Abstract
Abstract We present the analytical framework for converting projected light distributions with a Sérsic profile into three-dimensional light distributions for stellar systems of arbitrary triaxial shape. The main practical result is the definition of a simple yet robust measure of intrinsic galaxy size: the median radius r med, defined as the radius of a sphere that contains 50% of the total luminosity or mass, that is, the median distance of a star to the galaxy center. We examine how r med depends on projected size measurements as a function of Sérsic index and intrinsic axis ratios, and demonstrate its relative independence of these parameters. As an application we show that the projected semimajor axis length of the ellipse enclosing 50% of the light is an unbiased proxy for r med, with small galaxy-to-galaxy scatter of ∼10% (1σ), under the condition that the variation in triaxiality within the population is small. For galaxy populations with an unknown or a large range in triaxiality an unbiased proxy for r med is 1.3 × R e , where R e is the circularized half-light radius, with galaxy-to-galaxy scatter of 20%–30% (1σ). We also describe how inclinations can be estimated for individual galaxies based on the measured projected shape and prior knowledge of the intrinsic shape distribution of the corresponding galaxy population. We make the numerical implementation of our calculations available.
Highlights
The spatial distribution of stars in a galaxy encodes key information about its formation history, whether dissipative or dissipationless processes dominated and whether angular momentum has been retained or lost
We present the analytical framework for converting projected light distributions with a Sersic profile into three-dimensional light distributions for stellar systems of arbitrary triaxial shape
The main practical result is the definition of a simple yet robust measure of intrinsic galaxy size: the median radius rmed, defined as the radius of a sphere that contains 50% of the total luminosity or mass, that is, the median distance of a star to the galaxy center
Summary
The spatial distribution of stars in a galaxy encodes key information about its formation history, whether dissipative or dissipationless processes dominated and whether angular momentum has been retained or lost. One limiting factor is the missing link between the projected size (the half-light radius that we measure) and a physically more directly meaningful quantity such as the average or median distance of a star to the center of its galaxy. In this paper we present the analytical framework and numerical implementation for the conversion of 2D light profiles to 3D light distributions for galaxies of arbitrary triaxial shape With this machinery can we take full advantage of the available high-quality data and make accurate comparisons with theoretical predictions. This papers is organised as follows: Section 2 describes how triaxial shapes project in 2D; Section 3 depicts the deprojection of Sersic profiles; Section 4 introduces the definition and derivation of the median radius, rmed; Section 5 outlines how to infer, in practice, rmed from projected size and shape measuremts; Section 6 concludes with a brief description of implications of our findings for galaxy size estimates
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