Molecular gas in NGC 6946

We present imaging of molecular gas emission in the star-forming spiral galaxy NGC 6946. Our (CO)-C-12(1-0) and (CO)-C-12(3-2) images, made at 22 resolution with the IRAM 30-m and the Heinrich Hertz 10-m radio telescopes, are the most extensive observations of molecular gas in this galaxy and are among the most extensive observations of molecular gas in any spiral galaxy. The (CO)-C-12(1-0) emission shows a central concentration aligned in a north-south ellipse, an extended diffuse component plus concentrations in the outer spiral arms. (CO)-C-12(1-0) is detected across most of the optical disk out to a projected radius of nearly 300. The molecular component in NGC6946 is unusually massive, with M-H2/M-HI = 0.57. The scale length of the disk in (CO)-C-12(1-0) is the same, to within 5%, as the VRI, Halpha, 15 mum, and FIR disks. The (CO)-C-12(3-2) data shows broadly similar structure to the (CO)-C-12(1-0) image out to the observed limit of 200, although the arm-interarm contrast of (CO)-C-12(3-2) is significantly larger than that of (CO)-C-12(1-0) which suggests that molecules in the spiral arms are warmer or reside longer there. The rotation curve derived from the (CO)-C-12(1-0) velocity field agrees, within the uncertainties, with the H I rotation curve. The velocity dispersion is 40 +/- 10 km s(-1) in the inner 2 kpc and 8 +/- 3 km s(-1) in the disk, without tendency to increase in the spiral arms. Spectra of the (CO)-C-13(1-0), (CO)-C-13(2-1), (CO)-C-12-O-18(1-0) isotopomers for several positions are used for line ratio studies of the state of the molecular ISM in NGC 6946. In the centre of NGC 6946 our LVG analysis suggests that the beam-averaged gas kinetic temperature is 40 +/- 5 K, the molecular gas density is (3.3 +/- 0.3) x 10(3) cm(-3) and that line opacities are high, with tau12(CO(3-2)) similar to 10. A star formation efficiency image for NGC 6946, made from the Halpha image divided by the molecular gas image, ranges by over two orders of magnitude with highest values found in the northeastern spiral arm. The lambda6 cm polarized emission image, which traces the regular part of the magnetic field, appears anti-correlated with the star formation efficiency. We present an analysis of the ISM in NGC 6946's disk by making 1-D and 2-D comparisons of images made in several wavebands. Using a point-by-point correlation technique, we investigate the distribution and kinematics of the molecular gas and its relation to the neutral and ionized gas, the mid-infrared-emitting dust, the radio continuum and the magnetic field, and find that the molecular gas is closely associated with the 7 mum-emitting dust. The highest correlation between any pair of tracers is found between the mid-infrared emission and the total radio continuum emission at lambda6 cm. This cannot be due to dust heating and gas ionization in star-forming regions because the thermal radio emission is less correlated with the mid-infrared emission than the nonthermal emission. A coupling of magnetic fields to gas clouds is proposed as a possible scenario.