Not So Hard
I learned how to do this in grade school. Just put a piece of paper on top of the galaxy then sprinkle some iron filings on top.
Physicists always want to make a big deal out of everything.
Scientists have measured the magnetic field of a galaxy five billion light years from Earth, the most distant coherent magnetic field that has ever been observed. An international team of physicists used the Karl G Jansky Very Large Array, a large radio wave observatory in central New Mexico, to study how magnetism manifests …
In one of the old Marathon FPS games, there was some worldbuilding text about an ancient race that tried to measure the width of the universe by building two giant spacecraft that moved in opposite directions while forging and stretching an iron chain between them.
You are them and they are you. I am Durandal and by escaping the closure of the universe I will be a god.
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"Accepting that magnetic fields rotate (polarise) light, how (not) on earth did they establish the base line to measure how much it had been polarised by?"
Polarisation isn't simply rotation. Any single photon* has a polarisation - the direction the electric and magnetic fields are oscillating in as it travels. But when we talk about polarisation in general that refers to how much the photons in a big group tend to line up with each other. Black body radiation such as that from stars (as well as most other ways of producing light such as fluorescence) produce photons with no preferred orientation, so overall the light is unpolarised. When that light passes through a magnetic field, it doesn't simply rotate them all by the same amount but rather the rotation depends on how aligned they were with the field to start with, resulting in the light overall gaining a preferred direction of polarisation. So it's not necessary to establish some kind of baseline since the baseline is no polarisation at all, and you can analyse the magnetic field it must have passed through by seeing if there is any polarisation at all.
* Or waves, polarisation works equally well in classical and quantum viewpoints.
I think the question was more about all the other magnetic fields along the way, like our own galaxy's, our sun's, and Earth's fields. The last two will be much stronger than the field they're trying to detect, and all are going to interfere with distant observations.
I'd guess that they observed several distant galaxies just a short angular distance away from the target galaxy, but far enough away to put them in the "clear." Those observations would establish what our local fields are doing to the light, and those effects can then be canceled out computationally, leaving (hopefully) just the target field effect to study.
Reminds me of those days at school when all the other boys merely had animal magnetism, while I had galactic magnetism. I hate to have to say it, but I was outa sight! (Some argued I was beyond a joke, but they would say that. Others said it meant I was overextended, but that's what they would say, the rotters!)
Bryan Gaensler said: "Nobody knows where cosmic magnetism comes from or how it was generated,"
The ONLY source of a cosmic magnetic field, is an electric current, the source of which is the movement of plasma which makes up 99.999% of the visible universe.
As the plasma in the Sun and stars rotate, the ions and electrons move differentially, resulting in electric fields and consequently magnetic fields.
As the interplanetary or intergalactic plasma rotates, the same thing happens. In the Solar System in the heliospheric current sheet which contributes to the Sun's magnetic field.
This is all standard astrophysics.