MAGNETIC FIELDS and the early universe

1. MAGNETIC FIELDS and the early universe Joshua Goldston Ay 228 11 28 02 Note: This is a modification of a presentation given to C.-P. Ma’s Astronomy 228 course (Cosmology) on 11/28/02 in the berkeley astronomy department. The red text is an approximation of my spoken notes during the slide show, and the rest is, essentially, the show presented to the class. Also please excuse the extremely bad html export technology offered by Microsoft Powerpoint. Bill Gates should hang his head in shame. Joshua Goldston, 12/07/02 Much of cosmology is involved in the derivation, contemplation and deduction of the so-called cosmological constants, parameters that define various aspects of the history and structure of our universe. This line of thinking sheds light on the cosmos as a whole, but we can also investigate the history of the universe, and its structure via other means. In this report I attempt to lay out the current understanding of cosmic magnetic fields both in the present and in the past. I explain the current understanding of galactic magnetic fields and the techniques used to observe them, as well as laying out some constraints for the age at which these magnetic fields sprung into being. I outline a few of the processes by which fields could have come to exist, and narrow them down to the influence of the ‘Biermann Battery’ term in the expanded magneto-hydrodynamics equations. I then go on to show a simplified analytic model of magnetic field generation in proto-galaxies and show what the current advanced computer models predict for the magnitude of this process. I explain the significance of this magnetic field scale and the importance of magnetic dynamo theory in the bootstrapping of this field.

2. What yer gettin’ yerself into: What are current magnetic field strengths and Where do we observe them? When did they come to exist? How did they come to exist? Who knows a whole heck of a lot more about this stuff than I do?

3. We can measure magnetic fields in our own galaxy in the present epoch by looking for synchrotron emission in our galaxy, as well as polarization of dust grains. In the case of synchrotron emission, two main parameters contribute to the signal strength; the magnetic field present and the electron energy distribution function. Usually, in the case of extra-galactic sources, the argument is made that in the minimum energy configuration there will be as much energy in the magnetic fields themselves as in the electron kinetic energy, and that fields will tend to be this way. This is typically referred to as the ‘equipartition argument’, which I will not go through in detail. In the case of the galactic magnetic fields we can somewhat verify this claim by taking a direct measurement of the energy distribution of cosmic ray electrons, which does seem to agree with the more gross assumption. By looking at the polarization percentage of dust grains in the galaxy, we can determine the extent to which the field is totally random or aligned in a poloidal (radial or z directed) or toroidal (phi directed) manner. Observations seem to show that about 2/3 of the field is toroidally oriented. This begs the question of the origin of these coherent fields. Current observations of magnetic fields: Synchrotron Emission + Equipartition / minimum energy arguments Direct measurement of cosmic ray electron energy density

4. The age of these magnetic fields is in question, so we should start at the beginning, before combination, z > 1000. In terms of observational constraints, magnetic fields are notoriously hard to see, as is their CMB signature. The essential difficulty is that perturbations in the ‘traceless fluid’ element of matter and 3-curvature will have exactly the same effect upon the CMB as an early magnetic field: they both leave a shear anisotropy in the CMB. This means that the upper limit on magnetic fields must assume that the entirety of the shear anisotropy comes from magnetic fields, as if we assumed that any of the shear came from the other perturbations, we would be lowering that limit. The limit imposed, |B| < 10-9 Gauss, is a very weak one, as there would need to be no other magnetic process, other than compression, to amplify the field up to the current levels. Very weak constraints from CMB: How old could magnetic fields possibly be, and at what strength? Perturbation in traceless fluid + 3-curvature Shear anisotropy in CMB Assumption: Magnetic fields dominate contribution to shear

5. There are a few ideas as to how the universe could create very early magnetic fields. Some complex inflationary theories and very early unification theories predict some contribution to the magnetic field, but none of them are any more than theoretical possibilities at this point, and therefore do not allow us to put any reliable limits on the early fields. A less exotic idea is that vortices could have been created in the primordial fluctuations. These vortices would rotate matter through the CBR photons, and the drag on electrons would vastly exceed the drag on ions. This would generate a current in the vortex, and therefore a magnetic field. These modes, though, are highly suppressed compared to other perturbations, and even at the maximum allowable intensities, given constraints from modern galaxy angular momentum, they would only yield very, very small magnetic field strengths, |B| < 10-21 Gauss, too small to be used for galaxy magnetic field formation. Mechanisms for Magnetic field production pre-combination: 1. Crazy early stuff: During QCD/Electroweak first order cosmic phase transitions During inflation Problems: No constraints, unproven, speculative 2. Vorticity in primordial fluctuations Drag on electrons by CMB photons creates currents Problems: Vorticity highly damped by irrotational modes So where do magnetic fields come from, huh? Mr. Smartypants?

6. In this slide I try to motivate the derivation of the Biermann battery term. This is the most direct derivation of one of the equations of MHD, and is interesting because it gives us the change in the magnetic field with time in a conducting fluid. We are interested in charting the history of the magnetic field, so the structure of this equation is of the utmost importance. Speed MHD! force/volume relation: negligible electron inertia: maxwell: maxwell: maxwell:

7. The Biermann Battery term is of interest because it is the only ‘non-bootstrapping’ term in the equation; all other terms require a seed magnetic field to increase the magnetic fields strength. The Biermann Battery term is usually written as dependent upon the cross product of the temperature gradient and the free electron gradient, as it is in the final form on this slide. But Josh, you may ask, what does it all mean?? Depend upon pre-existing magnetic field term Magnetic field independent! Possible generator for seed magnetic fields! Biermann Battery Term

8. This term is frequently seen as useful in the propagation of ionization fronts in the early universe. It is thought that in the early universe, young, hot stars (and perhaps quasars) formed and began to emit photons with frequencies in the UV and higher, capable of ionizing the then bound hydrogen. As these ionization fronts expanded through the over dense protogalaxies, they encountered non-zero temperature gradients that were not entirely collinear with the ionization fronts, which could have generated some magnetic fields. Where, pray tell, do we get a gradient in electron density? Early stars or quasars (z ~ 7) UV and soft X-ray photons Ionization fronts / expanding HII regions

9. In a simple, analytic calculation, we can imagine an overdensity with a warmer core, as pictured in the rendering. An illustrative example: Imagine a neutral temperature / density distribution:

10. Ionization fronts could then propagate through the region, as below. The top (purple) of the z axis is 100% ionization and the bottom (green) is 0%.

11. This can create a magnetic field: The ionization front propagates through the overdensity, generating a magnetic field as the electron gradient moves through the temperature perturbation.

12. The magnetic field, seen here in cross-section, is just an example of a possible generated magnetic field. Its geometric form is highly dependant upon the functions that define the ionization front and the overdensity. It is important to see, though, that in any simple configuration magnetic fields will be generated and persist. In cross section:

13. In recent simulations based on these processes, you can see that in later epochs, as over-dense regions lose their neutral hydrogen, i.e. become ionized, magnetic fields are created. These fields have typical values on the order of 10-18 Gauss. Enough of analytics: What do the simulations say? z=5.9 z=5.5 magnetic field strength neutral H magnetic field strength neutral H gas temperature gas density gas density gas temperature Punchline: this generates

14. Of course these levels of magnetic field strength are too small to be directly relevant to today’s magnetic fields, but they are coherent, and they are strong enough to serve as seed field for the other terms in the equation to bootstrap the magnetic field to something more reasonable. These effects are usually framed within the theory of galactic dynamos. In essence, galactic dynamos depend on the differential rotation of the galactic disc to stretch out B field lines, called the effect, and the cyclonic motion from the coriolis force that tends to wind up toroidal magnetic fields off the plane of the galaxy, called the effect. These effects, though, depend on coherent, large scale fields, as produced by the Biermann Battery in primordial reionization in the early epoch. They are also limited somewhat by the age of the galaxy, and the number of rotations it has gone through. In the age of the universe, given the number of rotations of a galaxy since formation, current theories require about the field given by the simulations at reionization (z~5). Hold on a second, buster, you may exclaim, you said 10-6 G! Galactic dynamos able to use coherent fields to ramp up field strength

15. Some conclusions! Magnetic fields are coherent and on the order of 10-6 Gauss in galaxies There are no obvious ways to create magnetic fields before combination Reionization can generate magnetic fields via the Biermann battery term These magnetic fields are simulated to have a strength on the order of 10-18 Gauss Galactic Dynamos can increase this ‘seed’ field to the observed values.

16. Some good info on the topic: Beck, astro-ph/0012402. (observed galactic magnetic fields) Barrow et al, PRL Vol. 78 No. 19. (constraints on pre-CMB fields) George Field, Notes for A213: Magnetohydrodynamics, Harvard University, Chapters 1& 9,1997. (MHD, biermann batttery) Shu, Gas Dynamics, Chapter 20. (HII regions, theory) Gnedin et al, ApJ 2000 539:505. (simulations of reionization) Kulsrud et al, ARA&A 1999 37:37-64. (galactic dynamos)

17. Some puppies: