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3 SPECTRAL LINES IN STARS

somewhere between giants and supergiants. Supergiants are luminosity class I. We further divide supergiants into Ia and lb, with Ia being larger. When we look at the spectral lines from a star we can actually tell something about the size. Stars of different sizes will have different accelerations of gravity near their surface. The surface gravity affects the detailed appearance of certain spectral lines.

There are also stars that appear below the main sequence. These stars are typically 10 mag fainter than main sequence stars of the same temperature. They are clearly much smaller than main sequence stars. Since most of these are in the middle spectral types, and therefore appear white, we refer to them as white dwarfs. (Do not confuse dwarfs, which are main sequence stars, with white dwarfs, which are much smaller than ordinary dwarfs.)

2.0 Example 3.3 Size of white dwarfs B- V [mag] Suppose that some white dwarf has the same

(a) spectral type as the Sun, but has an absolute mag­

Temperature (K)

SO,OOO 10,000 5,000 JSOO

----Ia

<II Supergiants ,.,.

'C

E ·= c.o '" ~

r oo2 = 3

-; = "' ;> +S

:;· 0

"' ~· <II :; 0 "' .Q

+10 <

~ +IS

'

V> 0 iii .,

10- 2

w-4

OS 80 AO FO GO KO

Spectral Type

(b)

1~111 .. (a) HR diagram for over 40 000 nearby stars

studied by the Hipparcos satellite, designed to measure

trigonometric parallaxes , so distances are known for all of

these stars. In this figure, the color represents the number of

stars in each category, with red being the most and blue

being the least. (b) A schematic HR diagram, showing the

main features of the actual diagrams. Luminosity classes are

indicated by roman numerals. [(a) Michael Perryman, ESA.

Hipparcos]

nitude that is 10 mag fainter than the Sun. What is the ratio of the radius of the white dwarf, Rwct • to that of the Sun, R0 ?

SOLUTION

The luminosity is proportional to the square of the radius, so

We use equation (2.2) to find the luminosity ratio for a 10 mag difference:

Lwct/ Lo = lO(M - Mw,)/2.5

= 10- 4

Combining these two results to find the ratio of the radii yields

Rwct/ R . = (Lwct/ l o ) 1 '2

= (10 - 4)1 /2

= 10- 2

The radius of a white dwarf is 1% of the radius of the Sun!

For any cluster for which we plot an HR dia­gram , we only know the apparent magnitudes ,

,

~~~ ,

P),J $~ oc~y tL ~ •

tv..,.. ~I ~ CfoCCI'.)NAcIfJ,ko­o ~l~ cJU~

~ tu"C.,/oud k.. 64 C41V~.«,. ta.'«' .s~ ~ NA~I: ~ ~ udt.s

,

Temperature (K)

5,00050,000 10,000

N -5

\00 If\S

4)

~ 0E ·2 ~ e i; :::l III.s:

+5 ~ :::l (5 III

.&J

<

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~ Ia Supergiants

Ib

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~III __~_ RReedd Itgiiaanntt:s

10·

o .r ..J

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IV 0., MGJSpectral type

(b)

Figure 3.11 (a) H-R diagram. (b) Schematic H-R diagram. Luminosity classes are indicated by Roman numerals.

,

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