Spectroscopic parallax
6.8 Spectroscopic parallax
The fact that the spectra of stars can be measured, even for stars at great dis- tances, allows the stellar distance scale to be extended across the galaxy and even out to the nearest galaxies. The method used is called spectroscopic parallax – though it has nothing to do with parallax! It is based on the very simple premise that all stars of the same spectral type, such as Type F0 star, will have the same intrinsic luminosity. Suppose then that we observed a Type F0 star that appeared
10 000 times less bright than a nearby Type F0 star which was at a distance of
8 pc as measured by the method of parallax. The inverse square law tells us that the distant star would be (10 000) 1/2 or 100 times further away, so would lie at a distance of 800 pc.
Introduction to Astronomy and Cosmology
As a further example, we observe a Type G2 star which has an apparent magni- tude of ⫹9.8. We know that our Sun has an absolute magnitude of ⫹4.8 – which is the apparent magnitude that it would have at a distance of 10 pc. The distant G2 star is thus 5 magnitudes fainter than our Sun would appear if it were to be at a distance of 10 pc. However, 5 magnitudes correspond to a brightness ratio of 100, so the distant star must be (100) 1/2 or 10 times further away than 10 pc. Hence, the distant G2 star lies at a distance of 100 pc.
As a fi nal example, consider two B8 stars (like Rigel, in Orion). Rigel has an absolute magnitude of ⫺6.7, this being the apparent magnitude that it would have at a distance of 10 pc. The distant star lies in a daughter galaxy of our own Milky Way Galaxy called the Large Magellanic Cloud (LMC) and has an apparent magnitude of ⫹11.7. The magnitude difference is thus 18.4 magnitudes corre- sponding to a brightness ratio of:
From the inverse square law it will thus lie at a distance of: 10 ⫻ (23 ⫻ 10 6 ) 1/2 pc ⫽ 10 ⫻ 4800 pc ⫽ 48 000 pc This is thus a measure of the distance of the LMC.
The method of spectroscopic parallax suffers from two fundamental problems. The fi rst is that stars of the same spectral type do not necessarily have the same luminosity as the intrinsic luminosity of a star depends to an extent on what is called the star’s metallicity – the percentage of elements heavier than helium or hydrogen in its makeup – so reducing the accuracy of the method. The second is that the correlation between spectral type and luminosity is not perfect: the main sequence is not a thin line, but a band and the scatter in magnitude for a specifi c spectral type (such as F0) is of order ⫹/⫺1 magnitude. One magnitude is
a brightness ratio of 2.512, so this gives a distance error of ⫹/⫺ (2.512) 1/2 which equals 1.6, so spectroscopic parallax is not that precise. The measurements of the luminosity of distant stars suffer from a further problem; that of extinction . (This is the name given to the absorption of light by intervening dust.) This would reduce the observed brightness of a star and so make it appear to be further away. There is, however, a way in which this can be detected and corrected for to some extent. The spectral type will indicate that the star has a particular surface temperature. We have also seen how the temperature can be estimated from the colour index. In the absence of extinction these should
be approximately the same. However, dust absorbs more light in the blue (shorter
The Properties of Stars
wavelength) end of the spectrum than it does at the red (longer wavelength) end of the spectrum. Thus the light from a star whose light has passed through dust clouds will appear redder than it should. This will alter its colour index and indi- cate a lower surface temperature than that indicated by the spectral index of the star. From this difference it is possible to estimate the effect on the star’s apparent brightness and so make a suitable correction.