Two Parameters Used for Modeling Solar Wind Speed

Arge (2003) found the solar wind speed at the first Lagrangian point can be roughly modeled by $v_\textrm{sw}=265+\dfrac{25}{f_s^{2/7}} \left(5-1.1\times \exp(1-(\theta_b/4)^2)\right)~\mathrm{km/s},$ and two parameters in this formula are defined as:

• Magnetic field expansion factor $f_\textrm{s}(\varphi, \vartheta, r)= \left(\dfrac{R_0}{R_1}\right) ^2 \dfrac{B_r(\varphi_0, \vartheta_0, R_0)} {B_r(\varphi_1, \vartheta_1, R_1)},$ where $(\varphi_0, \vartheta_0, R_0)$ are the target coordinates traced from $(\varphi, \vartheta, r)$ to the inner boundary of $r=R_0$, and $(\varphi_1, \vartheta_1, R_1)$ are the target coordinates traced from $(\varphi, \vartheta, r)$ to the outer boundary of $r=R_1$.
• $\theta_b(\varphi, \vartheta, r)$, the minimum angular distance of an open-field footpoint from a coronal hole boundary.
• For a closed field line, its rboundary is 11, its $f_\mathrm{s}$ is set to 1000., its $\theta_b$ is set to 0., these default values can be adjusted in par2solarwind.pro (par2solarwind.py)

This program can be downloaded with the command

git clone https://github.com/el2718/par2solarwind

And FastQSL2 should be downloaded first

git clone https://github.com/el2718/FastQSL2

Please address comments and suggestions to Dr. Chen, Jun (陈俊)

If your markdown reader can not can not render the formulae in README.md, please read README.html directly.

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This program is licensed under a CC BY-NC-SA 4.0 License.

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Cite as

• Jun Chen*, Thomas Wiegelmann, Li Feng*, Chaowei Jiang, and Rui Liu. FastQSL 2: A Comprehensive Toolkit for Magnetic Connectivity Analysis. 2026, SCIENCE CHINA Physics, Mechanics & Astronomy, submitted

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Computation of theta_b.f90 with Fortran

• For Linux and macOS (either by ifx/ifort or gfortran):

  ifx -o theta_b.x theta_b.f90 -fopenmp -O3 -xHost -ipo
  

  ifort -o theta_b.x theta_b.f90 -fopenmp -O3 -xHost -ipo
  

  gfortran -o theta_b.x theta_b.f90 -fopenmp -O3 -march=native
  

• For Windows (either by ifort or gfortran): executing "C:\Program Files (x86)\Intel\oneAPI\setvars.bat" in cmd first would be necessary

  ifort /o theta_b.exe theta_b.f90 /Qopenmp /O3 /QxHost /Qipo
  

  gfortran -o theta_b.exe theta_b.f90 -fopenmp -O3 -march=native
  

  • In Windows 11, also in some upgraded Windows 10, the pop-up window for theta_b.exe can not be closed automatically, please uncomment this line in theta_b.f90 to kill the pop-up window (delete !):

    ! call system('taskkill /im theta_b.exe /f')
    

  • for ifx, the compilation should be the same as ifort, while I have not tested it

Path of theta_b.x

• please specify the path of theta_b.x,
  • in par2solarwind.pro, please correct the line of

    spawn, '/path/of/theta_b.x'
    

  • in par2solarwind.py, please correct the line of

    subprocess.run(r'/path/of/theta_b.x', shell=True)
    

• or move theta_b.x to the $PATH (e.g. /usr/local/bin/) of the system and delete the text /path/of/
  • you can append this line to ~/.bashrc

    export PATH=$HOME/bin:$PATH
    

    then $HOME/bin is a $PATH of the system
• For Windows, use theta_b.exe instead of theta_b.x

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Parameters

• b_lon, b_lat, b_r, lon_rad, lat_rad, radius have same meaning of Bz, By, Bx, xa, ya, za in FastQSL2 when spherical is invoked

• RK4Flag, step, tol, maxsteps, nthreads, silent, preview, qsl are the same as those in FastQSL2

• bottomFlag: to compute only at the bottom layer

  • default is 0 (the whole 3D domain)

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Products

If use par2solarwind.pro, the results are returned by the keywords fs, theta_b, qsl

If use par2solarwind.py, the results are returned by the tuple (fs, theta_b, qsl), see the example of demo_par2_charge4.py

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Demos

If use fastqsl.pro

IDL> .r demo_par2_charge4.pro

If use fastqsl.py

python3 demo_par2_charge4.py

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History

• Feb 26, 2026 Jun Chen, version 1.0, suggested by Chaowei Jiang