Guest post by Rud Istvan

This guest post was inspired by a long delayed lunch (by Covid-19, with our first two traditional restaurants found still closed for lunch by Wuhan virus fears despite now open South Florida) between CtM and myself. We discussed much, including WUWT. I complemented Charles on the recent months more eclectic science coverage, for example his recent post on a new independent purely geometric method for measuring the discrepancy between standard model theory and observations of the Hubble constant (using 4 gravitationally lensed galaxies), strongly implying the model is wrong—but nobody knows why, or how to fix. This post follows that.

A few days ago, Live Science posted a piece on a new astrophysics paper showing observationally that Einstein’s general relativity universal gravitational acceleration postulate, the Strong Equivalence Principle (SEP), holds true in deep gravitational wells. The paper analyses a two white dwarf plus one neutron pulsar system, one white dwarf closely orbiting the neutron pulsar, both then orbiting the more distant other (probably much more massive) white dwarf. Although the analysis is a bit complex, the precise ‘clock’ of the rapidly spinning pulsar showed that gravitational acceleration was at the same rate always for all three stars in the system. Showing Einstein’s SEP holds in extreme gravitational fields is very cool.  

Galileo first showed that all masses gravitationally accelerate at the same rate on Earth via the Leaning Tower of Pisa by simultaneously dropping equally sized metal balls of different masses (lead, iron). Apollo astronauts again proved this on the Moon by dropping a feather and a hammer simultaneously in the Moon’s vacuum,…but those are astrophysically VERY weak gravity fields.

Even the Sun’s gravity holding together the solar system is weak compared to general relativity applied to the universe. So the new neutron star+two white dwarf paper provides a much stronger demonstration of general relativity’s SEP correctness.

Now, I am for sure NOT an astrophysicist. But I have studied Feynman’s Lectures on Physics (and have 13 issued US patents in electromagnetic (EM) involved fields like RFID, wireless patient monitoring, and energy storage materials).  We know Maxwell’s EM field equations must be ~correct because electricity generators and electric motors both actually work! Dyson’s switched reluctance vacuum cleaner motors are another Maxwell demonstration.

I got to thinking, how the heck can a neutron star have a magnetic field necessary to become a pulsar? It doesn’t have any electrons for the corresponding electric field. Butscept, we know they do have magnetic fields because those fields create the rapidly flashing pulsar EM radiation that we see in our telescopes!  What follows is a layman’s explanation of this apparent astrophysical puzzle. The solution is similar to many WUWT climate ‘puzzles’: first grasp the basic science facts, then think things through.

Astrophysical stellar objects come in five basic flavors (ignoring planets), distinguished by their EM spectra or lack thereof.

1. Red dwarfs. These are the smallest main sequence stars. They have enough gravity to initiate hydrogen fusion at lowish levels, and last almost forever. Mainly hydrogen spectra.
2. Regular stars. These come in various spectral flavors depending on mass.
3. White dwarfs. These are the many, many stellar remnants not having enough gravity to fuse beyond carbon. The ‘standard candle’ 1a supernovas are white dwarfs that accumulated more mass via gravity from a companion star, to the point that they initiate carbon fusion, and then in just seconds blow themselves to smithereens. (Type 1b and 1c are for purposes of this post just uninteresting variations on 1a carbon intensive spectra). Type 1a supernova can have two outcomes depending on the white dwarf mass: nothing left for smaller ones, or a neutron star as explained below having a minimum mass of about 1.4 solar masses (sol), and a maximum of about 2.1 sol.
   As an aside, white dwarfs are dense/small enough that their heat cannot dissipate inside the time frame of the currently known universe since the big bang, so even the oldest still radiate at several thousand ‘white hot’ kelvins. So there are LOTS around, so sufficient T1a standard candles.
4. Type 2 supernova. These originate from larger stars of at least 8 sol. Their greater gravity allows them to fuse all the way through iron (which is energy negative, so iron ‘ashes’ are the end of stellar fusion). They produce T2 supernova at the end (no hydrogen, lots of iron spectra) that ‘instantaneously’ produce all of the heavier than iron elements in the universe as a result of their gravitational implosion then explosion. The non-gravitational ‘mechanical’ shock waves of T2 enable further energetic fusions. They leave behind either neutron stars or black holes depending on mass.
5. Black holes, which form when the supernova remnant mass is greater than about 2.1sol. These are ‘infinite’ gravitational anomalies explained only by Einstein’s general theory of relativity, with an event horizon within which spacetime is so curved by gravity that even light cannot escape. Super massive black holes formed by accretion of lesser black holes sit at the center of most galaxies. Ours is Sagittaurius A. The one in galaxy Messier 87 was recently ‘imaged’ as a black center surrounded by the glow of matter falling into it. More black hole quantum weirdness follows.

What separates white dwarfs from neutron stars from black holes?

The answer lies in the quantum physics of Pauli’s Exclusion Principle (which is surprisingly easy to prove mathematically). It states simply that two fermions (elementary subatomic particles with non-whole number quantum spins, for example electron spin 1/2) CANNOT occupy the same place at the same time. For the mathematically inclined, the quantum ‘place’ is some multiple of the Plank constant, ‘hbar’, roughly E-35 meters. Pauli’s exclusion principle applies to electron degeneracy, neutron degeneracy, and (probably) quark degeneracy—from which a black hole math puzzle follows since quarks are still fermions.

1. Electron degeneracy. Pauli’s exclusion theorem says no two fermions can occupy the same space at the same time. Electron degeneracy is easy to ‘comprehend’. As gravity increases, electrons disproportionally occupy their lowest quantum mechanical orbitals around the atomic nucleus. When these are filled, electrons cannot descend further in energy, nor overlap (exclusion principle) and hence generate a quantum counter ‘pressure’ to gravity. This works up a limit of about 1.4-1.44 solar masses in a white dwarf depending on its angular momentum (angular momentum = energy = mass per E=MC^2).
2. Neutron degeneracy. Past the electron degeneracy limit, gravity forces protons to merge with electrons to become more neutrons via the weak force, creating neutron stars. (I might be missing a neutrino somewhere). This is just the inverse of Weak Force radioactive beta decay, and also the speculated inverse weak force physics behind observational LENR (explained and illustrated in my ebook The Arts of Truth). The concept is the same as for electron degeneracy, but the forces are different. Neutron stars are about 1.4- 2.1 sol depending on angular momentum. Below 1.4 they remain white dwarfs without electron/proton merger. Above 2.1, they further collapse into black holes.
3. In theory, there should be a third gravitationally degenerate state of fermion matter, a quarkstar, since neutrons are ‘just’ bundles of quarks, in quantum theory still fermions. In fact there is serious astrophysical speculation that in larger neutron stars, the core IS a ‘quarkstar’. Nothing such has been observed except (inferred from their surroundings) black holes. This leads to two weird possibilities. Either general relativity is ‘wrong’ in this extreme, and black holes are not an ‘infinite’ gravitational  well ‘point’ as general relativity would predict, but rather a quarkstar (by definition not a singularity point). OR all the quark fermions are somehow directly converted to bosons (like photons) concentrated by extreme gravity into a ‘point’ boson singularity. The problem with that is bosons do not have mass to create black hole gravity. Quantum weirdness.

Nobody knows (yet) about black hole details, because macro general relativity gravity and micro quantum physics have not been reconciled even using string theory. There is no viable theory of quantum gravity, unlike for the other three known forces. Just here an none asrophysicist noodling a deep astrophysics conundrum.

Original post question answered given the background astrophysics

If neutron stars are all neutrons, where the heck do their magnetic fields come from since Maxwell’s equations are likely correct????

Turns out, we dunno. There are three plausible theories presented below, ranging in (IMHO) order from probably at least partly true to maybe not true.

1. The neutron star pulsar magnetic field is a fossil, a ‘magnetic field conserved’ remnant of the original white dwarf’s magnetic field before its electrons and protons merged. The speculative issue is that Maxwell’s EM equations are ‘instantaneous”=>speed of light, so partial field collapse in small places should occur. Because the original white dwarfs are so ‘big’, and the neutron star collapse result so ‘small’ ( about 12-15km, with field strength a function of radius), the magnetic ‘fossil’ field calculations can get to about 10^12G assuming no partial collapse (G=Gauss—with super cooled superconducting magnets we have only been able to get to ~12 Gauss on Earth). But such speculative ‘fossil’ calculations still do not explain neutron star magnetars with inferentially observed magnetic fields up to >10^15G.
2. There is an additional ‘residual’ EM force during a neutron stars very rapid formational collapse. From first gravitational field considerations, the electron/proton collapse from ‘ordinary matter’ to ‘just’ neutrons must start at the bottom of the gravitational well, the star center. So the outer layers are still electrons and protons (increasingly rapidly rotating thanks to conservation of angular momentum as the object shrinks in diameter). And as these accelerate thanks to conservation of angular momentum, they create the extra Maxwell equation dynamo forces for magnetars.
3. Neutron stars are never only just neutrons. They have a thin (think 3 cm of ‘normal matter’ comprised of atoms with a nucleus and electrons) residual ‘atmosphere’ just outside their neutron star gravity well, and this ‘atmosphere’ creates the observed magnetic field in a rapidly rotating (up to 700 revolutions/second measured, the figure skater conservation of momentum spin effect in the extreme)) neutron star. The issue here is what keeps the thin supposed normal atomic ‘atmosphere’ from eventually also collapsing? Frictional heating from the enormous angular momentum at the interface?

I dunno. But I do find astrophysics conceptual modeling interesting to noodle.

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