Strong Prevalence of Hammerhead Velocity Distributions Close to the Heliospheric Current Sheet

Abstract

The solar wind undergoes non-adiabatic heating as it travels away from the Sun. The velocity phase space distribution of non-equilibrium ions in the solar wind indicate a source of free energy that could contribute significantly to this heating. Parker Solar Probe (PSP) has observed velocity distributions containing highly anisotropic, perpendicularly diffused proton beams with a distinctly constricted gap between the core and beam populations. These distributions resemble a ``hammerhead" shape and were first reported in the fourth PSP encounter. Numerical simulations have reproduced the qualitative nature of hammerheads under certain initial conditions, but have not convincingly captured the prevalence or extreme attributes of the observed beam. This necessitates a broad study of the occurrence conditions and the associated plasma processes to better guide simulations. We statistically investigate the occurrence of these structures from 20 recent PSP encounters, and find that hammerheads dominantly occur around the Heliospheric Current Sheet (HCS). As the inclination of the HCS at PSP crossing points increases over the rising phase of the solar cycle, the occurrence of hammerheads is increasingly concentrated in narrow time periods around the HCS crossings. For comparison with previous work, we present statistical trends in the anisotropy of the proton beam and its connection to the density of proton beams as well as the drift speed of the beam to the core. Our study establishes a consistent occurrence pattern of hammerhead distributions around the HCS indicating hammerheads are diagnostics of energization processes associated with the HCS and its escaping wind.

Figures (9)

• Figure 1: Schematic summary of our hammerhead detection algorithm used in hampy. All velocity phase-space plots are presented on a $E-\theta$ plane. The $V_x- V_z$ coordinates are calculated by using $\phi \sim 163.125^{\circ}$. (a) $\phi$-collapsed $f(v_x, v_z)$ in the SPAN-I instrument frame before pre-processing. (b) $f(v_x, v_z)$ after removing spurious count bins which do not form a contiguous distribution in the 2D $(v_x, v_z)$ space. (c) Same as panel (b) but plotted using contour levels in a cell-centered convention. The black lines represent slices along different instrument elevation angles. The red lines at $\theta \sim -37^{\circ} \, \& \, 22^{\circ}$ correspond to elevations for the detected necks for the shown hammerhead distribution. The red grids in panels (e) & (f) show the detected necks using the corresponding 1D convolution profiles showed in panels (d1) & (d2). All VDF values are presented in log base 10.
• Figure 2: Figure showing (left ordinate) the scaled radial component of magnetic field $r^2 B_R(r)$ as a function of degrees from perihelion from E04 - E23. The corresponding hammerhead occurrence fraction from hampy is plotted as gray histograms in the background (right ordinate). The histograms are normalized to unit area for each encounter. This figure was generated using Plotbot, an open-source Python package plotbot.
• Figure 3: Heliographic projection to compare in-situ $B_R$ field sign reversals to hammerhead occurrence rate. Positive in-situ $B_R$ is marked in red and negative in-situ $B_R$ is marked in blue. PSP trajectory (back-mapped to 2.5$R_{\odot}$) is colored by $B_R$ where the perihelion is marked by higher opacity and larger markers. The fainter colored parts of the trajectory fall outside the dates we consider for the encounter, where we do not use hampy to detect hammerheads. We plot the fractional occurrence rate of hammerheads as lime-green circles in $1^{\circ}$ bins in heliographic lat-lon. The sizes of these circles are proportional to the fraction of VDFs which get flagged as hammerheads in the specific lat-lon bin. The solid black line marks the HCS at 2.5$R_{\odot}$ using PFSS. The top panel shows E04 while the bottom panel shows E22. The orange (blue) shaded regions indicated coronal holes formed by radially outgoing (incoming) open magnetic field lines.
• Figure 4: Characterizing hammerheads flagged by hampy to compare trends of temperature anisotropy of the hammer$T_{\perp}^{\mathrm{ham}}/T_{\parallel}^{\mathrm{ham}}$ vs. (a) fractional density $n^{\mathrm{ham}}/n^{\mathrm{total}}$ and (b) normalized drift speed $v^{\mathrm{ham}}_{\mathrm{drift}}/v_{\mathrm{A}}$. The 2D histograms are normalized to a maximum value of 1. The white dashed lines represent $50^{\mathrm{th}}$ and $25^{\mathrm{th}}$ quantiles. The hammerheads are chosen from E04 within the radial distance bin $25-30R_{\odot}$ as a comparison against the result reported in Verniero_Beams_2022. Panels (c) shows 1D histogram for the densities of core, neck and hammer components while panel (d) shows a 2D histogram for the fractional neck vs. the fractional hammer densities (both normalized with respect to the core). The vertical dashed black, blue and red lines in panel (c) show the statistical mean of the histograms for core, neck and hammer, respectively. The solid black line in panel (d) denotes a $x=y$ line.
• Figure 5: Histogram as a function of SPAN-i anode index for cases where hampy did not flag a VDF as hammerhead vs. when it was flagged as a hammerhead. The anode index is colored according to the legend shown. The counts are normalized to have a maximum value of 1 for both the 'Not detected' and 'Detected' cases. We considered measurements during perihelia across E04 - E23 in this figure.