Significance of Bernoulli Integral Terms for the Solar Wind Protons at 1 au

The Bernoulli integral describes the energy conservation of a fluid along specific streamlines. The integral is the sum of individual terms that contain the plasma density, speed, temperature, and magnetic field. Typical solar wind analyses use the fluctuations of the Bernoulli integral as a criterion to identify different plasma streamlines from single spacecraft observations. However, the accurate calculation of the Bernoulli integral requires accurately determining the plasma polytropic index from the analysis of density and temperature observations. To avoid this complexity, we can simplify the calculations by keeping only the dominant terms of the integral. Here, we analyze proton plasma and magnetic field observations obtained by the Wind spacecraft at 1 au, during 1995. We calculate the Bernoulli integral terms and quantify their significance by comparing them with each other. We discuss potential simplifications of the calculations in the context of determining solar wind proton thermodynamics using single spacecraft observations.

Invariant submodels of rank 3 and rank 2 monatomic gas with the projective operator

The system of gas dynamics equations with the state equation of the monatomic gas admits a group of transformations with a 14-dimensional Lie algebra. A projective operator is specific to this algebra. We consider all one-dimensional subalgebras containing the projective operator. Invariants are calculated and invariant submodel of rank 3 is constructed for each of subalgebras. All submodels are stationary type. They are reduced to the canonical form. Area hyperbolicity of obtained system were specified. Integral entropy is obtained along the flow lines. An ordinary differential equation to the invariant functions is obtained along the flow lines (analogue of a Bernoulli integral for stationary motions). We consider all two-dimensional subalgebras containing projective operator. Invariant submodel of rank 2 stationary type is constructed for each of subalgebras. Submodels are reduced to the canonical form.

Accretion Processes in Magnetic Binaries

In this paper, we give a brief summary of the talks on accretion processes in AM Herculis systems which were presented at the ANU Astrophysical Theory Centre workshop on ‘Magnetic Fields and Accretion’. One of the topics to be discussed was the mechanism that leads to the formation of magnetically funnelled accretion flows in close interacting magnetic binaries. New solutions to the Bernoulli integral indicate that the field lines must be twisted and have a strong toroidal component at the base of the funnel in order for channelled flow to be possible. The magnetic field pressure of these toroidal fields first lifts the material out of the orbital plane allowing it to ‘levitate’ before freely falling along magnetic field lines towards the stellar surface. Results of recent calculations of the thermal structure and radiation properties of accretion funnels were also presented. These new 3D calculations allow for heating by the soft X-rays originating from the accretion shock, and by magnetic heating at the base of the funnel, and determine self-consistently the thermal structure, and the continuum and line emissions, allowing for both transfer of the external radiation field and the trapping of radiation within the funnel. Calculations were also presented of the expected properties of H- and He-like Fe lines originating from the accretion shock itself at the stellar surface. These lines are predicted to be rather strong and can be used as diagnostics of the accretion flow. Finally, the stability of the accretion shock was also addressed. In particular, it was shown that radiative cooling may cause thermal instability and an oscillatory behaviour, with two competing processes coming into play: bremsstrahlung cooling, which promotes instability, and cyclotron cooling, which tends to dampen the oscillations.