When we measure how fast stars orbit far from the center of spiral galaxies, what unexpected pattern of speed tells us about the presence of unseen dark matter?

When we measure how fast stars and gas clouds orbit far from the center of spiral galaxies, the unexpected pattern of speed observed is that their orbital velocities remain remarkably constant, even at great distances from the galactic center. This observation is known as a "flat rotation curve." Based solely on the visible matter in a galaxy, which includes all the stars, gas, and dust that emit or reflect light, astronomers would expect a different pattern. According to standard gravitational physics, specifically Keplerian mechanics, objects orbiting a central mass (like planets orbiting the Sun, where most of the mass is concentrated at the center) should slow down significantly as their distance from the center increases. Therefore, stars and gas clouds far from the visible galactic center should orbit progressively slower due to the decreasing amount of visible mass enclosed within their orbits. However, observations using the Doppler shift of light, which allows us to measure how fast objects are moving towards or away from us, reveal that these distant stars and gas clouds maintain a high, nearly constant orbital speed. This plot of orbital speed versus distance from the galactic center, known as a rotation curve, does not decline as expected but instead stays flat. This constant high speed at vast distances indicates that there must be a substantial amount of additional mass present that we cannot see. This unseen mass, which does not interact with light in any detectable way, is what we call dark matter. Dark matter is inferred to form a vast, spherical halo extending far beyond the visible parts of the galaxy, providing the necessary extra gravitational pull to keep the distant stars and gas orbiting at their observed high, constant speeds, thus explaining the flat rotation curve and the unexpected pattern of speed.