So far, the total energy input has been kept fixed for all simulations. This section will investigate how altering the energy of each discrete energy burst, and thus ET otal
affects the loop apex temperature for the three spatial heating cases. Logically, it would be expected that as more energy is released into the loop that the temperature will rise. Conversely, as energy is removed, the temperature will be expected to drop.
In this section, the number of strands is kept fixed at 125, α (the power law index from Equation 5.1) is kept fixed at α = 2.3, and the timing and locations of the energy bursts are kept the same. The only difference to the simulations in Section 5.2 is the energy content of each burst, thus meaning a change in ET otal. Only SUH is considered. Figure 5.14 displays the energy distributions for three ranges of ET otal from a slection of the simulations undertaken. The results of the same three
Figure 5.14: Energy histograms for three different total energy ranges, with straight lines fitted to show the power-law slop, which has a value of α = 2.3 in all cases.
simulations are shown throughout this section, with results for 0.001ET otal, 0.1ET otal
and 10ET otal. Table 5.2 displays the simulation parameters used throughout this section.
5.3.1 Effect on Loop Temperature
Figure 5.15 displays the emission measure weighted apex temperature for the three different ET otal cases, whilst Figure 5.16 displays the mean temperature profile along the half-loop. With a total energy input of 0.001ET otal, the mean apex temperature reaches approximately 0.3 MK. As the energy is increased to 0.1ET otal, the mean apex temperature increases to 1.23 MK, and further to 3.69 MK for 10ET otal.
So far in this section, only three different cases of total energy have been dis-cussed. However, Figure 5.17 (left) displays the average loop apex temperature for a far greater number of simulations for the three spatial heating cases, in the range 0.001ET otal ≤ Total Energy ≤ 10ET otal. This plot clearly identifies how the average loop apex temperature changes, as the total amount of energy deposited in the loop
Table 5.2: Changing ET otal: simulation parameters
No. No. Total Energy Energy Range Power Law
Strands Bursts (×ET otal erg) (erg) Index (α) 125 57 0.001 1.00 × 1020− 5.38 × 1021 -2.30 125 57 0.005 5.00 × 1020− 2.69 × 1022 -2.30 125 57 0.01 1.00 × 1021− 5.38 × 1022 -2.30 125 57 0.05 5.00 × 1021− 2.69 × 1023 -2.30 125 57 0.1 1.00 × 1022− 5.38 × 1023 -2.30 125 57 0.5 5.00 × 1022− 2.69 × 1024 -2.30 125 57 1.0 1.00 × 1023− 5.38 × 1024 -2.30 125 57 5.0 1.00 × 1023− 2.69 × 1025 -2.30 125 57 10.0 1.00 × 1024− 5.38 × 1025 -2.30
Figure 5.15: Emission measure weighted temperature at loop apex for different levels of ET otal: 0.001ET otal, 0.1ET otal and 10ET otal (SUH).
Figure 5.16: Average emission measure weighted temperature of the loop for different levels of ET otal: 0.001ET otal, 0.1ET otal and 10ET otal (SUH).
Figure 5.17: Average emission measure weighted temperature at the loop apex (left), and the average deviation of the temperature along the loop apex, over a range of total energy inputs
varies. The average absolute deviation (or average deviation) is used as a method to quantify the fluctuations in the mean temperature (and later, the mean velocity).
As can be seen in Figure 5.15, the apex temperature corresponding to 10ET otal has a much higher degree of variation than the the cooler temperatures displayed. At higher temperatures, the loop will cool at a much faster rate, whilst the higher en-ergy content of the enen-ergy bursts will also heat the loop more rapidly, causing the higher level of fluctuations observed. Figure 5.17 (right) illustrates this, showing an increase in average deviation with increasing energy.
5.3.2 Effect on Loop Line-of-Sight Velocity
Si VII 275.36 ˚A
In the Si VII line filter, the 0.001ET otalcase is predominantly blue shifted (see Figure 5.18). We believe that this is caused because the loop is not being heated sufficiently by the low energy bursts, and a “one-way-traffic” situation occurs. Also, at this lower temperature, the density is much lower, and, as Del Zanna (2008) suggests, it is much easier to see blue shifts at lower densities. As the energy is increased, the loop becomes increasingly more red shifted, going from 20% red shifted at 0.001ET otal to 95% at 10ET otal.
The mean velocity moves from a blue shift of 4 km s−1 up to a red shift of 3.5 km s−1.
Fe XI 188.23 ˚A
The Fe XI line filter has a temperature range of 0.4 − 3.16 MK, and therefore the 0.001ET otal case is not within this range. At 0.1ET otal, the footpoints are predom-inantly blue shifted, with red and blue shifts occurring along the rest of the loop length, with average blue shift velocities reaching 3.5 km s−1. As the energy is in-creased further, the loop becomes predominantly red shifted (90%), with red shift
Figure 5.18: Si VII line-of-sight blue/red shifts for the three selected cases of ET otal
(left), their corresponding histograms (centre), and the time-averaged mean blue/red Vcf along the loop (right). For SUH only.
Figure 5.19: Fe XI line-of-sight blue/red shifts for the three selected cases of ET otal
(left), their corresponding histograms (centre), and the time-averaged mean blue/red Vcf along the loop (right). The top row of diagrams can be ignored, but are included for completeness. For SUH only.
Figure 5.20: Fe XV line-of-sight blue/red shifts for the three selected cases of ET otal (left), their corresponding histograms (centre), and the time-averaged mean blue/red Vcf along the loop (right). The top row of diagrams can be ignored, but are included for completeness. For SUH only.
velocities reaching 2 km s−1.
Fe XV 284.16 ˚A
Again, the 0.001ET otal temperature falls below the temperature range of the Fe XV filter. At 0.1ET otal, the loop is predominantly blue shifted (82%), with mean velocities reaching 9 km s−1at the footpoints. As the energy is increased to 10ET otal, the loop becomes more red shifted, although still has a predominance of blue shift at 59%, and mean blue shift velocities of 1 km s−1 at the footpoint.
Figure 5.21: Percentage of red shifted pixels (left column), maximum mean velocity ranges (centre column), and average velocity deviation (right column) over a range of total energy inputs, and line filters. From top-to-bottom: Si VII, Fe XI, Fe XV
5.3.3 Discussion
Figure 5.21 (left column) displays the percentage of red shift in the loop for each line filter. For all three line filters there is a trend of increasing red shift with increasing energy. The Si VII and Fe XI filters show an increase in red shift velocities and a decrease in blue shift velocities with increasing energy. The Fe XV shows an decrease in both red and blue velocities with increasing temperature. The average deviations show similar trends to the maximum mean velocities.
Figure 5.22 shows another comparison between the simulation velocities and the Tripathi et al. (2009) velocities. The 0.1 and 0.5ET otal cases represent the closest
Figure 5.22: Comparison of Tripathi et al. (2009) average footpoint velocities (left) and the average simulation Vcf at s = 4.5 Mm (right) for 0.1 and 0.5 ET otal
matches to the observations. The velocities do not match exactly, but are within a reasonable limit, and show red shifts where red shifts are expected, and blue shifts where blue shifted are expected. The temperature of the loop at 0.1 and 0.5ET otal
matches closely to that of the observed loop. The cool loops (1 MK) observed in Del Zanna (2008) are blue shifted in the footpoints in the Fe XII line filter, matching well with the 1 MK (0.1ET otal) loop in the Fe XI filter.