Can Fractal Dimension Distinguish between Grand-design and Flocculent Spiral Arms?

Abstract About two-thirds of disk galaxies host spiral arms, ranging from well-delineated grand-design spirals to fragmented flocculent spiral galaxies. We introduce fractal dimension D B as a nonparametric measure to distinguish between grand-designs and flocculents. We calculate the D B of 197 grand-designs and 322 flocculents from Sloan Digital Sky Survey (SDSS) DR18, using the samples of R. J. Buta et al. (2015) and S. Sarkar et al. (2023). Our calculated median values of D B are <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.2</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.04</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.06</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.3</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.06</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.05</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for the grand-designs and flocculents, respectively. In addition, a Kolmogorov–Smirnov (K-S) test rejects the null hypothesis that these distributions are drawn from the same population. Finally, using a random forest model, we compare the effectiveness of D B in classifying spiral arm morphology with that of five other parameters: the total atomic hydrogen H I mass, M HI; the ratio of atomic hydrogen mass to blue luminosity, M HI / L B ; concentration index, C i ; clumpiness, S ; and arm contrast, C . Our results indicate that D B has the highest feature index (30.8%), followed by C i (26.0%) and M HI (21.0%). In fact, C—the metric routinely used to distinguish between the spiral morphologies—has a feature importance of 8.3%. Further, D B for grand-designs is found to anticorrelate with the central velocity dispersion with a correlation coefficient of −0.3 and p ≪ 0.05. The high value of central velocity dispersion indicates a central Q -barrier, which favors the formation of grand-designs according to the density wave theory. Thus, the fractal dimension serves as a robust metric to distinguish between spiral morphologies and also links to the formation mechanism of the spiral features.