Classification of Stars By Luminosity

Apparent Magnitude

Hipparchus of Rhodes (aound 160 BC)

Developed a system to compare the apparent brightness of stars in the sky with which he recorded the relative brightness of the stars in a catalogue listing 850 stars.

He called the brightest stars in the sky first magnitude and the dimmest visible to the naked eye sixth magnitude. Stars of intermediate brightness were given intermediate values.

This system with modifications is still used today.

THE EXTENDED APPARENT MAGNITUDE SCALE

Apparent magnitude

• Apparent magnitude is not necessarily related to the amount of light actually produced by the star but is simply a measure of how bright it appears to be from Earth.

• (Some bright stars are simply close neighbours while other giant stars may appear equally bright but are also very distant.)

The systemisation of apparent magnitude

In the nineteenth century systems were developed for measuring exactly how much light was arriving from a star. The intensity of the light (the energy arriving every second per metre 2 at Earth) was calculated. This is sometimes referred to as the apparent brightness of the star

Astronomers were able to show that a first magnitude star was about 100x as intense as a sixth magnitude star.

As a result apparent magnitude was redefines to so that a magnitude difference of 5 EXACTLY corresponds to a factor of 100 in the light energy received

1 2 3 4 5 6

100x brighter

The difference in apparent brightness

1 2 3 4 5 6

x 2.512 x 2.512 x 2.512 x 2.512 x 2.512

brighter than 2

brighter than 3

brighter than 4

brighter than 5

brighter than 6

So it takes about 2 ½ third magnitude stars to be as bright as 1 second magnitude star

So it becomes apparent that eye is a logarithmic detector, and the magnitude system is based on the response of the human eye, it follows that the magnitude system is a multiplicative (logarithmic scale).

Apparent brightness

The actual apparent brightness of a star (its Intensity at Earth) actually obeys the inverse square law:

24 d

PI

Where P is the power produced by the star and d is the distance from the Earth.

Apparent magnitude

• By itself the apparent magnitude of a star does not give us enough information to calculate how bright a star really is.

• To do this we need to know the distance to the star.

Units of distance

• Although we could measure distances simply in metres it is useful to have a larger distance unit:

the light year is the distance travelled by light in 1 year = 9.46 x1015km.

The parsec

The parsec is the distance at which parallax of an object would be 1 second of arc

The observed ellipse is tiny even for nearby stars

θWhen the angle θ is 1 second of arc (1/3600 degree) the distance x is 1 parsec

x

1 parsec = 3.26ly

Absolute Magnitude

• Imagine that you could bring every star in the sky to the exact distance of 10 parsecs.

• We could then directly compare their true brightness.

• The absolute magnitude of a star is defined as the apparent magnitude it would have at a distance of 10 parsecs.

• If the Sun were moved to a distance of 10 parsecs its apparent magnitude would be +4.8 therefore the absolute magnitude of the Sun is 4.8.

The relationship between absolute magnitude and apparent magnitude

10log5

dMm

Where m is the apparent magnitude

M is the absolute magnitude

d is the star’s distance in parsecs