8:Tracing HI
James R. Graham
UC, Berkeley
AY 216 178
The Radio Astronomy Revolution
l Radio astronomy is generally regarded as havingstarted when Jansky (1932) detected short-waveradiation• Later identified as coming from the plane of the Milky Way
l Slow progess for a decade• 1938-1943 Reber mapped the Milky Way• Solar Radio emission detected in 1942 (Hey 1946)• WW II communications and radar R&D improved receivers
l Early radio studies were of the continuous spectrum• Hot HII regions (Mathews & O’Dell 1969 AARA 7 67)• Microwave background (Thaddeus 1972 AARA 10 305)• Pulsars (Smith 1972 Rep. Prog. Phys. 35 399)
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Grote Reber (1911-2002)
Reber's back yard9-m telescope.Wheaton, IL, ~1938
Strip charts from Reber'stelescope made in 1943. Thebroad peaks are due to theMilky Way and the Sun. Thespikes are interference fromautomobile ignition (Reber1944 ApJ 100 279).
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Radio Continuum
• Between 1938 and 1943, Reber made the first radio surveys of theGalaxy and detected discrete soruces in Cygnus (76.2, +5.8) &Cassiopeia (111.7, -2.1)• Measured brightness in physical units & showed emission was non-thermal
l
b
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HI 21 cm Emission
l A new dimension entered radio astronomy in 1951 withthe detection of the 21 cm line of atomic hydrogen• Generally in emission but also in absorption against a
background continuum radio source, e.g., an HII region
l HI is a major constituent of the interstellar gas• 21 cm line measures the quantity of interstellar HI• Excitation temperature• Doppler shift gives radial velocities
l Van de Hulst (1945) predicted the HI line• Discovered by Ewen & Purcell (1951 Nat 168 356) at Harvard
+ Confirmed very soon afterwards by Dutch and by Australians+ Reports of the three observations appeared together in Nature
u The Dutch lost the race after fire destroyed their original receiver
• The 21 cm line was the only astronomical radio spectral lineuntil 1963 detection of OH
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HI Regionsl H I regions nHI / nH ≈ 1l Early 21 cm observations
• nHI ~ 1 cm-3 in spiral arms and 0.1 cm-3 outside arms• T ~ 125 K
l Increasing sensitivity and angular resolution showslarge variations in density and temperature• Density and temperature tends to be anticorrelated
+ Consistent with heating ~ n and cooling ~ n2
l Raisin pudding model (Clark/Field Goldsmith & Habing)• Cold, dense clouds + warm, low-density intercloud medium• Approximate pressure equilibrium nCNM TCNM ≈ nWNM TWNM
• The intercloud medium was thought to contain about half theneutral atomic hydrogen
+ TWNM ≈ 8000 K and nWNM ~ 0.4 cm-3
+ TCNM ≈ 80 K and nCNM ~ 40 cm-3
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HI Hyperfine Structure
l HI has one electron, spin S = 1/2, and a proton withspin I = 1/2
l In the ground state 1s2S1/2 the orbital angularmomentum L = 0 and the total angular momentum
F = I +S
with quantum number F ={0,1}• The triplet level (↑↑) F = 1 has higher energy than the singlet
(↑Ø) F =0
l The F=1-0 transition measured in the lab usinghydrogen masers:
n10 = 1420,405,751.786 ± 0.01 Hz
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HI 21-cm Line & Analogs
l F = 0 and F = 1 have zero electric dipole• F=0 Ÿ 1 is a magnetic dipole transition
A10 = 2.85 x 10-15 s-1
mean lifetime is 11 Myr• Natural line width A10 /4" = 4.5 x 10-16 Hz• Critical density nCR = A10/q10 ≈ 3 x 10-4 T-1/2 cm-3
l2H has nuclear spin I = 1, which combines with S = 1/2• F = {1/2, 3/2}
n 3/2,1/2 = 327, 384, 352.51 ± 0.05 Hz (92 cm)A 3/2,1/2 = 4.69 x 10-17 s-1
l3He+ has nuclear spin I = 1/2 due to the unpairedneutron, which combines with S = 1/2• F = {0, 1}
n 10 = 8,665.65 MHz (3.460 cm), A01 = 1.96 x 10-12 s-1
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Hyperfine Level Population
l Populations n0 in F = 0 and n1 in F =1
defines Ts the spin temperaturel Populations are determined by atomic collisions such
that TS ≈ Tkin• Spin-exchange collisions (ìî+îì Ÿ ìì+îî)
H(1s, F = 0) + H Ÿ H(1s, F = 1) + H• Discussed first by Purcell & Field (1956 ApJ 124 542)• For interstellar densities this is usually much faster than the
spontaneous radiative decay rate
†
n1
n0
=g1
g0
exp -hnkTS
Ê
Ë Á
ˆ
¯ ˜ = 3exp -
hnkTS
Ê
Ë Á
ˆ
¯ ˜
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Spin Temperature
l In steady state detailed balance yields
†
• n0 nq01 + B01un( ) = n1 A10 + B10un + nq10( ) Solve for n1 /n0 in the limit hn /kT <<1
n1
n0
ª 3 kTR /hn + n /nCR (1- hn /kT)1+ kTR /hn + n /nCR
È
Î Í
˘
˚ ˙ ,
where un = 8p kTR /cl2
• From the definition of TS we have n1 /n0 ª 3(1- hn /kTS )
Thus TS ªT + yTR
1+ y,
where y ≡kThn
nCR
nª
T0.068 K
3¥10-4 T-1/ 2
n= 4.4 ¥10-3T1/ 2 /n
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Spin Temperature
l Cold HI (CNM)• n = 40 cm-3, TK = 80 K• y ≈ 10-3, TS ≈ TK
l Warm HI (WNM)• n = 0.4 cm-3, TK= 8000
K• y ≈ 1, TS ≈ 0.5 TK
l Modified by scatteredLya, which tends toequalize TS and TK
• Even allowing for thisif n is low TS << TK
• e.g., outer regions ofthe Milky Way(Corbelli & Salpeter1993 ApJ 419 94)
TR = 2.7 K
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HI 21-cm Line
l Galactic 21 cm radiation can be detected in virtually alldirections• It is normally seen in emission, but in front of a
source of continuum radiation it can appear inabsorption
l The splitting is ≈ 5.9 µeV, or hn/kB =0.068 K• Lower limit for much of the ISM is the 2.7 K• hv << kT is a good approximation• n1 /n0 = 2.98 at 10 K, so n1 /n0 = 3 is a good approximation
l At the temperature of HI regions nearly all H is in 1sn = n0 + n1 = 4 n0
l 21-cm emission gives a good measure of total H• Provided optical depth is small
l Absorption strength is very sensitive to Ts
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21-cm Line Radiative Transfer
l The equation of transfer from detailed balance
†
dIn
ds=
hn4p
Ê
Ë Á
ˆ
¯ ˜ n1
n A10 - n0n B01 - n1
n B10( ) 4pIn
cÈ
Î Í ˘
˚ ˙
kn ≡hnc
n0n B01 - n1
n B10( ) absorption coefficient
Sn ≡c
4pn1
n A10
n0n B01 - n1
n B10
source function
dtn
ds≡kn optical depth
dIn
dtn
= Sn - In with solution In (tn ) = In (0)e-tn + Sn (1- e-tn )
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21-cm Line Radiative Transfer
†
• The optical depth is
tn =hnc
N0n B01 - N1
n B10( ) =hnc
N1n B01 1- e-hn / kTs[ ]
ªhnc
N0n hn
kTs
B01
=3hcl
8p kTS
N H
4A10f(n) where N0
n dn = N0f(n)dn
• Optical depth at line center for a Gaussian
t 0 =3hcl2
32p 3 / 2 kTS
N H
bA10 ª
N H
4.19 ¥1020cm-2 T2S-3 / 2,
where T2S = TS /100 K
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Optical Depth
l For a typical column of NH = 2 x 1020 cm-2
• The CNM is optically thick
• The WNM is optically thin
†
• In the CNM
t 0 ª 0.6 N H /2 ¥1020cm-2
T2S b5
and in the WNM
t 0 ª 6 ¥10-4 N H /2 ¥1020cm-2
T4 S b6
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Optical Depth
l Convert from frequency to velocity units
†
• The optical depth is
tn =3hcl
8p kTS
N H
4A10f(n )
In terms of velocity
f(V )dV = f(n )dn or f(V ) = lf(n )
tV =3hcl2
8p kTS
N H
4A10f(V )
• The integral over the line
tVlineÚ dV5 =
N H /TS
1.83¥1018cm-2K-1 km/s
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HI Radiative Transfer
†
• Equation of radiative transfer
dIn
ds= jn -kn In can be written
dIn
dtn
= Bn (TS ) - In
• Define In ≡ 2kTB /l2 where TB is brightness temperature
dTB
dtn
= TS - TB
Using the integrating factor etn rewrite as
d
dtn
(etn TB ) = etn TS
etn TB - TB (0) = (etn -1)TS for TS = const. • Define TBG ≡ TB (0) and DT = TB - TBG
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HI Radiative Transfer
†
• DTB = (TS - TBG )(1- e-tn )
• DTB = TB - TBG > 0 corresponds to an emisison line
DTB = TB - TBG < 0 corresponds to an absorption line
TS
TBG
T
V
∆T
TB
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TS >> TBG: Emission Lines
l Brightness temperaturedepends only on N(HI)not on TS
l In the optically thin limitcount hot & cold atoms
†
• DTB = TS (1- e-tn )
dtV =3hcl2
8p kTS
nHI
4A10f(V ) ds
• Eliminate TS
DTB dtV
1- e-tn=
3hcl2
8p knHI
4A10f(V ) ds
The inferred column is
N HI =1.83¥1018 DTBtV
1- e-tndV5
lineÚ
• In the optically thin limit
N HI =1.83¥1018 cm-2 DTB dV5lineÚ
TS TBG
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TS < TBG: Absorption Lines
l Evidence for the CNM/WNM• Clark 1965 ApJ 142 1298• Radhakrishnan 1972 ApJS 24 15• Dickey 1979 ApJ 228 465• Payne 1983 ApJ 272 540
TSTBG
†
• Towards a bright source
DTB (on) = (TS - TBG )(1- e-tn ) < 0• Off source
DTB (off) = TS (1- e-tn ) > 0 assuming uniformity of TS and tn
• Two unknowns, two equation solve for TS and tn
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Evidence for CNM/WNMR
adha
kris
nan
1972
ApJ
S 2
4 15
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Evidence for CNM/WNM
l Emission is ubiquitious-absorption is not• N(HI) in emission is typically > 5 x 1019 cm-2
• Emission is broader than absorption
l Cold gas in clouds with small filling factor (CNM)
l Warm gas in intercloud medium (WNM)• Payne et al. observed ~ 50 sources with Arecibo 300-m
• For lines of sight with no detectable absorption
+ <1/TS>-1 = 5300 K, i.e., TWNM > 5300 K
• Local ISM from UV absorption (Linsky et al. 1995 ApJ 451 335
+ T = 7000 ± 300 K
+ Distinguish thermal and turbulent motions from observations ofmultiple ions
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Evidence for CNM/WNM
l Temperature of CNM• TS is inversely related to t (Lazareff et al. 1975 ApJS 42 225)
• TS ≈ 55 (1-e-t )-0.34 K with TS up to ~ 250 K (Payne et al. 1983)
• Model as a cold core at TS ≈ 55 K embedded in a warmenvelope of constant temperature
• A wide range of inhomogeneous models fit the observations(Liszt et al. 1983 ApJ 275 165)
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Spatial Distribution
l Total vertical column through the disk• N(HI) ≈ 6.2 x 1020 cm-2 or AV ≈ 0.3 mag
• Roughly 60% WNM 40% CNM• Locally, we live in a hole and the vertical column is 50%
smaller (Kulkarni & Fich 1985 ApJ 289 792)
6.2 x 1020<nHI(0)>=0.57Total
1.59 x 10200.06 exp[-|z|/403]WNM2
1.82 x 10200.11 exp[-1/2(z/225)2]WNM1
2.74 x 10200.40 exp[-1/2(z/90)2]CNM
N(HI) [cm-2]<nHI(z)> [cm-3]Component
Kul
karn
i & H
eile
s 19
88
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