A simplified model for timing the arrival of solar flare‐initiated shocks

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Abstract
The solar flare‐initiated shock can be considered to be an initially driven shock that converts into a blast wave as it propagates through the interplanetary medium. In our simplified shock modeling, to estimate the time of the shock arrival at a specified position in space we assume that the shock is initially driven from the flare position at the velocity indicated by the type II solar radio burst. We assume the shock is driven until the initiating solar flare energy is somewhat expended. After this initially driven phase, the shock front then propagates with the characteristic speed expected of the shock front of a blast wave. In the interplanetary medium with its 1/r² density dependence, the blast wave shock front speed should be proportional tor−0.5. We find that thisr−0.5speed dependence is a general characteristic of the shock front speed when the speeds are determined in the solar wind reference frame. The blast wave “rides over” the preexisting solar wind so that the disturbance speed of the shock front at any instant of time is the speed of the shock front added vectorially to the solar wind speed. Application of these principles enables a consistent “timing” of solar flare‐initiated shock waves that is event independent. We show that this concept is consistent with the time position profile derived from the analysis of kilometric type II events that are associated with interplanetary shocks.