Regulating Star Formation in Nearby Dusty Galaxies: Low Photoelectric Efficiencies in the Most Compact Systems
Jed McKinney, Lee Armus, Alexandra Pope, Tanio Diaz-Santos, Vassilis Charmandaris, Hanae Inami, Yiqing Song, Aaron Evans
DDraft version January 7, 2021
Typeset using L A TEX twocolumn style in AASTeX61
REGULATING STAR FORMATION IN NEARBY DUSTY GALAXIES: LOW PHOTOELECTRICEFFICIENCIES IN THE MOST COMPACT SYSTEMS
J. McKinney,
1, 2
L. Armus, A. Pope, T. D´ıaz-Santos,
3, 4, 5
V. Charmandaris,
5, 6
H. Inami, Yiqing Song, andA.S. Evans
9, 8 Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA. Infrared Processing and Analysis Center, MC 314-6, Caltech, 1200 E. California Blvd., Pasadena, CA 91125, USA. N´ucleo de Astronom´ıa de la Facultad de Ingenier´ıa y Ciencias, Universidad Diego Portales, Av. Ej´ercito Libertador 441, Santiago, Chile Chinese Academy of Sciences South America Center for Astronomy, National Astronomical Observatories, CAS, Beijing 100101, China Institute of Astrophysics, Foundation for Research and Technology-Hellas, GR-71110, Heraklion, Greece Department of Physics, University of Crete, GR-71003, Heraklion, Greece Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan Astronomy Department, University of Virginia, 530 McCormick Road, Charlottesville, VA 22904, USA National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
ABSTRACTStar formation in galaxies is regulated by the heating and cooling in the interstellar medium. In particular, theprocessing of molecular gas into stars will depend strongly on the ratio of gas heating to gas cooling in the neutralgas around sites of recent star-formation. In this work, we combine mid-infrared (mid-IR) observations of PolycyclicAromatic Hydrocarbons (PAHs), the dominant heating mechanism of gas in the interstellar medium (ISM), with [C II ],[O I ], and [Si II ] fine-structure emission, the strongest cooling channels in dense, neutral gas. The ratio of IR coolingline emission to PAH emission measures the photoelectric efficiency, a property of the ISM which dictates how muchenergy carried by ultraviolet photons gets transferred into the gas. We find that star-forming, IR luminous galaxiesin the Great Observatories All-Sky LIRG Survey (GOALS) with high IR surface densities have low photoelectricefficiencies. These systems also have, on average, higher ratios of radiation field strength to gas densities, and largeraverage dust grain size distributions. The data support a scenario in which the most compact galaxies have more youngstar-forming regions per unit area, which exhibit less efficient gas heating. These conditions may be more common athigh − z , and may help explain the higher star-formation rates at cosmic noon. We make predictions on how this canbe investigated with JWST . a r X i v : . [ a s t r o - ph . GA ] J a n INTRODUCTIONStar-formation in a galaxy is dependent on processeswhich remove energy allowing gas to cool. Only thecoldest phases will collapse under self-gravity to formstars, and so characterizing the mechanisms by whichgas heats and cools is critical to our understanding ofstar-formation, and galaxy evolution. The cold gas asso-ciated with star-formation emits strongly in low energyatomic and molecular transitions, bright at infrared (IR)wavelengths.Studies with the
Infrared Space Observatory (ISO) were key in unveiling the 5 − µm wavelength regimeof the electro-magnetic spectrum of galaxies, which isrich in strong atomic and molecular emission lines thattrace the ISM (Malhotra et al. 1997, 2001; Dale et al.2000). Amongst the brightest of these features are [O I ]63 µm , and [C II ] 157 . µm which can contain 0 . −
1% oftotal infrared luminosities (Malhotra et al. 2001; Staceyet al. 2010; D´ıaz-Santos et al. 2013; Brisbin et al. 2015;Ibar et al. 2015). The
Herschel Space Telescope wasused to significantly increase the number of galaxies de-tected in the far-IR lines (e.g., Sturm et al. 2000; vander Wel et al. 2014; D´ıaz-Santos et al. 2011), and studieswith the
Spitzer Space Telescope added other prominentcooling lines such as [Si II ] 34 . µm , as well as PolycyclicAromatic Hydrocarbon (PAH) vibrational lines between3 − µ m that trace photoelectric heating.[C II ], [O I ], and [Si II ] are well-established asstrong coolants in Milky Way photodissociation re-gions (PDRs), the transition zones between H II regionsand the cold-neutral-medium (e.g., Wolfire et al. 1990,2003). As the boundary layer between warm and coldgas, PDRs are an excellent place to study the processesof heating and cooling, as the relative balance of en-ergy gains and losses can impact future star-formation.Emission from small grains, PAHs, provide an excellenttracer of the photoelectric heating of gas in PDRs (Gal-liano et al. 2008; Tielens 2008). Photoelectrons ejectedfrom PAH grains share energy with H and H , whichgo on to collisionally excite fine-structure transitions ofC + , O, and Si + . Although [C II ] and [O I ] emission arethe dominant cooling channels in more normal PDRs(e.g., Tielens & Hollenbach 1985; Kaufman et al. 1999),[Si II ] can also act as a significant coolant at high inter-stellar radiation field densities (Kaufman et al. 2006).Thus, the cycle of gas heating and cooling in PDRs istraced by [C II ], [O I ], [Si II ], and PAH emission, whichcollectively make for a powerful diagnostic of the ISM inextragalactic sources (e.g., Malhotra et al. 2001; Helouet al. 2001; Croxall et al. 2012; Beir˜ao et al. 2012; Sutteret al. 2019. The deficit of [C II ] emission per unit L IR in warmer(higher dust temperatures; T dust ), and more compactLuminous IR Galaxies (LIRGs: log L IR / L (cid:12) = 11 − IR / L (cid:12) >
12) as compared to less extremegalaxies is a well-studied phenomenon (e.g., Malhotraet al. 1997, 2001; Luhman et al. 1998, 2003; Stacey et al.2010; Herrera-Camus et al. 2015; D´ıaz-Santos et al. 2013,2014, 2017; Ibar et al. 2015; Smith et al. 2017). More-over, PAH emission and other far-IR fine-structure lineskey to PDR heating and cooling show similar deficits(e.g., Brauher et al. 2008; Wu et al. 2010; Graci´a-Carpioet al. 2011; Pope et al. 2013; Stierwalt et al. 2014; DeLooze et al. 2014; Cormier et al. 2015; D´ıaz-Santos et al.2017). The IR emission line deficits can be due tochanges in ISM densities and the strength of the ra-diation field impinging upon PDR surfaces (e.g., D´ıaz-Santos et al. 2017), and/or opacity effects, thermal linesaturation, and evolution in dust grain properties (Luh-man et al. 1998; Malhotra et al. 2001; Helou et al. 2001;Mu˜noz & Oh 2016; Smith et al. 2017); however, thedeficits largely disappear in normal star-forming galax-ies when the line emission is normalized by total PAHemission (Helou et al. 2001; Croxall et al. 2012; Sutteret al. 2019). This reinforces the link between the ejectionof photoelectrons from PAH grains and the collisionalexcitation of [C II ] and other fine-structure lines, andsuggests that the heating and cooling processes withinPDRs behave similarly for normal star-forming condi-tions over a range of T dust and L IR . Interestingly, McK-inney et al. (2020) found lower [C II ]/PAH emission at z ∼ z ∼
0, suggesting evolution in the heatingand cooling balance with redshift. However, the cool-ing/heating ratio has yet to be fully characterized in z ∼ II ], [O I ], and [Si II ] emission to PAH emission inthe Great Observatories All Sky LIRG Survey (GOALS;Armus et al. 2009). GOALS is comprised of 244 galaxynuclei within 202 LIRGs and ULIRGs spanning a rangein merger stage and morphology. The range in IR lumi-nosities and stellar masses of galaxies in GOALS makesthe sample a bridge between normal star-forming galax-ies and the most extreme, compact starbursts that hostatypical PDR conditions exposed to stronger radiationfields (D´ıaz-Santos et al. 2017). Whether or not the gascooling/heating properties are fundamentally differentin such extreme environments remains an open questionwhich this work aims to address.GOALS has been the subject of extensive study withobservations spanning the electromagnetic spectrum ,including mid- and far-IR measurements of PDR cool-ing lines and PAHs, the ratio of which is an empiricalmeasure of the photoelectric efficiency, (cid:15) PE : the fractionof energy, in UV photons, emitted by hot stars that isabsorbed by small dust grains and transferred into theneutral PDR gas via the photoelectric effect (e.g., Gerola& Schwartz 1976; de Jong 1977). There is evidence that (cid:15) PE is a constant amongst normal star-forming galax-ies (Helou et al. 2001; Sutter et al. 2019); however, thishas yet to be tested in the starburst regime typical inluminous and ultra-luminous infrared galaxies poweredby star formation..The paper is organized as follows: We review themulti-wavelength observations in Section 2, and discussthe sample selection. Section 3 summarizes importantderived quantities of GOALS galaxies presented in otherworks, as well as key analysis steps we take in this pa-per to appropriately combine the multi-wavelength data.Our results are presented in Section 4, which we discussin Section 5 in the context of local star-formation andtrends in galaxy evolution. Section 6 summarizes thepaper. SAMPLE SELECTION AND DATAThis work focuses on data from
Spitzer /IRS (D´ıaz-Santos et al. 2010, 2011; Petric et al. 2011; Stierwaltet al. 2013, 2014; Inami et al. 2013),
Spitzer /IRAC(Mazzarella et al. 2020, in prep.),
Herschel
PACS andSPIRE (Zhao et al. 2013; D´ıaz-Santos et al. 2013, 2014,2017), and AKARI/IRC (Inami et al. 2018).To measure the ratio of cooling and heating in star-forming gas, we select from the 244 galaxies in GOALSall sources with [Ne V ] . µm / [Ne II ] . µm < . IV ] . µm / [Ne II ] . µm < f AGN , MIR ) derived in D´ıaz-Santos et al. (2017) toidentify sources with excess warm dust in the remainingsample, which we show in Figures to concentrate on thestar-forming properties of the sample galaxies. For a complete list, visit http://goals.ipac.caltech.edu/publications.html . To fully explore the properties of interstellar PAHgrains, we use AKARI 2 . − µm spectra of 145 GOALS(U)LIRGs presented in Inami et al. (2018), in whichthe 3.3 µm PAH feature was detected for 133 targets.This sub-sample spans the full range of L IR and lumi-nosity distance, and is representative of the range instar-formation properties of GOALS. ANALYSISIn addition to measured line fluxes, this work makesuse of a number of quantities from
Herschel /PACS ob-servations derived in D´ıaz-Santos et al. (2017): We sub-tract out the ionized component of [C II ] emission us-ing the neutral [C II ] PDR fractions ( f PDR ), estimatedwith [N II ] and [N II ] available for 54% of the sam-ple, and far-IR colors S ν, µm /S ν, µm otherwise, as de-scribed in D´ıaz-Santos et al. (2017). We use IR surfacedensities from D´ıaz-Santos et al. (2017) which are cal-culated from the effective area measured at 70 µm , andtotal IR luminosities from Armus et al. (2009). We alsouse measurements of the average intensity of the UV in-terstellar radiation field impinging onto the surface ofPDRs, G, measured in local units (G = 1 . × − ergs − cm − , Habing 1968), and neutral gas volume densi-ties, n H , derived using the Kaufman et al. (1999, 2006)PDR models through PDR TOOLKIT (PDRT; Pound &Wolfire 2008) which depend principally on the galaxy-integrated [C II ] and [O I ] line fluxes, as well as L IR .3.1. PAH Properties
The PAH line fluxes used in our analysis are reportedin Stierwalt et al. (2013, 2014), and Inami et al. (2018).We take the PAH luminosity, L
PAH , to be the sum offeatures measured between ∼ − µm by Spitzer
IRS.Specifically, L
PAH includes the 6 .
2, 7 .
7, 8 .
6, 11 .
3, and17 µm PAH lines and all sub-features therein, as mea-sured by
CAFE which fits the line fluxes, continuum andthe extinction simultaneously (Marshall et al. 2007). Onaverage, these five PAH lines account for 76% ±
9% of thetotal PAH luminosity measured by both the Short-Low(SL, 5 . − . µm ) and Long-Low (LL, 14 − µm ) slitsin GOALS galaxies (Stierwalt et al. 2014). Because theSL and LL slits have different widths, tied to the chang-ing PSF with wavelength, some highly resolved galaxiesshow a small jump between their SL and LL IRS spec-tra. This is discussed fully in Stierwalt et al. (2013),and we combine the SL and LL data using their scalefactors derived from the wavelength overlap between thetwo slits. L PAH is normalized to the SL slit. The 3.3 µm PAH luminosities (L . ) are also matched to the aper-ture extraction of IRS/SL data (see Inami et al. 2018Section 3); however, L . represents a small component log (L IR / L fl ) l og ( L [ C II ] / L P AH ) Normal Star-Forming Galaxies(U)LIRGs (This Work)0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 S ν µm /S ν µm Figure 1.
The ratio of [C II ] emission to the sum of 6.2, 7.7,8.6, 11.3 and 17 µm PAH emission in the nuclear regions ofGOALS star-forming galaxies as a function of total IR lumi-nosity. The ionized gas contribution to L [ C II ] has not beensubtracted out. Each data point is colored by the far-IR colormeasured with the ratio of continuum at 63 µm and 158 µm .Black contours contain 33%, 66%, and 95% of normal star-forming galaxies measured by ISO (Helou et al. 2001; Mal-hotra et al. 2001; Dale et al. 2000). Note that we have scaledthe ISOCAM PAH measurements by a factor of 42% to es-timate L
PAH from the 6.75 µm broadband photometry, cor-recting for the underlying continuum and longer wavelengthfeatures. The correlation between [C II ]/PAH and L IR inlocal LIRGs and ULIRGs is weak, with a great deal of scat-ter, but warmer objects tend to have lower [C II ]/PAH ratioscompared to normal star-forming galaxies and cooler LIRGs. of L PAH (5% ± . IR . The sum of PAH featuresbetween 6 and 18 µm traces the bulk of the total powerof PAH emission in GOALS.From the sub-sample of GOALS galaxies with AKARIobservations, 50 objects were selected as test-cases for CAFE-NG (Advanced
CAFE ; Bonfini et. al., in prep.,Marshall et al. 2007), which simultaneously fits contin-uum and spectral features in the 0 . − µm range.These galaxies have full spectral model fits to theAKARI+Spitzer data, which explicitly includes silicateabsorption and 3.05 µm ice feature absorption whichare fit independently. Joint fits to IR continuum andline measurements are important to get accurate linefluxes e.g., Smith et al. 2007; Lai et al. 2020), and we use these new CAFE fits to estimate extinction-corrected3.3 µm luminosities, L . , for the full AKARI sample.In general, the measured PAH intensity depends on howthe local continuum is estimated. Inami et al. (2018)adopt a spline technique (L . , spline ), which is known tounder-estimate the extinction-corrected flux of PAH fea-tures between 6 − µ m by 30 −
60% (Smith et al. 2007).From careful fits to the full PAH features (Bonfini et al.,in prep.) we find that L . , spline / L . = 0 . ± .
07. Forthe sample here we use this conversion and the resultsfrom Inami et al. (2018) to estimate L . for each sourcebefore comparing to the other PAH features.3.2. Aperture Matching
Galaxies in GOALS vary from extended sourcesspatially resolved by
Spitzer to unresolved point-likesources, which motivates a careful approach to aperturematching when comparing
Sptizer and
Herschel mea-surements. The effective area of the
Spitzer /IRS SL slitis 3 (cid:48)(cid:48) . × (cid:48)(cid:48) . II ] and [O I ] line fluxes mea-sured through the central spaxel of the PACS/IFU withdimensions of ∼ (cid:48)(cid:48) . × (cid:48)(cid:48) . Spitzer /IRAC8 µm images, assuming that it traces the co-spatialPAH and far-IR line emission from star-forming regionsin LIRGs, which is reasonable for the 2 − µm bandto have a median value of 70% in normal star-forminggalaxies, which increases only marginally when a morecareful subtraction of stellar continuum is done usingthe IRAC 3 − µm channels (e.g., Helou et al. 2004). Weuse the ratio of the 8 µm flux through each aperture toderive a correction, which is then used to scale down thePACS measurements to match the IRS aperture. Themedian of aperture corrections derived in this manneris 0.62 with upper and lower quartiles of 0.69 and 0.55respectively. We note that aperture matching does notintroduce any bias in the slope of trends we explore inthis paper.The [Si II ] 34.8 µm emission was measured in the Spitzer /IRS LL slit, using an effective extraction aper-ture of ∼ (cid:48)(cid:48) . × (cid:48)(cid:48) . II ] line flux down to the normalization of the SLspectrum using the same multiplicative factors appliedto the 17 µm PAH fluxes (Stierwalt et al. 2013). Asnoted in Stierwalt et al. (2014), 15 LIRGs in GOALS
Table 1.
Best-fit Parameters to to Line/PAH ratiosvs. Σ IR Line a a a σ (dex)[C II ] -0.278 -0.124 0.00 0.08 f PDR × [C II ] -2.378 0.242 -0.016 0.15[O I ] -1.997 0.013 0.00 0.19[Si II ] -14.325 2.487 -0.120 0.19 (cid:15) PEa -6.277 1.010 -0.050 0.12
Note —All line luminosities have been calculated fromaperture matched flux measurements as described inSection 3 unless otherwise noted. Fits are a functionof log Σ IR = log (0.5L IR /πR eff, µm ) in units ofL (cid:12) kpc − . The right-most column corresponds tothe 1 σ scatter about the trend. a See Equation 2. have scale factors > Her-schel /PACS and
Spitzer /IRS, and the measurements re-ported here are for the central regions ( ∼ − RESULTSFollowing early [C II ] surveys of low-redshift, mostlynormal star-forming galaxies with ISO , Helou et al.(2001) measured a constant [C II ]/PAH ratio over arange of far-IR colors that showed significantly lessscatter than [C II ]/L IR . This reinforced the link be-tween PAHs and [C II ] emission via photoelectric heat-ing inside PDRs. We find that the galaxy-integrated[C II ]/PAH ratio in luminous, infrared, star-forminggalaxies does not correlate strongly with either far-IRcolor or L IR as shown in Figure 1, although warmerLIRGs and ULIRGs tend to have lower [C II ]/PAH ra-tios compared to galaxies at log L IR / L (cid:12) (cid:46)
11. Trends inPDR gas cooling/heating within the GOALS sample arelikely to be more clear when measured against quantitiesthat better reflect the ionizing radiation or luminositydensity surrounding the young stars.4.1.
Line-to-PAH Ratios
The IR surface density is a more direct tracer offar-IR fine-structure line properties than color or L IR (D´ıaz-Santos et al. 2013, 2017; Smith et al. 2017), bothof which exhibit little to no influence on the ratio of [C II ]/PAH (Fig. 1). As Σ IR should scale with the num-ber density of massive star-forming regions in the beam,we expect Σ IR to be more sensitive to statistical trendsacross the sample. The [C II ] deficit vs. Σ IR among lu-minous infrared star-forming galaxies presented in D´ıaz-Santos et al. (2017) is re-created for comparison in Fig-ure 2 ( Left ). To test for trends in gas cooling over pho-toelectric heating, we calculate the [C II ]/PAH ratio as afunction of Σ IR , shown in Figure 2 ( Right ), color codedby log G / n H which scales linearly with IR surface den-sity above log Σ IR / [L (cid:12) kpc − ] ∼ . II ]/L IR ratio exhibits a maximumdeficit of ∼ IR / [L (cid:12) kpc − ] = 8 − II ]/PAH ratio falls by a factor of ∼ . IR exhibit [C II ]/L IR and [C II ]/PAH ratios comparable to those found in thespatially-resolved regions of NGC 1097 (Beir˜ao et al.2012), and the normal star-forming galaxies in Helouet al. (2001).Following D´ıaz-Santos et al. (2017), we fit a second-order polynomial function to the [C II ]/PAH ratio of theform:log(L line / L IR ) = a + a log Σ IR + a (log Σ IR ) (1)Note that the function is forced to a constant maximumat values of Σ IR less than where the turn-over occurs.While we do not include normal star-forming galaxiesin the fit, a constant line-to-PAH ratio below the turn-over yields the best agreement with observations of lowΣ IR galaxies (e.g., Helou et al. 2001; Beir˜ao et al. 2012;Croxall et al. 2012). The best-fit is shown as a blacksolid line in Fig. 2 ( Right ), the parameters for whichare given in Table 1. While the [C II ]/PAH ratio isnot constant, the magnitude of the drop with Σ IR issignificantly less.In addition to [C II ], [O I ] and [Si II ] are importantPDR cooling lines in terms of their overall contributionto the cooling budget (e.g., Rosenberg et al. 2015), andtheir strengths relative to the PAH emission are a di-agnostic of PDR structure. Large [O I ]/PAH ratioswhere [C II ]/PAH is low could indicate greater gas densi-ties, which would preferentially cool through the highercritical density [O I ] line. In Figure 3, we show the[C II ]/PAH, [O I ]/PAH, and [Si II ]/PAH ratios in sepa-rate panels for LIRGs and ULIRGs as a function of Σ IR .Because we are comparing different fine-structure cool-ing lines here and would like to focus on the PDR emis-sion alone, we subtract out the non-PDR component ofthe [C II ] emission using f PDR (e.g., D´ıaz-Santos et al.2017). At low IR surface densities, the line-to-PAH ra-tios are consistent with spatially-resolved measurements logΣ IR ≡ log(0 . IR / π R , µm ) [L fl kpc − ] l og ( L [ C II ] / L I R ) N = 212 σ = 0 . NGC1097 Nuclear RingNGC1097 Extranuclear logΣ IR ≡ log(0 . IR / π R , µm ) [L fl kpc − ] l og ( L [ C II ] / L P AH ) N = 182 σ = 0 . log(G / n H ) [G cm − ] Figure 2. ( Left ) The [C II ] deficit in GOALS as presented by D´ıaz-Santos et al. (2017), calculated with galaxy-integratedmeasurements of L [ C II ] and L IR . The data are colored by their average ratio of UV radiation field strength to neutral hydrogendensity in PDRs (G/n H ). The solid black line indicates the best-fit to the data from D´ıaz-Santos et al. (2017) using Equation1. Dotted lines correspond to ± σ about the best-fit. ( Right ) The ratio of L [ C II ] to L PAH (summing over all features between6 − µm ) for star-forming (U)LIRGs with Hershel /PACS [C II ] measurements and Spitzer /IRS observations of the PAHs. Tocompare our results with more normal star-forming conditions, we show measurements of the spatially resolved nuclear ringand extranuclear bar in NGC 1097 as open symbols (squares and circles respectively) from Beir˜ao et al. (2012) on both panels,as well as the range in [C II ]/L IR and [C II ]/PAH observed in the normal star-forming galaxy sample of Helou et al. (2001)and Malhotra et al. (2001) (shaded grey regions), scaled by a factor of 2.3 in the Right panel as described in Figure 1. Both[C II ]/L IR and [C II ]/PAH trend towards lower values in more compact systems, and the use of PAH emission as a normalizationfor [C II ] yields a lower scatter about the overall trend. of NGC 1097 (Beir˜ao et al. 2012), representative of morenormal star-forming conditions.[C II ]/PAH falls in the most compact sources atlog Σ IR / [L (cid:12) kpc − ] (cid:38)
10. [O I ]/PAH does not exhibit aturn-over at high Σ IR , but shows an increasingly largerscatter (higher than the other line ratios), mostly witha constant lower envelope. This could arise from vary-ing degrees of line self-absorption, as [O I ] originatesfrom deeper regions within PDRs, and/or the presenceof intervening (foreground) cold, neutral material. In-deed, IRASF1224-0624, and ICO860, the two galaxies > σ below the [O I ]/PAH trend both show signs ofself-absorption in the PACS spectra and have some ofthe highest τ . optical depths observed in the sample;however, [O I ] self-absorption is only observed in ∼ IR / [L (cid:12) kpc − ]= 10 − .
5, and istherefore unlikely to influence statistical trends in thesample over the full range in Σ IR .4.2. The Photoelectric Efficiency
The photoelectric efficiency ( (cid:15) PE ) is the fraction ofenergy that photoelectrons from PAHs transfer fromUV photons into the gas relative to the total heatingof dust. Observationally, (cid:15) PE can be traced by the ra-tio of far-IR line emission to total PAH emission be-cause photoelectrons from PAHs are one of the dom- inant heating mechanisms in PDRs, which cool pre-dominantly via far-IR fine-structure line emission (e.g.,Bakes & Tielens 1994; Malhotra et al. 2001; Croxallet al. 2012; Beir˜ao et al. 2012). In practice, the cool-ing budget is dominated by [C II ], [O I ], and [Si II ],and L PAH (cid:29) (L [ C II] +L [ O I] +L [ Si II] ). Assuming that thePAHs and ions are co-spatial such that the energy inputinto the gas by photoelectric heating powers the [C II ],[O I ], and [Si II ] lines, an empirical tracer of the photo-electric efficiency is (cid:15) PE ≈ L [C II] + L [O I] + L [Si II] L PAH (2)where the relative contribution of far-IR lines to (cid:15) PE canvary across the PDR (Kaufman et al. 2006). Neverthe-less, combined observations of these features capture anaverage (cid:15) PE of PDRs over a galaxy.We measure the average (cid:15) PE for 152 GOALS star-forming galaxies including five upper limits, and showthe combined sum of neutral [C II ], [O I ], and [Si II ]cooling over L PAH in Figure 4. A Kendall’s τ test sup-ports an anti-correlation between (cid:15) PE and Σ IR at ∼ σ (see Table 2). As shown in Fig. 4, LIRGs at low Σ IR exhibit fairly constant photoelectric efficiencies compa-rable to observations of normal star-forming galaxies(Beir˜ao et al. 2012; Croxall et al. 2012). At high Σ IR ,the sum of all cooling lines relative to the PAHs shows a logΣ IR ≡ log(0 . IR /π R , µm ) [L fl kpc − ] l og ( L / L P AH ) f PDR × L [CII] NGC1097 Nuclear RingNGC1097 ExtranuclearGOALS SFG logΣ IR ≡ log(0 . IR /π R , µm ) [L fl kpc − ] L [OI] logΣ IR ≡ log(0 . IR /π R , µm ) [L fl kpc − ] L [SiII] Figure 3.
IR cooling lines over PAH emission in GOALS star-forming (U)LIRGs vs. IR surface densities. On all panels, weshow the best-fit of Eq. 1 to the data (solid black line), where all parameters are left free. Dotted black lines indicated ± σ scatter about the trend. ( Left ) [C II ]/PAH with the ionized component of [C II ] subtracted out using the [C II ]/[N II ] and[N II ] /[N II ] ratio as described in D´ıaz-Santos et al. (2017). ( Center ) [O I ]/PAH. Galaxies with signs of [O I ] self-absorptionare marked with black dots, which comprise 5% of the sample. ( Right ) [Si II ] 34 . µm over PAH. In all panels, we compareGOALS star-forming galaxies to the star-forming, compact nuclear ring, and extranuclear emission from NGC 1097 presentedin Beir˜ao et al. (2012). The spatially resolved emission in a normal star-forming galaxy is consistent with extrapolation of thetrends observed in LIRGs and ULIRGs to low Σ IR . While the fraction of cooling-to-heating in [C II ] falls in the most compactsystems, [O I ]/PAH remains relatively constant over Σ IR in (U)LIRGs. The lack of a positive trend between [O I ]/PAH andΣ IR suggests that [O I ] cooling does not compensate for the negative trends observed in the other features. decreasing photoelectric efficiency, which suggests thatthe net cooling to photoelectric heating ratio is fallingacross the density and temperature structure of PDRsin compact objects. The relative contributions of [C II ],[O I ], and [Si II ] to the cooling budget within PDRs(i.e., the numerator of Eq. 2) are on average 32%, 20%,and 48% respectively, and these values do not changesignificantly when splitting the sample above and be-low log Σ IR / [L (cid:12) kpc − ]= 10 .
7. Therefore, low photo-electric efficiencies are the product of overall less coolingin PDRs in all channels relative to PAH heating.The anti-correlation between (cid:15) PE and Σ IR is robustagainst outliers, as demonstrated by the bootstrap fitson Figure 4. Nevertheless, there exist galaxies devi-ating from the trend by more than ± σ that warrantcloser inspection. At all IR surface densities, objectsin this class collectively have higher mean and median f AGN , MIR compared to the rest of the sample. Thus, thescatter above and below the best-fit trend may be par-tially due to sources with an excess of hot dust contin-uum emission in their mid-IR spectra. This may be dueto a weak, deeply buried AGN, even in sources whereL IR is dominated by star formation, which in turn maychange the ionization structure and the PAH proper-ties (Voit 1992; Langer & Pineda 2015; Langer et al.2017). Alternatively, these objects may harbor heav-ily obscured star-forming regions with high levels of lineself-absorption and/or continuum opacities. This ab-sorption should appear in the PACS line profiles, butonly 12 GOALS sources show evidence for absorption in the [O I ] line (D´ıaz-Santos et al. 2017). We notethat the detection of these signatures, presumably dueto compact (narrow velocity) foreground clouds, may belimited by the coarse spectral resolution ( ∼
85 km s − )of Herschel /PACS (Gerin et al. 2015).The photoelectric efficiencies we measure represent av-erages over the local properties of PDRs in the central( ∼ − IR .Indeed, galaxies in this domain with low (cid:15) PE also havethe largest ratios of G/n H , which is also sensitive tothe local physics of PDRs. We fit Equation 1 to thedata, the parameters of which are given in Table 1,and find that the photoelectric efficiency turns over atlog Σ IR / [L (cid:12) kpc − ] ∼ .
5, close to where G/n H scaleslinearly with logΣ IR (D´ıaz-Santos et al. 2017). Models ofheating and cooling in PDRs predict an anti-correlationbetween G/n H and (cid:15) PE as the size and charge of dustgrains are modified by the stellar radiation field (e.g.,Bakes & Tielens 1994; Tielens 2008), a trend which werecover in Figure 5 at high ( ∼ σ ) significance (see Tab.2). We find general agreement between modeled andmeasured (cid:15) PE for T gas = 50 − (cid:15) PE we measure inGOALS. The most extreme ULIRGs at high Σ IR and low (cid:15) PE also show the highest values of log (G / n H ) (cid:38) . logΣ IR = log(0 . IR / π R , µm ) [L fl kpc − ] l og † p e ≡ l og [ ( f P D R × L [ C II ] + L [ O I ] + L [ S i II ] ) / L P AH ] NGC1097 Nuclear RingNGC1097 Extranuclear0.5 0.0 0.5 1.0 1.5 log(G / n H ) [G cm − ] Figure 4.
The ratio of prominent IR cooling lines to total PAH luminosity, an estimate of the photoelectric efficiency in PDRs,vs. IR surface density. All measurements along the y -axis have been aperture-matched as discussed in Section 3. The data arecolor-coded by log(G / n H ), following previous Figures. The dash-dotted line corresponds to the best-fit of Eq. 1 to the data,with all parameters set to free. The shaded grey region contains the top 95% of 1000 boot-strapped model fits. Data pointsmarked with a + symbol have mid-IR AGN fractions > . µm equivalent widths, either due to a deeply buriedstarburst or AGN. For comparison with more normal star-forming conditions, we show measurements of the spatially resolvednuclear ring and extranuclear bar in NGC 1097 as open symbols (squares and circles respectively) from Beir˜ao et al. (2012).The Kendall’s τ and two-tailed log p − value for the (U)LIRGs are − . − . (cid:15) PE and Σ IR at a confidence level of ≈ σ (Tab. 2), driven largely by the turn-over in (cid:15) PE at logΣ IR > . / n H ) (cid:38) .
5. At these high surface densities, the average physical properties of PDRs depart from the more normalstar-forming conditions observed at lower Σ IR . supporting a link between the strength of the radiationfield and the heating efficiency within the PDR, whichis mediated by the properties of PAH grains. DISCUSSIONIn this work, we find that the cooling-to-heating ra-tios observed in the most compact luminous infraredgalaxies are low, and are accompanied by an increase inthe mean energy density per H atom (G / n H ) incident upon the surfaces of PDRs. The IR surface density isa global property of a galaxy, and both (cid:15) PE and G / n H measure the average physical conditions local to thePDRs. The trends between (cid:15) PE , G / n H , and Σ IR suggesta link between the global properties of a starburst andthe conditions of individual star-forming regions. Table 2.
Correlation Coefficients between the PhotoelectricEfficiency, as defined by the ratio of IR cooling lines to mid-IR PAH emission between 6 − µm , and other Quantities inGOALS star-forming Galaxies τ k log p SNR [ σ a ]L IR [L (cid:12) ] − . − . − . − . − . − . . . . S ν, µm /S ν, µm . . − . − . − . − . . . . Σ IR [L (cid:12) kpc − ] b − . − . − . − . − . − . . . . G / n H [G cm − ] c − . − . − . − . − . − . . . . EW(6 . µm ) [ µ m] 0 . . . − . − . − . . . . f AGN , MIR . . . − . − . − . . . . f PDR . . . − . − . − . . . . L . µ m / L . µ m . . . − . − . − . . . . L . µ m / L . µ m − . − . − . − . − . − . . . . L . µ m / L . µ md − . − . − . − . − . − . . . . Note —Kendall’s τ correlation coefficients ( τ k ) and p − valueswere calculated using pymccorrelation (Privon et al. 2020),which implements bootstrap error estimation on τ k and p with censored data (upper limits) as described in Curran(2014) and Isobe et al. (1986) respectively. We report 16%,50%, and 84% percentiles for each quantity. a Assuming normally distributed posteriors. b See Figure 4. c See Figure 5. d For the subset of GOALS (U)LIRGs with AKARI 3.3 µm PAH detections. See Figure 7.
Alternate Explanations for decreasing (cid:15) PE with Σ IR The low photoelectric efficiencies we measure in galax-ies with high Σ IR (Fig. 4) and high G / n H (Fig. 5) sug-gests a change in the thermal regulation of star-forminggas in compact LIRGs; however, a number of alternativephysical conditions may conspire to produce the trendswe observe with (cid:15) PE .The relative strengths of the far-IR cooling or PAHemission may be affected by any or all of the following:(1) Far-IR line fluxes may be suppressed by opticallythick continuum absorption (e.g., Scoville et al. 2017a).In this case, the [O I ]/L IR -deficit would have a steeperslope than [C II ]/L IR (e.g., Malhotra et al. 2001), a trendthat is not observed (D´ıaz-Santos et al. 2017). (2) Ion-ized gas from diffuse or H II regions, and/or AGN may log(G / n H ) [G cm − ] l og † p e ≡ l og [ ( f P D R × L [ C II ] + L [ O I ] + L [ S i II ] ) / L P AH ] D i ff u s e I S M β = − . β = − . T gas =1000KT gas =500KT gas =100KT gas =50K NGC1097 Nuclear RingNGC1097 Extranuclear
Figure 5.
The photoelectric efficiency calculated as the sumof [C II ], [O I ], and [Si II ] emission over the flux of PAH emis-sion including lines between 6 − µm vs. G / n H , the ratioof the average radiation field strength impinging upon PDRsto the mean neutral Hydrogen density. The curves corre-spond to theoretical photoelectric efficiencies of PAH grainsfrom Bakes & Tielens (1994) for gas temperatures between50 − n ( a ) ∼ a β . Black and red curves indicate β = − . β = − . PAH we use to measure (cid:15) PE includesonly ∼
75% of the total power in PAHs for GOALS (see Sect.3.1), and we have scaled the models accordingly to accountfor this difference. The shaded grey region corresponds toG / n H typical of the cold, diffuse ISM. Open symbols corre-spond to the average values of (cid:15) PE and G / n H for spatiallyresolved measurements of the nuclear ring and extranuclearbar (square and circle respectively) in NGC 1097, a morenormal star-forming galaxy (Beir˜ao et al. 2012). The mod-els, which depend on the PAH grain ionization state and sizedistribution, can account for both the overall trend and scat-ter observed in (U)LIRGs, suggesting that the strong correla-tion between the photoelectric efficiency and G / n H originatesfrom the photoelectric properties of the PAH grains withinPDRs. contribute to the [C II ] and [Si II ] line fluxes owing totheir ionization potentials being lower than that of neu-tral hydrogen. This is unlikely to drive trends in oursample, as the photoelectric efficiency does not correlatewith the fraction of [C II ] emission from PDRs ( f PDR ;Tab. 2). Moreover, the neutral PDR fraction of [Si II ]would have to be larger at low Σ IR or smaller at high Σ IR to maintain constant (cid:15) PE , both of which are inconsistentwith the increase in PDR area filling factor with Σ IR inLIRGs and ULIRGs (D´ıaz-Santos et al. 2017). (3) PAHmolecules in galaxies with large G / n H absorb and re-0 log ( L . µ m / L . µm ) l og [ ( f P D R × L [ C II ] + L [ O I ] + L [ S i II ] ) / L P AH ] More Neutral f(AGN , MIR) 30%f(AGN , MIR) > log ( L . µ m / L . µm ) l og [ ( f P D R × L [ C II ] + L [ O I ] + L [ S i II ] ) / L P AH ] GrainSize
Figure 6. ( Left ) The photoelectric efficiency vs. the ratio of 11.3 to 7.7 µm PAH emission in our sample of star-forming GOALS(U)LIRGs. The L . µ m / L . µ m PAH ratio is a tracer of the average grain ionization, with higher values associated with moreneutral grains. (
Right ) Same as the
Left panel, now as a function of the ratio of 7.7 to 6.2 µm PAH emission, a tracer of theaverage Cationic grain size as both features arise from ionized PAHs. The low values of (cid:15) PE observed at high Σ IR and highG / n H do not exhibit notably different grain charge states and Cation grain sizes. emit more energy per unit dust mass because of the largeUV opacities of grains (Li & Draine 2001). If the PAHsand ions (C + , O, and Si + ) were de-coupled spatially,L PAH could increase with Σ IR without a correspond-ing increase in (L [ C II] +L [ O I] +L [ Si II] ), lowering the ob-served IR line-to-PAH ratio by Eq. 2. However, thisspatial decoupling of PAHs and ions is inconsistent withobservations of PDRs in the Milky Way (Okada et al.2013; Salgado et al. 2016), the LMC (Lebouteiller et al.2012; Chevance et al. 2016), and local galaxies (Croxallet al. 2012; Abdullah et al. 2017; Bigiel et al. 2020). (4)Metallicity may influence the strength of cooling linesand the PAHs (Cormier et al. 2015; Smith et al. 2017;Croxall et al. 2017; Cormier et al. 2019; Aniano et al.2020). However, direct effects on the PAH grains appearmost pronounced at metallicities well below those seenin GOALS galaxies, which typically have Z / Z (cid:12) ∼ − Dust Grain Properties and the PhotoelectricEfficiency
The photoelectric efficiency is not only a function ofG / n H , but also the size and ionization state of PAHgrains (Bakes & Tielens 1994; Galliano et al. 2008; Tie-lens 2008). Observations of PDRs in the Milky Wayindicate that (cid:15) PE falls as the grain charging parameter( γ ≡ G T / / n e ) rises, and grains become more ionized (Tielens 2008; Okada et al. 2013; Salgado et al. 2016).Indeed, the models of Bakes & Tielens (1994) shown inFigure 5 predict low (cid:15) PE at high G / n H , and the datafalls closer to the model with a grain size distributionweighted more towards larger grains. Thus, a link be-tween PAH properties and (cid:15) PE is to be expected if thedecrease in (cid:15) PE at high Σ IR arises from a change in thelocal physics of gas heating in PDRs as mediated by thecharge and size of PAHs.Ratios between the 6.2, 7.7, 8.6, and 11.3 µm PAHlines are well-established as tracers of grain size andionization (e.g., Draine & Li 2001; Tielens 2008), andlocal LIRGs exhibit comparable ratios to nearby, nor-mal star-forming galaxies and high- z ULIRGs (Stier-walt et al. 2014; Smith et al. 2007; Pope et al. 2008;Wu et al. 2010; Shipley et al. 2013). For example,star-forming LIRGs cluster tightly in L . µ m / L . µ m vs.L . µ m / L . µ m , tracing grain size and ionization re-spectively, which show a larger scatter in sources withAGN (Stierwalt et al. 2014).Figure 6 shows (cid:15) PE as a function of the L . µ m / L . µ m ratio, a tracer of grain charge, and the L . µ m / L . µ m ratio, a tracer of the average cationic grain size (Draine& Li 2001). We do not detect a correlation between (cid:15) PE and the grain ionization state at a significant confidencelevel (Tab. 2); however, (cid:15) PE and L . µ m / L . µ m areanti-correlated at a ∼ σ confidence level, albeit withlarge scatter, suggesting that that the average size ofPAH grains may influence the observed photoelectricefficiencies in local (U)LIRGs, consistent with the sen-1sitivity of theoretical photoelectric efficiencies on thegrain size distribution (Fig. 5).Smaller PAH grains emit more strongly in the shorterwavelength bands, whereas larger grains are brighter atlonger wavelengths (Allamandola et al. 1989; Schutteet al. 1993; Draine & Li 2001). Thus, the diagnosticutility of a PAH line ratio as a grain-size indicator isa function of the separation in wavelength of the twofeatures. The 7.7/6.2 µm ratio has been a wide-spreadtool in the literature as both features are bright in ex-tragalactic sources, relatively unaffected by the 9.7 µm silicate ice feature, and were observable simultaneouslywith IRS aboard Spitzer (Draine & Li 2001; O’Dowdet al. 2009; Sandstrom et al. 2012; Stierwalt et al. 2014).With the advent of AKARI/IRC, the 3.3 µm PAH fea-ture became accessible for large numbers of extragalacticsources while unlocking a longer baseline diagnostic ofgrain size.The ratio of 11 . µm to 3 . µm PAH intensity is one ofthe most robust tracers of PAH grain size because of thelarge baseline in wavelength (Allamandola et al. 1989;Jourdain de Muizon et al. 1990; Schutte et al. 1993; Moriet al. 2012; Ricca et al. 2012; Croiset et al. 2016; Maragk-oudakis et al. 2020). Using the available AKARI spectrain GOALS, we plot (cid:15) PE vs. L . µ m / L . µ m in Figure7 to further test if low (cid:15) PE is associated with larger orsmaller PAHs. We find that galaxies in the AKARIsub-sample of GOALS with low (cid:15) PE show systematicallyhigher values of 11.3/3.3 µm PAH emission (Tab. 2).This trend is not driven by systematic variations in the11.3 µm feature strength, as the L . µ m /L PAH ratio isconstant over the range in L . µ m / L . µ m , and exhibitsminimal 1 σ scatter of 0.05 dex about the average (Fig. 7,bottom panel). Instead, the strength of the 3 . µm fea-tures relative to L PAH decreases dramatically by nearlyan order of magnitude (Fig. 7, center panel). The anti-correlation between (cid:15) PE and L . µ m / L . µ m reinforcesthe importance of the mean grain size in dictating theobserved photoelectric efficiency.5.3. Physical Interpretation
The photoelectric heating efficiency of PAHs falls asthe number of carbon atoms per particle increases (e.g.,Bakes & Tielens 1994), and small grains are preferen-tially destroyed in the presence of harsh radiation fields(e.g., Jochims et al. 1994). This provides a simple phys-ical interpretation of the data presented so far: PDRsin the most compact starbursts (log Σ IR / [L (cid:12) kpc − ] (cid:38) .
7) have, on average, more intense radiation fields pergas density (D´ıaz-Santos et al. 2017), which leads toa preferential destruction of the smallest PAH grains,raising the average grain size and leaving behind large l og [ ( f P D R × L [ C II ] + L [ O I ] + L [ S i II ] ) / L P AH + . ] GrainSize f(AGN , MIR) 30%f(AGN , MIR) > l og ( L . µ m / L P AH + . ) log ( L . µ m / L . µm ) l og ( L . µ m / L P AH + . ) Figure 7. ( Top ) The photoelectric efficiency vs. the ratioof 11 . µm to 3 . µm PAH emission, a size tracer for PAHgrains. Note that L . is not included in L PAH . (U)LIRGswith higher (cid:15) PE are low in 11.3/3.3 µm . We fit a linear re-lation to the data letting the slope and y − intercept varyfreely, and find that y = − . x − .
10. The shaded greyregion spans the domain of 1000 bootstrapped model fits. AKendall’s τ test returns ( τ k , log p ) = ( − . , − . ∼ . σ confidence. Galaxies with f AGN , MIR >
30% (open circles) exhibit a 1 σ scatter aboutthe best-fit of 0 .
11 dex, larger than the 0 .
07 dex scatter inlow f AGN , MIR (U)LIRGs ( ≤ Center )The L . / L PAH ratio as a function of the 11.3/3.3 µm ratio.( Bottom ) The contribution of the 11 . µm PAH feature tothe total PAH luminosity. (U)LIRGs with lower photoelec-tric efficiencies tend towards higher values of 11.3/3.3 PAHratios without exhibiting changes to the fractional strengthof the 11 . µm feature with respect to L PAH , supporting alink between (cid:15) PE and the PAH grain-size distribution probedby the 3.3 µm feature luminosity. / n H are associated with younger PDR systemsthat have yet to evolve away from their host star, andare more likely to be found in galaxies with higher star-formation rate surface densities (e.g., D´ıaz-Santos et al.2017). The low photoelectric efficiencies at high Σ IR areplausibly linked to higher fractions of young, short-lived,and dust-cocooned star-forming regions, where the highratios of G / n H destroy small dust grains, hindering thecoupling between the radiation field strength and PDRgas temperatures. Such PDRs may be continuously re-plenished by the compaction of gas and dust during amajor merger (Sanders et al. 1988; Hopkins et al. 2008).Indeed, the majority of late-stage mergers (80%) areabove log Σ IR / [L (cid:12) kpc − ] ∼ . . µ m / L . µ m andL . µ m / L . µ m ratios in LIRGs and ULIRGs are con-sistent with predominantly ionized PAHs containing onaverage ∼ −
150 C atoms per particle when com-pared to the modeled PAH spectra of Maragkoudakiset al. (2020) . PAHs with N C (cid:46)
40 tend to be photo-destroyed in PDRs (Jochims et al. 1994), which is closeto the lower bound on grain sizes we observe for LIRGsand ULIRGs in Fig. 8. Other mechanisms for grain de-struction include shock-induced fragmentation and/orshattering; however, interstellar shocks tend to destroylarger grains which is the opposite effect we see in thedata (Jones et al. 1996). Therefore, G / n H may be a crit-ical factor for determining the photoelectric efficiencyin (U)LIRGs with the grain size distribution acting asan intermediary between the radiation field, and gascooling and heating.5.4. Prospects for Star-Formation at High-Redshift
The rise and fall of the cosmic star-formation rate den-sity may be accompanied by an increase in the efficiencyof star-formation at earlier times, although this remainsa subject of debate (e.g., Lilly et al. 1996; Madau et al.1996; Madau & Dickinson 2014; Tacconi et al. 2010, We adopt the Maragkoudakis et al. (2020) models correspond-ing to a mean photon energy of 10 eV. L(11 . µ m) / L(3 . µ m) -1 L ( . µ m ) / L ( . µ m ) . . . . . .
50 75 100 125 150 175 N c = numberofCatoms Figure 8.
The L . µ m / L . µ m vs. L . µ m / L . µ m PAHratio in GOALS (U)LIRGs with AKARI observations of the3.3 µm PAH feature. The model grid from Maragkoudakiset al. (2020) is a function of grain size (N C , see colorbar),and the relative mix of neutral and cationic PAH grains asindicated on the Figure, all assuming an average photon en-ergy of 10 eV. (U)LIRGs have, on average, mostly ionizedPAHs with sizes between 60 and 150 C atoms per grain. (cid:15) PE could play a role in mediating thestar-formation efficiency today and in the past by rais-ing or lowering the energy transfer from stellar photonsinto the gas. When the photoelectric efficiency is low,photo-electrons convert a lower fraction of the incidentradiation field into raising the gas temperature. In otherwords, gas may remain cold despite overall less coolingrelative to photoelectric heating because the mechanismby which gas heats in the first place is weak at low (cid:15) PE . This may be more common at earlier times, be-cause normal star-forming galaxies at high-redshift aremore compact than local galaxies at a given stellar mass(Buitrago et al. 2008; Conselice 2014; van der Wel et al.2014; Mowla et al. 2019), and Σ IR anti-correlates with3 (cid:15) PE . In addition, efficient star-formation in the thickdisks of high − z dusty, star-forming galaxies could con-tain a number of star-forming regions that each resem-ble the central regions of local (U)LIRGs (e.g., Tacconiet al. 2008; Bothwell et al. 2010; Stacey et al. 2010; Bris-bin et al. 2015), in which case high G / n H and low (cid:15) PE could be common in PDRs across a high − z starburst.These conditions may play a more important role athigh-redshift as the contribution of ULIRGs to the to-tal star-formation rate density increases from z = 0 to z = 2 by a factor of ∼
21 (Murphy et al. 2011).Recent efforts to combine mid- and far-IR measure-ments of gas heating and cooling at z ∼ − Spitzer /IRS spectra (Brisbin et al. 2015; McKinneyet al. 2020). Using ALMA, McKinney et al. (2020) com-pared the [C II ] and 6.2 µm PAH emission for GS IRS20,a luminous, compact starburst galaxy at z = 1 . II ]/6.2 µm ratio at high IR surface densitythat could indicate a low photoelectric efficiency. Thisgalaxy has a L [ C II] /L . ratio of 0.11, which would cor-respond to a 11.3/3.3 µm ratio of 21.5 if z ∼ II ] as in local (U)LIRGs. If this is thecase, then GS IRS20 would have a 3 . µm PAH flux of7 × − W m − , which can be easily detected in un-der 15 minutes by JWST /MIRI. While MIRI will beexcellent at measuring bright PAH lines at high − z , ourability to probe much of the rest-frame mid and far-IR regime at high − z remains limited. Future facilities,such as the Origins Space Telescope , a proposed flag-ship mission covering the near-far infrared with power-ful imaging and spectroscopic capabilities and a large,cold telescope, would be a powerful tool for measuringthe full energy budget in distant star-forming galaxies,and testing the idea that the star-formation efficiency islinked to the balance of gas cooling and heating. SUMMARY AND CONCLUSIONWe combine observations of PAH emission with mea-surements of the far-infrared fine-structure [C II ], [O I ],and [Si II ] lines to infer the properties of gas heating andcooling in local, star-forming, luminous infrared galax-ies. The ratio of IR cooling lines to PAH emission tracesthe photoelectric efficiency, (cid:15) PE , and measures the cou-pling between stellar radiation field and gas tempera-tures in photodissociation regions (PDRs). Our mainconclusions are: https://origins.ipac.caltech.edu/
1. In local LIRGs, the ratio of [C II ] to PAH emissiondoes not correlate with L IR or far-IR color, bothof which trace a mix of the diffuse and PDR dust.2. We find an anti-correlation between [C II ]/PAHand IR surface density (Σ IR ) where the most com-pact ULIRGs have low ratios of [C II ] cooling toPAH emission compared to normal star-forminggalaxies by ∼ . II ]/PAH ra-tio exhibits less overall scatter in GOALS thanL [ C II] /L IR , as well as a lower magnitude of declinebetween low- and high-Σ IR galaxies.3. [Si II ]/PAH and [O I ]/PAH exhibit constant ratiosup to the most compact ULIRGs, were some ob-jects fall below the average value by a factor of ∼ I ]/PAH does notincrease when [C II ]/PAH is low: enhanced coolingvia the [O I ] channel is not sufficient to compen-sate for the deficiencies observed in the [C II ] linewhen considering the total cooling budget.4. We measure the photoelectric efficiency as (L [ C II] +L [ O I] +L [ Si II] )/L
PAH , which is a factor of ∼ IR / [L (cid:12) kpc − ] > . H ).Compact ULIRGs have low photoelectric efficien-cies and more extreme ISM conditions, indicatinga link between the large-scale energy density of astarburst and the gas cooling and heating proper-ties on PDR scales.5. LIRGs with low photoelectric efficiencies have highratios of 11 . . µm PAH emission, a tracer ofthe mean PAH grain size. We estimate typicalgrain sizes of N C ∼ −
150 C atoms per grain inLIRGs, and find that the PAHs are predominantlyionized. Large, ionized grains produce both lessand weaker photo-electrons, which may contributeto the low photoelectric efficiencies in the mostcompact ULIRGs if small grains are preferentiallydestroyed. Spectral signatures of grain emissioncan be used to understand the role played by dustin regulating the star-formation of galaxies.The photoelectric efficiency may be key for regulatingthe evolution of the ISM, and can influence the overallstar-formation efficiency by mediating the coupling be-tween stellar radiation fields and gas temperatures. Thetrends between (cid:15) PE , Σ IR , and G/n H reflect vigorous,compact star-formation where dusty and young PDRsexhibit less efficient gas heating. Low photoelectricefficiencies may be common in the high-redshift Uni-verse where compact star-formation is ubiquitous, and4may also contribute to changes in the star-formation effi-ciency. The link between the efficiency of star-formationand the cooling/heating balance will be further testedwith JWST and ALMA, but ultimately a large space-based IR telescope like
Origins is needed to measurethe mid and far-infrared emission and track the full en-ergy budget in star-forming galaxies over a significantfraction of cosmic time.
We thank the referee for the thoughtful comments and recom-mendations. J.M. thanks S.Linden for the constructive feedbackon the paper. J.M. was supported by the IPAC Visiting GraduateFellowship. A.S.E. and Y.S. were supported by NSF grant AST1816838. H.I. acknowledges support from JSPS KAKENHI GrantNumber JP19K23462. This work is based on observations madewith the
Herschel Space Observatory , a European Space Agency(ESA) Cornerstone Mission with science instruments provided byEuropean-led Principal Investigator consortia and significant par-ticipation from NASA. The
Spitzer Space Telescope is operatedby the Jet Propulsion Laboratory, California Institute of Tech-nology, under NASA contract 1407. This research is based onobservations with AKARI, a JAXA project with the participationof ESA. This research has made use of the NASA/IPAC Extra-galactic Database (NED), which is operated by the Jet Propul-sion Laboratory, California Institute of Technology, under con-tract with the National Aeronautics and Space Administration,and of NASA’s Astrophysics Data System (ADS) abstract ser-vice. This research has made use of the NASA/IPAC InfraredScience Archive, which is operated by the Jet Propulsion Lab- or-atory, California Institute of Technology, under contract with theNational Aeronautics Space Administration.
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