What is the relationship between HI, CO and star formation in spiral arms? The gas is generally compressed more than the stars in a spiral density wave or swing-amplified transient spiral, and if star formation follows the gas, then the blue light from star formation will be enhanced more than the yellow and red light from old stars. This makes the spirals arms blue. The Bigiel et al. (2008) and Leroy et al. (2008) correlation between SF rate and CO, which is a very tight correlation, implies that there is little difference in the rate per unit CO molecule for gas in strong-arm galaxies compared to gas in weak-arm galaxies.
The morphology of gas in the arms tells something about the star formation process. Grabelsky et al. (1987) showed that most of the CO clouds in the Carina arm of the Milky Way are clustered together in the cores of 107 M HI clouds. Elmegreen & Elmegreen (1987) found the same for the Sagittarius spiral arm. Lada et al. (1988) observed a similar HI envelope-CO core structure in a piece of a spiral arm in M31. Engargiola et al. (2003) showed a complete map of M33 with numerous CO clouds in the cores of giant HI clouds. The presence of giant HI clouds in spiral arms has been known for a long time (e.g., for the Milky Way: McGee & Milton 1964; for NGC 6946: Boulanger & Viallefond 1992). Now it looks like most dense molecular clouds are in the cores of giant spiral arm HI clouds, or if the gas is highly molecular at that radius in the disk, in the cores of giant clouds that are also highly molecular. This means that GMCs form by condensation inside even larger, lower-density clouds. The large HI/CO clouds, in turn, probably form by gravitational instabilities in the spiral arm gas, particularly in the dust lanes where the spiral shock brings the gas to a high density. Recall from Lecture 1 that the largest unstable clouds have the Jeans mass in a galaxy disk, given the observed turbulent speed and column density (i.e., M ~ 4 / G2 gas ~ 107 M).
In the Milky Way and M33, giant spiral arm clouds are mostly atomic, but in M51, they are mostly molecular (Ranf & Kulkarni 1990). This difference is presumably because the arms in M51 are much stronger than the arms in the Milky Way and M33, and the gas is denser overall in M51 as well. Thus, the pressure is higher in M51, particularly in the arms, and the gas is more highly molecular there and everywhere else in the inner disk. The physical process of giant cloud formation should be the same in all three cases, however.
Gravitational instabilities also seem to initiate cloud and star formation on the scale of whole galaxies. This process is clear in many regions, such as Stephan's quintet (Mendes de Oliveira et al. 2004), NGC 4650 (Karataeva et al. 2004), and in the tidal arcs of NGC 5291 (Bournaud et al. 2007), where there are massive condensations in tidal features.
Dobbs & Pringle (2009) studied gravitationally bound clouds in an SPH simulation. In the spiral arms, large regions formed by gravitational instabilities where gravity balanced thermal, turbulent and magnetic energies. When they used a star formation rate equal to 5% of the bound gas column density divided by the dynamical time, plotted versus the total gas column density, they reproduced the Kennicutt (1998) and Bigiel et al. (2008) star formation laws over the range of overlap. They noted that the star formation law is linear with column density because the dynamical time inside each bound cloud is the same, i.e., they all have the same density. They answered the long-time question of whether density waves trigger star formation (Elmegreen & Elmegreen 1986) by saying, no, there is no correlation between the average column density of star formation and the spiral arm potential depth. The reason is that stronger spiral waves make clouds with higher velocity dispersions and they are harder to bind into gravitating cloud complexes. The fraction of the bound gas in spiral arms increases with the spiral strength, but not the star formation rate.
Observations of spiral arm star formation and gas distributions also suggest there is little triggering (Foyle et al. 2010). The primary effect of the spiral is to concentrate the gas in the arms without significantly changing the star formation rate per unit gas.