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Gravitational lensing takes advantage of statistically uniform distributions of background objects in order to infer a credible map of dark matter concentrations that isn't too noisy. If there are too many background objects and is not clear there is an uniform pattern of distribution that one can compensate numerically, then the noise of the measurement makes the reading essentially worthless

So, I'm curious if there is any research attempt to try to pull this kind of local measurement of lensing in the "backyard". If one takes the Milky Way's galactic rotation curve, and compares it on what's expected given baryonic matter, one would be able to have a radial distribution of expected dark matter in order to compare with the results of lensing

But is that kind of lensing measurement something that is possible today?

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Well, there are microlensing experiments, the results of which have largely removed MACHOs as a significant source of Dark Matter. The background field of stars is usually a nearby galaxy (a Magellanic cloud one or Andromeda, say), or the galactic bulge, and the experiment looks for lensing objects between us and there. In particular, they're pretty much always looking for the microlensing effect within our own Milky Way or its halo. These experiments have detected a number of microlensing events (and many, many more candidates that were due to other things), so, yes, this is not only possible, it is already done.

The wiki page I started with linking has this to say, in particular:

The first two microlensing events in the direction of the Large Magellanic Cloud that might be caused by dark matter were reported in back to back Nature papers by MACHO and EROS in 1993, and in the following years, events continued to be detected. The MACHO collaboration ended in 1999. Their data refuted the hypothesis that 100% of the dark halo comprises MACHOs, but they found a significant unexplained excess of roughly 20% of the halo mass, which might be due to MACHOs or to lenses within the Large Magellanic Cloud itself. EROS subsequently published even stronger upper limits on MACHOs, and it is currently uncertain as to whether there is any halo microlensing excess that could be due to dark matter at all. The SuperMACHO project currently underway seeks to locate the lenses responsible for MACHO's results.

Despite not solving the dark matter problem, microlensing has been shown to be a useful tool for many applications. Hundreds of microlensing events are detected per year toward the Galactic bulge, where the microlensing optical depth (due to stars in the Galactic disk) is about 20 times greater than through the Galactic halo. In 2007, the OGLE project identified 611 event candidates, and the MOA project (a Japan-New Zealand collaboration) identified 488 (although not all candidates turn out to be microlensing events, and there is a significant overlap between the two projects). In addition to these surveys, follow-up projects are underway to study in detail potentially interesting events in progress, primarily with the aim of detecting extrasolar planets. These include MiNDSTEp, RoboNet, MicroFUN and PLANET.
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