Published May 17, 2019 | Version 1.0
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Supplement to: Electron energy partition across interplanetary shocks

  • 1. NASA Goddard Space Flight Center
  • 2. Astronomy Department, University of Maryland, College Park
  • 3. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder
  • 4. Space Sciences Department, The Aerospace Corporation
  • 5. Harvard-Smithsonian Center for Astrophysics, Harvard University
  • 6. University of Michigan, Ann Arbor, School of Climate and Space Sciences and Engineering, Ann Arbor
  • 7. Department of Physics, University of Helsinki
  • 8. Department of Astronomy and Astrophysics, University of Chicago
  • 9. University of California Berkeley, Space Sciences Laboratory


Quick Summary:

The three files herein comprise supplemental information and standalone datasets for a three-part study of Electron energy partition across interplanetary shocks that describe the modeling of solar wind electron velocity distribution functions (VDFs) near interplanetary shocks observed by the Wind spacecraft.  Part I of the study (published in the The Astrophysical Journal Supplement Series on July 3, 2019 doi:10.3847/1538-4365/ab22bd) describes the methodology and how the two ASCII files (i.e., those stored here) were created and their contents.  Part I also explains the nuances of the analysis, the limitations of the dataset, and how to use the data within the two ASCII files.  Parts II and III (in preparation) present the statistical results and the detailed analysis of these results in the context of the dependence on relevant interplanetary shock parameters.  Below are the descriptions of each data product starting with the PDF supplemental file to the three-part study and then the associated ASCII files.  First we provide some background/definitions of jargon and terms used in each.

Solar Wind Electrons:

The solar wind electron VDF below ~1 keV is comprised of cold, dense core (subscript c or ec) population with thermal energies typically in the ~5-15 eV range, a hot, tenuous halo (subscript h or eh) population with thermal energies typically >20-30 eV, and an anti-sunward, field-aligned beam called the strahl or beam/strahl (subscript b or eb) population with thermal energies typically ~few 10s of eV.  Most previous work modeled the core as a bi-Maxwellian and the halo and beam/strahl as bi-kappa VDFs.  The work described in Part I (and the PDF supplement stored here) show that the core is more accurately described by a self-similar model VDF, which reduces to a bi-Maxwellian under appropriate conditions/limits and deviation from Maxwellian quantifies inelasticity in the plasma collisions.  That is, if the plasma were controlled by elastic Coulomb particle-particle collisions (e.g., in the low corona or chromosphere or photosphere), the VDF would relax to a Maxwellian in the absence of other forces.  When the plasma particles undergo inelastic collisions, the VDF profile changes from a Gaussian to something more like a "flattop" or box-like shape.

Wind Spacecraft:

The Wind spacecraft ( was launched on November 1, 1994 and currently orbits the first Lagrange point between the Earth and sun.  It holds a suite of instruments from gamma ray detectors to quasi-static magnetic field instruments, Bo.  The instruments used in this study and these datasets are the fluxgate magnetometer (MFI), the radio receivers (WAVES), ion Faraday cups (SWE), and the electron and ion electrostatic analyzers (3DP).  The MFI measures 3-vector Bo at ~11 samples per second (sps); the SWE measures reduced VDFs of the thermal proton and alpha-particle populations from which velocity moments are derived and used herein; WAVES observes electromagnetic radiation from ~4 kHz to >12 MHz which provides an observation of the upper hybrid line (also called the plasma line) used to define the total electron density; and 3DP observes full 4π steradian VDFs of electrons and ions from a few eV to ~30 keV which provide both ion velocity moments and the electron VDFs modeled herein.

PDF Supplement Description:

The PDF document contains descriptions and definitions of relevant interplanetary shock parameters and shock analysis techniques used by the Harvard Smithsonian Center for Astrophysics' Wind shock database at  It describes the details of the symbols/parameters used on the database website and their translation to plasma parameters or shock parameters.  The PDF also defines the shock normal finding techniques listed as two-four character inputs on the database website.  The PDF file lists the shocks analyzed and their relevant parameters in two tables, with the second listing the relevant critical Mach numbers.  Next the PDF provides some extra statistics of the analysis performed in the three-part study on Electron energy partition across interplanetary shocks in the form of histograms comparing differences for different selection criteria (e.g., low versus high Mach number shocks).  Finally, there are detailed descriptions and definitions of the model functions used to fit to the solar wind electron VDFs.

Both ASCII files have detailed headers outlining and defining the parameters contained therein.  They also provide column headings where the labels/names of each are defined and/or described in the header.  The headers also provide links to the analysis software used to perform the model fits to the VDFs.  We will first describe the contents of the file labeled Wind_ip_shock_3dp_fit_constraints_electrons.txt (FCONSTS for brevity) and then the file labeled Wind_ip_shock_3dp_fit_results_electrons.txt (FRESULTS for brevity).  Below use the following definitions:

  • \(N_{s}\) = number density of species s [cm-3] (s = ec for core, eh for halo, eb for beam/strahl, p for proton, etc.)
  • \(B_{o, j}\)= jth component (GSE coordinate basis) of quasi-static magnetic field vector [nT]
  • \(V_{Ts, j}\) = jth component (relative to Bo) of thermal speed of species s [km/s]
    • \(V_{Ts,j} = \sqrt{{2 k_{B} T_{s,j} \over m_{s}}}\), where \(T_{s, j}\) is the jth component (relative to Bo) of the temperature of species s [eV]
  • \(V_{os, j}\) = jth component (relative to Bo) of drift speed of species s [km/s] in ion rest frame
  • \(V_{s, j}\) = jth component (GSE coordinate basis) bulk velocity of species s [km/s] in spacecraft frame
  • \(T_{s, tot} = {1 \over 3} (T_{s, \parallel} + 2 \ T_{s, \perp})\), where \(\parallel(\perp)\) is the parallel(perpendicular) component relative to Bo
  • \(s_{es}\) = exponent for the symmetric self-similar model VDF of species s
  • \(\kappa_{es}\) = kappa value for the bi-kappa VDF of species s
  • \(p_{es}(q_{es})\) = parallel(perpendicular) exponent for the asymmetric self-similar model VDF of species s
  • \(\chi_{s}^{2}\) = least chi-squared of fit to species s
  • \(\phi_{sc}\) = spacecraft electric potential [eV]
  • \(\delta R = \lvert 1 - Median(f^{data}/f^{model}) \rvert\) = excess median deviation of fit [%]

FCONSTS File Description:

The FCONSTS file contains all the pertinent information used during the fit process for all VDFs that were analyzed including the fit results.  The columns are organized by electron component from core to halo to beam/strahl, in that order, sorted by the time stamp (UTC) of the observed VDF (very first column).  The first column in each set of electron component groups is a numerical indicator of the fit status for that component of the ith VDF.  This is followed by 30 columns consisting of 5 sets of 6 numbers.  Each model function has six fit parameters:  \(N_{s}\) [0], \(V_{Ts, \parallel}\) [1],  \(V_{Ts, \perp}\) [2],  \(V_{os, \parallel}\) [3],  \(V_{os, \perp}\) [4] (or \(p_{es}\) for asymmetric self-similar model VDF), and exponent of fit (i.e., \(s_{es}\), \(\kappa_{es}\), or \(q_{es}\)).  Thus, there are six columns for each of the following for each of the three components (i.e., 18 columns for each of the following in total):  initial guess values, returned fit values, lower limit constraints, upper limit constraints, and a logical value indicating whether the ith fit value sits on the lower (-1) or upper (+1) limit or neither (0).  These columns are followed by four more containing the number of iterations necessary to find the fit values, the least chi-squared value of the fit, the degrees of freedom in the fit process, and a two-letter designator of the model fit function used (defined in the ASCII file header).

FRESULTS File Description:

The FRESULTS file contains the fit results used in the three-part study.  Again, the first column starts each row with the time stamp (UTC) of the observed VDF.  In the following, all parameters listed with subscript j will correspond to three columns (one for each component) except the drift velocities which only have two for \(\parallel(\perp)\).  That is followed by:  \(N_{p}\) (SWE), \(N_{\alpha}\) (SWE), \(N_{i}\) (3DP), \(T_{p, j}\) (SWE), \(T_{\alpha, j}\) (SWE), \(T_{i, j}\) (3DP), \(B_{o, j}\) (MFI), \(V_{p, j}\) (SWE), \(V_{\alpha, j}\) (SWE), \(V_{i, j}\) (3DP), \(\phi_{sc}\) (multiple instruments), \(\delta R\) (3DP),  \(N_{ec}\) (fit), \(T_{ec, j}\) (fit), \(V_{oec, j}\) (fit), \(\kappa_{ec}\) (fit), \(s_{es}\) (fit), \(p_{es}\) (fit), \(q_{es}\) (fit), reduced \(\chi_{ec}^{2}\) (fit), core fit status, and repeats for the halo and beam/strahl fits.  The last four columns contain, in the following order, the total reduced chi-squared of the model fit of all components combined and fit flags (0 = worst, 10 = best) for each electron component.  Note that all possible exponents are provided for each component but only the one that is not set as a fill value corresponds to the functional form used to model that electron component (e.g., if \(s_{ec}\) is the only non-fill exponent for the core, then the core was modeled as a symmetric self-similar VDF).



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Additional details

Related works

Is supplement to
arXiv:1902.01476 (arXiv)
10.3847/1538-4365/ab22bd (DOI)


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