The Magnitude System of Brightness

• We distinguish between intrinsic luminosity the brightness of a star due to the amount of energy that it radiates, and apparent luminosity, how bright it appears from Earth (at a given distance). The brightest stars in the skies above are either intrinsically bright, pumping out lots of photons, or those which merely appear bright because they lie closest to Earth.

• We can measure and compare the intrinsic and apparent brightnesses of stars using the magnitude system, a logarithmic system. A change of one in magnitude corresponds to a factor of roughly 2.5 in brightness.

• First-magnitude stars are those which appear the brightest from Earth, second-magnitude star are a little fainter, and sixth-magnitude stars are the faintest ones that can be seen in a dark sky by the naked eye. Stars with greater than sixth-magnitude can only be seen with the aid of a telescope.

• If we compare the amount of energy being produced, and sent to Earth, by two stars, we can compute their difference in magnitudes. Remember that the amount of energy seen from a star at Earth is a combination of the amount of energy it outputs and how far it lies from Earth.
  and so

• How much fainter is a sixth-magnitude star than a first-magnitude star?
  
  The faintest star you can pick out by eye is roughly one-hundred times fainter than the brightest star you can see.

• Magnitudes are typically measured at certain wavelengths, so a B (for blue) magnitude represents how bright a star appears at 4000 Angstroms, in blue colors, and a V (for visual) magnitude represents how bright a star appears at 5000 Angstroms in green colors (the center of the visual spectrum). You can also measure how bright a star is at ultraviolet or infrared wavelengths, for example, at wavelengths where our eyes are not sensitive.

• We can compute colors for stars by comparing how bright they appear at different wavelengths. For example, the B–V color of a star is the difference between its magnitude measured at blue (B) and at visual (V) wavelengths. Because less light translates to a larger magnitude value, for B–V colors a negative value means that the blue magnitude is a smaller number, and thus that the star is brighter at blue than at visual wavelengths. We call the stars with the smallest B–V color "blue", and those with the largest B–V magnitudes "red".
  

• The following table shows examples of star that are brighter, or fainter, than the Sun, and bluer, or redder, than the Sun, all seen from a distance of just under 500 light-years. At this distance, the Sun would have a B magnitude of 14.86 and a V magnitude of 14.20, with a B–V color of 0.66. Try to connect the visual appearance of each star with the listed B and V magnitude and the B–V color. Roughly how bright is the brightest star shown, compared to the faintest star shown?

  	Blue			Red
  Bright	B = 9.93	B = 11.54	B = 14.31	B = 13.73	B = 13.24	B = 11.43
  	V = 10.03	V = 11.33	V = 13.80	V = 12.94	V = 12.41	V = 10.48
  	B–V = -0.10	B–V = 0.21	B–V = 0.51	B–V = 0.79	B–V = 0.83	B–V = 0.95
  Faint	B = 15.07	B = 15.25	B = 15.54	B = 16.08	B = 16.23	B = 16.37
  	V = 14.49	V = 14.65	V = 14.92	V = 15.40	V = 15.52	V = 15.54
  	B–V = 0.58	B–V = 0.60	B–V = 0.62	B–V = 0.68	B–V = 0.71	B–V = 0.83
  [Laugalys et al. 2004; Robert Lupton and the Sloan Digital Sky Survey]

• Two stars of the same intrinsic luminosity (absolute magnitude) which lie at the same distance from Earth will have the same apparent magnitude. The difference between absolute and apparent magnitude is the same for all stars which lie at the same distance from Earth – we can call this value the distance modulus.