NGC 4388: a test case for relativistic disc reflection and Fe K fluorescence features

We present a new analysis of the Suzaku X-ray spectrum of the Compton-thin Seyfert 2 galaxy NGC 4388. The spectrum above ~2 keV can be described by a remarkably simple and rather mundane model, consisting of a uniform, neutral spherical distribution of matter, with a radial column density of $2.58\pm 0.02 \times 10^{23} \ \rm cm^{-2}$, and an Fe abundance of $1.102^{+0.024}_{-0.021}$ relative to solar. The model does not require any phenomenological adjustments to self-consistently account for the low-energy extinction, the Fe Kα and Fe Kβ fluorescent emission lines, the Fe K edge, and the Compton-scattered continuum from the obscuring material. The spherical geometry is not a unique description, however, and the self-consistent, solar abundance MYTORUS model, applied with toroidal and non-toroidal geometries, gives equally good descriptions of the data. In all cases, the key features of the spectrum are so tightly locked together that for a wide range of parameters, a relativistic disc-reflection component contributes no more than $\sim 2{{\ \rm per\ cent}}$ to the net spectrum in the 2-20 keV band. We show that the commonly invoked explanations for weak X-ray reflection features, namely a truncated and/or very highly ionized disc, do not work for NGC 4388. If relativistically broadened Fe Kα lines and reflection are ubiquitous in Seyfert 1 galaxies, they should also be ubiquitous in Compton-thin Seyfert 2 galaxies. The case of NGC 4388 shows the need for similar studies of more Compton-thin AGN to ascertain whether this is true.