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We know that the uniform rotation curve of individual spiral galaxies does require presence of some form of dark entity (matter). Does the attraction between two (or more) spiral galaxies also require same dark entity? Have such calculations been done? If there is dark matter, it should be required in same amount by both phenomena - 1) uniform rotation curve of individual galaxies, and 2) mutual interaction of two (or more) such galaxies.

This is not necessarily about clusters because the dark matter cloud can span galaxies in a cluster. I am trying to see whether local (rotation curve) effects of dark matter match the inter galactic effects where the dark clouds of two galaxies are disjoint.

In the same manner as above two clusters can be considered for comparing local and inter cluster effects as long as the dark clouds of two clusters are disjoint.

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  • $\begingroup$ Do you mean rotation curves and orbital interaction for the same pair of galaxies? Zwicky's original observation of dark matter was from the gravitational interactions in the Coma cluster, but as far as I know this hasn't been backed up by rotation curve measurements for the galaxies in the Coma cluster. $\endgroup$ – John Rennie Oct 26 '18 at 6:38
  • $\begingroup$ @JohnRennie: Yes. Rotation curves of two galaxies will require some amounts of dark entity in each. Mutual interaction of same two galaxies should require same amounts of dark entity in each. Cluster may be different as the dark matter cloud can span galaxies in a cluster. I am trying to see whether local (rotation curve) effects of dark matter match the inter galactic effects $\endgroup$ – kpv Oct 26 '18 at 6:44
  • $\begingroup$ I think that would be challenging. You'd need to calculate the orbital parameters of the galaxies and that would require observations on a timescale of millennia. $\endgroup$ – John Rennie Oct 26 '18 at 6:46
  • $\begingroup$ @JohnRennie: I have updated the question to add details about your comment. $\endgroup$ – kpv Oct 26 '18 at 6:54
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Observations imply that there is a considerable amount of dark matter or unseen matter on astronomical scales ranging from clusters of galaxies to individual galaxies themselves. For instance the masses of galaxies in a cluster as estimated from the virial theorem to account for their observed velocity dispersion (v^2 ) giving the dynamical mass, Md ~ (v^2 )R/G turns out to be at least a factor of ten higher than what one would except from the luminosity(Faber and Gallagher 1979). Even groups of galaxies seem to have inadequate luminous mass by a similar factor. To account for their dynamical dispersion, the proportion of unseen non luminous mass should increase with increasing scales. Again studies of the dynamics and structure of large spiral galaxies suggest that a universal feature of all the rotation curves is that at large galacto centric distances they are either flat or slowly rising, there being no large spiral galaxy whose rotation curve falls (Rubin et al. 1982). The rotational velocities for a point mass (keplerian) are given by v^2 being proportional to GMr /r, Mr being the mass contained within a radius r. These observations of flat , v = constant, rotation curves imply Mr increasing linearly with r indicating the presence of much unseen dark matter up to large distances from the centre of the spiral galaxies. The progressive increase in the dynamical mass with radius is a characteristic feature of all these galaxies, i.e. individual galaxies are surrounded by massive dark halos, which have as much as ten times the mass of the visible matter. It is now known that x-ray emitting hot gas (e.g. from clusters and galactic coronae) would account for only a small fraction of the required missing mass. Other propositions for DM ranging from black holes to very low mass stars have met with various difficulties, So finally the presence of dark matter in halos and beyond halos (in clusters) imply a large ratio of dynamical mass to luminous mass. This non baryonic mass is present for large distances from the galaxy. The orbital velocity remains constant at larger distance from the galactic core.

The galaxy as has long been suspected has at its centre a massive black hole, with estimated mass of around 3million suns. If the galaxy was held together by the attraction of that mass, and the motion around it was circular. Thus the effective value of M increases with distance, and the rotation velocity v in the denser parts of the galaxy may falls off less steeply than like 1/r. However, beyond densest part, v should drop off, and this fall off should be close to 1/r. But in practice the velocity of the objects beyond the halos become constant. The matter implies still present but its not radiating. One can give some models. Conclusion: Several observations imply that the rotational curves of the galaxies for long distances are flat. It indicates the presence of DM or unseen matter.Considering suitable models for these DM halos, one can plot the flat rotation curves. If we consider the effects of cosmological constant on large scales, the flat curves take a dip at very large distances. From this we can get the formula for the distance beyond which the dark energy dominates. By applying different values for ω in the generalized metric, we conclude that the ω value should be always< -1/3. Sorry for such long answer, I haven't mentioned the mathematical formulae as I thought this is sufficient.

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  • $\begingroup$ @kpv Did I misunderstand your question? $\endgroup$ – MayukJ Oct 26 '18 at 15:51

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