Modelling Solar Orbiter Dust Detection Rates in Inner Heliosphere as a Poisson Process

Solar Orbiter provides dust detection capability in inner heliosphere, but estimating physical properties of detected dust from the collected data is far from straightforward. First, a physical model for dust collection considering a Poisson process is formulated. Second, it is shown that dust on hyperbolic orbits is responsible for the majority of dust detections with Solar Orbiter's Radio and Plasma Waves (SolO/RPW). Third, the model for dust counts is fitted to SolO/RPW data and parameters of the dust are inferred, namely: radial velocity, hyperbolic meteoroids predominance, and solar radiation pressure to gravity ratio as well as uncertainties of these. Non-parametric model fitting is used to get the difference between inbound and outbound detection rate and dust radial velocity is thus estimated. A hierarchical Bayesian model is formulated and applied to available SolO/RPW data. The model uses the methodology of Integrated Nested Laplace Approximation, estimating parameters of dust and their uncertainties. SolO/RPW dust observations can be modelled as a Poisson process in a Bayesian framework and observations up to this date are consistent with the hyperbolic dust model with an additional background component. Analysis suggests a radial velocity of the hyperbolic component around $(63 \pm 7) \mathrm{km/s}$ with the predominance of hyperbolic dust about $(78 \pm 4) \%$. The results are consistent with hyperbolic meteoroids originating between $0.02 \mathrm{AU}$ and $0.1 \mathrm{AU}$ and showing substantial deceleration, which implies effective solar radiation pressure to gravity ratio $\gtrsim 0.5$. The flux of hyperbolic component at $1 \mathrm{AU}$ is found to be $(1.1 \pm 0.2) \times 10^{-4} \mathrm{m^{-2}s^{-1}}$ and the flux of background component at $1 \mathrm{AU}$ is found to be $(5.4 \pm 1.5) \times 10^{-5} \mathrm{m^{-2}s^{-1}}$.