Expert: Philip Stahl - 10/21/2008

Question
How do visual telescopes show the temperature and luminosity of stars?

Answer
Hello,

Visual telescopes in and of themselves cannot show either the temperature or luminosity of stars.  One must fit additional instruments to telescopes to gain an idea of their temperature - for example the spectroscope - which is capable of showing the spectral lines and whether these are absorption lines or emission lines.

A most useful device today is the *spectrophotometer* which is capable of showing the variation of the radiative intensity with the wavelength. (And able to show a span of wavelengths not just those in the visual region). The hotter as star, then, the SHORTER the wavelength of the PEAK in the light profile obtained.

Bear in mind here that stars radiate like what we call "blackbodies" - where a blackbody displays what is called a "blackbody shape" meaning a *Planck curve*. (Which you can google to learn more about).  The visible range is only a small part of the whole blackbody spectrum.

The main points to be aware of so far are: i) a wide range of a star's spectrum must be measured to find the peak of its Planck curve (and hence the temp.) and this is why a spectrophotomer is superior to just a spectroscope, and ii) one must be cognizant that for a certain subset of stars the radiation at the peak may be absorbed by the Earth's atmosphere. These will be stars whose blackbody curve peaks in the ultraviolet. (Fortunately, however, we have UV instruments outside the atomsphere!)

Once one obtains the surface (or effective) temperature of a given star, using spectrophotometer techniques - one can than obtain a star's luminosity since the luminosity (L) is related to the surface or effective temperature (T_eff) according to:

L =   4 (pi) r^2 (q) T_e^4

where r is the star's radius, T_e is the effective (surface) temperature and q is a constant called Stefan's constant.

In terms of the radius, r, optical interferometry can provide estimates of the radius for many stars. However, the details of how it works are beyond the scope of this particular answer  - though you can certainly google then read as much (or as little!) as your physics background enables.

Hope this helps!