The Early History of Heliospheric Science and the Spacecraft That Made It Possible.

Our understanding of the interaction of the large-scale heliosphere with the local interstellar medium (LISM) has undergone a profound change since the very earliest analyses of the problem. In part, the revisions have been a consequence of ever-improving and widening observational results, especially those that identified the entrance of interstellar material and gas into the heliosphere. Accompanying these observations was the identification of the basic underlying physics of how neutral interstellar gas and interstellar charged particles of different energies, up to and including interstellar dust grains, interacted with the temporal flows and electromagnetic fields of the heliosphere. The incorporation of these various basic effects into global models of the interaction, whether focused on neutral interstellar gas and pickup ions, energetic particles such as anomalous and galactic cosmic rays, or magnetic fields and large-scale flows, has profoundly changed our view of how the heliosphere and LISM interact. This article presents a brief history of the conceptual and observation evolution of our understanding of the interaction of the heliosphere with the local interstellar medium, up until approximately 1996.

Shocks in the Very Local Interstellar Medium.

Large-scale disturbances generated by the Sun's dynamics first propagate through the heliosphere, influence the heliosphere's outer boundaries, and then traverse and modify the very local interstellar medium (VLISM). The existence of shocks in the VLISM was initially suggested by Voyager observations of the 2-3 kHz radio emissions in the heliosphere. A couple of decades later, both Voyagers crossed the definitive edge of our heliosphere and became the first ever spacecraft to sample interstellar space. Since Voyager 1's entrance into the VLISM, it sampled electron plasma oscillation events that indirectly measure the medium's density, increasing as it moves further away from the heliopause. Some of the observed electron oscillation events in the VLISM were associated with the local heliospheric shock waves. The observed VLISM shocks were very different than heliospheric shocks. They were very weak and broad, and the usual dissipation via wave-particle interactions could not explain their structure. Estimates of the dissipation associated with the collisionality show that collisions can determine the VLISM shock structure. According to theory and models, the existence of a bow shock or wave in front of our heliosphere is still an open question as there are no direct observations yet. This paper reviews the outstanding observations recently made by the Voyager 1 and 2 spacecraft, and our current understanding of the properties of shocks/waves in the VLISM. We present some of the most exciting open questions related to the VLISM and shock waves that should be addressed in the future.

Parker Solar Probe Enters the Magnetically Dominated Solar Corona.

The high temperatures and strong magnetic fields of the solar corona form streams of solar wind that expand through the Solar System into interstellar space. At 09:33 UT on 28 April 2021 Parker Solar Probe entered the magnetized atmosphere of the Sun 13 million km above the photosphere, crossing below the Alfvén critical surface for five hours into plasma in casual contact with the Sun with an Alfvén Mach number of 0.79 and magnetic pressure dominating both ion and electron pressure. The spectrum of turbulence below the Alfvén critical surface is reported. Magnetic mapping suggests the region was a steady flow emerging on rapidly expanding coronal magnetic field lines lying above a pseudostreamer. The sub-Alfvénic nature of the flow may be due to suppressed magnetic reconnection at the base of the pseudostreamer, as evidenced by unusually low densities in this region and the magnetic mapping.

Alfvénic velocity spikes and rotational flows in the near-Sun solar wind.

The prediction of a supersonic solar wind1 was first confirmed by spacecraft near Earth2,3 and later by spacecraft at heliocentric distances as small as 62 solar radii4. These missions showed that plasma accelerates as it emerges from the corona, aided by unidentified processes that transport energy outwards from the Sun before depositing it in the wind. Alfvénic fluctuations are a promising candidate for such a process because they are seen in the corona and solar wind and contain considerable energy5-7. Magnetic tension forces the corona to co-rotate with the Sun, but any residual rotation far from the Sun reported until now has been much smaller than the amplitude of waves and deflections from interacting wind streams8. Here we report observations of solar-wind plasma at heliocentric distances of about 35 solar radii9-11, well within the distance at which stream interactions become important. We find that Alfvén waves organize into structured velocity spikes with duration of up to minutes, which are associated with propagating S-like bends in the magnetic-field lines. We detect an increasing rotational component to the flow velocity of the solar wind around the Sun, peaking at 35 to 50 kilometres per second-considerably above the amplitude of the waves. These flows exceed classical velocity predictions of a few kilometres per second, challenging models of circulation in the corona and calling into question our understanding of how stars lose angular momentum and spin down as they age12-14.

New Closures for More Precise Modeling of Landau Damping in the Fluid Framework.

Incorporation of kinetic effects such as Landau damping into a fluid framework was pioneered by Hammett and Perkins, by obtaining closures of the fluid hierarchy, where the gyrotropic heat flux fluctuations or the deviation of the fourth-order gyrotropic fluid moment are expressed through lower-order fluid moments. To obtain a closure of a fluid model expanded around a bi-Maxwellian distribution function, the usual plasma dispersion function Z(ζ) that appears in kinetic theory or the associated plasma response function R(ζ)=1+ζZ(ζ) has to be approximated with a suitable Padé approximant in such a way that the closure is valid for all ζ values. Such closures are rare, and the original closures of Hammett and Perkins are often employed. Here we present a complete mapping of all plausible Landau fluid closures that can be constructed at the level of fourth-order moments in the gyrotropic limit and we identify the most precise closures. Furthermore, by considering 1D closures at higher-order moments, we show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing convergence of the fluid and collisionless kinetic descriptions.

Global anisotropies in TeV cosmic rays related to the Sun's local galactic environment from IBEX.

Observations with the Interstellar Boundary Explorer (IBEX) have shown enhanced energetic neutral atom (ENA) emission from a narrow, circular ribbon likely centered on the direction of the local interstellar medium (LISM) magnetic field. Here, we show that recent determinations of the local interstellar velocity, based on interstellar atom measurements with IBEX, are consistent with the interstellar modulation of high-energy (tera-electron volts, TeV) cosmic rays and diffusive propagation from supernova sources revealed in global anisotropy maps of ground-based high-energy cosmic-ray observatories (Milagro, Asγ, and IceCube). Establishing a consistent local interstellar magnetic field direction using IBEX ENAs at hundreds to thousands of eV and galactic cosmic rays at tens of TeV has wide-ranging implications for the structure of our heliosphere and its interactions with the LISM, which is particularly important at the time when the Voyager spacecraft are leaving our heliosphere.

The heliosphere's interstellar interaction: no bow shock.

As the Sun moves through the local interstellar medium, its supersonic, ionized solar wind carves out a cavity called the heliosphere. Recent observations from the Interstellar Boundary Explorer (IBEX) spacecraft show that the relative motion of the Sun with respect to the interstellar medium is slower and in a somewhat different direction than previously thought. Here, we provide combined consensus values for this velocity vector and show that they have important implications for the global interstellar interaction. In particular, the velocity is almost certainly slower than the fast magnetosonic speed, with no bow shock forming ahead of the heliosphere, as was widely expected in the past.

Magnetic-field-line random walk in turbulence: a two-point correlation function description.

The standard theory of field-line random walk is based on the description of turbulence in the wave number space. The latter description takes into account the details of turbulence at small scales. Such details, however, are not important in the theory of random walking magnetic field lines. In the present paper we therefore use simple decorrelation models to estimate the field-line diffusion coefficient. Previous results are recovered as special limits. It is shown that a full analytical description is possible and that the only parameter controlling the field-line diffusion coefficient is the Kubo number.

Comparison of Interstellar Boundary Explorer observations with 3D global heliospheric models.

Simulations of energetic neutral atom (ENA) maps predict flux magnitudes that are, in some cases, similar to those observed by the Interstellar Boundary Explorer (IBEX) spacecraft, but they miss the ribbon. Our model of the heliosphere indicates that the local interstellar medium (LISM) magnetic field (B(LISM)) is transverse to the line of sight (LOS) along the ribbon, suggesting that the ribbon may carry its imprint. The force-per-unit area on the heliopause from field line draping and the LISM ram pressure is comparable with the ribbon pressure if the LOS approximately 30 to 60 astronomical units and B(LISM) approximately 2.5 microgauss. Although various models have advantages in accounting for some of the observations, no model can explain all the dominant features, which probably requires a substantial change in our understanding of the processes that shape our heliosphere.

Global observations of the interstellar interaction from the Interstellar Boundary Explorer (IBEX).

The Sun moves through the local interstellar medium, continuously emitting ionized, supersonic solar wind plasma and carving out a cavity in interstellar space called the heliosphere. The recently launched Interstellar Boundary Explorer (IBEX) spacecraft has completed its first all-sky maps of the interstellar interaction at the edge of the heliosphere by imaging energetic neutral atoms (ENAs) emanating from this region. We found a bright ribbon of ENA emission, unpredicted by prior models or theories, that may be ordered by the local interstellar magnetic field interacting with the heliosphere. This ribbon is superposed on globally distributed flux variations ordered by both the solar wind structure and the direction of motion through the interstellar medium. Our results indicate that the external galactic environment strongly imprints the heliosphere.

Analytical description for field-line wandering in strong magnetic turbulence.

We investigate analytically the random walk of magnetic field lines. In previous analytical treatments of field line wandering or random walk, it was assumed that the turbulent magnetic field is much weaker than the mean field. In the present paper, we develop an improved analytical method to describe the stochastic properties of turbulent magnetic fields. This approach is an extension of the standard theory of field line wandering and can be applied to weak as well as to strong magnetic turbulence.

Passive scalar spectrum in high-Schmidt-number stationary and nonstationary turbulence.

Chasnov [Phys. Fluids 10, 1191 (1998)] reviewed the results for passive scalar spectra in high-Schmidt-number stationary turbulence as derived by Kraichnan [J. Fluid Mech. 64, 737 (1974)] and generalized them to simple nonstationary flows. In two-dimensional turbulence, the Kraichnan spectra are usually fitted by numerically solving the spectral equation using the derived asymptotic behavior for small and large wave numbers. In this Brief Report, we show that the Kraichnan passive scalar spectrum over the entire range of k is essentially a modified Bessel function of the second kind. We also present analytical forms of the spectra in three-dimensional nonstationary turbulence, where as shown by Chasnov, the nonstationarity can be responsible for different asymptotic behavior than the usual Kraichnan's three-dimensional stationary form. Our results considerably simplify the "fitting" of passive scalar spectra from experimental and numerical data, with the simple analytical form valid for the whole range of k , instead of just the asymptotes, which are usually valid only for a small fraction of resolved wave numbers.

Nearly incompressible fluids: hydrodynamics and large scale inhomogeneity.

A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as "nearly incompressible hydrodynamics," is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term "locally incompressible" to describe the equations. This term should be distinguished from the term "nearly incompressible," which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly incompressible equations for higher order fluctuation components are derived and it is shown that they converge to the usual homogeneous nearly incompressible equations in the limit of no large-scale background. We use a time and length scale separation procedure to obtain wave equations for the acoustic pressure and velocity perturbations propagating on fast-time-short-wavelength scales. On these scales, the pseudosound relation, used to relate density and pressure fluctuations, is also obtained. In both cases, the speed of propagation (sound speed) depends on background variables and therefore varies spatially. For slow-time scales, a simple pseudosound relation cannot be obtained and density and pressure fluctuations are implicitly related through a relation which can be solved only numerically. Subject to some simplifications, a generalized inhomogeneous pseudosound relation is derived. With this paper, we extend the theory of nearly incompressible hydrodynamics to flows, including the solar wind, which include large-scale inhomogeneities (in this case radially symmetric and in equilibrium).

Nonlinear flows in nearly incompressible hydrodynamic fluids.

Nearly incompressible viscous hydrodynamic fluids are investigated using nonlinear fluid simulations. Nearly incompressible fluids possess acoustic modes through high frequency fluctuations associated with the subsonic fluid Mach number. These modes, in combination with the fluid modes, drive linearly unstable modes and nonlinearly excite flows. The nonlinear flows damp the long wavelengths in our simulations, and are dissipated resonantly when certain nonlinear conditions are satisfied. In agreement with our analytic analysis, the nonlinearly saturated flows in nearly incompressible fluids are generated through the action of the Reynolds stress forces.