I came across an article in New Scientist recently on the topic of cosmological magnetism. The piece is about an article by Leonardo Campanelli, which is available on the arXiv and which is apparently due to be published in Physical Review Letters. So it must be right.
Here’s the abstract
We calculate, in the free Maxwell theory, the renormalized quantum vacuum expectation value of the two-point magnetic correlation function in de Sitter inflation. We find that quantum magnetic fluctuations remain constant during inflation instead of being washed out adiabatically, as usually assumed in the literature. The quantum-to-classical transition of super-Hubble magnetic modes during inflation, allow us to treat the magnetic field classically after reheating, when it is coupled to the primeval plasma. The actual magnetic field is scale independent and has an intensity of few \times 10^(-12) G if the energy scale of inflation is few \times 10^(16) GeV. Such a field account for galactic and galaxy cluster magnetic fields.
So why is this interesting? Let me explain….
If you’re stuck for a question to ask at the end of an astronomy seminar and don’t want to reveal the fact that you were asleep for most of it, there are some general questions that you can nearly always ask regardless of the topic of the talk without appearing foolish. A few years ago, “how would the presence of dust affect your conclusions?” was quite a good one, but the danger these days is that with the development of far-infrared and submillimetre instrumentation and the proliferation of people using it, this could actually have been the topic of the talk you just dozed through. However, no technological advances have threatened the viability of another old stalwart: “What about magnetic fields?”.
In theory, galaxies condense out of the Big Bang as lumps of dark matter. Seeded by primordial density fluctuations and amplified by the action of gravity, these are supposed to grow in a hierarchical, bottom-up fashion with little blobs forming first and then merging into larger objects. The physics of this process is relatively simple (at least if the dark matter is cold) as it involves only gravity.
But, by definition, the dark matter can’t be seen. At least not directly, though its presence can be inferred indirectly by dynamical measurements and gravitational lensing. What astronomers generally see is starlight, although it often arrives at the telescope in an unfamiliar part of the spectrum owing to the redshifting effect of the expansion of the Universe. The stars in galaxies sit inside the blobs of dark matter, which are usually called “haloes” although blobs is a better name. In art the whole purpose of a halo is that you can see it.
How stars form is a very complicated question to answer even when you’re asking about nearby stellar nurseries like the Orion Nebula. The basic idea is that a gas cloud cools and contracts, radiating away energy until it gets sufficiently hot that nuclear burning switches on and pressure is generated that can oppose further collapse. The early stages of this processs, though, involve very many imponderables. Star formation doesn’t just involve gravity but lots of other processes, including additional volumes of Landau & Lifshitz, such as hydrodynamics, radiative transfer and, yes, magnetic fields. Naively, despite the complicated physics, it might still be imagined that stars form in the little blobs of dark matter first and then gradually get incorporated in larger objects.
Unfortunately, it is becoming increasingly obvious that this naive picture doesn’t quite work. Deep surveys of galaxies suggest that the most massive galaxies formed their stars quite early in the Big Bang and have been relatively quiescent since then, while smaller objects contain younger stars. In other words, pretty much the opposite of what one might have thought. This phenomenon (known as “downsizing”) suggests that something inhibits star formation early on in all but the largest of the largest haloes. It could be that powerful feedback from activity in the nuclear regions associated with a central black hole might do this, or it could be something a little less exotic such as stellar winds. Or it could be that the whole scheme is wrong in a more fundamental way. I personally wouldn’t go so far as to throw out the whole framework, as it has scored many successes, but it is definitely an open question what is going on.
A paper in Nature a few years ago by Art Wolfe and collaborators revealed the presence of an enormously strong magnetic field in a galaxy at the relatively high redshift of 0.692. Actually it’s about 84 microGauss. OK, so this is just one object but the magnetic field in it is remarkably strong. It could be a freak occurrence resulting from some kind of shock or bubble, but it does seem to fit in a pattern in which young galaxies generally seem to have much higher magnetic fields than previously expected. Obviously we need to know how many more such magnetic monsters are lurking out there.
So why are these results so surprising? Didn’t we already know galaxies have magnetic fields in them?
Well, yes we did. The Milky Way has a magnetic field with a strength of about 10 microGauss, much lower than that discovered by Wolfe et al. But the point is that if we understand them properly, galactic magnetic fields are supposed to be have been much lower in the past than they are now. The standard theoretical picture is that a (tiny) initial seed field is amplified by a kind of dynamo operating by virtue of the strong differential rotation in disk galaxies. This makes the field grow exponentially with time so that only a few rotations of the galaxy are needed to make a large field out of a very small one. Eventually this dynamo probably quenches when the field has an energy density comparable to the gas in the galaxy (which is roughly the situation we find in our own Galaxy).
Hopefully you now see the problem. If the field is being wound up quickly then younger galaxies (those whose light comes to us from a long way away) should have much smaller magnetic fields than nearby ones. But they don’t seem to behave in this way.
A few years ago, I wrote a paper about a model in which the galactic fields weren’t produced by a dynamo but were primordial in origin and quite large from the start. If that’s the case then the magnetic field need not evolve as quickly as it needs to if the initial field is very tiny.
The problem is that it has previously been thought very difficult for any cosmological model involving inflation to generate a significant primordial magnetic field without invoking very exotic physics, such as breaking the conformal invariance of electrodynamics (which would mean, among other things, giving the photon a rest mass).
The interesting thing about Campanelli’s paper is that it suggests a straightforwardmechanism for inflation to generate interesting magnetic phenomena. I’m not an expert on the techniques used in this paper, so can’t comment on the accuracy of the calculations. I’d be very grateful for any comments on this, actually. Me, I’m an old fogey who’s very suspicious of anything that relies too heavily on renormalization. I do however agree with Larry Widrow, quoted in the New Scientist piece.
But even if primordial magnetic fields can be generated by inflation, their impact on the origin and evolution of galaxies and other cosmic structures remains unsolved. Although we know magnetism exists, it is notoriously difficult to understand its behaviour when it is coupled to all the other messy things we have to deal with in astrophysics. It’s a kind of polar opposite of dark matter, which we don’t know (for sure) exists but which only acts through gravity, so its behaviour is easier to model. This is the main reason why cosmological theorists prefer to think about dark matter rather than magnetic fields. I’d hazard a guess that this is one problem that won’t be resolved soon either. Things are complicated enough already!
It is also worth considering the possibility that magnetic fields might play a role in moderating the processes by which gas turns into stars within protogalaxies. At the very least, a magnetic field generates stresses that influence the onset of collapse. Although the evidence is mounting that they may be important, it is still by no means obvious that magnetic fields do provide the required missing link between dark matter haloes and stars. On the other hand, we now have fewer reasons for ignoring them.
has a normal distribution with zero mean and variance 
. Consider the variable
is a constant. What is the probability density of 
?
, under the action of a force given by the derivative 
, opposed by a “frictional” force depending on the ball’s speed; in the inflationary context the frictional force depends on the expansion rate 
. If the slope of the potential is relatively shallow then there is a slow-rolling regime during which the kinetic energy of the field is negligible compared to its potential energy; the term in 
then becomes negligible in the above equation. The universe then enters a near-exponential phase of expansion, during which the small Gaussian quantum fluctuations in 
become Gaussian classical metric perturbations.
describes a quadratic contribution to the overall metric perturbation 
: you can think of this as being like a power series expansion of the total fluctuation in terms of a Gaussian component 
; the term in angle brackets is just there to ensure the whole thing averages to zero. This definition of non-Gaussianity is not the only one possible, but it’s the simplest and it’s the one for which Planck has produced the most dramatic result:
. The quadratic terms are therefore of order 
, so the upper limit on the level of non-Gaussianity allowed by Planck really is minuscule. This is one of the reasons why some people have described the best-fitting model emerging from Planck as the Maximally Boring Universe…
In the Dark 
