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