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When you wish upon a star... shows what a dweeb you really are ..! Luminosity and all that •Luminosity •Inverse square law •Magnitudes •Distance, temperature, composition .. •H-R diagram Getting our bearings Luminosity • Observing apparent brightness. • Brightness is the amount of energy striking per unit area of the human eye or a detector. • The amount we receive is affected by distance according to the inverse square law. Apparent brightness (energy flux) Luminosity/distance2 Luminosity and magnitudes • Apparent brightness. • Absolute brightness. • Apparent magnitude • Absolute magnitude To compare intrinsic or absolute properties of stars, use a standard distance of 10 pc. Lets make this difficult (actually the ancient Greeks are to blame) • Around second century B.C.E., Hipparchus scaled naked eye stars into a ranking of 1 to 6 ( brightest to least bright). • 1 – 6 range spans a factor of 100 in apparent brightness. ( a 1st magnitude star is 100 X brighter than a 6th magnitude star). • The physiology of the human eye dictates that each magnitude change of 1 corresponds to a change of 2.5 in apparent brightness. • Combining both concepts: 2.55 100 A 1 st magnitude star is approximately 100 X brighter than a 6 th magnitude star But what does it mean? • Well, lets look at the 10 pc thing: 10 pc Apparent Mag. > Absolute Mag. Earth Apparent Mag. < Absolute Mag. Apparent brightness vs. absolute brightness? Oh ! Brightness decreases this way ! Graph of apparent magnitudes of some common things in the sky . Brightness increases this way ! Luminosity and magnitude • We know from Apparent brightness luminosity/distance2 And 2.55 100 -> 1001/5 2.5. So for every magnitude change we see with our eyes the brightness changes 10X. IDEA! We can build a chart to relate luminosity to magnitudes: luminosity magnitude Recipe: brightness to luminosity • To determine a star’s luminosity: • 1. Determine apparent brightness (use a chart or for a new star, measure amount of energy detected per unit time). • 2. Measure the star’s distance (parallax method for nearby stars). • 3. Use: apparent brightness ~ luminosity/ d2 Using our recipe for more stuff • Let m = apparent brightness • Use our recipe: luminosity = d2 m. • Star A: {d = 0.707 pc, m = 1}, Star B:{ d = 2.12 pc, m = 1}. • Find luminositys for Star A and Star B More luminosity & magnitude stuff Making things simpler • Scale luminosities to solar luminosity – this way we won’t have to deal with units • Let m – apparent magnitude, M – absolute magnitude. • Throw in the inverse square relationship and some math and…. Tah Dah!!! D = 10 pc x 10(m –M)/5 We have another formula for distance, D! Do we believe it! Lets look at an example. (alot like More Precisely ex., page 447) Luminosity, temperature, size …. • We know relationship between luminosity and magnitude (Table previous slide). • Using Wien’s Law: (peak emission) 1/temperature • And Stefan’s law: total energy emitted temperture4 Wien’s law: the hotter the object the bluer is its emission. Stefan’s law: energy emitted per unit area increases as the 4th power of the temperature….. Luminosity radius2 * temperture4 Stellar size! More tools from what we know • Knowledge of color/temperature relationship and now, luminosity/radius/tem -perature relationship combined with emission/absorption spectrum we get from certain stars, lets us classify our spectra (OBAFGKM) according to temperature. H-R Diagram Sizes, Temperature, Luminosities And: Stellar Lifetime: Star life time ~ 1/(star mass)3 Features: 1. 2. 3. 4. H-R Diagram http://instruct1.cit.cornell.edu/courses/astro101/java/evolve/evolve.htm • stellar mass determines lifetime behavior of star With regards to mass, you may want to note size/masses of stars that spend: • all their lives on the main sequence • some of their lives on the main sequence • leave main sequence early