Hanle signatures of the coronal magnetic field in the linear polarization of the hydrogen L alpha line

Aims. This paper is dedicated to the assessment of the validity of future coronal spectro-polarimetric observations and to prepare their interpretation in terms of the magnetic field vector. Methods. We assume that the polarization of the hydrogen coronal L alpha line is due to anisotropic scattering of an incident chromospheric radiation field. The anisotropy is due to geometrical effects but also to the inhomogeneities of the chromospheric regions which we model by using Carrington maps of the L alpha. Because the corona is optically thin, we fully consider the effects of the integration over the line-of-sight (LOS). As a modeling case, we include a dipolar magnetic topology perturbed by a non-dipolar magnetic structure arising from a prominence current sheet in the corona. The spatial variation of the hydrogen density and the temperature is taken into account. We determine the incident radiation field developed on the tensorial basis at each point along the LOS. Then, we calculate the local emissivity vector to obtain integrated Stokes parameters with and without coronal magnetic field. Results. We show that the Hanle effect is an interesting technique for interpreting the scattering polarization of the L alpha lambda 1216 line in order to diagnose the coronal magnetic field. The difference between the calculated polarization and the zero magnetic field polarization gives us an estimation of the needed polarimetric sensitivity in future polarization observations. We also obtain useful indications about the optimal observational strategy. Conclusions. Quantitative interpretation of the Hanle effect on the scattering linear polarization of L alpha line can be a crucial source of information about the coronal magnetic field at a height over the limb h < 0.7 R(circle dot). Therefore, one needs the development of spatial instrumentation to observe this line.