| | 23 | ---- |
| | 24 | |
| | 25 | '''Jet Sims''' |
| | 26 | ---- |
| | 27 | |
| | 28 | Jets are the other simple geometry of flow, again being largely one-dimensional. Dense jets (njet > namb) ram their way through any environment like a flying phone pole. In our case where the ambient density falls off quickly with distance, a jet may interact strongly with the local gas near the nucleus, but after it reaches regions of low external density the jet feels little "headwind". |
| | 29 | |
| | 30 | [[Image(https://dl.dropboxusercontent.com/s/6fj7kgz66u6w4i9/jets.jpeg?dl=0)]] |
| | 31 | |
| | 32 | |
| | 33 | The images above illustrate this. The jet on the left is 100x denser than the inner environment right from the start and moves a full speed, 200 km/s through the time of the simulation. It compresses and then sheds the ambient material to the side. The ambient material is shocked to a high temperature so a hot sheath forms around the sides of the head of the jet and falls behind. Its thermal expansion forms the lobe edges out of compressed ambient material. These expand laterally at modestly supersonic speeds to form the outer lobe walls. The reverse shock (located immediately behind the leading shock) works its way into undisturbed jet gas. This shock also squirts jet gas sideways, but this gas is much cooler and forms a thin ribbon-like tail close to the main jet. The velocity of this tail has a Hubble-like pattern. That is, the forward speed of the material in the tail declines with distance from the head. This previously shocked gas may explain the Doppler-like patterns seen commonly in pPne. |
| | 34 | |
| | 35 | The panel on the right shows a jet whose density is generally lower than that of the ambient surroundings. The leading surface develops a wedge-like shape as it emerges from the densest part of the core. The density of the wedge is very high yet the gas is not particularly hot (~10,000K) where it an cool rapidly. The thin wedge quickly breaks apart for much the same reason that the spherical rim of a low0density wind does: the thin-shell instability. Note that the thin cone that lies atop the flow near the y axis may arise from a numerical artifact of the simulation. This may go away as we learn to deal with the same problems of early wiggles that we encountered near the y axis for low-density spherical flows. Once the wedge develops wiggles the thin-shall instability amplifies them. |
| | 36 | |
| | 37 | The middle panel is the intermediate case. Its motion speeds up as it clears the dense core of the ambient environment. |
| | 38 | |
| | 39 | A technical point is worth mentioning. I used Rjet=2 for these computations since I wanted to make sure that the head of the jet was well resolved spatially in the simulations. This width, 1000AU, is much larger than the solar system and is probably not realistic. 1000 AU corresponds to 1 arcsecond at a distance of 1 kpc. |
| | 40 | |
| | 41 | |
| | 42 | ---- |
| | 43 | |
| | 44 | '''Cone Sims''' |
| | 45 | ---- |
| | 46 | |
| | 47 | Cones are spherical flows that are sharply truncated at some zenith angle from the symmetry axis. So you can expect that the behavior of cone-like flows will bear similarities to spherical flows at angles up to the cone opening angle. This turns out to be the case. As a result, I ran only one sim whose opening angle is 15 deg. This value is slightly on the high side bit is still roughly in accord with images of bipolars. I selected the large width in order to study the flow patterns at the head of the cone and to avoid the "wiggle" problems near the y axis for low-density conical flows. |
| | 48 | |
| | 49 | A variation of a cone is a "tapered cone" in which the density and the speed of the streamlines decrease with zenith angle. The results of these sims will come in future missives. |
| | 50 | |
| | 51 | [[Image(https://dl.dropboxusercontent.com/s/bzurrmizztnqq4d/cone.jpg?dl=0)]] |
| | 52 | |
| | 53 | The cone sims vary from dense (left) to sparse (right) with one extra sim on the far right. Leaving the right sim aside momentarily, the behaviors of the others are the same as the spheres within zenith angles of 15 deg. I used Rjet=2 for these sims, again to resolved the leading edges of the flows and to help avoid the y-axis wiggle issue. The environment is a simple AGB wind since the torus is essentially empty where the cone otherwise comes through it. |
| | 54 | |
| | 55 | The sim on the right is another low-density model with namb and njet both increased by factors of 100 (keeping the ratio of njet/namb fixed). These densities are much more characteristic of real flows such as CRL618. The results would be identical except that the heated gas can cool much more quickly at the higher densities. This is clear: the dense inter-shock zone at the head of the flow cools to 100K so that it becomes a good (albeit wrinkled) battering ram. The speed of the flow is 50% higher (300 km/s) so the flow grows 50% more quickly. Again, there are no big surprises. However, the wiggle issue near the y axis is far less important than in the sim to its left -- another mystery that awaits a sensible explanation. Note that the lateral edges of the lobes are very dense -- and possibly easily visible. One issue that needs thought is this: the proper motions of CRL618 are found to be about 250 km/s, not 70 as in the simulation. What does this imply? Might the winds be much faster than 300 km/s? How could we tell since the interior of the conical jet itself is not visible. |
| | 56 | |
| | 57 | |
| | 58 | ---- |
| | 59 | '''Tapered Sims''' |
| | 60 | ---- |
| | 61 | |
| | 62 | ''Part One (Outcomes)'' |
| | 63 | |
| | 64 | Tapered conical flows sound as if they might not be especially new or interesting territory for this parameter study. In fact, they provide us with information with several useful features: (1) real flows are quite possibly "sloppy" with momentum roll-off from the symmetry axis (that is, think of an axially concentrated spray), and (2) those streamlines at low (equatorial) latitudes can interact with a torus or other equatorially enhanced environmental structures with potentially interesting effects. As you'll see, the outcomes of tapered models hold very good promise of matching the shapes of HST images. |
| | 65 | |
| | 66 | [[Image(https://dl.dropboxusercontent.com/s/agyyytpiuhso4j0/tapered1.jpg?dl=0)]] |
| | 67 | |
| | 68 | All six of the images above share the same environmental structure (AGB + torus), the same central environmental density (4e4) and the flow same speed (vjet=200) and orifice (Rjet = 0.5). Each column shows the results for different taper angles (30, 45, and 60 deg). (I left out the results of tapers of 15 deg don't show anything new or interesting.) The top row of sims has njet = namb = 4e4. The lower row has njet = 4e2 = 0.01 namb. It is obvious at a glance that the range of morphologies is highly varied -- a good thing indeed! It is also clear that these models produce narrow-ish lobes -- just what we need. |
| | 69 | |
| | 70 | It is instructive to look at the images and to draw your own conclusions. A lengthy characterization of the results is boring. One thing that strikes me is that in addition to the various morphologies, the structure of the lobe evolves quickly until the tip of the flow is well beyond the torus. |
| | 71 | |
| | 72 | As always, beware of thin features near the y axis. They evolve from knots that materialize early (100y) at the leading tip of the lobe (near the y axis). In many cases at later times the flow streamlines smash into the knots and form various types of structures behind the flow tips. These pesky artifacts that form at 100 y thus poison all of the time steps that follow. (We'll eventually figure out how to control them.) |
| | 73 | |
| | 74 | ''Part Two (y-axes artifacts)'' |
| | 75 | |
| | 76 | This section probes the symptoms and causes of those pesky y-axis knot/jet problems. The issue is that dense, cold, and generally slow-moving knots form along the y axis in the first 100 years after a sparse flow is launched into a centrally denser environment. These knots are artifacts -- that is, their characteristics depend on choices of some of the initial conditions. Previous sections touched on this problem. |
| | 77 | |
| | 78 | This section explores the issue of the "slow knots" for tapered flows. The next one deals with the slow knots that form in spherical flow sims. |
| | 79 | |
| | 80 | [[Image(https://dl.dropboxusercontent.com/s/mexskev95crjgls/tapered2.jpg?dl=0)]] |
| | 81 | |
| | 82 | [[Image(https://dl.dropboxusercontent.com/s/8oaprbf9gbfh7f0/tapered3.jpg?dl=0)]] |
| | 83 | |
| | 84 | The two sets of panels below show a parameter study for 15-deg tapered flows (top) and 45-deg tapered flows (bottom). Rjet is the only variable that changes from left (Rjet=2) to right (Rjet=0..5). |
| | 85 | |
| | 86 | Note first that the size of the flow changes with Rjet. This is not important. All it means is that the momentum flux of the flow at its base is largest for a large orifice. That is, in two dimensions the momentum flux is given by njet*Rjet*vjet. Although njet and vjet are fixed, Rjet is not. |
| | 87 | |
| | 88 | Next note that the shapes of the flow edges also vary. The lobes produced by sims with larger Rjet are wider (larger width/length ratio). I suspect that this is partly the result of the ways in which the flows interact with their environment at t=0. That is, the launch sphere covers the central part of the environment so the flow never sees much of the external density gradient. This is clearly the case in the upper row where most of the torus is visible to the sim for Rjet=0.5 but much less of the torus is encountered for Rjet =2. Again, this isn't a major issue. |
| | 89 | |
| | 90 | Now focus on the development of structure along and adjacent to the y axis in each of the series of images. There is no doubt that this knot and the faster winds that strike it create far more artificial structure for Rjet=0.5 than for Rjet=2. This might be explained by the accuracy of the portrayal of the launch sphere since small spheres will be much more pixelated than large ones. Of course, the wider lobes may also play a role. That's why we have been looking at spherical winds. |
