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The Magnitude scale Relative brightness on a backwards (!) log scale. Dates to Hipparchus. E.g., apparent relative luminosities of stars a & b are given by, la = 100(m b −m a )/ 5 = 10 0.4(m b −m a ) = 2.512 ×10 m b −m a , lb Or, mb - ma = 2.5 log10(la/lb). € A difference of 5 mags. = factor of 100 in luminosity. mV(sun) ≈ -26.7. Absolute Magnitude and Distance Modulus To factor out the distance effect in apparent magnitudes (m) we define the absolute magnitude M as - the magnitude a star would have if we put it at a standard distance of 10 pc. In terms of apparent luminosity l, and absolute luminosity L, we have, 2 L d = . l 10 pc since luminosity falls off as the inverse square of the distance. Then in magnitudes € m - M = 2.5 log(L/l) = 5 log(d/10 pc) = 5 log(d) - 5. or, M = m + 5 - 5 log(d(pc)). MV (sun) = 4.8. The quantity m-M (generally > 0) is called the distance modulus. E.g., m - M = 0 --> d = 10 pc. 5 100 pc. 10 1000 pc. Thus, if we can determine L or M independently, and measure m, we get the distance. In practice we also have to worry about the effects of dust absorption.