Axions and magnetic field From what I know about the hypothetical particles "axions":

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*Axions are candidates to be cold dark matter particles

*Dark matter interacts only gravitationally

*Some experiments use strong magnetic fields to convert axions to photons and vice versa (for example, https://home.cern/science/experiments/osqar)

I am confused: If axions are candidates to be dark matter and dark matter interacts only gravitationally, shouldn't axions also interact only gravitationally and not respond to a magnetic field? and what motivates us to use a magnetic field to convert between axions and photons in the first place?
 A: From the various astrophysical observations, we conclude that dark matter does interact gravitationally. Also, we can constrain other interactions to be weak at best (where the exact meaning of "weak" depends on the interaction and observation in question). So, yes, it is indeed entirely possible that dark matter interacts with us only gravitationally, and not through any other forces. Just as well it is possible that axions don't even exist.
Many hypotheses exist for what dark matter could be made of. WIMPs and Axions are probably the two most popular ones, sterile neutrinos or primordial black holes two other common candidates. Axions, if they exist, would interact with magnetic fields, but only weakly. This comes out of how they were invented in the first place, as a possible way to solve some naturalness issues with Quantum Chromodynamics. This interactions of axions with magnetic fields would be so weak that they could still satisfy all known dark matter constraints. Thus, axions are dark matter candidate particles, motivated by QCD.
A: There are several dark matter models where the particles that make up DM can interact very weakly through forces other than gravity. In principle, this doesn't contradict the astrophysical observations.
In this specific case, the theory says that axions can interact with quarks. The motivation is that axions are "designed" to solve a problem related to the strong nuclear force (see "strong CP problem").
The result of this is that axions can interact indirectly with photons, through their interaction with quarks. This includes virtual photons, which make up magnetic fields.
