Observational Studies and Experiments chapter 11 Basics of Observational studies.
ISM Lecture 7 H I Regions I: Observational probes.
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Transcript of ISM Lecture 7 H I Regions I: Observational probes.
ISM Lecture 7
H I Regions I:
Observational probes
H I versus H II regions
T and nH are different in H I regions Different processes play a role Different observational techniques
H II regions Mostly emission lines at optical wavelengths
H I regions H I radio line at 21 cm Optical absorption lines
Ref: Kulkarni & Heiles 1987, in Interstellar Processes, p.87 Burton 1992, in Galactic ISM
7.1 Review of radiation transport Radiative transfer equation
or
with the optical depth
General solution of radiative transport equation
with r = total opacity from s=0 to s=r
d d dI I s j s
d d s
d d dI Ij
FHG
IKJ
I I e ej
r
r
FHG
IKJ
z( )00
d
Source function
Special case: Thermodynamic Equilibrium
In thermodynamic equilibrium, Kirchhoff’s Law applies:
I=Bν(T) is the Planck function
The radiative transfer equation then becomes
j T T B T ( ) ( ) ( )
B Th
c eh kT
( )
/
2 1
1
3
2
I I e B T e
( ) ( ) ( )( ) 0 1
General ISM case (non-TE)
Suppose line has Gaussian profile
Vone-dimensional velocity dispersion
V2=kT/M for thermal velocities
( )
( ) /
/
/ FHG
IKJ
F
HGIKJ1
2 1 2
1
2
2
ce
o
co o
V
V
( )d z 1
Absorption and emission coefficients
jn A
hu ul
4
( )
FHG
IKJ
LNM
OQP
LNM
OQP
LNM
OQP
LNM
OQP
n n
nn
n
g
g
ne
mcf
n
n
g
g
ng
g
A n
n
g
g
l lu u ul
lu
l
l
ulu
l luu
l
l
u
lu
l
ul u
l
l
u
1
1
81
2
2
2
( )
( )
Excitation temperature Tex
with excitation temperature
j n
n
g
g
h
nn
gg
h
c nn
gg
h
c e
u
l
l
u u
l
l
u
l
u
u
l
h kTex
LNM
OQP
LNM
OQP
2 1
1
2 1
1
2 1
1
2
3
2
3
2 /
Th k
nn
gg
ex
u
l
l
u
FHG
IKJ
/
ln
General radiation transport
=>
Rayleigh-Jeans limit: h<<kT
jB Tex
( )
I I e B T eex
( ) ( )( )0 1
BkT
c
kT
2 22
2 2
Antenna temperature The antenna temperature TA is defined by
Advantage TA is a linear function of I For h/kT<<1, B(TA)=I
=> Rayleigh-Jeans limit, which is a good approximation at radio wavelengths Disadvantage
For h/kT1, B(TA)<I
=> e.g. at sub-mm wavelengths TA does not correspond to a physical temperature, even if emission is thermal
TI
kc
I
kA( )
2 22 2
2
7.2 H I 21 cm line emission
H atom consists of 1 proton + 1 electron Electron: spin S=1/2 Proton: nuclear spin I=1/2 Total spin: F = S + I = 0, 1
Hyperfine interaction leads to splitting of ground level: F = 1 gu = 2F+1 = 3 E = 5.8710–6 eV F = 0 gl = 2F+1 = 1 E = 0 eV
H I 21 cm line emission
Transition between F = 0 and F = 1: ν = 1420 MHz, λ = 21.11 cm ΔE / k = 0.0682 K Aul = 2.86910–15 s–1 = 1/(1.1107 yr) (very small!)
flu=5.7510-12
For all practical purposes kTex >> hν
Tex for H I is called “spin temperature” TS n
n
g
ge n n
n n
u
l
u
l
h kTu
l
ex
/ ( )
( )
33
4
1
4
HI
HI
Spin temperature and kinetic temperature
Often excitation is dominated by collisions TS = Tkin (e.g., in cold clouds with n 0.05 cm–3)
In warm, tenuous clouds (T 300 K): TS < Tkin
In some regions: upper level pumped by Lyα radiation TS > Tkin
Optical depth of H I line
Consider uniform cloud of length L and Gaussian line with FWHM Δν = ν/c ΔV (see eq. 7.1, with V=22V )
N(HI) = 4 nl L is the total HI column density V=FWHM in km s-1
o
Sc g
gA
n L ce
n L
T
N
T
o
u
lul
l
o
h kT
l
S
S
2
2
18
19
8
0 939441
2 20 101
5 50 101
.[ ]
.
.( )
/
V
V
HI
V
Example of optical depth H I line
TS = 100 K, ΔV = 3 km/s τ << 1 for N(HI) << 5.5 1020 cm–2
For τ << 1
or N(H I)1.8181018TAV
=> TA proportional to N(H I), independent of TS
In most cases N(H I) << 5.5 1020 cm–2
=> 21 cm emission usually gives information on column density of H I, but not on temperature
T T T e T
N
A S bg S
( )( )
.( )
1
5 5 10 19
H I
V
7.3 H I emission-absorption studies
Study extended cloud in front of extragalactic radio source
Observe two positions (on-source and off-source = blank) Assume that cloud is uniform properties of H I are the same in source and
blank positions
H I emission-absorption studies (cont’d)
Measure on-line and off-line at each position
)1()(
)(
)1()(
)(
eTeTsrcT
TsrcT
eTeTblankT
TblankT
Ssrcon
srcoff
Sbgon
bgoff
ebgsrc
bgsrc
offoff
ononTT
eTT
blankTsrcTblankTsrcT
)()()()(
SbgbgSblankoffe
blankTblankTTTTTToffon
)(
1
)()(
H I emission-absorption studies (cont’d)
Both τ and TS can be measured both N(H I) and TS can be determined!
Holds only over small regions need small beam size (3 for Arecibo 330 m, 30 for VLA and Westerbork interferometers)
Recall
τ very small if TS large
warm H I regions cannot be measured in absorption
5 5 10119.
( )N
V TS
HI
Two clouds along the line of sight: apparent TS
Assume Tbg<<TS =>definition of “naïvely-derived” spin temperature at velocity V
If cloud homogeneous, TS = TN
Often, there are two H I clouds along the line of sight with overlapping V. Assume cloud 1 closer than cloud 2
=> TN depends on V and lies between T1 and T2
T T e TS A N( ) ( ) / [ ] ( )V V V 1
T VT e T e e
eNS S( )
[ ] [ ]
[ ], ,
1 21 1
1
1 2 1
1 2
Consider 3 examples
Optically thick foreground: >>1 => TN(V)=TS,1
no information on cloud 2 Optically thick background, thin foreground:
TN(V)=TS,11(V)+TS,2
=> TN is larger than TS,2
Both clouds optically thin (usual case):
TN is weighted harmonic mean of T1 and T2
TN N
N T N TNS S
( )( ) ( )
( ) / ( ) /, ,
VV V
V V
1 2
1 1 2 2
Effect of foreground cloud on observed TS
Example: T1 = 8,000 K, T2 = 80 K, N2/N1 = 0.1
Small cold cloud can reduce “naïvely derived” spin temperature of warm background cloud from 8,000 K to 800 K
TN
11
1 8000 0 1 80800
.
/ . /K
7.4 Evidence for two-phase ISM
Good agreement between narrow absorption lines and narrow peak emission lines: V3 km/s
There is emission outside region over which absorption occurs (dashed lines): V9 km/s
H I emission and absorption spectrum
Note that the absorption features are sharper than the corresponding emission spectrum
=> Observations indicate that H I consists of 2 components
1. Cold Neutral Medium Cold diffuse clouds with T 80 K => narrow
absorption + emission components Every velocity component corresponds to an
individual cloud CNM occurs in clumps throughout the disk of
the Milky Way with z 100 pc Typically in disk: N(HI)full thickness 61020 cm-2
Locally: N(HI) 41020 cm-2 => We live in a “H I hole”
2. Warm Neutral Medium Broad emission component => temperature
difficult to estimate V9 km s-1 => T<10000 K Limits on => T>3000 K
WNM is distributed throughout Milky Way with substantial filling factor “raisin-pudding” model of ISM
Large scale height (Gaussian z 250 pc or exponential z 500 pc >> z of CNM) => warm H I halo?
=> T8000 K
T – relation?
Clouds with higher optical depth tend to have lower temperatures
‘Luke-warm’ H I in Milky Way?
In general, absorption lines narrower than corresponding emission features => do cold clouds have a warm (T500 K) envelope? T lower if larger
Maps indicate Clumps are responsible for H I absorption
T30-80 K, n20-50 cm-3
Filaments/sheets have T500 K and are responsible for 80% of the H I emission not seen in absorption
7.5 Optical absorption lines:Voigt profiles and equivalent widths
Traditional way of studying H I clouds: mostly Na I and Ca II lines
Optical lines => ΔE >> kT for T 80 K neglect (stimulated) emission
where =Nl with Nl=column density in level l
dI
dI I I e
( )0
Line broadening mechanisms
Upper level has finite radiative lifetime Lorentzian profile with damping width αL
Thermal and random / turbulent broadening Gaussian profile with HWHM αD
L o
L
L oL ul
l
A( )/
( )
2 2
1
4 with Hz
D o
D
o
D
( ) exp ln F
HGIKJ
LNMM
OQPP
12
2
Do D
o D
c
kT
M
T M
LNM
OQP
22
3 5825 10
1 2
7 1 2
ln
. ( / )
/
/amu Hz
Gaussian vs. Lorentzian profiles
Measures of Doppler width
αD is HWHM by definition; units are Hz
FWHM in velocity units is Frequently the width of the Gaussian is
given in terms of the “Doppler parameter”
V 2c
oD
b V V
2 2 1 6651 2(ln ) ./
( ) . maxv v Vd z 1 065
Voigt profile
Convolution of Lorentzian and Gaussian profiles
Define
Voigt profile: with
Here
x yo
D
L
D
(ln ) ; (ln )/ /2 21 2 1 2
N K x yl o ( , )
K x yy t
y x tt K x y x( , )
exp( )
( ); ( , ) /
z z
2
2 21 2d d
e
m cf K x y
e
m c
f f
elu o
oe
lu
D
lu
D
2
2 1 220 012466
FH IK
zz( ) ( , )
ln.
/
d d
cm 2
Equivalent width of spectral lines
In practice, resolution at optical wavelengths often insufficient to resolve line measure only line strength or equivalent width
Definition of equivalent width of line:
Wν is the width of a rectangular profile from 0 to Iν(0) that has the same area as actual line
Wν measures line strength, but units are Hz In wavelength units
W eI I
I
L
NMOQP
z z10
0c hd d Hz
( )
( )
W Wc
W
d
d cm
2
Schematic drawing of equivalent width of line
Curve of growth analysis
Goal: relate equivalent width Wν or W to column density Nl
Relation is monotonic, but non-linear Classical theory developed in context of stellar
atmospheres, but equally applicable to ISM Three regimes, depending on τ at line center: τ0 << 1, linear regime
τ0 large, flat regime
τ0 very large, square-root (damping) regime
Curve of growth (schematic)
D
D
L
L
Universal curve of growth
Curve of growth: linear regime
Weak lines, τ0 << 1
Linear regime: WNl
If Wλ and λ in Å,
W Ne
m cN fl
el lu
zzd d( )2
NW
fllu
113 10202
2.
cm
Curve of growth: flat regime
Large τ0: all background light near line center o is absorbed, line is “saturated”
Far from line center there is partial absorption because σ is smaller
=> Wν grows very slowly with Nl: flat part of the curve of growth
Onset if deviation from linear >10%, depends on Doppler parameter:
N f bl lu / . 187 1014 s 1
Curve of growth: square root regime
Very large τ0: Lorentzian wings of profile dominate the absorption
Asymptotic form
Square-root or damping regime: WNl1/2
x l oN
yx
1 22
/
Examples of interstellar Na absorption lines
Linear and flat regimes
Flat regime
Square-root regime
Hobbs 1969
UV absorption lines in ISM towards ζ Oph
7.6 Optical absorption line observations
Technique limited to bright background sources Mostly local (< 1 kpc), mostly AV < 1 corresponding
to N(H) < 51020 cm–2 Strong Na I lines in every direction, same clouds as
seen in H I emission and absorption, also seen in IRAS 100 μm cirrus CNM
H I column densities from Lyα observations in UV at 1215 Å
Information about T, nH from excitation C II, C I lines (see later): T80 K, nH100 cm-3
Depletions Absorption line studies of various atoms
abundances w.r.t. H information on depletions In diffuse clouds many abundances are much
smaller than solar depletion onto grains log D = log abundance meas – log abundance cosmic
Ca: log D –4 10,000 times less than solar Plot log D as a function of condensation
temperature Tc strong correlation elements with large Tc condensed onto grains when formed in circumstellar envelopes
Depletions log D versus condensation temperature
Jenkins 1987, in Interstellar Processes