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The main evidence for the existence of dark matter is the flat rotation curve of galaxies, and high peculiar velocities of galaxies in galaxy clusters.The mass eclosed in a radius R is derived from the Keplerian equation M(R) = v2R/G .Also we know about the existence of gravitational lensing.My question is this: was gravitational lensing taken into account when galactic rotation curves were plotted? Because here is an effect of gravitational lensing that I didn`t find mention of:The photon emmited by the star can`t travel directly to the observer because it is gravitationally pulled to the center of the galaxy, so its trajectory is bent. And because of this bending effect the observer will see the star as being farther away from the galactic center. This in turn will push the observer to the conclusion that there is more mass enclosed in the observed radius. If the orbital speed of the star is not calculated from it’s red shift then it will also appear to be bigger then it actually is, since v = w*r, where w – angular velocity, r – observed radius.Consequences:1) All massive celestial objects appear greater then they actually are.2) The farther away the celestial object from the observer the stronger the magnification effect.3) Most of the distant celestial object that we observe are not actually in the direction that we observe them.P.S.: The fish is also distorted
My question is this: was gravitational lensing taken into account when galactic rotation curves were plotted? Because here is an effect of gravitational lensing that I didn`t find mention of:
1) All massive celestial objects appear greater then they actually are.2) The farther away the celestial object from the observer the stronger the magnification effect.
Thanks a lot for your replies, guys. I was wrong apperantly.
If the gravitational-lensing-effect was noticeable the far-half of a galaxy would appear bigger than the half closest to us ...
... If curving occurs at the far side of the galaxy, then it should occur at the close side too, so your bottom line of sight should also be curved, which would change the apparent position of the bottom star down from its real one, and which would tilt the galaxy plane towards the observer a bit.
The observed speed is 2-3 times the expected speed. If that was due to gravitational-lensing expanding radial measurements the far half of the galaxy would appear conspicuously bigger than the near half.
let's work out an example and see if this is even feasible. We'll assume a galaxy 100,000 light years across with a mass of 100,000,000,000 solar masses which is 1 billion light years away.The light from a source behind this galaxy and just skimming its edge, would by gravitational lensing be deflected by 0.258 sec of arc. Since 1/2 of this deflection occurs on the inbound path, the most we can expect light coming from a star at the edge to be bent on its outward path to us is 0.129 sec of arc.At a distance of 1 billion light years, this equates to an apparent displacement of ~625 light years ( meaning the galaxy would appear to be 50,625 light years in radius instead of 50,000.)Calculating the difference in orbital speed at 50,000 vs. 50625 light years produces orbital velocities of 167 km/sec vs. 168 km/sec.If we work out how much extra mass it would take to make that 1 km/sec difference at a fixed radius of 50625 light years, it works out to a difference of ~1.2%, or far short of the amount of dark matter needed to make up for the missing mass according to the actual orbital velocities we measure.In addition, gravitational lensing in fact gives us additional evidence for dark matter. Because of the extra mass due to DM, the light passing galaxies bends more than and differently from what we would expect from just the matter we see.On top of that, we have the case of the Bullet Cluster, in which dark matter has been "knocked loose" from the visible matter in a collision between galaxy clusters. In this situation we see gravitational lensing of objects behind the cluster where there is no visible matter to cause it.Galaxy rotation curves may have set us on the road to dark matter, but there has been a great deal of other supporting evidence uncovered since the first step on that path.
Thanks for the calculations Janus. So you came to the conclusion that this kind of bending cannot account for dark matter, but it sure can account for the flatness of the curve though, because both the exaggerated speed and the apparent bending are caused by the same importance of the curved space at the same distance from the center of mass, so if we do the calculations for different distances, we should get a rotation curve which would be similar to the predicted one, but a bit higher on the graph. Am I right?