We measure the pitch angle ( \varphi ) of spiral arms in a sample of 79 galaxies to perform a systematic study of the dependence of \varphi on galaxy morphology , mass , and kinematics to investigate the physical origin of spiral arms .
We find that \varphi decreases ( arms are more tightly wound ) , albeit with significant scatter , in galaxies with earlier Hubble type , more prominent bulges , higher concentration , and larger total galaxy stellar mass ( M _ { * } ^ { gal } ) .
For a given concentration , galaxies with larger stellar masses tend to have tighter spiral arms , and vice versa .
We also find that \varphi obeys a tight inverse correlation with central stellar velocity dispersion for \sigma _ { c } \ga 100 km s ^ { -1 } , whereas \varphi remains approximately constant for \sigma _ { c } \lesssim 100 km s ^ { -1 } .
We demonstrate that the \varphi - \sigma _ { c } and \varphi - M _ { * } ^ { gal } relations are projections of a more fundamental three-dimensional \varphi - \sigma _ { c } - M _ { * } ^ { gal } relation , such that pitch angle is determined by \sigma _ { c } for massive galaxies but by M _ { * } ^ { gal } for less massive galaxies .
Contrary to previous studies , we find that \varphi correlates only loosely with the galaxy ’ s shear rate .
For a given shear rate , spirals generated from N -body simulations exhibit much higher \varphi than observed , suggesting that galactic disks are dynamically cooler ( Toomre ’ s Q \approx 1.2 ) .
Instead , the measured pitch angles show a much stronger relation with morphology of the rotation curve of the central region , such that galaxies with centrally peaked rotation curves have tight arms , while those with slow-rising rotation curves have looser arms .
These behaviors are qualitatively consistent with predictions of density wave theory .