7.3 Phase 3: Improved Models
7.3.1 Improved 3D Model
The ad-hoc test models and subsequent CO line calculations presented in§7.2, suggested that perhaps the error in the Phase 1 model had its source in the upper boundary condi- tion applied to the hydrodynamic simulation. Recalling §3.1.3, the uppermost layer has its velocity structure held constant, density gradient hydrostatic and uppermost energy spatially constant. Seeing as the CO lines were forming in such high layers, perhaps the incoming gas from the uppermost layer may not have had time to properly cool and equilibrate to its surroundings in the intergranular regions by the time it reached CO line formation heights. To test this hypothesis, despite the questionable nature of the equation of state, LTE approximation and ICE treatment at the low densities of such high layers, an attempt to extend the model atmosphere beyond 1 Mm was undertaken.
Figure 7.6: The same as Fig. 7.1 but using the standard extension, standard boundary Phase 3-82 improved model atmosphere. The profile and bisector agreement are excellent and very good respectively; both clearly show better agreement with observation than those of either Phase 1 or 2.
§7.3 Phase 3: Improved Models 73
were run and completed. Four new atmospheres were produced, two with the original ex- tent and two extending to heights of almost 1.2 Mm. The extended simulations were run at a resolution of 50 ×50 ×88 and those with the original extension at 50 ×50 ×82. The lower resolution was chosen over the 200 ×200 ×82 of the Phase 1 model due to computational time constraints. This was despite the findings of Asplund et al. (2000a) that not all simulation properties are converged at such resolution, as the new model atmospheres were intended only for qualitative testing of the boundary equilibration hy- pothesis. The purpose was not to produce the most accurate description of the solar atmosphere available, nor could it be given the questionable validity of the model assump- tions at heights above 1 Mm. The 50× 50× 82 models served as a control sample for the drop in resolution, and it was anticipated that they would resemble the Phase 1 model.
Two models were run at each resolution so that a new energy condition could be applied to the upper boundary, with one model at each resolution having the original boundary condition and the other the new condition, again providing control samples. It was felt that the existing energy condition could cause extreme horizontal temperature fluctuations across the top layer in the 50 ×50 ×88 case, due to the response of the equation of state at such low densities. In order to avoid this, the flat horizontal energy gradient at the top of the domain was replaced by a zero vertical energy gradient across the top layer, where horizontal inhomogeneity was permitted. For ease of reference, the original height atmospheres will be designated ‘82’, the taller ones ‘88’ and those with the new boundary condition by an ‘e’, so that e.g. the ‘Phase 3-82e’ model atmosphere is the non-extended version with the new boundary condition, whereas that with the original boundary is the ‘Phase 3-82’ model.
Given that the Phase 1 model atmosphere was generated in 1999, the hydrodynam- ical simulations have undergone some slight improvements since its creation. These im- provements were expected to cause only minor differences in the output atmosphere, es- pecially given the previous successes of the Phase 1 model (e.g. Rosenthal et al. 1999; Asplund et al. 2000b,c, 2004a,c). However, it was still thought best if the most modern version of the simulations available were used, if brand new model atmospheres must be generated. For this reason, a version of the Stein-Nordlund code in use by Trampedach (2004) was employed rather than the slightly older version (Asplund et al. 2000b) used to generate the Phase 1 model. The newer code contained an improved treatment of the numerical viscosity, and drew on an updated Uppsala package containing improved contin- uous opacities. The version of the MHD equation of state was also more recent, including the 17 most abundant solar elements (as opposed to the previous 16, where argon was not included) as well as drawing on slightly altered abundances. The manner in which radiation pressure and energy was included by the MHD tabulation program was also al- tered. Finally, the mean density and temperature structures used in each case to generate equation of state and opacity tables were slightly different, though it is not clear whether this was a primary difference or a secondary effect caused by other updates.
Line formation simulations were carried out for all lines in Table B.1 on each of the four new atmospheres. Each new atmosphere had been run for 120 snapshots, though due to some relaxation effects early in the new simulations (caused by the combination of the newer code and altered extent and/or boundary condition), some earlier snapshots were not used in the final production of line profiles and bisectors. The starting snapshot of the simulations was the same as the starting snapshot of the Phase 1 model, itself taken from a previous simulation. The final snapshot of each new atmosphere also contained a computational artefact, arising from a bug in an existing snapshot manipulation utility
Figure 7.7: Differences be- tween observed and synthetic bisectors generated with the Phase 3-82 model for all 31 lines. In comparison to Fig. 7.2, the large discrepancy in the upper parts of the bisectors has been remedied, reflecting the ‘turning- back’ of bisector tops by the im- proved model. The improvement over the Phase 1 bisector agree- ment is at least as good as that produced by the Phase 2-v16 model (Fig. 7.5), resulting in very good agreement overall be- tween observed and theoretical bisectors.
used to implant the starting snapshot, so the final profiles and bisectors are a temporal average of a 105-snapshot period extending from snapshot 11 to snapshot 115 inclusive.