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Star Brightness and Colour

Stars vary enormously in their brightness. As a general rule, the bigger they are, the brighter they are.  The apparent  brightness of an object varies with distance - ie, if you stand 1 m from a 100 W bulb it is very bright. Stand 10 m away, and it looks much dimmer. If you are on earth, the sun looks brighter than it does from Mars, or from Pluto! 

Astronomers chose a standard reference distance for measuring the brightness of stars -- a distance of 10 parsecs, which is about 32.6 light years. The absolute brightness of a sun is the brightness that star would appear to an observer, if that observer were 10 parsecs away.

Brightness can be expressed in terms of how many times brighter it is than our sun, or in a rather obscure measure called visual magnitude. This system is funny, in that a bigger number means a dimmer star. Magnitude works like this: each increase of 1 in magnitude is equal to a decrease in brightness of about 2.5 (actually 2.512). A star of magnitude three is 2.5 times dimmer than a star of magnitude two. Conversion tables are provided below so you don't have to actually do the calculations.

 

mag

x sun

 

 

x sun

mag

-10

8.48E+05

 

 

100000

-7.68

-9

3.37E+05

 

 

50000

-6.93

-8

1.34E+05

 

 

10000

-5.18

-7

5.35E+04

 

 

5000

-4.43

-6

2.13E+04

 

 

1000

-2.68

-5

8.48E+03

 

 

500

-1.93

-4

3.37E+03

 

 

100

-0.18

-3

1.34E+03

 

 

50

0.57

-2

5.35E+02

 

 

10

2.32

-1

2.13E+02

 

 

5

3.07

0

8.47E+01

 

 

1

4.82

1

3.37E+01

 

 

0.5

5.57

2

1.34E+01

 

 

0.1

7.32

3

5.35E+00

 

 

0.05

8.07

4

2.13E+00

 

 

0.01

9.82

5

8.47E-01

 

 

0.005

10.57

6

3.37E-01

 

 

0.001

12.32

7

1.34E-01

 

 

0.0005

13.07

8

5.34E-02

 

 

0.0001

14.82

9

2.13E-02

 

 

0.00005

15.57

10

8.47E-03

 

 

0.00001

17.32

11

3.37E-03

 

 

 

 

12

1.34E-03

 

 

 

 

 

 

The surface temperature of a star affects the colour of the star, as well as just the brightness. A table of colour and classification is also provided.

 

T (K)

colour

Spectral Type

>27000

Blue - white

O

27000-11000

Blue - white

B

11000-7200

White

A

7200-6000

yellow-white

F

6000-5100

yellow

G

5100-3700

orange

K

<3700

red

M

 

Our sun has a surface temperature of about 6000 Kelvin, and is a yellow type G star. Ou sun, if viewed from a distance of 10 parsecs would have a visual magnitude of 4.8. As a reference, a star of magnitude 4.8 is not visible from even the suburbs; you need really dark skies. In other words, almost every star you can see in the sky from the city is brighter than the sun!

Now the trouble is, if a star looks dimmer when it is farther away, and brighter when it is close, how can we tell just how far away it is -- in order to determine how bright it is?

There are two main methods for determining distance of stars within our galaxy -
Parallax, and the Hertzprung-Russel diagram.

Parallax

Hold a pen or pencil at arm's length, close one eye, and look at your pen (or pencil) with a distant background. Move your head slightly, and you will see the pen shift its position relative to the background. This is parallax. The Earth moves around the sun such that it changes position (ie opposite sides of the sun) throughout the year. Even though this motion is small compared to stellar distances, we can observe the slight parallax of nearby stars (up to a few tens of light years) relative to distant objects (stars or galaxies we know to be very distant) and judge their distance with great accuracy.

Armed with this information, astronomers were able to plot data on these nearby stars. Two of these astronomers were Ejnar Hertzsprung and Henry Norris Russel. They plotted luminosity of stars versus surface temperature (and thus colour). The resulting diagram, named for these two astronomers, gives interesting results:

Herzsprung-Russell diagram for 300 bright stars as seen from Earth

H-R_plot.PNG

If we colour code the diagram, and put more information on the axes, the diagram makes a bit more sense. The following diagram is an approximation of an H-R diagram that might be representative of most of the stars in our region of space:

H-R diagram.PNG

The curve of stars marked A is composed of stars in their main sequence, ie hydrogen fusing stage. The stars marked B are red giants - small and mid-sized stars that have "puffed up" outer envelopes, and helium-fusing cores. The stars marked D are white dwarfs, the naked helium fusing cores that remain after the outer envelope of small to mid-sized stars has been ejected as a planetary nebula.  The stars marked C are supergiants - large stars that have left the main sequence, and are fusing helium and heavier elements. When these stars begin fusing iron, they will undergo cataclysmic core collapse, and eject the shell in a Type II supernova, leaving a neutron star or a black hole.

The real power of the Hertzsprung-Russell diagram is that it can be used to determine the distance to a star based solely on its colour! If, for example, you see a moderately distant star that is white with a surface temperature of about 8000K, we know by the H-R diagram that that star is around 10 x brighter than the sun, in absolute brightness. By how bright it appears to us, we can determine how far away it is.  

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