Observational Consequences of Fine‐Structure Line Optical Depths on Infrared SpectralDiagnosticsAuthor(s): Nicholas Abel, Adam Bryant, Prabodh Dhakal, Ashley Gale, Alva Gibson,William Goddard, Chad Howard, Ameya Kolarkar, Pey Lian Lim, Gargi Shaw, andGary FerlandSource: Publications of the Astronomical Society of the Pacific, Vol. 115, No. 804 (February2003), pp. 188-192Published by: The University of Chicago Press on behalf of the Astronomical Society of the PacificStable URL: http://www.jstor.org/stable/10.1086/367546 .

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188

Publications of the Astronomical Society of the Pacific, 115:188–192, 2003 February� 2003. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.

Observational Consequences of Fine-Structure Line Optical Depthson Infrared Spectral Diagnostics

Nicholas Abel, Adam Bryant, Prabodh Dhakal, Ashley Gale, Alva Gibson, William Goddard,Chad Howard, Ameya Kolarkar, Pey Lian Lim, Gargi Shaw, and Gary Ferland

Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506; npabel2@uky.edu, albrya0@hotmail.com,prabodhdhakal@hotmail.com, aagale2@uky.edu, apgibs0@pop.uky.edu, goddard@pa.uky.edu, chad_howard77@hotmail.com,

askola2@uky.edu, klangjaya@hotmail.com, gshaw@pa.uky.edu, gary@pa.uky.edu

Received 2002 October 29; accepted 2002 November 19

ABSTRACT. It has long been known that infrared fine-structure lines of abundant ions, such as the [Oiii]88 mm line, can become optically thick in Hii regions under certain high-luminosity conditions. This could mitigatetheir potential as diagnostic tools, especially if the source is too dusty for optical spectroscopy to otherwise determinethe system’s parameters. We examined a series of photoionization calculations that were designed to push the nebulaeinto the limit where many IR lines should be quite optically thick. We find that radiative transfer effects do notsignificantly change the observed emission-line spectrum. This is due to a combination of grain absorption of thehydrogen ionizing continuum and the fact that the correction for stimulated emission in these lines is large. Giventhese results and the likelihood that real objects have nonthermal line broadening, it seems unlikely that line opticaldepth presents a problem in using these lines as diagnostics of the physical conditions or chemical composition.

1. INTRODUCTION

The infrared spectral region makes it possible to observeobjects that may be heavily shrouded in dust and to see familiarobjects in new ways. For instance, the ultraluminous infraredgalaxies (ULIRGs) are among the most luminous objects inthe universe (Sanders & Mirabel 1996) but are difficult to studyusing conventional optical emission-line methods (see Oster-brock 1989) because of their high obscuration. Infrared spec-troscopy must lead the way in understanding these and relatedphenomena. IR line spectroscopy provides new insights to suchfamiliar objects as active galactic nuclei (AGNs; Sturm et al.2002). In some objects, little associated visible emission willbe detectable and an analysis must rely solely on IR lines.

Rubin (1968) and Simpson (1975) showed that infrared for-bidden lines can become optically thick under some conditions.This introduces an uncertainty that diminishes their usefulness forobservational analysis. When transitions become optically thick,line photons scatter before escape, and it is possible that ratios offorbidden lines will no longer indicate density and temperature orreflect the chemical composition of the emitter. Under what con-ditions do forbidden lines become optically thick, and what impactdoes this have on the diagnostic power of the lines?

In this paper, we explore a range of model Hii regions, ex-tending across plausible parameters, to determine when the lineoptical depths become large. We also show how this will affectconventional IR-line forbidden line diagnostics. This follows inthe footsteps of previous investigations of the infrared forbiddenlines done by Spinoglio & Malkan (1992) and Voit (1992).

2. PHOTOIONIZATION CALCULATIONS

The purpose of this paper is to examine what happens to theinfrared forbidden line spectrum where the lines are expectedto become optically thick. We focus on lines that form withinthe3P ground term of astrophysically abundant ions, since theseare among the strongest lines and are commonly used densityindicators. We first estimate the parameters where the lines willbecome optically thick and then examine the consequences byrunning a grid of photoionization simulations.

2.1. Optical Depth of the [O iii] 88.4 mm Line

We first develop an analytical expression for the expectedoptical depth of the3P0–

3P1 [O iii] transition. We concentrateon this transition since the oxygen abundance is large and theline is strong, and so it should suffer the largest effects.

The hydrogen ionization balance for a plane-parallel slab isgiven by (Osterbrock 1989)

�2 �1F ≥ n n a l [cm s ], (1)e p B

whereF is the flux of hydrogen-ionizing photons striking thecloud, l is the Stro¨mgren length of the H� zone, and aren ne p

the electron and proton densities, and is the case B recom-aB

bination coefficient to all levels but the first. This inequalityholds if dust is present and removes some of the ionizingradiation (see Bottorff et al. 1998). We can define an ionization

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FINE-STRUCTURE LINE OPTICAL DEPTHS 189

2003 PASP,115:188–192

Fig. 1.—Efficiency with which the cloud converts ionizing radiation intohydrogen recombination lines is shown vs. ionization parameter. This showsthe luminosity actually emitted by Hb divided by the Hb emission that wouldhave occurred had no dust been present. For low-ionization parameters, almostall ionizing radiation is absorbed by hydrogen and produces hydrogen recom-bination lines. As increases, a greater fraction of the incident starlight isUabsorbed by grains rather than hydrogen, the nebula becomes “dust bounded,”and the cloud becomes predominantly an infrared emitter. Analytical calcu-lations (Bottorff et al. 1998) show that this occurs when for a Galactic�2U ≈ 10dust-to-gas ratio.

parameterU as

FU { . (2)

n cH

Then the ionization balance equation can be rewritten as

�2N ≤ cU/a [cm ], (3)H B

where is the hydrogen column density.N p lnH H

In general, the optical deptht of a line is

glt p a N � N , (4)n l u( )gu

where is the line-center absorption cross section, anda n nn l u

are the populations of the lower and upper levels, and areg /gl u

the statistical weights of the lower and upper levels. If stim-ulated emission is neglected, then the term in parentheses be-comes simply , which is equal ton(O��) in this case. Thennl

the optical depth is

��n(O ) n(O)��t ≈ a N(O ) p a N , (5)n n H[ ][ ]n(O) n(H)

where is the oxygen to hydrogen abundance ration(O)/n(H)

and is the fraction of oxygen that is doubly ion-��n(O )/n(O)ized, averaged over the column.

The line-center absorption coefficient is related to theoscillator strength by

2�pe lfij�2a p [cm ], (6)n m c Due D

where is the Doppler line width in velocity units.DuD

Emission lines in Hii regions often have widths that cor-respond to supersonic motions. This nonthermal line broad-ening can amount to several hundred km s�1 in extragalacticH ii regions (Melnick, Tenorio-Tagle, & Terlevich 1999). Thenature of this turbulence and the physical scale this motionoccurs on are not known. The velocity width that enters intoequation (6) is given by

2 2�Du p Du � Du , (7)D th turb

where is the line width due to thermal mo-1/2Du p (2kT/m)th

tions andDuturb is themicroturbulent line width.Macroturbul-ence, due to bulk motions of entire clouds, does not add aturbulent term to equation (6), but microturbulence, in whichgas motions occur over a scale of the order of the photon meanfree path for scattering, does.

Here we assume that only thermal line widths contribute toline broadening, to obtain the largest line-absorption cross sec-tion and so maximize the effects of line optical depths. Wecarry through the ratioDuth/DuD, the ratio of the thermal tototal Doppler line width, as a reminder. Our assumption abovemakes this ratio equal to 1, but this ratio would be 10�1 to10�1.5 if the line widths observed in the extragalactic Hiiregions were due to microturbulence.

Substituting equation (3) into equation (5) gives the opticaldepth:

��Du n(O) n(O ) a cUth nt ≤ . (8)

Du n(H) n(O) aD B

Substituting the atomic data for [Oiii] 88.4 mm (Osterbrock1989), assuming an oxygen abundance ofn(O)/n(H) p

(Cowie & Sonaglia 1986; Savage & Sembach�43.2# 101996), and assuming a temperature of 104 K, we find

��n(O) Du n(O )th5t ≤ 4.5# 10 Un(H) Du n(O)D

��n(O)/n(H) Du n(O )th2≤ 1.44# 10 U. (9)�43.2# 10 Du n(O)D

For comparison, typical Hii regions have , so line�2U ∼ 10optical depths cannot generally be ignored.

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190 ABEL ET AL.

2003 PASP,115:188–192

Fig. 2.—Temperature of the carbonaceous dust component is plotted vs. theflux of ionizing photons. Our calculations do not extend beyond the upperlimit of cm2 s�1 that is set by the requirement that the grains survive.19F ≈ 10crit

Dust temperature increases with increasing flux and the dust would sublimatewhen . The simple estimate of the energy density temperature givenF 1 Fcrit

in the text generally reproduces this curve. Deviations are due to a combinationof grain opacity effects and grain-gas collisions.

Fig. 3.—Optical depth for the [Oiii] ll51.8, 88.356 lines is shown as afunction of the ionization parameter. The simple estimate given in the textpredicts that the optical depth should increase linearly withU and reach unityat . Note that the optical depth actually approaches an asymptote�2U ∼ 10crit

at large values of . This is because of grains absorbing the incident continuumUand the very large correction to the line opacity due to simulated line emission.

2.2. A Series of Model Calculations

Next, we will compute a series of blister-style model Hiiregions and examine the effects that line optical depth has onthe predicted forbidden-line diagnostics. Version 96 of the spec-tral synthesis code Cloudy is used (Ferland 2002), and Bottorffet al. (1998) and Armour et al. (1999) give further details ofour assumptions. This calculation includes the improved grainphysics described by van Hoof et al. (2001). For comparison,this produces less photoelectric heating than the previous sim-pler grain models. We use interstellar medium (ISM) abun-dances—a few relative to hydrogen are He/Hp 0.098,C/H p , N/H p , O/H p ,�4 �5 �42.5# 10 7.9# 10 3.2# 10Ne/Hp , and Ar/Hp . The geometry is�4 �61.2# 10 2.8# 10given by Baldwin et al. (1991)—a plane-parallel slab irradiatedby a stellar continuum. The continuum source used is a 40,000K blackbody. This was chosen for simplicity and because wedo not expect our results to strongly depend on the continuumshape.

For simplicity, the hydrogen density was assumed to be con-stant. Models with logn(H) p 2, 3, and 4 were computed. Theline optical depth (eq. [9]) has no explicit dependence on den-sity, but level populations do.

We examined a range of ionization parameters, or equiva-lently the ratio of the flux of H-ionizing photonsF to density.There is no lower limit to the value ofU that can occur, althoughvery low ionization Hii regions are not observed. Note thatvery few doubly ionized ions are present when .�2.5U ≥ 10There is an upper limit toU, however, because we assume thatgrains exist, which limits models to those in which the grain

temperatures are below their sublimation points. Grains tendto equilibrate at a temperature a bit above the energy densitytemperature of the local radiation field, so the grain temperatureis a function ofF rather thanU. A typical grain sublimationtemperature is on the order of 103 K, therefore we can definea critical valueFcrit such that at higher flux the grains will betoo hot to survive. We findFcrit p cm2 s�1 as the192.46# 10upper limit to the flux (and corresponding ionization parameter)that we consider.

Settingt equal to 1 in equation (9), we can find a valueUcrit

such that the [Oiii] lines are optically thick for values of:U ≥ Ucrit

�43.2# 10 Du n(O)D�3U ≥ 6.9# 10 . (10)crit ��n(O)/n(H) Du n(O )th

All calculations were carried out over a range ofU that ex-ceeded this limit.

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FINE-STRUCTURE LINE OPTICAL DEPTHS 191

2003 PASP,115:188–192

Fig. 4.—Ratios of lines from the3P ground terms of five ions. Panels give the ratio of the intensity of the stronger line relative to the weaker line as a functionof the ionization parameter. [Neiii] ll15.5, 36; [Oiii] ll51.8, 88.356; [Nii] ll121.7, 205.4; [Siii] ll18.67, 33.47; and [Ariii] ll8.98, 21.82 are plotted. Theseions are not the predominant stage of ionization for all values ofU; for instance, oxygen is predominantly doubly ionized only when .log (U) ≥ �2.5

3. RESULTS

Bottorff et al. (1998) show that there is a critical value ofthe ionization parameter above which grains, rather than hy-drogen, will absorb ionizing radiation. Figure 1 shows theefficiency with which the cloud converts ionizing radiation toionized hydrogen for our calculations. WhenU is low, almost

all of the radiation goes into ionizing hydrogen, while at largeU most of the radiation is absorbed by dust and the cloudbecomes “dust bounded.” The hydrogen column density(eq. [3]) and associated optical depth (eq. [9]) are overestimatesin this limit since the size of the H� zone is overestimated.This will prevent the IR line optical depths from becoming aslarge as equation (9) suggests.

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192 ABEL ET AL.

2003 PASP,115:188–192

The calculations include a complete description of the grainphysics, including charge, drift velocity, and temperature (vanHoof et al. 2001). Figure 2 shows the temperature of the averagecarbonaceous grain versus the flux of ionizing photons. Grainswill sublimate when is greater than cm�2 s�1 as a result19F 10of their high temperature. This flux corresponds to an upper limitof log for logn(H) p 4, the largest hydrogen density con-U ≈ 5sidered in our simulations, and log for logn(H) p 2.U ≈ 7

Figure 3 shows the optical depth of the [Oiii] lines versusU for three values of the hydrogen density. For smaller valuesof increasingU, the optical depths increase as expected fromequation (9), but for higherU the lines approach an asymptotethat is not predicted by equation (9). Part of this is because,as mentioned above, the dust absorption that occurs at highvalues ofU makes equation (9) an upper limit.

A further contributor is the fact that the correction for in-duced emission (eq. [4]) is not negligible for these lines atdensities near or above their critical density. This means thatthe term present in equation (4) cannot be neglected.N (g /g )u l u

The excitation temperatureTexc is defined as

n /n { (g g ) exp (�x/kT ), (11)u l l u exc

wherex is the line excitation energy. When the density is ator above the critical density,Texc will approach the gas kinetictemperature, which is given by the electron temperature . WeTe

can rewrite equation (4) as

t p a N [1 � exp (�x/kT )]. (12)n l exc

Then we see that, since K and , we can4T ∼ 10 kT k xe exc

expand equation (4) as

t ≈ a N x/kT p a N . (13)n l exc n l

Hence, the line optical depths are much smaller than expected.Multiple scattering of marginally optically thick transitions

will have a similar effect at lower densities: the population ofthe upper level relative to the lower level increases, makingthe correction for stimulated emission large. All of these pro-cesses prevent the line optical depth from ever becoming large.

We made several plots showing the ratio of the stronger toweaker line for the five3P ions with greatest abundance(Fig. 4). This ratio can be used as a density indicator for someconditions (Osterbrock 1989). These plots show that these ratiosremain valid density indicators, even for conditions where wewould have expected that the lines would become optically thick.

The top two plots, the neon and argon ratios, show that theratios of line intensities start to increase significantly for largevalues ofU. These transitions have the highest critical densitiesof those shown, and so they are well below their critical den-sities, and so , for the parameters shown. This meansT p Texc e

that the correction for stimulated emission is small, so opticaldepths do affect the ratios, but only at the very largestU.Objects withU this large would have remarkably high dusttemperatures, close to their sublimation point.

4. CONCLUSIONS

The possibility that infrared fine-structure lines could becomeoptically thick mitigated their utility by introducing a basic un-certainty. We have presented calculations that span the full densityand ionization range that occurs in Hii regions. These includedparameters where the IR lines should be very optically thick.

With few exceptions, optical-depth effects are not as importantas one might have thought. First, the Stro¨mgren length does notincrease monotonically with increasingU because of grain ab-sorption of the incident continuum. This makes gas column den-sities and optical depths smaller than predicted by simple esti-mates. Second, the correction for stimulated emission is verylarge for infrared transitions at nebular temperatures, and thisagain makes the line opacity and optical depths much smaller.On top of this, real Hii regions have nonthermal componentsto their line widths, which may further reduce the optical depth;our calculations assumed thermal broadening only.

For all of these reasons, the IR lines are largely opticallythin and should be a useful diagnostic of the physical conditionsin most reasonable circumstances.

This work has been supported by NSF through grant AST00-71180 and by NASA with NAG 5-12020 and NAG 5-8212.We thank the referee for a careful review of the manuscript.

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