Legend:

blue = all effects
red = no polarization amplitude (i.e. no precession effects included in this term; it still has the LISA motion)
black = no polarization phase
green = no polarization amplitude OR phase
cyan = no intrinsic 2PN phase (beta and sigma modulations)
magenta = no intrinsic precessional phase ("Thomas precession phase")


The masses seem most strongly influenced by the intrinsic phase, although the polarization terms play a role in some cases (esp. bad ones!). I had thought the polarization terms played a bigger role, since they are the only modulations Vecchio has (beta and sigma are constant for him). Then again, who can trust Vecchio's equal mass results? And it does make sense that, given the additional modulation, the intrinsic phase would help more than the extrinsic phase since the masses are intrinsic parameters. The reduced mass, in particular, may benefit, since at higher order in the intrinsic phase, it's mixed up with beta and sigma. (I think this degeneracy is mentioned several places?)

The sky position is a disaster. The blue (all effects) line follows the cyan one for most of the points, so the intrinsic phase seems to be no help at all. This makes sense. Oddly enough, the errors get better in those cases if the other terms are removed! I guess this shows the complexity of the effects and how we can't really separate them (especially since they all derive from one very simple motion of the binary). In general, though, the polarization terms seem to dominate. The precession correction to the orbital phase ("Thomas precession," though it isn't) actually plays its biggest role here. In most of the other examples, it tends to follow the blue curve in almost all cases. Perhaps Vecchio was justified in leaving it out, but it does some good for us.

No contest here: the angular momentum direction is all determined by the polarization stuff. Note that if either the amplitude or the phase is shut off, things don't get so bad, but if they both are, disaster strikes. They seem to be redundant effects. By the way, this (and some of the next graphs) are probably the reason why the intrinsic phase does a terrible job at everything if it is the ONLY effect included. (Maybe the Thomas precession helps out just enough to make the matrix not totally singular so that the green lines don't go crazy for every parameter.)

More of the same for the spin directions:


And for the spins. However, spin 2 expecially seems to depend a bit more on the intrinsic phase. I guess beta and sigma depend more on the spin magnitudes than on the spin directions (they only depend on relative direction, not absolute).


And finally (since I didn't bother with t_c and phi_c), the luminosity distance is a mess. Again, cyan tracks blue, so the intrinsic phase is useless. It's hard to tell too much here. In many cases, the polarization terms are helpful. Note how the red is more promimnent in many cases, often tracking the green. This suggests that the polarization amplitude is more important than the phase, which makes sense for D, since it appears in the rest of the amplitude.

Summary: Take these results with a grain of salt, since the conditions are artificial. Also, take a look at the plots yourself too since I may have bringing some bias into it. It's hard to read them because of the clutter and also because some of the lines might overlap so that we only see the last plotted one. Is there any other combination of effects that would be useful to look at? In any case, we've got a little better understanding of the impact of precession now.