Hydromagnetic Steady Magnetized Plasma Encountered by Voyager in the Interstellar Space

Abstract

With the spacecraft Voyager 1 and 2, we observe from the inside the near interstellar medium that is a very strongly magnetized (|B| equal or larger than 0.4 nT) medium, which is very dilute. We deal with a medium about 8-orders of magnitude less dense than the best vacuum possible to achieve in the laboratory. For the considered matter densities the plasma energy is quite small at a random equivalent thermal value of no more than 30,000°K, so that a B-field of 1/2 nT constitutes a very strong magnetic field. Consequently, the medium’s pressure is dominated by the B-field. Based on these everyday measurements, we proceed to interpret the nature of the medium, assuming the reasonable, consistent result, we check with observation that its overall property satisfies hydromagnetism (MHD). The intensity of the B-field is consistent with remote sensing of the 21 cm split of the e-line of the atomic Hydrogen, and permits to understand the ancient nature of the medium, for example, constituting an example of permanent magnetism, and in this way we infer a few possibilities on the nature of the whole structure of the surrounding local interstellar magnetic cloud and the evolution of the home galaxy.

1. Introduction

The medium we refer is evaluated to have a mixture of neutral 90% and plasma 10% with a particle density of about one particle (atoms + ions) per cm³. This value indicates a dilute electron density of 0.1 per cm³. Also, the dominant feature Is the strong presence of a steady magnetic field (B-field) with a value that varies from about 0.4 to 0.7 nT. This medium has been in astrophysics already monitored remotely well before the arrival of the spacecraft (SC) Voyager 1 and 2 by the observation of 21 cm frequency signal provided by the e-flip in the orientation of its spin. These remote measurements have a localization uncertainty of ±200 astronomic units (AUs), to which the Voyager SC brings a far better knowledge on the strong B-field localization through its in situ measurement. (Stone [1], announces that Voyager 1 entered local interstellar medium (LISM)). The AU is defined by the mean distance of the Earth to the Sun which is equivalent to 150 solar radii (1 solar radius is the distance from the star center to its photosphere and is well-known to be 700,000 km with an uncertainty of possibly 0.1%). The in situ observations are achieved using in SC located magnetic field, radio, energetic particles, plasma instruments, respectively described respectively in [2, 3, 4, 5, 6].

In this work, we use both in situ observation by the SC (Sections 2, 3.1, 3.2, and by its combination with studies also performed by the author in similar strong magnetized MHD matter in Sections 3.3 and 3.4). Further, in Section 4, the author extrapolates the findings to astrophysical conditions from the realm solely of remote sensing (e.g. the Hubble telescope, and other more recent similar missions). Conclusions are drawn in Section 5.

2. The local interstellar medium (LISM)

The LISM encloses the plasma region generated by the Sun in what is known as solar wind (SW), plus its shocked plasma region known as the heliosphere sheath. The interstellar medium, which its in-situ known region we call the very LISM is of uncertain origin. Some workers attribute its formation to be the wake of a supernova that occurred millions of years ago. This region is known as the local interstellar molecular cloud, of which Figure 1 shows a sketch, and an artistic representation is shown in Figure 2.

Figure 1.

A sketch, and plane of sky projection of the local molecular cloud including location of the Sun and other stars.

Figure 2.

An artistic representation by Linda huff and Priscilla Frisch.

This interstellar molecular cloud is in the path of the solar system, which by now and from hundreds of thousands of years has been immersed in it. The very LISM is then the region of the molecular cloud modified/surrounding the plasma pushing out of the Sun and the LISM region we explore with SC Voyager since the year 2012 with Voyager 1 (V1), and 2018 with Voyager 2 (V2), see, e.g. Berdichevsky [7] on the sheath region before the arrival of the SC to the heliopause.

Figures 1 and 2 identifiers (e.g. representation of the star Sun) are not at scale, but the distances are, and in the bottom right, it is indicated a ‘parsec as the reference unit giving an idea of the dimensions involved in the sketch. The Voyager 1, currently at ∼7·10⁻⁴ parsec, in several years will arrive at 0.001 parsecs from the Sun at their velocity as it moves, escaping the gravitational field attraction of the solar system.

Observed in the interstellar medium, since its entrance in 2012 by V1, see the announcement by NASA [1], see Figure 3, are the large intensity of the B-field, and the four times occurrence of a compression process in which changes in B-field magnitude coincide with the change of density observed, [8]. Good measurements of the plasma in the LISM have been achieved using the radio instrument in both V1 and V2 [5]. On the other hand, the plasma instrument design to measure properties of the SW, [3], is not optimal for identifying the LISM plasma properties, but they achieve reasonable evaluations with large errors in V2 (in V1, that instrument failed a long time ago).

Figure 3.

Approximately ten years of in situ record by V1 of the B-field in the very LISM.

The solar system displaces relative to the LISM at solely a few tens of kms⁻¹. At such speed, no shock at the heliopause interface is expected nor it has been encountered. Here, we assume a shock in magnetic field frozen matter (see, e.g. [9]) that had been identified to be consistent with a process called collision-less [10]. However, there are some workers in the field who brought the idea of shocks in the LISM medium that, in their view, are collisional, and that is a current subject of debate (see, e.g. [11]). Then at their suggestions in Figure 3, there are compressions labeled as shocks and others just compressions. We will come to the subject of these types of compressions later.

The global representations of the interface between heliosphere and very LISM are shown in Figure 4, top panel [12] and bottom panel [13, 14] are competing interpretations which currently dominate the debate on the subject. In the bottom panel, the meridional cut of a 3-D representation is indicated, different main regions of the magnetosphere as well as the location of the V1 and V2 SC relative to a reference astrophysical coordinate system where the top is pointed in a direction which approximately is defined by our heliosphere standard North definition.

Figure 4.

Two MHD modeling of the interface between LISM and heliosphere.

Figure 3, in [8], shows that V1 encounters four compression jumps in which density and magnetic field data indicate an equal value for the change, both in the magnitude of the B-field as well as in the plasma density content. Based on that fact and also the orientation of the LISM B-field wrapped around the heliosphere plasma with its expansion stopped (Figure 5) at the heliopause (hp), and which are well identified, we make the educated assumption that the medium possesses the properties of a simple ideal MHD state, see, e.g. [15]. This subject introduces us to the next section.

Figure 5.

The orientation of B-field observed both by V1 and V2 outside heliopause (hp).

3. On the MHD nature of the LISM medium

3.1 On the nature of the medium

The supportive arguments for a medium consistent with ideal MHD are the followings:

First, we point out the behavior of magnetic field and plasma density exquisitely agreeing within error uncertainty as observed and listed in Table 1, at compressional discontinuities in Figure 3.

Event	Date (approx.)	B2/B1	N2/N1	N2/N1
sh 2	2014-236	1.13	1.11	1.11
pf1	2017-001	1.19	1.17	1.12
pf2	2020-146	1.35	1.36	1.36

Table 1.

Three examples of compression properties observed in the interstellar medium.

Second, we identify both at V1 and at V2 a B-field consistent with a draping of the B-field around the magnetopause (Figure 5).

Third, the B-field shows along the path of V1 (see Figure 3) and V2 a steadiness, which is quite characteristic of low plasma pressure and ideally negligible changes. But there are interesting oscillatory changes, which transitioned since the start of V1 immersion in the LISM from mainly compressional to dominatingly transversal self-vibrational modes (see, e.g. [15]) present in low temperature (low plasma pressure) plasmas, plainly known in the field as low beta plasmas.

Fourth, these ripple variations in the B-field intensity (see Figure 6), occur at sharp compression transition and illustrate there the presence of self-modes (frequency) of the magnetized media up to the resolution of our measurements of the magnetic field (ideal MHD self-mode oscillations).

Figure 6.

Presence of self-oscillation modes, in the B-field for DOY 147, the year 2020.

The conditions above illustrated, [8], indicate a consistency of the medium to be quite close to the ideal MHD. Further, we have a likely existence of these long-lasting magnetized plasma, which indicates that diffusion, loss of the magnetic field has to be negligible and further constitute an argument for a LISM of magnetized matter that satisfies being ideal MHD.

In Figure 6 (top) are presented observations of distributions of

$${\mathrm{dB}}_{\mathrm{\text{N1}}}={\mathrm{B}}_{\mathrm{N}}\left(\mathrm{n}\right)–{\mathrm{B}}_{\mathrm{N}}\left(\mathrm{n}-\mathrm{1}\right)$$E1

and

$${\mathrm{dB}}_{\mathrm{\text{T1}}}={\mathrm{B}}_{\mathrm{T}}\left(\mathrm{n}\right)–{\mathrm{B}}_{\mathrm{T}}\left(\mathrm{n}-\mathrm{1}\right)\left(\mathrm{\text{oscillations}}\mathrm{are}\mathrm{\text{in the bottom panels in}}\mathbf{\text{Figure}}\mathbf{6}\right)$$E2

and time series of the 1-hr increments of ‘dB_N1 and dB_T1’ from the beginning of the magnetic hump on day 147, 2020 to the end of the magnetic hump. The matter we observe from within a very LISM is extremely dilute see Abstract. For the matter densities considered, the observation of an average B-field close to 1/2 nT results to be a very strong magnetic field. This quite strong B-field can be understood this way when comparing its energy with the kinetic random energy of the matter there present. Other relevant aspects to be considered are the forces acting on this LISM:

• (a) Gravitational self, (b) gravitational with compact objects in its neighborhood, e.g. stars, (c) and gravitational with the galaxy as a whole.

• Magnetic stresses

• Interface stresses with the Sun changing pressures reaching the hp, with other stellar ‘winds’ possibly enclosed/in-the-local-range of the LISM

The apparent long life of the LISM suggests it is stable, and we assume: ∼thermal equilibrium.

Next, we proceed to make some conservative assumptions on size and mass of the local, interstellar molecular cloud (the magnetized plasma structure in which we observe the measurements of the two Voyager SC). From Figure 1, let us assume we got a good representation of its base projected on a plane. Hence, we can estimate its size to be:

$$\sim \mathrm{3}\times \mathrm{8}\times \mathrm{8}{\mathrm{\text{parsec}}}^{\mathrm{3}}$$E3

being conservatives and assuming homogeneous mass distribution and rounding the mass estimated to be observed at the Voyager locations, and here the presence of heavier element contributions are included.

$$\sim \mathrm{2}\mathrm{\text{nucleons}}/{\mathrm{cm}}^{\mathrm{3}}$$E4

this gives a mass ∼4/100·10³⁰ kg, about 1/50th the mass of the Sun (= 2·10³⁰ kg).

Next, we ask ourselves the fundamental question: ‘What could hold the cloud undisturbed?’ and we know that we observe in situ the magnetic field, actually observed values are consistent with the remote observation from Earth of the splitting of the 21 cm electron-line in atomic H.

• We also observe plasma, and remember the region of plasma waves (= Plasma-Noise).

• So we think the system to be, by nature magnetohydrodynamic (MHD). i.e. a structure that is superconductor, diamagnetic, super-elastic with unusual properties.

• Henceforth: the idea of thermodynamics MHD equilibrium is strengthened.

Then we proceed to think of the presence of the V1 and V2 SC, in situ observers, in a magnetohydrodynamic steady state. And we further add to the inferences we make that we are in the presence of a magnetized matter with the properties:

• Of a matter medium which possesses a coalescence state, following Hannes Olof Gösta Alfvén ideas, e.g. [16]. See, e.g. [17].

• Of a matter medium that moves (90% neutrals and 10% plasma, i.e. neutrals/ions) attached—frozen to the magnetic field.

• We speculate further that such material would have those properties of the one we learn to be familiar with, which are those of a ‘solid,’ a very porous amorphous crystalline solid with homogeneous domains cross sections of 10¹⁰ km² … or more …

Figure 7 represents the outlined view of a charge neutral (i.e. q-neutral) structure. E.g. [18] present conjecture on this amorphous in nature, matter ‘atoms/ions’ anchored to B-field (as a 3-D Langmuir lattice). B intensity low to high is represented in the light to the dark blue gradation of Figure 7. The privilege of working with an impressive suite of high-sensitivity instruments in Ulysses and Wind SC provided the opportunity of advancing on the understanding of the constitutive properties of the MHD medium, in its own right, a very stable long-live magnet (permanent magnet) as it is possible to learn about from the WWW archive pages for the Ulysses mission, e.g. https://www.esa.int/Science_Exploration/Space_Science/Sun_set_Ulysses_soarl_mission_on_1_July2, and WWW pages for the currently active Wind SC mission, e.g. https://wind.nasa.gov.

Figure 7.

A representation of the outlined constitutive nature of the LISM environment.

When in a breathing mode process, we have that in small oscillations, the e-gas compresses, i.e. pressure increases, a rise that decreases magnetization and the internal energy of the e-gas by decreasing ‘T’ in a ‘diamagnetic’ process (i.e., B-field magnitude also decreases). This is a quite subtle effect that the in situ resources available in the Voyager instruments are not capable of observing. In following Section 3.4, we re-visit these understandings and observations.

Nevertheless, features observed in V1 and V2 appear to give the opportunity to learn about the constitutive nature of the diamagnetic permeability of the medium when the observation of the equilibration location at heliopause between heliosphere pressure and pressure of the medium surrounding it suggests a pressure larger than the one of the very LISM as it would be essentially provided by a vacuum μ₀ of the strong B-field observed intensity value of about 0.4 nT at V1.

This value of the B-field is too low, assuming the permeability μ₀ of vacuum, and fails to be identified as an equilibration value as it is pointedly indicated in [19]. The understanding that the LIMS medium would have a μ ≠ μ₀-vacuum permeability is made plausible in studies for similar strong B-field conditions, which are described in the following Sections 3.3 and 3.4.

3.2 About the conditions on the mass supported by the MHD structure

We may, at this point, idealize the local molecular cloud region as composed of a closely connected set of curved MHD tubes as suggested in the right panel of Figure 8, see also the following Figure 9. These are expected to be MHD ideal structures (negligible diffusion loss through the millions of years of their existence). Then the stability would be the result between the self-gravitating force of the matter and the magnetic stresses of the magneto-matter state.

Figure 8.

Idealization of a structure of self-sustained B-field MHD element and environment.

Figure 9.

The matter-magnetized in equilibrium flux tube idealization of a part of the LISM.

Figure 9 shows the simplified MHD structure, tube-shaped with its source currents of its B-field which equilibrium conditions are assumed for the interstellar molecular cloud that interacts in its very LISM with the heliosphere region we study in situ with the Voyager SC.

When considering the self-gravitational force of the matter, we obtain along the symmetry axis: F_x = $\nabla$ − $\nabla$ϕ)_x =

$$–\mathit{2}\pi \mathit{G}\mathit{N}\left\{\mathit{\text{2x}}\mathit{+}{\left({\mathit{R}}^{\mathit{2}}\mathit{+}{\left[\mathit{L}/\mathit{2}–\mathit{x}\right]}^{\mathit{2}}\right)}^{\mathit{1}/\mathit{2}}–{\left({\mathit{R}}^{\mathit{2}}\mathit{+}{\left[\mathit{L}/\mathit{2}\mathit{+}\mathit{x}\right]}^{\mathit{2}}\right)}^{\mathit{1}/\mathit{2}}\right\}\mathit{\text{for}}–\mathit{L}/\mathit{2}\le \mathit{x}\le \mathit{L}/\mathit{2}$$E5

$$–\mathit{2}\pi \mathit{G}\mathit{N}\left\{\mathit{L}\mathit{+}{\left({\mathit{R}}^{\mathit{2}}\mathit{+}{\left[\mathit{L}/\mathit{2}–\mathit{x}\right]}^{\mathit{2}}\right)}^{\mathit{1}/\mathit{2}}–{\left({\mathit{R}}^{\mathit{2}}\mathit{+}{\left[\mathit{L}/\mathit{2}\mathit{+}\mathit{x}\right]}^{\mathit{2}}\right)}^{\mathit{1}/\mathit{2}}\right\}\mathit{\text{for}}\mathit{x}\mathit{>}\mathit{L}/\mathit{2}$$E6

of the two ranges labeled with (5) and (6) for independent variable ‘x’ above-discussed cylindrical shape when a homogeneous matter distribution is considered. For x >> L/2 > R, the asymptotic expression for the gravitational force field of a point mass, i.e.∝ − x⁻², is recovered.

The approximate force expression at a distance ρ from the axis ‘near’ cylinders center is given by the expression:

$${\mathit{F}}_{\mathit{\rho }}=-\text{∇ϕ}){}_{\mathit{\rho }}=$$

$$–\mathit{1/2}\mathit{GN}\mathrm{\rho }\mathrm{\text{for}}\mathit{0}\le \rho \le \mathit{R}\mathit{,}$$

$$–\mathit{1/2}{\mathit{GNR}}^{\mathit{2}}{\mathrm{\rho }}^{\mathit{-}\mathit{1}}\mathrm{\text{for}}\mathit{R}\mathit{<}\rho \le \mathit{L}/\mathit{2}\mathit{,}$$E7

In this case, the Gaussian theorem is used to obtain the above-approximated solution that can be used reasonably well in the range 0 ≤ ρ ≤ L/2 for R < L/2 and – L/4 ≤ x ≤ L/4. The solution will be exact for any location in space, although unrealistic, for the self-gravitating field of the mass of the structure in the simplifying case of an infinite homogeneous cylinder of the medium.

Depending on the orientation of the magnetic field of the structures, if the conditions are right in an encounter of two magnetized tubes through their contact in their basis/tops extremes, the annihilation of the magnetic field is bound to occur (flux-tubes with opposed helicity/axial-currents) and the unbalanced attractive gravitational force will produce the matter agglutination which may be the cause of the so-called explosive formation of stars, i.e. cradle of the birth of stars as observed in astrophysics, see, e.g. [20, 21].

3.3 On the constitutive property of these permanent magnetized matter structures

Here we present our understanding on the conditions we identified through a variety of studies of low beta MHD from the low corona to observations in situ at 1 AU. This simple realization, our model, is a [22] flux tube with a twist, i.e. a flux rope (FR) free of magnetic stresses, see left panel in Figure 8. It has a 3-D time-evolving solution [23].

Figure 8, left shows a mass fraction Δm_P in volume ΔV_P at location X_P = ρe_ρ + xe_x from the center of an FR with axial magnetic fieldB₀ and also five other B-field lines wrapping around the FR axis. The distance R₀ where the axial field changes sign is indicated on the top.

The analytical solution represented in left panel of Figure 8 is

$$\mathbf{B}={\mathit{B}}_{\mathit{0}}{\left({\mathit{r}}_{\mathit{0}}/\mathit{r}\right)}^{\mathit{2}}\left[\mathit{H}{\mathit{J}}_{\mathit{1}}\left(\mathit{a}\mathit{r}\right){\mathbf{e}}_{\mathbf{\phi }}+{\mathit{J}}_{\mathit{0}}\left(\mathit{a}\mathit{r}\right){\mathbf{e}}_{\mathbf{x}}\right],$$E8

Assuming homogeneous mass distribution; self-gravitational force

$$\mathbf{F}\left(\mathrm{r},\mathrm{\phi },\mathrm{x}=\mathrm{0}\right)=-\mathrm{2}\mathrm{\pi }\mathrm{G}\mathit{r}{\mathbf{e}}_{\mathbf{r}}\left(\mathrm{cyl}\right);\mathrm{\text{and for}}\mathrm{r}<<\mathrm{R}\left(\mathrm{\text{torus}},\mathrm{\text{not}}\mathrm{so}\mathrm{\text{everywhere in space}}\right)$$E9

with the magnetic field expressed in polar coordinates, consistent with a right coordinate system, and for historical reasons, e_x is employed instead of e_z [24].

Then distortion in current/field(s) will happen, and magnetic stresses appear, as it is shown in [25], and there is ‘no more a magnetic stress free MHD solution’:

The J × B ‘stresses’, in addition is the magnetic force that equilibrates the region of interface between the local interstellar medium (LISM) and the sheath of the solar plasma (SP), as observed with Voyager 1.

Here we consider extremely short time scales, i.e. from a quarter of a day, to even year(s) when we think of the possible Hundreds of millions of years of existence of the molecular interstellar cloud which V1 and V2 explore in the very LISM as well as conditions at heliopause (HP) and the very LISM interface. At the start of the LISM (the local ‘molecular cloud’) [26] noticed the occurrence of a plasma depletion layer (PDL) in the LISM. The presence of such kind of PDL is a well-established feature at sheath—magnetosphere studies of Earth and other planets, see, e.g. Caan, McPherron, Russell, [27], Singh, [28].

An evaluation of J × B (magnetic stresses) equilibration of gravitation and pressure forces shows estimate studies to which we refer here considering:

1. pressure of gas (P_gas) at heliopause (hp) with solar origin (3·10⁻¹² dyn)

2. self-gravitational Force at Helio-Sheath-LISM interface at ‘hp’ (∼10 orders less intense than above distortion)

3. self-organization as a 3-D Langmuir lattice (see, e.g. [29])

4. also a negligible ionization source by trapped cosmic ray isotropic population in the LISM has been measured (frequency of 10⁻¹⁷ sec⁻¹ in [30]).

It is noted that the self-gravitational force, being attractive, would try to pull particles frozen in B-field together. This effect will be counteracted by the magnetic stresses to reduce the magnetic tension trying to keep a close equilibrium, i.e.,

$$\mathbf{J}\times \mathbf{B}+{\mathbf{F}}_{\mathrm{g}}=\mathrm{0}$$E10

A superconducting nature of the structure with a permeability much smaller than in vacuum is helpful to support larger amounts of mass in interstellar molecular clouds having a superconducting MHD nature.

Hence, to equilibrate the gas pressure (P_gas) in heliosheath implies same pressure from the magnetic field force, J × B in the LISM at hp interface and this requires a magnetic permeability of about (1/2 ± 1/4) μ₀, detailed in the Appendix B.

This μ would allow equaling magnetic force to the gravitational push of the Sun-system pressure (with the achievement of equilibrium) as it is required from observational studies, e.g. [19], see also [31].

An interesting theoretical perspective of the interaction has been attempted with quite a thorough mathematical approach in Usmanov et al. [32]. Usmanov et al. work considers the role of turbulence transport. Turbulence in MHD shock interfaces is assumed to be responsible for the acceleration of particles. The plasma pressure contribution in the sheath—LISM interface has its main contribution from these accelerated particles, e.g. in [19], and [31], better known in the literature as anomalous cosmic rays present in the heliosphere sheath region as discussed, e.g. in these two works.

We consider studies in which conditions show key similarities to the ones we just identified in the LISM: Long life duration of the structure, supportive of understanding that we are in the presence of self-sustained strong magnetic fields in a medium in which we took the initiative to investigate constitutive properties [18]. In a much longer line of work by several authors, it has been possible to describe MHD evolutionary behavior analytically of low beta MHD structure’s basic properties, and there has been active research since the earlier 1990, see, e.g. [33, 34, 35, 36].

With a full set of high-resolution data having a very low uncertainty in the instrumentation of the SC Wind, we were able to find/go beyond that and introduce ourselves to the constitutive manifestations of the low beta long-living MHD steady structure(s):

The magnetized MHD plasma stability was evaluated in a case study where it was identified as quite long duration and stable for an evolution in time and space in which the size changed by a factor 200 and consistent with preservation of its magnetic flux content suggesting isotropic behavior. A needed condition for the stability of the constitutive material and consistent with the ‘no’ measurable presence of any process of diffusion of the magnetic field lines, or loss of it.

Of the structure of the strongly magnetized plasma medium, we can get information with the help of the observations of the Wind SWE instrument, as illustrated in Figure 10 panels, left for the protons, from [37], and right panel for the electrons from Nieves-Chinchilla and Figueroa-Viñas [38]. Here, we have to focus on the narrow distributions, the left panel proton is a pure random distribution, but on the right panel electron distribution, we discuss solely the narrow part of the distribution. When doing that, we notice that Figure 10 left and right panels for different strong B-field intervals like the one discussed in [18] makes plausible the here proposed 3-D Langmuir conditions of the medium when we observe that matter turns the B-field structure elastic, and with matter frozen independently to it, will show displacements consistent with the Hook’s law of the oscillator, and statistically random (i.e., wholly independent, see, e.g. [39]). This behavior is well described by Langmuir (see, e.g. in Langmuir’s adsorption theory of an ‘ideal lattice gas,’ presented in a textbook on statistical mechanics by [29], and also [40]). This is understood here as a 3-D Langmuir amorphous crystal structure. And as we can simply show by partition energy under thermodynamic equilibrium Figure 10 constitutes a strong support to the view as it follows:

Figure 10.

‘p’ simpler and more complex ‘e’ density’s structure illustrated by their Maxwellians.

The ‘frozen matter’ (electrons and protons here identified) for equal elastic strength will show a random distribution of the oscillating masses (see, e.g. [41]) with a mean amplitude which depends on the mass, for the same elasticity constant ‘K.’ For the evaluation of the validity of the assumption, we analyze the proton and electron (narrow e-)distribution function shown in left and right panels of Figure 10. In this focused analysis of the distributions we notice first the pure random (vibration) motion of the frozen protons observed in the left panel of Figure 10. In the case of the electrons, we distinguish two clear regions, a narrow and a wide distribution. Here we interpret that frozen electrons are the narrow ‘Gaussian’ part of its distribution, and have once more the type of distribution in velocity consistent with random oscillation motion for frozen electrons and the same elasticity constant ‘K’ as it corresponds to the crystalline amorphous medium assumed, see the detailed analysis in Appendix A.

Figure 10, right panel shows that when focused on the broad part of the e-distribution, if in equilibrium, there it gives information on temperature ‘T’ from the e-gas of the structure (see, e.g. [42]). In our interpretation, the distribution of electrons, in Figure 10, right panel also has contributions from e-lattice, and e-gas, as well as e-current aligned (J_e).

Here we are in the presence of an example beyond the notion of a frozen matter system in which far more complex features are shown for electrons than for ions and, in that way, giving room to further the investigation on the constitutive nature of this very stable matter as it is manifested in the presence of matter that through thousands of millions of years refused to agglutinate by the presence of gravitational laws of universal attraction between material objects.

The wider Gaussian (more commonly known as a Maxwellian in plasma astrophysics) illustrates a different behavior for a subset of the electrons in the structure that, since the start of the study of the solar wind, has been a challenge to the interpretation of the worker in the field. In our case, we see that population as the dilute gas that pervades the medium, in a solid would be interpreted as the upper band that defines the metallic nature of the solid in consideration. We take that view which is well supported in the more detailed analyses we did in [18] and we proceed to detail below. There we expand on [43] pioneer description and understanding of the matter presence in magnetic clouds, ‘strongly magnetized matter.’ (Section 3.4 further discusses the understanding achieved elsewhere on the central subject of this chapter: the MHD medium studied by Voyager SC in the very LISM.)

3.4 Properties and peculiar characteristics of the dilute e-gas of strong magnetized matter

We can further our observational understanding by doing a deeper analysis of the electron’s distribution shown in Figure 10. And Figure 11 reveals us more about this state of matter.

Figure 11.

Parts of e-vel distribution function F(v,θ,φ), including Strahl aligned to B-field.

Figure 11 illustrates for a steady matter MHD case with intense/dominating B-field a set of 8 ‘skymaps’ showing an angular map of the electron’s distribution. In addition, point and arrow indicate in the plane the orientation of the B-field at the time interval considered, see Figure 1 in Figueroa Viñas et al. [44], see also [45].

The ‘e’ velocity distribution function (VDF) in spherical coordinates is represented in Figure 11 by a function f(v,θ, ϕ), where the independent variables are the velocity, polar angle (elevation in the figure), and azimuthal angle (Phase label, bottom, in the figure) respectively. Figure 11 shows a subset not contiguous of the 30 energy steps of one VDF measurement, see instrument description in Ogilvie et al. [46]

The 2-D Figure 11 choice of the longitude scale (from -180 to 180°) in each panel produces a split view of the selective one-dimensional distribution for MC (This distribution, along the B-field, is shown in Figure 10, right panel for the electrons (see ref. [38]). The location of the direction B-field is shown. The different panels below show from bottom up, on the right and continued on the left panels the intensity variation (from lowest values in lighter dark with increasing electron intensity through green, then yellow reaching the maximum intensity with red and most intense electron presence in dark red at the center of the distribution). Additionally, the plots show the orientation of the B-field direction through all panels (see arrowhead maintains the direction (θ = −30°, ϕ = 90°), and base of it seen in the right panes at (θ = 30°, ϕ = −90°), and indicates the current flowing in the direction opposite to the B-field intensity at energies of about more than 70 keV (all panels where the B-field electron aligned current J_e appears and in this case study extending beyond the upper energy interval shown of 268.3 keV.

Figure 12 shows that the electrons data are ‘3s averages,’ also from the SWE instrument, but an instrument part built in GSFC (all in SC Wind) [47]. Fitting parameter γ = 1/2 is the overall value of the polytropic exponent index on a strongly B-field dominated structure (MC interval with date 6/2/1998 observed) which passes Wind in its motion away from the Sun.

Figure 12.

An example of anomalous gas properties in the SW for a B-field MHD medium.

The γ for the FR region observed with Wind (see enclosed in black values on the right) would indeed show a smaller value for the relationship between temperature ‘T’ of electrons and density of the plasma (γ ∼ 0.7).

From a case study, see [18], obtained values of T, v_s, μ,J_free. And also_:

$$\mathrm{T}=\mathrm{1.24}·{\mathrm{10}}^{\mathrm{5}}\mathrm{K}>\mathrm{1}/\mathrm{2}{\mathit{m}}_{\mathit{e}}<{\left({\mathsf{V}}_{\mathsf{e}}\mathbf{-}\mathbf{<}{\mathsf{V}}_{\mathsf{e}}\mathbf{>}\right)}^{\mathrm{2}}>\mathrm{\text{which is proved right}}$$E11

• v_s(T) = 0.95·10⁵ ms⁻¹, structure’s acoustic speed, from e-gas relation v_s = [γ_akBT/m_e]^1/2

• μ(T)/μ₀ = 0.5·10⁻³, from relation: α = μ H·dm / PdV and value of v_s(T)

• J_free = 5·10⁻⁹ Am⁻², free current density, from J_free = Ha/μ B where the flux-ropeB-field evolution is

$$\mathbf{B}={\mathrm{B}}_{\mathrm{0}}{\left({\mathrm{t}}_{\mathrm{0}}/\mathrm{t}\right)}^{\mathrm{2}}\left[\mathrm{H}{\mathrm{J}}_{\mathrm{1}}\left(\mathrm{a}\mathrm{r}\right){\mathbf{e}}_{\mathbf{\phi }}+{\mathrm{J}}_{\mathrm{0}}\left(\mathrm{a}\mathrm{r}\right){\mathbf{e}}_{\mathbf{x}}\right],$$E12

own overall polytropic behavior on June 2, 1998, as it is shown in Figure 12.

The characteristics of the gas being of so considered anomalous kind, as the graph in Figure 13 bottom panel shows. The top panel in Figure 13 shows the usual ideal gas dependence of T (temperature) on ρ (density) for an adiabatic branch. It corresponds to the entropy conserving adiabatic process with polytropic exponent ϒ = 5/3, see, e.g. [48].

Figure 13.

Normal (top) vs. anomalous (bottom) gas.

The actual observations summarized in Figure 14 are based on a direct observation of the effect inside strongly magnetized matter in the form of a MC, already introduced earlier, suddenly ejected from the Sun and its interpretation based on data shown below in Figure 14. Our complete illustration in Figure 14 of the B-field and bulk plasma conditions in an electron 3 s time series of a duration of a little more than two minutes of the properties present in this ideal B-field dominated matter includes from the top to bottom a sequence of eight panels ordered 1, 2, 3, 4, 5, 6, 7, and 8. In the present description: (a) panels 1 and 2 show the estimated convection velocity, in (1) the bulk velocity magnitude, named V_B, and in (2) on the left labels the longitude, and on the right the elevation of V_B in cthe orthogonal coordinate system GSE (e.g. [49]); (b) panels 3, 4, and 5 show the vector B-field, where panel 3 illustrates the steadiness of the intensity of the magnetic field, and the direction minimal changes are emphasized in panels 4 for elevation and 5 for longitude. Meanwhile, (c) panels 6–8 show the features of the medium in which panel 6 on the right shows the coherent variations showing anti-correlation between the 3 s mean B-field magnitude (on the left) and the electron density (on the right). Panel 7 on the right shows the clear anti-correlation between the electron T_e (left label) and density (right label); These panels 6 and 7 are at the core of the interpretation of a diamagnetic medium, consistent with past identification of this MHD constitutive property at interplanetary magnetic holes (see [50, 51]). Finally, (d) the bottom panel 8 checks the thermodynamic equilibrium condition showing negligible anisotropy in the internal electrons energy (right side of panel 8) while substantial changes, also shown in panel 7, (also illustrated in the left side of panel 8) take place indicating the diamagnetic nature of the medium, i.e. thermal equilibrium holds and further entropy conservation is well-established supporting the conservation of the energy of this matter–magnetic field structure. Further, the Figure illustrates the ends of the described coherence effects discussed at the passing of the time/location of the observation suggesting the presence of domains in the structure that would interact solely through their vibrational contact keeping the observed gas (wide part of the electrons distribution, Figure 10 right panel, typical characteristic of the SW (rooted in the presence of a dilute gas in each domain), which constitutes a key element to understand the thermal short equilibration times in the low solar corona in our consistent interpretation of the here discussed medium, see, e.g. [52].

Figure 14.

Illustration of key constitutive properties of the MHD-dominated structure.

Figure 14 coherence of the diamagnetic coupling between plasma and B-field suggests again a presence in electron dilute gas of two works, which we discuss in the next paragraphs.

The presence of an anomalous polytropic index is the result of the two works done by the electron gas in the domains of the magnetized plasma structure (see [18, 52, 53]):

• ideal gas work only:

$${\mathit{V}}^{\mathit{\Upsilon }}\mathit{=}\mathit{\text{Constant}}\mathit{\text{with}}\mathsf{\Upsilon }\mathit{=}{\mathit{c}}_{\mathit{p}}/{\mathit{c}}_{\mathit{v}}\mathit{=}\mathit{1}\mathit{+}\mathit{R}/{\mathit{c}}_{\mathit{v}}\mathit{=}\mathit{5}/\mathit{3}$$E13

$$\mathit{P}\mathit{V}\mathit{=}\mathit{N}\mathit{R}\mathit{T}\left(\mathit{\text{equation of state}}\right)\mathit{\text{If}}\mathit{N}\mathit{\text{constant}}\mathit{,}\mathit{\text{then}}$$E14

$$\mathit{T}/{\mathit{\rho }}^{\mathit{\gamma }\mathit{-}\mathit{1}}\mathit{=}\mathit{K}➔\mathit{\text{with constant}}\mathit{K}\mathit{=}\mathit{\text{constant}}/\left({\mathit{N}}^{\mathit{\Upsilon }}\mathit{R}\right)$$E15

Ideal gas and magnetic work: ϒ = 1+ R/c_v(1 – α) where α = [magnetization work/gas work].

Then it can be shown the relationship between e-gas and magnetic work that enables anomalous γ (γ_a = 1/2) at position P in the FR in Figure 8. … for a noninteracting e-gas with internal energy dU = c_V dT, and its equation of state PV = RT (for 1 mole, and R being the universal gas constant) the relationship for the reversible adiabatic exponent γ_a is obtained from

$${\mathit{c}}_{\mathit{V}}\mathit{dT}+\mathit{R}\left(\mathrm{1}–\mathit{\alpha }\right)\mathit{T}\mathit{dV}/\mathit{V}=\mathrm{0}.$$E16

and the condition of point-like e-gas with three degrees of freedom, where c_V/R = 3/2, then α = 7/4. (In Eqs. (13)–(16), V is the internal energy velocity of the gas and not the bulk velocity (V_B).)

4. Discussion; on the presence of large amounts of matter in gaseous state in galaxies

When we consider that in situ observation allows us to infer reasons for the stability of strongly magnetized matter as it is being explored by the in situ observations of V1 and V2, we may consider other presences of so-called molecular clouds and make educated argumentation for the lack of formation of small and large bodies on the argumentations of matter frozen to strong magnetic fields, which depending on relation of particle to magnetic field pressure we observe that condition well satisfied in the very LISM. The LISM is a structure that, for its characteristics, also seems not to collapse due to its own gravitation. Consequently, as we do here, it is possible to consider that the magnetic field’s presence may be related to large amounts of matter in our galaxy, which stays in a gaseous form to be understood. In that respect, Figure 15 illustrates a law of velocity of matter as a function of the distance of its center, which is common to many galaxies including ours. Distribution of velocities which resulted in easier capture from its outside.

Figure 15.

Velocity of rotation in spiral galaxy messier Triangulum, see, e.g. [54].

Then, as we know, the result suggests the possibility that the common state of matter in the galaxies is of the dilute kind like the Voyager SC identified in our own local interstellar magnetized matter MHD state. We could speculate that perhaps in the neighborhood of the Sun, we could be in the presence of a formation of dilute matter old in nature, e.g. that in its origin constituted a proto-nebula as the one discussed in [55], a simple proto-nebula constituted of plasma under magnetohydrodynamic conditions. The presence of this kind of structure as a galaxy has indeed been observed, as illustrated in Figure 16.

Figure 16.

The Hoag object is a ring-shaped galaxy.

Figure 15 shows, at scale, the galaxy view in the projected plane of the sky. Similar rotation velocities with the distance from the center have been identified for many galaxies, including the via Apia, our home galaxy. Notice the indicated departure with distance from the expected gravitational law when correlated with the matter’s mass.

Here, it is possible to invoke that a proto-nebula as the one envisioned in [55] due to instabilities related to the cooling by radiation may have produced the instabilities responsible for partial collapse due to self-gravitational forces which generated the formation of stars, i.e. the evolution of the structure into a galaxy of the Hoag kind (Hoag’s object).

When we make the standard assumption of considering the mass distribution in the ring galaxy (Figure 16) to be homogeneous, and we further consider that its larger amount happens to be in an MHD state, it is straightforward to write the analytical solution for the medium, where it should be only included the gaseous part of the mass and its attachment to the magnetic field in the type of magnetohydrodynamic nature we described for the proto-nebula in [55]. There the magnetic force solution is given by

$$\mathbf{B}={\mathit{B}}_{\mathit{0}}\left[{\mathit{J}}_{\mathit{0}}\left(\mathit{A}\left(\mathit{\rho },\mathrm{\varphi }\right)\right){\mathbf{e}}_{\mathbf{x}}+\mathit{H}{\mathit{J}}_{\mathit{1}}\left(\mathit{A}\left(\mathit{\rho },\mathrm{\varphi }\right)\right){\mathbf{e}}_{\mathbf{\varphi }}\right],$$E17

with argument

$$\mathit{A}\left(\mathit{\rho },\mathrm{\varphi }\right)\mathit{=}\mathit{a}\left(\mathit{\rho }\right)\left[\mathit{1}\mathit{+}\mathit{\rho }/{\mathit{R}}_{\mathit{cFR}}\left(\mathit{cos}\left(\mathrm{\varphi }\right)–|\mathit{sin}\left(\mathrm{\varphi }\right)|\right)\right]$$E18

would be the time stationary limit of the solution presented earlier [18, 25] in a different context, where a(ρ) = A ρ, and A = j₀/R_FRcore, J_0,1 are the well-known orthogonal, grade 0 and 1, cylindrical Bessel functions of first kind⁹, and the value of ρ = R_FRcore defines the radius of ‘the circular cross section’ of an approximated cylinder-section of the torus at the location where the axial magnetic field has its first node, is identically zero, i.e., J₀(j₀) = 0. In this case study, there is no volume (Vol) change of the matter-magnetized structure with time (Figure 17).

Figure 17.

A torus-shaped solution to B- and self-gravitational fields stable equilibrium.

Next we drop subindices for R_cFR, and instead, we use R. The summatory of all ‘torus’ elements and gravitational forces acting on each infinitesimal element ‘δM_Torus ‘at the torus’ locus is oriented to the center of the torus, defined as

$${\mathbf{F}}_{\mathrm{g}}\left({\mathrm{\delta M}}_{\mathrm{\text{Torus}}}\right)=-\mathrm{G}{\mathrm{M}}_{\mathrm{\text{Torus}}}{\mathrm{\delta M}}_{\mathrm{\text{Torus}}}\mathbf{R}\left({\mathrm{\delta M}}_{\mathrm{\text{Torus}}}\right)/{\left|\mathbf{R}\right|}^{\mathrm{3}}$$E19

for circular symmetry of the simple case of homogeneously distributed matter in a magnetized field (defined in Eq. (17)). Also, any mass particle m located at a distance from the center of the torus | r – R| is bound to feel such gravitational pull,

$${\mathbf{F}}_{\mathrm{g}}\left(\mathit{m}\left(\mathbf{r}–\mathbf{R}\right)\right)=-\mathrm{G}{\mathrm{M}}_{\mathrm{\text{Torus}}}\mathit{m}\left(\mathbf{r}–\mathbf{R}\right)/{\left|\mathbf{r}–\mathbf{R}\right|}^{\mathrm{3}}$$E20

Once with the expression for the magnetic field and the current, it is easy to find the equilibrium condition for

$$\sum \mathbf{F}=\mathbf{0}$$E21

where we here solely consider magnetic and gravitational forces, i.e.

$${\int }_{\mathrm{M}}{\mathbf{F}}_{\mathrm{g}}\left({\mathrm{dM}}_{\mathrm{\text{Torus}}}\right)\mathrm{dM}+{\int }_{\mathbf{J}}\mathrm{d}{\mathbf{J}}_{\mathrm{C}}\mathrm{X}\mathbf{B}=\mathbf{0}$$E22

and, considering the solution of Eq. 17 in [25] for a truncated torus, we proceed to the generalization of the simpler case of a whole torus developed here, which for us, corresponds to the simplified equilibrium expression:

$$\mathit{G}{\left({\mathit{M}}_{\mathit{\text{Torus}}}\right)}^{\mathit{2}}+\left(\mathit{25}{\mathit{\mu }}_{\mathit{0}}/\mathit{4}\right)\left[{{\mathrm{\Phi }}_{\mathrm{\varphi }}}^{\mathrm{2}}\right]=\mathrm{0}.$$E23

The mass of the torus (M_Torus) and the poloidal magnetic flux (Φ_ϕ) forces in equilibrium are simply related, as shown in Eq. (23). In this way, we obtain, for a simple limit, the condition for the matter to be attached to the ‘protogalaxie magnetic field’ generated by convective currents, which stabilize the matter in a cold frozen matter condition. Preliminary studies [18, 51] suggest that this, ‘stable structure,’ will possess specific thermodynamic properties characteristic of a diamagnetic environment. A possible explosive disruption of this stable condition is addressed below.

4.1 From the Hoag’s object to spiral galaxies

A process of destabilization of the structure could be caused by the interaction of two proto nebulas of the kind described above, producing changes to the morphology of the simple formulations presented. In such a collision scenario of two rings Hoag’s nebula or proto-nebula, there would be gravitational cause for strong dislocation of the toro generating reconnections between magnetic domains with opposing polarity and causing a spreading in regions presenting a collapse of the structure MHD in this way freeing the matter in multiple locations of the fresh forming spiral galaxy in an explosive process of formation of stars with the same birthmark in their matter ratio of elements constitutive inside of the new nebula/galaxy.

This origin, with still the presence of a majority of matter in a dilute state frozen to the magnetic field, clearly gives a straightforward explanation of the no Keplerian distribution of velocities in the known spiral galaxies, including our Via Apia, the home of our solar planetary system.

In the actual galaxies, the amount of matter available would be far from being exhausted (see Star Formation Sputtering Out Across the Universe by Space.com Staff, November 07, 2012).

The majority of the known galaxies would still be holding their matter in a stable MHD state of matter frozen to the B-field. The consequence of this would be the presence of a fragmentary toro-shaped dilute cold matter (<10,000 K), which occasionally would form new stars in renewed disruptive processes, see, e.g. [20], generating the so-called ‘cradles of the new stars.’

5. Conclusions: about our learning with the in situ observation using Voyager SC

In this chapter, it is probed a variety of key properties of the local to solar system interstellar molecular cloud and its millions-of-year presence of a very strong magnetic field. The proof was achieved by the in situ measurements of a variety of its properties for a whole set of data recollected by several instruments in the mission Voyager (V1 and V2 SC) as we reported: Magnetometer, Radio Instrument, Plasma Instrument, low and high energy particle instrument of the Voyager SC. In this way, the Voyager SC can identify the presence of a medium that has very long-lasting permanent magnet characteristics and an origin foreign to the solar magnetized plasma, which has its source in the solar corona.

Further, it is presented the consistency of the interpretation of the medium being matter in a strong B-field with a 3 D Langmuir amorphous crystal gas. The role of the frozen matter, the dilute electrons, and the presence of B-field convected currents is the source of a very stable magnetic field, as we know from some simple modeling illustrated in Section 4.

Section 3 discussed the identification of a consistent constitutive permeability property differing from the permeability of the vacuum smaller by a factor 1/2 appears to be the case considering its consistency by observations by V1 and V2. (See V2 preliminary estimate in Appendix B.)

A simple estimate is made of the mass of the local molecular clouds in which the Sun, Alpha Centauri, and a few other stars found in its neighborhood of the sketched molecular cloud complex, which also approximately co-move with it around the galaxy center.

Finally, in our discussion (Section 4), we extrapolate the interpreted properties of the medium to a possible origin of our home galaxy and other structures observed in astrophysics.

Among key subjects in need of further study are: (a) energy/nature arguments on the reasons for nonradial orientation of the magnetic B-field at heliopause in the heliosphere sheath and very LISM. A matter which is still in need of understanding. (b) Stronger validation of assumptions made in this work which so far offer consistent support of the nature of the permanent magnetized state of matter here introduced to a wider range of readers until now mostly limited to members of the geophysical and astrophysical communities. (c) The role and range of cosmic rays’ possible modification of the properties of the MHD structure.

Acknowledgments

The collaboration with all team members, also the consideration by the current instrument manager Adam Szabo for my work is warmly thanked. Continuous NASA NNG15CR65C grant support to Voyager SC magnetometer enabled and supported the expenses of this book contribution. I acknowledge the benefit of my learning and the opportunity to study due to my father’s love, the late Carlos David Grünfeld Berdichevsky.

A. Appendix

Essential differences are present in each panel of Figure 10, there are both plots, which are simply related to the elaboration pursued in their generation. A panel of the left for the protons gives just the proton flux observed in a steady (undisturbed) strong B-field interval as a function of a very well-collimated radial velocity from the Sun of the proton population selected through a process of triple coincidence that includes detectors independent evaluation of the start time each proton enters, followed of the time of impact in the stopping location, and charge, mass, and energy by a strong magnetic field sweep that by deflection of the particle identifies the ion’s unique properties of interest, see, e.g. [56]. Further, the plot evaluates the intensity of the proton’s flux from the Sun as a physical invariant property of the interval of observation which is extremely small and consistent with the well-known high vacuum of the interplanetary medium near the distance Ulysses is found at the time of observation in its initial trajectory from the Earth to Jupiter, as indicated in the work of these observations, i.e. [37]. While in the case of the very detailed study of the electron distribution in Nieves-Chinchilla and Figueroa Viñas [38] with the SWE instrument in Wind SC

$$\begin{array}{c}<\mathrm{\text{Energy}}\left(\mathrm{\text{electron}}\sim \mathrm{1/2}{\mathrm{m}}_{\mathrm{e}}{\left(\mathrm{0.8}{\mathrm{kms}}^{-1}\right)}^{\mathrm{2}}\right)/\mathrm{\text{Energy}}{\left(\mathrm{\text{proton}}\sim \mathrm{1/2}{\mathrm{m}}_{\mathrm{p}}{\left(\mathrm{21}{\mathrm{kms}}^{-1}\right)}^{\mathrm{2}}\right)}^{\ast }\\ \mathrm{\text{mass}}\left(\mathrm{p}\right)/\mathrm{\text{mass}}\left(\mathrm{\text{electron}}\right)\mathrm{\text{is in the order of}}\mathrm{1836.6}.\end{array}$$E24

But still, we can do one more normalization related to the general radiative cooling of the strong magnetized matter, which increases with SC distance from the Sun, which for Ulysses is close to 3 AU from the Sun versus 1 AU for the location of Wind SC, and the time of the respective measurements. This is valid when we consider the radiative cooling of matter with time in the interplanetary space and relate the observations with Ulysses of the proton. This behavior is well understood for a frozen matter estate of nature which depending on its mass produces tighter oscillation for smaller mass; versus larger oscillation amplitude for larger masses. Henceforth, strong support for the constitutive nature of the ideal magnetized matter is identified through very delicate analysis using very clean SWE in Wind SC, and SWICS in Ulysses SC plasma instruments. Here we deal with far smaller uncertainties resolution than what is available with most instruments from past and planned missions.

Hence, the obtained ratio close to one is a quite strong argument favoring the 3-D Langmuir amorphous crystalline nature of the low beta ideal MHD matter structure.

B. Appendix

On the subject of units, we start with the relationship of equivalence for the pressure of

$$\mathrm{1}\mathrm{dyn}/{\mathrm{cm}}^2=\mathrm{0.1}\mathrm{\text{Pascal}},$$E25

and considering that 1 fPa = 10⁻¹⁵ Pa. We notice that [19] reached a value for the particle pressure pushing the surrounding LISM by the heliopause with a pressure intensity of 3.57 ± 0.71·10⁻¹³ Pa, and in its independent work, [31] proposed the observational value of 267 ± 55 fPa. This is the same that 2.67 ± 0.55·10⁻¹³ Pa at heliopause crossing by V1. In a way agreeing within less than two standard deviations the two studies. Here we take advantage of the consistency of both studies to assume a pressure onto the LISM from the heliosphere of 300 ± 50 fPa, which would correspond to an equilibration local interstellar magnetic field of 0.7 ± 0.1 nT, which is about a much higher value of the average magnetic field of the very LISM of about 0.4 nT and which can simply be explained by our understanding of a medium which due to an anomalous electrons gas has as a consequence through the presence of magnetization work coupling to the gas pressure a medium permeability μ close to (1/2 ± 1/4) μ₀. Equilibrium with μ!

Burlaga et al. [47] show in V2 an ‘expected’ B-field barrier at heliopause with a B-field intensity of approximately 0.45 nT on the sheath side of the Heliopause. On the LISM side, the B-field is ∼0.7 nT. This implies a push by the sheath of about 500 fPa onto the interstellar medium, while at ‘hp’ interface, the LISM B-field stresses equilibrate that push for a similar small value for the constitutive permeability of the medium μ ∼ 1/2 μ₀ (see, e.g. [19])_. This is consistent with our interpretation of the presence of magnetization work discussed in Section 3.4 with the help of more detailed studies from more advanced experimental quality plasma and equally good magnetic field data available from Ulysses and Wind SC.