astrophysics - Is there evidence of dark matter in our galaxy?

Is there evidence of dark matter in our galaxy?

How can we measure this, say, how many percent of the center of our galaxy is dark matter?

I did not find the answer in the question What's dark matter and who discovered it?

Answer

A star in the disk of our Milky Way galaxy orbits around the galactic center, much like planets in the solar system orbit the Sun, owing to the gravitational attraction of all the stars and other matter in the galaxy that are closer to the galactic center than the star in question. For our galaxy, the orbital speed for the Sun and other stars at the same distance from the galactic center as our Sun, is about 220 km/s, resulting in an orbital period of about 200 million years.

For our solar system, 99.9 % of the mass is in the sun, so the speed of the planets orbiting it drops off as the inverse square root of the distance from the Sun (a result easily derived from Newton's law of gravity, whereby the gravitational force drops off as the inverse square of the distance). Earth's orbital speed is 30 km/s, and Jupiter, 5.2 times further away, has an orbital speed of 13 km/s. The orbital speed also depends on the square root of the mass at the center, so if our Sun became four times as massive, the Earth's orbital speed would double.

For an extended object, such as our galaxy, it can be derived from Newton's law that the gravitational force from the whole galaxy acting on a star is just equal to what would be expected from all the matter closer to the galactic center than is the star. All forces from stars and matter further out from the center cancel themselves out.

If all the mass of our galaxy were at the center, then the orbital speed would drop off as the inverse square root of the distance from the center, just as for the solar system. But, since the galaxy's mass is extended, then the orbital speed will drop off more slowly than that. In fact, if the mass located within a given distance from the center goes up as the square of that distance (as it would for a flat disk of constant thickness and density), then the orbital speed will be more or less constant as we go further and further out. The same would be true for a spherical halo, where the density drops off as the 2/3 power of the distance from the center.

In the 1970's astronomers studying orbital speeds around the centers of other galaxies found that the orbital speed is indeed roughly constant, against all expectations. Around the same time, other astronomers studying radial velocities of distant stars in our galaxy found that to be true for our galaxy as well. And studies of the 21-cm of interstellar hydrogen have revealed that this constant speed continues way out from the centers of galaxies, much beyond the furthest stars that can be seen.

But it has been long known that the distribution of stars in all normal galaxies, whether spiral or elliptical, is strongly concentrated toward the center, and so it was expected that orbital speed would continuously decrease as we moved away from the center. The only explanation for the anomaly was that there was another source of matter beyond what we can see in stars and interstellar matter, that was responsible. This has become known as the 'dark matter'.

In fact, consequences of the dark matter had been seen as long ago as the 1950s when it was noticed that the speeds of galaxies milling about in distant clusters of galaxies was much higher than one would expect from the total masses of all the stars. But these were so far away that we couldn't be sure that there wasn't some faint matter component that was responsible. Having it in our own galaxy as well brings home the result that the matter causing the excess speeds is indeed dark.

It is difficult to measure the percentage of dark matter in our galaxy since, being inside it, we can't determine how far away from the galactic center the most distant clouds of neutral hydrogen are. It is easier to measure the distances to the edges of other galaxies and galaxy clusters. Best guesses are that about 80 % of the mass in our galaxy is dark matter.