The graph displayed shows the effect of the planet on the star. They did a fantastic job teasing that out of the noise. But looking at the paper, it's pretty convincing. Heck, the star's rotation is three times that big. The Doppler shift in the starlight amounts to a mere half meter per second - slower than walking speed! When I read that I was stunned that low of a signal is incredibly hard to detect. In this case, the planet is low mass but very close in. and you get the added benefit of a short orbital period, so you don't have to observe as long to see the cycle of the Doppler shift. Also, the closer in a planet is, the larger the signal is. The more massive the planet is, the harder it tugs on the star, and the bigger the signal (making it easier to detect). This sets up a very small but detectable Doppler shift in the starlight. As it orbits Alpha Cen B, the planet tugs on the star, like two children holding hands and swinging each other around. The other reason this is important is that the signal from the planet is incredibly weak. If it has a planet, it's too small or too far out from the star (or both) to detect it easily. Those earlier findings have been shown to be wrong, though.
Planets searches have looked there for decades, and in fact for a while it was thought the dinky red dwarf Proxima might have a planet. Because of that it's very bright, and well studied. For one, Alpha Cen is the closest star system in the sky.
The reason this is a big deal is twofold.
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