Let's consider a nearby star with a surrounding spherical barrier or boundary (like the barrier or boundary I hypothesize for the sun at 52.6 AU). Maybe the star can achieve an apparent Doppler acceleration toward us, in two ways. One way, is if a distant companion, outside the star's barrier, accelerates the star and its barrier as a unit toward us.
Another way, is if a close companion, inside the star's barrier, accelerates the star relative to the barrier. There is a wavetrain between us and the star. Part of this wavetrain is within the star's barrier: call that part's length, L. If the first time-derivative of L is negative, blueshift may occur.
Let the star have a small distant companion whose distance is twice the barrer radius. If the "barrier" occurs at that surface in space where the magnitude of the gravitational field vector is such-and-such, then a distant companion causes the barrier to be indented, like a "flat tire", a small distance proportional to the mass of the small companion. Let the small companion be seen in inferior conjunction. As the small companion slowly orbits at inferior conjunction, the star and barrier are accelerated toward us. Also, we see the star's light through a part of the "tire" that is less and less indented. The first and second time-derivatives of L (see previous par.) are positive. There is accelerating positive "apparent radial velocity" due to the asphericity of the rotating barrier. The barrier's indentation is proportional to the mass of the small companion. So, the distortion of the barrier commonly could appear to cancel up to about half, of the entire barrier's acceleration toward us.
Now let's consider an equal-mass binary near conjunction, both sunlike, separated by a distance of order 50 AU. The barrier in such a binary might be a dumb-bell or it might be two flattened spheres which are not connected (dumb-bell with no handle). Either way, light from the more distant star passes twice through the barrier of the nearer one. Plausibly, the apparent (from apparent radial velocity, "RV", red/blueshift measurement) acceleration, of the farther partner, inferred from the progessive blueshifting of its light, is the sum of five terms:
1. The acceleration of its own barrier toward us.
2. The acceleration of its partner's barrier away from us (#1 & #2 cancel, because the light passes through both these equal but oppositely accelerated "icebergs").
3. The second time derivative of L1, the length of wavetrain within its own barrier (zero for a spherical barrier).
4A. The second derivative of L2, the length of the farther partner's wavetrain, within the nearer partner's barrier, but only that part due to the shortening at the surface nearest us.
4B. This term is the same as 4A except that it is that part due to shortening at the surface farthest from us, and has sign opposite the sign of 4A. That is, shortening at the surface nearest us simulates movement toward us, and shortening at the surface farthest from us simulates movement away from us.
The orbital elements (see Aitken, "Binary Stars" for clear definitions of these symbols) of 36 Ophiuchus AB (Irwin et al, 1996, op. cit.) make it relatively easy to calculate what the apparent "RV"-based acceleration of the farther partner toward us, should be if the foregoing theory is correct. With a slide rule, trigonometry and careful approximation (considering, to first order, the distortion of the barriers), I found that the "RV"-based apparent acceleration toward us should be 1.64 times the celestial mechanics prediction. Irwin et al found 1.64 times.
"Web of science" (the online Science Citation Index) shows only six papers citing Irwin's. None of these measure binaries like Irwin's. 36 Ophiuchus AB is special because the stars are far enough apart to be outside each other's barriers, yet close enough to conjunction that the farther partner's light must pass through the "barrier" hypothetically surrounding the nearer partner. The nearer partner's hypothetical "barrier" eclipses the farther partner.
