A theoretical study of identifying co-rotation radii and galactic resonances of spiral galaxies

Abstract

This study delved into the dynamic behaviours of spiral galaxies, employing a robust approach to analyse co-rotation radii and galactic resonances within the framework of Density Wave Theory. It aimed to develop new methods for identifying resonance locations and co-rotation radii, conduct comparative analyses across ten diverse spiral galaxies, predominantly grand-design spiral galaxies with different pattern speeds, and validate these methods against existing techniques. The first method used rotation curve analysis to identify Inner Lindblad Resonances, 4:1 resonances, co-rotation radii, and Outer Lindblad Resonances, utilising two pattern speeds from literature for comparative purposes. The first pattern speeds yielded co-rotation radii closer to literature values for galaxies NGC 1566, NGC 4254, NGC 4303, NGC 4321, and NGC 5247. Conversely, for NGC 5194 and NGC 5248, the second pattern speeds yielded better alignment. However, NGC 1365 and NGC 5236 showed deviations from literature values for both pattern speeds, while NGC 4535 posed challenges in determining its corotation radius. A comparative analysis of co-rotation radii against mean literature values indicated successful alignment despite significant uncertainties for NGC 1365, NGC 4254, and NGC 4303. The second approach used 3D surface intensity plots to identify resonance regions, focusing on low star formation areas, enhancing understanding of dynamic structures. It compared co-rotation radii with literature values, highlighting probable regions and addressing uncertainties, particularly in NGC 1365, NGC 5236, and NGC 5247. Methodological precision was crucial, given the nuances revealed by these plots. Comparing Method I and II, Method I aligned better with literature values for NGC 4254, NGC 4303, NGC 4321, NGC 5194, NGC 5247, and NGC 5248, while Method II showed closer alignment for NGC 1566 and NGC 4535. NGC 1365 and NGC 5236 exhibited discrepancies in co-rotation radii values across both methods compared to the literature. The third methodology employed theoretical calculations to align empirical observations with theoretical predictions, enhancing the understanding of galactic resonant dynamics. NGC 4535 was excluded due to data limitations. The systematic approach derived theoretical resonance locations for co-rotation radii, outlining an analytical roadmap. Comparative analysis between empirical and theoretical resonance values revealed close alignment for most galaxies, enriching insights into resonant phenomena within galactic systems. The fourth method involved measuring spiral arm pitch angle measurements across multiple wavelengths (3.6 μm, 8.0 μm, B-band, Hα). A custom Python code facilitated the overlaying of spiral arm patterns from different wavebands onto FITS images, enabling detailed comparative analyses. The identification of crossing points, coupled with consideration of pitch angle uncertainties, offered a sophisticated approach to delineating resonance locations on the galactic disk. Challenges in measuring and comparing pitch angles highlighted the complexities of detecting outer arms and resolving discrepancies across imaging wavelengths. In conclusion, each method employed in this study has its unique strengths and challenges while no single method was universally superior, as galaxies showed varying compatibility with each approach. These findings enhance the understanding of galactic morphology and evolution, including implications for galactic habitable zones.