What determines a progenitor's fate as a spiral or elliptical? I was thinking about my answer to Are the inner planets on planar orbits because there was more dust in the inner solar system (early on in planetary accretion)?
- when it occurred to me that maybe I was reversing cause and effect. Specifically, that perhaps spiral galaxies simply arise from high-angular-momentum progenitors, while elliptical arise from low angular-momentum progenitors. In this scenario, the spiral wave-pattern would merely be how that excess angular momentum organizes itself, and the matter can't help but stir itself.
For a warm-up question and consistency checker, do spiral galaxies in fact have substantially greater total angular momentum than elliptical?
 A: Elliptical galaxies are thought to be the result of mergers - in galaxies clusters, where the density of galaxies is (relatively) high, then elliptical galaxies are more common, and clusters are often dominated by a single giant elliptical galaxy in the core (which coincides with the peak of X-ray emission from diffuse intracluster gas). Galaxies in lower-density environments, such as our own Local Group, are more likely to be spiral. 
If you examine the merger of two spiral galaxies, a process known as 'violent relaxation' driven by the rapid change of gravitational potential in the merger transforms the ordered spiral orbits of stars around the core of the spiral into a random motion, which is what we observe in elliptical galaxies. Further evidence for mergers is that we see huge bursts of star formation in interacting galaxies (e.g. the Antennae), leaving little gas left for ongoing star formation after the merger is complete, and elliptical galaxies tend to contain very few new stars compared to spirals. 
