Let's start with the big, sweeping images of nebulas and star-forming regions. We can't talk about these space images without taking a quick look at the electromagnetic spectrum. We can only see a narrow band of it, visible light. But on the shorter end tending towards x-rays and the longer end tending towards microwaves, there is still a lot of information for scientists to glean, so they use telescopes that can see in these wavelengths that are invisible to our eye.
Astronomers take that data and shift the colour information to frequencies that we can see while keeping relative colours constant. This doesn't mean they're not real. It's sort of like changing the key of a song - it sounds different but still the same. Let's take Hubble as an example. Hubble can see in visible light like we can, but using specialized instruments it can also see in ultraviolet and infrared light. Light information hits the digital camera sensor as a grayscale image - meaning, yes, those amazing hubble images have no color.
Then astronomers add color data and adjust for known wavelengths, adding corresponding colors and patching different shots together to give a complete picture.
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