TESTING MODELS of LOW-EXCITATION PHOTODISSOCIATION REGIONS with FAR-INFRARED OBSERVATIONS of REFLECTION NEBULAE Rolaine C

Home , HD 259431, Reflection nebula

TESTING MODELS OF LOW-EXCITATION PHOTODISSOCIATION REGIONS WITH FAR-INFRARED OBSERVATIONS OF REFLECTION NEBULAE Rolaine C. Young Owl Department of Physics and Astronomy, University of California at Los Angeles, Mail Code 156205, Los Angeles, CA 90095-1562 Margaret M. Meixner1 and David Fong Department of Astronomy, University of Illinois, Urbana, IL 61801; [email protected], [email protected] Michael R. Haas NASA Ames Research Center, MS 245-6, Moﬀett Field, CA 94035-1000; [email protected] Alexander L. Rudolph1 Department of Physics, Harvey Mudd College, 301 East 12th Street, Claremont, CA 91711; [email protected] and A. G. G. M. Tielens Kapteyn Astronomical Institute, P.O. Box 800, 9700 AV Groningen, Netherlands; [email protected] Received 2001 August 2; accepted 2002 June 24

ABSTRACT This paper presents Kuiper Airborne Observatory observations of the photodissociation regions (PDRs) in nine reflection nebulae. These observations include the far-infrared atomic fine-structure lines of [O i]63 and 145 lm, [C ii] 158 lm, and [Si ii]35lm and the adjacent far-infrared continuum to these lines. Our analysis of these far-infrared observations provides estimates of the physical conditions in each reflection nebula. In our sample of reflection nebulae, the stellar effective temperatures are 10,000–30,000 K, the gas densities are 4 102 2 104 cm3, the gas temperatures are 200–690 K, and the incident far-ultraviolet intensities are 300–8100 times the ambient interstellar radiation field strength (1:2 104 ergs cm2 s1 sr1). Our observations are compared with current theory for low-excitation PDRs. The [C ii] 158 lmto[Oi]63lm line ratio decreases with increasing incident far-ultraviolet intensity. This trend is due in part to a positive correlation of gas density with incident far-ultraviolet intensity. We show that this correlation arises from a balance of pressure between the H ii region and the surrounding PDR. The [O i] 145 to 63 lm line ratio is higher (greater than 0.1) than predicted and is insensitive to variations in incident far-ultraviolet intensity and gas density. The stellar temperature has little effect on the heating efficiency that primarily had the value 3 103, within a factor of 2. This result agrees with a model that modifies the photoelectric heating theory to account for color temperature effects and predicts that the heating efficiencies would vary by less than a factor of 3 with the color temperature of the illuminating field. In addition to the single-pointing observations, an [O i]63lm scan was done across the molecular ridge of one of our sample reflection nebulae, NGC 1977. The result appears to support previous suggestions that the ionization front of this well-studied PDR is not purely edge-on. Subject headings: dust, extinction — infrared: ISM — ISM: lines and bands — reflection nebulae

1. INTRODUCTION Far-infrared (FIR) spectroscopy is a standard tool for studying the energetics of PDRs. FIR emission from the Photodissociation regions (PDRs) are regions of the fine-structure transitions of singly ionized atomic carbon interstellar medium in which the astrochemistry, structure, ([C ii] 158 m) and neutral atomic oxygen ([O i] 63 and 145 and physical processes are determined by the interaction of l lm) dominate the cooling of the PDR gas (Tielens & far-ultraviolet (FUV; h ¼ 6 13:6 eV) radiation with inter- Hollenbach 1985a, hereafter TH85). Because dust grains stellar gas and dust. PDR chemistry is dominated by FUV absorb FUV photons and reemit the energy in the FIR, the photodissociation of molecular bonds. Many important FIR continuum dust emission is proportional to the inci- chemical reactions in PDRs are initiated by FUV-pumped dent FUV flux. Hence, PDRs in massive star-forming vibrationally excited molecular hydrogen. Most of the inci- regions were productive sites for early FIR analysis because dent FUV flux (e99%) is absorbed by dust grains and ree- mitted in the infrared continuum. A small percentage of their very bright FIR line and continuum emission. The regions proximal to massive stars contain very dense (e105 (d1%) of the incident FUV photons cause the photoejec- cm3) gas being illuminated by very strong UV fields tion of electrons from small dust grains and large molecules; G e 5 G these electrons then collisionally heat the PDR gas. Energy ( 0 10 , where 0 is in units of the average interstellar radiation field [ISRF] intensity of 1:2 104 ergs cm2 s1 balance is maintained by radiative cooling, predominantly sr1; Habing 1968). FIR observations of massive star-form- through line emission in the far-infrared ( 30 200 lm). ing regions in Orion (Melnick, Gull, & Harwit 1979; Russell et al. 1980; Genzel & Stutzki 1989 and references therein; Stacey et al. 1993; Herrmann et al. 1997; Luhman et al. 1 NSF CAREER Fellow. 1997) and M17 SW (Storey, Watson, & Townes 1979; 885 886 YOUNG OWL ET AL. Vol. 578

Russell et al. 1981; Harris et al. 1987; Stutzki et al. 1988; illuminated by stars of spectral type ranging from B0 to Meixner et al. 1992) have been well modeled by the theory B9.5. The results are compared with predictions from the low- of dense PDRs (TH85; Sternberg & Dalgarno 1995; Hollen- density PDR theory of Hollenbach, Takahashi, & Tielens bach & Tielens 1997 and references therein). Because the (1991, hereafter HTT91) and from Spaans et al. (1994). 2 2 5 sensitivity of FIR detectors has continued to increase stead- HTT91 modeled PDRs with density 10 cm < n0 < 10 2 3 ily over the past 25 yr, it has become possible to extend the cm and incident FUV intensity 1 G0 10 . Spaans et FIR study of PDR energetics to the lower energy and lower al. (1994) modeled the effects of color temperature on the density regimes more commonly found in the interstellar energetics of PDRs around cool stars. medium (ISM). An initial focus was on the lower excitation PDRs found in reflection nebulae illuminated by early B stars (e.g., Makinen et al. 1985; Chokshi et al. 1988; Howe 2. OBSERVATIONS AND RESULTS et al. 1991; Steiman-Cameron, Haas, & Tielens 1997). Table 1 lists our target sample consisting of nine reflection Visual reflection nebulae are expected to be excellent can- nebulae illuminated by stars of spectral type ranging from didates for studying low-excitation PDRs. The stars illumi- B0 to B9.5 and effective temperatures 10,000–30,000 K. nating them are usually type B or later stars, compared to These sources were chosen to study the neutral work func- the O-type stars that illuminate massive star-forming tion and photoelectric yield of interstellar dust grains under regions. Because of the lower UV flux emitted from later- a range of low-excitation conditions. The sample consists of type stars, the ionization of atomic hydrogen is expected to six quiescent reflection nebulae, two reflection nebulae near balance recombination at a smaller Stro¨mgren radius than active star-forming regions (NGC 1333 and NGC 1977), for O-type stars, resulting in a smaller H ii region. More- and a reflection nebula illuminated by a post–asymptotic over, confusion caused by shock-excited [O i] is less likely, giant branch (AGB) star (Red Rectangle). The observations because the gas is more quiescent (i.e., the ionization shock were carried out in 1989 March and in 1992 January, June, fronts are weaker). Another advantage to observing reflec- and July using the 91 cm telescope of the Kuiper Airborne tion nebulae is that even though the IR surface brightness Observatory (KAO) with the facility cryogenic grating spec- may be lower than in very luminous high-density PDRs, trometer (CGS; Erickson et al. 1984). Each reflection nebula reflection nebulae PDRs are likely to be more spatially was observed at the peak in its FIR continuum emission. extended because of more gradual FUV attenuation, allow- Guiding was done using offsets D (arcsec), D (arcsec) from ing the structure to be spatially resolved. A reflection nebula the illuminating star. The exception was NGC 1333, where PDR is expected to be less dense by a factor of 10–104 than BD +30549 was the guide star instead of SVS 3, which the PDR in a massive star-forming region such as Orion, illuminates the FIR peak. 5 6 3 which has n0 10 10 cm . Standard chopping techniques were employed through- In this paper, FIR analysis following the method in out; the chopper amplitude was 50–90, and the chopper Chokshi et al. (1988) is used to estimate the physical condi- rotation angle was individually selected for each source to tions in reflection nebula PDRs and to test how spectral type avoid background contamination (see Table 2). The detec- affects PDR energetics. FIR line and continuum observa- tor arrays were flat-fielded by dividing each spectrum by tions were conducted for a group of reflection nebulae that of a known calibration source (Table 2). In 1989 March

TABLE 1 Target Reflection Nebulae for FIR Spectroscopy

Oﬀsets R.A. Decl. L* (arcsec) Distance a Name Illuminating Source (B1950.0) (B1950.0) Stellar (L) (D, D) (pc) Reference

NGC 1977...... 42 Ori 05 32 55.1 04 52 11 B1 V 29,000 176, 284.b 450 40 0.70 1, 2 190, 283.c 450 40 0.70 1, 2 249, 211.d 450 40 0.70 1, 2 NGC 2068...... HD 38563N 05 44 10.9 00 04 17 B2 IIIII 3,000 0, 0 500 100 0.65 3, 4, 5 IC 446 ...... IC 446 No. 1 06 28 21 10 29 42 B2.5 V 2920 0, +24 1200 0.65 6, 7 Parsamian 18 = NGC 2316 ...... Star A 06 57 16.6 07 42 16 B23e 1400 9, +2.e 800 300 0.65 8, 9, 10 1400 9, +32.f 800 300 0.65 8, 9, 10 NGC 2247...... HD 259431 06 30 19 10 21 38 B6pe 2300 7, 14 900 0.45 6 NGC 1333...... BD +30549 03 26 14.1 31 14 33 B6 2300 119, 185 500 200 0.35 11, 12 NGC 2245...... Lk H 215 06 29 56 10 11 24 B78 II 1020 (550) 0, +24 900 0.40 6 Red Rectangle...... HD 44179 06 17 37.0 10 36 52 B9 I 1050 0, 0 330 0.30 13 Ced 201...... BD +69 1231 22 12 14 70 00 11.4 B9.5 V 56 0, +17 420 0.30 6

Note.—Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. a Fraction of the bolometric stellar ﬂux emitted in the FUV. b NGC 1977 C ii location in 1989 March. c NGC 1977 C ii location in 1992 January. d NGC 1977 O i peak of the crosscut scan. e Parsamian 18 H2 peak. f 00 Parsamian 18 30 north of H2 peak. References.—(1) Howe et al. 1991; (2) Makinen et al. 1985; (3) Strom et al. 1975; (4) Strom, Grasdalen, & Strom 1974; (5) Lada, Evans, & Falgarone 1997; (6) Casey 1991; (7) Herbst et al. 1982; (8) Lopez et al. 1988; (9) Ryder et al. 1998; (10) Sellgren 1986; (11) Harvey, Wilking, & Joy 1984; (12) Strom, Vrba,& Strom 1976; (13) Cohen et al. 1975. No. 2, 2002 PDRs IN REFLECTION NEBULAE 887

TABLE 2 varied to fit the lines that had high signal-to-noise ratios, KAO Observations but the line widths were fixed at the instrumental values for the low signal-to-noise ratio spectra in which the line width a b c Source Date Chop P.A. Calibrator could not be properly constrained. The line intensities, con- NGC 1977...... 1992 Jan 9 7 85 KL tinuum flux densities, and measured beam sizes for all sour- NGC 1977...... 1989 Mar 17 8.5 45 KL, Jupiter ces are listed in Table 3, except for the [O i]63lm scan of NGC 2068...... 1992 Jan 10 6 80 KL NGC 1977, which is listed in Table 4. The quoted errors are IC 446 ...... 1992 Jan 7 6 90 KL statistical only and represent one standard deviation of the P18...... 1989 Mar 17 5.8 105 KL, Jupiter mean. They do not include the absolute calibration error, NGC 2247...... 1992 Jan 9 7 80 KL which is estimated to be 30% (3 ). NGC 2245...... 1992 Jan 9 7 70 KL The strongest FIR lines, [C ii] 158 lmand[Oi]63lm, NGC 1333...... 1992 Jan 10 6 100 KL were detected for all of the reflection nebulae except the Red Red Rectangle...... 1989 Mar 15 6 90 KL, Jupiter Rectangle and Ced 201. For the Red Rectangle, no fine- Ced 201...... 1992 Jun 16 5.25 0 Saturn structure lines were detected, and for Ced 201, only the [C ii] a Chopper amplitude in arcmin. 158 lm line was detected. In addition, the [O i] 145 lm line b Position angle of chopper on sky; counterclockwise from north. was measured for NGC 2245 and IC 446, and [O i] 145 lm c Flux and flat-field calibrator. When there are two listed, the first is and [Si ii]35lm were measured for NGC 1333, Parsamian primary. 18, and NGC 1977. Because NGC 1977 has an edge-on orientation, a scan was made through the previously observed [O i]63lm peak, perpendicular to the ionization front and 1992 January, the calibration source was Becklin- revealed in the 6 cm map of Makinen et al. (1985). Neugebauer/Kleinmann-Low (BN/KL), so the reference The Red Rectangle stands apart from the other reflection spectra were taken at nearby wavelengths that had minimal nebulae in our sample. No FIR atomic lines were detected. telluric absorption and were free of astrophysical line emis- Using the more sensitive Infrared Space Observatory Long sion. Laboratory measurements were used to remove the Wavelength Spectrometer, Fong et al. (2001) detected the differential instrumental response, and the absolute flux cal- Red Rectangle in the [O i]63lm, and their detected line flux ibration was derived from Erickson et al. (1981) with a is smaller than our 3 upper limit and thus consistent. Our correction for the difference in beam size (see Steiman- observations reveal weak emission from the high-J transi- Cameron et al. 1997 for details). Corrections were also tion, CO J ¼ 17 16. High-J transition CO probes warm applied to account for diffraction effects (0.9 at 34.8 lmto (103 K), dense (107 cm3) gas that is generally located close 0.7 at 157.7 lm). In 1989 March, Jupiter served as a secon- to the exciting star (Justtanont et al. 1998). This lone CO dary flux calibrator and gave results that were roughly 20% transition is insufficient for the FIR analysis done here. higher than BN/KL, but the diffraction correction is more However, an excitation temperature Tex ¼ 33 K, which is a difficult for Jupiter, because the source is comparable in size lower limit to the gas kinetic temperature for the Red Rec- to the CGS beam. In 1992 June/July, the calibration source tangle, was derived from the CO J ¼ 17 16 line intensity. was Saturn, so the calibration spectra were taken at the same wavelengths as the source spectra; the absolute flux 3. THE GEOMETRY OF THE NGC 1977 PDR: calibration was accomplished by multiplying the ratioed i spectra by the flux of Saturn as computed from the disk [O ]63lm SCAN (Bezard, Gautier, & Marten 1986) and ring (Haas et al. The PDR of NGC 1977 is the best-studied source of our 1982) contributions using the geometric model of Matthews sample. Makinen et al. (1985) provided a detailed study of & Erickson (1977). the dust of the interface region and demonstrated that the No atmospheric correction is required for [Si ii], as there molecular cloud to the southwest was externally illuminated are no absorption features in the bandpass 2%. To correct by the B1 V star 42 Ori. In a companion paper, Kutner et al. the other lines for atmospheric absorption, the water vapor (1985) provided a detailed study of the chemical composi- overburden was determined from observations of an iso- tion and structure of the molecular cloud. They claim that lated water line at 85.4 lm and/or the wing of a heavily the H ii region/molecular cloud interface is not edge-on, as saturated line at 63.3 lm, which falls in the [O i]63lm band- the bright rim globule suggests, but rather tilted or curved, pass. These water lines were measured in absorption against so that a significant portion is more face-on, a geometry pre- bright continuum sources and fitted with theoretical trans- viously suggested by Wootten et al. (1983). This tilted geom- mission curves generated by the atmospheric modeling etry is supported by the overlap of CO and 6 cm continuum program ATRAN (Lord 1992). The zenith water vapor emission, as well as the spatial coincidence of CO and C76 overburden varied from 4 to 8 precipitable microns. In the emission. More recently, Howe et al. (1991) mapped the vicinity of the [O i] 145 lm, CO (J ¼ 17 16) 153 lm, and interface in the [C ii] 158 lm line and modeled the region as [C ii] 158 lm lines, the primary absorber is ozone. The ozone an edge-on PDR. They successfully demonstrated that overburden was obtained from the Total Ozone Mapping clumpiness can explain the extended nature of the [C ii] Spectrometer (R. S. Stolarski 1990, private communication; emission. Stolarski et al. 1991). Ratios of ATRAN spectra, including In order to better understand the structure and energetics air-mass corrections, were used to remove atmospheric of this interface region, we have made an [O i]63lm cross- effects from the measured spectra. cut perpendicular (P:A: ¼ 45) to the H ii region/molecular The final corrected spectra were least squares fitted with a cloud interface that passes through the peak in the 6 cm flat continuum and a superposed Gaussian line profile. The map of Kutner et al. (1985). The [O i]63lm line intensities four free parameters are the continuum strength and the line are listed in Table 4. Figure 1 shows the structure of the [O i] strength, width, and wavelength. All four parameters were 63 lm crosscut normalized with respect to the peak position 888 YOUNG OWL ET AL. Vol. 578

TABLE 3 FIR Line Intensities

Line Intensity Continuum Beam Date Name lm (104 ergs s1 cm2 sr1) (Jy) (arcsec) (GMT)

NGC 1977a ...... [O i] 63 7.1 0.3 300 30 41.9 1992 Jan 9 10 0.5 230 30 32.7 1989 Mar 17 [C ii] 158 7.6 0.2 280 20 40.0 1992 Jan 9 [O i] 145 1.4 0.1 330 10 40.2 1992 Jan 9 [Si ii] 35 1.3 0.4 52 20 48.7 1992 Jan 9 NGC 1977b ...... [O i] 63 4.9 0.5 380 50 41.9 1992 Jan 9 [C ii] 158 6.2 0.2 200 20 40.0 1992 Jan 9 NGC 2068...... [O i] 63 2.3 0.3 210 40 41.9 1992 Jan 10 [C ii] 158 8.1 0.2 150 30 40.0 1992 Jan 10 [O i] 145 0.9 0.2 190 30 40.2 1992 Jan 10 IC 446 ...... [O i] 63 0.7 0.2 58 20 41.9 1992 Jan 7 [C ii] 158 1.8 0.1 23 20 40.0 1992 Jan 7 Parsamian 18c ...... [O i]63 11 0.5 290 30 32.7 1989 Mar 17 [C ii] 158 4.6 0.3 150 40 41.2 1989 Mar 17 [O i] 145 1.4 0.5 150 100 42.2 1989 Mar 17 [Si ii]35 4.1 (3 ) 220 60 36.3 1989 Mar 17 Parsamian 18d ...... [O i]63 2.1 (3 ) ... 32.7 1989 Mar 17 NGC 2247...... [O i] 63 2.5 0.3 81 20 41.9 1992 Jan 9 [C ii] 158 2.1 0.2 ... 40.0 1992 Jan 9 NGC 2245...... [O i] 63 3.6 0.4 ... 41.9 1992 Jan 9 [C ii] 158 2.7 0.2 80 10 40.0 1992 Jan 9 [O i] 145 0.5 0.1 82 10 40.2 1992 Jan 9 NGC 1333...... [O i]63 14 0.8 580 60 41.9 1992 Jan 10 [C ii] 158 4.8 0.1 390 10 40.0 1992 Jan 10 [O i] 145 3.4 0.3 510 30 40.2 1992 Jan 10 [Si ii] 35 1.2 0.4 170 30 48.7 1992 Jan 10 Red Rectangle...... [O i]63 1.1 (3 ) 210 30 32.7 1989 Mar 15 [C ii] 158 0.58 (3 ) ... 42.0 1989 Mar15 [Si ii]35 3.8 (3 ) 220 40 36.3 1989 Mar15 CO J=17–16 153 0.5 0.2 ... 42.1 1989 Mar15 Ced 201...... [O i]63 0.76 (3 ) 78 (3 ) 43.8 1992 Jun 16, Jul 1 [C ii] 158 0.33 0.02 15 1 41.6 1992 Jul 1

a Observed at C ii peak of NGC 1977. b The NGC 1977 O i crosscut peak. c Parsamian 18 H2 peak. d 00 30 N of the Parsamian 18 H2 peak.

(S8; see Table 4). The [O i]63lm peak is well separated from the 6 cm continuum emission, which traces the ionized gas (Kutner et al. 1985), suggesting an edge-on orientation. On the other hand, the [O i] emission appears spatially coinci- TABLE 4 dent with the [C ii] 158 lm (Howe et al.1991), which traces NGC 1977 [O i] 63 lm Crosscut the ionized carbon zone of the PDR, and the CO J ¼ 1 0 (Kutner et al. 1985) and C18O J ¼ 2 1 (Minchin & White R.A. Offseta Decl. Offseta I [O i](63 lm)b Continuumb 1995) line emission, which trace the molecular gas. (arcsec) (arcsec) (104 ergs cm2 s1 sr1) (Jy) An edge-on PDR that is clumpy, as suggested by Howe et i 185 ...... 147 2.4 0.5 2 28 al. (1991), cannot explain the spatial coincidence of the [O ] 207 ...... 169 3.3 0.4 96 19 and [C ii] emission, because in an edge-on clumpy region, 228 ...... 190 4.6 0.4 214 24 one would expect the [O i]63lm emission to decrease more 249c ...... 211c 6.2 0.5 193 25 rapidly than the [C ii] 158 lm emission. Specifically, if we 270 ...... 232 6.0 0.5 181 26 assume Howe et al.’s (1991) edge-on clumpy model 313 ...... 275 5.7 0.5 ... 4 3 (nc ¼ 3 10 cm , R ¼ 0:4 pc) and an incident FUV flux 355 ...... 317 5.1 0.5 ... 398 ...... 360 2.3 0.7 ... density of G0 ¼ 5000 at the edge of the region (r ¼ 0:69 pc), then at a distance of 1.08 pc from the star, the FUV flux inci- Note.—1989 March observations. dent on a clump would decrease to G0 800. Using a Offset from 42 Ori located at R.A. (B1950.0) 05h32m5591, decl. 0 00 Figure 13 of HTT91 for line intensity estimates versus G0, (B1950.0) 04 52 11 . we find that the [C ii] line emission would be 0.5 times the b Beam size FWHM is 32>7(2:85 108 sr). i c [O i]63lm emission peak: R.A. (B1950.0) 05h32m3894, decl. (B1950.0) peak value, the [O ] line emission would be 0.3 times the 045504200. The observed C ii peak is located at R.A. (B1950.0) peak value, and the ratio of the [O i]/[C ii] intensity would 05h32m4393, decl. (B1950.0) 045605500, at offsets D ¼17600, be almost half the peak values. Since the [O i]/[C ii] intensity D ¼28400 from 42 Ori. No. 2, 2002 PDRs IN REFLECTION NEBULAE 889

Fig. 2.—FIR analysis at the C ii 158 lm emission peak in NGC 1977 gen- Fig. 1.—Our observed [O i]63lm scan of NGC 1977 from Table 4 is erates this plot of boundary curves in T0-n0 parameter space. The pair of overlaid with crosscuts taken from published NGC 1977 maps for [C ii] 158 horizontal solid lines are the excitation temperatures of the observed [O i] lmat5500 resolution from Howe et al. (1991), 12CO J ¼ 1 0at6000 reso- 63 lm and [C ii] 158 lm line intensities. The other line pairs are upper and lution from Kutner et al. (1985), C18O J ¼ 2 1at2000 resolution from lower limits on the calculated values considering the 30% calibration error Minchin & White (1995), and 6 cm continuum emission at 2000 resolution in the FIR measurements. The pair of slanted solid lines are calculated from from Makinen et al. (1985). The relative intensity normalized to the peak the observed heating eﬃciency and incident FUV ﬂux density using the intensity in each line is plotted as a function of distance in arcsecs and par- photoelectric theory of Bakes & Tielens (1994). The pair of broken lines are secs (assuming a distance of 450 pc) from the ionizing star. The peak inten- from detailed balance calculations using the line intensity ratios. The 4 3 2 1 3 3 sities in the scan for O i and C ii are 6 10 and 1:8 10 ergs cm s asterisk represents an estimate of n0 (9 10 cm ) and T0(420 K) based 1 1 sr , respectively, and for the 6 cm continuum, 0.4 mJy beam . The scan on the boundary curves. G0 5040. crosses an unresolved point source in the 6 cm map that is thought to be a background source that is unrelated to the H ii region (Kutner et al. 1985). We have interpolated a 6 cm peak that represents the H ii region. the photoelectric heating theory of Bakes & Tielens (1994; see the Appendix). The broken line pairs are from detailed balance calculations using the observed line intensity ratios ratio is relatively constant if not increasing at larger distan- [C ii] 158 lm/[O i]63lm(dotted line), [C ii] 158 lm/[Si ii] ces into the cloud, we conclude that the PDR of NGC 1977 is not an edge-on clumpy PDR. Rather, the PDR of NGC 1977 is much like Kutner et al. (1985) envisioned it, a tilted and perhaps curved PDR.

4. PHYSICAL CONDITIONS For each reflection nebula, we can obtain estimates of the gas temperature (T0), gas density (n0), incident FUV flux (G0), and heating efficiency of the PDR gas () by analyzing the observed FIR continuum and line emission. The details of this analysis have been presented by Chokshi et al. (1988) and Steiman-Cameron et al. (1997) for the reflection nebulae NGC 7023 and NGC 2023. The relevant equations are summarized in the Appendix. Here, we summarize the results. Boundary curves in T0-n0 parameter space generated by our analysis are used to constrain n0 and T0 for each reflection nebula. Two examples of these plots are shown in Figures 2 and 3 for NGC 1977 and IC 446, respectively. All four of the targeted FIR fine-structure lines ([C ii] 158 lm, [O i] 145 lm, [O i]63lm, and [Si ii]35lm) were detected in Fig. NGC 1977. The horizontal solid lines indicate the excitation 3.—Boundary curves in T0-n0 parameter space are based on the only temperatures of [O i]63lm and [C ii] 158 lm, which provide cooling lines detected at the FIR peak of IC 446: [C ii] 158 lm and [O i]63 lm. The pair of horizontal solid lines are the excitation temperatures of the lower limits on the gas kinetic temperature derived from the observed line intensities. The line pairs are upper and lower limits on the observed line intensities (see the Appendix). The other line calculated values considering the 30% calibration error in the FIR measure- pairs are upper and lower limit values that were calculated ments. The pair of slanted solid lines are calculated from the observed from the observed line intensities considering the 30% cali- heating efficiency and incident FUV flux density using the photoelectric theory of Bakes & Tielens (1994). The pair of dashed lines are from detailed bration error in FIR measurements. The pair of slanted balance calculations using the [C ii] 158 lm/[O i]63lm line intensity ratio. 3 solid lines in Figure 2 are calculated from the observed heat- The asterisk represents an estimate of the physical conditions: n0 10 3 ing efficiency, , and incident FUV flux density, G0, using cm and T0 280 K. G0 772. 890 YOUNG OWL ET AL. Vol. 578

TABLE 5 Results of FIR Analysis on Reflection Nebulae

HTT Teﬀ Td Td n0 T0 3 3 Name (K) (K) (K) G0 (cm ) (K) (10 ) I158/I63 I145/I63 I35/I63

Diﬀuse ISMa ...... 30,000 20 ... 1 102 80 3.0 ...... Ced 201...... 10,000 40b 32 300 4102 200 3.0 0.43 ...... NGC 2245...... 12,500 40b 35 350 5103 570 7.6 0.75 0.1 0.14 0.03 ... IC 446 ...... 19,200 51 36 770 1103 280 2.7 2.6 0.7 ...... NGC 7023c ...... 17,000 50 42 2600 4103 200 2.9 0.85 0.3 ...... NGC 2068...... 20,300 41 43 2800 5103 250 3.4 3.5 0.5 0.39 0.04 ... NGC 2247...... 14,400 40b 45 4400 4103 370 4.7 0.84 0.1 ...... NGC 1333...... 14,000 45 46 4800 2104 690 4.1 0.34 0.02 0.24 0.03 0.08 0.001 NGC 1977...... 25,400 40 46 5000 9103 420 2.9 0.93 0.1 0.16 0.01 0.18 0.05 Parsamian 18 ...... 30,000 65 49 8100 1104 690 1.8 0.42 0.03 0.13 0.05 ... NGC 2023d ...... 23,000 53 53 15,000 2104 400 2.6 0.19 0.01 0.06 0.01 0.06 0.001 Orion Bare...... 38,000 75 63 44,000 2105 230 4.0 0.11 0.01 0.07 0.001 ... M17f ...... 48,000 68 65 56,000 3104 500 2.5 0.18 0.03 0.13 0.03 0.85 0.05 Red Rectangleg ...... 13,000 50 71 100,000 ... 33 0.46 ......

Note. HTT —Teff is the effective temperature of the illuminating source. Td is the dust temperature from the modified blackbody fit. T d is the dust temperature estimated from G0 using low-density HTT91 theory. G0 is the incident FUV field. T0 and n0 are the gas temperature and density. is the observed heating efficiency (see eq. [A4]). I158/I63, I145/I63, and I35/I63 are line intensity ratios of [C ii] 158 lm, [O i] 145 lm, and [Si ii]35lmto [O i]63lm. a Td for the diffuse ISM is from Schlegel, Finkbeiner, & Davis 1998. Heating efficiency is calculated from COBE data (Wright et al. 1991; Bennett et al. 1994) and is averaged over the entire galaxy (Hollenbach & Tielens 1999). b Td is from Casey 1991. c All data are from Chokshi et al. 1988, except Td (Harvey, Thronson, & Gatley 1980). d All data are from Steiman-Cameron et al. 1997. e All data are from Tielens & Hollenbach 1985b, Herrmann et al. 1997, and Goudis 1982. f All data are from Meixner et al. 1992. g Teff, Td, and G0 are from Jura, Turner, & Balm 1997.

2 4 3 35 lm(triple-dot–dashed line), and [C ii] 158 lm/[O i] n0 ¼ 10 10 cm . The diffuse ISM in which G0 ¼ 1and 4 145 lm(dashed line; see the Appendix). For IC 446, only the our reflection nebulae PDRs in which G0 < 10 clearly fall [C ii] 158 lm and [O i]63lm lines were detected (Fig. 3). within the low-excitation regime of HTT91. The illuminat- Approximate values for T0 and n0 are obtained at the point ing stars of the reflection nebulae present a range of spectral of convergence for the curves, which is estimated by eye and types to test the effects of color temperature as modeled by indicated by an asterisk in Figures 2 and 3. Our method Spaans et al. (1994). For the entire list of PDRs in Table 5, approximates T0 and n0 to within a factor of 10. the observed cooling line intensity ratios and the estimated T0, n0, and for each reflection nebula are listed in gas densities, heating efficiencies, and dust temperatures are Table 5 in order of increasing G0, along with the ratios of discussed in the context of these PDR models. observed fine-structure line intensities, the effective temperature of the star (Teff), and the estimated dust temperature, 5.1. Cooling Line Intensity Ratios Td (see the Appendix, following eq. [A1]). Previously pub- 5.1.1. [C ii] 158 lm/[O i] 63 lm lished values for NGC 2023 (Steiman-Cameron et al. 1997), NGC 7023 (Chokshi et al. 1988), Orion (Tielens & Hollen- The standard PDR model (TH85) predicts that [O i] bach 1985b), and M17 SW (Meixner et al. 1992) have been 63 lm will dominate the cooling in high-excitation high- added to Table 5. In the last three columns of Table 5, we list density PDRs. The low-density PDR model (HTT91) predicts that the [C ii] 158 lm intensity will be comparable the line ratios of [C ii] 158 lm/[O i]63lm(¼ I 158=I 63), [O i] to or exceed the [O i]63lm. Our sample in Table 5 covers 145 lm/[O i]63lm(¼ I 145=I 63), and [Si ii]35lm/[O i] the range between high- and low-excitation PDRs. The 63 lm(¼ I 35=I 63). In x 5, we discuss the resulting relations between the listed physical parameters in Table 5. observed line intensity ratios [C ii] 158 lm/[Oi]63lm are plotted against G0 values in Figure 4. Theoretical curves from TH85 and HTT91 for densities ranging from 102 to 106 cm3 are also plotted in Figure 4 for comparison with 5. DISCUSSION the observations. The [C ii] 158 lmto[Oi]63lm line inten- In this section, the observed and derived physical proper- sity ratio is clearly higher for low-excitation conditions, i.e., ties of our sample reflection nebula PDRs are compared smaller G0 and smaller n0 values. HTT91 predicts that [C ii] with the predictions of current PDR theory and with 158 lm will dominate the cooling line emission from low- 4 3 3 previous observations of high-excitation PDRs and obser- density (nd10 cm ) PDRs with low G0 (d10 ) because of vations of the diffuse interstellar medium. The standard the relatively low transition energy (92 K) and low critical 3 6 3 3 PDR theory (TH85) considered the ranges G0 ¼ 10 10 density (ncr ¼ 2:8 10 cm ) of the collisionally excited 3 6 3 2 2 and n0 ¼ 10 10 cm , making it appropriate for modeling [C ii] fine-structure transition P1/2– P3/2 at 158 lm (TH85). high-excitation PDRs found near massive star-forming The data show that the [C ii] 158 lm/[O i]63lm intensity regions like Orion and M17. The low-density PDR theory ratio decreases with increasing G0 and n0. This result is also 4 of HTT91 extended these parameters to G0 ¼ 1 10 and consistent with the HTT91 model’s prediction of a gradual No. 2, 2002 PDRs IN REFLECTION NEBULAE 891

TH85 calculated the [O i]145lm/[O i]63lm line ratios. When both lines are optically thin, the line ratio never rises above 0.1, and when both lines are optically thick, the line ratio rises above 0.1 only for T0d100 K. But our estimated gas temperatures are 200–690 K (see Table 5). In PDRs, the [O i]63lm line is usually optically thick and the [O i] 145 lm is optically thin (Tielens & Hollenbach 1985a). Ostensibly, the line ratio [O i] 145 lm/[O i]63lm may be elevated above 0.1 because the optically thick [O i]63lm line would appear lower relative to the [O i] 145 lm line, which is optically thin. In recent years, Kaufman et al. (1999) performed new model calculations with updated chemical reaction rates and photoelectric heating rates using small grains and molecules. In agreement with earlier models, over the entire parameter space of their homogeneous model, 0:5 6:5 7 3 G0 ¼ 10 10 and n0 ¼ 10 10 cm , the [O i] 145 lm/[O i]63lm line ratio did not exceed 0.09. The observed line ratios above 0.1 may be alternatively explained by an inhomogeneous PDR model with two den- Fig. 4.—Observed line intensity ratio of [C ii] 158 lmto[Oi]63lmis sity components, a hot high-density component and a plotted against G0 for each reflection nebula (see Table 5). Theoretical PDR cooler low-density component (Meixner & Tielens 1993). curves of constant density are plotted for comparison (TH85; HTT91). The [O i]63lm line emission may be suppressed by self- absorption in the cooler low-density component if the column density is significant. This explanation has been i increase in [O ]63lm emergent line intensity with increas- invoked to explain the high [Si ii]34lm/[O i]63lminM17 ing G0 and n0, because of its high transition energy (228 K) SW (Meixner et al. 1992). The cooler low-density compo- 5 3 and high critical density (4:7 10 cm ). Interestingly, the nent has insignificant optical depths in the [O i] 145 lmand higher G0 PDRs also have higher n0, a trend that is further [Si ii]34lm lines. Hence, in a clumpy, two-component discussed in x 5.5. PDR, one may expect higher [O i] 145 lm/[O i]63lm ratios than calculated for homogeneous PDRs. 5.1.2. [O i] 145 lm/[O i] 63 lm The line intensity ratio [O i] 145 lm/[O i]63lmis 5.2. Density Estimates plotted against G in Figure 5. For comparison, theoreti- 0 To compare the densities from our FIR analysis with cal curves for a range in densities are also plotted on Fig- HTT91 theory, we used the observed line intensities for ure 5. No trend is apparent; however, all the observed the reflection nebulae to obtain density estimates inde- line ratios are higher than expected from theoretical mod- pendent from the HTT91 model. Figures 6, 7, and 8 els—above 0.1, except for NGC 2023 and the Orion Bar. show our line intensities (represented by asterisks) overlaid on scans of Figures 16, 15, and 17 (respectively) from HTT91. In the figures, only the reflection nebulae from this paper are labeled; the original labels on the data points have been suppressed for clarity. Each solid line is the predicted emergent cooling line intensity as a function of G0 for a given n0 calculated from the HTT91 model. These overlays were used to estimate the PDR gas density in the reflection nebulae from the observed [Si ii]35lm, [O i]63lm, and [C ii] 158 lm line intensities and from the calculated G0 values. The results are shown in the first three columns of Table 6. For Ced 201, the [C ii] 158 lm line intensity falls outside the density curves, so only an upper limit to n0 was obtained. For the eight reflection nebulae with observed fine-structure lines, HTT91 theory predicts the density ranges 2 3 3 n0 ¼ 5 10 6 10 cm from [O i]63lm emergent 2 3 3 3 cooling line intensity, n0 < 10 cm to n0 3 10 cm from the [C ii] 158 lm line intensity, and 4 5 3 n0 2 10 1 10 cm from [Si ii]35lm emergent line intensities. For each reflection nebula, the predicted densities from HTT91 are compared to the densities Fig. 5.—Observed line intensity ratio of [O i] 145 lmto[Oi]63lmis obtained from our FIR analysis (the column labeled plotted against G0 for each reflection nebula (see Table 5). Theoretical PDR curves of constant density are plotted for comparison (TH85; HTT91). The ‘‘ FIR ’’ in Table 6) and are also compared to previously line types of these curves are the same as in Fig. 4 and are not repeated here published values (the column labeled ‘‘ Literature ’’ in because of confusion. Table 6). The densities from our analysis agree to within 892 YOUNG OWL ET AL. Vol. 578

6 10 [OI] (63 µ m) 5 [SiII] (35 µ m) 10

4 6 10 10

1333 5 10 * P18* *P18 2245 1977* 3 1977 * 2247 10 2068* 1333 * 4 * * 10 C201 * *I446

2 -3 10 cm 3 -3 10 cm

Fig. 8.—Our reflection nebula data (asterisks) were added to a scan of ii Fig. 6.—Our reflection nebula data (asterisks) were added to Fig. 16 Fig. 17 from HTT91 showing the emergent [Si ]35lm line intensity vs. G0 from HTT91 showing the emergent [O i]63lm line intensity as a function for the low-density PDR model. In all other aspects, this figure is the same 2 3 6 3 as Fig. 6. of G0 for the low-density (10 cm < n0 < 10 cm ) PDR model. The uncertainties are approximately 2.7 times the size of the asterisk. The squares are PDRs associated with H ii regions, the triangles are PDRs associated with dark clouds, planetary nebulae, and reflection nebulae, and ii the circles are the inner 4500–6000 of external galaxies. Only the reflection by the low-density PDR model from the [Si ]35lm line nebulae from this paper have been labeled; the original labels from HTT91 intensities agree with our analysis. have been clearly suppressed. The observed points assume a unit filling factor in the beam. 5.3. Heating Efficiency Spaans et al. (1994) modified the Bakes & Tielens (1994) photoelectric heating model, which included the 1 order of magnitude with the low-density PDR model contribution by polycyclic aromatic hydrocarbons calculations from the [O i] line intensities, except for the (PAHs) in addition to very small grains (VSG) in the three cases in which Si ii is detected (NGC 1333, NGC standard TH85 model to predict the effects of changing 1977, and Parsamian 18). There the densities calculated the color temperature of the illuminating source. The Spaans et al. (1994) model found that the heating efficiency, , for PDRs illuminated by stars with Teff 6000 10; 000 K would be only a factor of less than 10 lower than the for PDRs illuminated by stars with µ [CII] (158 m) Teff 20; 000 30; 000 K. They calculate that a higher effective quantum yield for the photoelectic effect partially compensates for the fewer FUV photons available from 2068 * 1977* 3 the lower temperature stars. When exposed to the intense 1333* *P18 10 FUV field from very young type O stars, the dust grains 2245* 2247 *I446 involved in photoelectric heating may become positively * 2 10 charged and thereby decrease the efficiency of the photoelectric effect. However, in cooler stars of spectral type C201 * B0 and later, the lower FUV flux permits less ionization of the grains that may in fact be neutrally or even negatively charged and thereby maintain the photoelectric effi- 4 5 6 -3 10 10 10 cm ciency despite the lower photon energies. The grain Beam dilution 0:5 charging depends on the quantity, G0T0 =ne (ne is electron density), with values much higher than 5 104 creating positively charged grains and values much lower creating neutrally or negatively charged grains. In Figure 9, the observed heating efficiencies from Table 5 are plotted against the effective temperature of Fig. 7.—Our reflection nebula data (asterisks) were added to a scan of the illuminating stars. The plot shows that over the range Fig. 15 from HTT91 showing the emergent [C ii] 158 lm line intensity vs. Teff ¼ 10; 000 56; 000 K, the heating efficiencies are all G0 for the low-density PDR model. For beam-diluted sources, the observed points should move at 45, as indicated by the dashed line. In all other the same to within a factor of a few, with a median value aspects, this figure is the same as Fig. 6. of 3 103. This is similar to the heating efficiency calcu- No. 2, 2002 PDRs IN REFLECTION NEBULAE 893

TABLE 6 Estimated Densities

Source [O i]a [C ii]b [Si ii]c FIR d Literaturee Tracerf Referenceg

2 2 2 3 Ced 201...... 9 10 <10 ... 4 10 2 10 LFIR Casey 1991 3 2 3 3 NGC 2245...... 6 10 4 10 ... 5 10 2 10 LFIR Casey 1991 2 2 3 2 IC 446 ...... 5 10 2 10 ... 1 10 5 10 LFIR Casey 1991 3 2 3 2 NGC 2247...... 2 10 3 10 ... 4 10 5 10 LFIR Casey 1991 NGC 2068...... 9 102 3 103 ... 5 103 2 105 CS Lada et al. 1997 NGC 1333...... 4 103 5 102 2 104 2 104 104 CO Warin et al. 1996 NGC 1977...... 2 103 2 103 3 104 9 103 3 104 CO Makinen et al. 1985 3 2 5 4 4 Parsamian 18 ...... 3 10 5 10 1 10 1 10 2–4 10 H2 Ryder et al. 1998

Note.—Densities are in cm3. a The [O i]63lm emergent intensity calculated from the low-density PDR model of HTT91 vs. G0 (see Fig. 6). b The [C ii] 158 lm emergent intensity calculated from the low-density PDR model of HTT91 vs. G0 (see Fig. 7). c The [Si ii]35lm emergent intensity calculated from the low-density PDR model of HTT91 vs. G0 (see Fig. 8). d The densities estimated by the FIR analysis in this paper. e Density estimates from the literature. f The tracer used to estimate the densities from the literature. g References for the density values from the literature. lated from COBE measurements of the diffuse ISM the range of our sample. Thus, variations in grain charg- (Wright et al. 1991; Bennett et al. 1994), which is ing at different Teff may well account for the apparent 3 3 10 averaged over the entire galaxy (Hollenbach & constancy of with respect to Teff. Tielens 1999). The lines in Figure 9 represent the predicted photoelectric heating efficiency as a function of Teff (Spaans et al. 1994). The lines differ in the value for 5.4. Dust Temperature T versus G 0:5 4 4 d 0 G0T0 =ne, which is 10 for the top (solid ) line, 5 10 for the middle (dashed ) line, and 105 for the bottom The dust temperature Td, obtained from the literature (dotted ) line. and from the modified blackbody described previously (see The almost constant value for is consistent with the Table 5), is plotted as a function of G0 in Figure 10. The Spaans et al. (1994) prediction that color temperature of solid line is the 60 lm/100 lm color temperature versus G0 1 the radiation field has moderate to little effect. Moreover, as calculated by HTT91. They used a dust emissivity law and assumed that the grains are in a plane-parallel slab the values for at the lowest Teff appear to fit well with 0:5 4 illuminated on one side by a UV field. Heating of the grains the lowest G0T0 =ne of 10 . As we go to higher Teff, 0:5 was assumed to be from the incident FUV flux, from the requires a higher value for G0T0 =ne. This trend would indicate that the dust grains go from neutral or nega- infrared continuum reemission by the surrounding dust, and from the cosmic microwave background. The 1 emis- tively charged to positively charged as Teff increases over sivity law should hold for these classical dust grains at G0e10. Figure 10 shows that the observed dust temperatures agree well with HTT91 theory for 4 300 G0 6 10 .

5.5. The n0,G0 Correlation One of the surprising results from our study is the correlation between the gas density, n0, of the PDRs and the incident far-ultraviolet radiation, G0. In Figure 11, we plot the logarithms of n0 against G0 as listed in Table 5. There is a clear linear correlation in this log-log plot to which we ﬁt a line:

logðn0Þ¼ð0:83 0:15ÞlogðG0Þþð0:88 0:57Þ : ð1Þ This line ﬁt is shown as a solid line in Figure 11. The physical meaning behind this correlation may be the balance of gas pressures between the PDR and the H ii region it surrounds:

n0T0 ¼ 2neTe ; ð2Þ Fig. 9.—Observed heating efficiencies, , are plotted against Teff using the data from Table 5. The error bars for the heating efficiencies assume a where n and T are the gas density and temperature of the generous factor of 2 uncertainty. The lines present the theory from Spaans 0 0 PDR and ne and Te are the electron density and electron et al. (1994) that predicts only a slight variation of with respect to Teff. The 0:5 4 temperature of the H ii region. Assuming nominal values of theoretical curves differ in their values for G0T0 =ne, which equals 10 for 5 the solid line, 5 104 for the dashed line, and 10 for the dotted line. Te ¼ 8000 K and T0 ¼ 400 K, we find that n0 ¼ 40ne. 894 YOUNG OWL ET AL. Vol. 578

The incident FUV flux on the PDR is L G0 ¼ 2 ; ð5Þ 4Rs where is the fraction of the luminosity above 6 eV. Substi- tuting in equation (4), normalizing the stellar luminosity to 5.320 10 L, which corresponds to an O7.5 star (Vacca et al. 1996), and normalizing the incident FUV flux to the ISRF (1:5 103 erg s1 cm2; Habing 1968), we find that 49 2=3 4=3 4 10 ne L G0 ¼ 1:1 10 3 5:320 : ð6Þ Q0 10 10 L 1

Finally, substituting ne ¼ 0:025n0, 49 2=3 10 n0 4=3 L G0 ¼ 80:4 3 5:320 : ð7Þ Q0 10 10 L 1 While the above formula is explicitly correct for an O7.5 Fig. 10.—Logarithm of the dust temperature Td is plotted against the star, it is also correct to within a factor of 1.5 for the range logarithm of G0 for each reflection nebula. The solid line is predicted from of stars in our sample, because the changes in Q , L , and the HTT91 model. 0 * almost cancel out for the different spectral type stars. Thus, we can simplify the above relation to n0 4=3 G0 ¼ 80:4 : ð8Þ The density in the H ii region, ne, and its Stro¨mgren 103 radius, R , are related through the ionizing flux, Q : s 0 In log-log format, this equation becomes 1=3 3Q0 logðn0Þ¼0:75 logðG0Þþ1:58 ð9Þ Rs ¼ 2 : ð3Þ 4ne and is plotted in Figure 11 as a dashed line. The theoretically Taking ¼ 3:09 1013 cm3 s1, which results from our derived slope agrees with the best-fit line slope within the assumption of Te ¼ 8000 K (Spitzer 1978), and normalizing errors of the line fit. The intercept is slightly higher than 49 1 Q0 to 10 s , which corresponds to an O7.5 star (Vacca, allowed by the errors but still in rather remarkable agree- 3 3 Garmany, & Shull 1996), and ne to 10 cm , we find that ment, given some of the simplifications of the derived expression. 1=3 3 2=3 Q0 10 18 In some sense, this correlation between n0 and G0 is a relic Rs ¼ 2:0 10 49 : ð4Þ 10 ne of the star formation process. Higher mass stars have a higher luminosity and thus a larger G0 value. These more massive stars also have more substantial H ii regions that exert a larger pressure on their surrounding molecular clouds, resulting in a larger density in the PDR to balance the H ii region pressure. It is possible that other factors related to the star formation process may underly this n0, G0 relation. For example, higher mass stars require higher density environments to form than lower mass stars. However, the balance of pressures between the H ii region and the PDR appears to be an adequate explanation.

6. CONCLUSIONS We present observations of FIR fine-structure lines and FIR continuum emission from nine reflection nebulae illuminated by stars ranging in spectral type from B9 to B0, representing stellar effective temperatures Teff ¼ 10; 000 30; 000 K. Our FIR analysis provides estimates of the physical conditions in reflection nebulae. For 2 our sample, the gas densities ranged from n0 ¼ 4 10 to 2 104 cm3, and the gas temperatures ranged from T0 ¼ 200 to 700 K. The dust temperatures, estimated from fitting a modified blackbody curve to FIR continuum obser- Fig. 11.—Logarithm gas density n0 is plotted against the logarithm of G0 for each reflection nebula. The solid line is the best fit to the data. The vations, are Td 65 K. These results are compatible with dashed line is the theoretical relation that results from pressure balance of HTT91’s low-density PDR theory. We find several interest- the H ii region and PDR gas. ing trends in the data: No. 2, 2002 PDRs IN REFLECTION NEBULAE 895

1. The [C ii] 158 lmto[Oi]63lm line ratio decreases The authors would like to thank E. Erickson, J. Baltz, with increasing G0 and n0. S. Lord, J. Simpson, S. Colgan, and M. Burton and the 2. The [O i]145lmto63lm line ratio is higher (greater KAO staff for help with the observations. Thanks are than 0.1) than predicted by HTT91. extended to P. Carral for help with the 1989 March data 3. The effective temperature of the illuminating stars reduction and to S. Colgan for doing the 1992 June data caused no noticeable trend in the observed heating efficien- reduction. Support of the instrument team by NASA cies, which primarily had the value 3 103, within a factor under UPN 352 is acknowledged. R. C. Young Owl, of 2. This result is consistent with the Spaans et al. (1994) M. Meixner, and D. Fong were partially supported by model, which modified the photoelectric heating theory of NASA grants NAG2-1067 and NAG5-3350. In addition, Bakes & Tielens (1994) to account for color temperature M. Meixner received partial support from NSF effects. CAREER award AST 97-33697. R. C. Young Owl 4. The dust temperatures obtained from the modified received additional support from a University of Illinois blackbody fitting roughly agree with those predicted by the Dissertation Completion Fellowship and from a UC HTT91 dust temperature theory. Presidential Postdoctoral Fellowship. D. Fong was also 5. An unanticipated correlation of gas density, n0,and supported by a University of Illinois Research Board incident FUV fluxes, G0, appears in our sample. This corre- Grant. Meixner, Young Owl, and Fong acknowledge lation can be adequately explained by a pressure balance support from the Laboratory for Astronomical Imaging between the H ii region and PDR. at the University of Illinois and NSF grant AST 96- 6. An [O i]63lm scan perpendicular to the molecular 13999. A. Rudolph was supported by the NSF Young ridge of NGC 1977 supports previous suggestions (Wootten Faculty Career Development (CAREER) Program via et al. 1983; Kutner et al. 1985) that the geometry of this NSF grant 96-24924 and by a New Faculty Research well-studied PDR is not purely edge-on. Grant at Harvey Mudd College.

APPENDIX

THE PHYSICAL CONDITIONS IN PDRs Here, we present the relevant equations for the analysis of the physical conditions in PDRs. Details of the methodology are described in Chokshi et al. (1988) and Steiman-Cameron et al. (1997). The observed far-IR dust continuum provides a rather direct estimate for the incident FUV field, G0, between 6 and 13.6 eV, I G ¼ 2 fir ; ðA1Þ 0 1:2 104 where the factor 2 accounts for the geometry of the cloud (Meixner et al. 1992; Steiman-Cameron et al. 1997) and the factor 1:2 104 converts the IFUV incident field intensity into units of the average interstellar radiation field (Habing 1968). The factor represents the fraction of the stellar flux between 6 and 13.6 eV (see Table 1). The FIR dust continuum was con- 1 structed from the KAO data by fitting an optically thin blackbody function, S BðTd Þ, to the observed FIR continuum with Td, the dust temperature, and S, a normalization factor proportional to the dust optical depth. The G0 derived this way are consistent with the incident fluxes estimated from the stellar characteristics and the projected distances, as given by L G 8:5 108 ; ðA2Þ 0 r2 where r2 ¼½ðDÞ2 þðDÞ2d2, d is the distance in parsecs from the cloud to the observer, is the fraction of the star’s luminosity emitted in the far-ultraviolet, and L* is the bolometric luminosity in L. Theoretically, the photoelectric heating efficiency depends on the local physical conditions (Bakes & Tielens 1994), 3 102 : A3 ¼ 1=2 ð Þ 1 þ 2=3G0T0 =n0 Observationally, the heating efficiency is measured by ratioing the observed intensities of the cooling lines to the incident FUV intensity, ÀÁ I ii þ I i þ I i þ I ii ½C ;158 lm ½O ;63 lm ½O ;145 lm ½Si ;35 lm ; A4 ¼ 4 ð Þ G0 1:2 10 where the incident FUV intensity is described in terms of G0, derived above from the observed FIR dust continuum. Using the G0 derived above, this analysis provides a relationship between the density, n0, and temperature, T0, of the emitting gas. The kinetic temperature of the gas can be estimated from the observed line intensities. Assuming plane-parallel semi-infinite slab geometry with constant temperature and density under LTE conditions, Tex and the observed integrated line intensity, I, are related by v I ¼ B ðT Þ f ðÞ ; ðA5Þ ex c 896 YOUNG OWL ET AL.

1 where is the frequency of the line (s )andB(Tex) is the Planck function, v is the turbulent Doppler line width (taken to be 1.5 km s1; HTT91 and Chokshi et al. 1988), c is the speed of light in km s1, and f() is the optical depth factor from TH85. Observationally and theoretically, the [O i]63lm and [C ii] 158 lm lines are expected to have moderate optical depth (TH85) and f ðÞ1. At densities below the critical density (2 103 cm3 for [C ii]and3 105 cm3 for [O i]), the excitation temperatures derived this way provide lower limits to the actual kinetic temperature of the gas. Finally, the line ratios I158 lm/I63 lm, I158 lm/I145 lm, and I158 lm/I35 lm can be calculated from detailed balance for the level populations as a function of the density and temperature of the emitting gas (cf. TH85). This can be inverted to derive a relationship between n0 and T0 from the observed line ratios. This requires an assumption on the elemental abundances for which we adopted C=H ¼ 3:0 104 and O=H ¼ 5:0 104. Relevant atomic parameters have been taken from the compilation of TH85.

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