How the area of solar coronal holes affects the properties of high-speed solar wind streams near Earth: An analytical model

¹ Institute of Physics, University of Graz, Graz, Austria
² Columbia Astrophysics Laboratory, Columbia University, New York, USA
³ Leibniz Institut for Astrophysics Potsdam, Germany
e-mail: shofmeister@aip.de
⁴ Department of Physics, University of Helsinki, Finland
⁵ Institute of Experimental and Applied Physics, University of Kiel, Germany
⁶ CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, Hefei, PR China
⁷ Max Planck Institute for Solar System Research, Göttingen, Germany
⁸ Centre for mathematical Plasma Astrophysics (CmPA), Department of Mathematics, KU Leuven, Belgium
⁹ Solar-Terrestrial Centre of Excellence – SIDC, Royal Observatory of Belgium, Brussels, Belgium
¹⁰ Institute of Physics, University of Maria Curie-Skłodowska, Lublin, Poland
¹¹ National Space Institute, Technical University of Denmark, Copenhagen, Denmark
¹² Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz, Austria
¹³ Hvar Observatory, Faculty of Geodesy, University of Zagreb, Croatia

Received: 30 July 2021
Accepted: 29 November 2021

Abstract

Since the 1970s it has been empirically known that the area of solar coronal holes affects the properties of high-speed solar wind streams (HSSs) at Earth. We derive a simple analytical model for the propagation of HSSs from the Sun to Earth and thereby show how the area of coronal holes and the size of their boundary regions affect the HSS velocity, temperature, and density near Earth. We assume that velocity, temperature, and density profiles form across the HSS cross section close to the Sun and that these spatial profiles translate into corresponding temporal profiles in a given radial direction due to the solar rotation. These temporal distributions drive the stream interface to the preceding slow solar wind plasma and disperse with distance from the Sun. The HSS properties at 1 AU are then given by all HSS plasma parcels launched from the Sun that did not run into the stream interface at Earth distance. We show that the velocity plateau region of HSSs as seen at 1 AU, if apparent, originates from the center region of the HSS close to the Sun, whereas the velocity tail at 1 AU originates from the trailing boundary region. Small HSSs can be described to entirely consist of boundary region plasma, which intrinsically results in smaller peak velocities. The peak velocity of HSSs at Earth further depends on the longitudinal width of the HSS close to the Sun. The shorter the longitudinal width of an HSS close to the Sun, the more of its “fastest” HSS plasma parcels from the HSS core and trailing boundary region have impinged upon the stream interface with the preceding slow solar wind, and the smaller is the peak velocity of the HSS at Earth. As the longitudinal width is statistically correlated to the area of coronal holes, this also explains the well-known empirical relationship between coronal hole areas and HSS peak velocities. Further, the temperature and density of HSS plasma parcels at Earth depend on their radial expansion from the Sun to Earth. The radial expansion is determined by the velocity gradient across the HSS boundary region close to the Sun and gives the velocity-temperature and density-temperature relationships at Earth their specific shape. When considering a large number of HSSs, the assumed correlation between the HSS velocities and temperatures close to the Sun degrades only slightly up to 1 AU, but the correlation between the velocities and densities is strongly disrupted up to 1 AU due to the radial expansion. Finally, we show how the number of particles of the piled-up slow solar wind in the stream interaction region depends on the velocities and densities of the HSS and preceding slow solar wind plasma.