Pulsars

But they have another characteristic which seems to melt our brains! They vary in brightness (in either or both of visible and radio frequencies). Why is this a problem?

An object which has immense brightness, say a million times the apparent radiation brightness of our Sun, seems to us to necessarily have to be rather large in physical size. Our Sun is nearly a million miles in diameter, and we assume that any object which radiates a million times as much radiation MUST BE a hundred million miles in diameter or larger.

Why is THIS a problem? Because light and all other known radiation can only travel at the speed of light, around 186,000 miles per second. Light and heat from the Sun's surface takes around 8 minutes to travel the 93 million miles to get to the Earth.

So say you have a giant ball that is 100 million miles in diameter. And the surface of it somehow changes in temperature rapidly (by some unknown process) every few seconds. The problem arises due to geometry! If the location on the surface which happens to be NEAREST the Earth and Sun gets hottest and brightest, then there is a CIRCLE of surface which is farther away from us. The object is large enough so that difference can easily be a few light seconds distance. So we might be getting MAXIMUM radiation from the surface area nearest us, but at that time we would be receiving MINIMUM radiation from that circle of surface area which was that few light-seconds farther away from us. And a MAXIMUM from another larger circle that was twice that differential distance away from us. And a MINIMUM from another even larger circle of surface that was farther away, and so on.