No evidence for Keplerian taper of far-out galactic rotation

Abstract

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 ($V(r)\propto 1/\sqrt{r}$) germane to a convergent mass distribution in typical spherical halo models agrees with observational data. The null hypothesis is Rubin's flat-rotation curve, $V(r)=\text{constant}$ -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 \emph{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\%.

20 pages, 7 figures Revised according to referee observations

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