  In this brief note, we clarify certain aspects related to the magnetic (i.e.,
odd parity or axial) tidal Love numbers of a star in general relativity.
Magnetic tidal deformations of a compact star had been computed in 2009
independently by Damour and Nagar and by Binnington and Poisson. More recently,
Landry and Poisson showed that the magnetic tidal Love numbers depend on the
assumptions made on the fluid, in particular they are different (and of
opposite sign) if the fluid is assumed to be in static equilibrium or if it is
irrotational. We show that the zero-frequency limit of the Regge-Wheeler
equation forces the fluid to be irrotational. For this reason, the results of
Damour and Nagar are equivalent to those of Landry and Poisson for an
irrotational fluid, and are expected to be the most appropriate to describe
realistic configurations.
