AY216 1

10:Tracing HI: 21 cmEmission & Absorption

James R. Graham

UC, Berkeley

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Reading

• Tielens, Ch. 8, § 8.9.1– Radiative transfer background is in § 2.3.2

• Dopita & Sutherland § 4.2

• Binney & Merrifield, “Galactic Astronomy”,§ 8.1.4

• Spitzer, § 3.3b, 3.4a, & 4.1b

• Dickey & Lockman 1990 AARA, 28, 215

• Kulkarni & Heiles in “Galactic &Extragalactic Radio Astronomy”

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Outline

• Early radio astronomy

• The hyperfine 21 cm HI line and itsdiscovery

• Spin temperature

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The Radio Astronomy Revolution

• Radio astronomy is generally regarded as havingstarted when Jansky (1932) detected short-wave (20MHz) radio noise– Later identified as coming from the plane of the Milky Way

• Slow progess for a decade– 1938-1943 Reber mapped the Milky Way– Solar Radio emission detected in 1942 (Hey 1946)– R&D for WW II communications and cm-wavelength radar

improved receivers

• 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 of drift scans fromReber's telescope made in Nov-Dec1943. Time increases to the leftThebroad peaks are due to the Sun andthen the Milky Way. Spikes areinterference from auto ignitions(Reber 1944 ApJ 100 279).

MW +

MW

MW

MW

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Radio Continuum

From 1938–1943 Reber made the first Galactic radio surveys & detecteddiscrete sources in Cygnus (76.2, +5.8) & Cassiopeia (111.7, -2.1)• Measured brightness in physical units & showed emission was non-thermal

l

b160 MHz

480 MHz

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1951: HI 21 cm Discovery• A new dimension entered radio astronomy with the

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

• 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

• Henk Van de Hulst (1945) predicted the HI line– Discovered by Ewen on March 25 1951 (Ewen & Purcell 1951

Nature 168 356) at Harvard• Confirmed on May 11 1951 by C. A. Muller in the Netherlands

and later in July by Christiansen & Hindman in Australian• Reports of the three observations appeared together in Nature

– The Dutch lost the race after fire destroyed their original receiver

– Only radio spectral line until 1963 detection of OH

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HI Regions: CNM/WNM• H I regions nHI / nH ≈ 1• Early 21 cm observations

– nHI ~ 1 cm-3 in spiral arms and 0.1 cm-3 outside arms– T ~ 125 K

• 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

• 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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Pioneer 10 Plaque• Pioneer 10 was

the first spacecraftto leave our solarsystem. It carries aplaque designedby Carl Sagan &Frank Drake– The system of

units employed aredefined in term ofthe hyperfinetransition of HI

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HI Hyperfine StructureDirac

n=2 2P3/2

n=22P1/22S1/2

10.8691 GHz

n=1

2.46607 PHz

QED

1.0579 GHz

2S1/2 8.6 GHz

2S1/2

2P1/2

2P3/2

2S1/2

Not to scale!

F=2

F=123.7 MHz

177.56 MHzF=1

F=0

59.19 MHzF=1

F=0

F=1

F=0

1,420, 405, 751. 7 Hz

Hyperfine

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HI Hyperfine Structure

• HI has one electron, spin S = 1/2, and a proton withspin I = 1/2

• 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

(↑↓) F =0

• The F=1-0 transition measured in the lab usinghydrogen masers:

ν10 = 1420,405,751.786 ± 0.01 Hz

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The HI 21-cm Line

• In 1H 2S1/2 F = 0 and F = 1 have zeroelectric dipole– F=0 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 10-5 T2-1/2

cm-3

• q10 is for H-H collisions: q10 ~ 9.5x10-11 T21/2 s-1

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Hyperfine Transitions of 2D & 3He

• 2D has nuclear spin I = 1, which combines withS = 1/2– F = {1/2, 3/2}

ν 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

• 3He+ has nuclear spin I = 1/2 due to theunpaired neutron, which combines with S = 1/2– F = {0, 1}ν 10 = 8,665.65 MHz (3.460 cm), A01 = 1.96 x 10-12 s-1

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HI 21-cm Line & Analogs

1/215N………016O

2.752.80

1.404,301.412,24

F2, F= 3/2,5/2 - 1/2,3/2F2, F= 3/2, 3/2 -1/2,3/2

1H2+

1/213C………012C

3/27Li………04He

1/23T

5.561.771,612S3/2, F=1-23/2NaI

1.78 x 10-5

3.84 x 10-60.026,120.015,67

4S3/2, F=3/2 - 5/2F=1/2 - 3/2

114NI

6508.665,662S1/2, F=1-01/23HeII

0.04640.327,384,3492S1/2, F=1/2 - 3/212D

2.851.420,405,7512S1/2 F=0-11/2HI

A ( 10-15 s-1)ν (GHz)TransitionSpinAtom

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Hyperfine Level Population• Populations n0 in F = 0 and n1 in F =1

defines Ts the spin temperature– hv ≈ 5.87 µeV = 68 mK

• Populations are determined by atomic collisions suchthat TS ≈ Tkin– Spin-exchange collisions (+ +)

H(1s, F = 0) + H 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

€

n1n0

=g1g0exp − hν

kTS

= 3exp −

hνkTS

≈ 3 1− hν kTS( )

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Spin Temperature• In steady state detailed balance yields

€

n0 nq01 + B01uν( ) = n1 A10 + B10uν + nq10( ) Solve for n1 /n0 in the limit hν /kT <<1

n1

n0

≈ 3 kTR /hν + n /nCR (1− hν /kT)1+ kTR /hν + n /nCR

,

where uν = 8π kTR /cλ2

• From the definition of TS we have n1 /n0 ≈ 3(1− hν /kTS )

Thus TS ≈T + yTR

1+ y,

where y ≡ kThν

nCRn

≈T

0.068 K3×10−4T−1/ 2

n= 4.4 ×10−3T1/ 2 /n

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Spin Temperature• Cold HI (CNM)

– n = 40 cm-3, TK = 80 K

– y ≈ 10-3, TS ≈ TK

• Warm HI (WNM)– n = 0.4 cm-3, TK= 8000 K

– y ≈ 1, TS ≈ 0.5 TK

• Modified by scattered Lyα,which tends to equalize TS

and TK

– Even allowing for this if n islow TS << TK

– e.g., outer regions of theMilky Way (Corbelli &Salpeter 1993 ApJ 419 94)

TR = 2.7 K

TR = 0 K

€

TS ≈T + yTR

1+ y, y ≡ kT

hνnCRn

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The Milky Way in HI (NHI )

• Dickey and Lockman, ARAA 28, 1990, 215– Top linear; bottom log 1020-1023 cm-2

– http://skyview.gsfc.nasa.gov/

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HI 21-cm Line• Galactic 21 cm radiation can be detected in virtually all

directions– It is normally seen in emission, but in front of a

source of continuum radiation it can appear inabsorption

• The splitting is ≈ 5.9 µeV, or hν/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

• At the temperature of HI regions nearly all H is in 1sn = n0 + n1 = 4 n0

• 21-cm emission gives a good measure of total H– Provided optical depth is small

• Absorption strength is very sensitive to Ts

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21-cm Line Radiative Transfer

• The equation of transfer from detailed balance

€

dIνds

=hν4π

n1

ν A10 − n0νB01 − n1

νB10( ) 4πIνc

κν ≡hνc

n0νB01 − n1

νB10( ) absorption coefficient

Sν ≡c4π

n1ν A10

n0νB01 − n1

νB10 source function

dτνds

≡κν optical depth

dIνdτν

= Sν − Iν with solution Iν (τν ) = Iν (0)e−τν + Sν (1− e

−τν )

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21-cm Line Radiative Transfer

€

The optical depth is

τν =hνc

N0νB01 − N1

νB10( ) =hνcN1

νB01 1− e−hν / kTs[ ]

≈hνcN0

ν hνkTs

B01

=3hcλ

8π kTSNH

4A10φ(ν) where N0

ν dν = N0φ(ν)dν

Optical depth at line center for a Gaussian, given φ(0) = λ πb

τ 0 =3hcλ2

32π 3 / 2 kTSNH

bA10 ≈ NH

4.19 ×1020cm-2 T2S−3 / 2,

where T2S = TS /100 K if b = 2kTS mH

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Optical Depth

• For a typical column of NH = 2 x 1020 cm-2

– The CNM is optically thick

– The WNM is optically thin

€

• In the CNM

τ 0 ≈ 0.6 NH /2 ×1020cm-2

T2S b5 and in the WNM

τ 0 ≈ 6 ×10−4 NH /2 ×1020cm-2

T4S b6

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Optical Depth• Convert from frequency to velocity units

€

The optical depth is

τν =3hcλ

8π kTSNH

4A10φ(ν)

In terms of velocity φ(V )dV = φ(ν)dν or φ(V ) = λφ(ν)

τV =3hcλ2

8π kTSNH

4A10φ(V )

The integral over the line

τVline∫ dV5 =

NH /TS1.83×1018cm−2K−1 km/s

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HI Radiative Transfer

€

• Equation of radiative transfer

dIνds

= jν −κν Iν can be written dIνdτν

= Bν (TS ) − Iν

• Define Iν ≡ 2kTB /λ2 where TB is brightness temperature

dTBdτν

= TS −TB

Using the integrating factor eτν write the equation of transfer

ddτν

(eτνTB ) = eτνTS

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HI Radiative Transfer

€

The radiative transfer equation

ddτν

(eτνTB ) = eτνTS

can now be integrated for TS = const.

eτνTB 0

τν= eτνTS dτν0

τν∫ eτνTB −TB (0) = (eτν −1)TS for TS = const. • Define TBG ≡ TB (0) and ΔT = TB −TBG

ΔTB = (TS −TBG )(1− e−τν )

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HI Radiative Transfer

€

• ΔTB = (TS −TBG )(1− e−τν )

• ΔTB = TB −TBG > 0 corresponds to emission ΔTB = TB −TBG < 0 corresponds to absorption

TS

TBG

T

V

∆T

TB

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TS >> TBG: Emission Lines

• Brightness temperaturedepends only on N(HI)not on TS

• In the optically thin limitcount hot & cold atoms

€

• ΔTB = TS (1− e−τν )

dτV =3hcλ2

8π kTSnHI4A10φ(V ) ds

• Eliminate TS

ΔTB dτV1− e−τν

=3hcλ2

8π knHI4A10φ(V ) ds

The inferred column is

NHI =1.83×1018 ΔTBτV1− e−τν

dV5line∫

• In the optically thin limit

NHI =1.83×1018 cm-2 ΔTB dV5line∫

TS TBG

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TS < TBG: Absorption Lines

• 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

ΔTB (on) = (TS −TBG )(1− e−τν ) < 0

• Off source

ΔTB (off) = TS (1− e−τν ) > 0

assuming uniformity of TS and τν• Two unknowns, two equation solve for TS and τν

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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• Emission is ubiquitiou—-absorption is not

– N(HI) in emission is typically > 5 x 1019 cm-2

– Emission is broader than absorption

• Cold gas in clouds with small filling factor (CNM)

• 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• Temperature of CNM

– TS is inversely related to τ (Lazareff et al. 1975ApJS 42 225)

– TS ≈ 55 (1-e-τ )-0.34 K with TS up to ~ 250 K (Payne etal. 1983)

– Model as a cold core at TS ≈ 55 K embedded in awarm envelope of constant temperature

– A wide range of inhomogeneous models fit theobservations (Liszt et al. 1983 ApJ 275 165)

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Spatial Distribution• Total vertical column through the disk

– N(HI) ≈ 6.2 x 1020 cm-2 or AV ≈ 0.3 mag

– 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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HI Summary• About 60% of the HI is in the WNM

– Typical column is ~ 1020 cm-2

– The WNM fills ~ 60% of the volume in the plane—more at higher b– Two scale heights: Gaussian h ~ 250 pc & exponential h ~ 500 pc– About 50% of the WNM is thermally unstable (500 K < T < 5000 K)– About 40% of the HI is CNM

• Typical CNM column is 5 x 1019 cm-2

– Column weighted temperature ~ 70 K, with some as cold as 15 K– Highly turbulent & sheet like– Exponential scale height ~ 100 pc

• High velocity gas—does not participate in Galactic rotation– Generally at high latitude & associated with large scale disturbances– About 10% of the sky is covered with Vlsr > 90 km/s gas NHI > 1018 cm-2

– Some of this gas may be a Galactic fountain (30 km/s < Vlsr < 90 km/s)– Some is extragalactic, e.g., the Magellanic Stream