Flux is a term used to describe the brightness of a star and is a measure of the energy from an object per unit area over time. Flux calculations are used to calculate luminosity, a more meaningful representation of a stars brightness.

The Inverse Square Law

Flux (F) is scientifically defined as "the total flow of light energy perpendicularly crossing a unit area per unit time". Flux has units of J s^{–1} m^{–2} or W ^{–2} (that's Joules per second per metre squared, or simply Watts per second)

In the article about the magnitude scale we saw that Pogson devised a scale whereby a 1st magnitude star is 100 times brighter than a 5th magnitude star. This logarithmic scale states that a 1st magnitude star is 2.512 times brighter than a 2nd, which is 2.512 times brighter than a 3rd and so on...

We can use this constant ratio per magnitude to obtain a formula for the ratio of fluxes. Consider two stars that have apparent magnitudes m and n and measured fluxes of F_{m} and F_{n}, the ratio of the fluxes is given by:

Equation 18 - Ratio of Fluxes

If one star is 6th magnitude (n = 6) and another star is 1st magnitude (m = 1) then the magnitude difference is given by (n–m) = 6–1 = 5. We can use Equation 18 to calculate the ratio of these fluxes.

Equation 19 - Ratio of Fluxes

We can see that this equation has shown that a difference in 5 magnitudes affects magnitude by a factor of 100 as per Pogson's rule. We can further reinforce this relationship between flux and magnitude by showing that the magnitude difference between two objects can be expressed in terms of the logarithm of the flux ratio. This form is known as Pogson's relation and one form or another one of the most useful equations in the astronomers toolbox.

Equation 20 - Pogsons Relation

We will see this equation again when we look in more detail at the magnitude scale.

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Tim is a professional software engineer, designer, photographer and astronomer from the United Kingdom. You can follow him on Twitter to get the latest updates.

This really helps. Thanks