No evidence for Keplerian taper of far-out galactic rotation in the SPARC galaxy database

We present a statistical analysis of the 175 SPARC galactic rotation curves to test the hypothesis of whether the Keplerian velocity tapering at large radii ( V ( r ) ∝ 1 / r ) germane to a convergent mass distribution in typical spherical halo models agrees with observational data. The null hypothesis is Rubin’s flat-rotation curve, V ( r ) = constant -such as can be obtained from a spherical, isothermal-like density profile, or alternatively with a very prolate halo-. To decide whether we adopt the null (Rubin behaviour) or alternative (Keplerian behaviour) hypothesis, we evaluate the derivative in each galaxy of V ( r ) with its last data points. The test is model independent inasmuch we are testing for the slope of the dark matter rotation curve, whether it is or not compatible with zero. We conclude that the data is presently compatible with the null hypothesis -no taper off, no decline of V ( r ) is seen. Separately, beyond SPARC, our own Milky Way galaxy, for which recent data sets have been reported, does show clear V ( r ) fall-off at the level of 20%.