An Empirical Relationship Between Coronal Density and Solar Wind Velocity in the Middle Corona With Applications to Space Weather

Accurate predictions of ambient solar wind conditions are a central component of space weather forecasting. A recent advancement is to use the distribution of electron density at a heliocentric distance of 8 R⊙, gained by applying coronal rotational tomography to coronagraph data, as an inner boundary condition for the time-dependent Heliospheric Upwind eXtrapolation solar wind model. This approach requires conversion of densities into solar wind velocity at the inner boundary. Based on comparison of the distribution of in situ measurements of density and velocities, this work finds a scaled exponential equation relating the density and outflow velocity at 8 R⊙, with three key parameters found as a function of time between years 2007–2021. Based on this relationship, comparison of modeled and in situ measurements of velocities at Earth, STEREO A and STEREO B over the past solar cycle give a mean absolute error of 61.2, 69.0, and 66.1 km s−1 respectively. An analysis of thousands of events (defined as solar wind streams above 450 km s−1) gives an accuracy score of 76%. This agreement validates the density-velocity relationship, and shows that an inner boundary based on coronagraph observations is a robust complement, or alternative, to commonly-used magnetic model constraints for solar wind modeling and forecasting.

Key Points
In this work an empirical relationship between Coronal electron density and solar wind velocity at a distance close to the Sun is presented

Novel inner boundary conditions for solar wind models, that bypass the need for Photospheric magnetic field extrapolations, are generated

The model solar wind predictions showed a strong agreement with observations at various locations at 1 AU

Plain Language Summary
Space weather can have damaging effects on both space-based and ground-based technologies, on which society is becoming increasingly dependent. The risk of damage on these technologies can be mitigated through accurate forecasting of the solar wind conditions. In this work, a statistical approach is used to derive an empirical conversion model between coronal density and solar wind velocities at distances close to the Sun. The resultant velocities are then used to provide an input or 'an inner boundary condition` for heliospheric solar wind models, where the solar wind conditions are modeled to 1 AU. This novel approach yields model predictions that consistently provide a strong statistical agreement with solar wind conditions observed at multiple locations at 1 AU.