Review of Model Fitting Procedure

Some notes...

Models from Run 414

It would seem to me that a percentage of the files from Zeno's output aren't necessary for the model matching itself. The disks are still pretty much undisturbed and so if this process was to be automated, we could find a way of quickly calculating which models are relevant. In the case of i414.dat, I think looking at any output earlier than r414_0040.dat isn't terribly productive. At this stage the disks are noticeably deformed but still nowhere near fulfilling the required shape.

Moving forward to r414_0050.dat, it seems to me that we're getting into the right area. The disks now have quite noticeable tidal tails, although while rotations finally move the blue tail (disk 1) into a region where I feel we have a good match for the southern tail, the match to the northern tail is still pretty poor.

The bulges seem to be the key to getting into the right area - as you mentioned before you want them to overlap in the x-y plane. This is achieved by a simple rotation about the x axis. This also leads to pretty good fits in the Vz-Y and x-Vz planes.

r414_0060.dat: Once again, it seems to be pretty easy to get a fit for the southern tail with disk1, key 5. The fit to the northern tail using disk 2, key 7 is okay. With the best fit for both of the tail, there is a stream of material emanating for each disk which is well askew of the northern and southern tails. Scaling r doesn't really remedy this. I made a p-file (pr414_0060) of the best configuration. This fit is by no means perfect and it is at the expense of the bulges, which no longer overlap. Problem: alignment of features on Vz-Y plane; note that the blue "tail" does not curve sufficiently (if at all!) to match to the southern "tail".

r414_0070.dat: In this case, the best fit involves key 5 of disk 1 and key 7 of disk 2, scaled to 450 radial units. Same Vz-Y problem arises as for r414_0060.dat, although the bulges do overlap in this case somewhat more in this case. Click here for the best configuration. The p-file is named pr414_0070.

r414_0090.dat: I decided to go to a later time; in this case, the southern "tail" of disk 1 seems to be developing a curve in the Vz-y plane which seems promising, although I don't think it can be improved upon by mere radial or velocty scaling. In terms of tail matching in the X-Y plane, the disk1 tails seem too broad and long irrespective of rotations. The same holds true for disk2.

r414_00b0.dat: I quickly examined the output for a later time - r414_00b0.dat; the results seemed to improve for Vz-Y while the those in the X-Y plane were reasonably good. A snapshot is shown here. In this case, disk1 had a key value of 8 and disk2 had a key value of 11; the radial and velocity scalings were 260 and 100 respectively.

I quickly jumped forward to r414_00c0.dat, but my feeling is that we're moving away from the domain of best fit. Simply concentrating on disk 1, the tails produced seem to me to be too curved, making it very difficult to get any kind of decent alignment, irrespective of applying rotations and scalings. I didn't bother to pursue this any further.

Conclusions based on my analysis of Run 414 - the earlier models can be discarded in the matching process; the disks have not been tidally perturbed sufficiently to have any of the necessary elongated features. As mentioned above, things only started to become interesting from r414_0040 onwards. The bulges play a key role in the initial stages - I used them try and get a "zero point" for my rotations. At that stage I concentrated on disk 1, trying various rotations, generally about the z axis to start with, then finetuning with a y rotation and an x rotation if needed. Once I had achieved a best fit with that disk, I moved onto disk2 and cycled through the keys. If I saw one that looked promising, I started the z, then y then x finetuning I mentioned for disk1. This was concentrated on the results in the X-Y plane; for the earlier "best fits" - r414_0040 for example - the fit of the southern tail in Vz-Y was not so good but this seemed to improve and things looked very promising at about r414_0090. I think the results obtained in r414_00b0 are pretty decent. Scalings are something that need to be judged, and I'm not sure how easy it would be to implement them. If you do get the NASA money, then maybe have a scalebar attached to the control panel which allows the user to quickly scan through a scaling range. At the moment, I try and take 100 off the scale factor, see what that gives me, and then tweak around, normally incrementing by factors of 50, then 10.

My feeling is that the best fit can be found in the models between r414_0090 and r414_00b0.

Models from Run 409

In each case, the initial step is to scale the radial factor to 220 and align the bulges so that they overlap.

r409_0020.dat: This was the first model examined. Quickly cycling through the key values, I decided that the disks had not evolved sufficient tidal features to match the observed features.

r409_0030.dat: It seems to me that the scale factor is completely inappropriate for this particular case (and perhaps the entire set, but that is something that will reveal itself with time) - the tidal features are simply not elongated and extended enough for a match to be possible. Scaling up to a radial scale factor of 500 improved the ability to match disk1 with the southern tail, but at the expense of the bulges separating to north and south. I decided to try a later time.

r409_0040.dat: At this point, I departed from the usual initial step and merely aligned the bulges. I concentrated on disk 1, trying a few arbitrary rotations about the z then the y axes using each all the available keys. (I feel I can tell at an early stage how good the match will be.) It doesn't appear to me that the condition for the bulges to overlap can be satisfied with this key set.

Revised Runs 409 and 414

#       Multiple-disk test-particle  experiments.
#       Run     Gal1    i1      Gal2    i2      eccent  r_peri  r_apo
#       r409    td9     45      td9     45      0.5     0.6     1.8
#       Multi-disk versions of above experiments; eccent = 0.5  
#       Run     Gal1    i1      w1      Gal2    i2      w2      r_peri
#       r414    bdh1    45              bdh2    45              0.5

I decided to rerun these model encounters, ensuring that the output was written to file under the same conditions. In this case, the options to treecode were:

freq=64 eps=0.025 options=out-phi tstop=4.0 freqout=16

r414_0090.dat: I decided to start with the model that seemed to give the best results in my initial examinations of r414, this time simply concentrating on getting a match for the tail, negelcting alignment of the bulges. This time I concentrated my attention on disk 1, quickly cycling through the keys, using the kink in the SW tail and also the Vz-Y view as my guide. The radial scaling was set to 320. Best fit seemed to be achieved with disk 1, key 6 and disk 2, key 9. The configuration is shown here; the associated p-file is saved here. A quick ~180 degree rotation about the x axis in the north south direction, followed by a rough alignment clockwise about the z axis and then some fine tuning about the y axiz gets you into the right area.

r409_0090.dat: It seemed appropriate to see how the test disk case differed at this stage. Using the model from the same timeframe, I scaled to a radial factor of 400 after it became apparent that 320 was too small. A quick ~180 degree rotation about x, followed by fine tuning with y and z rotations, and we get this best fit. P file is here. The fit itself is poor compared to the self consistent case; the kink in the SW tail doesn't seem to be forthcoming and the northern tail seems to be a big problem - neither disk1 nor disk2 throw material in a curve that arches enough to fit the H1 data. This problem would seem to stem from the bulges being excluded.

r409_088.dat: Initial radial scale factor set to 300, followed by the standard rotations ( ~180 degrees about x, finetuning clockwise abot z and y). Best fit configuration here and p file here.

Models 418 and 419

#       Self-consistent experiments; eccent = 0.5  
#       Run     Gal1    i1      w1      Gal2    i2      w2      r_peri
#       r418    bdh1    45      75      bdh3    45      15      0.6
#       r419    gbdh1   45      75      gbdh3   45      15      0.6

These two runs were chosen because

Last Updated: Friday, 10th September 1999