I'm using a spectrum analyser to see the harmonics of various instruments so as to recreate their tone (or approach it) with additive synthesis. I've found that it detects some noise at around -100 dB, even though I have no inputs plugged into my audio interface. I should add that I can't hear this noise, it's only visual (spectrum). Is this normal, and if not, what can I do about it? The same noise isn't present in similar graphs you can find on google. Are the creators of those graphs using specialist equipment, or is it a problem that can be solved with a home-recoding setup?
All audio electronics create noise, including your interface itself. It's actually pretty good that the self noise of the interface is at around -100 dB.
Even when all other sources of noise are eliminated in an electronic device (e.g., leakage from the power supply, EM radiation from outside the device, etc.), there is no way to eliminate thermal noise. That's noise generated inside elecrical components by the vibrations of atoms and molecules in those components. It may sound like a small thing, but all sound in electronic devices is due to the motion of very small things (electrons), and when the gain of a circuit is high, even very low level noises can be amplified to a significant level.
It is impossible to eliminate 100% of noise. The best we can do is make the noise as quiet as possible relative to the desired sounds.