  Hypervelocity stars (HVS) are a class of stars moving at high enough
velocities to be gravitationally unbound from the Galaxy. Ejection from a close
binary system in which one of the components undergoes a thermonuclear
supernova (SN) has emerged as a promising candidate production mechanism for
the least massive specimens of this class. This study presents a thorough
theoretical analysis of candidate progenitor systems of thermonuclear SNe in
the single degenerate helium donor scenario in the relevant parameter space
leading to the ejection of HVS. The primary goal is investigation of the,
previously unclear, characteristics of the velocity spectra of the ejected
component. Presented are the results of 390 binary model sequences computed
with the MESA framework, investigating the evolution of supernova progenitors
composed of a helium-rich hot subdwarf and a accreting white dwarf. Results are
then correlated with an idealized kinematic analysis of the observed object US
708. It is seen that the ejection velocity spectra reach a maximum in the range
$0.19~M_\odot < M_{HVS} < 0.25~M_\odot$. Depending on the local Galactic
potential, all donors below $0.4~\text{M}_\odot$ are expected to become HVS.
This channel is able to account for runaway velocities up to $\sim1150~\text{km
s}^{-1}$ with a Chandrasekhar mass accretor, exceeding $1200~\text{km s}^{-1}$
if super-Chandrasekhar mass detonations are taken into account. It is found
that the previously assumed mass of $0.3~M_\odot$ for US 708, combined with
more recently obtained proper motions, favor a sub-Chandrasekhar mass explosion
with a terminal WD mass between $1.1~M_\odot$ and $1.2~M_\odot$. The presence
of clear ejection velocity maxima provides constraints on the terminal state of
a supernova progenitor. It is possible to discern certain types of explosion
mechanisms from the inferred ejection velocities alone.
