Radial evolution of the accuracy of ballistic solar wind backmapping

¹ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 Place Jules Janssen, 92195 Meudon, France
² IRAP, Observatoire Midi-Pyrénées, Université Toulouse III – Paul Sabatier, CNRS, 9 Avenue du Colonel Roche, 31400 Toulouse, France
e-mail: jdakeyo@irap.omp.eu
³ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
⁴ Mullard Space Science Laboratory, University College London, Holmbury House, Dorking RH5 6NT, UK
⁵ Laboratoire Cogitamus, rue Descartes, 75005 Paris, France

Received: 9 December 2023
Accepted: 1 February 2024

Abstract

Context. Solar wind backmapping is a technique employed to connect in situ measurements of heliospheric plasma structures to their origin near the Sun. The most widely used method is ballistic mapping, which neglects the effects of solar wind acceleration and corotation and instead models the solar wind as a constant radial outflow whose speed is determined by measurements in the heliosphere. This results in plasma parcel streamlines that form an Archimedean spiral (the Parker spiral) when viewed in the solar corotating frame. This simplified approach assumes that the effects of solar wind acceleration and corotation compensate for each other in the deviation of the source longitude. Most backmapping techniques so far considered magnetic connectivity from a heliocentric distance of 1 au to the Sun.

Aims. We quantify the angular deviation between different backmapping methods that depends on the location of the radial probe and on the variation in the solar wind speed with radial distance. We assess these differences depending on source longitude and solar wind propagation time.

Methods. We estimated backmapping source longitudes and travel times using (1) the ballistic approximation (constant speed), (2) a physically justified method using the empirically constrained acceleration profile Iso-poly, derived from Parker solar wind equations and also a model of solar wind tangential flows that accounts for corotational effects. We compared the differences across mapped heliocentric distances and for different asymptotic solar wind speeds.

Results. The ballistic method results in a Carrington longitude of the source with a maximum deviation of 4″ below 3 au compared to the physics-based mapping method taken as reference. However, the travel time especially for the slow solar wind could be underestimated by 1.5 days at 1 au compared to non-constant speed profile. This time latency may lead to an association of incorrect solar source regions with given in situ measurements. Neglecting corotational effects and accounting for acceleration alone causes a large systematic shift in the backmapped source longitude.

Conclusions. Incorporating both acceleration and corotational effects leads to a more physics-based representation of the plasma trajectories through the heliosphere compared to the ballistic assumption. This approach accurately assesses the travel time and provides a more realistic estimate of the longitudinal separation between a plasma parcel measured in situ and its source region. Nonetheless, it requires knowledge of the radial density and Alfvén speed profiles to compute the tangential flow. Therefore, we propose a compromise for computing the source longitude that employs the commonly used ballistic approach and the travel times computed from the derived radial acceleration speed profile. Moreover, we conclude that this approach remains valid at all radial distances we studied and is not limited to data obtained at 1 au.