Linking Magnetic Field Diagnostics with 3D CME 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 ($h_{\rm crit}$) of torus instability onset, the overlying field strength ($B_{\rm t}$), and ribbon flux ($R_{\rm f}$), provide physically motivated measures of eruption onset. The two main aims of this work are to (i) show that $h_{\rm crit}$ and $B_{\rm t}$ 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 $h_{\rm crit}$, $B_{\rm t}$ and $R_{\rm f}$ 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 $\approx$ 1.8, 3.7, and 7.3 Mm), centered on the PIL, weighted $h_{\rm crit}$ from the 7.3x7.3 ROI provides the strongest correlation ($r = 0.73$), while mean $B_{\rm t}$ at 150 Mm is weaker ($r = 0.33$). Combining both offers little improvement ($r = 0.74$), confirming $h_{\rm crit}$ as the dominant predictor. CME speed correlates moderately with $B_{\rm t} \times R_{\rm f}$ ($r = 0.44$), and highest when combined with $h_{\rm crit}$ ($r = 0.76$). 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, $h_{\rm crit}$ alone consistently shows the highest predictive power for CME speed.