Astronomy 218 What color is that Star? Colored Stars When you look at the stars in the night sky, another Meissa noticeable feature, for a Betelgeuse few stars, is their color. Bellatrix To the naked eye, only a few bright stars have colors Mintaka discernibly different than Alnilam Alnitak white, because your color vision is less sensitive that your monochrome vision. Hatsya Rigel The Sun’s yellow color is Saiph an obvious example. Betelgeuse is another example. Spectra The perceived color or a star (or any other object) is a product of its spectrum. A star has a flux that depends on wavelength (or frequency), Fλ. This is defined such that Fλ dλ is the star’s flux in the range of wavelengths from λ to λ+dλ. The total, or bolometric, flux is Blackbody Spectrum An opaque object emits a characteristic, temperature dependent, spectrum. Wien’s Law 3 2.898 10− λ = × The Planck function max T explained the observed shape of the Blackbody.
There are two useful limits to consider. For low energy photons, For high energy photons, E << kT, we have the E >> kT, we have the Rayleigh-Jeans Limit. Wien Limit. Blackbody Flux The flux of energy emitted per unit area, per unit time in a interval of wavelength, can be calculated by integrating the intensity over the solid angle. The result,
-1 -1 Fλ = πIλ has units of s m .
The total flux is calculated by integrating over wavelength -8 -1 -2 -4 where σSB = 5.67×10 J s m K
Total Luminosity is Flux × area of emitting surface. 2 4 L = 4πR σSB T Bolometric Magnitude From the bolometric flux, it is natural to calculate a bolometric apparent magnitude,
mbol = Cbol − 2.5 log Fbol For visual apparent magnitude, C was chosen based on Vega having a nearly zero and very stable apparent magnitude. However, it is hard to measure fluxes across all wavelengths, thus the uncertainties in the bolometric flux are relatively large. For this reason, the Sun was chosen to be the “zero” of bolometric magnitude, with the Sun’s absolute bolometric magnitude defined as Mbol,☉ = 4.74.