The authors describe a windowed Fourier transform method for measuring spiral arm pitch angles. You cannot test whether a constant-pitch logarithmic spiral fits a galaxy if you force an m=2 solution on galaxies that may have m=1, m=3, or asymmetric structures. The method bakes in the assumption it claims to test.
1. Your Fourier method fixes the azimuthal mode number m=2 (the 2Θ term). How do you distinguish between a galaxy with genuine two-arm symmetry versus one where forcing m=2 simply produces a best-fit artifact? What happens when you apply the same method to a known one-armed or three-armed spiral?
2. In the AGN section, the polarization model adds Stokes parameters from jet and shock components with different Doppler exponents (2+α vs 3+α). This assumes incoherent addition. But if both originate from the same relativistic plasma, aren’t they coherent? How do you justify ignoring interference terms?