Hydrodynamic Loop Model

Two-fluid EBTEL model of Barnes et al. (2016a),

$$\begin{align} \frac{dp_e}{dt} =& \frac{\gamma - 1}{L}(\psi_{TR} - (\mathcal{R}_{TR} + \mathcal{R}_C)) + k_Bn\nu_{ei}(T_i - T_e) + (\gamma - 1)Q_e \\ \frac{dp_i}{dt} =& -\frac{\gamma - 1}{L}\psi_{TR} + k_Bn\nu_{ei}(T_e - T_i) + (\gamma - 1)Q_i \\ \frac{dn}{dt} =& \frac{c_2(\gamma - 1)}{c_3\gamma Lk_BT_e}(\psi_{TR} - F_{ce,0} - \mathcal{R}_{TR}) \\ p_e =& k_BnT_e,\quad p_i = k_BnT_i \end{align}$$

Heat electrons or ions dynamically and model spatially-averaged coronal quantities

Heating Parameter Space

Emission Measure Diagnostics

• True emission measure from simulated thermodynamic quantities, $$\mathrm{EM}(T) = \int_{\mathrm{LOS}}\mathrm{d}h\,n^2(h,T)$$
• Bin in temperature $5.6<\log{T}<7.0$ with width $\Delta\log{T}=0.05$
• Predicted EM from regularized inversion code of Hannah and Kontar (2012)
  • Assume 25% uncertainty on our intensities to balance acceptable $\chi^2$ and smoothness
  • Apply to pixel-averaged and full AR
• Fit power-law to cool side such that $\mathrm{EM}\sim T^a$
  • Fit between 1 MK and $T_{peak}$ (4 MK true, 3 MK predicted), where $\mathrm{EM}_{max}=\mathrm{EM}(T_{peak})$
  • Only fit to pixels where $\mathrm{EM}(T)>10^{25}$ cm^-5 and acceptable fit $R^2>0.95$

Pixel-averaged Emission Measures

Global AR Emission Measure – True

Global AR Emission Measure – Predicted

Emission Measure Slopes

Emission Measure Slopes

Conclusions

• Global active region modeling a powerful tool for studying dynamically-heated AR cores
  • Efficient
  • AR Geometry
  • Detailed loop physics (with 1D models)
  • Atomic physics and instrument effects
• Relationship between predicted $a$ and $t_N$ much "messier" compared to true $a$
• Predicted EM peak at lower temperatures than true EM, independent of heating frequency
• Observed slopes most consistent with intermediate to low frequency heating, but spread is large
• Caution when computing emission measure from model results