**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.**


**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 selfvibrational 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).

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

$$\mathbf{dB\_{N1}} = \mathbf{B\_N(n)} \mathbf{-B\_N(n-1)} \tag{1}$$

and

dBT1 <sup>¼</sup> BTð Þ <sup>n</sup> –BTð Þ <sup>n</sup> � <sup>1</sup> oscillations are in the bottom panels in **Figure 6** (2)

and time series of the 1-hr increments of '*dBN1 and dBT1*' 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

**Figure 6.** *Presence of self-oscillation modes, in the B-field for DOY 147, the year 2020.*

### *Hydromagnetic Steady Magnetized Plasma Encountered by Voyager in the Interstellar Space DOI: http://dx.doi.org/10.5772/intechopen.112362*

densities considered, the observation of an average **B**-field close to ½ 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:


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:

$$
\sim \clubsuit \times \ $ \times \$  \,\text{parse}\,\text{c}^3\tag{3}
$$

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.

$$
\sim 2 \text{ nucleons/cm}^3 \tag{4}
$$

this gives a mass 4/100<sup>10</sup><sup>30</sup> kg, about 1/50th the mass of the Sun (= 2<sup>10</sup><sup>30</sup> 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*.


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].


**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. h ttps://wind.nasa.gov.

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 μ<sup>0</sup>* 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 *μ<sup>0</sup>* 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* 6¼ *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 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: *Fx =* ∇ � ∇*ϕ)x* =

$$-2\pi \,\mathrm{G} \,\mathrm{N} \left\{ 2\pi + \left( \mathrm{R}^2 + \left[ \mathrm{L}/2 \cdot \mathrm{x} \right]^2 \right)^{1/2} \mathrm{-} \left( \mathrm{R}^2 + \left[ \mathrm{L}/2 + \mathrm{x} \right]^2 \right)^{1/2} \right\}\_{\ldots\infty}^{\mathrm{for}\,\mathrm{-L}/2 \leq \mathrm{x} \leq \mathrm{L}/2} \quad \text{(5)}$$

$$-2\pi \,\mathrm{G} \,\mathrm{N} \left\{ \mathrm{L} + \left( \mathrm{R}^2 + \left[ \mathrm{L}/2 \mathrm{-} \mathrm{x} \right]^2 \right)^{1/2} \mathrm{-} \left( \mathrm{R}^2 + \left[ \mathrm{L}/2 + \mathrm{x} \right]^2 \right)^{1/2} \right\} \text{for } \infty > \mathrm{L}/2 \tag{6}$$

of the two ranges labeled with (5) and (6) for independent variable 'x' abovediscussed 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. � *<sup>x</sup>*�*<sup>2</sup>* , is recovered.

**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.*

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

$$F\_{\rho} = -\nabla \Phi \rangle\_{\rho} = $$

$$-\sharp \xi \,\mathrm{GN}\rho \quad \text{for } 0 \le \rho \le R,$$

$$-\sharp \xi \,\mathrm{G} \mathrm{N} \mathrm{R}^2 \rho^{-1} \text{ for } R < \rho \le L/2,\tag{7}$$

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 *ΔmP* in volume *ΔVP* at location **X***<sup>P</sup>* = *ρ* **e<sup>ρ</sup> +** *x* **ex** from the center of an FR with **axial magnetic field** *B0* 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

$$\mathbf{B} = B\_0 \left( r\_0/r \right)^2 \left[ H \, J\_1(a \, r) \, \mathbf{e}\_\Psi + J\_0(a \, r) \, \mathbf{e}\_\mathbf{x} \right],\tag{8}$$

Assuming homogeneous mass distribution; self-gravitational force

*Hydromagnetic Steady Magnetized Plasma Encountered by Voyager in the Interstellar Space DOI: http://dx.doi.org/10.5772/intechopen.112362*

**<sup>F</sup>**ð Þ¼� r, <sup>φ</sup>, x <sup>¼</sup> <sup>0</sup> <sup>2</sup>π<sup>G</sup> *<sup>r</sup>* **er** cyl ; and for r< <R torus, not so everywhere in space (9)

with the magnetic field expressed in polar coordinates, consistent with a right coordinate system, and for historical reasons, *ex* is employed instead of *ez* [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 (*Pgas)* at heliopause (hp) with solar origin (3�10�<sup>12</sup> dyn)


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.,

$$\mathbf{J} \times \mathbf{B} + \mathbf{F}\_{\mathfrak{g}} = \mathbf{0} \tag{10}$$

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 (*Pgas*) 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 (½ � ¼) 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. [33–36].

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

#### *Hydromagnetic Steady Magnetized Plasma Encountered by Voyager in the Interstellar Space DOI: http://dx.doi.org/10.5772/intechopen.112362*

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:

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 *edistribution,* if in equilibrium, there it gives information on temperature '*T'* from the *egas* 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 ecurrent aligned* (**Je**).

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.)
