An analytical model for the Maxwell radiation field in an axially symmetric galaxy

33 pages, including 9 figures. V2: redactional improvements in Sects. 1, 2.1, 2.3 (with additional explanations), 2.5, 3.4. The outgoing spherical scalar wave (19) is now being used.International audienceThe Maxwell radiation field is an essential physical characteristic of a galaxy. Here, an analytical model is built to simulate that field in an axisymmetric galaxy. This analytical model is based on an explicit representation for axisymmetric source-free Maxwell fields. In a previous work, the general applicability of this representation has been proved. The model is adjusted by fitting to it the sum of spherical radiations emitted by the composing ``stars". The huge ratio distance/wavelength needs to implement a numerical precision better than the quadruple precision. The model passes a validation test based on a spherically symmetric solution. The results for a set of ``stars'' representative of a disk galaxy indicate that the field is highest near to the disk axis, and there the axial component of ${\bf E}$ dominates over the radial one. This work will allow us in the future to check if the interaction energy predicted by an alternative theory of gravitation might be a component of dark matter