New radial velocity observations of AH Her: evidence for material outside the tidal radius

Spectroscopic observations of AH Herculis during a deep quiescent state are put forward. We found the object in a rare long minima, allowing us to derive accurately the semi-amplitudes: $K_1 =121 \pm \, 4$ \kms\ and $K_2 =152 \pm 2$ \kms\ and its mass functions $M_W{ \sin }^{ 3 }i=0.30 \pm 0.01$ M$_{\odot}$ and $M_R{ \sin }^{ 3 }i=0.24 \pm 0.02$ M$_{\odot}$, while its binary separation is given by $a \sin i =1.39 \pm 0.02$~R$_{\odot}$. The orbital period $P_{orb}$~=~ 0.25812~$\pm~0.00032$~days was found from a power spectrum analysis of the radial velocities of the secondary star. These values are consistent with those determined by \citet{Horne:1986}. Our observations indicate that K5 is the most likely spectral type of the secondary. We discuss why we favour the assumption that the donor in AH Her is a slightly evolved star, in which case we find that the best solution for the inclination yields $i = 48^\circ \pm 2^\circ$. Nonetheless, should the donor be a ZAMS star, we obtain that the inclination is between $ i = 43^\circ$ and $i = 44^\circ$. We also present Doppler tomography of H$\alpha$ and H$\beta$, and found that the emission in both lines is concentrated in a large asymmetric region at low velocities, but at an opposite position to the secondary star, outside the tidal radius and therefore at an unstable position. We also analyse the H$\alpha$ and H$\beta$ line profiles, which show a single broad peak and compare it with the previous quiescent state study which shows a double-peaked profile, providing evidence for its transient nature.