Answer to Question 1
When astronomers measure the masses of galaxies, they often find that the measured masses are much larger than expected from the luminosities of the galaxies. Measured masses of galaxies amount to 10 to 100 times more mass than you can see. Dark matter is difficult to detect, and it is even harder to explain. Some astronomers have suggested that dark matter consists of low-luminosity white dwarfs and brown dwarfs scattered through the halos of galaxies. Searches for white dwarfs and brown dwarfs in the halo of our Galaxy have found a few but not enough to make up most of the dark matter. The dark matter can't be hidden in vast numbers of black holes and neutron stars, because astronomers don't see the X-rays these objects would emit. The evidence indicates there is 10 to 100 times more dark matter than visible matter in galaxies, and if there were that many black holes they would produce X-rays that would be easy to detect. Because observations imply that the dark matter can't be composed of familiar objects or material, astronomers are forced to conclude that the dark matter is made up of unexpected forms of matter.
Answer to Question 2
The most precise method for measuring the mass of a galaxy is called the rotation curve method. It requires knowing the following: (1 ) the true sizes of the orbits of stars or gas clouds within a galaxy, which in turn requires knowing the distance of that galaxy; and (2 ) the orbital speeds of the stars or gas clouds, measured from the Doppler shifts of their spectral lines. That is enough information to use Kepler's third law and find the mass of the part of the galaxy contained within the star orbits with measured sizes and velocities. The rotation curve method works only for galaxies near enough to be well resolved. More distant galaxies appear so small that astronomers cannot measure the radial velocity at different points across the galaxy and must use other, less precise, methods to estimate masses.
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