Why do stars have different colors?

Some stars are yellow, like our Sun. Some are blue and some are white. There are even green, purple, rose and amethyst-colored stars. The color of a star depends very largely on its temperature. The red stars are cooler than the yellow ones. The yellow stars are cooler than the white, and the white are cooler than the blue-white. If you have ever seen a blacksmith or a worker in metals heating a piece of iron, you know that at first the iron glows with a reddish color. As it becomes hotter, it changes to yellow, then white, and, if the temperature becomes very high, sometimes it takes on a bluish white color.
If you look carefully at the stars on a clear night, you may be able to discover the colors of some of them for yourself. Many stars appear white, but some show a definite tint of color. Sirius, the dog star in the constellation Canis Major the Great Dog, is a white star, with a temperature of almost 11,000° Celsius. Capella, the bright star in the constellation Auriga, is a yellow star like the Sun, and has a temperature of about 6,000° Celsius. Both Arcturus, in Bootes, and Aldebaran, in Taurus, are orange stars with temperatures of more than 3,500° Celsius. In the case of a binary star, one star of the pair may be one color, and the other star, another.

Additional reading:
Stellar classification (Wikipedia)

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