Tapered Flow Model Series‏

This series of models is one of the most interesting and, in some ways, probably the most realistic. That is, purely cylindrical flows are an idealization. More likely the "cylindrical" flow is a bit sloppy along its lateral perimeter. The Gaussian taper is a way to develop a conical jet whose density and velocity roll off at the edges. As it turns out, the lobes take on quite a nice variety of morphologies depending on the ratios of wind and core densities. This may yet prove to be very useful for explaining he shapes of HST images of prePNe.

(Martin implemented the Gaussian tape in this way: one specifies a spherical flow (opening angle of 90 degrees) AND a flow taper function for the density and the velocity with angle, theta, from the flow axis such that both n_jet and v_jet fall off with elevation according to a Gaussian of angle tf = 1/e angle. I used tf=15 deg.)

The results are shown below. The window sizes are highly variable. The density and temperature are shown in the left panels. A zoom-in of the kinematics is shown to the right.

Bear in mind that observers NEVER see any emission from the jet. Rather, they observe shock-excited emission from the tip (speeds 100-200km/s), the gas along the lateral edges that is (or has been) shocked at the head (shock speeds 10-50 km/s), or both. That is, since the emissivity scales as density squared they observe the lobe tip and the relatively dense outer skin of the lobe.

The top panels show a light jet (nJet << namb(core)). A triangular lobe emerges. Its dense and fast leading edge is susceptible to thin-shell instabilities as it propagates into the ambient medium. The middle panels show an intermediate case where nJet = namb(core). A thin tapered lobe develops and maintains its shape after it reaches a distance where the ambient gas density (pressure) is low. The bottom panels show a heavy jet that simply blasts its way forward like a rounded piston. Its shape and propagation speed never change.

Look in the upper-right corner of the left panes where I show that average speed of the tip of the jet, <v_tip>. The top row (light jet emerging at 200 km/s) is significantly decelerated by the ambient medium at first. <v_tip> is just 90 km/s averaged over 400 y. The other two cases have <v_tip> ~ 200 km/s.

In the bottom row a hot sheath of gas (that was originally shock-heated near the leading tip) forms between the tapered flow and the lateral edges of the lobe. It's thermal pressure is significant, and the lobe edges expand nearly laterally and slowly. In the other cases the momentum of the wind suppresses the formation of a large and hot sheath. Nonetheless a warm sheath (at 10,000K) forms where the gas radiates its heat. Even so, a thin hot zone forms where the tapered wind rams into the sheath. I can't recall seeing this sort of behavior before.

One final note. The early hydro tapered-jet computations of Sahai & Lee (2003) at coarse resolution found that the walls of the jet are where wind streamlines slide and converge towards the tip of the lobe. That's the concept behind the Canto model developed originally to explain H-H outflows. Very smooth walls are essential if the streamlines are to move coherently towards the lobe tip. In our sims we see no trace of streamlines sliding up the lobe walls, nor do we see any evidence of flow convergence at the lobe tips.