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We examine angular broadening of radio wave scattering by density irregularities within the outer heliosphere and the very native interstellar medium (VLISM), incorporating an interior scale, latitudinal, and radial dependencies for the density fluctuation spectra and radiation propagation paths each close to and out of the ecliptic airplane.
Outer Heliospheric Radio Emission
Low-frequency radio wave emission was found within the distant heliosphere by the Voyager missions. A lot of investigations [e.g., Gurnett et al., 1998] demonstrated that these radio emissions are apparently generated near the boundary between the photo voltaic wind and the interstellar medium. Evidently, scattering by density irregularities performs a major function within the propagation and angular broadening $theta_{SC}$ of low-frequency 2 – 3 kHz radio emission (Cairns, 1995), particularly radio wave depth, angular dimension, propagation path, and temporal and spectral variability.
Pickup Ion (PUI)-mediated excessive latitude quick Photo voltaic Wind vs Voyager Information within the Ecliptic Airplane
The pickup ion (PUI)-mediated photo voltaic wind and the MHD turbulence transport mannequin of Zank et al., 2018, that describes background photo voltaic wind, turbulence, and PUI properties from 1 AU to 84 AU, is used to guage density turbulence all through the heliosphere. A easy scaling extends the theoretical predictions of the PUI mannequin to the excessive latitude wind past the heliospheric termination shock (HTS). The close to ecliptic photo voltaic wind and turbulence portions are calculated utilizing plasma and magnetometer knowledge from the Voyager 2 (V2) spacecraft over the interval 1977 to 2018. We observe noticeable variations within the excessive latitude and V2 plasma and magnetic subject variables.
Determine 1 – Plots present (a) density, (b) photo voltaic wind pace, (c) proton temperature, (d) azimuthal magnetic subject, (e) radial magnetic subject, and (f) heliolatitude with growing heliocentric distance over the interval March 1, 1995 to March 31, 1996.
To test the consistency of the PUI mannequin predictions, in Determine 1 we evaluate, the theoretical plasma parameters and magnetic subject parts derived at $45^circ$ latitude with the Ulysses observations. We use Ulysses observations of plasma parameters at $0^circ$ to $80^circ$ latitudes. The determine exhibits similarities between Ulysses observations at excessive latitudes ($gtrsim 40^circ$) and PUI mannequin predictions at $45^circ$ latitude in radial profiles of the photo voltaic wind density, pace, and radial and azimuthal magnetic subject parts.
Internal Scale and Density Turbulence Amplitude
To estimate the interior scale $l_i$, we make use of the Tasnim et al., 2020 interior scale mannequin and the theoretical PUI mannequin outcomes and V2 knowledge. We use $l_i = beta l_u$ when $beta l_u geq r_{pg}$ and $l_i = 2pi r_{pg}$ when $beta l_u < r_{pg}$. Right here, $l_u$ is the speed correlation size, $r_{pg}$ is the thermal proton gyroradius and $beta$ is the ratio between the interior scale and velocity correlation size. We estimate the worth of $beta$ based mostly on the calculated size of the magnetic subject fluctuation and the dissipation size scale of the magnetic subject fluctuation. The inclusion of $l_i$ has a major impact on the predictions of $theta_{SC}$. Word that the correlation size controls the cascade charge (cascade charge $propto l_u^{-1} propto l_i^{-1}$) of turbulence.
Determine 2 – Density turbulence amplitude $C_N^2$ as a operate of radial distance from 1 AU to 118 AU at excessive latitude and within the close to ecliptic airplane. (Backside panel) Radial variation of the angular broadening $theta_{SC}$ derived from Equation 1 for the PUI mediated quick photo voltaic wind, the ecliptic gradual photo voltaic wind, and estimates of the noticed supply dimension (inexperienced diamonds). Equation 1 contains interior scale results. The analytic prediction for $theta_{SC}$ by Cairns (1995) is overplotted within the determine.
Determine 2 (prime) exhibits that the estimated $C_N^2$ (utilizing two totally different approaches: described as mannequin 1 and mannequin 2) for the excessive latitude quick wind PUI mannequin is way smaller than the $C_N^2$ calculated within the ecliptic airplane utilizing V2 observations. The distinction in $C_N^2$ signifies that the variance of the density turbulence ${<delta rho>}^2$ is way bigger within the ecliptic airplane than that within the excessive latitude area. The bigger ${<delta rho>}^2$ within the ecliptic gradual photo voltaic wind than within the excessive latitude quick photo voltaic wind helps the suggestion of Armstrong et al. (2000) that density turbulence is weaker at excessive latitudes. The vertical cyan damaged line exhibits the situation of the HTS utilizing the V2 knowledge whereas the inexperienced dashed line identifies the assumed HTS location at excessive $45^circ$ latitudes.
Angular Broadening of the Radio Supply using the Parabolic Wave Equation (PWE) Formalism
We apply the parabolic wave equation (PWE) concept to calculate the angular broadening of the radio waves on account of scattering by density irregularities. We derive [theta_{SC}^2(R)=pi^{-2}Bigg[4pi^2 r_e^2 times int^{R_{so}}_{R_{ob}}dRfrac{C^2_N(R)lambda^{alpha}_{fs} Gamma(2-frac{alpha}{2})2^{2-alpha} }{big(1-frac{f^2_{p0}(R)}{f^2}big)Gamma(alpha/2)(alpha-2) }q_i^{4-alpha}Bigg]^{frac{2}{alpha-2}}]
The integral within the above equation is numerically solved for the density turbulence fashions. Based mostly on the turbulence fashions and observations, we calculate the scattering angle of the radio sources within the excessive latitude and close to ecliptic wind. Lastly, we evaluate the numerical outcomes with the analytic predictions from Cairns 1995 and the noticed supply sizes. As well as, Determine 2 (backside) compares the predictions of $theta_{SC}$ for the PUI-mediated excessive latitude photo voltaic wind with the obvious supply dimension from Voyager 1 and a couple of observations, discovering good settlement between the observations and the theoretical predictions at excessive latitudes.
Conclusions
To summarize, our investigation supplies an prolonged description of the angular broadening of outer heliospheric low frequency radio waves, addressing three important elements: i) the interior scale, ii) the radially various variance of density fluctuations that leads to totally different radial profiles within the photo voltaic wind past 1 AU, and most significantly, iii) the contribution of the excessive latitude quick photo voltaic wind.
Based mostly on latest paper by Tasnim et al., Density Turbulence and the Angular Broadening of Outer Heliospheric Radio Sources at Excessive Latitudes and within the Ecliptic Airplane, The Astrophysical Journal, 928, id.125, DOI: 10.3847/1538-4357/ac5031
References
Armstrong, J. W. , Coles, W. A., Rickett, B. J., J. Geophys. Res. 105 (2000): 5149-5156.
Cairns, I. Geophys. Res. Lett. 22, no. 24 (1995): 3433-3436.
Gurnett, D. A., Allendorf, S. C. ,Kurth, W. S. Geophys. Res. Lett. 25 (1998): 4433-4436.
Tasnim, S., Zank, G. P. , Cairns, I. H. , et al. Journal of Physics: Convention Sequence 1620, no. 1 (2020).
Zank, G. P., Adhikari, L., Zhao, L. -L., et al. Astrophys. J. 869, no. 1 (2018).
*Full record of authors: Samira Tasnim, Gary. P. Zank, Iver H. Cairns, and L. Adhikari
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