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Dissecting Bad Models (Part 1) Astrophysical "Magnetic Slinkies"
by Michael Gmirkin

May 22, 2009
 
A number of astrophysical assumptions and deductions have gone unchallenged for far too long. Rational, skeptical scientists must occasionally take an introspective look at their own discipline and excise any persistent errors. Let's shall...
 
"Magnetic slinky" in Orion
The Orion Molecular Cloud superimposed on the Orion constellation.
The inset shows the Slinky-like coils of the helical magnetic field
surrounding the filamentary cloud.
Credit: Saxton / Dame / Hartmann / Thaddeus / NRAO / AUI / NSF
[Click to enlarge]
 
In 2006, observations from the Green Bank Telescope revealed the presence of magnetic fields associated with a filamentary portion of the Orion Molecular Cloud.
Using the GBT, Robishaw and Heiles found that the magnetic field reversed its direction, pointing towards the Earth on the upper side of the cloud and away from it on the bottom When they combined all available measurements, the picture emerged of a corkscrew pattern wrapping around the cloud.
But how accurate are the conceptual models in which the observations are couched? Unfortunately, it seems that many incorrect and outdated assumptions still manage to creep their way into interpretations.

Not least of all, there still seems to exist an erroneous notion that magnetic field lines are real-world entities that can be likened to a string or a rubber band and can be cut, twisted, stretched or otherwise manhandled.
The field might be wrapped around the front of the cloud.
That is simply not the case. Magnetic field lines are only an aid to help visualize the strength and direction of magnetic fields. Magnetic fields themselves do not congregate in "lines" or "ropes" with regions void of magnetic field falling between and around them. The fields are continuous and smooth not discrete and broken up.

This error of reification (assuming something is real or physical when it is no more than a conceptual tool to aid in understanding a significantly different real-world object or process) leads to other erroneous assumptions and theories that follow from it.
[A] shock wave [could] have carried the magnetic field along with it, [Heiles] said, “until it reached the molecular cloud! The magnetic field lines would get stretched across the face of the cloud and wrapped around the sides.”
Not only does the error of reification occur in claiming that magnetic field lines are real entities that could have been "draped" around the molecular cloud, two other more serious physical errors creep into the same thought.

Firstly, in "draping" magnetic fields around a real-world object, one would have to presuppose that magnetic fields could be "cut" or made "open-ended." This is far too common an error.

According to Maxwell's second equation (∇ · B = 0), that simply cannot physically happen. It states that the net magnetic flux leaving (or entering) any closed surface is zero. In real-world terms, this means that the same number of conceptual "field lines" must be drawn entering the surface as are drawn exiting the surface and vice versa. When properly understood this means that magnetic "field lines" can only be drawn as completed loops. They must close. There can be neither magnetic monopoles nor "cut," "open" or "dangling" field lines. Put simply, magnetic fields are solenoidal (they have neither a beginning nor an end, with no exceptions).

Electrical engineers are very careful when drawing schematics involving magnetic fields to show that, if any lines would be too large to fit completely on a page, where a line leaves the page, an equivalent line must be somewhere shown to re-enter the page and vice versa. To do otherwise conceptually and mathematically violates Maxwell's second equation (Gauss's law for magnetism).

As such, a magnetic field line cannot be "cut" and "draped" over a real-world object (such as a molecular cloud), regardless of any astrophysicists wishing it could be so.

Secondly, more egregiously and unfortunately more commonly, the statement presupposes that magnetic fields can be "frozen in" to plasma and carried along with it in the absence of sustaining electric currents. Again, that simply is not so.

The notion of "frozen in" field lines presupposes that plasma is an ideal conductor (a superconductor that does not resist a current flowing through it), immediately neutralizes any charge imbalances, does not support internal electric fields and thus any magnetic fields cannot vary over time.

However, as electrical engineer Don Scott has pointed out, plasma is not an ideal conductor. It has non-zero resistance, as experiment has shown repeatedly in the lab.

This can be demonstrated simply by applying the mathematical definition of resistance to the diagram of plasma discharge modes. Resistance is defined by the equation R = V / I. Resistance R (measured in ohms) is the ratio of voltage V (measured in volts) to current I (measured in amperes).
 
Plasma glow discharge
[Click to enlarge]
 
It is quite clear from the diagram above that if you draw a line from the origin of the graph in the lower left to any point on the diagram of plasma's discharge regimes, the slope of the line will always be positive and non-zero. That is to say, the diagram never touches the X axis at any point. Voltage V never decreases to zero. Ergo resistance R never decreases to zero. Ergo plasma is not a superconductor.

Charge imbalances are not immediately neutralized and weak electric fields (voltage potentials) can exist between discrete regions within a plasma. As such, magnetic fields cannot be "frozen in" to plasma and carried along with it. Understanding of magnetic fields in plasma must therefore be understood in terms of the relationship between electricity and magnetism. Namely, the magnetic fields in plasma are generated by electric currents flowing within it. The strength of the magnetic field is dependent upon the strength of the electric current. This simple relationship is recognized in all other disciplines.

Despite the problems with the article, a few glimmers of hope remain, if they can be sifted from the rubble. One such potential saving grace comes from an offhand comment:
In making theoretical models of these clouds, most astrophysicists have treated them as spheres rather than finger-like filaments. However, a theoretical treatment published in 2000 by Drs. Jason Fiege and Ralph Pudritz of McMaster University suggested that when treated properly, filamentary molecular clouds should exhibit a helical magnetic field around the long axis of the cloud.
While the quote above may seem unassuming to the uninitiated observer, it may hold a profound grain of truth. Most astrophysicists have treated such structures as spheres rather than long, straight filaments.

Why is it important though, to treat such features as long straight filaments rather than as spheres? Because the equations governing how the influence of the magnetic force drops off over distance may be different if you treat the structure as a sphere rather than as a filament.

Consider that the influence of gravity drops off with the inverse square of the distance from an object with gravitating mass.

Now, for a magnetic dipole (more-or-less a spherical magnetic field), the influence of the magnetic field drops off according to an inverse cube relationship. But what happens when we consider the magnetic field generated by a long, straight electric current? Does it follow the lead of the spherical configuration and adhere to an inverse cube relationship? No!

In fact, in the long, straight current scenario, it drops off with the inverse of the distance (a first power relationship). That means its influence drops off more slowly than the influence of gravity and much more slowly than the influence of a magnetic dipole, making it the longest range force of the three.

Is it possible that astrophysicists have underestimated the reach and role of magnetic fields in the cosmos due to a simple error of geometry? If so, this simple error may have monumental implications.

As Fiege and Pudritz imply, treating the filaments as filaments (and allowing for the reality that electric currents are the progenitors of magnetic fields) may yet yield comprehensible and more accurate results. In the Plasma Cosmology view, where electric currents are recognized as the sole sources of magnetic fields in cosmic plasmas, it would seem that the filaments are electrical in nature and that the magnetic fields are a natural consequence of the currents found there.

In fact, helical currents and filaments are not unexpected in the plasma model. It is well known that parallel currents will tend to form entwined ropes or filaments, due to their long range attraction and short range repulsion.

Moreover, other statements quickly fall in line with an electrical interpretation.
“You can think of this structure as a giant, magnetic Slinky wrapped around a long, finger-like interstellar cloud,” said Timothy Robishaw, a graduate student in astronomy at the University of California, Berkeley. “The magnetic field lines are like stretched rubber bands; the tension squeezes the cloud into its filamentary shape.”
Ignoring the erroneous reification of "magnetic field lines," the analogy to rubber bands isn't completely hopeless.

In fact, a well-known behavior of plasma is the "Bennett pinch" (pinch, pinch effect, magnetic pinch, electromagnetic pinch, plasma pinch and z-pinch are all alternate names for the process). In a "pinch," magnetic forces generated by the current may serve to compress the current inward toward its axis (not unlike rubber bands holding the stems of roses together in a bouquet). Physically, the pinch effect is the same process that causes static sparks and lightning to occur in thin filaments.

While the results of the GBT observations were couched in poor terminology, the underlying observations seem both sound and salvageable once interpreted within a valid physical framework.

Long story short, the filament in the Orion Molecular Cloud is electrified.

Metaphorically speaking, river(s) of electric current run through it. Said current(s) generate the observed magnetic field. Filamentation is an expected feature of such a theoretical current and the magnetic field generated by it may serve to pinch (compress) the materials therein.

Plasma Cosmology offers an integrated and internally consistent interpretation of the observations while neither violating Maxwell's equations by "cutting" or leaving "open-ended" magnetic field lines nor incorrectly asserting that plasmas are superconductive and able to "drag" magnetic field lines along with them, in the face of laboratory experiments to the contrary.

If astrophysicists are willing to introspectively assess their own discipline and excise some erroneous assumptions and deductions, greater understanding of the cosmos than has heretofore been gained may yet be at hand.

Michael Gmirkin
 
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