Linking Magnetic Field Diagnostics with 3D Coronal Mass Ejection Speeds in Solar Active Regions

Understanding how active-region properties influence coronal mass ejection (CME) dynamics is essential for constraining eruption models and improving space-weather prediction. Magnetic diagnostics derived above polarity inversion lines (PILs), including the critical height (hcrit) of torus instability onset, the overlying field strength (Bt), and ribbon flux (Rf), provide physically motivated measures of eruption onset. The two main aims of this work are to (i) show that hcrit and Bt can equally well predict CME speeds when evaluated over the region of interest (ROI) not directly above the PIL, and (ii) assess the value of hcrit, Bt, and Rf in predicting CME speed. Photospheric magnetograms are modeled with potential-field extrapolations to obtain decay index profiles. Critical heights above PILs correlate strongly with 3D CME speed (r = 0.71). Using ROIs of ≈1.8, 3.7, and 7.3 Mm, centered on the PIL, weighted hcrit from the 7.3 × 7.3 ROI provides the strongest correlation (r = 0.73), while mean Bt at 150 Mm is weaker (r = 0.33). Combining both offers little improvement (r = 0.74), confirming hcrit as the dominant predictor. CME speed correlates moderately with Bt × Rf (r = 0.44), and highest when combined with hcrit (r = 0.76). Thus, in potential field models, ROI-based critical heights are as predictive as those above the PIL, indicating that the broader active-region field structure is equally valid as a diagnostic. When all parameters are considered together, hcrit alone consistently shows the highest predictive power for CME speed.