Download - Star Formation in our Galaxy
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Star Formation in our Galaxy
Dr Andrew Walsh (James Cook University, Australia)
Lecture 2 – Chemistry and Star Formation
1. Basic chemical interactions
2. Abundances
3. Depletion and enhancement
4. Line surveys and common lines
5. Column density
6. Virial equilibrium
7. Rotation diagrams
8. Chemical clocks
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Basic chemical interactions• High dust column densities block optical and UV-light in dark cores: molecules can form and survive
• Formation of molecules is an energy problem Possibilities: - Simultaneous collision with 3rd atom carrying away energy unlikely at the given low densities
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Basic chemical interactions
Chemical reactions on earth:
A + B AB* (excited state, unstable, lifetime 10-12 s)
followed by
AB* + C AB + C + ΔEkin
the collision with a third particle C within the lifetime of AB* is needed toremove excess energy, otherwise the reaction
AB* A + B
will occur. Due to momentum conservation, the excess energy cannot beconverted into kinetic energy.
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Basic chemical interactions
Chemical reactions in space:
The density is so low that no particle C will come by withinthe lifetime of AB*, so only reactions of the type
A + B C + D
or
A + B AB + hν
are possible. The second reaction product obeys energy andmomentum conservation laws.
In space, temperatures are between 10 and 300 K, so most endothermic reactionscannot occur since not enough energy is available.
In space, we have a low-energy, two-body-in two-body-out chemistry.
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Basic chemical interactions• High dust column densities block optical and UV-light in dark cores: molecules can form and survive
• Formation of molecules is an energy problem Possibilities: - Simultaneous collision with 3rd atom carrying away energy unlikely at the given low densities
- Ion-molecule or ion-atom reactions can solve energy problem
- Neutral-neutral reactions on dust grain surfaces (catalytic) important
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Basic chemical interactions - Neutral-neutral reactions on dust grain surfaces (catalytic) important
Dustgrain
H
H
HH
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Abundances
The Chemical Elements
Z Element Parts per million
1 Hydrogen 739,000 2 Helium 240,000 8 Oxygen 10,4006 Carbon 4,600 10 Neon 1,340 26 Iron 1,090 7 Nitrogen 960 14 Silicon 650 12 Magnesium 580 16 Sulfur 440
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Abundances
Molecule/Ion/Radical Relative Abundances
Molecule/Ion/Radical Relative Abundance
Reference
H2 1
CO 2 × 10–5 Dickman & Clemens 1983
13CO 1 × 10–6 Irvine et al. 1987
C18O 1 × 10–7 Frerking et al. 1982
CH3OH 2 × 10–6 Bisschop et al. 2007
CH3CN 1 × 10–7 Bisschop et al. 2007
CS 4 × 10–8 Garay et al. 2010
HCO+ 4 × 10–8 Hogerheijde et al. 1998
HCCCN 5 × 10–8 Sorochenko et al. 1986
NH3 1 × 10–8 Johnstone et al. 2010
C34S 4 × 10–10 Wilson & Rood 1994
N2H+ 2 × 10–10 Walsh et al. 2007
SiO 5 × 10–11 Garay et al. 2010
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Abundances
“CS abundance is 3 × 10-9 on average, ranging from (4-8) × 10-10 in the cold source GL 7009S to
(1-2) × 10-8 in the two hot-core-type sources.”
van der Tak et al. 2000
In the coldest and densest regions, species suffer “depletion” (decrease in abundance) whereby they freeze-out onto dust grains
Shocks can increase the abundance of some species
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Depletion in B68
1.2 mm Dust Continuum C18O N2H+
Optical Near-Infrared
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Depletion
Common depleting molecules:
• ALL of them
• Some suffer strong depletion (eg. O-bearing and S-bearing species like CO, HCO+ and CS)
• Some are relatively robust against depletion (eg. N-bearing species and H-only species like NH3, N2H+ and H2D+)
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Shock Enhancement
Walsh et al. 2007
Red & Blue = HCO+ (1-0)
Greyscale = N2H+ (1-0)
+ = dust continuum cores
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Shock Enhancement
Species affected: CO, HCO+, CS, CH3OH, HCN, HNC, SiO...
N2H+ and NH3 tend to “avoid” shocked regions
Due to reactions with CO and HCO+ that quickly react with N2H+ and NH3 to form CH3CN, CH3OH and similar byproducts
both N2H+ and NH3 are reliable tracers of quiescent gas
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Line Surveys and Common Lines
Line Survey:
• Observe as large a range of frequencies as possible
• Usually done in the millimetre or sub-millimetre
• Show the range of species that are detectable
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Line Surveys and Common Lines
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The Mopra Radiotelescope
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Recent Mopra Upgrades
• On-the-fly mapping to quickly scan the sky
• New 3mm receiver covers 77-116GHz
• New 12mm receiver covers 16-28GHz
• The new spectrometer (MOPS) has instantaneous 8GHz bandwidth with up to 32,000 channels (2 polarisations) 0.25MHz per channel in broadband mode
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Mopra Radiotelescope
The new Mopra spectrometer (MOPS)
• Instantaneous 8GHz bandwidth split between 4 IFs of 2.2GHz width each
IF0IF1
IF2IF3
8.4GHz
2.2GHz
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G327.3-0.6
Glimpse 3-colour mid-infrared image4.5, 5.8 and 8.0 microns
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Line surveys of many sources
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OrionG327.3-0.617233-3606G305.2+0.2
83
Frequency (GHz)
8785 8684 88 89 90 91 92
Frequency (GHz)
91 92 93 94 95 9796 98 10099
99 100 101 102
Frequency (GHz)
103 104 105 106 107 108
Frequency (GHz)
107 108 109 110 111 112 113 114 115 116
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
Orion
G327.3-0.6
17233-3606
G305.2+0.2
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
Orion
G327.3-0.6
17233-3606
G305.2+0.2
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
Orion
G327.3-0.6
17233-3606
G305.2+0.2
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83
Frequency (GHz)
8785 8684 88 89 90 91 92
Orion
G327.3-0.6
17233-3606
G305.2+0.2
CH3OCH3
(El/k = 1059K)
CH3OH(El/k = 1443K)
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Molecules in SpaceAlClAlFAlNCFeOHClHFKClMgCNMgNCNaClNaCNPNCP
SiCc-SiC2
SiC2
SiC3
SiC4
SiCNSiHSiH4
SiNSiNCSiOSiS
C2SC3SCH3SHCSH2CSH2SH2S+
HCS+
HNCSHSHS+
OCSS2
NSSOSO+
SO2
C3NC5NCH2CHCNCH2CNCH2NHCH3C3NCH3CH2CNCH3CNCH3NCCH3NH2
CNCN+
H2C3N+
H2CNHCNHNCHCCNHC3NHC4NHC5NHC7NHC9NHC11NHCCNCHCNH+
COCO+
CO2
CO2+
H2CCOH2COH2OH2O+
H3CO+
H3O+
HC2CHOHCOHCO+
HCOOCH3
HCOOHHOC+
HOCH2CH2OHHOCO+
OHOH+
C2
C2HC2H2
C2H4
C3
c-C3Hl-C3Hc-C3H2
C4HC5
C5HC6HC6H2
C6H6
C7HC8HCHCH+
CH2
CH3
CH3CCHCH3C4HCH3CH3
CH4
H2CCCH2CCCCHCCCCHHCCCCCCH
H2
H3+
HNCCCHNCOHNCO-
HNON2H+
N2+
N2ONHNH2
NH3
NH4+
NH2CNNH2CHONOc-C2H4OCH3CH2OHC2OC3H4OC3OCH2OHCHOCH3CH2CHOCH3CHOCH3COCH3
CH3COOHCH3OCH3
CH3OH
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Molecules in SpaceAlClAlFAlNCFeOHClHFKClMgCNMgNCNaClNaCNPNCP
SiCc-SiC2
SiC2
SiC3
SiC4
SiCNSiHSiH4
SiNSiNCSiOSiS
C2SC3SCH3SHCSH2CSH2SH2S+
HCS+
HNCSHSHS+
OCSS2
NSSOSO+
SO2
C3NC5NCH2CHCNCH2CNCH2NHCH3C3NCH3CH2CNCH3CNCH3NCCH3NH2
CNCN+
H2C3N+
H2CNHCNHNCHCCNHC3NHC4NHC5NHC7NHC9NHC11NHCCNCHCNH+
COCO+
CO2
CO2+
H2CCOH2COH2OH2O+
H3CO+
H3O+
HC2CHOHCOHCO+
HCOOCH3
HCOOHHOC+
HOCH2CH2OHHOCO+
OHOH+
C2
C2HC2H2
C2H4
C3
c-C3Hl-C3Hc-C3H2
C4HC5
C5HC6HC6H2
C6H6
C7HC8HCHCH+
CH2
CH3
CH3CCHCH3C4HCH3CH3
CH4
H2CCCH2CCCCHCCCCHHCCCCCCH
H2
H3+
HNCCCHNCOHNCO-
HNON2H+
N2+
N2ONHNH2
NH3
NH4+
NH2CNNH2CHONOc-C2H4OCH3CH2OHC2OC3H4OC3OCH2OHCHOCH3CH2CHOCH3CHOCH3COCH3
CH3COOHCH3OCH3
CH3OH
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
HI - atomic hydrogen
Frequency(GHz)1.420
Ubiquitous low density gas tracerCritical density ~ 101 cm-3
Strong enough to be easilydetected in other galaxies – traces outer edges
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
GASS (Galactic All Sky Survey)
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
OH - Hydroxyl Radical
Maser and thermal emission
Found towards star forming regions,Evolved stars (post-AGB), SNRs,Extragalactic sources
Frequency(GHz)1.6121.6651.6671.7204.7656.035
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
NH3 - Ammonia
Maser and thermal emission
Ubiquitous medium to high densityGas tracer > 103 cm-3
Closely traces density structure
Frequency(GHz)23.69423.72223.87024.13924.53225.056
etc
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
Optical Depth:
Tmain (1 - e-τ)
Tsat (1 - e-aτ)
a = 0.28 (inner)a = 0.22 (outer)
τ = 0.5
=
Main line
Inner satellite
Outer satellite
NH3 (1,1)spectrum
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
H2O - Water
Maser only
Most common maser known
Traces outflows in star forming regions
Also found in other astrophysical objects(eg. evolved stars, extragalactic megamasers)
Frequency(GHz)22.235
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
HCN - Hydrogen Cyanide
Frequency(GHz)88.632Ubiquitous high density gas tracer
Hyperfine structure
Bright enough to be seen in thecentres of other galaxies
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
CO - Carbon Monoxide
Frequency(GHz)
115.271110.201109.978112.358
13COC18OC17O
Ubiquitous low density gas tracerCritical density ~102 cm-3
Strongly influenced byoutflows in our Galaxy
Found in the cores of galaxies
Can be traced right across the universe
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
CO - Carbon Monoxide
(Dame, Hartmann & Thaddeus, 2000)
Second most abundant moleculeX ~ 10-4 H2
CO (1-0) is the brightest thermal line
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
HCO+ - Oxomethylium
Frequency(GHz)89.18886.75485.162
H13CO+
HC18O+
Occurs in similar regions to COHigher critical density~2 105 cm-3
Like CO enhanced in outflows andsuffers from freeze-out onto dust grainsin cold, dense regions
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
N2H+ - Diazenylium
Frequency(GHz)93.173
Reliable high density gas tracer
Hyperfine structure gives optical depth
Critical density ~ 2 105 cm-3
Does not show up in outflows
Less prone to freeze-out/depletion
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
CH3OH - Methanol
Frequency(GHz)6.66912.17924.93344.06996.741
etc
Both thermal and maser
MANY spectral lines (asymmetricrotor)
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
Thermal Methanol
Lines in 12mm and 3mm bands → rotation diagram
12mm ladder:24.928 CH3OH (32,1-31,2) E Energy = 35K24.933 CH3OH (42,2-41,3) E Energy = 44K24.959 CH3OH (52,3-51,4) E Energy = 56K25.018 CH3OH (62,4-61,5) E Energy = 70K…27.472 CH3OH (132,11-131,12) E Energy = 232K
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
Methanol Masers
Class I masers collisionally excitedClass II masers radiatively excited
Class I usually found offset from star formation sites
Class II closely associated with sitesof high-mass star formation (and nothing else)
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
CH3CN – Methyl Cyanide
Frequency(GHz)91.987
110.353
Useful rotational ladders(close together)
Velocity (km/s)
Rotation diagram using the J=(5-4) & J=(6-5) transitions.
CH3CN Spectrum
(Purcell et al. 2006, MNRAS, 367, 553)
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
SiO – Silicon Monoxide
Frequency(GHz)43.42386.24386.847
Both maser and thermal emission
Maser emission in vibrationallyExcited states only seen towards2 or 3 sources. But results veryproductive in Orion.
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
SiO – Silicon Monoxide
Frequency(GHz)43.42386.24386.847
Both maser and thermal emissionMaser emission in vibrationallyExcited states only seen towards2 or 3 sources. But results veryproductive in Orion.
Matthews et al. 2007
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
SiO – Silicon Monoxide
Frequency(GHz)43.42386.24386.847
Both maser and thermal emissionMaser emission in vibrationallyExcited states only seen towards2 or 3 sources. But results veryproductive in Orion.
Thermal SiO closely associated withOutflows in star forming regions
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
SiO – Silicon Monoxide
IRAS 20126+4104Cesaroni et al. 1999 IRAS 20126+4104
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
CS – Carbon Sulfide
Frequency(GHz)48.99197.981
Ubiquitous tracer of high density gas
Critical density ~ 2 106 cm-3
Suffers from freeze-out ontodust grains (depletion)
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Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
HCCCN - Cyanoacetylene
Frequency(GHz)18.19627.29436.39290.980
100.078
Hot core molecule(tracer of high mass star formation)
![Page 56: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/56.jpg)
Some of the more important lines
H OH NH3 H2O HCN CO HCO+ N2H+ CH3OH CH3CN SiO CS HCCCN
HCCCN - Cyanoacetylene
Frequency(GHz)18.19627.29436.39290.980
100.078
Hot core molecule(tracer of high mass star formation)
HOPS results
HCCCN
NH3
![Page 57: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/57.jpg)
Calculating Column Densities
![Page 58: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/58.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
![Page 59: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/59.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Nu = Column density in upper energy level
![Page 60: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/60.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
k = Boltzmann’s constant = 1.38 10-23 m2 kg s-2 K-1
![Page 61: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/61.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
= frequency of line transition (eg. 115.271 GHz for CO(1-0))
![Page 62: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/62.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Aul = Einstein A coefficient for transition = 1633
3ohc3
|2|
![Page 63: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/63.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Aul = Einstein A coefficient for transition = 1633
o = permittivity of free space = 8.854 10-12 m-3 kg-1 s4 A2
3ohc3
|2|
![Page 64: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/64.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Aul = Einstein A coefficient for transition = 1633
= magnetic dipole moment(eg, for N2H+ =
3ohc3
|2|
![Page 65: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/65.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Aul = Einstein A coefficient for transition = 1633
= magnetic dipole moment(eg, for N2H+ = 3.4 Debye
3ohc3
|2|
![Page 66: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/66.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Aul = Einstein A coefficient for transition = 1633
= magnetic dipole moment(eg, for N2H+ = 3.4 Debye = 1.13 10-29 C m)
3ohc3
|2|
![Page 67: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/67.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
Integrated Intensity(area under the curve)
![Page 68: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/68.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )
= optical depth
![Page 69: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/69.jpg)
Optical Depth
Optically thick
Optically thin
1 TB TB B
1 TB TB B
→ Temperature probe
→ Column density probe
![Page 70: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/70.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )N = Nu
gu
eEu/kT Q(Tex)
![Page 71: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/71.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )N = Nu
gu
eEu/kT Q(Tex)
gu = upper energy level degeneracy = 2J+1
![Page 72: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/72.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )N = Nu
gu
eEu/kT Q(Tex)
Eu = upper energy level (K)
![Page 73: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/73.jpg)
Calculating Column Densities
Nu = 8 k 2
Aul h c3 ∫-∞
∞Tb dv
1 - e-( )N = Nu
gu
eEu/kT Q(Tex)
Q(Tex) = partition function (a sum over all energy states) at a given temperature, Tex
![Page 74: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/74.jpg)
Calculating Column Densities
Values for , , Eu and Q(Tex) can be found at “CDMS”(http://www.astro.uni-koeln.de/site/vorhersagen/)
Note that CDMS quotes El, rather than Eu and unitsare in cm-1, rather than K. (1K = 100 hc/k cm-1)
![Page 75: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/75.jpg)
Applying Column DensitiesWalsh et al. 2007, ApJ, 655, 958
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Applying Column DensitiesGiven column density of N2H+ clump in NGC1333:
• Assume LTE
• Assume size of clump
• Assume relative abundance of N2H+ to H2
(~1.8 x 10-10)
• Assume mean molecular weight 2.3
Mass of clump
![Page 77: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/77.jpg)
Applying Column Densities
Compare to Virial Mass:
MVIR = 210 v2 r
M⊙ km/s pc
Assumes uniform density profileIf density falls off as r-2,
210 changes to 126.
![Page 78: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/78.jpg)
Applying Column Densities
![Page 79: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/79.jpg)
Applying Column Densities
N = Nu
gu
eEu/kT Q(Tex)
![Page 80: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/80.jpg)
Rotation Diagrams
Nu N Eu
gu Q(T) kTex( )ln = ln( )
• Plot ln (Nu/gu) vs. Eu/k
• Slope = 1/T
• Y-intercept = ln (N/Q(T))
![Page 81: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/81.jpg)
Rotation DiagramsAmmonia in a high mass star forming region
(1,1)
(2,2)
(4,4)
(5,5)
(Longmore et al. 2007, MNRAS, 379, 535)
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Use chemical rate equations, together with an initial model of the physical conditions
• Abundance
• Temperature
• Density
• Structure
Chemical Clocks
![Page 83: Star Formation in our Galaxy](https://reader031.vdocuments.site/reader031/viewer/2022020718/56813733550346895d9ec0e7/html5/thumbnails/83.jpg)
T = 100KNH
2 = 1.8 x 104 cm-3
T = 200KNH
2 = 1.8 x 104 cm-3
T = 100KNH
2 = 8 x 104 cm-3
T = 200KNH
2 = 8 x 104 cm-3
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Summary
Lecture 2 – Chemistry and Star Formation
1. Basic chemical interactions
2. Abundances
3. Depletion and enhancement
4. Line surveys and common lines
5. Column density
6. Virial equilibrium
7. Rotation diagrams
8. Chemical clocks