  A variety of nonthermal characteristics like kinetic, e.g., temperature,
anisotropies and suprathermal populations (enhancing the high energy tails of
the velocity distributions) are revealed by the in-situ observations in the
solar wind indicating quasistationary states of plasma particles out of thermal
equilibrium. Large deviations from isotropy generate kinetic instabilities and
growing fluctuating fields which should be more efficient than collisions in
limiting the anisotropy (below the instability threshold) and explain the
anisotropy limits reported by the observations. The present paper aims to
decode the principal instabilities driven by the temperature anisotropy of
electrons and protons in the solar wind, and contrast the instability
thresholds with the bounds observed at 1~AU for the temperature anisotropy. The
instabilities are characterized using linear kinetic theory to identify the
appropriate (fastest) instability in the relaxation of temperature anisotropies
$A_{e,p} = T_{e,p,\perp}/ T_{e,p,\parallel} \ne 1$. The analysis focuses on the
electromagnetic instabilities driven by the anisotropic protons ($A_p \lessgtr
1$) and invokes for the first time a dynamical model to capture the interplay
with the anisotropic electrons by correlating the effects of these two species
of plasma particles, dominant in the solar wind.
