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b  1 / d 2

II-2b. Magnitude 2015 (Main Ref.: Lecture notes; FK Sec.17-3). Lec 2. b  1 / d 2. 2b-(i). m. naked-eye. Therefore, six magnitudes must have ratios = 100 1/5 = 2.512 1 2.512 2.512 2 2.512 3 2.512 4 2.512 5

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b  1 / d 2

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  1. II-2b. Magnitude 2015 (Main Ref.: Lecture notes; FK Sec.17-3) Lec 2 b  1 / d2

  2. 2b-(i) m naked-eye

  3. 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.)

  4. 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

  5. Fig. II-6: Apparent Magnitudes

  6. 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)

  7. 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.

  8. EX 11

  9. 2b-(ii) Absolute Magnitude M • Absolute Magnitude M = m a star would have if it were located at 10 pc

  10. 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

  11. EX 12  Note: If we use the exact value of 1pc = 2.066 x 105 AU  get Msun = 4.8!

  12. 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

  13. 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

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