The radiation from most stars can be approximated as black body radiation. We can use this fact, along with measurements of the stars luminosity through two different filters, to measure the temperature of the stars.
The black body radiation law (Planck function) is
where \(F_{\lambda}\) is the flux per unit wavelength emitted by a unit area, \(h\) is Planck’s constant, \(c\) the speed of light, \(k\) the Boltzmann constant and \(T\) the temperature.
Use this equation to derive the ratio in flux at two different wavelengths as a function of \(T\). Hence, with this equation, take the magnitudes measured through two different filters and use this to derive the temperatures of your stars.
How hot are they? The Sun has a surface temperature of about 6000K. How do the temperatures compare to that of the Sun? Do they all have similar temperatures or is there a range? Is there a correlation between brightness and temperature?
Use the Planck function to derive the surface area of your stars and hence their radii (be careful converting units!). For comparison, the Sun has a radius of \(7\times 10^{8}\) m. How do they compare?
If you’ve got this far and still have time and energy left, consider a few of the following.
If the sun were taken away and replaced by one of your stars, how hot would the Earth get? (the Sun is roughly 8 light-minutes away). How far away would a planet have to be from this sun to sustain liquid oceans? (Hint: assume planets are black bodies and use the Stefan-Boltzmann equation).
Some of your stars are very luminous. The luminosity of a star goes as roughly their mass to the power 2.5 (ie. \(L\propto M^{2.5}\)) for main sequence stars like the sun and blue supergiants. How massive are these things compared to the Sun? The Sun has an expected lifetime of \(10^{10}\) years: how long will these ones last?
How near would one of these stars need to be, to be visible in the daylight? (Hint: the moon is only just visible in daylight).
Precisely how bright is the night sky over Siding Spring Observatory? (Express this in magnitudes per arcsec\({}^{2}\))