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

b 1 / d2

Lec 2

2

2b-(i) m

naked-eye

3

= 1001/5

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

•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

•EX 7 Modern Magnitude

(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

5Fig. II-6: Apparent Magnitudes

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Math Expression

m = m2 – m1 = 2.5 log ( b1 / b2 ) Eqn(6)

See examples in FK Box 17-3.

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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

(#)

(#) Note: If use m = 1.12, we get 2.8 times as bright.

EX 10

2.8

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.)

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Study more examples in FK Box 17-3.

Luminosity Function: The Population of Stars

(See FK pp 472-473)

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•Stars of relatively low luminosity are more common than more luminous stars•Our own Sun is a rather average star of intermediate luminosity

Fig. II-7: The Luminosity Function = FK Fig. 17-5