When we look at a spiral galaxy like the one on the left, we see most of its light coming from the central region. Most of the mass is concentrated at the centre of the galaxy which keeps the stars in circular orbit in the galaxy. Because most of the mass of the galaxy is concentrated in the centre, then we would expect that stars further from the centre would move at a slower velocity than stars closer to the centre. For example, in the solar system, most of the mass of the solar system is concentrated in the Sun.The velocities of planets decreases outwards. If we plot a graph of orbital speed of stars against distance from the centre of galaxy you would except the graph to be going downwards as the orbital speed of the stars will decrease as the distance from the centre increases but what we found when we made the measurements that in spiral galaxies the velocities of stars far from the centre are much faster than expected. Normally circular motion is governed by a balance between gravity (pulling the star towards the galactic centre) and an effective centrifugal force (pulling the star outwards). The faster a star moves the stronger the centrifugal force. If we count up all the stars and estimate the mass of the galaxy, the force of gravity is not large enough to balance the centrifugal force associated with these fast stars. We would expect these stars to be ripped out of the galaxy. But the stars are in stable circular orbits! This suggests that there is more mass in the galaxy than what we can see. We call this mass dark matter since we can't see it. This the first evidence for the existence of dark matter! Second evidence is the galaxies in the cluster. Galaxies in the cluster seem to spin so fast that the stars in them should fly away from each other but thats not what we see so there must be some other kind of matter that is holding these galaxies together and thus this was called dark matter. This was observed by two astronomers Fritz Zwicky in 1930s, Vera Rubin in 1962. Now we know that the clusters of galaxies are indeed surrounding by dark matter. Third evidence comes from gravitational lensing. Imagine youself outside in a clear sky and looking at the Andromeda galaxy. You will see andromeda galaxy because of the light from this galaxy travelling through the universe and then entering your eye. You will know where the galaxy is because of the direction of the ray of light coming from. Now suppose if i place in the middle (between andromeda and milky way) a cluster of galaxy and obviously dark matter surrounding the cluster, now the ray of light will be deflected as predicted by Einstein so now you will see the rays of light would lie on a cone so you would see something called Einstein ring like the one's above in the images. It will only be a perfect ring if the galaxy, cluster of galaxy and the observer lie in a straight line. Now based on the distortion we can calculate how much mass there is in this cluster of galaxy and what we find is that the mass of this cluster is about 10 times more than we would see, the presence of dark matter.
so we have 3 evidence why dark matter must exist and those are: * The speed of the stars in the galaxy. * The speed at which the galaxies spin in clusters * The gravitational lensing effect
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