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Could black holes' near light speed rotation cause galaxies to move like an irrotational vortices?

Ryan S.
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  • The gravity of a black hole far away from the event horizon is essentially indistinguishable from Newtonian gravity, even with frame dragging. – CuriousOne Sep 16 '14 at 06:22
  • Could then the movement of the interstellar medium cause the rate of the galactic rotation speed? – Ryan S. Sep 16 '14 at 06:28
  • Not if "interstellar medium" denotes the thin cloud of ordinary gas and dust that exists in galaxies. – CuriousOne Sep 16 '14 at 06:31

2 Answers2

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If we take the Milky Way as an example, the black hole at the centre, Sagittarius A$^*$, has a mass of about 4 million times the Sun. However the mass of the Milky Way is somewhere around a trillion Suns. So the central black hole makes up 0.0004% of the total mass. While the central black hole may have been important in the formation of the Milky Way, its effect on the overall dynamics is negligable.

In any case, the rotation curves of galaxies are almost flat and do not in the least resemble an irrotational vortex.

John Rennie
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  • The mass of the luminous part of the Milky Way is much smaller than that, probably a few percent. Since there is still no clear-cut argument that dark matter is rotating (though it clearly makes theoretical sense that it does) the OP could be reformulated to ask whether the BH might account for the rotation of the luminous part of the Galaxy, the only one for which we have uncontroversial evidence of rotation. Even in this case, though, the dynamical effect of the BH is negligible, though by a narrower margin (a factor of 100 or so). – MariusMatutiae Sep 16 '14 at 15:36
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Comment to the question (v1): Besides what John Rennie wrote in his correct answer, note that the velocity profile of an irrotational/free vortex falls off as

$$\tag{1} v~\propto~ 1/r,$$

while a galactic rotation curve may actually increase with $r$, and in any case, it never falls off faster than$^1$

$$\tag{2} v~\propto ~1/\sqrt{r},$$

so the analogy mentioned in the title has no merit whatsoever.

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$^1$ The lower limit (2) corresponds to Newton gravity without dark matter and all mass concentrated in the center.

Qmechanic
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