Gravitational wave distortion

Question

Gravitational waves detected are from merging of black holes few millions of light years away. While waves have reached us after travelling so far, they must have encountered many black-holes and have reached us after refracting/gravitational lens effects. Then how do one decide the correct direction of those merging black holes?

Answer 1

Gravitational waves are affected by gravitational lensing in the same way as light. Most lensing events are not caused by black holes, but by more common objects with similar mass.

There largest deflection examples of the light from distant galaxies, quasars etc being diverted by foreground sources (clusters of galaxies) is about an arcminute (e.g. Zitrin et al. 2014). Current gravitational wave detectors are not capable of locating sources even to a few degrees. So source location isn't an issue at present.

Source strength might be. A lensed source can be magnified or even split into multiple images that arrive at different times. This will lead to a luminosity distance underestimate from a gravitational wave source and an overestimate of its mass.

For those that are interested, Oguri et al. (2018) have done an extensive set of simulations, showing the effects of gravitational lensing on estimates of mass and redshift distributions for black hole binary gravitational wave sources.

The conclusion is that for detectors like LIGO there should be a (very) small tail of highly magnified events with underestimated redshifts and overestimated masses. These are predominantly at (chirp) masses $>40 M_{\odot}$ (which is also roughly the minimum mass of the primary component in a binary) and more massive than any of the LIGO events seen so far.

The "optical depth" to lensing as a function of source redshift is shown in Fig. 3 of that paper. What this shows is that the chance of any individual source being strongly ($>$ factor of 10 or split into multiple images) lensed is less than one in a million at typical LIGO source distances of a billion light years (redshifts of less than 0.1). But this probability can increase by several orders of magnitude at the high redshifts that might be probed by detectors in the future.

Answer 2

Gravitational waves detected by the LIGO that originate a few million light years away is not far away, relatively speaking, at all. As user Chappo has noted, space is mostly empty. Although gravitational waves can be scattered or distorted by an sufficiently massive and dense celestial body, it has a very low probability of happening. Although the technology today has no way of determining the original position of where the waves originate if the waves are disturbed, such disturbance is very unlikely. So it is safe to say that almost all waves detected by the LIGO can be traced back to their original positions.