Dynamical Centers and Non-Circular Motions in THINGS Galaxies: Implications for Dark Matter Halos

We present harmonic decompositions of the velocity fields of 19 galaxies from THINGS (The \HI Nearby Galaxy Survey) which quantify the magnitude of the non-circular motions in these galaxies and yield observational estimates of the elongations of the dark matter halo potentials. Additionally, we present accurate dynamical center positions for these galaxies. We show that the positions of the kinematic and photometric centers of the large majority of the galaxies in our sample are in good agreement. The median absolute amplitude of the non-circular motions, averaged over our sample, is $6.7 \kms$, with $\sim 90$ percent of the galaxies having median non-circular motions of less than $\sim 9\kms$. As a fraction of the total rotation velocity this translates into 4.5 percent on average. The mean elongation of the gravitational potential, after a statistical correction for an unknown viewing angle, is $0.017\pm 0.020$, i.e., consistent with a round potential. Our derived non-circular motions and elongations are smaller than what is needed to bring Cold Dark Matter (CDM) simulations in agreement with the observations. In particular, the amplitudes of the non-circular motions are not high enough to hide the steep central mass-density profiles predicted by CDM simulations. We show that the amplitudes of the non-circular motions decrease towards lower luminosities and later Hubble types.