Mapping the secondary star in QQ Vulpeculae

We present high- and medium-resolution phase-resolved far-red spectra of the magnetic cataclysmic variable QQ Vul. The spectra show the Na i doublet absorption features near ? 8190 Å from the cool secondary star, and the lines of He ii, O i, Mg ii, C i, N i, Ca ii and Paschen in emission. Using a Doppler imaging technique, we find that the H i, He ii, C i and O i lines have a narrow component originating near the L1 point and a strong component from the stream, while the Mg ii and Ca ii emission arises solely from the illuminated hemisphere of the red dwarf. We carry out an exhaustive analysis of the emission- and absorption-line velocities and fluxes seen in the QQ Vul spectrum. By simultaneously fitting the radial velocity and flux information we are able to produce surface maps of each line on the secondary star using a technique analogous to the one employed by Davey. The Na i and Mg ii maps show an asymmetric distribution akin to that seen in AM Her. Although the observed velocity semi-amplitudes (K2) of the lines can potentially be corrected for the effects of irradiation, we find that time-dependent changes in the degree of heating on the secondary can lead to large discrepancies in the results, significant enough to give inconsistent values from data taken at different epochs. We discuss the limitations of the surface mapping method as a means of correcting the observed K2. Our results also suggest that the emission features from the red dwarf are likely to be formed at quite high levels of the stellar chromosphere, in some cases probably even beyond the L1 point and inside the Roche lobe of the white dwarf, with the different lines possibly forming at different depths. Using the Na i absorption doublet, we find a velocity semi-amplitude for the secondary star of K2=219±6 km s-1 and a projected rotational velocity of vrot sin i=110±15 km s-1. Thus we estimate the mass ratio to be q=0.54±0.14. Based on the results of the best-fitting surface maps on all the lines, and the nature of the phase-dependent variations of the continuum and lines, we infer a binary inclination of i=65°±7°, and obtain a complete set of binary parameters for QQ Vul. We classify the secondary star as M4V from the TiO band ratios.