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Current research suggests that the Milky Way's dark matter halo may extend up to about 10 - 15 times the size of the visible galaxy, and is believed to be roughly spherically symmetrical. But I don't understand how we deduce that.

In the case of a spherically symmetrical matter distribution, such as the classic "planet with a hole drilled through it", the matter within the radius of the object acts as a single mass at the centre, and the matter outside that radius makes no net contribution to force or motion. So if we somehow stood in such a shaft drilled through the Earth, and had no idea how far above us the shaft extended, we couldn't deduce the mass of any thin shell of matter at distance D from Earth's centre, because the net contribution would cancel out whatever that mass was. So we couldn't conclude much about Earth's higher-up mass distribution, or where this became effectively zero. (We also couldn't deduce anything from depth if we couldn't measure ambient pressure, which might help.)

By analogy, I don't understand how we can draw conclusions about the extent of matter outside a star or region's galactic orbit.

So how can we deduce the mass distribution, or effective extent/size, of a galaxy's dark matter halo, in a "thin shell" region of space far from the galaxy's centre, if there are no visible stars of that galaxy to provide evidence of the local force of gravity at distances beyond the visible galactic extent?

My present understanding, for info:

I understand in overview some of the principles about a galaxy's dark matter halo, including why we believe dark matter is present and such a large proportion of a galaxy's mass, the need for extra mass to explain how a galaxy retains cohesion/rotation, and the fact that unlike visible matter, dark matter is limited in how dense it can get (Virial theorem? of which I think I may understand the conclusion and recognise the name, but nothing more?). I also understand that given a star (or galactic region's average) motion, we can deduce how much mass lies within that orbit, but I would naively expect a symmetrical "thin shell" of matter outside that orbit to have zero net contribution? But while this seems applicable, I'm less sure.

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A rotation curve cannot be measured beyond the point at which no visible matter can be seen.

Rotation velocity measurements can come from clouds of hydrogen gas, distant planetary nebulae or globular clusters and satellite galaxies. The latter are numerous and extend to about 400 kpc from the centre of the Milky Way. The exponential scale length for the Milky Way's luminosity is a few kpc, so indeed observing these objects does explore the Galactic potential, and hence the matter distribution, to many times the size of the visible matter disc.

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  • $\begingroup$ Ahh, I didn't realise rotational data was accessible along those lines, and was wondering if there was perhaps some more esoteric method. Thank you! $\endgroup$
    – Stilez
    Mar 3, 2021 at 15:29
  • $\begingroup$ For some galaxies (e.g. massive ellipticals) you can also get information about the DM halo at large distances from observations of their hot, X-ray-emitting (gaseous) halos — though in that case it’s from hydrostatic pressure as a function of radius rather than rotation velocity. $\endgroup$
    – Peter Erwin
    Mar 5, 2021 at 8:41
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A brief point about the Milky Way and most galaxies, at some point I was taught intergalactic space between stellar objects was essentially empty. I've since learned that where a galaxy "ends" is inaccurate at best. They can stretch well beyond their visible structure. Objects like gas clouds or the always exciting dust deposits can be light years in size, and while dark, still very detectable. A Galaxy doesn't so much end, as much as it gradually loses density.

I think pointing out the fallacy of empty space is important here. I think it was easy to grow up with some misleading information.

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