  The stellar density profile a galaxy is typically summarised with two
numbers: total stellar mass and half-light radius. The total mass of a galaxy,
however, is not a well-defined quantity, due to the finite depth of photometric
observations and the arbitrariness of the distinction between galaxy and
diffuse intra-group light. This limits our ability to make accurate comparisons
between models and observations. I wish to provide a more robust two-parameter
description of the stellar density distribution of elliptical galaxies, in
terms of quantities that can be measured unambiguously. I propose to use the
stellar mass enclosed within 10 kpc in projection, $M_{*,10}$, and the
mass-weighted stellar density slope within the same aperture, $\Gamma_{*,10}$,
for this purpose. I measured the distribution in $M_{*,10}$ and $\Gamma_{*,10}$
of a sample of elliptical galaxies from the Sloan Digital Sky Survey and the
Galaxy And Mass Assembly survey, using photometry from the Hyper Suprime-Cam
survey. The pair of values of $(M_{*,10},\Gamma_{*,10})$ can be used to predict
the stellar density profile in the inner 10 kpc of a galaxy with better than
20% accuracy. Similarly, $M_{*,10}$ and $\Gamma_{*,10}$ can be combined to
obtain a proxy for stellar velocity dispersion at least as good as the stellar
mass fundamental plane. As a first application, I then compared the observed
$M_{*,10}-\Gamma_{*,10}$ relation of elliptical galaxies with that of similarly
selected galaxies in the EAGLE Reference simulation. Observed and simulated
galaxies match at $M_{*,10}=10^{11}M_\odot$, but the EAGLE
$M_{*,10}-\Gamma_{*,10}$ relation is shallower and has a larger intrinsic
scatter compared to observations. This new parameterisation of the stellar
density profile of massive elliptical galaxies provides a more robust way of
comparing results from different photometric surveys and from hydrodynamical
simulations.
