Inelastic scattering off shifting or oscillating density fluctuations results in broadening of radio indicators propagating within the photo voltaic corona and photo voltaic wind. Utilizing an anisotropic density fluctuation mannequin from the kinetic scattering idea for photo voltaic radio bursts, we deduce the plasma velocities (perpendicular to the road of sight) required to elucidate observations of spacecraft sign frequency broadening. The kinetic vitality related to these inferred bulk velocities cascades to smaller and smaller scales, the place it’s finally dissipated by damping of ion-sound waves. The inferred vitality deposition charge related to this course of compares very favorably with these required to warmth the corona and drive the photo voltaic wind.
Inelastic Scattering of Radio Waves and Frequency Broadening Measurements
Contemplating a distant level supply, Azzollini et al (2024) calculate the results of inelastic scattering within the presence of motions perpendicular to the road of sight, they usually derive the related diffusion tensor for radio waves in anisotropic turbulent plasma. The frequency broadening charge (per unit journey distance alongside the course of propagation $z$) is proportional to the sq. of the velocities within the two instructions perpendicular to the road of sight. In anisotropic density turbulence (with a continuing anisotropy issue $alpha$, with values of $alpha<1$, similar to fluctuations preferentially aligned with the magnetic area), the impact of velocities within the course of the photo voltaic radial is weighted by $alpha^2$, in order that such motions have a a lot smaller impact than motions which can be transverse to the photo voltaic radius within the airplane of the sky. These expressions could be built-in alongside the road of sight to provide the frequency broadening $Delta f$ noticed on the Earth, which could be in contrast with observations (left panel of Determine 1) to find out the typical magnitude of the perpendicular velocities. The strong and dashed strains in the fitting panel of Determine 1 present the $Delta f$ derived utilizing the nominal density fluctuation spectrum (see Kontar et al. 2023 for particulars), for 2 totally different anisotropy components: $alpha=0.25$ (relevant to emission of radiation on the basic) and $alpha=0.4$ (relevant to radiation on the second harmonic). (We think about each values of $alpha$ as a result of we don’t a priori know whether or not we’re observing basic or harmonic radiation.) The gray space exhibits the vary in $Delta f$ values obtained; the decrease sure is set by a density fluctuation amplitude of half the nominal expression of density fluctuations and an anisotropy issue $alpha=0.25$, and the higher sure is set by a density fluctuation amplitude of twice the nominal expression of density fluctuation and an anisotropy issue $alpha=0.4$.
Determine 1. Left: Noticed spectral broadening (the sq. root of the variance) of spacecraft indicators noticed by the corona from varied research, the place every provider sign is scaled to $f=1$ GHz utilizing $Delta f/f propto 1/f^2$. Proper: Derived type of $Delta f$, for $v_{perp}=30$ km s$^{-1}$ (decided from measurements of non-thermal line broadening), and $v_parallel=sqrt{v_s^2 + v_{mathrm{sw}}^2}$, the place $v_s$ is the sound velocity and $v_{mathrm{sw}}$ is the photo voltaic wind velocity.
Determine 2. Left: Aircraft-of-sky velocity $v_{perp}$ calculated utilizing the frequency broadening measurements from Determine 1. The inexperienced and crimson factors present the conversion of particular person $Delta f$ information factors from Determine 1, for various values of $alpha$, with binned averages and weighted uncertainties on every bin. Center: Parallel and perpendicular velocities $v_{parallel}$ (blue) and $v_{perp}$ (black) required to solely clarify the frequency broadening measurements in Determine 1. The gray dots and stars present a abstract of the measured values of the non-thermal velocity customary deviation from the fitting panel. Additionally proven is the photo voltaic wind velocity $v_{mathrm sw}$, the ion-sound velocity $v_s$, and the Alfvén velocity $v_A$, obtained utilizing the density and magnetic area fashions in Kontar et al. 2023. Proper: $1sigma$ non-thermal velocities $v_{mathrm{nth}}$ from line-of-sight Doppler broadening of coronal strains.
Alfvén Wave Cascade and Damping of Ion-Sound Waves
Velocity fluctuations alongside the road of sight are sometimes interpreted as manifestations of motions perpendicular to the magnetic area (Doyle et al. 1998), and comparable motions within the airplane of the sky result in frequency broadening of radio indicators. Such motions are generally interpreted as Alfvén waves, which may bear turbulent cascade to smaller scales (e.g., Holloweg 1978). The ability per unit mass (erg g$^{-1}$ s$^{-1}$) accessible to be deposited by such a Kolmogorov cascade in robust MHD turbulence (Goldreich & Sridhar 1995) is estimated to be
[ epsilon_{ell_perp} simeq frac{ v_{perp}^2 }{tau} simeq frac{ v_{perp}^3}{ell_perp}~, ]
the place $ell_perp $ is a measure of the transverse correlation size (Hollweg 1986). Vitality might be equipped to the corona and photo voltaic wind by way of absorption of the vitality contained within the strongly damped parallel propagating ion-sound or gradual magneto-sonic waves. The inferred vitality deposition charge, built-in over the vary of heights (2-3 $R_odot$) (the place it’s handiest) corresponds to an vitality flux $sim 3 occasions 10^5$ erg cm$^{-2}$ s$^{-1}$ (300 W m$^{-2}$). Such an vitality flux is broadly in step with that required to steadiness vitality losses and warmth the corona (see e.g., Withbroe 1988).
Determine 3. Left: Out there energy per unit mass (erg/g/s) utilizing perpendicular velocity fluctuations from Determine 1. The strong and dashed strains correspond to the vary (20-70) km~s$^{-1}$ (black) from frequency broadening measurements, and (20-40) km~s$^{-1}$ for $r < 1.4~R_odot$ for non-thermal velocities from coronal strains (crimson). Proper: Coronal heating charge per unit mass (erg/g/s) from Landau damping of ion-sound waves. The strong and dashed strains present the outcomes for the nominal density fluctuation amplitude for anisotropy components $alpha=0.25$ and $alpha=0.4$, and the gray space corresponds to the vary of values from one-half to double the nominal density fluctuation amplitude, taking each values of $alpha$ into consideration.
Conclusions
The inferred velocities are in step with motions which can be dominated by the photo voltaic wind at distances $gtrsim 10~R_odot$, however the ranges of frequency broadening for $lesssim 10 ~R_odot$ require further radial speeds of about 300 km s$^{-1}$ and/or transverse speeds of about (20-70) km s$^{-1}$. The inferred radial velocities additionally seem in step with the sound or proton thermal speeds, whereas the speeds perpendicular to the radial course are in step with non-thermal motions measured by way of coronal Doppler-line broadening, interpreted as Alfvénic fluctuations. Landau damping of parallel propagating ion-sound (gradual MHD) waves ends in a proton heating charge that’s corresponding to the charges accessible from a turbulent cascade of Alfvénic waves at giant scales, suggesting a coherent image of vitality switch, by way of the cascade or/and parametric decay of Alfvén waves to the small scales the place heating takes place.
Primarily based on the latest paper by Francesco et al, Plasma Motions and Compressive Wave Energetics within the Photo voltaic Corona and Photo voltaic Wind from Radio Wave Scattering Observations, ApJ 968 72 (2024), DOI: 10.3847/1538-4357/ad4154
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