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

Abstract 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 ( h crit ) of torus instability onset, the overlying field strength ( B t ), and ribbon flux ( R f ), provide physically motivated measures of eruption onset. The two main aims of this work are to (i) show that h crit and B t 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 h crit , B t , and R f 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 h crit from the 7.3 × 7.3 ROI provides the strongest correlation ( r = 0.73), while mean B t at 150 Mm is weaker ( r = 0.33). Combining both offers little improvement ( r = 0.74), confirming h crit as the dominant predictor. CME speed correlates moderately with B t × R f ( r = 0.44), and highest when combined with h crit ( 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, h crit alone consistently shows the highest predictive power for CME speed.