We present a detailed temperature and magnetic investigation of the T Tauri star V410 Tau by means of a simultaneous Doppler- and Zeeman-Doppler Imaging. Moreover we introduce a new line profile reconstruction method based on a singular value decompo
sition (SVD) to extract the weak polarized line profiles. One of the key features of the line profile reconstruction is that the SVD line profiles are amenable to radiative transfer modeling within our Zeeman-Doppler Imaging code iMap. The code also utilizes a new iterative regularization scheme which is independent of any additional surface constraints. To provide more stability a vital part of our inversion strategy is the inversion of both Stokes I and Stokes V profiles to simultaneously reconstruct the temperature and magnetic field surface distribution of V410 Tau. A new image-shear analysis is also implemented to allow the search for image and line profile distortions induced by a differential rotation of the star. The magnetic field structure we obtain for V410 Tau shows a good spatial correlation with the surface temperature and is dominated by a strong field within the cool polar spot. The Zeeman-Doppler maps exhibit a large-scale organization of both polarities around the polar cap in the form of a twisted bipolar structure. The magnetic field reaches a value of almost 2 kG within the polar region but smaller fields are also present down to lower latitudes. The pronounced non-axisymmetric field structure and the non-detection of a differential rotation for V410 Tau supports the idea of an underlying $alpha^2$-type dynamo, which is predicted for weak-lined T Tauri stars.
The major challenges for a fully polarized radiative transfer driven approach to Zeeman-Doppler imaging are still the enormous computational requirements. In every cycle of the iterative interplay between the forward process (spectral synthesis) and
the inverse process (derivative based optimization) the Stokes profile synthesis requires several thousand evaluations of the polarized radiative transfer equation for a given stellar surface model. To cope with these computational demands and to allow for the incorporation of a full Stokes profile synthesis into Doppler- and Zeeman-Doppler imaging applications as well as into large scale solar Stokes profile
