II2 b Magnitude Main Ref Lecture notes FK

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

2 b-(i) m naked-eye 2

Therefore, six magnitudes must have ratios = 1001/5 = 2. 512 1 2. 5122 2. 5123 2. 5124 2. 5125 1 2. 512 6. 310 15. 851 39. 818 1/5 = 100. 023 Note” the smaller the magnitude, the brighter the star! Table II-1 • 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. ) 3

Astronomers often use the magnitude scale to 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 4

Fig. II-6: Apparent Magnitudes 5

Math Expression m = m 2 – m 1 = 2. 5 log ( b 1 / b 2 ) Eqn(6) See examples in FK Box 17 -3. ********************************** EX 8: Venus m 1 = 4; dimmest star we can see m 2 = + 6. How many times brighter is Venus than the faintest star w can see? Ans: 10, 000 times brighter (See class notes, also FK Box 17 -3, Example 1) 6

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) EXEX 1010 (#) 2. 8 7 (#) Note: If use m = 1. 12, we get 2. 8 times as bright.

EX 11 8

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

Math Expression m – M = 2. 5 log ( b. M / bm ) Eqn(7) m – M = 5 log ( dm / d. M ) Eqn(8 a) d. M = 10 pc; dm = true distance m – M = 5 log d (pc) – 5 Eqn(8 b) (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 +20 d = 1. 6 10 5 10

EX 12 Note: If we use the exact value of 1 pc = 2. 066 x 105 AU get Msun = 4. 8! 11

EX 13: A Star with m = +6 (faintest we can see by unadied eyes) at d = 20 pc. 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) 12

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 13 luminosity