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## Stars have Unique Properties

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**Stars have Unique Properties**Note the different colors of stars in this portion of a Hubble Space Telescope photo above. What do these colors mean? What about their brightness? Does their image size mean anything? How do astronomers known their distance? There’s more than meets the eye!**The Magnitude Scale**• This is the first step in determining what properties stars have…so lets review: • The first astronomers (Greeks) developed the magnitude system • Magnitude is proportional to size on a photograph, or measured with a photometer**Magnitude Vs Intensity**Intensity is related to magnitude: definition of intensity is energy/second reaching a unit area at the observer “Solar Constant” = 1500 Watts/sq. Meter--this is the amount of energy reaching the earth’s surface per second, per square meter…**Magnitude vs. Intensity: nuts and bolts**Magnitude is a convenient measure of intensity! A Magnitude difference of 5 = Intensity ratio of 100. • if MA- MB= 5 (Where M represents the magnitude of the star) , then • IB/IA = 100 (where I represents Intensity) Intensity = IA Magnitude = MA Intensity = IB Magnitude =MB**Intensity--continued**• Only about half of this power reaches the earth's surface, meaning that a one square meter solar panel that is 15% efficient can generate about 100 watts while the sun is shining…that is enough to light six compact florescent bulbs • Intensity can be measured with a solar cell--the current coming out is directly proportional to the intensity.**Absolute Magnitude vs. apparent magnitude**apparent Magnitude is a measure of intensity, which is determined by both distance and intrinsic brightness. Intensity can be the same for a flashlight close up, or a car headlight far away. If all objects were at same distance,however, magnitude would measure Luminosity (intrinsic brightness) Luminosity = Total energy output of object. The Sun’s luminosity is about 1025 watts (that is a lot of 100 watt light bulbs!)**Absolute Magnitude--Continued**• Where apparent magnitude is a measure of the intensity of light reaching the earth, Absolute magnitude is a measure of how much light the object is putting out. • So...Absolute Magnitude is a measure of objects Luminosity • By definition, Absolute Magnitude = apparent magnitude if object was 10 Parsecs away (32.6 light years) • Read on or see text for definition of the Parsec (by use of the Parallax method).**The Weird Equation relating apparent and absolute magnitude**m = apparent magnitude M = absolute Magnitude D = distance to Star, so the weird equation is……. M-m = -5log(d) + 5 So what good is it? Answer: If you know both M and m, you can find distance. If you know m and d, you can find M.**The Weird Equation…continued**• I could explain how and why this works in detail, but You might drop the class. • Try putting M = m…you get d = 10 parsecs …or take my word for it! • This also means that if you know the distance to a star (d), and the apparent magnitude (which you can measure by the size of an image on a photograph), then you can use this equation to find distance... • Example if you are intersted. Star A has a magnitude of 5 and an absolte magnitude of 12. Thus: 12 - 5 = -5log(d)+ 5 • Solving: log(d) = 7 - 5 = 2, • d= 10^2 = 100 parsecs . Likewise, if you knew the star was 100 parsecs away, and had an aparent magnitude of 5 you would solve for an absolute magnitude of the star = 12!**Luminosity of Nearby Stars**This chart is a plot of number of stars as a function of luminosity. Note that most stars are less luminous than our sun But a few are much more luminous….imagine a star Putting out 100 times the energy of our sun…but they are out there!**Astronomers have a “distance Ladder”**• Different distances require different methods. • Parallax method works to 300pc--beyond this, the parallax angle is too small to measure accurately • Beyond 300 parsecs we need to use the “weird equation”--i.e. we need to know the absolute magnitude, and apparent magnitude. The equation then allows us to calculate distance.**The Distance Ladder**• But…how do we know the absolute magnitude for stars when we don’t know the distance? • …hmmm…not an easy question! • Beyond 300 parsecs we use the spectroscopic parallax method (otherwise known as the the “weird equation method). • This works as long as we can obtain spectra from individual stars**Parallax method works out to 300 PC**• 1 PC is the distance of an object with parallax angle of 1” • 1pc =3.26 yr. • nearest star is 4 lyrs away, so its parallax angle is < 1’’ and its angle is the largest of any star. • Since the parallax method uses the distance from the Earth to Sun as a baseline, we need to know the exact size of an astronomical unit in meters**Parallax Method--Continued**• We do this by using radar imaging --bouncing radio waves off of Venus and timing how long they take to come back • Since Venus is .7 Au from the Sun, and radio waves travel at the speed of light, we can calculate the distance from the time. • If we know how far Venus is from us, we know how far we are from the Sun!**Spectroscopic parallax**• Since there are thousands of stars within 300 pc of the Earth, we measure the distance and apparent magnitude for all them via the parallax method and a photometer (or taking a photograph and looking at the size of the image). • Using the “weird equation” we can calculate the absolute magnitude for all these stars**Spectroscopic Parallax--continued**• We can then make up a chart listing the absolute magnitude for all these stars and everything else we know about them, including spectral type. Absolute Magnitude**More on spectroscopic parallax...**We find that there is a direct correlation between absolute magnitude and spectral type…in other words Stars of the Spectral type have the same Absolute magnitude!**Normal vs. “Strange” Stars**• This relationship is true for “normal” or Main Sequence Stars! • You can see this by the straight line relationship on the “Hertzsprung Russell diagram below: For more info: http://www.enchantedlearning.com/subjects/astronomy/stars/startypes.shtml**The HR Diagram**• This is primary tool for astronomers • They use to find distances, temperatures, mass, and even age of stars and star clusters • Click on the link below to see HR diagram from the: Astronomy picture of the Day