Final answer:
A blue star is hotter than a red star, with the former being potentially five times hotter than our Sun and the latter, about 2.4 times cooler. Temperature greatly affects luminosity, with the relationship showing in stars twice as hot being significantly brighter. Main-sequence O stars, despite a similar temperature range to the hottest white dwarfs, are more effective at ionizing hydrogen.
Step-by-step explanation:
A blue star has a greater temperature than a red star. Our Sun, which is a type G yellow dwarf star, has a surface temperature of 5800 K, and it is cooler than a type O star and hotter than a type M star. The hottest type O stars can reach temperatures over 30,000 K, which is more than five times hotter than our Sun. On the cooler end, the coolest type M stars have temperatures as low as 2,400 K, making them about 2.4 times cooler than the Sun. When it comes to stellar brightness, the luminosity of a star is related to its temperature; hotter stars tend to be more luminous. For example, if star A has a surface temperature of 6000 K and star B's temperature is 12,000 K, star B would be significantly more luminous due to its higher temperature.
Considering two stars with identical diameters and the same distance from us, one with a temperature of 8700 K will be brighter than the other with a temperature of 2900 K, in fact, it will be approximately 81 times brighter according to the Stefan-Boltzmann law which relates luminosity to temperature. Lastly, despite the hottest white dwarfs and main-sequence O stars both having temperatures hotter than 25,000 K, the O stars have a much greater ability to ionize hydrogen and create H II regions due to their greater size and energy output.