In this work , we analyze the kinetic stability of a solar wind electron distribution composed of core and strahl subpopulations . The core is modeled by a drifting Maxwellian distribution , while the strahl is modeled by an analytic function recently derived in [ ] ] horaites18 from the collisional kinetic equation . We perform a numerical linear stability analysis using the LEOPARD solver \citep astfalk17 , which allows for arbitrary gyrotropic distribution functions in a magnetized plasma . In contrast with previous reports , we do not find evidence for a whistler instability directly associated with the electron strahl . This may be related to the more realistic shape of the electron strahl distribution function adopted in our work , as compared to previous studies . We however find that for typical solar wind conditions , the core-strahl distribution is unstable to the kinetic Alfvén and magnetosonic modes . The maximum growth rates for these instabilities occur at wavenumbers kd _ { i } \lesssim 1 ( where d _ { i } is the ion inertial length ) , at moderately oblique angles of propagation , thus providing a potential source of kinetic-scale turbulence . We therefore suggest that if the whistler modes are invoked to explain anomalous scattering of strahl particles , these modes may appear as a result of nonlinear mode coupling and turbulent cascade originating at scales kd _ { i } \lesssim 1 .