Pulsar B1237+25 Aberration/Retardation Analysis from Decimeter to Decameter Wavelength: Challenge to "Radius-to-Frequency Mapping"

PSR B1237+25 is perhaps the canonical example of a pulsar with a core/double cone profile. Moreover, it is bright with little spectral turnover, and its profile perhaps uniquely remains undistorted by scattering far into the decametric band. Here we assemble more than a dozen of the highest quality profiles (30 MHz to 5 GHz) from half a dozen observatories, where possible polarimetric. The pulsar's 2.6$^{\circ}$ core component marks the magnetic axis longitude, and we confirm that this point coincides both with the linear polarization angle inflection point and the zero-crossing of its antisymmetric circular signature -- thus providing the possibility to estimate emission heights over a very broad band using aberration/retardation (A/R). We then carefully fit the profile components with Gaussians to identify and study the subtle asymmetries produced by A/R. We find a consistent A/R in the pulsar's profiles of some 0.5$^{\circ}$ longitude or 2 ms -- corresponding to a putative conal emission height of 200-400 km -- with a formal error of about 100 km. Our analysis finds no evidence whatsoever for an emission height increase with wavelength, the so-called ``radius-to-frequency mapping''. Nor do we find any significant difference in A/R effect between the outer and inner cones.