Journal of Molecular Spectroscopy 280 (2012) 11–20

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Journal of Molecular Spectroscopy

journal homepage: www.elsevier .com/ locate / jms

An analysis of a preliminary ALMA Orion KL spectrum via the useof complete experimental spectra from the laboratory

Sarah M. Fortman a, James P. McMillan a, Christopher F. Neese a, Suzanna K. Randall b, Anthony J. Remijan c,T.L. Wilson d, Frank C. De Lucia a,⇑a Department of Physics, Ohio State University, 191 W. Woodruff Ave., Columbus, OH 43210, USAb European Space Agency, Karl-Schwarzschild-Str. 2, 85748 Garching, Germanyc National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475, USAd Naval Research Laboratory, Code 7210, Washington, DC 20375, USA

a r t i c l e i n f o

Article history:Available online 15 August 2012

Keywords:MillimeterSubmillimeterRotationalAstrophysicsALMA

0022-2852/$ - see front matter � 2012 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.jms.2012.08.002

⇑ Corresponding author. Fax: +1 614 292 7557.E-mail address: fcd@mps.ohio-state.edu (F.C. De L

a b s t r a c t

Preliminary Atacama Large Millimeter/Submillimeter Array (ALMA) science verification data for a singlepixel centered on the hot core of Orion KL (R. A. = 05 h 35 m 14.35 s, Dec = �05�2203500 (J2000)) are avail-able as this special issue on broadband spectroscopy is coming to press. As part of this verification processit is useful to compare simulations based on laboratory spectroscopy with ALMA results. This providesnot only a test of instrumentation and analysis, but also a test of astrophysical assumptions such as localthermodynamic equilibrium (LTE) and the temperature variations within telescope beams. However,these tests are spectroscopically limited because it is well known that astrophysical spectra contain largenumbers of unknown lines, many of which are presumably due to unanalyzed rotational spectra inexcited vibrational states of a relatively few molecules. To address this issue we have previously dis-cussed the use of broadband complete experimental spectra (CES) that is obtained from the analysis ofseveral hundred intensity calibrated spectra taken over a range of temperatures. In this paper we willcompare these CES with the similarly complete astrophysical spectra.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

The preliminary Science Verification data from ALMA providean opportunity to compare the astrophysical data from a largebroadband interferometer with the underlying laboratory data-base. In the millimeter and submillimeter spectral region (mm/submm) both laboratory [1–3] and astrophysical spectroscopy[4–10] began as narrow band experimental subjects, limited bythe availability of technology. In the laboratory, quantum mechan-ical (QM) models were developed to select observation frequenciesfor the narrow band bootstrap observation, analysis, and predic-tion cycles. The resultant QM models were then used to calculatesynthetic spectra for astrophysical use over broad spectral regions[11,12].

This approach has been enormously successful, as testified to bythe development of ALMA, Herschel, SOFIA [13–15], their host ofantecedent telescopes, and the growth of ever larger user commu-nities. This success has led to telescopes of not only greater sensi-tivity and angular resolution, but also considerably greaterbandwidth. One example is the WIDAR digital cross correlator,

ll rights reserved.

ucia).

which was produced by Canada for use on the Karl G. Jansky VeryLarge Array (VLA). WIDAR cross-correlates the data from the 27individual antennas to produce 351 independent correlations forspectral bands covering up to 8 GHz of bandwidth in each polariza-tion. The 8 GHz band can be divided into 128 independent sub-bands, at a spectral (channel) resolution ranging from 1 MHz toless than 0.1 Hz. The ALMA instrument has two correlators withsimilar design specifications. At 275 GHz, 1 km s�1 is equivalentto 922 kHz for low redshifts, so the ALMA device can be used toanalyze 8000 km s�1 of velocity or nearly 3% of the rest frequency.Such a large instantaneous coverage is conducive for line searches.

A byproduct of the enormous advances in sensitivity and spec-tral coverage of these telescopes is the rapidly growing number ofastrophysically observable lines that are not included in the QMbased astrophysical catalogs. It is generally assumed that manyof these unassigned lines, typically referred to as the astrophysicalweeds, are due to unanalyzed low lying excited vibrational statesof a relatively few molecules [16]. While in some sense these unas-signed lines are due to the small cumulative amount of mm/sub-mm spectroscopy, there is a more fundamental reason. Briefly,the excited vibrational states are typically perturbed, often in verycomplex ways, and their analyses can be orders of magnitude morechallenging than for the states included in the QM catalogs.

12 S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20

We have previously described and demonstrated a laboratoryapproach to this problem that eliminates the need for the compli-cated and time consuming assignment and analysis process[17,18]. It depends upon the collection of intensity calibrated, com-plete laboratory data at many (in principle two, but typically 100–1000) temperatures. From these data it is possible to calculate theastrophysically significant line strengths and lower state energiesof spectral lines without the need for quantum assignment. Morerecently we have shown an additional frequency point-by-pointanalysis procedure that is especially useful for regions of overlap-ping spectral features [18]. It is this latter procedure we will usein this paper to calculate the spectral simulations at astrophysicaltemperatures.

It was anticipated that the impact of unknown lines would begreater in ALMA than for earlier telescopes because its high angularresolution would (1) make possible the study of smaller, hotter re-gions and (2) the linewidths (and thus the ability to resolve moreand weaker lines) could be narrower because the beam wouldaverage turbulence and other relative motion over smaller regions.Additionally, the larger S/N would often drive the astronomicalspectra to the noise free, spectroscopic confusion limit.

In this paper we will (1) very briefly review our general strategyand laboratory procedures, (2) consider the ALMA spectrum from asingle pixel of the Science Verification data, (3) show a comparisonbetween the ALMA data and simulations based on very simplemodels, and (4) consider straightforward extensions to these sim-ple models.

2. Background

We have previously described the spectroscopic methods andprocedures used to generate CES across broad spectral regions inthe mm/submm as a function of temperature [17–19].

2.1. Analysis

For each species and spectral region, we first selected 50–200assigned lines that are included in the QM catalogs [11,12] to useas intensity references. With the strengths Sijl2 and lower state en-ergy levels El (from the QM analyses) and Doppler widths dmD andline frequencies m0 (from the temperatures and measured frequen-cies from the experiment), we fit the measured peak absorbance ofthese reference lines to

Apeak ¼ LapeakðTÞ ¼nLQ

8p3

3chð1� e�hm0=kTÞSijl2e�El=kT

ffiffiffiffiffiffiffiffiffiffiffilnð2Þp

rm0

dmDð1Þ

to obtain the spectroscopic temperature T and nL/Q for each of the100–1000 spectra of varying temperature. Here n is the numberdensity, L the effective path length, and Q the partition function.Because we use this equation not only for the determination of Tand nL/Q but also inversely for the calculation of the simulatedspectrum, errors associated with linewidths and other systematicexperimental errors cancel.

Although we originally used an inversion of Eq. (1) to calculatethe line strengths Sijl2 and lower state energy levels El for themany experimental lines not in the QM catalog, we have more re-cently first processed the data without the identification of individ-ual lines in the spectra. This analysis predicts the spectra as afunction of temperature on a frequency point-by-point basis.

The Doppler width (HWHM) is given by

dmD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Nak lnð2Þ

Mc2

s ffiffiffiTp

m0 ¼WffiffiffiTp

m0 ð2Þ

and the absorbance as a function of frequency can be rewritten as

AðmÞ ¼ 8p3

3ch

ffiffiffiffiffiffiffiffiffiffiffilnð2Þp

rnLQ

m0ð1� e�hm0kT Þ

dmDSijl2e�

ElkT e� lnð2Þðm�m0

dmDÞ2 ð3Þ

where Na is Avogadro’s number, and M is the molecular mass. Theabsorbance normalized by the nL/Q factor becomes

AðmÞnL=Q

¼ 8p3

3ch

ffiffiffiffiffiffiffiffiffiffiffilnð2Þp

r1Wð1� e�

hm0kT Þffiffiffi

Tp Sijl2e�

ElkT e�

lnð2ÞW2Tð1� m

m0Þ2

¼ Kð1� e�

hm0kT Þffiffiffi

Tp ~Sijl2e�

~EðmÞkT ð4Þ

with

~EðmÞ ¼ EL þ klnð2ÞW2 1� m

m0

� �2

ð5Þ

In Eq. (4) every frequency slice of the data (� 2 � 106 frequencypoints at each temperature) is represented by two parameters ~Sijl2

and ~E. On line center ~E is the lower state energy and ~Sijl2 corre-sponds to the line strength. Off of line center, the meanings of~Sijl2 and ~E are less physical, but Eq. (4) is still a valid fitting func-tion for describing the spectral intensity. To present these data inthe usual astrophysical catalog format, we simply use a peak finderto identify the lines and catalog the on-line-center values of ~Sijl2

and ~E.

3. Comparison of laboratory and ALMA spectra

The hot core of Orion KL (R. A. = 05 h 35 m 14.35 s,Dec = �05�2203500 (J2000)) [20] was chosen as one of the targetsof ALMA’s Science Verification program for Band 6 (211–275 GHz) [21] because it is one of the most studied molecularsources and one for which a number of spectral surveys exist forcomparison [22–25]. Preliminary data for a single pixel (of a1024 � 1024 array of pixels) centered on the hot core of Orion KLhave become available and it is these data that we use in this work.

In this section we will consider how well simple models basedon CES can simulate this ALMA spectrum for a number of the astro-physical ‘weed’ molecules. Issues that are addressed include thecompleteness of the laboratory spectroscopic basis in the contextof this real astrophysical example and how well the simplest LTEmodels of the interstellar medium can account for the astrophysi-cal spectrum.

While it is possible to do numerical fits of the CES simulations tothe ALMA spectrum (in a similar fashion as in our laboratory fits todetermine nL/Q and T, but with additional consideration of line-shapes and optical depth) to determine astronomical column den-sity and temperature, we have chosen not to do so in thesepreliminary results. It will be especially interesting to see the sta-tistical results of such analyses, especially in regards to the detec-tion of species with many weak lines.

3.1. How complete are astrophysical catalogs?

We have previously asked the question, ‘‘How complete areastrophysical catalogs?’’ and have answered this question experi-mentally by sorting both synthetic spectra based on the QM cata-logs and experimental spectra according to intensity [26]. Fig. 1reproduces two of these comparisons at 300 K. The location ofthe divergence between the QM and experimental results in theseplots can be quantitatively calculated and is related to the firstunassigned vibrational state for each molecule. We have calculatedthe location of this point as a function of temperature for a numberof species. These results are shown in Fig. 2. At the 190 K used inthis paper for the simulations of ethyl cyanide, vinyl cyanide, and

0.001

0.01

0.1

1

Scal

ed A

bsor

banc

e

40003000200010000Intensity Sorted Line Index

0.001

0.01

0.1

1Sc

aled

Abs

orba

nce

25002000150010005000Intensity Sorted Line Index

Ethyl Cyanide

Vinyl Cyanide

Fig. 1. Absorbances at 300 K (normalized to the strongest line) sorted according tostrength of the QM catalogs (lower red) in comparison to the experimental results(upper black). The denseness of the points for the individual lines is such that theyappear as lines. The predicted divergence of these two graphs, based on thevibrational energy of the fist state not included in the catalogs, is shown by thehorizontal line.

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Inte

nsity

Rat

io

5004003002001000Temperature / K

Acetaldehyde

Methyl Cyanide

Vinyl Cyanide

Ethyl CyanideMethyl Formate

Methanol

Dimethyl Ether/

Sulfur Dioxide

Fig. 2. Intensity ratio relative to the strongest lines in the spectrum of the firstuncataloged line as a function of temperature for several astrophysical ‘weeds’.

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nsity

/ (J

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236.414236.407236.400Frequency / GHz

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nsity

/ (J

y/be

am)

221.316221.309221.302Frequency / GHz

S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20 13

methyl cyanide, these correspond to factors of approximately 0.2,0.07, and 0.005 respectively.

While these are interesting results, they do not directly addressthe astrophysically interesting question, ‘‘How many uncatalogedlines are there in a particular astrophysical spectra?’’ The answerto this question is also a function of telescope and astrophysicalsource parameters (the temperature of the source, the abundanceof the species in the source, and noise floor of the telescope). Thesedata from ALMA allow us to address this question.

1.0

0.5

0.0Inte

nsity

/ (J

228.022228.015228.008Frequency / GHz

Fig. 3. Relatively isolated lines of intermediate strength that were used for theALMA lineshapes of methyl cyanide, ethyl cyanide, and vinyl cyanide (top tobottom). The solid black traces are the ALMA data and the dashed colored traces arethe convolution of the simulated lineshape with the CES.

3.2. A simple model

For this preliminary comparison between the new ALMA dataand our experimental results, we will adopt a simple model: Eachspecies is characterized by: (1) a column density, with terrestrialisotopic abundances, (2) a single temperature, (3) a lineshape thatis characteristic of its velocity distribution within the beam, (4) anoptical depth parameter (for the strongest species), and (5) a con-stant continuum that is subtracted from the astronomical data.

For our simulation in the optically thin case, to convert labora-tory absorbance A(m) (Eq. 4) to Jy/beam,

I ¼Z

AðmÞK 0Sðm� m0Þdm0 ð6Þ

where S(m) is a normalized lineshape function based on the numer-ical lineshape functions derived from Fig. 3. K0 was adjusted empir-ically so that the ALMA spectra in units of Jy/beam matched theintensity of the simulation and was .0025, .002, and .16 for methylcyanide, ethyl cyanide, and vinyl cyanide respectfully. This factor,which absorbs nL/Q, is related to the astronomical column densityand molecular partition function and has units of Jy/beam.

If Imax is the intensity for an optically thick line, then

I ¼ Imaxð1� e�ðI

ImaxÞÞ ð7Þ

After we present the results of such a comparison, we will dis-cuss prospects for straightforward extensions of this model.

3.3. Spectral comparisons

Fig. 3 shows relatively isolated lines of intermediate strength,whose shapes observed in the ALMA spectrum are characteristicof the lineshapes of methyl cyanide, ethyl cyanide, and vinyl cya-nide. The lines of the latter two show clear shoulders on theirlow frequency sides, which are due to the kinematics of the regionprobed by the ALMA beam. These lineshape are convolved with theCES to produce the simulations that are compared with the ALMAresults below.

6

5

4

3

2

1

0

Inte

nsity

/ (J

y/be

am)

220.60220.55220.50220.45220.40220.35220.30 Frequency / GHz

Fig. 4. Spectral comparison in the region of a methyl cyanide ground vibrational state bandhead. The upper black trace is ALMA and the lower gold trace a CES LTE simulationat 190 K, including effects of optical thickness. Also in gold is a stick spectrum that shows methyl cyanide at laboratory resolution.

4

3

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1

0

Inte

nsity

/ (J

y/be

am)

221.40221.35221.30221.25221.20 Frequency / GHz

Fig. 5. Spectral comparison in the region of a methyl cyanide v8 = 1 bandhead. The upper black trace is ALMA and the lower gold trace a CES LTE simulation at 190 K, includingeffects of optical thickness. Also in gold is a stick spectrum that shows methyl cyanide at laboratory resolution.

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nsity

/ (J

y/be

am)

240.58240.56240.54240.52240.50 Frequency / GHz

Fig. 6. Spectral comparison in the region of a methyl cyanide v8 = 2 bandhead. The upper black trace is ALMA and the lower gold trace a CES LTE simulation at 190 K. Also ingold is a stick spectrum that shows methyl cyanide at laboratory resolution.

14 S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20

2.0

1.5

1.0

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nsity

/ (J

y/be

am)

232.25232.20232.15232.10232.05232.00 Frequency / GHz

Fig. 7. Spectral comparison in the region of a methyl cyanide ground vibrational state, 13C methyl group bandhead. The upper black trace is ALMA and the lower red trace aCES LTE simulation at 190 K. Also in red is a stick spectrum that shows methyl cyanide at laboratory resolution. To account for the differences in interstellar and terrestrialabundances, the intensity of the simulation has been increased by a factor of 2.5.

3.0

2.5

2.0

1.5

1.0

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Inte

nsity

/ (J

y/be

am)

239.00238.95238.90238.85 Frequency / GHz

Fig. 8. Spectral comparison in the region of a methyl cyanide ground vibrational state, 13C cyanide group bandhead. The upper black trace is ALMA and the solid red trace aCES LTE simulation at 190 K. Also in red is a stick spectrum that shows methyl cyanide at laboratory resolution. The dashed lower gold trace is from the 12C simulation ofFigs. 4 and 5. To account for the differences in interstellar and terrestrial abundances, the intensity of the 13C simulation has been increased by a factor of 2.5.

S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20 15

3.3.1. Methyl cyanideWe will start with methyl cyanide to illustrate effects of optical

thickness, rotational and vibrational temperatures, and isotope ef-fects. In the comparisons the offset of �1 Jy/beam between thesimulation and the ALMA spectrum is due to the non-spectral linecontinuum of the Orion KL hot core region measured by ALMA.While we have normalized the intensity of the simulation to thatof the spectral lines of the ALMA spectrum, we have left the offsetbecause it facilitates comparison between the simulation and theALMA spectrum. For other comparisons of weaker spectra shownbelow, this offset is reduced so as to minimize white space.

Methyl cyanide has a strong spectrum that in a number ofplaces is relatively unobscured by overlapping lines. A number ofits lines are also optically thick. It was possible to match manystrong features of both the ground state and v8 = 1 vibrationalstates in ALMA with an LTE simulation at 190 K. Figs. 4 and 5 showthe excellent agreement between the ALMA data and the simula-tion, to include blends, overlaps, and shoulders. The agreement iseasiest seen in the v8 = 1 spectrum of Fig. 5 where the line emissionis largely compact and optically thin.

Although the lines in the v8 = 2 vibrational state shown in Fig. 6are not contained in the current catalogs, we infer their assignmentfrom their location relative to the ground and v8 = 1 vibrationalstates and their intensity. Additionally, since our analysis returnsthe lower state energy of each line, we observe a correct vibra-tional energy for this band. Fig. 6 shows the comparison betweenthe observed and simulated spectra. We presume that the signifi-cantly stronger (and broader) ALMA feature near 240.54 GHz(which shows a shoulder) includes a contribution from an overlap-ping line. Taken together we see that the intensities of the groundand two excited vibrational states show that LTE or near LTE de-scribes at least these vibrational states, along with the rotationalstates.

It is well known that the interstellar isotopic abundances differfrom the terrestrial abundances, but that care needs to be taken toinclude the impact of optical thickness. Figs. 7 (13C on the methylgroup) and 8 (13C on the cyanogen group) show comparisons be-tween the ALMA spectrum and simulations. However, since theCES is based on terrestrial abundances, the strength of the labora-tory spectrum was increase by a factor of 2.5 to optimize the match

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0

20

40

60

Absp

rptio

n C

ross

Sec

tion

/ cm

-1

242.8242.6242.4242.2242.0Frequency / GHz

Fig. 9. A comparison of the Complete Experimental Spectra (blue, upward going) and a QM catalog (black, downward going).

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y/be

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242.6242.4242.2242.0Frequency / GHz

Fig. 11. A region of intermediate strength ethyl cyanide lines near 242 GHz that illustrates the fine detail in which the simulation based on the CES and LTE reproduces theALMA spectrum. The ALMA spectrum is the upper black trace and the simulation is the lower blue trace. The stick spectrum in blue is that of the CES at laboratory resolution.

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y/be

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224.3224.2224.1224.0223.9223.8Frequency / GHz

Fig. 10. The bandhead of ethyl cyanide near 224 GHz. The ALMA spectrum is the middle black trace, the simulation with optical depth effects included is lower blue trace, andthe simulation without optical depth effects is the dashed upper red trace for the stronger lines.

16 S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20

on the less overlapped spectrum from the 13C on the methyl group.While the ratio for the spectrum due to the 13C on the cyanogen

group may be different, the overlaps are such that an independentadjustment was not merited.

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242.6242.4242.2242.0

Frequency / GHz

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2

0

Fig. 12. A region dominated by intermediate strength ethyl cyanide lines near 242 GHz. In the lower composite panel, the ALMA spectrum is the upper black trace, the bluetrace immediately below is the simulation based on the CES, and the red dashed trace at the bottom is the simulation based only on the QM catalog. The top panel (blue) is thedifference between the ALMA spectrum and a simulation based on the CES and the second panel from the top (red) is the difference between the ALMA spectrum and asimulation based on the QM catalog.

S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20 17

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228.4228.2228.0227.8Frequency / GHz

Fig. 13. A region of intermediate strength ethyl cyanide and vinyl cyanide lines near 228 GHz that illustrates the fine detail in which the simulation based on the CES and LTEreproduces the ALMA spectrum for these two species. The ALMA spectrum is the upper black trace and the lower traces the simulations in solid light blue and dashed darkblue for vinyl cyanide and ethyl cyanide, respectively. The stick spectra are those of the CES at laboratory resolution.

18 S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20

Less specifically, but more inclusively, the intensities of all ofthe lines simulated from the CES for methyl cyanide and that arenot overlapped by interfering spectra are consistent with this sim-ple model for the interpretation of the ALMA data. It will be inter-esting to see if deviations from this simple single temperature LTEmodel occur as both the ALMA and the spectroscopic analysis arerefined and expanded to include more species simultaneously.

3.3.2. Ethyl cyanideNext we consider ethyl cyanide to illustrate the impact of a

more complex spectrum with many uncataloged lines, a morecomplicated lineshape, and optical thickness.

Ethyl cyanide has a considerably denser and more complexspectrum than methyl cyanide. Fig. 9 shows a stick spectrum com-parison of the QM simulation of the ethyl cyanide spectrum withone based on the CES. It should be first noted for lines that are inboth the QM catalog and the CES the intensities are in goodagreement. This is a required byproduct of using the QM intensitiesto calibrate the intensities in our experimental spectra and theaccuracy of the experimental intensity calibration. More impor-tantly, this figure shows the many uncataloged lines that contrib-ute both to new features in the ALMA spectra, and shoulders andadditional intensity where there is overlap. This can be seen in

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231.5231.4Frequen

ALMA Spectrum Laboratory Vinyl Cyanide Laboratory Ethyl Cyanide Laboratory Methanol Laboratory Methyl Formate Laboratory Dimethyl Ether Laboratory Methyl Cyanide

Fig. 14. A region of the ALMA spectrum sh

more detail in Fig. 11 where we combine the CES and astrophysicallineshapes to simulate the ALMA spectrum in this region.

We have chosen the region near 224 GHz shown in Fig. 10 todetermine the intensities and optical thickness of ethyl cyanide. Inthis figure the ALMA spectrum is shown in black, in blue is the sim-ulation (including effects of optical depth), and in dashed red is thesimulation without the effects of optical depth. It is clear that opticalthickness plays a major role in the ALMA spectrum of ethyl cyanide.

When lineshape and optical thickness effects are convolvedwith the 190 K simulation from the CES of Fig. 9, the result isFig. 11. Not only does the completeness of the CES result in thesimulation of many new features, but it also accounts for manysubtle lineshape effects. It is also significant that the intensity scal-ing factor and optical depth that were determined by the intensityfit near the bandhead in Fig. 10, were applied in Fig. 11 without fur-ther adjustment. Given the very substantial contributions of theuncataloged lines to the good agreement in Fig. 11, this showsthe importance of these contributions to showing the simple LTEmodel used here accounts for a wide range of rotational and vibra-tional states.

Fig. 12 provides additional detail. The top trace (blue) is the dif-ference between the ALMA spectrum and the CES and the secondtrace from the top (red) is the difference between the ALMA spec-

231.7231.6cy / GHz

owing contributions from six species.

S.M. Fortman et al. / Journal of Molecular Spectroscopy 280 (2012) 11–20 19

trum and a simulation based on the QM catalog. Positive differencecan be attributed to lines other than those of the ethyl cyanide sim-ulation. For a more direct comparison, below the ALMA spectrumare the simulations based on the QM catalog (red – dashed) andthe CES simulation (blue). While the CES simulation is very good,we expect that when we do a more careful adjustment of intensi-ties and lineshapes in a global fit that additional reductions in theresiduals will occur, especially in the regions that include opticallythick lines.

3.3.3. Vinyl cyanideVinyl cyanide is another species with prominent spectral fea-

ture in the ALMA spectrum of the Orion KL hot core region.Fig. 13 shows a region that includes lines of vinyl cyanide, alongwith those of ethyl cyanide. The intensity for the ethyl cyanidewas fixed as above and the column density of vinyl cyanide ad-justed to match the astronomical spectrum in this (and other re-gions as well) region. Inspection of this figure shows excellentagreement. The largest apparent difference is for the relativelystrong line near 227.95 GHz, but this difference can be ascribedto overlap with the adjacent strong line for a species not includedin the simulation.

3.3.4. Methyl formate, dimethyl ether, and methanolMethyl formate, dimethyl ether, and methanol also make signif-

icant contributions to the ALMA spectrum of Orion KL. However, itis well known that the spatial distribution of these oxygen bearingspecies are offset from the cyanide species already described above[20]. Not pointing at the emission peak of the oxygen bearing spe-cies results in distorted lineshapes. Therefore, we have not at-tempted to do detailed lineshape or intensity simulations ofthese species as we have done for the cyanides. Additionally, meth-anol requires at least a two-temperature description, and we donot attempt such a simulation in this paper.

Nevertheless, it is useful to compare stick spectra simulations ofall six of these species simultaneously with the ALMA results.Fig. 14 shows such a comparison for a small portion of the ALMAspectrum of the Orion KL hot core region. In this simulation thecyanide species had the column densities and temperature(190 K) as above; and methyl formate, dimethyl ether, and metha-nol were all simulated at 150 K. The sticks are semi-quantitative(except for methanol). Although overlaps and convolutions signif-icantly complicate the quantitative comparison of the stick spec-trum with that of ALMA, many features are readily identifiable.

4. Conclusions and the path forward

While the model used in this paper is in many ways remarkablysuccessful, it clearly is an oversimplification. There are straightfor-ward extensions. The need for some of these may be revealed by amore numerical fitting and exploration of the residuals, especiallyin more comprehensive analyses that include ‘all’ molecularspecies. Others are already well known in the astronomicalcommunity.

4.1. Two or more component models

Although the higher angular resolution of ALMA reduces beamaveraging, there is still significant averaging, especially along theline of sight. We have not quantitatively included methanol in thisanalysis because it is well known to have contributions from morethan one component [27]. Since the ALMA data of these astrophys-ical weeds contains many spectral lines that can be compared withthe CES it is likely that this information can be used to determine

multiple, perhaps many, components – each with its own columndensity, temperature, and lineshape.

4.2. Isotopic abundances

The impact of non-terrestrial isotopic abundances was illus-trated in Figs. 7 and 8. A small extension of the analysis presentedabove addresses this issue. Briefly, since the ground vibrationalstates of the less abundant isotopomers are in general much easierto analyze than the excited states of the main isotopomers (eventhought they often contribute weaker lines to the astrophysicalspectra) many analyses of these isotopomers are included in theQM catalogs. In these cases, simulations that include the abun-dance of these isotopomers as free variables address this issue.

If the astrophysical data are sensitive enough to allow observa-tions of excited vibrational states in these less abundant isotopo-mers and for which there are not QM analyses, the CES fromisotopically enriched species can provide laboratory references,with the isotopic abundance as one additional free parameter.

4.3. The ALMA data

The comparisons in this paper were made with preliminary re-sults toward the Orion KL hot core region, which is a single pixel ina 1024 � 1024 array of pixels. More complete processing, supple-mented with single dish data and utilizing data from other regionsin the Orion KL complex, will provide greater opportunity to ex-plore and challenge simulation strategies.

Acknowledgments

We would like to thank the National Science Foundation andNASA for their support of this work. This work was also supportedby NASA Headquarters under the NASA Earth and Space ScienceFellowship Program – Grant NNX09AP10H. The National RadioAstronomy Observatory is a facility of the National Science Foun-dation operated under cooperative agreement by Associated Uni-versities, Inc. This paper makes use of the following ALMA data:ADS/JAO.ALMA#2011.0.99001.CSV. ALMA is a partnership of ESO(representing its member states), NSF (USA) and NINS (Japan), to-gether with NRC (Canada) and NSC and ASIAA (Taiwan), in cooper-ation with the Republic of Chile. The Joint ALMA Observatory isoperated by ESO, AUI/NRAO and NAOJ.ADS/JAO.

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