1. Compressibility and scaling in the solar wind as measured by ACE spacecraft Bogdan A. Hnat Collaborators: Sandra C. Chapman and George Rowlands; University of Warwick

2. Solar wind: Introduction Stream of supersonic and super-Alfvénic particles originated from the Sun Velocity ~500 km/s, density ~5 cm -3, IMF ~5 nT (at Earth’s orbit) Consists of electrons, protons (96%), ions (4%) Exhibits slow and fast components with different properties

3. Solar wind propagation

4. Objectives The main objective of this study was to characterise solar wind fluctuations and develop a stochastic model for their dynamics. Scaling, if exists, can simplify the description Some quantities are known to be fractal and are difficult to model (velocity, magnetic field) We will examine other quantities, such as density (solar wind often assumed to be incompressible) Which quantities are active and which are passively advected?

5. Scaling: basic concepts Building blocks Fluctuations: Scaling Segments: Length depends on scaleStatistics depends on scale self-similarity

6. How to determine scaling Fluctuations: Generalized Structure Functions: PDF rescaling: Conditioning: consider events < 15 σ(τ)

7. Scaling in ρ and |B| ESSESS Conditioning: events < 15 σ(τ)

8. Is density a passive scalar ACE spacecraft data for density and magnetic field Comparison of HD and MHD turbulence simulations Hnat, Chapman, Rowlands, Phys. Rev. Lett. 94 (2005) B is a passive scalar but density is not Suggests that solar wind plasma is compressible

9. Passive scalars Passive scalar: quantity passively advected in the turbulent velocity field. ∂ t T = - (v i ∂ i ) T + κ ∂ i ∂ i T (1) Magnetic field magnitude B is a passive scalar in solar wind [Bershadskyi, PRL 2005] Incompressible MHD was used to cast equation for B in form (1) Density should then also be a passive scalar ∂ t ρ = - (v i ∂ i ) ρ (2)

10. Model of the density fluctuations Fluctuations in density are approx. self-similar This result suggests that a Fokker-Planck approach could be used to describe the PDF. Consider following equation and solve for P

11. Fokker-Planck model Red line: self-similar solution of the F-P equation Hnat et al., Phys. Rev. E 67 (2003) Result: complete statistical characterization of density fluctuations up to 15 standard deviations

12. Conclusions Scaling in |B| and ρ are very different Fluctuations in density are well approximated by the self-similar scaling F-P approach gives good solutions for PDF dynamics Density appear to play important role in the ecliptic Results could be used to develop sub-grid models for solar wind turbulence Part of the ongoing effort to describe solar wind turbulence