View
3
Download
0
Category
Preview:
Citation preview
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)
AY 216 179
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).
AY 216 180
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
AY 216 181
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
AY 216 182
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
AY 216 183
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
AY 216 184
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
AY 216 185
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
¯ ˜
AY 216 186
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
AY 216 187
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
AY 216 188
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
AY 216 189
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 )
AY 216 190
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
AY 216 191
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
AY 216 192
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
AY 216 193
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
AY 216 194
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
AY 216 195
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
AY 216 196
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
AY 216 197
Evidence for CNM/WNMR
adha
kris
nan
1972
ApJ
S 2
4 15
AY 216 198
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
AY 216 199
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)
AY 216 200
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
Recommended