We report the discovery of a low-mass companion to the nearby (d = 47 pc) F7V star HD 984. The companion is detected 0.19 away from its host star in the L band with the Apodizing Phase Plate on NaCo/VLT and was recovered by L-band non-coronagraphic imaging data taken a few days later. We confirm the companion is co-moving with the star with SINFONI integral field spectrograph H+K data. We present the first published data obtained with SINFONI in pupil-tracking mode. HD 984 has been argued to be a kinematic member of the 30 Myr-old Columba group, and its HR diagram position is not altogether inconsistent with being a ZAMS star of this age. By consolidating different age indicators, including isochronal age, coronal X-ray emission, and stellar rotation, we independently estimate a main sequence age of 115$pm$85 Myr (95% CL) which does not rely on this kinematic association. The mass of directly imaged companions are usually inferred from theoretical evolutionary tracks, which are highly dependent on the age of the star. Based on the age extrema, we demonstrate that with our photometric data alone, the companions mass is highly uncertain: between 33 and 96 M$_{rm Jup}$ (0.03-0.09 M$_{odot}$) using the COND evolutionary models. We compare the companions SINFONI spectrum with field dwarf spectra to break this degeneracy. Based on the slope and shape of the spectrum in the H-band, we conclude that the companion is an M$6.0pm0.5$ dwarf. The age of the system is not further constrained by the companion, as M dwarfs are poorly fit on low-mass evolutionary tracks. This discovery emphasizes the importance of obtaining a spectrum to spectral type companions around F-stars.
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