A PDF PSA, or Never gonna set_xscale again -- guilty feats with logarithms

TL;DR

This paper emphasizes the importance of correctly adjusting density values when plotting data on logarithmic scales in astronomy, rather than just setting the axis to log, to avoid misrepresentations.

Contribution

It highlights a common mistake in astronomical plotting and provides guidance on proper density adjustments for logarithmic plots.

Findings

Incorrect density scaling can lead to misinterpretation of data.

Proper adjustment of densities is crucial for accurate logarithmic plots.

The paper offers pedagogical examples and discusses exceptions.

Abstract

In the course of doing astronomy, one often encounters plots of densities, for example probability densities, flux densities, and mass functions. Quite frequently the ordinate of these diagrams is plotted logarithmically to accommodate a large dynamic range. In this situation, I argue that it is critical to adjust the density appropriately, rather than simply setting the x-scale to `log' in your favorite plotting code. I will demonstrate the basic issue with a pedagogical example, then mention a few common plots where this may arise, and finally some possible exceptions to the rule.