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Register a new userEvolution of The Proton Velocity Distribution due to Stochastic Heating in the Near-Sun Solar Wind
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We investigate how the proton distribution function evolves when the protons undergo stochastic heating by strong, low-frequency, Alfven-wave turbulence under the assumption that $beta$ is small. We apply our analysis to protons undergoing stochastic heating in the supersonic fast solar wind and obtain proton distributions at heliocentric distances ranging from 4 to 30 solar radii. We find that the proton distribution develops non-Gaussian structure with a flat core and steep tail. For $r >5 R_{rm S}$, the proton distribution is well approximated by a modified Moyal distribution. Comparisons with future measurements from emph{Solar Probe Plus} could be used to test whether stochastic heating is occurring in the solar-wind acceleration region.
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Various remote sensing observations have been used so far to probe the turbulent properties of the solar wind. Using the recently reported density modulation indices that are derived using angular broadening observations of Crab Nebula during 1952 - 2013, we measured the solar wind proton heating using the kinetic $rm Alfvacute{e}n$ wave dispersion equation. The estimated heating rates vary from $approx 1.58 times 10^{-14}$ to $1.01 times 10^{-8} ~rm erg~ cm^{-3}~ s^{-1}$ in the heliocentric distance range 5 - 45 $rm R_{odot}$. Further, we found that heating rates vary with the solar cycle in correlation with density modulation indices. The models derived using in-situ measurements (for example, electron/proton density, temperature, and magnetic field) that the recently launched Parker Solar Probe observes (planned closest perihelia $rm 9.86~ R_{odot}$ from the center of the Sun) are useful in the estimation of the turbulent heating rate precisely. Further, we compared our heating rate estimates with the one derived using previously reported remote sensing and in-situ observations.
The fourth orbit of Parker Solar Probe (PSP) reached heliocentric distances down to 27.9 Rs, allowing solar wind turbulence and acceleration mechanisms to be studied in situ closer to the Sun than previously possible. The turbulence properties were found to be significantly different in the inbound and outbound portions of PSPs fourth solar encounter, likely due to the proximity to the heliospheric current sheet (HCS) in the outbound period. Near the HCS, in the streamer belt wind, the turbulence was found to have lower amplitudes, higher magnetic compressibility, a steeper magnetic field spectrum (with spectral index close to -5/3 rather than -3/2), a lower Alfvenicity, and a 1/f break at much lower frequencies. These are also features of slow wind at 1 au, suggesting the near-Sun streamer belt wind to be the prototypical slow solar wind. The transition in properties occurs at a predicted angular distance of ~4{deg} from the HCS, suggesting ~8{deg} as the full-width of the streamer belt wind at these distances. While the majority of the Alfvenic turbulence energy fluxes measured by PSP are consistent with those required for reflection-driven turbulence models of solar wind acceleration, the fluxes in the streamer belt are significantly lower than the model predictions, suggesting that additional mechanisms are necessary to explain the acceleration of the streamer belt solar wind.
The solar wind escapes from the solar corona and is accelerated, over a short distance, to its terminal velocity. The energy balance associated with this acceleration remains poorly understood. To quantify the global electrostatic contribution to the solar wind dynamics, we empirically estimate the ambipolar electric field ($mathrm{E}_parallel$) and potential ($Phi_mathrm{r,infty}$). We analyse electron velocity distribution functions (VDFs) measured in the near-Sun solar wind, between 20.3,$R_S$ and 85.3,$R_S$, by the Parker Solar Probe. We test the predictions of two different solar wind models. Close to the Sun, the VDFs exhibit a suprathermal electron deficit in the sunward, magnetic field aligned part of phase space. We argue that the sunward deficit is a remnant of the electron cutoff predicted by collisionless exospheric models (Lemaire & Sherer 1970, 1971, Jockers 1970). This cutoff energy is directly linked to $Phi_mathrm{r,infty}$. Competing effects of $mathrm{E}_parallel$ and Coulomb collisions in the solar wind are addressed by the Steady Electron Runaway Model (SERM) (Scudder 2019). In this model, electron phase space is separated into collisionally overdamped and underdamped regions. We assume that this boundary velocity at small pitch angles coincides with the strahl break-point energy, which allows us to calculate $mathrm{E}_parallel$. The obtained $Phi_mathrm{r,infty}$ and $mathrm{E}_parallel$ agree well with theoretical expectations. They decrease with radial distance as power law functions with indices $alpha_Phi = -0.66$ and $alpha_mathrm{E} = -1.69$. We finally estimate the velocity gained by protons from electrostatic acceleration, which equals to 77% calculated from the exospheric models, and to 44% from the SERM model.
The first two orbits of the Parker Solar Probe (PSP) spacecraft have enabled the first in situ measurements of the solar wind down to a heliocentric distance of 0.17 au (or 36 Rs). Here, we present an analysis of this data to study solar wind turbulence at 0.17 au and its evolution out to 1 au. While many features remain similar, key differences at 0.17 au include: increased turbulence energy levels by more than an order of magnitude, a magnetic field spectral index of -3/2 matching that of the velocity and both Elsasser fields, a lower magnetic compressibility consistent with a smaller slow-mode kinetic energy fraction, and a much smaller outer scale that has had time for substantial nonlinear processing. There is also an overall increase in the dominance of outward-propagating Alfvenic fluctuations compared to inward-propagating ones, and the radial variation of the inward component is consistent with its generation by reflection from the large-scale gradient in Alfven speed. The energy flux in this turbulence at 0.17 au was found to be ~10% of that in the bulk solar wind kinetic energy, becoming ~40% when extrapolated to the Alfven point, and both the fraction and rate of increase of this flux towards the Sun is consistent with turbulence-driven models in which the solar wind is powered by this flux.
Whether the phenomenology governing MHD turbulence is Kolmogorov or Iroshnikov-Kraichnan (IK) remains an open question, theoretically as well as observationally. The ion heating profile observed in the solar wind provides a quantitative, if indirect, observational constraint on the relevant phenomenology. Recently, a solar wind heating model based on Kolmogorov spectral scaling has produced reasonably good agreement with observations, provided the effect of turbulence generation due to pickup ions is included in the model. Without including the pickup ion contributions, the Kolmogorov scaling predicts a proton temperature profile that decays too rapidly beyond a radial distance of 15 AU. In the present study, we alter the heating model by applying an energy cascade rate based on IK scaling, and show that the model yields higher proton temperatures, within the range of observations, with or without the inclusion of the effect due to pickup ions. Furthermore, the turbulence correlation length based on IK scaling seems to follow the trend of observations better.
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