If dark matter bends light, how do we know the stuff in the sky is where we think it is?

We measure movement, position, and many other things of an object in space because of its light and what we can measure with it. But as far as I know there's supposed to be a HUGE amount of dark matter in space whose mass and size we don't know, and because it has mass it has gravity and it can bend light.

I know physics can take into account the gravity of stars and huge stuff in space, but how can they be certain of any of their measurements (specially the position) if they don't know how that light has deviated from a straight line?

• The analysis of Gaia astrometry does need to take into account the lensing effects of the Sun, planets and even major asteroids. But not dark matter, which is likely reasonably homogeneous on local scales apart from gravitational focus caused by the Sun. – Rob Jeffries Jan 17 '17 at 18:11

The local dark matter density is actually quite tiny, on the order of $\rho\sim10^{-19}\text{ g/cm}^3$ (see e.g. Bovy & Tremaine (2012)). This means that there is roughly $0.001$-$0.01M_{\odot}$ of dark matter per cubic parsec - a staggeringly small amount. 1000 cubic parsecs would contain about one solar mass of dark matter - and that's a cube 10 parsecs in length on each side! Now, the distribution of dark matter in galaxies is not homogeneous - it follows, roughly, a Navarro-Frenk-White profile, decreasing in density from the center of the galaxy - but on the scale of parsecs (and certainly in the Solar System), we can consider it to have roughly uniform density.

On small scales, then, we have approximate homogeneity and low density. This means that any gravitational lensing effects from dark matter should be extremely low or self-cancelling, arising only from inhomogeneities containing large clumps of dark matter. However, such clumps are unlikely to form solely through dark matter's interaction with itself (if we discount the MACHO hypothesis, which, as far as I know, is not currently favored).

On intergalactic scales, however, dark matter can have some effects. Weak lensing is a commonly-observed phenomenon in galaxy clusters, which may have extremely high fractions of dark matter. There are several techniques currently used to model the mass distribution of the lensing galaxy (see the KSB+ method) and to reconstruct the image and position of the original galaxy via deconvolution (see Chantry & Magain; a visual example is given here). I'm not too familiar with either technique, though, so I can't give you a good overview.

Even large-scale lensing has large mass requirements. zephyr pointed out that the foreground object that created the Einstein cross contained $\sim10^{10}M_{\odot}$ of dark matter (van de Ven et al. (2010)). That is enormous!

• Just to add some additional numbers on the other end of the scale to this great answer: The Einstein Cross, a well-known strong lensing event, is caused by $10^{10}\:M_{\odot}$ of dark matter (source). And that is generally a "weaker" strong lensing event. That just gives you the scale of mass needed to cause the effects OP asks about in their question. – zephyr Jan 17 '17 at 16:38
• Wow, great answer! Thanks! This was something I've been wondering for quite some time, I'll make sure to check all the links! – Sebastian Araneda Jan 17 '17 at 17:31
• I've asked a related question. – uhoh Jan 18 '17 at 1:03
• There's an NFW profile, and they didn't ask anyone with an S surname to be coauthor? such a missed opportunity. – Emilio Pisanty Jan 18 '17 at 9:05
• @EmilioPisanty They could have asked Sérsic, but he was doing his own thing. – HDE 226868 Jan 18 '17 at 19:49