decreases.

## 4. Can luminosity and flux be measured for all celestial objects?

Yes, luminosity and flux can be measured for all celestial objects as long as we have accurate measurements of their distance and temperature. However, for some objects, such as black holes, it may be more challenging to accurately measure these properties.

## 5. How can understanding luminosity and flux equations help us in studying the universe?

Understanding luminosity and flux equations allows us to measure the properties of celestial objects, such as stars and galaxies. By studying these objects, we can gain a better understanding of the universe and its evolution. Additionally, these equations help us to calculate distances to celestial objects and analyze their energy output, which can provide valuable insights into the nature of the universe.

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