A statistical study of the subsurface structure and eruptivity of solar active regions

A statistical study of 77 solar active regions (ARs) is conducted to investigate the existence of identifiable correlations between the subsurface structural disturbances and the activity level of the active regions. The disturbances examined in this study are $<|\delta \Gamma_1/\Gamma_1|>$, $<|\delta c^2/c^2|>$, and $<|\delta c^2/c^2-\delta \Gamma_1/\Gamma_1|>$. where $\Gamma_1$ and $c$ are the thermodynamic properties of first adiabatic index and sound speed modified by magnetic field, respectively. The averages are over three depth layers: $0.975-0.98 R_\odot$, $0.98-0.99 R_\odot$ and $0.99-0.995 R_\odot$ to represent the structural disturbances in that layer. The level of the surface magnetic activity is measured by the Magnetic Activity Index (MAI) of active region and the relative and absolute MAI differences (rdMAI and dMAI) between the active and quiet regions. The eruptivity of each active region is quantified by its Flare Index, total number of coronal mass ejections (CMEs), and total kinetic energy of the CMEs. The existence and level of the correlations are evaluated by scatter plots and correlation coefficients. No definitive correlation can be claimed from the results. While a weak positive trend is visible between dMAI and $<|\delta \Gamma_1/\Gamma_1|>$ and $<|\delta c^2/c^2|>$ in the layer $0.975-0.98 R_\odot$, their correlation levels, being approximately 0.6, are not sufficiently high to justify the correlation. Some subsurface disturbances are seen to increase with eruptivity indices among ARs with high eruptivity. The statistical significance of such trend, however, cannot be ascertained due to the small number of very eruptive ARs in our sample.