The Diffuse Interstellar Medium ISM

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• The Diffuse Interstellar Medium (ISM)
• Lecture Topics
• the 21-cm line in emission and absorption
• heating-cooling balance and the phases of the
  ISM
• turbulence and structure in the Diffuse ISM
• magnetic fields, polarization and Faraday
  tomography

John M. Dickey University of Tasmania 21 February
2008
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• The presence of magnetic fields in the
  interstellar
• medium has been known since the 1940s due to
• coherent patterns in the polarization of
  starlight.
• These are explained by variations on the Davis-
• Greenstein Effect (1951, Ap.J.), which predicts
  that
• grains should align with their short axis
  parallel to
• the magnetic field due to
• non-spherical grain shapes
• rapid spin rates by equipartition of energy
• paramagnetic relaxation (some Fe atoms)
• Recent variations include diamagnetic inclusions
• in the grains, electric charge on the grains,
• eddy currents, and different behavior in
  different environments.

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Once the grains are aligned, the polarization of
the starlight happens because the E field of the
radiation is more attenuated by inducing currents
in the grain in the direction of the long axis
than in the direction of the short axis of the
grain. The overall effect is a small fraction (a
few percent) of the total attenuation of the
radiation by the grain, AV. The direction of the
resulting linear polarization is parallel to the
magnetic field direction. A common expression
for the fractional () linear polarization of
light is
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Observations show that P increases with AV,
but to a power between 0.5 and 1.0. This is to
be expected if the magnetic field is partly
random along the line of sight, partly ordered.
(from Jones et al. 1992 Ap. J. 389, 602)
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Nearby magnetic field structures are mostly seen
in both starlight polarization and the linear
polarization of the diffuse synchrotron emission
from cosmic ray particles at radio frequencies.
But the radio polarization (perpendicular to the
magnetic field direction) also shows Faraday
rotation, a frequency dependence of the position
angle of the linear polarization.
Neininger et al. 1993
In spiral galaxies the field usually follows the
spiral arms, although M31 seems to have an
azimuthal field. Faraday rotation suggests a
bisymmetric spiral.
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Sofue and Fujimoto1, 1985, IAU Symposium 106, 251.
This was one of the very first presentations of
what is now the standard paradigm of the Milky
Way magnetic field.
1Nagoya University
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The physics of Faraday Rotation is similar to
that of plasma dispersion. Both effects cause a
non-linear relationship between frequency, f, and
wavenumber, k, for the electromagnetic waves.
This comes from the dielectric constant of a
plasma with n the electron density, e and m
the electron charge and mass, and w and k the
angular frequency and wave vector of the wave
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This leads to the dispersion relation
where wp and fp are the plasma frequency in
radians per second and in Hz, respectively.
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From the dispersion relation we can find the
phase velocity and, more important, the group
velocity, vg
In astrophysical environments fp is generally
less than 1 MHz, so fp/f is a small number.
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What is the difference in arrival time, ta, for a
pulse observed at 1000 MHz and 1001 MHz, if ne
0.03 cm-3 and L 300 pc.
Pulse arrival times depend on the column integral
of vg-1
So the arrival time, ta, as a function of
frequency, f, gives the dispersion measure, DM
with ne in cm-3
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For a magnetized plasma, the electrons will
gyrate around the magnetic field, making slightly
faster and tighter circles when driven by right
hand circular (rhc) polarization propagating
along the direction of the B field. Thus the
effective dielectric constant is slightly less
for rhc than for lhc polarization
Where wc is the cyclotron frequency
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At a given frequency, f, there is a difference in
the group velocities of the two circular
polarizations. An electromagnetic wave with
linear polarization can be decomposed into two
opposite circular polarization waves superposed,
with a phase difference, y, that sets the
direction of the plane of linear polarization.
This phase difference changes with time as the
wave propagates, so the plane rotates
What is the difference in arrival time, ta, for
the two circular polarizations of a pulse
observed at 1 GHz if ne 0.03 cm-3 L 300 pc,
and B 3 mG ?
Where RM is the rotation measure
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where U and Q are the Stokes parameters of linear
polarization, i.e. orthogonal components of the E
field.
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Faraday rotation of polarized point sources
probes lines of sight through the Galactic
interstellar medium
RM gt 0 RM lt 0
Figure courtesy Jo-Anne Brown via Marijke
Haverkorn
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Faraday rotation of polarized extragalactic point
sources probes a line of sight through the
Galactic interstellar medium
from Brown et al. 2007 (Jo-Anne Brown, Marijke
Haverkorn )
circle size shows the magnitude of RM, filled
vs. open shows positive vs. negative RM
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Large-scale structure in RMs of extragalactic
point sources
Brown, MH et al 2007
Figure 2 of Brown, Haverkorn et al. (2007)
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- Extrema in RM correlate with spiral arms - Sign
changes in RM indicate magnetic field reversals
Brown, MH et al 2007
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Modeling of the large-scale Galactic magnetic
field
Brown et al. 2007
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A single magnetic field reversal can explain the
RM structure
Brown, MH et al 2007
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• Han et al. 2006 (RMs of 388 pulsars)

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Linear Polarized Structures unrelated to the
total synchrotron intensity depolarization and
Faraday rotation
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At low latitudes there is lots of diffuse linear
polarized emission by cosmic ray electrons
producing synchrotron emission in the Galactic
magnetic field.
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This linearly polarized emission can be
depolarized by intense Faraday rotation that
changes over small scales, as in a region of
diffuse Ha emission
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Depolarization yields information on the
structure of the ISM
H II region RCW 94 (Gaensler et al. 2001)
- Mild depolarization in interior Brandom 1.2
mG, with outer scale l 0.2 pc
- Strong depolarization at rim due to RM
gradient in photodissociation region
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Structures unrelated to the total synchrotron
intensity depolarization and Faraday rotation
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New method of detecting magnetic structures
CO images courtesy of Naomi McClure-Griffiths and
NANTEN CO survey group given to JD by Marijke
Haverkorn.
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The Penticton Lens - Gray et al. 1999, Uyaniker
et al. 2003
Structures in the linear polarization of the
Galactic synchrotron emission
due to Faraday rotation in the intervening
medium.
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Linear polarized emission from radio synchrotron
emission modulated by the intervening Faraday
rotation.
Schnitzeler et al. 2007
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Structure Functions for the Emission Measure and
for the Rotation Measure in the Diffuse Ionized
Medium (Minter and Spangler 1996)
RM
EM
log (structure function)
0.1o 1o 10o
0.1o 1o 10o
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Structure function of the RM (and DM
)between spiral arms (top row) and through
spiral arms (bottom row) Haverkorn et al. 2006

Question On what scales does the magnetic
field dominate the gas pressure to drive the
dynamics of the cascade?
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Gaensler et al. 2005 MPEG conference p.
209 (MPEG Magnetized Plasma in Galaxy
Evolution)
LMC
from Klein et al. (1993)
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• Rotation Measures in the LMC

gray scale Ha emission
filled and open circles measured positive and
negative RMs
Gaensler et al. 2005 Science 307, 1610.
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Evidence for random B fields with magnitude gt 5
mG on scales of lt 0.5 pc in the LMC that cause
in-situ depolarization of emission.
Gaensler et al. 2005 Sci 307, 1610.
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Faraday Tomography We use the fact that
Faraday Rotation has the form of a Fourier
Transform, to determine the distribution of
the linearly polarized emission along the line
of sight.

• New concepts
• Stokes Q and U (components of the linear
  polarization)
• become the real and imaginary axes of the
  complex plane.
• The measured polarized brightness becomes a
  complex
• function, i.e. it has a real and an imaginary
  value.
• Faraday depth becomes the Fourier conjugate
  variable to
• l2 (observed)
• The position angle of the radiation as a
  function of l2
• is a function whose Fourier Transform gives
  the
• distribution of the emission as a function
  of Faraday depth

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from before
and
f
from Brentjens and de Bruyn (2005 AA 441, 1217)
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Faraday depth is analogous to optical depth
Note f is not just an observed number, it is an
independent variable that increases or decreases
along the line of sight, just like t, but f does
not have to increase monotonically with s.
This is a continuum process, so f is not a
function of f, as tf is, but Faraday rotation is
a function of l2, so we need to do spectroscopy
in order to measure the emission, F(f) as a
function of f.
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s
s
from Brentjens and de Bruyn (2005 AA 441, 1217)
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From Brentjens and de Bruyn Superposition of
polarized emission from different places along
the line of sight, with different Faraday depths,
f.
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The Fourier conjugate relationship between the
observed linear polarized brightness as a
function of wavelength squared, and the emission
as a function of Faraday depth along the line of
sight
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• Polarized Intensity vs. Faraday Depth
• (Faraday Depth is Fourier conjugate to l2)

Brentjens and de Bruyn, 2005 Astron. Astrop. 441,
1217.
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de Bruyn et al. 2006 Astronomische Nachrichten
327, 487.
This is one plane from a cube of data.
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Mapping the diffuse polarized emission from the
Milky Way and then Fourier Transforming with
respect to l2 gives us a Faraday cube, analogous
to a spectral line cube, with emission vs. right
ascension, declination, and Faraday depth. The
challenge is to make such a cube for the entire
sky the GMIMS survey (Global Magneto-Ionic
Medium Survey) Wolleben and Landecker (DRAO -
Canada) plus team.
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Spectral line absorption of polarized continuum
emission
Dickey 1997 Ap. J. 488, 258.
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• Conclusion
• Galactic astronomy can be fun and interesting.
• There is lots more to do, and we have the tools
  we need to do new things.
• The international community of Galactic
  astronomers is a lot of friendly, happy people.
• You should join us!

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Depolarization canals
are almost everywhere!
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Conclusion

• Soon we will fill in the gaps by measuring on all
  scales from a few thousand km to a few kpc
• density
• velocity (magnitude and direction)
• magnetic field (magnitude and direction)
• ionization fraction
• The Square Kilometer Array telescope will do it!

(Dickey et al. 2005 New Astr. Rev.)
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Ground state excitation of CI shows the
interstellar pressure distribution function is
bimodal 102 lt p lt 107
p107
p106
p105
p104
Jenkins and Tripp 2001 Ap. J. Supp. 137, 297.
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The Pressure Fluctuations associated with tiny
scale structure are not a problem.

• But why is the pressure
• distribution function bimodal?

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• What about the magnetic field?
• The magnetic field shows a spectrum of
  irregularities superposed on a large scale
  pattern. Does this reflect the same underlying
  turbulence as seen in the density and velocity
  fields? If not, can we understand why not? If
  so, which forces dominate the dynamics on what
  scales?