When you wish upon a star...

Luminosity and all that 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: Earth Apparent Mag. > Absolute Mag. 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 stellar mass determines lifetime behavior of star 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