The response of the upper atmosphere to various forms of time-dependent heating is calculated by use of approximate analytic solutions of the heat conduction equation. Time lags of maximum temperature and density behind peak heating are distinctly different and, for short-duration heating events, are strongly altitude dependent. The time and space characteristics of a one-dimensional heat source that produces a density change consistent with the observed drag on satellites during a geomagnetic disturbance are identified. The desired model for polar substorm heating maximizes in the 140- to 160-km altitude region with an average duration of 4 to 5 hours. The relationship between the amount of heat injected per unit column during a disturbance of maximum geomagnetic index ap is q ∝ (ap)1/2. This simple relationship suggests a common heating mechanism that is present at all levels of activity.
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Thomas et al. (1969) studied this question.