PowerPoint Presentation Cosmic Magnetic Fields: AY228 Presentation

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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. Mas 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.
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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?
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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
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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 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
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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 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?
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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
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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
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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
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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
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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.
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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.
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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
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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?
z5.9
z5.5
magnetic field strength
neutral H
neutral H
magnetic field strength
gas temperature
gas density
gas density
gas temperature
Punchline this generates
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Of course these levels of magnetic field strength
are too small to be directly relevant to todays
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 (z5).
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
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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.
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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 539505. (simulations of
reionization)
Kulsrud et al, ARAA 1999 3737-64. (galactic
dynamos)
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Some puppies