Brightnesses

A star's appearance in the sky depends on how much light it produces, and how far it is from us. The amount of light it produces is referred to in many ways: luminosity, total energy output, intensity, intrinsic luminosity, actual brightness, absolute magnitude, and M, among others. The appearance in the sky is called apparent brightness or, most commonly, apparent magnitude, indicated by m. "Magnitude" in astronomy is a relic of the original star catalog compiled by the classical Greek astronomer Hipparchus. He divided all the stars into six categories according to how bright they were - apparent brightness of course since he didn't know distances. The brightest were called 'first magnitude', the next 'second magnitude', the dimmest 'sixth.' This usage is still with us. The system has been expanded to accommodate the stars revealed by telescopes, so that the dimmest objects we can detect now are about magnitude 30 or so. A star 5 magnitudes brighter than another is producing 100 times as much energy. (Hipparchus didn't know that the range of visible stars' energy outputs was this nice round number, 100, but it makes some magnitude arithmetic simpler.)

To compare intrinsic brightnesses the artifice of imagining all stars to be the same distance from earth is used. The magnitude a star would have if it were at the (conventional, arbitrary) distance of 10 parsecs is called its absolute magnitude and is universally denoted by M. ( Don't confuse it with "mass".) M can be found if m and the distance are known. More generally, if any two of the three quantities m, M and distance are known, the third may be found from them. (I will write this (m,D) $\rightarrow$ M or (M,m) $\rightarrow$ D and refer to it often.)

Measured brightness depends on the technique used. The simplest example is the difference between photographic and visual magnitudes. Common photographic film is less sensitive to red light than it is to the rest of the visible spectrum. So a star which emits most of its light in the red part of the spectrum will appear dim in photos but brighter, compared to neighboring stars, when seen directly with the eye. This effect is commonly used to determine the color of a star and hence its temperature: The star's m is measured when seen through two different filters. The difference between the two m's (one filter simulates the eye and is called 'V', the other is blue colored and called 'B') is m_B - m_V and is called the 'B minus V color index' or simply 'B minus V' or 'the color index' or the CI. Notice that for any individual star m_B - m_V is the same as M_B - M_V .