A heliospheric density and magnetic field model^⋆

¹ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: GMann@aip.de
² Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse III (UPS), 14 av. Édouard Belin, 31400 Toulouse, France
³ Centre National de la Recherche Scientifique, UMR 5277, Université Paul Sabatier, 9 av. du Colonel Roche, 31028 Toulouse, France

Received: 23 September 2022
Accepted: 23 August 2023

Abstract

Context. The radial evolution of the density of the plasma and the magnetic field in the heliosphere, especially in the region between the solar corona and the Earth’s orbit, has been a topic of active research for several decades. Both remote-sensing observations and in situ measurements by spacecraft such as HELIOS, Ulysses, and WIND have provided critical data on this subject. The NASA space mission Parker Solar Probe (PSP), which will approach the Sun down to a distance of 9.9 solar radii on December 24, 2024, gives new insights into the structure of the plasma density and magnetic field in the heliosphere, especially in the near-Sun interplanetary space. This region is of particular interest because the launch and evolution of coronal mass ejections (CMEs), which can influence the environment of our Earth (usually called space weather), takes place there.

Aims. Because of the new data from PSP, it is time to revisit the subject of the radial evolution of the plasma density and magnetic field in the heliosphere. To do this, we derive a radial heliospheric density and magnetic field model in the vicinity of the ecliptic plane above quiet equatorial regions. The model agrees well with the measurements in the sense of a global long-term average.

Methods. The radial evolution of the density and solar wind velocity is described in terms of Parker’s wind equation. A special solution of this equation includes two integration constants that are fitted by the measurements. For the magnetic field, we employed a previous model in which the magnetic field is describe by a superposition of the magnetic fields of a dipole and a quadrupole of the quiet Sun and a current sheet in the heliosphere.

Results. We find the radial evolution of the electron and proton number density as well as the radial component of the magnetic field and the total field strength in the heliosphere from the bottom of the corona up to a heliocentric distance of 250 solar radii. The modelled values are consistent with coronal observations, measurements at 1 AU, and with the recent data from the inner heliosphere provided by PSP.

Conclusions. With the knowledge of the radial evolution of the plasma density and the magnetic field in the heliosphere the radial behaviour of the local Alfvén speed can be calculated. It can can reach a local maximum of 392 km s⁻¹ at a distance of approximately 4 solar radii, and it exceeds the local solar wind speed at distances in the range of 3.6−13.7 solar radii from the centre of the Sun.