Introduction to Astrophysics

Lecture 8: Observational properties of stars

Stars

Most of the objects visible with the naked eye in the night sky are stars. Like our Sun, they are large balls of hot gas, powered by nuclear fusion within their depths.

Stellar distances

Even the nearest stars are not that near. Their distances can be found by triangulation, a method known as parallax.

Because of the Earth’s motion around the Sun, the apparent position of nearby stars moves with respect to distant ones. The amount they move depends on their distance from the Earth.

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Parallaxes

Even for the nearest stars the parallaxes are very small indeed, less than one arcsecond.

A parsec is the distance at which an object would have a parallax of one arcsecond. From the radius of the Earth’s orbit, it can be shown that ...

One parsec = 3.086 x 1016 metres = 3.26 light years

To work this out, you have to figure out how far away a star has to be so that the size of the Earth’s orbit appears to be one arcsecond.

Stellar aberration

Parallax is not to be confused with stellar aberration. This is caused by the movement of the Earth, which means that objects are actually not in the direction the telescope is pointing!!

Stellar aberration is typically greater than the parallax and it must be carefully subtracted before parallaxes can be measured.

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Stellar motions

Stellar motions

Although stars do have measurable motions, very few move perceptibly on human timescales. The one which moves the most is Barnard’s star, which moves 10 arcseconds per year.

1950 1997

Properties of stars

Many of the differences in appearance of different stars are due to their being at different distances from us.

Once we know their distances we can correct for that and begin to compare their properties fairly.

Fundamental properties

Brightness

Colour

Apparent brightness

Long ago Hipparchus invented the magnitude scale, which divided stars into 6 classes, the brightest called 1st magnitude and the faintest 6th magnitude.

Astronomers have standardised his system, so that 5 magnitudes corresponds to a difference in brightness of a factor 100.

The scale is logarithmic, meaning each magnitude corresponds to a ratio of flux. Annoyingly the factor is 2.512, eg a 4th magnitude star is 2.512 times brighter than a 5th magnitude star.

2.512 x 2.512 x 2.512 x 2.512 x 2.512 = 100

Apparent brightness

Nowadays apparent magnitudes can refer to light at different wavelengths, and the range has been greatly expanded both to allow brighter objects and fainter ones.

Sun -26.5

Venus -12.5

Sirius (brightest star) -1.5

Naked eye limit 6.5

Binocular limit 10

4-metre telescope limit 26

Note that the bigger the magnitude, the fainter the object.

True brightness

The absolute magnitude is a measure of the true brightness of a star.

By convention, the absolute magnitude is the brightness that the star would have if it was at a distance of 10 parsecs.

Almost all stars are further than 10 parsecs, so their absolute magnitude is brighter than their apparent magnitude.

Colour and temperature

Although the human eye has difficulty seeing it, stars have colours. The colours are an indication of the temperature of the stars.

Hot stars are blue-white in colour, while cool ones are red.

Colour index

One way of defining colour is to compare the brightness of the star at two different wavelengths, eg blue and green. This ratio is a measure of the colour and is known as the colour index of the star.

The colour indicates the temperature, and is used as the basis for the stellar classification, which orders stars (from hot to cold) into classes as

O B A F G K M

Spectral class Colour Temperature (K)

O Violet > 28,000

B Blue 10,000 to 28,000

A Blue 7,500 to 10,000

F Blue - white 6,000 to 7,500

G White - yellow 5,000 to 6,000

K Orange - red 3,500 to 5000

M Red < 3,500