Understandings: Stellar spectra
Applications and skills: Explaining how surface temperature may be obtained from a star's spectrum
Data booklet reference: λ T = 2.9×10−3 m K
In the atomic physics topic we looked at how the electrons in the shells of atoms are able to be excited by the absorption of electromagnetic radiation with frequencies / wavelengths equivalent to the exact energy difference between two energy levels, and then re-emit that radiation in all directions when the electron drops to a lower energy level. If we observe the gas directly then we may see an emission spectrum of bright lines corresponding to the energy levels in the sample element. If we observe a broad spectrum light source shining through the gas then we will see an absorption spectrum with dark lines at those same wavelengths.
When we look at stars we see broad spectrum electromagnetic radiation (described as a black body spectrum) emitted from the surface of the star (the photosphere) with the absorption spectrum of the stars atmosphere superimposed. This combination as known as the stellar spectrum.
All objects emit a spectrum of electromagnetic radiation. A perfect emitter of radiation is known as a black body emitter. The amount of radiation emitted (per unit of surface area) is dependent on the Stefan-Boltzmann Law, but the distribution of the radiation is described by the Wien Approximation. A simplified version of the latter, Wien's Displacement Law, directly relates the peak frequency / wavelength of the black body spectrum to the temperature of the emitter. The relationship is given by λ T = 2.9×10−3 m K. Re-arranging, dividing 2.9×10−3 by the wavelength of the peak emission (in metres) will give you the surface temperature of the object (in kelvin). Stars are generally good black body approximations, so we can use this relationship to find the temperature of a star by using examining its spectrum using a spectroscope.
The Sloan Digital Sky Survey is an ongoing project to create a database of celestial objects and includes spectral data for many. My video above describes how to use it, but the most recent version of the survey is accessible here: https://www.sdss.org/
Oxford Physics: pp 649 - 652, including a worked example on page 652
Hamper HL (2014): pp 540 - 542, including a worked example and exercises 11 and 12 on page 541.
Pages 197 - 198