Spectral analysis: Wien’s Displacement
A red giant only 36.7 light years away. Arcturus is a cool star as can be seen from the low blue-violet intensities. We use Wien’s Displacement to calculate a surface temperature, by measuring the peak wavelength. Formally, Wien’s displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength given by…
peak = b/T
where T is the absolute temperature and b is called Wien’s displacement. We measure a peak wavelength of ~650 nm in our spectrum that gives T = 4468 K from Wien’s Displacement. The known surface temperature of Arcturus is 4290 K, which is within 5%. Our spectra is deterred by the camera’s H-alpha filtering.
Look at CN Bootis’ spectrum. It comes from a hot star as can be seen from the intensity of the blue-violet region. Using Wien’s Displacement, we measure a maximum wavelength peak of 488 nm that gives T = 5933 K. CN Bootis has a known surface temperature of T = 9250 K. One reason for this discrepancy is the UV cut-off near 425 nm for our grating optic, as seen in the spectrum. This will be a problem for hotter stars, like CN Bootis.
Below, three temperatures profiles are plotted with the visible spectrum overlayed for comparison.