We present imaging of molecular gas emission in the star-forming spiral galaxy NGC 6946 .
Our ^ { 12 } CO ( 1-0 ) and ^ { 12 } CO ( 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 ^ { 12 } CO ( 1-0 ) emission shows a central concentration aligned in a north-south ellipse , an extended diffuse component plus concentrations in the outer spiral arms . ^ { 12 } CO ( 1-0 ) is detected across most of the optical disk out to a projected radius of nearly 300″ .
The molecular component in NGC 6946 is unusually massive , with \mathrm { M } _ { \mathrm { H } _ { 2 } } / \mathrm { M } _ { \mathrm { HI } } = 0.57 .
The scale length of the disk in ^ { 12 } CO ( 1-0 ) is the same , to within 5 % , of the VRI , H \alpha , 15 \mu m , and FIR disks .
The ^ { 12 } CO ( 3-2 ) data shows broadly similar structure to the ^ { 12 } CO ( 1-0 ) image out to the observed limit of 200″ , although the arm-interarm contrast of ^ { 12 } CO ( 3-2 ) is significantly larger than that of ^ { 12 } CO ( 1-0 ) which suggests that molecules in the spiral arms are warmer or reside longer there .
The rotation curve derived from the ^ { 12 } CO ( 1-0 ) velocity field agrees , within the uncertainties , with the H i  rotation curve .
The velocity dispersion is 40 \pm 10 km s ^ { -1 } in the inner 2 kpc and 8 \pm 3 km s ^ { -1 } in the disk , without tendency to increase in the spiral arms .

Spectra of the ^ { 13 } CO ( 1-0 ) , ^ { 13 } CO ( 2-1 ) , ^ { 12 } C ^ { 18 } O ( 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 \pm 5 Â K , the molecular gas density is ( 3.3 \pm 0.3 ) \times 10 ^ { 3 } cm ^ { -3 } and that line opacities are high , with \tau _ { { } ^ { 12 } \mathrm { CO } ( 3 - 2 ) } \sim 10 .
A star formation efficiency image for NGC 6946 , made from the H \alpha image divided by the molecular gas image , ranges by over two orders of magnitude with highest values found in the northeastern spiral arm .
The \lambda 6 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 \mu m-emitting dust .
The highest correlation between any pair of tracers is found between the mid-infrared emission and the total radio continuum emission at \lambda 6 cm .
This can not 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 .