Determination of physical properties from molecular lines Kate Brooks Australia Telescope National Facility Mopra Induction Weekend May 2005

Ehrenfreund & Charnley 2000, ARA&A, 38, 427 Interstellar Molecules 137 molecules have been detected in space (205 including isotopomers, 50 in comets)

Talk Outline Radiative Transfer 12 CO(1-0): Workhorse of mm-line studies Optically thin density tracers (LTE Mass) Temperature tracers Non-LTE models Signatures for infalling gas Bipolar outflows

Radiative Transfer Fundamental equation of radiative transfer Absorption emission coefficients Kirchhoff’s law valid in TE and LTE Optical depth Planck law

Rayleigh-Jeans approximation to Planck law Brightness Temperature For isothermal medium Temperature that would result in brightness if source were a black- body in the Rayleigh-Jeans limit

Optically thin Optically thick

Integration along the line of sight: Absorption coefficient -> Optical depth  Level population -> Level column density N Total column density : Sum over all levels Column Density  is related to the level population

In LTE there is one excitation temperature T ex that describes the level population according to the Boltzmann distribution When collisions dominate: Level population can be described as Boltzmann distribution at kinetic gas temperature T kin One observed transition and adopting a value for T kin gives all level populations -> Total column density N Excitation Temperature T ex

Measuring Kinetic Temperature T kin 1.Optically thick transitions: 2. Line ratios e.g. 13 CO(2-1) / 13 CO(1-0) 3. Rotation Diagrams e.g. NH 3, CH 3 CCH, CH 3 CN

Critical Density Any spectral-line transition is only excited above a certain critical density Critical density is the density at which: Collisional deexcitation ~ spontaneous radiative decay 12 CO(1-0) GHZ4 x 10 2 cm -3 Lowest critical density CS(2-1) GHz1 x 10 5 cm -3 HCN( GHz1 x 10 5 cm -3 NH 3 (1,1) GHZ 1 x 10 3 cm -3

12 CO(1-0): Workhorse of mm-line studies Ubiquitous gas tracer - High abundance - Lowest critical density Excellent for global cloud parameters - Temperature - Mass - Structure Limitations - Optically thick - Complex velocity profiles - Confused towards Galactic plane - Depletion at high densities and low temperature

Example: The Carina Nebula “ It would be manifestly impossible by verbal description to give any just idea of the capricious forms and irregular gradations of light affected by the different branches and appendages of this nebula. In this respect the figures must speak for themselves.” Sir J. F. W. Herschel 1847

Mopra observations of the Carina nebula 12 CO(1-0) 115 GHz pointings 0.1 K rms per channel Brooks et al. 1998, PASA, 15, 202 Example Grid

Excitation Temperature 12 CO1-0 is optically thick T B = T ex = T kin Use ‘xpeak’ in miriad to find P( 12 CO)

Excitation Temperature Map “Treasure Cluster”

Mass estimates from CO observations Virial Mass Relies on the assumption that the cloud’s kinetic energy stabilizes it against gravitational collapse (Virialised) The overall velocity width of the CO emission line reflects the motion of the gas and ultimately the underlying mass (Virial mass) But … Are molecular clouds virialised? What about external pressure?

Mass estimates from CO observations X - Factor CO-to-H 2 Conversion factor Galactic Value: X CO ≈ 2.8 x cm -2 K (km s -1 ) -1

H 2 Column Density to Mass Mass = column density x spatial extent Average H 2 density Spherical with effective radius R 2R =  min +  maj Mass determined this way is often called the ‘CO mass’

But … To determine X co we need an independent measure of the mass of the cloud and the distance D in order to work out N(H 2 )

Independent Mass estimate for X co Virial Mass Not all clouds are virialised Radiative Transfer method Very difficult to do in for other galaxies (minimum 3 lines) Extinction Assumes standard reddening law and dust-to-gas ratio Dust Emission Assumes dust absorption coefficient and dust-to-gas ratio

Use X co with caution Problem for all determinations of the conversion factor. All of them have factors between 2-5 in uncertainty. Galactic: Constant for specific regions only Extra Galactic: Very difficult to measure X co Localised values that depend on metallicity and galaxy type Sometimes you have little choice e.g. z  6

Pre-stellar coreIons, Long Chains HC 5 N, DCO + Cold envelopeSimple species, Heavy depletions CS, N 2 H + Warm inner envelopeEvaporated species CH 3 OH, HCN Hot coreComplex organics CH 3 OCH 3, CH 3 CN Outflow: direct impactSi- and S-species SiO, SO2 Outflow: walls, entrainmentEvaporated ices CH 3 OH PDR, compact HII regionsIons, Radicals CN/HCN, CO + Massive DiskIons, D-rich species, photoproductions HCO +, DCN, CN Debris DiskDust, CO Chemical Characteristics of star-forming regions (E. F. van Dishoeck)

Example: 12 CO, 13 CO and CS intensities in the Carina nebula

Utilising other molecular-line transitions More than 40 emission lines in the Mopra 3-mm band Optically thin density tracers (LTE Mass) Temperature tracers Non-LTE models Signatures for infalling gas Bipolar outflows

Optically thin density tracers: Testing 13 CO, C 18 O and CS e.g. Alves et al., 1998 Lada et al., 1994

In the study by Lada et al “Dust extinction and molecular gas in the dark cloud IC 5146” Direct comparison of 13 CO, C 18 O and CS integrated intensities and column densities with A v to a range in A v between 0-32 mag of extinction. Integrated intensities I( 13 C0) = A v K km s -1 (A v ≤ 5 mag) I(C 18 0) = A v K km s -1 (A v ≤ 15 mag) I(CS) = A v K km s -1 (A v ≤ 15 mag) Between 8 and 10 mag the 13 CO emission appears saturated Uncomfortable prediction of molecular emission and 0 mag

Integrated Intensity to Column Density Integrated intensity W 13CO Case Study 13 CO(2-1) Only one transition is measured and an extrapolation to total column density is done by assuming a LTE population

We need a value for T ex -use value determined from 12 CO -assume a value (e.g. 35 K) The value of T ex has a large impact on optical depth but not on column density f(35 K) = 0.64

Back to the study by Lada et al Assuming LTE For 13 CO and C 18 O: Based on 12 CO data: T ex = 10 K For CS: Subthermal excitation: T ex = 5 K Column Densities N( 13 C0) LTE /A v = 2.18 x cm -2 mag -1 (A v ≤ 5 mag) N(C 18 0) LTE /A v = 2.29 x cm -2 mag -1 (A v ≤ 15 mag) N(CS) LTE /A v = 4.5 x cm -2 mag -1 (A v ≤ 15 mag)

Column density to H 2 density Not there yet! Gas-to-dust ratio of Savage & Drake (1978) N(H 2 ) = 0.94 x Av cm -2 Which leads to: N( 13 C0)/N(H 2 ) = 4 x 10 5 (A v  5 mag) Mass determined this way is often called the ‘LTE mass’

Depletion C 18 ODust Emission Bianchi et al. Dust Extinction 0.1 pc Alves et al. T 10 5 cm -3 CO and CS freeze out onto the dust grains Species linked to molecular nitrogen are less affected E.g. NH 3, N 2 H +, N 2 D +

Simple Line Ratio Analysis Beam filling factor: Ratio of lines with similar frequency (and hence similar  ) ->  cancels out Ratio of different species -> Optical Depth (if T ex and the isotopic abundance ratio is known) e.g. 12 CO(1-0) / 13 CO(1-0)[ 12 CO/ 13 CO] ≈ 89 Ratio of different transitions (  Excitation temperature e.g. C 18 O(2-1) / C 18 O(1-0)

Note: Different species and different transitions of one species arising in different parts of a region with different beam filling factors Good Thermometers: Molecules with many transitions with a large range of energy levels in a small frequency interval Symmetric top molecules: e.g.Ammonia NH 3 Methyl Acetylene CH 2 C 2 H Methyl Cyanide CH 3 CN NH 3 (1,1): 18 hyperfine components mixed into 5 lines Fitting all 18 components -> optical depth

Rotation Diagrams Integrated line intensity versus energy above ground If LTE plot is a straight line with slope ~ (-1/T) T rot = T kin Garay, Brooks et al., 2002

Non-LTE Modelling Additional Considerations - Stimulated emission - Radiative (photon) trapping Large Velocity Gradient (LVG) approximation - assume large-scale velocity gradient exists in cloud - photons are absorbed locally, then immediately escape Maximum Escape Probability models

Static envelope R2R2 R1R1 B2B2 B1B1 Optically thin line Infall asymmetry Optically thick line Constant line-of-sight velocity T ex (R 2 ) > T ex (R 1 ) T ex (B 2 ) > T ex (B 1 ) Infall region

Infall Protostar SMM4 in Serpens Narayanan et al., 2002, ApJ, 565, 319

evidence for infall infall velocities of 0.5 km s -1 are obtained using model of Myers et al. (1996) - M infall M sun yr -1 evidence for outflow - v outflow = 15 km s -1. Garay, Brooks, et al. 2003

Outflows Bourke et al. 1997

Outflows

Belloche et al., 2002, A&A, 393, 972 Protostar IRAM in Taurus

Integrated Intensity to Column Density Integrated intensity W 13CO Case Study 13 CO(2-1)