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In the Large-Scale-Structure (LSS) artifacts named fingers-of-god are apparent in the redshift space and justified by

"The large velocities that lead to this effect are associated with the gravity of the cluster by means of the virial theorem; they change the observed redshifts of the galaxies in the cluster"

There are few references, (Jackson 1972) (*), and Annu. Rev. Astron. Astrophys. 1988. 26: 631-86 in the WP article and I do no understand how the radial direction preference is justified and I could not find any source.

I've never heard of a N-Body simulation on Large Scale able to reproduce those artifacts. Am I correct? Can anyone make this issue more clear, please ?

(*) it is more a no-go than an explanation.

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Suppose you have a cluster of galaxies at a "spatial" redshift of $z=0.5$. The galaxies in the cluster are swirling around each other, much like the stars of a star cluster. The velocities are broadly spread out in all directions but the line-of-sight velocity leads to a Doppler shift. Now, if all you measure is change in frequency of spectral features relative to some lab standard, then your measurement is a superposition of the "distance" redshift (i.e. redshift because the object is far away and space is expanding) and the "velocity" redshift (i.e. redshift because of Doppler shifting from line-of-sight velocity in the potential of the cluster).

When you plot the galaxies of your cluster, you'll find that, instead of all sitting at $z=0.5$, they will occupy a spread in redshift space but the same point on the sky. That's because the tangential velocity doesn't contribute to the redshift at all: only the line-of-sight component does so only the redshift-direction is elongated into fingers.

This would probably make much more sense with a diagram but some quick Googling didn't get me anywhere.

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