What does this equation mean?

A second limit worth naming, because it is where the eternal-acceleration answer above starts to strain, is slow time dependence. Barbado and Visser worked out the response of a detector whose acceleration a($\tau$) varies with proper time, expanding in powers of $\dot a$ , $\ddot a$ , and higher proper-time derivatives of the acceleration [ 8 ] . At leading order, wherever the acceleration changes slowly compared to the local orthogonalization timescale it sets for itself, the detector reports the instantaneous Unruh temperature $T_U(a(\tau)$) at each moment, as though briefly and locally eternal. This adiabatic recovery is the second known limit this construction inherits rather than derives: it says $D_{\rm det}$ between a strictly eternal trajectory at acceleration a and a slowly varying trajectory that happens to pass through a at some instant should vanish to leading order in the rate of change, with corrections controlled by exactly the jerk and snap terms Barbado and Visser compute.