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 ISM
• magnetic fields, polarization and Faraday
  tomography

John M. Dickey University of Tasmania February
2008
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Different Names for Overlapping Concepts
Diffuse ISM Photo-Dissociation Region
Translucent Clouds
Diffuse ISM implies density nH less than 103
cm-3, as needed for collisional excitation of the
CO line at 3mm.
Photo-Dissociation Region implies molecular
destruction by ultraviolet (but not ionizing)
photons that do not penetrate beyond column
density NH 1021 cm-2. These are often called
Translucent Clouds, meaning light can get
through, but they are not transparent. These
terms come from the molecular-line community, for
whom the real diffuse medium is too thin to
notice
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• Why Study the Diffuse ISM at l21-cm?
• because 21-cm is an easy wavelength to observe
• because atomic hydrogen (HI) is very widespread
• because emission and absorption are both visible
• because it fills in the least understood part of
  the
• Cycle of Galactic Evolution

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Completing the Cycle
SN explosions
soft x-rays
Hot gas
shells
diffuse Ha pulsar dispersion and
scattering Faraday rotation
winds
chimneys
warm ionized medium
Turbulence
21- cm emission
nucleosynthesis
warm neutral medium
21- cm absorption
Diffuse clouds
Molecular clouds
OH, CO, NH3, HCN, HCO, emission
Star formation
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Next Basic equations from physics dealing with
radiation and excitation of energy levels. We
need to know simple spectroscopy concepts to be
able to interpret spectral line tracers of the
diffuse medium. These should be familiar to most
people, stop me if theyre not clear.
Check can you answer the questions in the blue
boxes in your head? What is a typical density
in the diffuse medium?
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Starting with the equations for excitation
of energy levels in an atom (Boltzmanns
equation)
Tex
and for the distribution of energy in a
black-body spectrum (Plancks equation), units
(e.g.) watt m-2 Hz-1 sterrad-1
Trad
where c is the speed of light, f is the
frequency, T is the temperature, h is Plancks
constant, k is Boltzmanns constant, gj is the
quantum mechanical multiplicity of level j, nj
is the number density of atoms in level j, Eij is
the energy separation between levels i and j, and
If Df is the energy emitted or absorbed in
frequency range Df (m-2 s-1 sterrad-1).
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For all centimeter-wave spectral lines, the
energy spacing of the levels must be very small,
much less than kT, whether or not the excitation
temperature, Tex, is the same as the
kinetic temperature, Tkin, or the radiation
temperature, Trad, so
What is for f 1.4 GHz?
So we can expand the exponentials in both the
Boltzmann equation and the Planck equation, as
The Planck Function reduces to the Rayleigh-Jeans
Law
with T Trad called the brightness temperature,
TB, and l the wavelength.
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For a two-level system, the level populations are
nearly independent of temperature, the total
density is proportional to the number density in
the lower state, ni
If the spectral line is optically thin, and if
the two levels contain most of the population of
atoms, then the total density is proportional to
the emission coefficient of the line, which gives
the number of photons emitted per unit volume.
This is roughly independent of temperature.
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The emission coefficient, jf, is proportional to
the density only, nearly independent of
temperature.
For the 21-cm line f 1.4204 x 109 Hz and A21
2.85 x 10-15 sec-1 is the Einstein
spontaneous deexcitation rate, so we get
Here p(f) is a line shape or profile function
(units Hz-1 1/Df) normalized to have integral
equal to 1
Red border means this applies to one particular
case, not all lines.
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If the line is optically thin the intensity of
the radiation we see is proportional to the line
of sight (los, step ds) integral of the
emission coefficient, this is proportional to the
column density,
Here we are using brightness temperature, TB, as
a shorthand for the intensity of the radiation,
If. But now If is not just the Planck function
but any spectrum, i.e. the radiation intensity as
a function of frequency.
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A Longitude-velocity diagram from the
SGPS McClure-Griffiths and Dickey 2007
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An aside on the line profile function, p(f)
For an optically thin spectral line the profile
is a Gaussian with linewidth determined by the
kinetic temperature and Doppler shift (through
the Maxwellian distribution of thermal
velocities)
The temperature derived from the linewidth is
sometimes called TDopp, the Doppler temperature.
It is usually two or three times greater than the
kinetic temperature!
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A handy formula for conversion of Bandwidth from
frequency units to velocity units (Doppler
shift)
This is true of all spectral lines at all
frequencies, even X-ray lines. It means that a
bandwidth of 1 MHz corresponds to a velocity
width in km s-1 which equals the wavelength in mm.
Example For the 115 GHz CO line, l 2.7 mm.
So a band of width 1 MHz will span velocity range
of 2.7 km s-1. What bandwidth would be needed to
span a velocity range of 100 km s-1 when
observing the CO line at 345 GHz? What
bandwidth spans 100 km s-1 for the 21-cm line?
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Next what about the absorption coefficient, kf,
and its line of sight integral, the optical
depth tf
Absorption at cm-waves generally involves a
slight imbalance between stimulated emission and
absorption, i.e. the Bij and Bji Einstein
coefficients.
kf is the amount of radiation absorbed per unit
volume, but since this is proportional to the
radiation field intensity, the units of kf are
just length-1. So tf is dimensionless, and
the equivalent width, , has units
km s-1 or Hz.
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To evaluate the optical depth, we use the
relationship from quantum mechanics between the A
and B coefficients
Plugging into the first equation on the
preceding slide with the Boltzmann equation for
excitation, we find to zero order in
there is no absorption at all, i.e. stimulated
emission balances absorption. Taking the first
order term in the expansion gives
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And for tf the line of sight (los) integral of
kf gives
(21-cm line)
Integrating the absorption line in velocity (or
frequency) gives the total column integral of
density, n, divided by temperature, T , which
can be expressed as the column density divided
by the density-weighted harmonic
mean temperature,
(21-cm line)
As before, the constant becomes 1.8 x 1018 for N
in cgs units (atoms cm-2).
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Putting together the emission and absorption
At l21-cm we can measure both the emission
and absorption over an area of a few beamwidths
on the sky. By combining the emission brightness
temperature and the optical depth we can
compute the harmonic mean temperature, channel by
channel as a function of velocity across the
spectrum
This generally gives a parabola shape, because
the emission lines are broader than the
absorption lines.
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Emission-absorption spectra from Strasser et al.
2007
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Measuring the l21-cm emission and absorption

• The emission TB(v) and absorption t(v) can both
  be
• measured over a small area, but not for exactly
  the
• same gas. Examples
• the background continuum comes from a pulsar
• a compact background continuum source can be
  separated from the surrounding emission
• cool, optically thick gas absorbs 21-cm line
  emission from gas further away on the line of
  sight (called H-I Self-Absorption, HISA)
• absorption of the polarized continuum emission
  (Stokes Q, U)

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21-cm emission and absorption and
self-absorption from the Southern Galactic Plane
Survey
McClure-Griffiths et al. 2004
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Leafy Sea Dragon (Australian marine animal) photo
by Victoria Graham
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Parkes-only map - resolution 15 (this is only
a factor of 7 lower than the SGPS).
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The two-phase approximation assume just two
components of gas at a given velocity on the
line of sight cool and warm assume the warm
phase temperature (typically 6000 K) is so large
that this phase does not contribute much to the
optical depth then the harmonic mean temperature
becomes simply If we know (or guess) the cool
phase temperature, Tcool, then we can
determine the fraction of gas in the cool phase,
fcool
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Dickey et al. 2000, Ap. J. 536, 756.
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Interpretation of emission- absorption spectra
together
slope Tcool
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Strasser et al. 2007 A.J. 134, 2252.
This cloud is at a distance of 16 to 17 kpc from
the Galactic center.
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The excitation temperature of the 21-cm line is
always close to the kinetic temperature of the
gas in Galactic ISM conditions.
At densities above about 1 cm-3 this is due to
collisions (with electrons and other H atoms).
At lower densities the dominant process is the
Wouthuysen-Field effect. This relies on the
presence of Ly-a photons that scatter very
efficiently so that the Ly-a spectrum picks up a
color temperature set by the gas motions.
An excellent recent review is Astro-ph/0608032v2
Furlanetto, Oh, and Briggs, 2006, Physics Reports
433, 181.
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Thermalization of the 21-cm line by the
Wouthuysen-Field Effect radiative coupling with
the Ly-a line, which has color temperature
tightly coupled to the kinetic temperature.
Pritchard and Furlanetto 2006
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Excitation temperature of cosmological HI as a
function of redshift, z, before reionization
(Furlanetto et al. 2006)
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Hypothetical 21-cm excitation temperature vs.
redshift for reionization by uv radiation from
Population II stars
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The 32 tile (32T) system of the Murchison
Widefield Array - Low Frequency Demonstrator (MWA
- LFD) telescope as of November 2007.
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