Textbooks explain the results solely when the observer is moving. There is no known explanation for the case when the source is moving. One can reliably determine the motion of individual stars of a binary system from their spectrum from the periodic Doppler shifting of the spectral lines of the star components. Therefore, stars of a binary system acquire sufficient relative transverse velocity to produce an important aberration. Such an aberration is not observed.
Some papers report non realistic hypotheses to explain aberration when the star is moving.
Mechanism of Aberration. Let us consider on figure 2, a stellar source S and a detector located on Earth. In physics, photons are conceived as being particles and are represented as bullets ejected from the surface of the emitter S with a velocity c. In this case, the star is moving upward with respect to the Earth. Photons emitted from the new direction b are now reaching the Earth.