2021325 Zoom

THz

30m (17/3/3) 30m (17/3/3) (19/12/21) 10 m30 m

0; Mpc 0; Mpc 10% 10$ 10# 10( 10% 10$ 10# 10( # 10 m 30 m 10 ( ( CI ?$ − ?% ( kpc CI ? − (? 10$ # $ 1 0 10% size 10&$ (AArHD E = 2 − 1 eam ( b &# I ( I 10 CII ?(⁄# − ?$⁄# 10&'10&( 10&# 10&$ 10%10&'10&( 10&# 10&$ 10% redshift redshift The Astrophysical Journal,743:94(19pp),2011December10 Rangwala et al.

(a)

(b) sub-mm–THz 000 221

The Astrophysical Journal,743:94(19pp),2011December10 Rangwala et– al. – O 111 O 312 2 2 + 111 303 312 413 211 514 • 11) 12) 13) 14) 15) 16) Arp 220 (ULIRG) H H – – O – – – – – – – – – – 9) 10) 11) 12) 2 2 – – – – 8) H NH NH

## ## – NH + + + Herschel, 17 − 40 2 2 O 202 O 312 O O 321 O 422 O 220 O 523 II 2 2 2 2 2 2 2 NH OH H OH CO (9 (12HCN H H (13HCN CO (10 H H H (14HCN CO (11 (15HCN CO (12 H (16HCN NH N CO (13 (17HCN (a) 5(?)

– ~ 6 − 15 kpc 6 + 202 – 5) – 3) 4) 5) 6) 7) 0) 1) – – – – – /HOC – – + + + + 2 + (1 (2 O O O 211 2 2 2 I I CO (4 C (6HCN HCO CO (5 CO (6 H H H CO (7 C CH NH OH CO (8 3 Jy

20 NH HF 10 (c) (b)

Flux 0 500 600 700 800 900 1000 1200 1400 Figure 1. Herschel SPIRE-FTS spectrum3 of4567 Arp 220. TheGHz spectrum shows the FIR continuum between 190 and 670 µm in (a). Red solid points in (a) are the continuum measurements from the SPIRE photometer and the dotted curves show the photometer(Rangwala bandpasses+ 11 with arbitrary normalization.) Line identiﬁcations are shown for several molecular and atomic species in (b) and (c) with like colors for like species. (A color version of this ﬁgure is available in the online journal.)

(c)

Figure 1. Herschel SPIRE-FTS spectrum of Arp 220. The spectrum shows the FIR continuum between 190 and 670 µm in (a). Red solid points in (a) are the continuum measurements from the SPIRE photometer and the dotted curves showFTS the photometer spectrum bandpasses we start with arbitrary resolving normalization. the broad Line identifications spectral lines are shown towards for rest frequencies, and integrated fluxes. The FWHMs mentioned several molecular and atomic species in (b) and (c) with like colors for like species. (A color version of this figure is available in the online journal.) the higher frequency end. We use a sinc function of variable in this section are from our sinc line fitting. FWHM to fit the emission and absorption lines using the MPFIT WedetectaluminousCOemissionladderfrom J 4–3 to J FTS spectrum we start resolving the broad spectral lines towards rest frequencies, and integrated fluxes. The FWHMs mentioned = = the higher frequency end. We use a sinc function of variablepackage inin IDL.this section In Table are from1 we our sincreport line the fitting. integrated line fluxes 13–12 and several water transitions with total water luminosity FWHM to fit the emission and absorption lines using the MPFIT 1WedetectaluminousCOemissionladderfrom J 4–3 to J package in IDL. In Table 1 we report the integrated linein fluxes Jy km s13–12for and emission several water lines transitions and equivalent with total water widths= luminosity in µmfor= comparable to CO. Compared to the velocity widths measured 1 − in Jy km s− for emission lines and equivalent widths in µmfor comparable to CO. Compared to the velocity widths measured the absorption lines along with their 1σ statistical uncertainties.the absorptionin CO lines from the along ground-based with their observations 1σ statistical (e.g., SC97; uncertainties. Greve in CO from the ground-based observations (e.g., SC97; Greve The observed spectral line shape suffers from small asymmetries et al. 2009), the higher-J CO lines in our spectrum are much from instrumental effects, and the line shapes could be affectedThe observednarrower. spectral These line high- shapeJ CO linessuffers are from not resolved small and asymmetries follows et al. 2009), the higher-J CO lines in our spectrum are much by blending from weak lines. The effect on the line fluxes from the resolution of FTS, which at the frequency of J 12–11 line is 1 = asymmetries is expected to be !2%. 310 km s− .Thissuggeststhateitherthehigh-J CO emission from instrumentalis∼ coming from effects, only one and of the the nucleiline shapes or that it could is a dynamically be affected narrower. These high-J CO lines are not resolved and follows 3. LINE IDENTIFICATIONS separate component from the low-J lines. On the other hand, by blendingthe from water linesweak are lines. much The broader effect with on a thevelocity line FWHM fluxes of from the resolution of FTS, which at the frequency of J 12–11 line is 1 The spectrum (Figure 1)showstheFIRcontinuumandthe 500 km s− implying that this emission could be coming from 1 = detection of several key molecular and atomic speciesasymmetries and ∼both is nuclei. expected The observed to be ! velocity2%. separation between the two 310 km s− .Thissuggeststhateitherthehigh-J CO emission 1 Figure 2 shows zoom-in views of some of the spectral lines nuclei in Arp 220 varies considerably from 50 km s− (Downes ∼ 1 discussed in this section. In Table 1, we list their transitions, &Solomon1998;Sakamotoetal.2008)to250kms− (Scoville is coming from only one of the nuclei or that it is a dynamically 3 3. LINE IDENTIFICATIONS separate component from the low-J lines. On the other hand, the water lines are much broader with a velocity FWHM of 1 The spectrum (Figure 1)showstheFIRcontinuumandthe 500 km s− implying that this emission could be coming from detection of several key molecular and atomic species and ∼both nuclei. The observed velocity separation between the two 1 Figure 2 shows zoom-in views of some of the spectral lines nuclei in Arp 220 varies considerably from 50 km s− (Downes 1 discussed in this section. In Table 1, we list their transitions, &Solomon1998;Sakamotoetal.2008)to250kms− (Scoville

• CO • [CI] • [NII] SFR • CH AGN • OH+ AGN + • H2O AGN + • ArH • HF + • H2O CO ()

The Astrophysical Journal,795:174(39pp),2014November10 Kamenetzky et al. 10& 108 7 to ) 10 Sgr B2 (M) SgrB2(M)

0 NGC 6240 SgrB2(N) − Mrk 273 MrkMrk 231231 $ 1

, 10 Sgr A*

scaled UGC 05101

NGC 1266 +

= Arp 299-A Arp 220 7 ⨀ NGC8 1068 NGC 253 10 @ NGC 253

I M82 10 cm IRAS F17207-0014

( M82 NGC 1222 %

CO NGC 4038 scaled to Mrk 231 CO J=1-0] M83 10 M83 % warm NGC 1365-SW Cen A Galactic Cen A H Center cool SgrB2 231 Extended Inner ' Luminosity [L Galaxy 6 & 10 10 Sgr B2 extended 10# Mrk Luminosity 2 4 6 8 10 12 2 4 6 8 10 12 # % $ & Upper J 2 4 6Upper 8J 10 12 10 10 10 10 5 Figure 5. Normalized CO SLEDS. All J 1 0luminositiesarescaledtomatchthatofMrk231(3.7 10 L ). SLEDs are colored to indicate increasing LFIR with increasing lightness. Placement in the= left→ or right panel is for clarity only. On the left panel, the SLEDs× of the⊙ Galactic center ( l < 2.5) and the Inner Galaxy Upper @ | | ◦ - K (2◦.5 < l < 32◦.5), also normalized, are shown in green for comparison (Fixsen et al. 1999). On the right panel, we show the SLEDs of two star-forming cores and ./0 the extended| | envelope of Sgr B2 (Etxaluze et al. 2013) and that of Sgr A* (Goicoechea et al. 2013). Because these SLEDs begin at J 4 3, we scale J 4 3to 107 L for visual comparison of the shapes. None of the SLEDs are corrected for dust extinction. = → = → ⊙ (A color version of this ﬁgure is available in the online journal.) (Kamenetzky+ 14 ; Kamenetzky+ 14 )

Table 6 Photometry Flux Densities in Jy: SPIRE Photometer

Galaxy 250 µm Fν σtot 350 µm Fν σtot 500 µm Fν σtot Mrk 231 5.40 0.878 1.92 0.354 0.567 0.238 IRAS F17207-0014 7.67 1.29 2.84 0.451 0.944 0.284 IRAS 09022-3615 2.48 0.399 0.732 0.470 0.197 0.321 Arp 220 32.6 3.76 11.7 0.955 4.01 0.421 Mrk 273 4.27 0.822 1.49 0.225 0.491 0.139 UGC 05101 5.77 0.941 2.23 0.322 0.687 0.166 NGC 6240 6.82 0.877 2.64 0.370 0.815 0.246 Arp 299-A 22.0 1.96 7.60 0.721 2.36 0.325 NGC 1068 103 6.12 41.3 2.69 14.0 1.04 NGC 4038 (Overlap) 37.8 2.50 14.9 0.984 5.04 0.464 NGC 1222 3.65 0.387 1.43 0.319 0.446 0.202 NGC 1266 3.71 0.522 1.30 0.201 0.411 0.147 Cen A 271 60.0 110. 17.6 44.9 5.12

Note. All are from this work, see Section 2.4.

2 The results are shown in Figures 6 (best-fit spectral energy and Md Sν D /κν Bν (T ) (statistical errors in Table 15 do not = L distribution; SEDs) and 7 (histogram of best-fit parameters). The include uncertainty in κ). The values of LFIR we find when 2 1000 µm individual parameter results are in Table 14.Inallcases,onlyone modeling the SED (L 4πD Sν dν)areslightly = L 8 µm mode in likelihood space was found, and the resulting likelihood higher than those derived from utilizing only the 60 and 100 µm distributions were very well defined by Gaussians (the best- fluxes (e.g., those presented in Table! 1 from Hyperleda), by fit and the mode and median of the resulting marginalized about a factor of 1.7 0.5. parameters all aligned). Casey (2012)modeled65localLIRGSandULIRGS,fixing± Table 15 also lists the results for parameters that can be λ0 200 µmandfindingameanβ 1.60 0.38 and derived from the model above: the optical depth at 100 µm α =2.0 0.5. We find, in Figure 7 that= β and±α can vary (τ100), the dust mass (Mdust), and the far-infrared luminosity significantly,= ± but cluster around similar values. When left to from 8 to 1000 µm(L8–1000 µm or LFIR). To calculate the dust vary, λ can often be higher than 200 µm. 2 1 0 mass, we utilize κ125 µm 2.64 m / kg (Dunne et al. 2003) = − 10 The Astrophysical Journal,795:174(39pp),2014November10 Kamenetzky et al.

80 Our finding of differing temperatures between dust, [C i], and CO, is in line with the findings of others in the literature. For 50 70 example, Mangum et al. (2013)foundthetemperaturesderived from ammonia (NH3), a well-known kinetic temperature probe, 60 differed from the dust temperatures for a sample of star-forming 40 galaxies (seven of which are in our sample). We found higher 50 dust temperatures by modeling the full SED instead of just 3 3 3 3 µ I [CI] T [K] using the 60 and 100 mfluxdensities(6to11Khigher), [C ] P – P & P – P 30 40 but still confirm that TNH3 >Tdust,andaddT[C i]

10]

⨀ formation (Carilli & Walter 2013). The picture becomes more complicated when considering the

, $ 10 6 [C ii]158µmline,whichhasbeenfoundtobeemittedbyfrom a variety of sources, and may be tracing the CO-dark H2 gas %5 described above. (Note that αCO is not sensitive to reservoirs CO of H where C+ or C is the dominant form of carbon.) Pineda

678 10 2 et al. (2013) found, via a study of the Galactic center, that [C ii] & emission is produced by a combination of PDRs ( 47%), CO- log [CI] LTE Mass [M 4 25 ∼ 10 dark H2 gas ( 28%), cold atomic gas ( 21%), and ionized gas ( 4%). Langer∼ et al. (2014)alsostudiedthecolumndensitiesof∼ , '3 ∼ 10 CO-dark H2 gas of individual clouds, a level of detail we do not 7 # 8 ( 9 ) 10*+ 11** have here. We have already discussed some differences between 10 10log Molecular10 Mass from10 CO [M ] 10 our galaxies and the Milky Way; can these distributions be valid Figure 23. C i and CO mass. The horizontal line represents the average in starburst galaxies? In Section 3.5 and Table 24,wepresented (X )inSection4.5,. , + [C i]/H2 -./.,23 ⨀ the estimated percentage of C emission from ionized gas using [CI] line ratios, and found that in most cases, the fractions are higher relationship (Figure 23). They adopted a relative abundance than 4%, with a median of 14%–25%. They are not correlated 5 (Kamenetzky+ 14) X[C i]/H 3 10− .Theweightedaverageabundanceof with L or [C ii]/L .Thismatcheswiththe27%(error 2 = × FIR FIR X[C i]/H2 MC/(Mgas/1.4) mH2 /mC;usingthegasmass range 19%–46%) found for the Carina Nebula (Oberst et al. derived from= the cold component× CO ﬁtting (and therefore 2006). However, we cannot say anything about the distribution

dependent upon XCO), we found log(X[C i]/H2 ) 4.0 0.5. of the remaining source contributions, only that there is less +20 5 = − ± In a linear ratio, this is 10 7 10− ,anotparticularlywell- (proportional) [C ii] line emission from the sum of PDRs, CO- − × constrained value but consistent with the values presented in dark H2 gas, and cold atomic gas in these galaxies than in the Papadopoulos & Greve (2004)fortheCloverleafquasar,the Milky Way. Pineda et al. (2013) found that the fraction of mass Orion A and B clouds, and the nucleus of M82 (ranging from from CO-dark H2 increases with Galactocentric distance, from 5 5 1–5 10− ), as well as with the mean of 8.4 3.5 10− 20% at 4 kpc to 80% at 10 kpc. Because the emission from our reported× for high-redshift galaxies in Carilli & Walter± × (2013). galaxies is more akin to that of the Galactic center, we expect We required a higher average abundance of [C i]tomatchour lower fractions of CO-dark H2 gas than in the Milky Way as CO-derived gas mass values than in Papadopoulos & Greve awhole.AstudysimilartothatofPinedaetal.(2013)and (2004), and this discrepancy is almost entirely due to our higher Langer et al. (2014)couldbeconductedforthenearestgalaxies measured [C i]fluxesforthethreegalaxiesthatoursamples or Milky Way satellites comparing the distribution of HI, C+, share (NGC 6240, Arp 220, and Mrk 231). We differed in how 12CO and 13CO, and possibly applied to this sample of galaxies. we determined the populations of the J levels: we used both Even absent formal modeling of PDRs, we see a picture [C i]lines,calculatedanexcitationtemperature,andthenused that contradicts traditional PDR models, even with additional Boltzmann distributed populations, as opposed to using one line heating from mechanical turbulence or enhanced cosmic rays and an estimate based on the gas conditions as in Papadopoulos (e.g., Wolfire et al. 2010). Detailed studies of individual galaxies et al. (2004). In the end the population levels were roughly the have consistently found that PDR models cannot explain the same, but the different line fluxes caused the difference in [C i] large luminosities in the mid- to high-J CO lines: Arp 220 mass. We confirm the conclusions of Papadopoulos & Greve (Rangwala et al. 2011), M82 (Kamenetzky et al. 2012), M83 (2004): [C i] is as good of a tracer of total molecular mass as (R. Wu et al., in preparation), NGC 6240 (Meijerink et al. 2013), radiative transfer modeling of CO, though further refinements Cen A (Israel et al. 2014), NGC 891 (Nikola et al. 2011), and the

of the value of X[C i]/H2 will aid in its precision. Galactic center (Bradford et al. 2005). In only a few instances

33 Publications of the Astronomical Society of Japan,(2014),Vol.00,No.0 11

3 3 3 3 [CI] P1– P0 & P2– P1

Publications ofCO the Astronomical Society of Japan,(2014),Vol.00,No.0 [CI] 11 (M83) The Astrophysical Journal Letters, 897:L19 (7pp), 2020 July 1 Michiyama et al. 3 3 pc + 103 $ 10# + pc s ⨀

A $ 10 km 104 K >?@ :

% 8 Σ

7 5 10 % $ 3 $ 3 ; 10 +

10 10 10 10 10 10 9 8

7 # $% < '6 <'( )*$+% 10 10 Figure 3. (a) L[]()C I 1-- 0L CO ( 4 3 )vs. L[]()C I 1- 0L FIR for PDRT calculations and observations. The red solid and blue dashed lines indicate the theoretical tracks for −3 , +$ 3 Fig. 8. (a) Plots+constant$ ofnH (cm ) asand U auv function[G0], respectively. of The+ black$ points,wherethedatawith indicate the nearby U/LIRG sample detected by SPIRE/FTSare(Kamenetzky represented et al. 2016 by). The gray yellow points, and the remaining graphs are Σmol I[CI](1−0) '6 & I[CI](1−0) < K4 σ km s pc star shows the [C I](1–0) upper limit of NGC6052 presented in this project. L C I 1- 0'(L TIR is) calculated*$+ without% any aperture correction, indicating that this figure K km s K km s , []() ) represented indoes the not sameconstrain mannerthe Uu,v. (b) [ asC I]( in1–0 Figure) line luminosity 6. The vs. CO best-fit(1–0) line rel luminosityation for with U/LIRG a fixed galaxies. slope The symbols of unity are the to same the comparison data with sampleI as[C(aI)](1.We−0) > 4 σ is shown by the solid line, & fl note that CO(1–0) luminosity is obtained−2 by single dish,−1 but− the1 upper limit of [C I](1–0) luminosity is obtained by array observation (the missing ux is not −2 −1 −1 correspondingcorrected to α[C). I] ∼ 3.8[M⊙ pc (K km s ) ]. The dashed line is the mean value of the local galaxies (7.3 [M⊙ pc (K km s ) ]) measured

by Crocker et al. (2019). In panels (b) and (c), the(Miyamoto+ radial variation of α21[C I]is plotted,Michiyama but in (c), the+ data20 are separated) into two halves using a division of ′′ Tdust =23K. The open boxes in panel (b) represent the values binned withawidthofr =10 .Theupwardanddownwardtrianglesinpanel(c)represent characterize the PDR. The ratio suggests Uuv=4–5. likely to originate predominantly from extended, low excitation ′′ the values binned(Díaz-Santos with a et width al. 2017 of )r. =10 as well, but for Tdust > 23gas.Kand On the≤ 23 otherK, respectively.hand, higher-J d)CO Plots emission of Σmol is likelyas a function of ICO(1−0) .Thebest-fit dominated by compact, high excitation gas and the contribution relation with a fixed slope of unity is shown by the solid line, corresponding to α ∼ 0.5[M pc−2 (K km s−1)−1]. The dashed line in panel (d) represents from moreCO diffuse gas. Thus,⊙ the [C I](1−0)/CO(4–3) and 4.2. Molecular− Gas2 Mass −1 −1 the averaged value αCO ∼ 3.1 [M⊙ pc (K km s ) ]innearbygalaxiesmeasuredbySandstrometal.(2013).Pan[C I](1–0)/CO(1–0) ratios may represent properties of very els (e) and (f) are the same as panel In this section, we investigate whether [C I](1–0) can different phases of the gas, and it is possible that the Morita (b), and (c), but reflect the data for CO(1–0). trace molecular gas mass inferred from previous CO(1–0) Array resolved out most extended emission from [C I](1–0). In measurements. Albrecht et al. (2007) reported the CO(1–0) such a case, the large difference seen in Figure 3(b) can be −1 ″ integrated intensity of 82 K km s within the 24 single-dish explained if >88% of the flux of [C I](1–0) was missing due to CO 8 beam. The expected molecular mass is MMH2 =´8 10 its extended structure, possibly larger than the Maximum Bolatto et al.assuming 2013). a CO Considering(1–0) to H2 conversion the low factor temperatureαCO=0.8Me andRecoverable nar- Scale4.3 of ∼ Excitation4.3kpc. While such temperature, large missing flux column density, and −1 2 −1 line (Kkms pc ) (where MLH2 = aline lin¢ e),oneofthesmallest is not generally seen in other galaxies, follow-up mosaic row velocityvalues width usually in considered the inter-arm and often region, applied to a ULIRGs low CO(Bolattoabundancemapping observationsabundance including 12 m, Morita of Array, atomic and total carbon Fig. 8. (a) Plots of Σmol as a function of I[CI](1−0),wherethedatawithI[CI](1−0) < 4 σ are represented by gray points, and the remaining graphs are may causeet the al. 2013 low).Usingtheupperlimitofthe optical depth, and[C consequentlyI](1–0) luminosity, we the higherpower would be important to check the possibility of an represented in the same manner as in Figurecan 6. estimate The best-fit an upper rel limitation to the with implied a fixed molecular slope mass of through unity to theextremely data with extendedI[CI](1[C−I]0)(1–>0) 4distributionσ is shown in NGC by the6052. solid In line, −1 2 −1 −2 the use− of1 a−[]CI1 = 7.3 Me(Kkms pc ) (Crocker et al. 2019). either case, whether [C I]-poor or−2 with an extremely−1 −1 extended corresponding to α[CI] ∼ 3.8[Mvalues⊙ pc of(Kα kmCO s.Thevaluesof) ]. The dashedα line isdo the not mean show value the of the system- local galaxies (7.3 [M⊙ pc (K km s ) ]) measured The upper limit of molecular gas[C massI] based on [C I] is then [C I] distribution, NGC6052 is a unique laboratory to by Crocker et al. (2019). In panels (b) and (c),MM[]CI the< 10 radial8 var).Thissuggeststhattheiation of α is plotted,[C I] (1–0) butCO in(1– (c),0) the data are separated into two halves using a division of atic radial dependenceH2 ( nor a significant[CI] difference /  betweeninvestigatelow how the merger process impacts the use of [C I] T =23K. The open boxes in panel (b) representratio as well the as the values[C I](1 binned–0)/CO( wit4–3hawidthof) ratio is low. Figurer =103(b′′) .Theupwardanddownwardtrianglesinpanel(c)representas a mass tracer. dust shows the the relation between CO(1–0) and [C I](1–0) and high′′ temperatures. The dependences of αCO and α on the values binned with a width of r =10 asluminosities well, but for otherT nearby> 23 galaxiesKand taken≤ 23 fromK, Kamenetzky respectively.[C d)I] Plots of Σ as a function of I .Thebest-fit dust mol 5. Summary CO(1−0) et al. (2016).Theupperlimitwemeasureforthe[C I](1–0)/ −2 −1 −1 relation with a fixed slope of unitythe is shown dust temperature by the solid line, arecorresponding consistent to withαCO the∼ 0 results.5[M⊙ pc shown(K bkmy s ) ]. The dashed line in panel (d) represents CO(1–0) ratio in NGC6052 is located an order of magnitude We report [C I](1–0) and CO(4–3) observations of the −2 −1 −1 the averaged value αCO ∼ 3.1Crocker[M⊙ pc et(K al.below km (2019). s the global) ]innearbygalaxiesmeasuredbySandstrometal.(2013).Pan However,relation obtained only in previous a few surveys [C (Ie.g.,](1–0) Jiao datanearby are merging galaxyels NGC (e)6052 and using (f) are the the ALMA same Morita as panel fi (b), and (c), but reflect the data for CO(1–0). et al. 2017, 2019).Thissuggeststhat[C I](1–0) may not be a Array. We detect CO(4–3) with high signi cance (signal-to- available forreliable low tracer dust of moleculartemperatures. gas mass in NGC6052. Although both noise ratio of >40), but [C I](1–0) is undetected to a stringent a[]CI and αCO depend on metallicity, such a [C I]-poor region upper limit of 0.07 times the strength of the CO(4–3) cannot be explained under the assumption of any metallicity (e.g., emission. Models of PDRs can explain the weakness of [C I] Bolatto et al. 2013;Glover&Clark2016;Heintz&Watson2020). as the result of gas densities that are unusually high Bolatto et al. 2013). Considering the low temperature and nar- 4.3 Excitation temperature,53- column density, and For example, at lower metallicities CO is would be more easily (nH > 10 cm ), which might arise naturally in the collision row velocity width in the inter-arm region,dissociated a low due to theabundance lack of dust shielding, and consequently front of the ongoing merger. In addition, [C I](1–0) is far more carbon wouldCO be observed as [C I]. abundanceweaker of than atomic expected carbon for the amount of molecular gas inferred may cause the low optical depth, and consequentlyAn alternative explanation the higher for the big difference between from the existing measurements of CO(1–0) and CO(2–1) in NGC6052 and other systems in Figure 3 is resolving out NGC6052. This may suggest a [C I]-poor, CO-rich system We comparedspatially the extended molecular diffuse gas gas emission. mass The (M emissionmol,dust from, Mmoland,CO/or, extremely extended diffuse molecular gas distribution values of αCO.Thevaluesofα[CI] do not show the system- [C I](1−0) and CO(1−0) are usually co-extensive, and both are that is not well documented in the literature. atic radial dependence norand a significantMmol,[C differenceI])inthestudiedareabyapplying between low GDR = −2 −1 −1 5 20, αCO =0.5 M⊙ pc (K km s ) ,andα[CI] = and high temperatures. The dependences of αCO and α[CI] on −2 −1 −1 the dust temperature are consistent3.8 M⊙ pc with(K the km results s ) shownto the b dusty surface density, includ- Crocker et al. (2019). However,ing the only atomic a few gas [ surfaceC I](1–0) density data are and the integrated intensities available for low dust temperatures.of CO(1–0) and [C I](1–0). The resulting masses are summa- rized in Table 3. Although the mass in the entire area is consis- Fig. 9. Spatial distribution of Tex derived by substituting the ratio between [C I](1–0) and [C I](2–1), retrieved from the Very Nearby Galaxy Survey tent within the error, [C I](1–0) tends to underestimate the mass (VNGS) with Herschel/SPIRE FTS (Wu et al. 2015), into equation (14). The due to non-detection in regions with low dust temperature such region indicated by the box represents the [C I](1–0) mapping area with as the inter-arm region. ASTE.

We compared the molecular gas mass (Mmol,dust, Mmol,CO, and Mmol,[CI])inthestudiedareabyapplyingGDR = −2 −1 −1 20, αCO =0.5 M⊙ pc (K km s ) ,andα[CI] = −2 −1 −1 3.8 M⊙ pc (K km s ) to the dust surface density, including the atomic gas surface density and the integrated intensities of CO(1–0) and [C I](1–0). The resulting masses are summa- rized in Table 3. Although the mass in the entire area is consis- Fig. 9. Spatial distribution of Tex derived by substituting the ratio between [C I](1–0) and [C I](2–1), retrieved from the Very Nearby Galaxy Survey tent within the error, [C I](1–0) tends to underestimate the mass (VNGS) with Herschel/SPIRE FTS (Wu et al. 2015), into equation (14). The due to non-detection in regions with low dust temperature such region indicated by the box represents the [C I](1–0) mapping area with as the inter-arm region. ASTE. 3 3 3 3 [CI] P1– P0 & P2– P1

• NGC 1808 (+ 21) M83 (Miyamoto+ 21) NGC 6052 (Michiyama+ 20) à CO J=1–0 ( HI)

(Michiyama+ 20) (1)

• [NII] (1461 GHz) A&A 587, A45 (2016) & we discuss above. We thus combine the NGC 891 and M 51 data, • $ representing normal star-forming regions, to deﬁne the best-ﬁt 10# relation as

kpc log ⌃ = (0.79 0.05) log F + (4.60 0.05), (2) SFR 10 SFR ± 10 [NII]205 ± % which is valid in the ranges of 8.9 < log10 F[NII]205 < 7.5 $ $% 10 and 2.4 < log10 ⌃SFR < 1.2, where the units are as stated previously. The scatter, deﬁned as the standard deviation of the yr residuals between the observed and predicted ⌃ , is 0.10 dex. SFR ± • SF ⨀ $& A similar yet o↵set relation to Eq. (2) is formed by M 83 and 10 NGC 4038/9 with a gradient m of 0.69 0.05, y intercept of / 4.38 0.05 and a 0.16 dex scatter. We stress,± however, all of the (Hughes+ 16) ± $' caveats and issues we mention above, especially the small sam- à SFR && 10 ple size, that should be considered when using these relations for

. estimating the star formation rate. (?) *,- )*+ $6 $7 $8 5. Conclusions

Σ 10 10 10 $& $% In this paper, we aimed to test whether the [Nii] 205 – 24 µm Fig. 3. The ⌃9SFR –:;;F[NII]205&#Antennae galaxies NGC 4038 and best-fitting linear relation from the M 51 and NGC 891 data. 4039, we have shown that not only is this empirical relationship also observed in face-on galaxies, but also that the correlation appears to be governed by the star formation rate (SFR). Both Simply combining all the data to define an average relation is the nuclear starburst in M 83 and the merger-induced star forma- prevented by the aforementioned o↵set in the individual galaxy tion in NGC 4038/9 exhibit less [Nii] emission per unit SFR sur- relations. To interpret this o↵set, we use the Starburst99 stellar face density than the normal star-forming discs. These regions of population synthesis code (Leitherer et al. 1999) to model the intense star formation exhibit stronger ionization parameters, as ⌃SFR–F[NII]205 relation following the approach of Herrera-Camus traced by the 70/160 µm far-infrared colour. The stronger ioniza- et al. (2015), who consider that gas heating by FUV photons tion parameters suggest the presence of higher ionization lines emitted from star-forming regions relate to gas cooling from the that may become more important for gas cooling, thereby re- [Nii] line via the photoelectric e↵ect in PAHs and dust grains. In ducing the observed [Nii] 205 µm line emission in regions with brief, we assume a stellar population with a constant SFR over 3 higher star formation rates. Alternatively, dust obscuration may 100 Myr and solar metallicity and adopt the Geneva evolution- become more e↵ective in more compact star-forming regions, ary tracks (zero rotation) and Kroupa initial mass function. From meaning more ionizing photons go towards dust heating instead the resulting spectrum, given as a function of the duration of the of gas heating. We used a simple model based on Starburst99 to star formation episode, td, we integrate across the energy range predict the ⌃SFR–F[NII]205 relation; we found that regions with of photons that dominate the dust grain photoelectric heating, more recent star formation in the merging Antennae galaxies specifically 6 < E < 13.6 eV. The product of the fraction of NGC 4038/9 and the central starburst in M 83 likely cause the these FUV photons responsible for the photoelectric heating of o↵sets in [Nii] emission per unit SFR surface density found be- dust grains and the photoelectric heating eciency of the dust tween these galaxies and the normal star-forming discs. Finally, gives the overall heating eciency, ", which we vary between we present a general relation between the [Nii] 205 µm line flux 0.1 and 3% to estimate the amount of gas heating. We further density and star formation rate for main-sequence star-forming assume that the cooling of the gas is typically dominated by the galaxies. [Cii] transition and that the [Cii]/[Nii]205 line ratio theoretically Clearly, future studies should seek to analyse spatially varies around 4 for a range of electron densities (see Oberst ⇠ resolved observations of other FIR lines (e.g. [Nii] 122, et al. 2006). The [Nii] and FUV flux densities are then related [Ci] 370 µm) for a larger sample that includes not only central by F 0.25 " F (t ) for a given ⌃ . [NII] ⇠ FUV d SFR regions of galaxies, but also sites of star formation along the spi- Comparing the model predictions to the observations in ral arms. Although observations of [Nii] 205 µm can be followed Fig. 3, we find the vast majority of regions in NGC 891 and up over a large redshift range by facilities such as NOEMA and M 51 may have been actively forming stars for t 20 Myr d ALMA, which can observe the line emission at z 0.6 in band- with " between 1 and 3%. As a result of the model degeneracy 10 and at z 3.2 in band-7, care should be taken⇠ in the use of between td and " (see Herrera-Camus et al. 2015 for details), the line as a⇠ star formation tracer given the apparent dependency M 83 and NGC 4038/9 exhibit a stellar population with either a of the local [Nii] emission on the ionization parameter. star formation duration of t 20 Myr and " . 1% or more re- d cent star formation episodes of td = 2 Myr and " between 1 and Acknowledgements. We thank the anonymous referee for the useful comments 3%. This suggests that these two galaxies also possess regions and suggestions that helped to improve this paper. T.M.H. and E.I. acknowledge with higher SFRs from recently triggered star formation, likely CONICYT/ALMA funding Program in Astronomy/PCI Project N:31140020. T.M.H. also acknowledges the financial support from the Belgian Science Policy due to the merger (NGC 4038/9) or central starburst (M 83), as Oce (BELSPO) in the frame of the PRODEX project C90370 (Herschel- PACS Guaranteed Time and Open Time Programs: Science Exploitation). 3 For Z = 0.2 Z , the y-intercepts of the model lines in Fig. 3 increase M.B. and I.D.L. acknowledge the financial support of the Flemish Fund for by a factor of 0.01 (i.e. lines shift upwards). Scientific Research (FWO-Vlaanderen). SPIRE was developed by a consortium

A45, page 6 of 7 (2) H 10#$ Ar+ • ArH+ (618 GHz, 1235 GHz) to ArH+ • 10#%& 10#%' • H2O (620 GHz) 10& PKS 1830-211 abundance #' 1.0 10 + H2O #(

38 + 10

/ 0.9 ArH fraction + O atom

3 ' H2O #) 0.8 H 10 & #' #( #) 36ArH+ 10 10 10 10

7 from surface mag −200 0 200 8 < = 0.88582 km s#% (Müller+15 Schilke+ 14) (3)

No. 1, 2005 INTERSTELLAR FLUORINE CHEMISTRY 265 • HF (1232 GHz) 80 60 () K • HF/H2 ~3.6×10 40

• 123 20 0 The Astrophysical Journal,785:22(5pp),2014April10 10- Monje et al.

8 H C+ 2 C0 CO 1.2 6 (. 1.0 ⁄ 10 emission 0.8 absorption 7 HF 0.6 10(/- F 1.0 0 6 CF+ Continuum

⁄ 0.8 HI −100 0.6 beam 0 2 4 6 −200 density ⁄ 2 3 absorption Fig. 2.—Gas temperature and abundances in a one-sided PDR with nH Fig. 3.—HF destruction rates in a one-sided PDR with nH 10 cmÀ and 0.4 −300 2 3 9: mag ¼ ¼ 10 cmÀ and UV 1. UV 1. Destruction rates are shown for photodissociation by ISUV (magenta

Flux ¼ curve¼)andforreactionswithC+ (red curve), Si+ (blue curve), He+ (cyan curve), −Figure200 2. Upper panel:0 spectrum of200 the ground-state400 transition of HF J 1–0 Figure 3. Normalized spectrum of the ground-state transition of HF J 1–0 and Hþ (green curve). The black curve shows the total HF destruction rate.

mJy 3 (black) normalized by the corresponding continuum toward NGC 253 and= the =

(/ (black) withFlux respect to the continuum toward NGC 4945 and two Gaussian fits Gaussian fit (green) of the emission component. Lower panel: HF normalized sight1 line to HD1 208440. Similar F/O abundances were inferred Velocity km s (dashed green lines) center at 543( kmMonje s− and 637+ km 14 s− with δV(FWHM)Neufeld+ 05) absorption profile (black) obtained after subtracting the Gaussian line. H i 47 km s 1 and δV(FWHM) 40 kmfrom s 1,respectively.HFUSE observationsi absorption spectrum of F=i in HD 209339A and from the − − face. Indeed, the abundance of HF closely mirrors that of H2 (as absorption spectrum (blue, in LSR velocities) toward the central continuum (blue, in LSR velocities) toward= theoriginal central continuum discovery source of from F i toward Ott et al. Sco (by Copernicus;Snow& source from Koribalski et al. (1995) is also shown for comparison, the conversion (2001)isshownforcomparison. expected, given the fact that HF is formed by direct reaction of between heliocentric velocities and LSR velocities is ν ν –2.95kms 1. York 1981). The assumed gas-phase fluorine abundance cor- LSR = HSR − (A color version of this figure is available in the online journal.) H2 with F). Figure 5 shows the same data presented in Figure 4, (A color version of this figure is available in the online journal.) responds to roughly 0.6 times the solar abundance of fluorine. now expressed in terms of the HF/H2 abundance ratio; its value The possible effects of fluorine depletion in dense regions are 8 continuum originating from the nucleus and moving away from always lies within an order of magnitude of 3:6 ; 10À , the value 3.1. Column Densities of the Absorbing HF Gas it and toward us along the lineconsidered of sight. The in redshifted3.4 below. emission achieved in the limit of large A when H and HF are the The strongx tendency toward HF formation is immediately V 2 in the HF profile, must then originate from gas behind the dominant reservoirs of gas-phase H and F nuclei. From the line-to-continuum ratio in the absorption profiles continuum source and moveapparent away from from the Figure nucleus 2: HF and accounts us. for at least 50% of the gas- we can obtain a direct measurement of the HF column densities. To estimate the molecularphase mass in fluorine the outflow, nuclei we at adopt all depths an AV k 0:1. Figure 3 compares 3.3. Two-Sided Illumination First, we derive apparent optical depths of the HF lines (τ HF abundance relative to H of 3.6 10 8,basedonthe = the2 rates of various− HF formation and destruction processes as ln[2TL/TC –1],wherethespectrumisnormalizedwithrespect chemical predictions of Neufeld et al.× (2005), consistent also We have extended the results presented in Figures 4 and 5 to − a function of depth into the cloud. At all A ,HFformationis to the single sideband continuum), assuming that the foreground with the HF abundances observed toward galactic diffuse clouds V the case in which radiation is incident upon both sides of a slab 7 dominated by reaction of F with H (reaction [R1]). At small absorption covers the continuum source entirely, and that all (Sonnentrucker et al. 2010; Monje et al. 2011a)andoutflows 2 of finite thickness. Here calculations made use of the modifi- HF molecules are in the ground rotational state, due to the AV (AV P 2forthisparticularcase),HFdestructionisdominated (e.g., Emprechtinger et al. 2012). In high-mass,+ star-forming cations to the PDR code described at the beginning of 3. In large spontaneous emission coefficient of HF and low rates regions, however, where theby densities reaction are with much C higher(reaction compare [R3]) and by photodissociation by x Figure 6, solid lines show the total H2 and HF column densities, of collisional excitation. The resulting normalized spectra are to those of diffuse clouds, theISUV obtained radiation. HF abundances These processes are lower become less rapid with increas- 2 3 shown in Figures 2 and 3.ForNGC253,wecalculatetheoptical + N(H2)andN(HF),ina slabwith UV 1andnH 10 cmÀ ; by about two orders of magnitudeing AV,(e.g., as the Emprechtinger C abundance et drops al. in favor of C and CO and the ¼ ¼ 10 the results are shown as a function of the total visual extinction depth from the absorption profile obtained after subtracting 2012 derived HF abundancesISUV as low field as 5 is10 attenuated− in the denser by dust absorption. For intermediate × through the cloud, A (tot). As expected from Figure 5, the H aGaussianlinecenteredatthesystemicvelocity,fittingthe parts of the massive star formationA (in the region range of2–4 NGC for 6334 this I). case), reaction with Si+ (reaction V 2 emission component of the HF spectrum (see Figure 2). The V 5 6 3 and HF column densities track each other closely. In Figure 7, The low abundance of HF[R4]) under these becomes dense dominant. (10 –10 cm Once− ) the Si+ density begins to drop at velocity integrated optical depth ( τdV) over the velocity and warm (100–150 K) conditions is most likely caused by we plot N(HF)asafunctionofN(H2)forseveralvaluesof UV 1 AV k 4, HF destruction is dominated by reaction with Hþ and interval from 63 to 295 km s− for NGC 253 and from 445 and the freeze-out of HF onto dust grains. The polar nature of HF 3 and n . The dashed line corresponds to N(HF)/N(H ) 3:6 ; 1 ! 1 He+. In this regime, the abundances of H and He+ are controlled H 2 720 km s− for NGC 4945, is 100 and 115 km s− , respectively. implies large desorption energy. However, dynamically active 3þ 10 8,thevalueobtainedinthelimitwhereH and HF¼ are the by the cosmic-ray ionization rate and are essentially independent À 2 We thus derive the HF column densities for the correspondent regions such as outflows and inflows can provide the needed sole gas-phase reservoirs of H and F nuclei. In Figure 8, N(HF) LSR velocity range using Equation (3) of Neufeld et al. (2010) energy for this desorption, andof A HFV; this abundances effect provides in these active a ‘‘floor’’ below which the total HF 14 8 is shown as a function of AV (tot). and obtain total HF column densities of 2.41 0.73 10 regions are similar to thosedestruction found in diffuse rate clouds never (few drops. 10− ; 14 2 ± × We note that the column densities and visual extinctions plot- and 2.77 0.85 10 cm− toward NGC 253 and NGC 4945, Emprechtinger et al. 2012). This explanation is supported by respectively.± The× uncertainties in the resultant column densities ted in Figures 6–8 all refer to a single slab viewed face-on. Geo- evidence for thermal desorption of another polar molecule,3.2. Parameter H2O, Study are originated from the random noise and the systematic errors in dynamically active outflow (Franklin et al. 2008; Kristensen metric effects can lead to significant multiplicative factors that introduced by the calibration uncertainties (Roelfsema et al. et al. 2010). Thus, using theWe theoretical also obtained HF/H2 resultsabundance for incident radiation with inten- affect the measured column densities and extinctions. For ex- 2012) 1 3 4 and a source size equal tosities the beam UV sizeof 10 17′′À (,1,10,100,10300 pc), the ,and10 times the average ample, a plane-parallel slab viewed at an inclination angle will 8 ∼ 7 mass of the outflowing gas is M(H2)out 0.97 10 M . show line-of-sight column densities and extinctions that exceed radiation field given by Draine⊙ (1978) and for H nucleus densi- 3.2. Gas Kinematics—Molecular Outflow in NGC 253 The outflow projected maximum (terminal)1.5= velocity2 × measured2.5 3 3.5 4 3 ties nH of 10 ,101 ,10 ,10 ,10 ,and10 cmÀ .InFigure4, the plotted quantities by a factor of sec . The presence of mul- ArotatingnucleardiskofcoldgasinNGC253wassuggested from the absorbing gas is about 130 km s− ,measuredfrom tiple clouds on a given sight line can lead to similar effects. the velocity interval, wherewe the present absorption HF isabundance deeper than profiles 3σ for selected cases covering a as a result of the velocity shift of the absorption feature seen 1 wide range of assumed density and ISUV field. Here the abun- in the H i spectrum (Koribalski et al. 1995). In addition to the (νSYS 100) km s− .TheoutflowinNGC253hasitscentral 3.4. Effects of Variable Fluorine Depletion axis− normal to the galaxydance disk (i.e., plottedi 12 is;Westmoquette normalized with respect the total gas-phase rotation, the P-Cygni profile present in the HF spectrum line = ◦ and also in the OH spectra (e.g., Sturm et al. 2011) indicates a et al. 2011), then the actualabundance maximum of outflow fluorine velocity nuclei. isThe tendency to HF formation is The theoretical results presented in 3allassumethatthede- 194 km s 1.Theoutflowextendsfromafewhundredparsecsstrikingly robust. In every case we considered, substantial HF pletion offluorine nuclei is independentx of A .Theobservational radial motion of gas, characteristic of an outflow. The blue- ∼ − V shifted absorption must arise from a region in front of the to tens of kiloparsecs, withabundances the majority are of the achieved molecular at depths gas AV > 2 below the cloud sur- data, however, suggest that the fluorine depletion is far greater

7 8 2 The continuum at 180 µmand350µmextentstoadiameterof 10 kpc The mass is given by MH2 mH µH2 NH2 D Ω,wheremH is the ∼ = × × × × (Melo et al. 2002)and 1.6 kpc (Gear et al. 1986), respectively, much larger H-atom mass, µH2 2.8 is the molecular weight per hydrogen molecule, D is ∼ than the HIFI beam at the∼ HF wavelength, equivalent to a 0.3 kpc diameter on the distance to the source, and Ω θ 2π/4 is the solid angle, with θ the the source. angular diameter. =

3 (4)

• CH (532/536 GHz, 1471/1477 GHz) • • ! CH⁄CO ~2×10+, à AGN • OH+ (909 GHz, 971 GHz, 1033 GHz) + • H2O (1115 GHz, 1139 GHz) • H+ • AGN The Astrophysical Journal,779:75(12pp),2013December10 Scoville & Murchikova

• • He/H

The Astrophysical Journal,779:75(12pp),2013December10The Astrophysical Journal,779:75(12pp),2013December10@A Scoville & Murchikova @A Scoville & Murchikova & implies an H ii region emission measure30 (EM 24nenp vol)22 of 20 50 41 37 34 32 ( 62 3 #$% 13 = 3 1 # EM 4.60 10 cm− (using αB 2.6 10− cm s− at Te 4 = × = × 31 3 =1

10 K). Using# the10 speciﬁc emissivity of 3 10 erg cm s × − − −

for H i-26α from Figure 2,oneﬁndstherecombinationline C 5000 K s 32 1 luminosity will be LH26α 1.38 10 erg s− .Forasource I II cm H He 7 = × 1 distance of 1 Mpc and a line width of 30 km s− ,thiscorresponds &

to a peak line ﬂux density of 3.3 mJy. This ﬂux density is ⁄ #&' > 7500 K readily detectable# at a signal-to-noise∼ ratio of 10σ within 1hr

10 F with ALMA Cycle 1 sensitivity. ∼ 1 10000 K 2.2. He Line Emission > > 10 CE , cm

10 K 10 K , He i has an ionization# potential&( of 24.6 eV, and its photoion- K ization requirements10 are not very different than7500 those of HKi. 7500 K C 15000 K

Thus, the He i recombination lines probe the ionizing UV radia- 7 tion ﬁeld in much the same way as H i (see Section 3). Since the > 20000 K He i submm lines will be weaker than those of H i because of the lower Heergs abundance,# we&$ do not examine the He i emission extensively here10 and instead focus on He ii. 10 Figure 1. Emissivities of the H i α recombination lines are shownThe for ionizationT potential of He ii is 54.4 eV, corresponding to

4 =7 + ++ 10 K. The emissivity is given per unit ne np,andthex-axisphotons has the lower with λ 228 Å for conversion200 of He to500 He .Since 800200 500 800 quantum number of the Hα transitions. The emissivities were calculated for = Figure 2. Emissivities of the H i submm recombination linesFigure are shown 3. Emissivities for of the He ii submm recombination lines are shown for 0 10 20 30 40 50 the most massive starT in7500 an and SB 10 will4 K. have The emissivity surface temperaturesis given per unit n n .Thetopborder 4 n 10, 1000, and for 104 cm 3, and the curves for all densities are coincident. e p T 7500 and 10 K. For He ii, it is per unit ne nHe++ .Thetopborderhasthe 2 8 e − 50,000 K, the ionizinghas= the EUV quantum from number such of a the populationα transitions, will and have their restFigure frequencies= 4. Emissivity are on ratios of He ii to H i are shown as a function of principal quantum number n for ne 10 –10 and Te 7500, 10,000, and 15,000 K. The = quantum number of the α transitions, and their rest4 frequencies are on the bottom4 3 ∼ frequency GHz 4 3 = = only a very small fractionthe bottom of the axis. photons The emissivities with energy were calculatedsufficient for tone emissivities10axis., 1000, The and emissivities are for normalized were calculated to H i foratn 10e K10, and1000, density and 10 cm 10− ,andcm− , so one can see the dependence on ion, temperature, and density. The line ratios are very nearly 4 3 = @A ++ 10 cm− , and the curves for all densities are coincident.+ the curves for all densities are coincident. Note= that the emissivities for He ii per 4/3 stimulated emission and associated nonlinear amplificationproduceHe (see .Thus,therecombinationlinesofHeii (He )that independent of density for all the temperatures, but they do depend on temperature as Te− for quantum number n 10–50. The latter is clearly shown in the Section 2.4). Since the submm H i lines (and theare free–freeproduced by recombination(A color version of of this e figure + He is++ availablecan be ina the strong online journal.)unit ne nHe++ are 4–5 times greater than those for H i at similar frequency—this 4 3 ∼ lower-rightpartially compensates panel where for the the lower emissivity He abundance ratio relative is shown to H if for their five ionized temperatures at ne 10 cm− . continuum) are also optically thin, their line fluxes are a linear = discriminant for the existence of an AGN with a relatively (A colorvolumes version are similar of (as this would figure be the is caseavailable for a very in hard the ionizing online continuum). journal.)(Scoville & Murchikova 13) tracer of the ionized gas emission measure (EM hardne n EUV–X-rayp vol). continuum.are from Hummer In SBs, there & Storey can be (1987 some)andStorey&Hummer He ii (A color version of this figure is available in the online journal.) Hence, these lines are an excellent probe of the EUV=emission luminosity associated(1995a with, Wolf–Rayet1995b). The stars. latter However, work includes the EM population transfer of OB stars and AGNs (assuming the EUV photonsof the are He++ notregion relativeby electron to that and of the ion H collisions+ region will and behas much emissivities for H i appreciably absorbed by dust). Lastly, we note thatless in thanvirtually for an AGN. opticalclear from depths, these figures and that hence increasing maserTe leads amplification to a decrease in of the line galaxies. We have therefore rescaled the optical depths to and He ii up to principal quantum number n 50. They also 1 all sources, the dust extinction of the recombination lines at =emission.the He ii/H Ini emissivity such instances, ratio. In Figure the4 recombination(lower right), the ratio line intensity v 100 km s .Wehavealsoscaledtheopticaldepth The emissivitiescalculate of the He opticalii recombination depth parameters lines are for ataken wide range of electron 4 3 ∆ FWHM − is shown for a single density ne 10 cm− ,butTe 5000 = e λ 350 µmto1mmwillbeinsignificant. from Storey & Hummertemperatures (1995a (,Te1995b)andelectrondensities(). For the interestedne).will We not make accurately use reflect the ionized gas EM and the associated to a specific optical depth τ per unit n n L ,whereL is the ∼ to 20,000 K and the temperature= dependence is clear= and the ion pc pc Early observations of the mm wave recombinationreader, lines a were simple modelof these for thenumerical scaling results of rate in coefficients this paper; be- FigureLyman1 shows continuum the emission rates of the stellar population. For path length in parsecs and the volume densities in cm 3. made in Galactic compact H ii—in these regions thetween continuum hydrogen andStorey hydrogenic & Hummer ions is (1995b developed)Hi recombination analytically linesame emissivities for all n transitions. Thus, the temperature and density − is entirely free–free, and hence one expects a fairlyin Appendix constant A,andthoserelationsarecomparedwiththenu-at T 104 K. thedependence submm H ofi theand He Heii toii Hlines,i line ratios we can at fixed analyzenα can the be possibility Figures 5 and 6 show the specific optical depths for the H i = empirically fit by line-to-continuum flux ratio if the mm-line emissionmerical arises fromresults from StoreyFigure &2 Hummershows the (1995b submm)inAppendix H i-nα line emissivitiesB. of maserϵ per amplification unit by using the optical depth information and He ii lines as a function of Te and ne. The actual optical 4 spontaneous decay in high density gas with little stimulatedThe He ii submmEM,α lines for T are7500 at higher and 10 quantumK. These numbers volumen emissivitiesof Storey were & Hummerϵ (1995a). They provide an optical depth depths for a particular source may be obtained by scaling these = 2 4 3 He ii-nα 0 4/3 emission contribution. This is indeed the case—Gordonthan those & of H i sincecomputed the energy for densities levelsn scale10 asand the nuclear10 cm− ,buttheseparate neTe− . (3) 2 parameter ,whichisrelatedtothelinecenteropticaldepthϵH i nα ∝ curves by the factor n n L / v .Intheseplots,thedashed Walmsley (1990)observedtheH40α line at 99 GHzcharge in 7Z H,i.e.,afactoroffourlargerforthesameprincipalii density curves are essentially= identical. This is because, for theseΩn,n′ - e p pc ∆ 100 + τ by lines are for transitions with a population inversion, and hence regions and found a mean ratio for the integrated-linequantum brightness number nlowin energyHe .ForthesubmmHe levels, the spontaneousii transitions, decay ratesn,n areAlthough′ very high the He ii/H i line ratios are temperature dependent, 1 1 1 1 (in K km s− )tocontinuumof31.6(Kkms− K−n). Less30–50, than versus 20–35(A∆n 1 for(H Hi) i>.InFigure200 s− for3,theexpectedHen<30). The levelii populations are negative optical depth. = = the actual range of temperatures expected for the ionized gas is 3% variation in the ratio is seen across the sample. Theline optically emissivities pertherefore unit ne determinednHe++ are shown mainly for by the the radiative submm cascade following τn,n′ nenionΩn,n′ L, (5) very limited, Te 7500–10,000 K in star-forming H ii regions The submm transitions of H i and He ii are principle quantum thin free–free emission provides a linear probe of theband. H ii Theregion values ofrecombination these emissivities to high are levels.5timesthoseofH The latter isi proportional to the = = ∼ because of the strong thermostating of the cooling function that numbers n 20–32 and 32–50, respectively. For both H i EM, and hence the OB star Lyman continuum production(Figure 1 rate.); however,recombination since the He/ rate,Habundanceratiois0.1,the and hence nenp. where L is the line-of-sight path length. is inversely decreases strongly at lower temperatures and increasesΩ steeplyn,n′ ∼ The observed constancy of the line-to-continuumactual ratios values then per unitTone n translatep are quite the similar curves in in a Figure plasma2 whereinto expectedproportionalat higher emission temperatures to the line (see width Osterbrock in Hz, & Ferland,andintheiroutput2006). For and He ii these particular transitions have positive specific strongly supports the assertion that the integrated recombinationall the H is ionizedline and luminosities, all the He is He one++ needs. to multiply by the total EM of each ∆n,n′ theythe used AGN sources, a thermal it is also Doppler unlikely width, that the temperatures implying a will velocity full optical depths, and hence no maser amplification at virtually line fluxes are also a linear probe of the Lyman continuum source. Consider the detectability of a luminousbe star-forming much higher since most of the heating is still provided by production rates. 2.3. He ii/H i Emission Line Ratios with T and n all densities and temperatures shown in Figures 5 and 6.The region in a nearby galaxy. In Sectione e3,weshowthatforanSBwidthLyc photonsat half near maximum the Lyman intensity limit (even though there are harder 6 3 type EUV spectrum with integrated luminosity inphotons the ionizing in their EUV spectra). exceptions to this are that at very high densities, ne > 10 cm− , 2.1. H ii Line Emissivities In Figure 4,theratiosofHeii/H i α recombination12 line 1/2 continuum at λ < 912 Å, LEUV 10 L ,thetotalLymanIn Appendix A,weshowthattherecombinationratescoeffi-8ln2kTe there can be population inversions (see Figure 6). However, even emissivities (Storey & Hummer 1995a) are shown as a= function⊙ 56 1 To calculate the expected H i line emission, we make use of continuum photon production rate is QLyC 1.20cients10 scales− as. ∆vFWHM (6) of principal quantum number for large ranges of both Te and= × = m at these high densities, significant amplification would occur standard recombination line analysis (as described in Osterbrock Scaling this down to the luminosity of an OB star cluster with ion ne. Two cautions in viewing these6 plots: (1) as noted above, the50 1 2 ! " + only if the scale factor is sufficiently large. &Ferland2006). The volume emissivity, ϵ,isthengivenby LEUV 10 L gives QLyC 1.20 10 s− .ForCaseBαHe+(Te) ZαH(Te/Z )withZ 2forHe . (4) lines of H i and Herecombinationii are not= at the in⊙ same which frequency all the photons= for each are× absorbedn, (i.e., the H ii 1 = 4 = An extreme upper limit for the H ii in a ULIRG SB nucleus and (2) the emissivity ratios are per n n ++ and per n n for or 21.7 km s− for H i at 10 K. In most situations relevant to is ionization bounded)e He and the Lymane seriesp linesHowever, are optically the line emission rates also depend on the radiative 4 4 9 6 ϵ nuAulhν He ii and H i,respectively.Inthecaseofthelatter,theEMfor the discussion here, the line widths will exceed the thermal might be nenpLpc 10 10 10 10 cm− pc and = ++ thick, the Lyman lines above+ Lyα do not escape. (Inand fact, collisional most cascade through the high n levels, and it is not 8 6 ∼ × × = bn nu(TE)Aulhν, He will(1) be almost always <0.1ofthatforH because of the = u of the Lyα may be absorbed by any residual dust.)widthpossible In this because case, to derive of the large-scale emissivity scaling bulk analytically motions to within better the host 10 cm− pc for He ii.Applyingthefirstscalefactortothe lower cosmic abundancethe standard of He. Stromgren¨ condition equating the supply of fresh ∼ where n and n (TE) are the actual and thermal equilibrium than a factor of two accuracy. u u Figure 4 (top andLyman lower continuum left) clearly photons shows (Q that)tothevolumeintegratedrate at a given upper-level population densities. The exact H i spontaneous Lyc temperature, Te, theofrecombination He ii/H i line ratioto states is virtually above the constant ground state, 2.4. Maser Amplification? 4 decay rates from levels u to l, Aul,areavailableintabularformas a function of both quantum number and electron density. online from Kholupenko et al. (2005). The most completeThus, varying and density in the ionized gas should have almost no As noted above, it is well known that the m/cm-wave up-to-date departure coefficients (from TE) (bn andinfluenced(ln bn)/dn on) the line ratios of He ii to H i.Ontheotherhand,itisQLyC αB nenp vol, recombination(2) lines (n>100) of H i have substantial negative = 2 3

• K=

& K 100

• % 0

. %)/ 1000 005 rad 10 )

à % %)0 K 10 10 20 Hz 0.5 %&1 K

& K 10 1 = = %

m %&& 1.0 10 = • W = 10%&2 " ) & 3 2

• ! 10 10 10 10 frequency GHz

• [CI] + + CO J=1–0 + HI • 10… () 36ArH+, HF [CI]