Signs of accretion in the white dwarf + brown dwarf binary NLTT5306

We present new XSHOOTER spectra of NLTT5306, a 0.44 $\pm$ 0.04\msun white dwarf in a short period (101\,min) binary system with a brown dwarf companion that is likely to have previously undergone common envelope evolution. We have confirmed the presence of H$\alpha$ emission and discovered Na I absorption associated with the white dwarf. These observations are indicative of accretion. Accretion is typically evidenced by high energy emission in the UV and X-ray regime. However our \textit{Swift} observations covering the full orbital period in three wavebands (uvw1, uvm2, uvw2) revealed no UV excess or modulation. We used the X-ray non-detection to put an upper limit on the accretion rate of 2$\times$10$^{-15}$\msun yr$^{-1}$. We compare NLTT5306 to similar accreting binaries with brown dwarf donors and suggest the inferred accretion rate could be from wind accretion or accretion from a debris/dust disk. The lack of evidence for a disk implies NLTT5306 is magnetically funnelling a weak wind from a potentially low gravity brown dwarf. The upper limit on the accretion rate suggests a magnetic field as low as 0.45\,kG would be sufficient to achieve this. If confirmed this would constitute the first detection of a brown dwarf wind and could provide useful constraints on mass loss rates.