Planetary nebulae as mass tracers of their parent galaxies: Biases in the estimate of the kinematical quantities

Multi-object and multi-fiber spectrographs on 4 and 8 m telescopes make it possible to use extragalactic planetary nebulae (PNe) in the outer halos of early-type galaxies as kinematical tracers, where classical techniques based on integrated stellar light fail. Until now, published PNe radial velocity samples are small, with only a few tens of radial velocity measurements (except for a few cases like NGC 5128 or M 31), causing uncertainties in the mass and angular momentum estimates based on these data. To quantify these uncertainties, we have made equilibrium models for spherical galaxies, with and without dark matter, and via Montecarlo simulations we produce radial velocity samples with different sizes. We then apply, to these discrete radial velocity fields, the same standard kinematical analysis as it is commonly done with small samples of observed PNe radial velocities. By comparison of the inferred quantities with those computed from the analytical model, we test for systematic biases and establish a robust procedure to infer the angular momentum distribution and radial velocity dispersion profiles from such samples.