**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

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

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.

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 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

**Figure 16.** *The Hoag object is a ring-shaped galaxy.*

$$\mathbf{B} = B\_0 \left[ J\_0(A(\rho, \phi)) \left| \mathbf{e}\_{\mathbf{x}} + H J\_1(A(\rho, \phi)) \right.\\ \left. \mathbf{e}\_{\Phi} \right], \tag{17}$$

with argument

$$A(\rho, \phi) = a(\rho) \left[ \mathbb{1} + \rho / R\_{\text{cFR}} \left( \cos \left( \phi \right) - \left| \sin \left( \phi \right) \right| \right) \right] \tag{18}$$

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/RFRcore*, *J0,1* are the well-known orthogonal, grade 0 and 1, cylindrical Bessel functions of first kind<sup>9</sup> *,* and the value of *ρ = RFRcore* defines the radius of *'the circular cross section'* of an approximated cylindersection 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**).

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

$$\mathbf{F\_{g}}\left(\delta\mathbf{M\_{Tors}}\right) = -\mathbf{G}\left(\mathbf{M\_{Tors}}\,\delta\mathbf{M\_{Tors}}\,\mathbf{R}\left(\delta\mathbf{M\_{Tors}}\right)\right) / \left|\mathbf{R}\right|^{\beta}\tag{19}$$

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,

$$\mathbf{F\_g} \left( m(\mathbf{r} - \mathbf{R}) \right) = -\mathbf{G} \, \mathbf{M\_{Tors}} \, m \left( \mathbf{r} - \mathbf{R} \right) / \left| \mathbf{r} - \mathbf{R} \right|^3 \tag{20}$$

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

**Figure 17.** *A torus-shaped solution to B- and self-gravitational fields stable equilibrium.*

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

$$
\sum \mathbf{F} = \mathbf{0} \tag{21}
$$

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

$$\int\_{\mathbf{M}} \mathbf{F}\_{\mathbf{g}} \left( \mathbf{d} \mathbf{M}\_{\text{Tors}} \right) \, \mathbf{d} \mathbf{M} + \int\_{\mathbf{J}} \mathbf{d} \mathbf{J}\_{\text{C}} \mathbf{X} \, \mathbf{B} = \mathbf{0} \tag{22}$$

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:

$$\left[\mathbf{G}\left(\mathbf{M}\_{\text{Tors}}\right)\right]^2 + \left(2\mathbf{5}\left\{\boldsymbol{\mu}\_0/\mathbf{4}\right\}\left[\boldsymbol{\Phi}\_\Phi\right]\right) = \mathbf{0}.\tag{23}$$

The mass of the torus (*MTorus*) and the poloidal magnetic flux (Φϕ) 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.'
