Why arent Galaxies

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Why arent Galaxies Brighter at l21-cm ?
John Dickey
University of Minnesota
SGPS team Naomi McClure-Griffiths, ATNF
Bryan Gaensler, Harvard Uni.
Anne Green, Sydney Uni.
ATNF 19 February 2003
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Outline
1. l21-cm line background, CNM/WNM
2. Emission/Absorption spectrum pairs
3. (aside) The spatial power spectrum of 21-cm
emission
4. k (r) - the absorption coefficient vs.
Galactic radius
6. The peak brightness temperature of the Milky
Way
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GBT longitude-velocity diagram, contour at 120 K
Dickey, Kavars, Lockman, McClure-Griffiths 2003?
in prep
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All over the inner Galaxy, and in the outer
Galaxy in spots, the 21-cm brightness temperature
rises to 100 to 125 K, but no higher.
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21-cm line formulae the emission
coefficient
density n
erg
-33
j 1.6 10 n f( )
n
sec Hz sterrad
n
the brightness temperature
T ( ) j ds
n
n
B
-2
cm
18
-1
K km s
If the line is optically thin all along the line
of sight !
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density n, temperature T
the optical depth
the equivalent width (velocity integral of the
optical depth)
EW
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• Velocity integrals (over one channel, the entire
• spectrum, or any velocity range in between) give
• the column density, N

• for the emission spectrum (for low optical depth,
  t),
• the equivalent width, EW, for the absorption
  spectrum

Combining the two gives the density weighted
excitation temperature, Tspin . Tspin is
generally equal to the kinetic temperature in
the neutral gas.
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Note that ltTspgt is not a physical temperature,
but a blend of warm and cool phases along
the line of sight. If we know the mean cool
phase temperature, Tcool , then ltTspgt tells us
the fraction of gas in the cool phase, fc
fc
Ncool
Tcool

Nwarm Ncool
ltTspgt
The two-phase model comes from heating-cooling
equilibrium (Field, Goldsmith, and Habing, 1969,
Ap. J. Lett. 155, L149).
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Wolfire, M.G., Hollenbach, D., McKee, C.F.,
Tielens, A.G.G.M., and Bakes, E.L.O., 1995, Ap.
J. 443, 152.
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Wolfire, M.G., Hollenbach, D., McKee, C.F.,
Tielens, A.G.G.M., and Bakes, E.L.O., 1995, Ap.
J. 443, 152.
pressure
density
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McKee and Ostriker 1977, Ap. J. 218, 148.
Result the ISM pressure is always bouncing
around.
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How to get the Emission and Absorption Spectra
out of the data

• Filter the maps to eliminate as much of the
  emission as possible.
• Average over the pixels where the continuum is
  bright,
• weighting by the (filtered) continuum.

Absorption

• Interpolate the emission over the area of the
  continuum source,
• using pixels where the continuum is weak.
• Find the error envelope (channel by channel)
  from the scatter
• in these off source pixels about the fitted
  function.

Emission
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The optimum filter to eliminate the
emission depends on the uv distribution of both
the line emission and the continuum brightness.
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Aside on the spatial power spectrum of the
interstellar neutral hydrogen.
Spatial fluctuations in the 21-cm line emission
set the limit on the absorption spectrum, i.e.
the errors in the absorption spectrum are
primarily due to our inability to fully subtract
the emission in the direction of the continuum
source.
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In order to determine the possibilities for
absorption spectra, we want to study the
spatial power spectrum of the emission.
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Region 1. ATCA plus Parkes
Dickey, McClure-Griffiths, Stanimirovic,
Gaensler, Green 2001 Ap. J. 561, 264
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Region 2. ATCA only (but mosaicked !)
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The spatial power spectrum is the Fourier
Transform of the Structure Function
sky brightness distribution
fringe visibility function
Fourier conjugates
magnitude squared
autocorrelation
spatial power spectrum
structure function
Fourier conjugates
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The Structure Function
In the ionized gas (the WIM) we see a turbulence
spectrum over many orders of magnitude in scale
size.
Figure from Armstrong, Rickett, and Spangler
1995, Ap. J. 443, 209.
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Region 1. Same data, but now using channel
width 20 km/s instead of 0.82 km/s.
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The slope of the power law changes with velocity
width !
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Turbulence theory predicts that the slope should
steepen by one unit when we go from a thin slice
to a thick slice of the medium (Lazarian and
Pogosyan 2000 Ap. J. 537, 720).
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The spatial power spectrum of a spectral line
tracer gives us the ability to trace the small
scale structure of the ISM dynamically. The
slope change with velocity width is direct
confirmation that the power law structure
function is actually tracing turbulence, rather
than some other random process with power law
statistics.
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(back on track) ...
Now we can define an optimum filter, remove the
emission, measure the absorption and emission
spectrum pairs, and we get ...
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What do we do with these ? 1. Study
the distribution of CNM in the Galaxy (for
this we use only the absorption spectra) 2.
Study the temperature of the CNM (for this
we combine the emission and absorption)
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The galactic rotation curve tells us the velocity
as a function of distance along the line of
sight, v(r).
The velocity gradient, dv/dr, tells us the
path length corresponding to a given
bandwidth (e.g. one channel).
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The velocity field due to Galactic rotation
sets v(r) , the radial velocity as a function of
distance along the line of sight.
r
Dr
v
DV
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We compute the opacity, lt k gt from the optical
depth integral divided by the corresponding path
length
EW is the equivalent width
lt k gt is the line-of-sight averaged opacity
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The opacity is larger in the inner Galaxy than it
is at the solar circle. It may be modulated by
the spiral arms.
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The higher opacity in the inner Galaxy suggests
that either there is more cool phase gas
(relative to warm, fc ) or the median cool phase
temperature (Tcool ) is colder in the inner Milky
Way than at the solar circle, or some of each.
This argues against most of the H I being
recently photo-dissociated H2.
e.g. Allen 2001
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What is the temperature of the cool HI (CNM) ?
We can measure this by combining the emission and
absorption spectra channel by channel. But we
must somehow separate the emission from the WNM,
that shows no absorption because it is too warm
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If all the gas at a given velocity were at the
same temperature, we could measure the
excitation temperature (spin temperature)
directly
But in each velocity channel there is overlap of
several regions with different temperatures
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We make the two-phase assumption, that
the absorption comes from the CNM only.
b
f
density n, temperature Tcool
The emission comes from the CNM, plus the WNM
(with brightness temp., Tw, proportional to
its column density) in front (f) and behind (b)
the cool gas.
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What we just had was
Next subtract the continuum to get the line
brightness temp
Define x ( 1 - e-t )
The warm gas has much broader linewidths than the
CNM, so over the velocity range covered by one
absorption line we can approximate the WNM
emission by a linear function of v
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Tw,b
Now define e to be the background fraction of Tw
, i.e. e
Tw,b Tw,f
We measure both x and TB for all velocities,
v, across each absorption line. We assume a
value for e and then least-squares fit the values
of co , c1 , and c2 separately for each
absorption line.
This is a linear least-squares fit. No first
guess, no local minima the solution is unique.
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Example Fitting two absorption lines toward a
continuum source at intermediate latitudes (data
from Heiles and Troland, 2003, Ap. J. in press,
from Arecibo).
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HISA HI self-absorption
Whenever the coefficient c2 is less than zero,
then the absorption line decreases the brightness
temp, i.e. this is HISA. Two out of three
absorption lines show c2 lt 0 !
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In the end, we get a distribution of CNM
temperatures among the different absorption
lines, depending on the assumed value of e.
The median value is 65 K, but note the tail
toward low temperatures (lt 30 K).
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Now we put together our results for lt k gt and
Tcool to explain the peak brightness temperature
(125 K for the Milky Way).
Low latitude lines of sight can be in either of
two regimes, depending on the dimensionless
parameter, r
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If r ltlt 1 then the gas is mostly optically thin,
we will see isolated absorption lines covering a
small fraction of the velocities.
If r gtgt 1 then the gas is mostly
optically thick, we see blended absorption
lines covering most of the velocity range. This
is the case in much of the inner Galaxy.
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In the case of r gt 1, the line of sight
distance through the medium, Ds, that would give
enough absorption to cover velocity width DV is

This comes from the definition
The warm phase column density over this path is
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This warm phase column density gives
emission with brightness temperature
(The approximation comes from the fact that the
linewidths in the WNM are broad, much broader
than the absorption lines.)
So.
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Note that the velocity width, DV, cancels out, so
whatever we assume for that we get the same
result,
nw

Tw
CH
lt k gt
-3
-1
-1
For nw in cm , lt k gt in (km s kpc ) and T
in K then CH has the value 5.9 10 .
-4
-3
-1
-1
If nw 0.25 cm , and lt k gt 5 km s kpc
then Tw 80 K. Call this Tw,u since it is
so far unabsorbed by the CNM.
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Now we mix this warm phase gas with the CNM to
get the total brightness temp
Taking Tcool 65 K and t 1 (assumed above)
then TB 96 K if e 0.5.
Variations in geometry, in Tcool, and in nw
can cause this number to vary by 25 K or so,
but not much more.
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Different galaxies have different peak brightness
temperatures. This suggests variations in
some or all of Tcool , lt k gt, nw , and our
vantage point (face-on vs. edge-on).
In the SMC 21-cm absorption is rare, the ratio of
absorption to emission is much less than in the
Milky Way.
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Dickey, J.M., Mebold, U., Stanimirovic, S., and
Staveley-Smith, L., 2000, Ap. J. 536, 756
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Wolfire, M.G., Hollenbach, D., McKee, C.F.,
Tielens, A.G.G.M., and Bakes, E.L.O., 1995, Ap.
J. 443, 152.
Heating-cooling equilibrium is a strong function
of metallicity, z, and dust to gas ratio, D/G.
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Conclusions

• From a small subset of the SGPS data, we find
• the spatial power spectrum slope change
• the radial variation of the CNM abundance
• the distribution of CNM temperatures
• the statistics of HISA (21-cm self-absorption)
• Putting these together leads to an explanation
• for the peak brightness temperature of the
• Milky Way 21-cm emission.

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What is the Distribution of HI Temperatures ?
The Old Picture
Log HI Column Density
1 2 3
4
Log Temperature (K)
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What is the Distribution of HI Temperatures ?
WIM
The New Picture
Molecular clouds
WNM
PDRs
Log HI Column Density
Diffuse clouds
1 2 3
4
Log Temperature (K)
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SGPS web site
http//www.astro.umn.edu/naomi/sgps.html