A dynamical mass estimator for high z galaxies based on spectroastrometry

Galaxy dynamical masses are important physical quantities to constrain galaxy evolutionary models, especially at high redshifts. However, at z~2 the limited signal to noise ratio and spatial resolution of the data usually do not allow spatially resolved kinematical modeling and very often only virial masses can be estimated from line widths. But even such estimates require a good knowledge of galaxy size, which may be smaller than the spatial resolution. Spectroastrometry is a technique which combines spatial and spectral resolution to probe spatial scales significantly smaller than the spatial resolution of the observations. Here we apply it to the case of high-z galaxies and present a method based on spectroastrometry to estimate dynamical masses of high z galaxies, which overcomes the problem of size determination with poor spatial resolution. We construct and calibrate a spectroastrometric virial mass estimator, modifying the classical virial mass formula. We apply our method to the [O III] or H{alpha} emission line detected in z~2-3 galaxies from AMAZE, LSD and SINS samples and we compare the spectroastrometric estimator with dynamical mass values resulting from full spatially resolved kinematical modeling. The spectroastrometric estimator is found to be a good approximation of dynamical masses, presenting a linear relation with a residual dispersion of only 0.15 dex. This is a big improvement compared to the classical virial mass estimator which has a non linear relation and much larger dispersion (0.47 dex) compared to dynamical masses. By applying our calibrated estimator to 16 galaxies from the AMAZE and LSD samples, we obtain masses in the ~10^7-10^10 Modot range extending the mass range attainable with dynamical modeling.