Chapter 4: Apparent Magnitude www.boyce-astro.org © BRIEF 2014 www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Overview: What do we mean by Apparent? An Apparent History Putting Math to Apparent Modern Magnitudes www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude QUESTION: When you hear the term something is “Apparent”…what does that mean to you? What is the opposite of “Apparent”? QUESTION: Looking at the picture below, how would you describe this scene to someone? How would you classify the stars? Most ways of counting and measuring things work logically. Ex. When the thing that you're measuring increases, the number gets bigger. However, Astronomy likes to do things differently www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Apparent Brightness: Historical Origin: Ancient Greeks were the 1st great astronomers. In 129 B.C. Hipparchus began to rank the visible stars Called the brightest: “Of the first magnitude” Next brightest: “Of the second magnitude”, and so on to the 6th Mag Around A.D. 140 Claudius Ptolemy added the words "greater" or "smaller" to distinguish between stars within a magnitude class Today this magnitude is formally known as apparent magnitude and is designated by the letter m (lowercase m). Stayed unchanged for the next 1,400 years until Galileo Discovered that stars existed that were fainter than Ptolemy's sixth magnitude "The largest of these . . . we may designate as of the seventh magnitude." Thus the magnitude scale became open-ended As telescopes got bigger and better, astronomers kept adding more magnitudes to the bottom of the scale Hubble Space Telescope has seen objects as faint as 31st magnitude. Your eye can only see to the 6th. www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Apparent Brightness: A 1st-magnitude star shines with about 100 times the light of a 6th-magnitude star. (NOTE: We’ll do the math soon.) 1856 the Oxford astronomer Norman R. Pogson proposed that a difference of five magnitudes be exactly defined as a brightness ratio of 100 to 1. This convenient rule was quickly adopted. One magnitude corresponds to a brightness difference of exactly the fifth root of 100, or very close to 2.512 Consequently, a one-magnitude difference is equal to a brightness change of 2.512 times (2.5125 = 100). www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Apparent magnitude: Practical Application What we know: The difference between two different magnitudes is……What? 2.512 Problem: The magnitude of #1 is 2.0 The magnitude of #2 is 5.0 Question: Which one is brighter? How many more times is it brighter? How do you solve this? How to solve: Take the difference in magnitudes between two stars Raise 2.512 to that power (the Δ𝑚) Example: How many magnitudes brighter is #1 than #2? 3 magnitudes star: 5 - 2 = 3 Take 2.512 to that power: 2.5123 = 15.85 times. #1 is almost 16 times brighter than #2! #1 #2 www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Modern Magnitudes: QUESTION: What about objects brighter than 1st Magnitude? Negative Magnitudes were developed Objects with negative magnitude appear brighter than objects with positive apparent magnitude. The Sun appears much brighter than any other star in the sky. It has an (apparent) magnitude of -26.73. The full moon, at its brightest, has an (apparent) magnitude of -12.6 Venus can be as bright as -4.4. Pasachoff_Fig. 4.15 © Cambridge University Press 2013 www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Extra Credit: QUESTION: How many more times brighter is the Sun than the faintest object observable with Hubble? Pasachoff_Fig. 4.15 © Cambridge University Press 2013 www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Questions? www.boyce-astro.org © BRIEF 2014
Stellar Brightness: Magnitude Example: Naked-Eye Stars Hipparchus & Ptolemy Stars Galileo www.boyce-astro.org © BRIEF 2014