Modelling the solar wind from the Sun to Earth’s orbit

: New Empirical Constraints and Boundary Conditions

Abstract

This thesis is concerned with studying the relationship between coronal electron density and solar wind velocity in the solar atmosphere to provide a space weather forecasting model that negates the need for magnetic field extrapolations.
Ambient solar wind conditions can cause adverse effects on Earth’s planetary system as well as on various technologies on which society is becoming increasingly dependent. To better predict the state of the solar wind at 1 AU, the origin of the solar wind; the solar corona, must be better understood. This work analyses the relationship between coronal electron density gained from tomographic methods, and solar wind velocities within the middle corona (8 R⊙). The derived velocities are then used as an inner boundary for a highly efficient Time-dependent Heliospheric Upwind eXtrapolation (HUXt) model. Chapter 1 provides a general introduction to the relevant theories and the characteristics of both the Sun and the solar wind. An extensive account of the solar wind model and tomography models, as well as details of the relevant instrumentation are presented in Chapter 2. Chapter 3 presents a novel inner boundary condition for ambient heliospheric solar wind models. We take density maps provided by the coronal rotational tomography (CRT) model at a height of 8 R⊙. The density maps provide a direct constraint of the coronal structure avoiding the need to model the complex lower corona. The aim of this work is to exploit CRT densities as an inner boundary condition for the HUXt solar wind model. This approach requires conversion of densities into solar wind velocities at the inner boundary. A simplistic empirical inverse linear relationship is used to convert the tomographic densities to solar wind velocities at 8 R⊙. The derived velocities are input to HUXt to predict ambient solar wind velocity at Earth. The parameters used in the density-velocity conversion model are optimised via an exhaustive search method which adjusts the velocity range of the lower boundary. The Dynamic Time Warping (DTW) algorithm is then used to quantify the agreement between tomography/HUXt output and in situ data at 1 AU for all parameter search values. Early results show up to a 32% decrease in mean absolute error between the modelled and observed solar wind velocities at 1 AU compared results gained via the coupled MAS/HUXt model. We also discuss the sensitivity of the latitudinal dependence on the outcome of the accuracy of solar wind predictions of Earth. The use of this model with both an ensemble approach and in a forecasting context are also explored. Chapter 4 builds on the foundations laid by the work undertaken in Chapter 3. The density-velocity conversion model is revisited with the aim of gaining more stable and consistent results of the ambient solar wind conditions at 1 AU across a longer time period than a single Carrington rotation. In this work, a statistical approach, based on the comparison of the distribution of in situ measurements of densities and velocities, is used to derive an empirical conversion model. 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, the comparison between modelled and in situ measurements of solar wind velocities were predicted at a range of locations at a distance of 1 AU namely, Earth, STEREO A and STEREO B over the past solar cycle. At these locations, the results give a mean absolute error (MAE) of 61.2, 69.0 and 66.1kms−1 when compared to OMNI, STEREO A and STEREO B observations respectively. An analysis of thousands of events (defined as solar wind streams above 450kms−1) gives an accuracy score of 76%. This novel approach yields model predictions that consistently provide a strong statistical agreement with solar wind conditions observed at multiple locations at 1 AU. In chapter 5, we extend the concept presented in the former chapters to include solar wind acceleration, and thus velocity profiles out to 1 AU. We use a similar scaled exponential density-velocity conversion model defined as as V0 = (75 ∗ e−[5.2∗ρN] + 108) kms−1,, and typically range from 100 to 180kms−1. ρN is defined as the value of normalized tomographic plasma density. V0 defines the subsequent acceleration as V (r) = V0 1 + αIP 1 − e(−[r−r0]/rH) ] , with αIP ranging from 1.75 to 2.7, and rH from 50 to 35 R⊙ dependent on V0. The acceleration profiles outlined are derived from the in situ distribution of velocity measurements from spacecraft at 1 AU as well as the Parker Solar Probe (PSP) spacecraft, at distances between 13 R⊙ and 1 AU. For the period of November
2018 to September 2021 these constraints are applied using the HUXt model to give good agreement with in situ observations at the PSP location (MAE of 64.3 kms−1), and with OMNI at 1 AU (MAE of 52.8 kms−1) - a ∼ 6% statistical improvement compared with using a simpler constant acceleration model presented in Chapter 4. We also exploit mass flux conservation to extrapolate the tomographical densities at 8 R⊙ to 1 AU. Results show a good agreement
with OMNI density measurements, giving a MAE of 2.9 cm−3. The conclusions can be found in Chapter 6.

Date of Award	2024
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Huw Morgan (Supervisor) & Balazs Pinter (Supervisor)