Density Fluctuations in the Solar Wind Based on Type III Radio Bursts Observed by Parker Solar Probe

Radio waves are strongly scattered in the solar wind, so that their apparent sources seem to be considerably larger and shifted than the actual ones. Since the scattering depends on the spectrum of density turbulence, better understanding of the radio wave propagation provides indirect information on the relative density fluctuations $\epsilon=\langle\delta n\rangle/\langle n\rangle$ at the effective turbulence scale length. Here, we have analyzed 30 type III bursts detected by Parker Solar Probe (PSP). For the first time, we have retrieved type III burst decay times $\tau_{\rm{d}}$ between 1 MHz and 10 MHz thanks to an unparalleled temporal resolution of PSP. We observed a significant deviation in a power-law slope for frequencies above 1 MHz when compared to previous measurements below 1 MHz by the twin-spacecraft Solar TErrestrial RElations Observatory (STEREO) mission. We note that altitudes of radio bursts generated at 1 MHz roughly coincide with an expected location of the Alfv\'{e}n point, where the solar wind becomes super-Alfv\'{e}nic. By comparing PSP observations and Monte Carlo simulations, we predict relative density fluctuations $\epsilon$ at the effective turbulence scale length at radial distances between 2.5$R_\odot$ and 14$R_\odot$ to range from $0.22$ and $0.09$. Finally, we calculated relative density fluctuations $\epsilon$ measured in situ by PSP at a radial distance from the Sun of $35.7$~$R_\odot$ during the perihelion \#1, and the perihelion \#2 to be $0.07$ and $0.06$, respectively. It is in a very good agreement with previous STEREO predictions ($\epsilon=0.06-0.07$) obtained by remote measurements of radio sources generated at this radial distance.