2019/02/22 by R. N. Henriksen, J. Irwin, Henriksen, R. N. +1
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Astrophysics of Galaxies (astro-ph.GA) #Complex Systems and Time Series Analysis #Data Visualization and Analytics #FOS: Physical sciences #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1902.08704
openalex publication_date 2019/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new systematic method of studying correlations between\nparameters that describe an astronomical (or any) physical system. We recall\nthat behind Dimensionless scaling laws in complex, self-interacting physical\nobjects lies a rigorous theorem of Dimensional analysis, known widely as the\nBuckingham theorem. Once a it catalogue of properties and forces that define\nan object or physical system is established, the theorem allows one to select a\ncomplete set of Dimensionless quantities or it Numbers on which structure\nmust depend. The internal structure takes the form of a functionally defined\nmanifold in the space of these Numbers. Simple and familiar examples are\ndiscussed by way of introduction. Correlations in properties of astronomical\nobjects can be sought either through the constancy of these Numbers or between\npairs of the Numbers. In either case, within errors, the functional dependences\ntake on an absolute numerical character. As our principal application, we study\na well defined sample of galaxies in order to reveal the implied Tully Fisher\nand Baryonic Tully Fisher relations. We find that L ,\∝ ,vrot4 for\nthe former and Mb ,\∝ ,vrot3 for the latter, suggesting that these\nrelations may have different causal origins.\n