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A spiral galaxy is a disk galaxy that has spiral arms, one of three galaxy classes described by Edwin Hubble along with elliptical galaxies and lenticular galaxies. The galaxy classification designations for spiral galaxies are SA or SB (or SAB for something between) followed by a letter, a, b, c or d, indicating how tight are the arms. SB is for barred, i.e., a barred galaxy, a spiral galaxy whose center appears like a bar between two opposing arms rather than just a circular mass of stars. Spiral galaxies are generally younger than elliptical galaxies with more interstellar gas and dust, and are generally forming stars. There is a correlation between color and spiral/disk versus elliptical: that flat galaxies tend to be blue, indicating early stars and star formation, and elliptical galaxies tend to be red. However red spiral galaxies do exist.
The dynamics that produces the galaxy's spiral structure (i.e., the spiral arms) is not immediately apparent: if the arm structure simply consisted of the position of the stars as they orbit around the galaxy, the inner stars getting around quicker than the outer stars would make the arms wrap tighter with time, and there would be more tightly-wrapped galaxies than are seen in surveys. A classic theory consists of spiral density waves (of higher-density intergalactic medium) feeding a visible spiral wave of star formation. Many of the created stars will be bright but short-lived, so a traveling line of star formation will show as a line of brightness, a spiral arm. N-body simulations have produced spiral structures, but under varying assumptions.
The stars' orbits are not simple circles, and probably not ellipses, and efforts to characterize the orbits in a useful way include breaking each into an epicyclic frequency (toward and away from the center) and vertical oscillation frequency (up and down from the plane).
Example spiral galaxies:
The Magellanic clouds have been considered irregular but are now sometimes cited as single-armed spiral galaxies, termed Magellanic spiral galaxies. An anemic galaxy is a spiral galaxy where the spirals and the portions between them show less contrast, i.e., like lenticular galaxies but with a visible spiral pattern. A flocculent spiral galaxy is one where the spiral arms are not continuous, but patches of brightness.