Predicted times of bow Shock crossings at Venus from the ESA/Venus Express mission, using spacecraft ephemerides and magnetic field data, with a predictor-corrector algorithm

CHARACTERISTICS
Planet: Venus
Radius: R_V = 6051.8 km (volumetric mean planetary radius)
Spacecraft: ESA/Venus Express
Spacecraft coordinates system: Venus Solar Orbital (VSO) equivalent to Sun-State coordinate system:

• +X_VSO points towards the Sun from the planet’s centre,
• +Z_VSO towards Venus’ North pole and perpendicular to the orbital plane defined as the X_VSO–Y_VSO plane passing through the centre of Venus,
• Y_VSO completes the orthogonal system.

Time span: 01/04/2006 to 25/11/2014
Total number N of candidate bow shock crossings in the database: N = 4950
Number of quasi-parallel bow shock crossings: N_|| = 844
Number of quasi-perpendicular bow shock crossings: N_\(\perp\) = 4106

ORIGINAL DATASETS USED
The original Venus Express/MAG data repository on which these algorithms were applied is available on ESA's Planetary Science Archive system (PSA) at: https://archives.esac.esa.int/psa/ftp/VENUS-EXPRESS/MAG/. For this study, 1-Hz magnetic field data was used.

METHOD
To construct this database from the original datasets above, the predictor and predictor-corrector algorithms used are described for the Mars case in:
Simon Wedlund, C., Volwerk, M., Beth, A., Mazelle, C., Möstl, C., Halekas, J., Gruesbeck, J. and Rojas-Castillo, D., (2021), A Fast Bow Shock Location Predictor-Estimator From 2D and 3D Analytical Models: Application to Mars and the MAVEN mission, Journal of Geophysical Research, 127, e2021JA029942. https://doi.org/10.1029/2021JA029942

They consist of two consecutive steps: 

1. Predictor geometric algorithm based on 2D or 3D existing fits for prediction of the Venus bow shock position. The original fits were taken from 2D conic fits in the plane \(\left(X_\text{VSO}, \sqrt{Y_\text{VSO}^2+Z_\text{VSO}^2}\right)\)performed on the datasets of Persson et al. (2023), Venusian bow shock crossings manually identified from measurements by the ASPERA-4 and MAG instruments onboard Venus Express, Zenodo (https://doi.org/10.5281/zenodo.7679677).
2. Corrector algorithm based on magnetic field measurements.

We also provide the angle between the average Interplanetary Magnetic Field (IMF) vector upstream of the shock and the shock normal, noted θ_Bn (ThetaBn). Assuming a locally smooth shock surface, this gives a first indication of the geometry of the shock, so that:

• 45^∘<θ_Bn<135^∘: quasi-perpendicular shock condition
• θ_Bn≤45^∘ and θ_Bn\(\geq\)135^∘: quasi-parallel shock condition

Uncertainty on these angles is estimated to be ± 5º. 

For details, see Simon Wedlund et al. (2022) above, §2.3 pp. 10-12.

VARIABLES DESCRIPTION

This database contains the following ASCII variables:

• Bow shock times in Venus Express' database (1-s resolution): T_bs
• Venus Solar Orbital coordinates of the shock, in units of Venus radius R_V (R_V = 6051.8 km):
  X_VSO, Y_VSO, Z_VSO and Euclidean distance \(R_{VSO} = \sqrt{X_{VSO}^2 + Y_{VSO}^2 + Z_{VSO}^2}\) (in R_V)
• Solar Zenith angle in degrees: SZA = \(\tan^{-1}{Y_{VSO}^2+Z_{VSO}^2 \over X_{VSO}^2}\) (in º) 
• Angle between average B-field direction and shock normal assuming a smooth shock surface \(\theta_{Bn}\) (ThetaBn, in º, calculated with atan2(norm(cross(B,ñ),dot(B,ñ)), with B the magnetic field vector and ñ the vector normal to the shock surface):
  • 45 < ThetaBn <  135 deg: quasi-\(\perp\) shock
  • ThetaBn \(\leq\) 45 deg & ThetaBn \(\geq\) 135 deg: quasi-|| shock
• Interplanetary Magnetic Field (IMF) upstream average vector in VSO coordinates, B_x, B_y, B_z (in nT).
• Flag for direction of crossing:
  • flag = 0: magnetosheath \(\longrightarrow\) solar wind (2447 events)
  • flag = 1: solar wind \(\longrightarrow\) magnetosheath (2503 events)

WARNING

1. This version of the database is currently in a preliminary stage of application and, as such, is not fully tested. Solar wind upstream magnetic field values (IMF) are given only as a first approximation for each orbit segment. See point 2 for caveats. For carefully manually picked shock crossings, the user is referred to the database of:
   Persson et al. (2023), Venusian bow shock crossings manually identified from measurements by the ASPERA-4 and MAG instruments onboard Venus Express, Zenodo (https://doi.org/10.5281/zenodo.7679677)
2. This database is based on an automatic statistical geometrical estimate, further refined by constraints on magnetic fields. This is aimed at giving a first approximation of the shock area times in the Venus Express data. It is particularly suited to statistical studies and region identification in the Venus Express datasets. As such, this database should be used as a first indicator of the shock location, and with caution: it CANNOT, and WILL NOT substitute, especially in case studies, for a careful analysis of the full magnetometer and plasma bow shock signatures. Moreover, the algorithm is optimised for detecting the first disturbance observed in the magnetic field immediately ahead of the shock's foot (in the foreshock area), and not for the detection of other structures in the shock, such as the shock ramp. The "shock" location is therefore given here with typical uncertainties of about 0.040 R_V (with R_V = 6051.8 km, i.e., about 250 km in the radial direction). Finally, for multiple shock crossings, the algorithm chooses the first occurrence of the shock starting from the undisturbed solar wind.

Current formatting optimised for MATLAB.

ACKNOWLEDGEMENTS
C. Simon Wedlund and M. Volwerk thank the Austrian Science Fund (FWF) project P32035-N36.    

LICENSE AND RIGHTS
This database is shared under a Creative Commons CC-BY-4.0 license.

Version 1 (c) Cyril Simon Wedlund @ Space Research Institute of Graz (IWF), 
                                                            Austrian Academy of Sciences, 2022-10-05
Contact email:        cyril.simon.wedlund@gmail.com