= Central obstruction to an outer halo mass offset
{title2=$M_h(r)\simeq V_\infty^2r/G-M_\star$}
Subtracting a finite stellar mass from the distant spherical mass required for a flat <galaxy rotation curve> gives the displayed asymptotic offset. Extending it to $r=0$ would give negative enclosed <mass>, so it cannot define a physical inner halo. Keeping only its positive leading term instead gives a singular isothermal halo with density proportional to $r^{-2}$ and a nonzero limiting central circular speed. These are different extrapolations, and neither is forced by an outer rotation curve.
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