Evolution of the critical torus instability height and coronal mass ejection likelihood in solar active regions

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Aims. Working towards improved space weather predictions, we aim to quantify how the critical height at which the torus instability drives coronal mass ejections (CMEs) varies over time in a sample of solar active regions. Methods. We model the coronal magnetic fields of 42 active regions and quantify the critical height at their central polarity inversion lines throughout their observed lifetimes. We then compare these heights to the changing magnetic flux at the photospheric boundary and identify CMEs in these regions. Results. In our sample, the rates of CMEs per unit time are twice as high during phases when magnetic flux is increasing than when it is decreasing, and during those phases of increasing flux, the rate of CMEs is 63% higher when the critical height is rising than when it is falling. Furthermore, we support and extend the results of previous studies by demonstrating that the critical height in active regions is generally proportional to the separation of their magnetic polarities through time. When the separation of magnetic polarities in an active region increases, for example during the continuous emergence and expansion of a magnetic bipole, the critical height also tends to increase. Conversely, when the polarity separation decreases, for example due to the emergence of a new, compact bipole at the central inversion line of an existing active region or into a quiet-Sun environment, the critical height tends to decrease.