# The O-Type Star α Cam

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##### The Hottest Stars

The stars of spectral class O are the hottest most luminous most massive and rarest normal stars in the univers. The live fast and die young (Kahler,1994). What does this all mean?

The fate of a normal star, i.e. a star with an hydrogen burning core, a main sequence star, a dwarf star. Be carefull, not a White Dwarf. Ok. The fate of a normal star only depends on the mass with what the star begins its life on the main sequence. This may be as long as many billion years for cooler stars of type M or as short as some million years for the very hot O-type stars. Later on the dwarfs become giants und move towards the top of the HR diagram where the most luminous stars reside to end as White Dwarfs or small neutron stars or even stellar black holes. wp (Carroll,Ostlie,2007).

Find a very nice, well commented HR diagram with stellar masses, effective temperatures, radii, luminosity, lifetime, and at least spectral classes at enigmar.net.

We will compare two very extreme not representative main sequence stars. The cold star becomes Van Biesbroeck's star VB10wp. A M8V-type star, cold small dim and near, only 20 light years away, but you won't see this 17mag star in a small telescope. The other star is BI253wp in the Tarantula Nebula in the Magellanic Cloud, hot large luminuos and far away. This star appears also dim. Visual magnitude is only 13mag but the star shines from a distance of 50,000 light years. The following table shows some properties of these stars as multiples of the solar ones. Temperature is in Kelvins.

stellarsolar VB10 BI253 range factor
Sp. Class M8V O2V-II
M/M 0.08 84 1000
R/R 0.1 11 100
T★eff 2600 K 50000 K 20
L/L 4·10-4 9·105 2·109

On the main sequence all four properties rise together from spectral class M to O. But with very different slopes. Typical main sequence O-type stars, not giants of course, are only twenty times larger than a typical M-type star, but their masses change by three orders of magnitude. Really impressive is the enormous rise in luminosity over nine orders, a factor of a billion. This shows directly that O-type stars consume their fuel very very quickly. Therefore the lifetime iof these hot stars is rather short. Some 10 million years, but remember the Sun will live for totally 10 billion years, it's half time now (Carroll,Ostlie,2007, p.342f).

The O-type stars give an outstanding performance at the end of their lifes. They enrich their neighbourhood with chemical elements heavier than helium in a glorious super nova. A neutron star remains or a stellar-mass black hole (Grunhut et. al,2016).

An obvious difference of cool and hot stars catches your eyes looking at Albireo or Rigel and Betelgeuse in Orion is the color of the stars. The hotter star looks bluish white, the cooler more orange. This change in hue is a property of every dense body and follows roughly Wien's displacement law wp that gives the wavelength where the spectrum shows maximal intensity. $\lambda_{\mathrm{peak}}=\frac{b}{T}$ where $$b \approx 2.898\cdot10^{-3}\,\mathrm{mK}$$ is called Wien's displacement constant. $$\lambda_{\mathrm{peak}}$$ is 1.1 µm for VB10, clearly an infrared wave length. Snugly warm at the right distance. BI253 is most prominent at 60 nm, this is extreme ultraviolet radiation wp. Better maintain a large distance not to get your skin burned.

Not only the short wavelength of 60 nm also the striking rise of the intensity of the radiation with photospheric temperature makes the hot stars unique. The Stefan-Boltzmann law wp gives the bolometric luminosity of a dense hot body: $L_{\mathrm{bol}}=\sigma A T^4$ where $$\sigma$$ is the Boltzmann constant $$A$$ the surface area and $$T$$ the temperature of the star's photosphere. So one square meter of BI253 emits approximatelly 160,000 times the radiation of one square meter on the surface VB10.