Notes on Plume et al. (2012), "A direct measurement of the total gas column density in Orion KL"

I read the following paper yesterday as part of my Nitrogen / HCN in Orion KL background.

http://adsabs.harvard.edu/abs/2012ApJ...744...28P  
Plume et al. (2012)

(which has my advisor as second-author).



Here's the abstract:

The large number of high-J lines of C¹⁸O available via the Herschel Space Observatory provide an unprecedented ability to model the total CO column density in hot cores. Using the emission from all the observed lines (up to J = 15-14), we sum the column densities in each individual level to obtain the total column after correcting for the population in the unobserved states. With additional knowledge of source size, V _LSR, and line width, and both local thermodynamic equilibrium (LTE) and non-LTE modeling, we have determined the total C¹⁸O column densities in the Extended Ridge, Outflow/Plateau, Compact Ridge, and Hot Core components of Orion KL to be 1.4 × 10¹⁶ cm^-2, 3.5 × 10¹⁶ cm^-2, 2.2 × 10¹⁶ cm^-2, and 6.2 × 10¹⁶ cm^-2, respectively. We also find that the C¹⁸O/C¹⁷O abundance ratio varies from 1.7 in the Outflow/Plateau, 2.3 in the Extended Ridge, 3.0 in the Hot Core, and to 4.1 in the Compact Ridge. This is in agreement with models in which regions with higher ultraviolet radiation fields selectively dissociate C¹⁷O, although care must be taken when interpreting these numbers due to the size of the uncertainties in the C¹⁸O/C¹⁷O abundance ratio.

My takeaway from the paper is this:
Basically, there's a super important star-forming cloud called Orion KL (the Kleinmann-Low nebula within the Orion Nebula Cluster), which contains a "Hot Core" of special interest to me, as well as other less-interesting (to me) components like outflows and ridges.

The data was collected from the Herschel "HEXOS" program, which used 45 hours of Herschel time on the HIFI instrument (the Herschel instrument most like a radio receiver, with amazingly high spectroscopic performance) in order to make a deep and complete scan that covers more than 1000 GHz (!!!) of spectral coverage from 480–1900 GHz. Orion KL was one of 4(ish) targets. The HEXOS program is described here:
http://adsabs.harvard.edu/abs/2010A%26A...521L..20B
Bergin et al. (2010)

Parameters of the Hot Core used:
T= 150 K,   Size = 10'',   V_LSR = 3–4 km s⁻¹,   n = 10⁷ cm⁻³

In this study, these authors measured, precisely, the total amount of *emitting* C¹⁸O gas towards the hot core (and the other, velocity-separated components) just from directly summing the emission over nine C¹⁸O transitions (seven from HIFI and two from ground-based CSO) between J=2–1 and J=15–14. This measurement is model-independent, i.e. independent of temperature and density. It's denoted , and for the Hot Core its value is . Then, by making use of a "correction factor" (which *is* somewhat model-dependent – the authors make use of an LVG model and use some assumptions about density and temperature), they can calculate the total amount of C¹⁸O via this equation: . For the Hot Core they find = 1.69, giving
= .
They note that, after doing both LTE (via WEEDS) and non-LTE (via RADEX) modeling, the derived value is consistent to the 5–10% level, and adopt LTE values for subsequent analysis. The high densities in Orion KL make LTE a reasonable assumption.

They also derive an H₂ column density. They use a flat factor of 500 × 10⁴ (with no reference given) to convert between C¹⁸O and H₂ "to obtain the canonical H₂ column density in these regions". For the Hot Core they find per cm^2.

Other notes:
"From our non-LTE analysis, we have found that all C¹⁸O and C¹⁷O lines in all components are optically thin." Hot Core τ ≤ 0.15 for all transitions of C¹⁸O.

"Canonical CO: C¹⁸O abundance ratio of 500" - no reference given, again.

Uncertainties are from size of source uncertainty - if Hot Core size is decreased by 20%, then column density increases by  24%. If size is increased by 20%, then column density decreases by 21%.

The total error budget therefore includes:

• 15% HIFI calibration error
• ~7.5% error introduced by using LTE models
• Column density errors introduced by 20% variations in source size.

The uncertainties presented in Tables 3 and 4, thus, reflect these errors added in quadrature. (NB: This feels a little like playing fast-and-loose with statistics, although I wouldn't know how to make it better.)

Final notes from Tom:
This'll be a super important paper to cite for my derivation of the H₂ column density. Some of the uncertainty sources may have been reduced or resolved in the post-ALMA age (I mean to say that the 10'' source size may no longer just be an "estimate", and I could do the corrections for source size / column density errors myself). Also the X factor assumed might have improved or be update-able. What's next for me? Tracking down the H2-to-dust conversion. Nieva?