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This text explores the magnitude scale in astronomy, from naked-eye observations to absolute and apparent magnitudes. Learn how astronomers measure star brightness and compare it to familiar celestial objects like the Sun and Venus. Discover the math expressions behind magnitude calculations and delve into examples illustrating the concepts discussed. Dive into the fascinating world of magnitudes and luminosity functions in stellar populations with this educational resource.
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II-2b. Magnitude 2015 (Main Ref.: Lecture notes; FK Sec.17-3) Lec 2 b 1 / d2
2b-(i) m naked-eye
Therefore, six magnitudes must have ratios = 1001/5 = 2.512 1 2.512 2.5122 2.5123 2.5124 2.5125 1 2.512 6.310 15.851 39.818 100.023 Note” the smaller the magnitude, the brighter the star! Table II-1 = 1001/5 • EX 7 Modern Magnitude • Sun : 26.7 • Full Moon: 12.6 • Venus: 4.4 • Serius (brightest star): 1.4 • Pluto: +15.1 • Largest telescope: +21 • Hubble Space Telescope: +30 • (See Fig. II-5 for more details.)
Astronomers often use the magnitude scaleto denote brightness • The apparent magnitude scale is an alternative way to measure a star’s apparent brightness • The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 parsecs Fig. II-5: The Apparent Magnitude Scale
Math Expression m =m2 – m1 = 2.5 log ( b1 / b2 ) Eqn(6) See examples inFK Box 17-3. ******************************************************************* EX 8: Venus m1 = 4; dimmest star we can see m2 = + 6. How many times brighter is Venus than the faintest star we can see? Ans: 10,000 times brighter (See class notes, also FK Box 17-3, Example 1)
EX 9: RR Lyrae, variable: bpeak = 2 bmin. What is the magnitude change? Ans: 0.75 (See class notes, also FK Box 17-3, Example 2) EX 10 EX 10 (#) 2.8 (#) Note: If use m = 1.12, we get 2.8 times as bright.
2b-(ii) Absolute Magnitude M • Absolute Magnitude M = m a star would have if it were located at 10 pc
Math Expression m – M = 2.5 log ( bM / bm ) Eqn(7) m – M = 5 log ( dm / dM ) Eqn(8a) dM = 10 pc; dm = true distance m – M = 5 log d (pc) – 5 Eqn(8b) (See lecture notes for derivation.) Distance Modulus DM = m – M Eqn(9) See FK Box 17-3 for DM(=m – M) vs d(pc) . e.g.,DM = 4 d = 1.6 +20 105
EX 12 Note: If we use the exact value of 1pc = 2.066 x 105 AU get Msun = 4.8!
EX 13: A Star with m = +6 (faintest we can see by unadied eyes) at d = 20pc. What is the absolute magnitude? Ans: M = + 4.5(See class notes.) ************************************************************** EX 14: Suppose we are at 100 pc away from Sun. Can we still see Sun with naked eyes? What is m of the sun then? Note: Msun = 4.8 (see Ex 12). Ans: No, too faint to be seen. Reason: m = 9.8 > 6 (See class notes and FK Box 17-3, Example 4.) ********************************************************************* Study more examples in FK Box 17-3. Luminosity Function: The Population of Stars (See FK pp 472-473) #/vol M
Fig. II-7: The Luminosity Function = FK Fig. 17-5 • Stars of relatively low luminosity are more common than more luminous stars • Our own Sun is a rather average star of intermediate luminosity