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Exam #1 is in class next monday 25 multiple-choice questions 50 minutes Similar to questions asked in class Review sheet to be posted this week. We will have two 1-hour review sessions Friday 5-6pm (with me) VanVleck B130 (here!) Today 6-7pm (with Ella) 3425 Sterling (the classroom where we had lecture on the very first day of class) Which property of a star would not change if we could observe it from twice as far away? a) Angular size b) Color c) Flux d) Parallax e) Proper Motion 1 Light and Distance • Brighter objects are not necessarily the closer objects – Comet Halley, to the upper left, is within our Solar System – The background stars are just as bright, but tens, hundreds or thousands of light years more distant • The total amount of energy a star emits to space is its luminosity, measured in Watts. • The amount of light reaching us from a star is its brightness The Inverse-Square Law • A star emits light in all directions, like a light bulb. We see the photons that are heading in our direction • As you move away from the star, fewer and fewer photons are heading directly for us, so the star seems to dim – its brightness decreases. • The brightness decreases with the square of the distance from the star – If you move twice as far from the star, the brightness goes down by a factor of 22, or 4! • Luminosity stays the same – the total number of photons leaving a sphere surrounding the star is constant. 2 You see this every day! • More distant streetlights appear dimmer than ones closer to us. • It works the same with stars! • If we know the total energy output of a star (luminosity), and we can count the number of photons we receive from that star (brightness), we can calculate its distance L d= 4!B • Some types of stars have a known luminosity, and we can use this standard candle to calculate the distance to the neighborhoods these stars live in. The Magnitude System • We can quantify the brightness of a star by assigning it an apparent magnitude – Brighter stars have lower magnitudes, possibly negative numbers – Dimmer stars have higher positive numbers • Differences in magnitudes correspond to ratios in brightness – Ex: One star of interest has a magnitude of 6 (dim), and another star has a magnitude of 1 (easily seen). The magnitude difference of 5 means that the brighter star is 100 times brighter than the dimmer star… 3 The Magnitude System • In 129BC, Hipparcos could see down to 6th magnitude. Today The Hipparcos sattelite can see down to 23rd magnitude = 10^9 times dimmer! • Hubble telescope can see 31st magnitude= 10^12 times dimmer! Absolute Magnitude • It is easier to compare two stars’ luminosities if they are at the same distance from the Sun • We can calculate how bright the stars would appear if they were all the same distance from us, say, 10 parsecs • The magnitude of a star “moved” to 10 parsecs from us is its absolute magnitude. 4 Stellar Surface Temperatures • Remember from Unit 23 that the peak wavelength emitted by stars shifts with the star’s surface temperatures – Hotter stars look blue – Cooler stars look red • We can use the star’s color to estimate its surface temperature – If a star emits most strongly in a wavelength λ (in nm), then its surface temperature (T) is: 2.9 #106 K " nm T= ! • This is Wien’s Law Measuring Temperature using Wein’s Law 2.9 #106 K " nm T= ! 5 The Stefan-Boltzmann Law flux = "T 4 Flux is energy / unit area Where, σ= 5.67×10− 8 W·m-2·K-4 L = flux • Area = "T 4 • 4 # r 2 • ! The Stefan-Boltzmann Law links a star’s temperature to the amount of light the ! star emits – Hotter stars emit more! – Larger stars emit more! • • A star’s luminosity is then related to both a star’s size and a star’s temperature We need an organizational tool to keep all of this straight… Two stars have the same surface temperature, but the radius of one is 100 times that of the other. How much more luminous is the larger star? a) 10 times more luminous. b) 100 times more luminous. c) 10,000 times more luminous. d) 100,000,000 times more luminous. e) The stars have the same more luminosity. 6 Photons in Stellar Atmospheres • • • Photons have a difficult time moving through a star’s atmosphere If the photon has the right energy, it will be absorbed by an atom and raise an electron to a higher energy level Creates absorption spectra, a unique “fingerprint” for the star’s composition. The strength of this spectra is determined by the star’s temperature. Classify: 1- variation in H line strengths…. “Spectral types” based on H lines strength: A B C D E F… 7 1901, Annie Jump Cannon > spectral classification Spectral Classification • Spectral classification system – Arranges star classifications by temperature • Hotter stars are O type • Cooler stars are M type • New Types: L and T – Cooler than M • From hottest to coldest, they are O-B-A-F-G-K-M – Mnemonics: “Oh, Be A Fine Girl/Guy, Kiss Me – Or: Only Bad Astronomers Forget Generally Known Mnemonics 8 A cool star that is very luminous must have : a) A small radius b) A large radius c) A small mass d) A great distance e) A low velocity How big are stars? How do we know? 9 Interferometry • Stars are simply too far away to easily measure their diameters! – Atmospheric blurring and telescope effects smear out the light • Can combine the light from two or more telescopes to pick out more detail – this is called interferometry – Two telescopes separated by a distance of 300 meters have almost the same resolution as a single telescope 300 m across! • Speckle interferometry uses multiple images form the same telescope to increase resolution Using eclipsing binary systems to measure stellar diameters 10