Kinemetry: a generalization of photometry to the higher moments of the line-of-sight velocity distribution

TLDR

The paper introduces a generalization of surface photometry to higher‑order moments of galaxies’ line‑of‑sight velocity distributions using integral‑field spectroscopy. The method fits ellipses to the velocity field, extracts moment profiles along them, models odd moments with a cosine law and even moments as constant, and then expands the profiles harmonically. Velocity profiles of early‑type galaxies follow a cosine law to within 2 % accuracy, with fifth‑order harmonics revealing multiple kinematic components; kinematic ellipses closely match photometric ones, and the authors provide kinemetric parameters to quantify velocity‑map features.

Abstract

We present a generalisation of surface photometry to the higher-order moments of the line-of-sight velocity distribution of galaxies observed with integral-field spectrographs. The generalisation follows the approach of surface photometry by determining the best fitting ellipses along which the profiles of the moments can be extracted and analysed by means of harmonic expansion. The assumption for the odd moments (e.g. mean velocity) is that the profile along an ellipse satisfies a simple cosine law. The assumption for the even moments (e.g velocity dispersion) is that the profile is constant, as it is used in surface photometry. We find that velocity profiles extracted along ellipses of early-type galaxies are well represented by the simple cosine law (with 2% accuracy), while possible deviations are carried in the fifth harmonic term which is sensitive to the existence of multiple kinematic components, and has some analogy to the shape parameter of photometry. We compare the properties of the kinematic and photometric ellipses and find that they are often very similar. Finally, we offer a characterisation of the main velocity structures based only on the kinemetric parameters which can be used to quantify the features in velocity maps (abridged).