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In classical thermodynamics the entropy is an extensive quantity, i.e.\ the sum of the entropies of two subsystems in equilibrium with each other is equal to the entropy of the full system consisting of the two subsystems. The extensitivity of entropy has been questioned in the context of a theoretical foundation for the so-called $\kappa$-distributions, which describe plasma constituents with power-law velocity distributions. We demonstrate here, by employing the recently introduced {\it regularized $\kappa$-distributions}, that entropy can be defined as an extensive quantity even for such power-law-like distributions that truncate exponentially., Comment: Preprint accepted for publication in Phys. Rev. E

In the more recent literature on cosmological evolutions of the universe the cosmic vacuum energy has become a non-renouncable ingredient. The cosmological constant $\Lambda$, first invented by Einstein, but later also rejected by him, presently experiences an astonishing revival. Interestingly enough it acts, like a constant vacuum energy density would also do. Namely, it has an accelerating action on cosmic dynamics without which, as it appears, presently obtained cosmological data cannot be conciliated with theory. As we are going to show in this review, however, the concept of a constant vacuum energy density is unsatisfactory for very basic reasons, since it would claim for a physical reality that acts upon spacetime and matter dynamics without itself being acted upon by spacetime or matter., Comment: 16 pages

According to present cosmological views the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S^4 with S being the scale factor of the universe. This behavior is expected, because General Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-Robertson-Walker) cosmological universes, leads to the conclusion that the photon wavelengths increase during their free passage through the spacetime metrics of the universe by the same factor as does the scale factor S. This appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during the recombination phase its temperature should have been about 3000 K, at an epoch of about 380 ky after the Big Bang, when the scale of the universe S_r was smaller by roughly a factor of S/S_r = 1+z_r = 1100 compared to the present scale S = S_0 of the universe. In this paper we start from putting the question whether the scale-behavior of the CMB energy density that enters the energy-momentum tensor of the field equations describing the expanding universe is really falling off like 1/S^4 and, if in fact a deviation from a behavior according to 1/S^4 would occur, why do we nevertheless presently observe a CMB energy density which appears to be in accordance with such a 1/S^4-scaling? This question arises from another basic and fundamental question, namely: Can we really assume that the wavelength of the freely propagating photon during its travel all the way along its light geodetic is permanently affected by the expansion of the universe, i.e continuously recognizes the expansion of the cosmic scale S? With other words: Do freely propagating photons ........, Comment: 6 pages

In the present days of modern cosmology it is assumed that the main ingredient to cosmic energy presently is vacuum energy with an energy density $\epsilon_\mathrm{vac}$ that is constant over the cosmic evolution. In this paper here we show, however, that this assumption of constant vacuum energy density is unphysical, since it conflicts with the requirements of cosmic thermodynamics. We start from the total vacuum energy including the negatively valued gravitational binding energy and show that cosmic thermodynamics then requires that the cosmic vacuum energy density can only vary with cosmic scale $R=R(t)$ according to $\epsilon _\mathrm{vac}\sim R^{-\nu }$ with only two values of $\nu$ being allowed, namely $\nu _\mathrm{1}=2$ and $\nu _\mathrm{2}=5/2$. We then discuss these two remaining solutions and find, when requiring a universe with a constant total energy, that the only allowed power index is $\nu _\mathrm{1}=2$. We discuss the consequences of this scaling of $\epsilon _\mathrm{vac}$ and show the results for a cosmic scale evolution of a quasi-empty universe like the one that we are presently faced by.

Understanding the outer heliospheric interface is a major challenge, especially in the light of recent observations by the IBEX and Voyager missions. We present further details on a new required theoretical correction that has been identified as substantial in a recent paper, the so-called source depletion effect. These results complement and expand earlier calculations of transit-time delays by presenting global skymaps of Energetic Neutral Atoms (ENAs) calculated with the depletion correction, comparing them with skymaps calculated without these corrections. Our results demonstrate that the depletion correction is critical for interpreting IBEX-Hi ENA fluxes generated in the inner heliosheath, and that any attempt to reconstruct the shape of the heliospheric boundary needs to include the depletion correction, unless arriving at considerably erroneous results., Comment: 5 pages, 15 figures

In a series of earlier papers, we have developed expressions for ion and electron velocity distribution functions and theirvelocity moments at the passage over the solar wind termination shock. As we have shown there, with introduction of appropriate particle invariants and the use of Liouville`s theorem one can get explicit solutions for the resulting total downstream pressure adding up from partial pressure contributions of solar wind protons, solar wind electrons and pick-up protons. These expressions deliver in a first step the main contributions to the total plasma pressure in the downstream plasma flow and consistently determine the shock compression ratio. Here now we start out from these individual fluid pressures downstream of the shock and thereafter evaluate for the first time the shock-induced entropy production of the different fluids, when they are passing over the shock to the downstream side. As is shown here, the resulting ion entropy production substantially deviates from earlier calculations using a pseudo-polytropic reaction of the ions to the shock compression, with polytropies selected to describe fluid-specific reactions at the shock passage similar to those seen by the VOYAGERs. From these latter models ion entropy jumps are derived that depend on the pick-up ion abundance, while our calculations, to the opposite, deliver an abundance-independent ion entropy production which only depends on the shock compression ratio and the tilt angle between the upstream magnetic field and the shock surface normal. We also do show here that only when including the strongly heated electrons into the entropy balance one then arrives at the total entropy production that just fulfills the thermodynamically permitted limit., Comment: 10 pages, 5 figures, under review

In the heliosphere, especially in the inner heliosheath, mass-, momentum-, and energy loading induced by the ionization of neutral interstellar species plays an important, but for some species, especially Helium, an underestimated role. We discuss the implementation of charge exchange and electron impact processes for interstellar neutral Hydrogen and Helium and their implications for further modeling. Especially, we emphasize the importance of electron impact and a more sophisticated numerical treatment of the charge exchange reactions. Moreover, we discuss the non-resonant charge exchange effects. The rate coefficients are discussed and the influence of the cross-sections in the (M)HD equations for different reactions are revised as well as their representation in the collision integrals. Electron impact is in some regions of the heliosphere, particularly in the heliotail, more effective than charge exchange, and the ionization of neutral interstellar Helium contributes about 40% to the mass- and momentum loading in the inner heliosheath. The charge exchange cross-sections need to be modeled with higher accuracy, especially in view of the latest developments in their description. The ionization of Helium and electron impact ionization of Hydrogen needs to be taken into account for the modeling of the heliosheath and, in general, astrosheaths. Moreover, the charge exchange cross-sections need to be handled in a more sophisticated way, either by developing better analytic approximations or by solving the collision integrals numerically., Comment: 18 pages, 9 Figures

A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points of the magnetic field within these flows. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfven Mach number for the corresponding stationary equilibria is finite. The topological structure determines the geometrical structure of the interstellar gas - stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail region beyond the reverse shock. The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfven Mach numbers in the case of subalfvenic flows., Comment: 19 pages, 17 figures, accepted for publication in A&A

Though pick-up ions (PUIs) are a well known phenomenon in the inner heliosphere their phase-space distribution nevertheless is a theoretically unsettled problem. Especially the question of how pick-up ions form their suprathermal tails, extending to far above their injection energies, still now is unsatistactorily answered. Though Fermi-2 velocity diffusion theories have revealed that such tails are populated, they nevertheless show that resulting population densities are much less than seen in observations showing power-laws with a velocity index of "-5". We first investigate here, whether or not observationally suggested power-laws can be the result of a quasi-equilibrium state between suprathermal ions and magnetohydrodynamic turbulences in energy exchange with eachother. We demonstrate that such an equilibrium cannot be established, since it would require too high pick-up ion pressures enforcing a shock-free deceleration of the solar wind. We furthermore show that Fermi-2 type energy diffusion in the outer heliosphere is too inefficient to determine the shape of the distribution function there. As we can show, however, power-laws beyond the injection threshold can be established, if the injection takes place at higher energies of the order of 100 keV. As we demonstrate here, such an injection is connected with modulated anomalous cosmic ray (ACR) particles at the lower end of their spectrum when they again start being convected outwards with the solar wind. Therefore, we refer to these particles as ACR-PUIs. In our quantitative calculation of the pick-up ion spectrum resulting under such conditions we in fact find again power-laws, however with a velocity power index of "-4" and fairly distance-independent spectral intensities., Comment: 9 pages, one figure, accepted for publication in A&A

Modeling of the global heliosphere seeks to investigate the interaction of the solar wind with the partially ionized local interstellar medium. Models that treat neutral hydrogen self-consistently and in great detail, together with the plasma, but that neglect magnetic fields, constitute a sub-category within global heliospheric models. There are several different modeling strategies used for this sub-category in the literature. Differences and commonalities in the modeling results from different strategies are pointed out. Plasma-only models and fully self-consistent models from four research groups, for which the neutral species is modeled with either one, three, or four fluids, or else kinetically, are run with the same boundary parameters and equations. They are compared to each other with respect to the locations of key heliospheric boundary locations and with respect to the neutral hydrogen content throughout the heliosphere. In many respects, the models' predictions are similar. In particular, the locations of the termination shock agree to within 7% in the nose direction and to within 14% in the downwind direction. The nose locations of the heliopause agree to within 5%. The filtration of neutral hydrogen from the interstellar medium into the inner heliosphere, however, is model dependent, as are other neutral results including the hydrogen wall. These differences are closely linked to the strength of the interstellar bow shock. The comparison also underlines that it is critical to include neutral hydrogen into global heliospheric models., Comment: 10 pages, 4 figures, submitted to a special section at A&A of an ISSI team "Determination of the physical Hydrogen parameters of the LIC from within the Heliosphere"

In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the mass of an infinitely extended, homogeneously matter-filled and expanding universe. To answer this question we produce a space-like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added-up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric applied to stars, but this time applied to the spacepoint-related universe. It is then shown that this leads to the added-up proper energy within a sphere of a finite outer critical radius defining the point-related infinity. As a surprise this radius turns out to be reciprocal to the square root of the prevailing average cosmic energy density. The equivalent mass of the universe can then also be calculated and, by the expression which is obtained here, shows a scaling with this critical radius of this universe, a virtue of the universe which was already often called for in earlier works by E.Mach, H.Thirring and F.Hoyle and others. This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so-defined mass of the universe., Comment: 4 pages. Published in AN 327(7)

Cosmological consequences of a strictly valid total energy conservation for the whole universe are investigated in this paper. Interestingly enough as one consequence of ergodically behaving universes very specific scaling laws with the diameter R of the universe can be derived for relevant cosmic quantities. Especially the 1/R^2- scaling of mass - and vacuum energy - density then automatically leads to a vanishing cosmic curvature parameter k=0 and also reveals, that for such universes no horizon problem occurs. In addition the longstanding problem of observationally indicated very low cosmic vacuum energies in contrast to the very large quantumfield estimates is easily solved when the vacuum energy density decay with 1/R^2 is taken into account reconciling presently observed vacuum energy density values with those from theoretical expectations. We also suggest why the mass of the universe can permanently increase and can in fact grow up from a Planck mass as a pure vacuum fluctuation., Comment: Accepted by AN, 8 pages

Various hydrodynamic models of the heliospheric interface have been presented meanwhile, numerically simulating the interaction of the solar wind plasma bubble with the counterstreaming partially ionized interstellar medium. In these model approaches the resulting interface flows are found by the use of hydrodynamic simulation codes trying to consistently describe the dynamic and thermodynamic coupling of the different interacting fluids of protons, H-atoms and pick-up ions. Within such approaches, the fluids are generally expected to be correctly described by the three lowest velocity moments, i.e., by shifted Maxwellians. We shall show that in these approaches the charge-exchange-induced momentum coupling is treated in an unsatisfactory representation valid only at supersonic differential flow speeds. Though this flaw can be removed by an improved coupling term, we shall further demonstrate that the assumption of shifted Maxwellians in some regions of the interface is insufficiently well fulfilled both for H-atoms and protons. Using a Boltzmann-kinetic description of the proton- and H-atom- distribution functions coupled by charge exchange processes we emphasize the fact that non-negligible deviations from shifted Maxwellians are generated in the interface. This has to be taken into account when interpreting inner heliospheric measurements in terms of interstellar parameters., Comment: Proc. 3-rd Annual IGPP-UCR Astrophysics Conference: Physics of the Outer Heliosphere, Riverside, January 2004, AIP, in press

It is well known that the Solar System is presently moving through a partially ionized local interstellar medium. This gives rise to a counter-flow situation requiring a consistent description of behaviour of the two fluids -- ions and neutral atoms -- which are dynamically coupled by mutual charge exchange processes. Solutions to this problem have been offered in the literature, all relying on the assumption that the proton fluid, even under evidently nonequilibrium conditions, can be expected to stay in a highly-relaxated distribution function given by mono-Maxwellians shifted by the local proton bulk velocity. Here we check the validity of this assumption, calculating on the basis of a Boltzmann-kinetic approach the actually occurring deviations. As we show, especially for low degrees of ionization, $\xi \le 0.3$, both the H-atoms and protons involved do generate in the heliospheric interface clearly pronounced deviations from shifted Maxwellians with asymmetrically shaped distribution functions giving rise to non-convective transport processes and heat conduction flows. Also in the inner heliosheath region and in the heliotail deviations of the proton distribution from the hydrodynamic one must be expected. This sheds new light on the correctness of current calculations of H-atom distribution functions prevailing in the inner heliosphere and also of the Lyman-$\alpha $ absorption features in stellar spectra due to the presence of the hydrogen wall atoms. Deviations from LTE-functions would be even more pronounced in magnetic interfaces, which via CGL-effects cause temperature anisotropies to arise., Comment: 18 pages, 8 figures, A&A in press

The Interstellar Mapping and Acceleration Probe (IMAP) is a revolutionary mission that simultaneously investigates two of the most important overarching issues in Heliophysics today: the acceleration of energetic particles and interaction of the solar wind with the local interstellar medium. While seemingly disparate, these are intimately coupled because particles accelerated in the inner heliosphere play critical roles in the outer heliospheric interaction. Selected by NASA in 2018, IMAP is planned to launch in 2024. The IMAP spacecraft is a simple sun-pointed spinner in orbit about the Sun-Earth L1 point. IMAP's ten instruments provide a complete and synergistic set of observations to simultaneously dissect the particle injection and acceleration processes at 1 AU while remotely probing the global heliospheric interaction and its response to particle populations generated by these processes. In situ at 1 AU, IMAP provides detailed observations of solar wind electrons and ions; suprathermal, pickup, and energetic ions; and the interplanetary magnetic field. For the outer heliosphere interaction, IMAP provides advanced global observations of the remote plasma and energetic ions over a broad energy range via energetic neutral atom imaging, and precise observations of interstellar neutral atoms penetrating the heliosphere. Complementary observations of interstellar dust and the ultraviolet glow of interstellar neutrals further deepen the physical understanding from IMAP. IMAP also continuously broadcasts vital real-time space weather observations. Finally, IMAP engages the broader Heliophysics community through a variety of innovative opportunities. This papersummarizes the IMAP mission at the start of Phase A development.