  We investigate the relationship between a dark matter halo's mass profile and
measures of the velocity dispersion of kinematic tracers within its
gravitational potential. By predicting the scaling relation of the halo mass
with the aperture velocity dispersion, $M_\mathrm{vir} - \sigma_\mathrm{ap}$,
we present the expected form and dependence of this halo mass tracer on
physical parameters within our analytic halo model: parameterised by the halo's
negative inner logarithmic density slope, $\alpha$, its concentration
parameter, $c$, and its velocity anisotropy parameter, $\beta$. For these
idealised halos, we obtain a general solution to the Jeans equation, which is
projected over the line of sight and averaged within an aperture to form the
corresponding aperture velocity dispersion profile. Through dimensional
analysis, the $M_\mathrm{vir} - \sigma_\mathrm{ap}$ scaling relation is devised
explicitly in terms of analytical bounds for these aperture velocity dispersion
profiles: allowing constraints to be placed on this relation for motivated
parameter choices. We predict the $M_{200} - \sigma_\mathrm{ap}$ and $M_{500} -
\sigma_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and
$56.2\%$, respectively. These halo mass estimates are found to be weakly
sensitive to the halo's concentration and mass scale, and most sensitive to the
size of the aperture radius in which the aperture velocity dispersion is
measured, the maximum value for the halo's inner slope, and the minimum and
maximum values of the velocity anisotropy. Our results show that a halo's
structural and kinematic profiles impose only a minor uncertainty in estimating
its mass. Consequently, spectroscopic surveys aimed at constraining the halo
mass using kinematic tracers can focus on characterising other, more complex
sources of uncertainty and observational systematics.
