On the Role of Chapman's Hydrostatic Solar Wind Mechanism in Parker's Hydrodynamic Solar Wind Model
Bhimsen Shivamoggi
TL;DR
The paper addresses whether Chapman's hydrostatic solar wind mechanism persists globally within Parker's hydrodynamic wind model. It employs the de Laval nozzle analogy to reinterpret solar gravity as a renormalization of the wind-channel cross-section, showing the gravity effect is captured by the Chapman's hydrostatic density factor via $\mathcal{A}(r)=A(r)[\rho_h(r)/\rho_0]$. The result holds for isothermal and polytropic winds and extends to $n$-dimensional underlying spaces, establishing the robustness of Chapman's mechanism on a global scale and explaining the near-equivalence of Chapman's and Parker's density profiles in the subcritical region $r \le r_*$. The analysis reveals the sonic point corresponds to a minimum of the effective nozzle cross-section, linking hydrostatic and hydrodynamic pictures and providing a unified geometric framework for gravity's role in solar wind acceleration, applicable across thermodynamic assumptions and spatial dimensions.
Abstract
The global role of Chapman's hydrostatic solar wind mechanism in Parker's hydrodynamic solar wind model is investigated by using the de Laval nozzle analogy for the generation of flow acceleration in the latter model. The action of solar gravity in Parker's hydrodynamic solar wind model is shown to be geometrically equivalent to a renormalization of the actual wind channel area via a multiplicative factor, which is precisely Chapman's hydrostatic density profile. So, Chapman's hydrostatic solar wind mechanism appears to continue to be operative, on a global level (not just locally near the coronal base), in Parker's hydrodynamic solar wind model, the effects of solar gravity in Parker's hydrodynamic model being essentially encapsulated by Chapman's hydrostatic model. This result is shown to be robust by considering both isothermal gas and polytropic gas models as well as an n-dimensional (n= 1, 2, 3) underlying space for the solar wind.