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1 Magnitude Scale • Method of scaling the apparent brightness and luminosity of stars. • Uses logarithms to create a scale that handles a wide range of brightness 2 Apparent Magnitude • Measure of the brightness of a star as seen from the Earth (equivalent of apparent brightness). • Denoted by m • The smaller the number, the brighter the star –m=0 –m=6 one of the brightest stars in the sky eye can barely detect star in the sky • Some stars or planets have negative magnitudes -- these are even brighter than m = 0. • With telescopes, we can detect stars as dim as m = 27! 3 Absolute Magnitude • Measure of the brightness of a star if observed from 10 parsecs away (equivalent of luminosity) • Denoted by M or MV • Absolute magnitude and apparent magnitude are the same at a distance of 10 parsecs. 4 Magnitude Formula m M 5 log( d ) 5 m = apparent magnitude M = absolute magnitude d 10 m M 5 5 d 10 10 - or - m M 5 d = distance in parsecs (1 parsec = 3.26 light years) Use this equation to find the distance to an object if you know the apparent and absolute magnitudes Color Index – Another way to describe temperature 5 Note: small or negative numbers = brighter Apparent Magnitude (bright) −5 U B V 0 5 • Measure the apparent magnitude at two different wavelengths bands (usually B and V) – U = low ultraviolet – B = blue – V = red 10 15 (dim) (short) Wavelength () (long) Color Index – Another way to describe temperature 6 Note: small or negative numbers = brighter Apparent Magnitude (bright) −5 U B V 0 • Color Index = B − V – The smaller (or more negative) the number, the more blue (and hot) the star. 5 10 15 (dim) (short) Wavelength () (long) Color Index – Another way to describe temperature 7 B − V = negative (blue, hot star) Apparent Magnitude (bright) −5 U B V B − V ≈0 (yellow, medium temp star) B − V = positive (cool, red star) 0 5 10 15 (dim) (short) Wavelength () (long) 8 Spectroscopic Parallax • If apparent magnitude (apparent brightness) and absolute magnitude (luminosity) are known distance can be determined. • Difficult to accurately measure luminosity for one star – Use spectra to get spectral type and class • Can use a cluster of stars • Distance to the cluster can be determined by comparing the HR diagram of the cluster with a template HR diagram 9 Spectroscopic Parallax Observations Template 0 -9 9 0 18 9 27 18 -0.4 hot 0.8 B-V 2.0 cooler d 10 10 -0.4 hot ( m M ) / 5 0.8 B-V 2.0 cooler