Persistence of the Solar Wind Velocity along Radial, Longitudinal, and Latitudinal Spacecraft Separation

(Science nugget #99 by D. Milošić¹, M. Temmer¹, S. G. Heinemann^1,2, S. J. Hofmeister³, Y. Cao⁴, and J. Guo⁴)

Introduction

The solar wind varies as multiple spacecraft probe it from different positions and at different times. Longitudinally, it shows an autocorrelation with a period of 27.27 days (Carrington rotation) when measured around Earth [1]. Latitudinally, it changes depending on the morphology of its source regions, like streamers (slow solar wind [2,3]) and coronal holes (fast solar wind [2,4]). Radially, the solar wind speed profile changes due to interaction between fast and slow streams, but also due to heating, acceleration and relaxation [5,6].

Solar Orbiter probes large parts of the inner heliosphere, and due to the eccentricity and inclination of its orbit, it is a perfect candidate for assessing the changes of the solar wind across longitude, latitude and radial distance. In addition to other spacecraft, we use its Solar Wind Analyzer suite [7] to assess the persistence of the solar wind bulk speed.

Persistence Simulation

To quantify the rates of change of the solar wind in all three dimensions, we use solar wind bulk speed measurements from five different positions and perform a ballistic simulation of the solar wind in 2D. The simulation consists of 10 years (2014–2024) of in-situ measurements from Parker Solar Probe, Solar Orbiter, STEREO-A, OMNI and MAVEN being propagated longitudinally with the solar rotation rate and radially with the in-situ measured speeds. The algorithm is purely based on ballistically propagating the data points and inelastic collisions [8]. Figure 1 shows the resulting 2D maps of solar wind speeds. The in-situ measured speed profile of each spacecraft was separately extended in longitude and radial distance, assuming persisting solar wind.

Figure 1. 2D-solar wind persistence simulation based on five different spacecraft measurements of the solar wind speed.

Results

After evaluation of the 2D persistence simulation at Earth (Figure 2), we compare the simulation results to the in-situ solar wind speed in the OMNI database. We calculate the mean absolute error (MAE) for the entire simulation and relate it to the positions of the spacecraft of origin for each data point.

Figure 2. Resulting time-series and errors from the solar wind speed simulation evaluated at the position of Earth.

Figure 3 shows the resulting trends. Each degree of latitudinal spacecraft separation introduces an error of 2.4 km s^-1. Longitudinally, we see a logarithmic trend for the MAE. Radially, the results are inconclusive.

Figure 3. Trends of the 2D persistence simulation errors across the three dimensions of spacecraft separations. (a) latitude, (b) longitude and (c) radial distance. Panel (d) shows the decay of the autocorrelation function over longitude (time).

Conclusions

Temporally, we find a characteristic decay time of the autocorrelation function of the solar wind bulk speed of roughly 53 days (Figure 3d). The exponential decay with longitude (time) also tells us about the average rate of change of the coronal sources of the solar wind. These findings could be supplemented with remote-sensing observations using Solar Orbiter, such as continuous tracking of solar regions [9] or investigations of small-scale activity in source regions of the solar wind [10] in order to link the solar wind time-scales to processes in the corona.

Latitudinally, we find a strong linear correlation of spacecraft separation and MAE of the solar wind. As Solar Orbiter moves to higher latitudes, it will provide more insight about the polar regions of the Sun [11] and the trend with the latitudinal separation can be investigated in more detail.

This nugget is based on the following work: Milošić, D., Temmer, M., Heinemann, S. G., Hofmeister, S. J., Cao, Y., & Guo, J., The Astrophysical Journal (2026).

Acknowledgements

D.M. and M.T. acknowledge the support by the FFG/ASAP Program under grant CASPER (900588). SGH acknowledges funding from the Austrian Science Fund (FWF) Erwin-Schrödinger fellowship [10.55776/J4560] and funding from the Research Council of Finland (RCF) Academy Fellowship (370747: RIB-Wind). SJH acknowledges support from the National Science Foundation (NSF; grant AGS-2229100). JG thanks the support by the National Natural Science Foundation of China (Grant Nos. 42130204, 42521007 and 42188101). The authors acknowledge the financial support by the University of Graz.

Affiliations

(1) Institute of Physics, University of Graz, Austria

(2) Department of Physics, University of Helsinki, Finland

(3) Columbia Astrophysics Laboratory, Columbia University, 538 West 120th Street, New York, NY 10027, USA

(4) University of Science and Technology of China, Hefei, China

References

[1] Owens, M. J., Challen, R., Methven, J., Henley, E., & Jackson, D. R. 2013, Space Weather, 11, 225 DOI: 10.1002/swe.20040
[2] Xu, F., & Borovsky, J. E. 2015, JGRA, 120, 70 DOI: 10.1002/2014JA020412
[3] Abbo, L. 2016, SSRv, 201, 55 DOI: 10.1007/s11214-016-0264-1
[4] Krieger, A. S., Timothy, A. F., & Roelof, E. C. 1973, SoPh, 29, 505 DOI: 10.1007/BF00150828
[5] Jian, L., Russell, C. T., Luhmann, J. G., & Skoug, R. M. 2008, AdSpR, 41, 259 DOI: 10.1016/j.asr.2007.03.023
[6] Rivera, Y. J. 2024, Sci, 385, 962 DOI: 10.1126/science.adk6953
[7] Owen, C. J. 2020, A&A, 642, A16 DOI: 10.1051/0004-6361/201937259
[8] Milošić, D., Temmer, M., Heinemann, S. G., Hofmeister, S., & Asvestari, E. 2025, A&A, 699, A267 DOI: 10.1051/0004-6361/202453096
[9] Kontogiannis, I. 2025, A&A, 704, A105 DOI: 10.1051/0004-6361/202556136
[10] Huang, Z. 2026, A&A, 708, A180 DOI: 10.1051/0004-6361/202557126
[11] Calchetti, D. 2025, ApJL, 995, L60 DOI: 10.3847/2041-8213/ae2850