Pitch Angle Calculation of Spiral Galaxies Based on the ROTASE Model

This paper demonstrates that the pitch angle of a spiral galaxy can be calculated from the spiral arm simulation based on the new ROTASE model for the formation of spiral arms of galaxies, the new spiral equations from the model are more universal than other spiral formulas. A spiral arm length weighed average method is proposed to more fairly calculate the average pitch angle for the entire galaxy. The spiral patterns of the galaxy J101652.52, the galaxy NGC 4314 and NGC 210 are nicely simulated by the ROTASE model and their average pitch angles are calculated. The spiral patterns of the galaxy J101652.52 is a Sbc type galaxy with well-defined short arms; the spiral pattern of NGC 4314 is made of two identical rings, each ring is made of a half small inner ring and a half large outer ring, each ring crosses other ring twice with chain-link style, the quality of the spiral arm decreases along the spiral arm line due to aging of X-matter stream. The NGC 210 shows a nice spiral-ring pattern. The special spiral patterns of galaxies NGC 4314 and NGC 210 fully match the ROTASE model. Total of 15 pitch angles of galaxies are calculated and listed in this paper. The size of the spiral arms may not be limited by 4/1 Lindblad resonance due to the possible non-gravitational/anti-gravitational property of the X-matter. The results show that the average pitch angle of the galaxy heavily depends on the length of the spiral arms and decreases quickly within the one loop of spiral arm winding range, the age of the spiral arms and the quality of the galactic disc have strong impact on the length of the spiral arms and on the value of the average pitch angle of the galaxies. If the spiral pattern of a galaxy can be well simulated by a formula, then the pitch angle obtained from the simulation will be more accurate than other methods with automated computer signal picking from images which have substantial interarm signals and strong background and foreground signals. The new findings in this study indicates that the correlation between the average pitch angle of the spiral arms and the mass of central supermassive black hole may be unreliable due to the heavy dependence of pitch angle on the length of the spiral arm. Spiral patterns with central symmetry can only be initiated/started at the galactic centers, any non-central spiral arm initiators cannot produce such patterns. The density waves proposed for the spiral arm formation do not exist in the disc galaxies. A completely new mechanism has to be adopted to describe the formation of the spiral arms. The ROTASE model is just the first attempt in this direction, but certainly not the last, other different models may come up in the future.