An Upper Limit on the Tightening of Galactic Spiral Arm Pitch Angle in Cosmic Time

We present Spirality, a novel method of measuring pitch angle by fitting galaxy images to spiral templates of known pitch. Using this algorithm in concert with 2-dimensional Fast Fourier Transform (2DFFT), we determined that the pitch angle of the redshift 2.011 galaxy GZ5001 (J2000 RA 189.14811 degrees, Dec 62.24002 degrees) is approximately (16.2 +/- 2.6) degrees. The redshift 2.3219 galaxy GS21 (J2000 RA 53.14863 degrees, Dec -27.95469 degrees), which is believed to be the most distant galaxy with visible spiral structure yet measured, has a pitch of approximately (-10.6 +/- 1.6) degrees. Using a large sample of galaxies from the Great Observatories Origins Deep Survey (GOODS), we place an upper limit on the tightening of average spiral arm pitch angle with cosmic time. With 68% confidence, we find that the average pitch for such galaxies has decreased (tightened) by no more than 9.94 degrees per unit redshift. If we constrain our data to be consistent with the local pitch angle mass function, we find a result that is consistent with a constant average pitch angle over cosmic time