  In the solar wind electron velocity distributions reveal two counter-moving
populations which may induce electromagnetic (EM) beaming instabilities known
as heat flux instabilities. Depending on plasma parameters two distinct
branches of whistler and firehose instabilities can be excited. These
instabilities are invoked in many scenarios, but their interplay is still
poorly understood. An exact numerical analysis is performed to resolve the
linear Vlasov-Maxwell dispersion and characterize these two instabilities,
e.g., growth rates, wave frequencies and thresholds, enabling to identify their
dominance for conditions typically experienced in space plasmas. Of particular
interest are the effects of suprathermal Kappa-distributed electrons which are
ubiquitous in these environments. The dominance of whistler or firehose
instability is highly conditioned by the beam-core relative velocity, core
plasma beta and the abundance of suprathermal electrons. Derived in terms of
relative drift velocity the instability thresholds show an inverse correlation
with the core plasma beta for the whistler modes, and a direct correlation with
the core plasma beta for the firehose instability. Suprathermal electrons
reduce the effective (beaming) anisotropy inhibiting the firehose modes while
the whistler instability is stimulated.
