4.2.4. Gas density versus Star Formation

Galactic-wide values     Star formation SF parameters have been determined for spiral galaxies, using the light integrated over the whole image of a galaxy. These published star formation rate parameters give galactic-wide SF_gal values, and they should be compared to galactic-wide gas density n_gal values and galactic-wide magnetic field B_gal values.

Caveat.     At low gas density values n 1 cm^-3, some authors used a relation SFR_gal ~ n_cloud^1.4 (e.g., Fig. 5 in Niklas & Beck 1997, with SFR from galactic-wide thermal radio emissivity and n from CO data from clouds) together with a relation B_gal ~ n_cloud^0.5 (e.g., Fig. 4 in Niklas & Beck 1997, with B from galactic-wide synchrotron electrons measured outside clouds and n from CO data from inside clouds) to eliminate n assuming n_gal = n_cloud (however only the density from the interstellar intercloud gas n_gal should be used, not the cloud density), and thus they predict a relation B ~ SFR^2.9 (e.g., Section 4.5 in Niklas & Beck 1997). Since these are different objects, n_gal n_cloud , then this data selection invalidates this claim, since both B OUTSIDE clouds and n OUTSIDE clouds should be used, and not B OUTSIDE with gas density n INSIDE extrapolated to predict n OUTSIDE.

The relationship B ~ SFR^j (Section 4.2.1), and the other relationship B ~ n^k for galactic wide gas density n < 100 cm^-3 over large scales (Section 4.2.3) can be used together to eliminate B, yielding the galactic wide relation SFR ~ n^k/j. With k = 0.17 ± 0.03 (Vallée, 1995d), and with j = 0.13 ± 0.04 (Vallée, 1994b), then one computes that the exponent k/j = 1.3 ± 0.1, i.e., one gets SFR ~ n^1.3 (Vallée, 1995d).

This exponent value 1.3 also agrees within the observational errors with the value of 1.5 ± 0.5 found elsewhere using the observed optical HII region emissivity measures (e.g., Shore and Ferrini 1995; Kennicutt 1992). It agrees with the value of 1.4 ± 0.3 found using the observed radio HII region emissivity (e.g., Niklas & Beck 1997). It also agrees within the errors with the rough value of 1.0 found in the galaxy NGC6946, and the favored value of 2 for the Milky Way galaxy (e.g., equation 3 in Young 1987). It agrees with the value < 2 for other spiral galaxies (e.g., Kamaya 1996). Such exponent values less than 2 are possibly indicative of a star formation process involving turbulences (e.g., Ikeuchi, 1988). Young et al. (1996) found that the SFE in interacting galaxies is 4 times the SFE in isolated galaxies.