Fu, H., ApJL, 963, L19 (2024) “Restoration of the Tully-Fisher Relation by Statistical Rectification”

In this Letter, I develop a new method to construct the well-known Tully-Fisher relation of disk galaxies: statistical rectification. The main advantage of the statistical method compared to the conventional method is that it eliminates one major source of uncertainty in the process: inclination angle estimation from axial ratio.

The Python notebook that implemented the method and the merged data catalog are shared on Github.

The method has a wide range of applicabilities in observational astronomy. It can be applied to any problems where (1) the observed properties can be converted from the intrinsic pfroperties by a relation that involves a “hidden” parameter and (2) the probability density function of the hidden parameter is precisely known.

Above: The observed distribution of ALFALFA-SDSS galaxies in the plane of projected i-band absolute magnitude vs. projected HI line width. Above: The statistically restored distribution of the ALFALFA-SDSS galaxies in the plane of face-on i-band absolute magnitude vs. edge-on HI line width. This is the Tully-Fisher relation.

Acknowledgement

The research benefited from the excellent data from two ground-based observational facilities: the Arecibo Observatory and the Sloan Digital Sky Survey. The work at Iowa was generously supported by the Natinoal Science Foundation (NSF) under grant AST-2103251.