Can fractal dimension distinguish between grand-design and flocculent spiral arms?

TL;DR

This study demonstrates that fractal dimension effectively distinguishes between grand-design and flocculent spiral galaxies, correlates with galaxy properties, and offers insights into spiral arm formation mechanisms.

Contribution

Introduces fractal dimension as a novel, non-parametric metric for classifying spiral galaxy morphology and compares its effectiveness with other parameters.

Findings

Fractal dimension differs significantly between galaxy types.

Fractal dimension has higher feature importance than traditional metrics.

Anti-correlation between fractal dimension and central velocity dispersion.

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 non-parametric measure to distinguish between grand-designs and flocculents. We calculate the $D_B$ of 197 grand-designs and 322 flocculents from SDSS DR18, using the samples of \citet{Buta..2015} and \citet{Sarkar..2023}. Our calculated median values of $D_B$ are $1.29^{+0.06}_{-0.04}$ and $1.38^{+0.05}_{-0.06}$ for the grand-designs and flocculents, respectively. In addition, a Kolmogorov-Smirnov (K-S) test rejects null hypothesis that these distributions are drawn from the same population. Finally, using a Random Forest (RF) model, we compare the effectiveness of $D_B$ in classifying spiral arm morphology, as compared to five other parameters viz. total atomic hydrogen HI mass $M_{HI}$, 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 anti-correlate with the central velocity dispersion with a correlation coefficient of -0.3 and $p \ll 0.05$. A 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, fractal dimension serves as a robust metric to distinguish between spiral morphologies and also links to the formation mechanism of spiral features.