Luminousity

What is it?
The total amount of energy given out by a star oer second - The power output, is a star's Luminousity. This luminousity measured accross all the wavelengths (remember e = hv) then it is called Bolometric Luminousity. Luminousity can also be measured over visible wavelengths alone or over x-ray wavelength.

How to measure it?
An early method of measuring the luminosity(L) of the sun was to put an oil drop on a piece of paper, so that it was translucent and then hold it to the sun. Also a light source of known Wattage is placed on the other side, and it is set at a distance from the light source so that the oil droplet and the surrounding paper are observed to have the same brightness. Then the flux from the sun is roughly equal to the flux from the light source.

F = L/4pd²

Knowing the ratio between the distances, can tell us how much brighter the sun actually is than the light source. The sophistication of measurement has increased since then but hte principle is the same. Greater the distance from the source, the flus decreases as it spreads over a larger area. So if one knows the distance and the flux, you can determine the luminousity of the star.

Our Sun's luminousity (L _sol) is 3.84 × 10²⁶ W. Any star's luminousity is generally specified with respect to that of the sun.

Dependent factors:
Temperature and Size determine the Luminousity of the star.

A black body radiates power based on its Temperature. Hotter the body, higher the power radiated. Temperature and power are related as below.

P proportional to sT⁴

If two stars have the same temperature but one of the stars is bigger, then it surely is more Luminous than the other. The surface area increses, increasing the Flux. Assuming spherical surface for stars we get,

L proportional to 4pr²

So together L proportional to 4pr²sT⁴  where is Boltzmann's constant ( 5.67 × 10^-8 W m^-2).