Exploring MBH-P Scaling Relations in Spiral Galaxies: A Comparative Analysis of Inner and Outer Arm Structures

We study the galactic spiral arm pitch angle dependence with wavelength as predicted by the density wave theory. A sample of ten barred and unbarred spiral galaxies with two distinct, well-defined arms is used for the measurements. The data sample consists of galaxies with inner arms and galaxies with both inner and outer arms. We use six wavebands, namely 3.6 μm, 8.0 μm, B-band, Hα, HI, and CO for the image analysis. The pitch angles are visually measured with the Python-OL script and more precise measurements are obtained using SPIRALITY. We find a 1:1 correlation between pitch angle measurements in the 3.6 μm and 8.0 μm bands. We predict super massive black hole (SMBH) masses for 3.6 μm waveband pitch angles using a standard scaling relation. We find that the black hole mass of a galaxy with both inner and outer arms is determined by the average pitch angle of the inner arms. Using only galaxies with inner arms, we find an SMBH mass- pitch angle relation of log (MBH/M_ )=(7.11 ± 0.33)+(0.003 ± 0.017)P. Using only galaxies with both inner and outer arms, we find an SMBH mass-pitch angle relation of log (MBH/M_ )=(7.56 ± 0.28)-(0.038 ± 0.013)P.