You're right that I inadvertently mischaracterized Siegel's article. I expected him to quantify the Z-motion of the solar system in the remainder of the text, and would have known that he did not if I had not lazily and sloppily declined to read the remainder. I simply relied on his reputation as a science popularizer while looking for a popular treatment rather than parametric quantities.
Turning to the latter, it is well known that the residual solar motion with respect to the average of local stars is U_sun ~ -10 km s^1, V_sun ~ 5-15 km s^-1, W_sun = 7 km s^-1, leading to the sun moving centre-ward, faster than the local standard of rest, and northward out of the galactic plane. (cf. Dehnen & Binney 1998 [1], and also Schönrich, Binney & Dehnen[2] figures of (U,V,W) = (11.1, 12.24, 7.25) km/s with uncertainties (+0.69-0.75, +-0.47, +0.37-0.36)). Although we are currently close to mid-plane, with a half-period of ~30 million years the solar system for the past six hundred million years has moved in the R,z plane +- 0.075 kpc from the mid-point.
This is simply not within the equatorial plane, as opposed to oscillating within the bulk of the stellar disc and through the equatorial plane. The distinction is, in my view, important. So is the point that other local stars move in the z-plane differently.
R,\theta is also a bit more complicated than suggested by Siegel's article; the orbit in that plane traces out a rosette shape around the galactic centre.[3]
None of this however addresses the key point, which is that the equatorial planes of stellar objects and collapsars are not in general parallel to the equatorial plane of the galaxy, and as a consequence polar jets are not perpendicular to it. The comment several generations up to which you initially replied asked about why the radio-loud steep-spectral-index filaments are all close to perpendicular to the galaxy's equatorial plane. It is a good question, and your answer was not correct.
Stellar collapses, no, but once a black hole has accreted one other stellar body its dragged frame's axis of rotation will be altered by about half. Ten others and the original spin will have a very small influence.
It's unlikely for accreted stars to be in the same galactic orbit, so the accreted stars will be adding to the rotation in the galactic plane.
Do you really think that? I suggest you try to write down a simple distribution of matter in the far region of the Kerr metric, and the simplest tractable Lagrangian expressed with respect to the angular variables as the generalized coordinates, and see where it takes you as an exercise just for yourself -- a sort of self-diagnostic comparing your intuitions about weak-field systems and what you get as you walk through this sort of exercise (cf. MTW chs 21 & 26, especially exercise 26.1, which seems obviously relevant).
(Near region and strong-field work has already been done for you, numerically but recently, in recent work on GW200129_065458 e.g. https://arxiv.org/search/?query=GW200129&searchtype=all&abst... and this excellent visualizer https://vijayvarma392.github.io/binaryBHexp/ . For extra self-credit you will already be wondering about the final parsec problem, and junction conditions for the previous problem as you adapt the Kerr metric for multiple black holes.)
Turning to the latter, it is well known that the residual solar motion with respect to the average of local stars is U_sun ~ -10 km s^1, V_sun ~ 5-15 km s^-1, W_sun = 7 km s^-1, leading to the sun moving centre-ward, faster than the local standard of rest, and northward out of the galactic plane. (cf. Dehnen & Binney 1998 [1], and also Schönrich, Binney & Dehnen[2] figures of (U,V,W) = (11.1, 12.24, 7.25) km/s with uncertainties (+0.69-0.75, +-0.47, +0.37-0.36)). Although we are currently close to mid-plane, with a half-period of ~30 million years the solar system for the past six hundred million years has moved in the R,z plane +- 0.075 kpc from the mid-point.
This is simply not within the equatorial plane, as opposed to oscillating within the bulk of the stellar disc and through the equatorial plane. The distinction is, in my view, important. So is the point that other local stars move in the z-plane differently.
R,\theta is also a bit more complicated than suggested by Siegel's article; the orbit in that plane traces out a rosette shape around the galactic centre.[3]
None of this however addresses the key point, which is that the equatorial planes of stellar objects and collapsars are not in general parallel to the equatorial plane of the galaxy, and as a consequence polar jets are not perpendicular to it. The comment several generations up to which you initially replied asked about why the radio-loud steep-spectral-index filaments are all close to perpendicular to the galaxy's equatorial plane. It is a good question, and your answer was not correct.
[1] https://academic.oup.com/mnras/article/298/2/387/1056582 https://arxiv.org/abs/astro-ph/9710077
[2] https://academic.oup.com/mnras/article/403/4/1829/1054839 https://arxiv.org/abs/0912.3693
[3] https://www.wolframalpha.com/input?i=parametricplot++%28%28%... for 660 Myr., parameters ibid. & [4], but very much my answer to "show your math". Spatial units are kpc.
[4] https://ui.adsabs.harvard.edu/abs/1986gss..conf...35B/abstra... http://www.as.utexas.edu/astronomy/people/fnb/pubs.html