Toappear in The Astrophysical Journal PreprinttypesetusingLATEXstyleemulateapjv.11/26/04 THE [Nii] 205 µm EMISSION IN LOCAL LUMINOUS INFRARED GALAXIES⋆ Yinghe Zhao1,2,3, Nanyao Lu1, C. Kevin Xu1, Yu Gao2,3, Steven D. Lord4, Vassilis Charmandaris5,6, Tanio Diaz-Santos7,8, Aaron Evans9,10, Justin Howell1, Andreea O. Petric11, Paul P. van der Werf12, and David B. Sanders13 (Dated: Received: Accepted:) To appear inThe Astrophysical Journal 6 ABSTRACT 1 Inthis paper, we presentthe measurementsof the [Nii]205µmline for a flux-limited sample of122 0 (ultra-)luminous infrared galaxies [(U)LIRGs] and 20 additional normal galaxies, obtained with the 2 Herschel Space Observatory (Herschel). We explore the far-infrared (FIR) color dependence of the n [Nii]205µm (L ) to the total infrared (L ) luminosity ratio, and find that L /L [Nii]205µm IR [Nii]205µm IR a onlydependsmodestlyonthe70-to-160µmfluxdensityratio(f /f )whenf /f .0.6,whereas 70 160 70 160 J such dependence becomes much steeper for f /f > 0.6. We also investigate the relation between 70 160 7 L and star formation rate (SFR), and show that L has a nearly linear correlation [Nii]205µm [Nii]205µm ] with SFR, albeit the intercept of such relation varies somewhat with f60/f100, consistent with our A previous conclusion that [Nii]205µm emission can serve as a SFR indicator with an accuracy of ∼0.4 dex, or ∼0.2 dex if f /f is known independently. Furthermore, together with the ISO G 60 100 measurements of [Nii], we use a total of ∼200 galaxies to derive the local [Nii]205µm luminosity . function (LF) by tying it to the known IR LF with a bivariate method. As a practical application, h we also compute the local SFR volume density (ρ˙ ) using the newly derived SFR calibrator and p SFR - LF.The resultinglog ρ˙SFR =−1.96±0.11M⊙yr−1Mpc−3 agreeswellwithpreviousstudies. Finally, o we determine the electron densities (n ) of the ionized medium for a subsample of 12 (U)LIRGs with e r both [Nii]205µm and [Nii]122µm data, and find that n is in the range of ∼1−100 cm−3, with a t e s median value of 22 cm−3. a Subject headings: galaxies: evolution—galaxies: luminosityfunction,massfunction—galaxies: ISM [ — galaxies: starburst — infrared: ISM 1 v 4 1. INTRODUCTION coolingtheinterstellarmedium(ISM),andforproviding 0 Emission from the forbidden atomic fine-structure criticaldiagnostic tools for the study of the star-forming 4 transitions in the far-infrared (FIR), such as the [Cii] ISM (e.g. Stacey et al. 1991;Lordet al. 1995;Malhotra 1 et al. 2001; Farrah et al. 2013; De Looze et al. 2014; 158 µm, [Nii] 122 µm and 205 µm, [Oi] 63 µm and 145 0 Fischer et al. 2014; Sargsyan et al. 2014). Among these µm, and [Oiii] 52 µm and 88 µm lines, is important for . lines,the[Cii]158µmemissionisprobablythemostim- 1 0 1Infrared Processing and Analysis Center, California Insti- portant and well studied, since it is the brightest single 6 tute of Technology 100-22, Pasadena, CA 91125, USA; zhaoy- lineinmostgalaxiesandaccountsfor0.1-1%ofthetotal 1 [email protected] FIR luminosity (e.g. Stacey et al. 1991; Diaz-Santos et 2Purple Mountain Observatory, Chinese Academy of Sciences, : al. 2013). v Nanjing210008, China 3KeyLaboratoryofRadioAstronomy,ChineseAcademyofSci- The [Nii]205µm line is of particular interest for the i X ences,Nanjing210008,China following reasons. Firstly, this 3P1 → 3P0 transition 4The SETI Institute, 189 Bernardo Ave, Suite 100, Mountain (205.197µm;hereafter[Nii]205µm)ofsinglyionizedni- r View,CA94043, USA a 5Department of Physics and ITCP, University of Crete, GR- trogenisexpectedtobeanexcellentindicatorofstarfor- 71003Heraklion,Greece mation rate (SFR) based on the following facts: 1) the 6IAASARS, National Observatory of Athens, GR-15236, Pen- ionization potential of nitrogen is only 14.53 eV. Thus teli,Greece the [Nii]205µm emission arises only from Hii regions, 7SpitzerScienceCenter,CaliforniaInstituteofTechnology,MS and essentially traces all warm ionized ISM. It can be 220-6,Pasadena,CA91125,USA 8Nucleo de Astronomia de la Facultad de Ingenieria, Universi- utilized to estimate the ionizing photon rate (e.g. Ben- dadDiegoPortales,Av. EjercitoLibertador441,Santiago, Chile nett et al. 1994); 2) the [Nii]205µm transition can be 9Department of Astronomy, University of Virginia, 530 Mc- easilycollisionallyexcitedbecauseofitslowcriticalden- Co1r0mNicaktiRonoaaldR,CadhiaorAlostttreosnvoilmle,yVOAbs2e2r9va0t4o,rUy,S5A20EdgemontRoad, sity (44 cm−3; Oberstet al. 2006)andexcitationenergy Charlottesville,VA22903,USA (∼ 70 K); 3) this emission is usually optically thin and 11Gemini Observatory, Northern Operations Center, 670 N. suffers much less dust extinction than optical and near A’ohokuPlace,Hilo,HI96720 infrared lines. Indeed, Zhao et al. (2013) have shown 12Leiden Observatory, Leiden University, PO Box 9513, 2300 that the [Nii]205µm line can serve as a SFR indica- RALeiden,TheNetherlands 13University of Hawaii, Institute for Astronomy, 2680 Wood- tor, which is especially useful for studying high-redshift lawnDrive,Honolulu,HI96822, USA galaxiesforwhichtheredshifted[Nii]205µmlineisread- ⋆BasedonHerschelobservations. HerschelisanESAspaceob- ilyobtainablewithmodernsubmillimetertelescopessuch servatorywithscienceinstrumentsprovidedbyEuropean-ledPrin- as the Atacama Large Millimeter/submillimeter Array cipalInvestigatorconsortiaandwithimportantparticipationfrom NASA. (ALMA). 2 Zhao et al. Secondly, this line can provide complementary infor- ing Receiver (SPIRE; Griffin et al. 2010) on board mation on the origin of the [Cii] 158 µm emission (e.g. Herschel. In that Letter we focused on the possibility Oberst et al. 2006; Walter et al. 2009; Decarli et al. of using the [Nii]205µm emission as a SFR indicator. 2014; Parkin et al. 2013, 2014; Hughes et al. 2015). Here we expand our analysis to our full Herschel sam- The [Cii] line can arise from both neutral and ionized pleof122LIRGs,whichisafluxlimited subsamplewith gases since it takes only 11.3 eV to form C+, while the f (8−1000µm)>6.5×10−13 W m−2 from the Great IR ionization potential of hydrogen is 13.60 eV. Therefore, ObservatoriesAll-SkyLIRGsSurvey(GOALS;Armuset it is important to know what fraction of the observed a. 2009). In addition, we include 20 additional nearby [Cii] line emission is from the ionized gas for the study large galaxies for which SPIRE/FTS mapping observa- of star-forming regions such as photodissociation region tions covering the entire galaxy disk are available from (PDR) modeling. Fortunately, the critical densities for the Herschel Science Archive (HSA). the[Nii]205µmand[Cii]158µmlinesinionizedregions Inthispaper,besidesfurtherinvestigatingtherelation are nearly identical (44 and 46 cm−3 at T =8000 K, re- between L and SFR, we also derive the lumi- [Nii]205µm spectively; Oberst et al. 2006), and both require similar nosity function (LF) of the [Nii]205µm line and SFR ionization potentials to further form N++ (29.6 eV) and density in the local Universe. It is important to con- C++ (24.4 eV). As a result, the [Cii]/[Nii]205µm line strain the LF of the [Nii] emission locally since now it ratio from ionized gas is a function of only the assumed becomespossibletobuildalargesampleforstudyingthe N+/C+ abundanceswithintheHiiregion,andtherefore [Nii] LF at high-redshift using modern facilities such as theobserved[Cii]/[Nii]205µmlineratioyieldsthefrac- ALMA.Thelocal[Nii]LFcanserveasabenchmarknec- tionofthe[Cii]emissionthatarisesfromtheionizedgas essary for observational and theoretical (e.g. Orsi et al. (Oberst et al. 2006,2011). 2014) studies on its evolution. Given the unprecedented Thirdly, the ratio of the [Nii] 122 µm to 205 µm lines sensitivity of Herschel at ∼200µm, and the large num- (hereafter R122/205) is an excellent density probe of low- berofgalaxiesinthelocalUniversealreadyobserved,for densityionizedgasduetotheirdifferentcriticaldensities the firsttime we canderivethe local[Nii]LF(see §3.2), (ncrit) required for the collisional excitations and being using a bivariate method and by utilizing the local IR atthe same ionizationlevel. Atan electrontemperature LF which has been studied extensively in the literature of 8000 K, ncrit are ∼ 293 and 44 cm−3 for the [Nii] with IRAS observations (e.g. Soifer et al. 1986; Sanders 122 and 205 µm lines, respectively (Oberst et al. 2006). et al. 2003). Therefore, R122/205 is sensitive to gas densities of 10 . In addition, we estimate the electron densities for a n .300 cm−3 (Oberst et al. 2006, 2011;also see §3.3). sub-sample of our (U)LIRGs by comparing the observed e However,the [Nii]205µmlineisgenerallyinaccessible R with theoretical predications. As shown in Ru- 122/205 to ground-based facilities for local galaxies, and for ex- bin et al. (1994; also see Oberst et al. 2006), R 122/205 tragalactic objects, only a handful were observed using variesfrom3forn ∼100cm−3to10forn &103cm−3. e e satelliteandairborneplatforms(Petuchowskietal. 1994; Although Petuchowski et al. (1994) and Lord et al. Lord et al. 1995) prior to the advent of the Herschel (1995) observed both the [Nii]205µm and [Nii]122µm Space Observatory (hereafter Herschel; Pilbratt et al. lines in M82, the use of R for estimating n was 122/205 e 2010). These studies have shown that the [Nii]205µm mostly limited to our own Galaxy (e.g. Wright et al. line is fairly bright, and the luminosity of [Nii]205µm 1991;Bennettetal. 1994;Oberstetal. 2006,2011)prior line (L ) may be up to ∼10−3.5 times the to- [Nii]205µm to the advent of Herschel. Furthermore, so far there are tal infrared luminosity (LIR; 8−1000µm; also see Zhao only a handful of normal galaxies (e.g. M51 & Cen A: et al. 2013). With such a high luminosity, this line of- Parkinet al. 2013, 2014;NGC 891: Hughes et al. 2015) fers an excellent method for studying SFR and ionized for which n of the low-density gas has been derived us- e gas properties in galaxies at high redshifts. The advan- ing the ratio of these two lines. For (U)LIRGs, it is still tage of [Nii]205µm line over other FIR lines, such as unclearwhatisthetypicaln forthe low-densityionized e [Cii]158µm, [Nii]122µm and [Oiii]λ88µm, is that it gas. starts to fall into atmospheric sub/millimeter windows The remainder of this paper is organized as follows: thathavehighertransmissionatlower-z,duetoitslonger we give a brief introduction of the sample, observations wavelength. The detectability of the [Nii]205µm line and data reduction in Section 2, present the results and anditspotentialforimportantastrophysicalapplications discussion in Section 3, and briefly summarize the main at high-z have already been demonstrated by a few ex- conclusions in the last section. Throughout the paper, perimental ALMA observing campaigns of a galaxy at we adopt a Hubble constant of H =70 km s−1 Mpc−1, 0 z = 4.76 (Nagao et al 2012), and by the IRAM 30m Ω =0.28, and Ω =0.72, which are based on the five- M Λ telescope and Plateau de Bure Interferometer detection year WMAP results (Hinshaw et al. 2009), and are the of distant, strongly lensed galaxies (Combes et al. 2012, sameas those usedby the GOALSproject(Armus etal. z ∼5.2; Decarli et al. 2012, 2014, z ∼3.9 and 4.7). 2009). In Zhao et al. (2013), we reported our first results on the [Nii]205µm line emission for an initial set of 70 2. SAMPLE,OBSERVATIONSANDDATAREDUCTION (Ultra-)Luminous infrared galaxies [(U)LIRGs; L ≥ IR 2.1. (Ultra-)Luminous Infrared Galaxies 1011(12)L ]15,observedwiththeFourier-transformspec- ⊙ trometer (FTS) of the Spectral and Photometric Imag- The primary sample studied in this paper is from the Herschel open time project Herschel Spectroscopic Sur- 15 LIR is calculated by using the IRAS four-band fluxes and vey of Warm Molecular Gas in Local Luminous Infrared the equation given in Sanders & Mirabel (1996), i.e., LIR(8− 1000µm) = 4πD2LfIR, where DL is the luminosity distance, and fIR=1.8×10−14(13.48f12+5.16f25+2.58f60+f100)(Wm−2) The [Nii] 205 µm Emission in Local LIRGs 3 Galaxies (OT1 nlu 1; PI: N. Lu). This project aims pri- marily at studying the dense and warm molecular gas properties of 125 LIRGs (e.g. Lu et al. 2014, 2015), whichcompriseafluxlimitedsubsetoftheGOALSsam- ple (Armusetal. 2009). Luetal. (2015;inpreparation) will give the program details and complete set of spec- tra for individual galaxies. The [Nii] observations were availablefor123targets,oneofwhichisamultiple-source systemandourtargetedobjectturnedouttobeaGalac- tic sourceaccordingto its SPIRE/FTSspectrum, conse- quently excluded fromouranalysis. Here we presentthe [Nii]205µmdataforthe122galaxies(hereafterGOALS- FTS sample), including 111 LIRGS and 11 ULIRGs. Of these sources, 48 galaxies are point-like sources with re- spect to the ∼17′′ Herschel SPIRE/FTS beam at ∼210 µm,and74areextendedsources,whichweredetermined according to their flux fractions of the FIR continuum emissions at both 70 and 160 µm observed within the SPIRE/FTS beam (see the following subsection for de- tails). The observations were conducted with the SPIRE/FTS in its point source spectroscopy mode and high spectral resolution configuration, yielding a spectral resolution of 0.04 cm−1 (or 1.2 GHz) over the spectral coverage of 194-672 µm. The data were reducedusingthe defaultversionofthe standardSPIRE reduction and calibration pipeline for point source Fig. 1.— The [Nii]122µm to [Nii]205µm emission ratio mode included in the Herschel Interactive Processing (R122/205) plotted against the IRAS FIR color. The upward and Environment (HIPE; Ott 2010) version 11.0. downwardarrowsrepresentlowerandupperlimits,respectively. In most cases the [Nii]205µm line is the brightest galaxies having Herschel SPIRE/FTS mapping observa- line in the SPIRE/FTS wavelength range (Lu et al. tions that cover the entire galaxy. As in Zhao et al. 2015, in preparation), and has high signal-to-noise ra- (2013), we further include another 53 unresolved galax- tios (S/N). As shown in Zhao et al. (2013), the line ies (23 detections and 30 upper limits) observed by the fluxes were obtained by fitting the observed profile us- Infrared Space Observatory (ISO; Kessler et al. 1996, ing the instrumental Sinc function convolved with a 2003) Long Wavelength Spectrometer (LWS), for which free-width Gaussian profile. This is because the line the [Nii]122µm fluxes were measured by Brauher et al. width of most (U)LIRGs is & 200kms−1 (e.g., see Ar- (2008; hereafter ISO sample). ribas et al. (2015) for ionized gas and Ronsenberg et al. (2015) for molecular gas). Given the instrumental 2.2.1. Herschel SPIRE/FTS Mapping Observations resolution (∼300kms−1 at 210µm), the observed line These observations were carried out by various Her- might be marginally resolved and could not be mod- schel projects [e.g. Very Nearby Galaxies Survey eled by a pure Sinc function. Therefore, we adopted (KPGT cwilso01 1; PI: C. D. Wilson; e.g. Spinoglio the Sinc-convolved-Gaussian (SCG) profiles for the in- et al 2012b; Parkin et al. 2013; Schirm et al. 2014; tegrated [Nii] line flux measurements except for a few Hughes et al. 2015) and the Beyond the Peak: Re- galaxieswhereapureSincprofilewasabetterchoicedue solved Far-Infrared Spectral Mapping of Nearby Galaxies to the intrinsically narrow line width and/or relatively with SPIRE/FTS (OT1 jsmith01 1; PI: J. D. Smith)]. lowS/Nintheline. Duringthefittingprocess,thewidth The level 0.5 raw data were obtained through HSA, and oftheSincfunctionwasfixedtobetheSPIRE/FTSres- reduced with the default pipeline for mapping observa- olution(1.2GHz), while the width ofthe Gaussianfunc- tions provided in HIPE 11. We then added up all pix- tionwasallowedtovary. The resultingfullwidthathalf els of the level 2 product which have valid data, and maximum (FWHM) of the [Nii] 205 µm line, which was measured the integrated [Nii]205µm fluxes using the obtained from the Gaussian part of the SCG profile, is ∼ 100−600 km s−1, with a median value of ∼ 300 km method described in Section 2.1 above. During this pro- s−1. Based on the 1σ statistical uncertainties, the lines cess, we have converted the units of the mapping data from MJy/sr to Jy/pixel using the area of an individual in most (>80%)sources are detected at better than 7σ, pixel. with the median at ∼14σ. The measured line fluxes are given in Table 1. 2.2.2. ISO LWS Observations 2.2. Local Normal Galaxies For the ISO sample, we derived their [Nii]205µm Almost all of our sample galaxies are (U)LIRGs, and fluxes(f[Nii]205µm)fromtheobserved[Nii]122µmfluxes hence have a rather limited dynamic range of several (f ) using the following empirical method. The [Nii]122µm physical parameters such as luminosity, FIR color, etc. R used in our conversion was estimated on the 122/205 To increase the sample size and dynamic range of our basis of the actual observations of these two lines study, we also include in our analysis 20 nearby normal for a sample consisting of 7 normal galaxies and 26 4 Zhao et al. TABLE 1 Fluxesof the [Nii]205µm Emission Galaxy R.A. Decl. ObsID f[Nii]205µma fcorr SFR f60 f100 Name (hh:mm:ss) (dd:mm:ss) (10−17 Wm−2) (R122/205) (M⊙yr−1) (Jy) (Jy) (1) (2) (3) (4) (5) (6) (7) (8) (9) GOALS-FTSSample NGC0023 00:09:53.4 +25:55:26.2 1342247622 10.79±0.75 1.58 23.0 9.03 15.66 NGC0034 00:11:06.5 −12:06:24.9 1342199253 2.55±0.49 2.33 55.0 17.05 16.86 MCG-02-01-051 00:18:50.9 −10:22:37.6 1342247617 3.80±0.54 1.00 50.3 7.48 9.66 ··· ··· ··· ··· ··· ··· ··· ··· ··· MappingGalaxySample NGC1266 03:16:00.7 −02:25:38 1342239353 2.85±0.42 — 5.6 13.13 16.89 NGC1377 03:36:39.1 −20:54:08 1342239352 0.58±0.10 — ··· 7.43 5.95 NGC1482 03:54:38.9 −20:30:10 1342248233 36.1±2.4 — 13.1 33.96 46.73 ··· ··· ··· ··· ··· ··· ··· ··· ··· ISOSample NGC0520 01:24:34.90 +03:47:30.0 77702295 39.2±16.3 1.2 15.4 31.10 47.12 NGC0986 02:33:34.10 −39:02:41.0 74300187 43.3±18.1 1.2 12.6 25.14 51.31 NGC1222 03:08:56.80 −02:57:18.0 82400836 8.7±4.0 1.5 8.3 13.07 15.38 ··· ··· ··· ··· ··· ··· ··· ··· ··· Note. —Columns: (1)galaxyname;(2)and(3)rightascensionanddeclination(J2000);fortheGOALS-FTSsample,thecoordinategivesthe positionwheretheHerschelSPIRE/FTSobservationwaspointed;(4)observationID(number)fortheHerschel(ISO)observation;(5)[Nii]205µm flux: measuredfromtheSPIRE/FTSspectrafortheGOALS-FTSandMappingGalaxysamples;obtainedfrom[Nii]122µmemissionfortheISO sample;(6)fortheGOALS-FTSsample,correctionfactor(fcorr)appliedtoColumn(5)toobtainthetotal[Nii]205µmflux(see§2.1.1fordetails); fortheISOsample,the[Nii]122µm-to-[Nii]205µmconversionfactor(R21);(7)starformationrate(§3.1);(8)and(9)IRASfluxesat60and100 µmrespectively. aFortheISOsample,thelistederrorhastakenintoaccountfortheuncertaintyofR122/205. (Thistableisavailableinitsentiretyinamachine-readableformintheonlinejournal. A portionisshown hereforguidanceregardingitsform andcontent.) (U)LIRGs. Besides our GOALS-FTS sources, about a this (un)correlation will not affect our main conclusions half of these (U)LIRGs are from Farrah et al. (2013) since the two R values adopted in the following 122/205 sample, for which the [Nii]122µm were observed with only differ by ∼0.3, which is negligible compared to the Herschel PACS, and f were adopted from Far- overalluncertainties. [Nii]122µm rah et al. (2013); whereas f[Nii]205µm were measured For sources with f60/f100 < 0.7, we adopt R122/205 = from the SPIRE/FTS data observed in the program 1.2 ± 0.5, and for the other warmer galaxies (with “OT1 dfarrah 1” (PI: D. Farrah). For our GOALS- f60/f100 < 1.0), R122/205 = 1.5±0.7. These adopted FTSobjects,theaperture-corrected(see§2.3)f[Nii]205µm R122/205 values are the median of the corresponding were used. detections, and are lower than the single value of 2.6 In Figure 1 we plotted R againstthe IRAS FIR adopted in Zhao et al. (2013). The latter was based 122/205 color, f /f . It seems that R shows some de- on the theoretical prediction for an electron density of 60 100 122/205 n = 80 cm−3, i.e. the median value of Hii regions in pendence on f /f . Kewley et al. (2000) found that e 60 100 latetypegalaxies(Hoetal. 1997). However,theadopted electron density tends to correlate with f /f . There- 25 60 n in Zhao et al. (2013) was measured from Hii regions fore, the weak dependence of R on f /f ap- e 122/205 60 100 in the centers of nearby galaxies, and thus might be an pears to be understandable. To further check whether overestimate of the mean n for the entire galaxy. As a there is a correlation between f /f and R , we e 60 100 122/205 result, the overall f obtained from f computedtheKendall’sτ correlationcoefficientusingthe [Nii]205µm [Nii]122µm cenken function in the NADA package within the pub- in Zhao et al. (2013) was somewhat underestimated. lic domainRstatisticalsoftwareenvironment16. Forthe Forthesenearbygalaxies,theredshift-independentdis- whole dataset presented in Figure 1, we have τ = 0.18, tance was adopted if a direct primary measurement dis- with a p-value of 0.13, and thus we do not reject the tance could be found in the NED17 database, otherwise null hypothesis that these two parameters are uncorre- it was derived with the same method as used for our lated at the 0.05 significance level. However, we have (U)LIRG sample (e.g. Armus et al. 2009), i.e. by cor- τ = 0.35 with a p-value of 0.03 if we limit the sample recting the heliocentric velocity for the 3-attractor flow to f /f < 0.9. Therefore, there exists a weak cor- model of Mould et al. (2000). 60 100 relation between f /f and R within this color 60 100 122/205 range. Since almost all of the ISO galaxies fall within 2.3. Aperture Corrections thiscolorrange,weadoptFIRcolor-dependentR122/205. Around 205µm the SPIRE/FTS beam can be well Nevertheless, we caution that such an analysis is possi- represented by a symmetrical Gaussian profile with a bly limited by the small size of the sample. However, FWHM of 17′′ (Makiwa et al. 2013; Swinyard et al. 16 http://www.R-project.org/ 17 http://ned.ipac.caltech.edu The [Nii] 205 µm Emission in Local LIRGs 5 2014). However,this beam cannotfully coverthe entire erally much colder. This is illustrated in Figure 2a, [Nii] emission region in most of our targets assuming in which we plotted the distributions of the FIR color their FIR sizes indicate the extent of the [Nii] emis- inside ((f /f ) ; dotted histogram) and outside 70 160 beam sion. To define a source as “extended” compared to ((f /f ) ; solid histogram) the SPIRE/FTS beam. 70 160 out the SPIRE/FTS beam, we calculated the fractional 70 We can see that (f /f ) and (f /f ) peak 70 160 beam 70 160 out and 160µm fluxes within a Gaussian beam of FWHM at ∼1.41 and ∼0.45 respectively. Therefore, it is nec- of 17′′ (see below). An extended source will have both essary to include more fiduciary data with cooler FIR fractions less than 90%. Based on this definition, 74 colors to better establish the L /L -FIR color [Nii]205µm IR galaxiesare classifiedas extended. Therefore, to achieve relationship. ourultimate goalsofderivingthe LFofthe [Nii]205µm For this purpose, we include in our analysis a emission,as wellas offurther exploringthe applicability dozen nearby, spatially resolved galaxies, which have of L as a SFR indicator, we need to apply an SPIRE/FTS mapping observations in the HSA and are [Nii]205µm aperture correction to the observed [Nii]205µm fluxes mainly from the same projects listed in section 2.2.1. for most sources. These SPIRE/FTS observations (3 of them are in the Zhao et al. (2013) found that L correlates sampleofthe20galaxiesmentionedin§2.2)werereduced [Nii]205µm almost linearly with L . Hence, the aperture correc- withthesamemethodasdescribedin§2.2.1. ThePACS IR tion can be done by utilizing PACS photometry im- imaging data of these nearby, very extended galaxies ages and estimating the L measured within the re- were reduced using the Scanamorphos technique (Rous- IR gion outside the SPIRE/FTS beam. However, as al- sel 2013) provided in HIPE 12.1, and then were con- ready shown in Zhao et al. (2013), the L /L volved from their native resolutions to the 17′′ resolu- [Nii]205µm IR ratio also depends somewhat on the FIR color. To ac- tionofSPIREat∼210µmusingthe samemethodasfor count for this dependence and to minimize the uncer- our GOALS-FTS sample. The convolved images were tainty in the final, total L , we used the FIR rebinned to maps with pixel size corresponding to the [Nii]205µm color-dependent L -L relation (see below) to SPIRE/FTS mapping observations. In order to increase [Nii]205µm IR correcttheL whichwasmeasureddirectlyfrom the S/N for the SPIRE/FTS mapping observations, we [Nii]205µm stackedspectra fromregionshavingsimilarf /f col- the SPIRE/FTS spectra. 70 160 To measure the L and FIR color within the 17′′ ors. Also, to reduce the uncertainties in the stacked IR spectrum and IR flux for each color bin, only pixels SPIRE/FTS beam near 205 µm for our sample of with S/N > 3 both at 70 and 160µm were used. The (U)LIRGs, we applied the following steps. Firstly, in [Nii]205µm fluxes of the stacked spectrum from these order to have the same resolution as the SPIRE/FTS, galaxies were measured using the same method as for we convolved the 70 and 160 µm images (e.g. Chu et the GOALS-FTS sample described in §2.1 above. al. 2015, in preparation), which were obtained with the The final L /L -FIR color relation is Photodetector Array Camera and Spectrometer (PACS; [Nii]205µm IR,PACS showninFigure3,whereL , L andFIR Poglitsch et al. 2010), with kernels computed through [Nii]205µm IR,PACS the algorithm described in Aniano et al. (2011). These color were measured within the SPIRE/FTS beam for convolution kernels were generated by comparing the allofourGOALS-FTS(U)LIRGs,andforothergalaxies PACSPSFsat70µmand160µmwithaGaussianprofile theseweremeasuredwithinthestackedspaxels. Thisre- ofFWHMof17′′ (asarepresentativeoftheSPIRE/FTS lation is rather flat for log(f70/f160) . −0.2 (equivalent beam around 210µm). Then we converted the units of to f60/f100 .0.46; after Dale et al. 2001), but becomes the convolved images from Jy/arcsec2 to Jy/beam by muchsteeper whenthe FIRcoloris gettingwarmer,and multiplying the area of the Gaussian profile. The fluxes has the largest scatter at the warmest end. To inves- within the SPIRE/FTS beam at 70 and 160 µm (here- tigate this relation, we used the Kaplan-Meier estimate afterf andf ,respectively)weremeasured (Kaplan & Meier 1958) for censored data18. The re- 70,beam 160,beam from the convolved PACS images at the SPIRE/FTS sulting L[Nii]205µm/LIR,PACS-f70/f160 relation is shown pointing position. The total fluxes (f and f ), by the solid line in Figure 3, with a scatter of 0.22 dex 70,tot 160,tot were also measured from the convolved images by doing (compared to the observed L[Nii]205µm/LIR,PACS). We aperture photometry. Therefore, the fluxes outside the usedthisrelationtocalculatetheL[Nii]205µm outsidethe SPIRE/FTS beam are f = f −f and SPIRE/FTSbeamforourGOALS-FTSsample,andthe 70,out 70,tot 70,beam f = f − f , for the 70 and 160µm uncertainty of 0.22 dex was propagated to the final un- 160,out 160,tot 160,beam respectively. Note that in this subsection the IR lumi- certainty values for L[Nii]205µm after taking a quadratic nosity (L ) is calculated using the f and f sum of all errors. IR,PACS 70 160 fluxes and the formula (L = 1.010νL(70µm)+ We also fitted the relation estimated by locfit.censor IR,PACS 1.218νL(160µm)) presented in Galametz et al. (2013) (i.e. thesolidlineinFigure3)withathird-orderpolyno- sincethePACSdatahavemuchhigherangularresolution mial function because an analytical form could be more than the IRAS data, which is necessary for our purpose. convenient for future studies. The best-fit gives However,the L used for the remainder of our analysis IR is derived from the IRAS four-band fluxes and the well log(L /L )=−3.83−1.26x−1.86x2−0.90x3, [Nii]205µm IR known equation given in Sanders & Mirabel (1996). (1) Since the galaxies in our sample are (U)LIRGs, and with x = log(f /f ), and a scatter of 0.01 dex, and 70 160 our SPIRE observations usually were targeted at the it is plotted as a dash line in Figure 3. Please note this center of each object, the measured FIR color within relation is only valid for the color range we have inves- the beam is very warm, whereas the part missed by the SPIRE beam, which needs to be corrected for, is gen- 18 Implementedinthelocfit.censorfunctioninthelocfitpackage inR 6 Zhao et al. Fig. 2.—Distributionsof(a)theFIRcolorsmeasuredinside(dottedline)andoutside(solidline)theSPIRE/FTSbeam. (b)theratios of aperture-corrected L[Nii]205µm to L[Nii]205µm,beam (solid) and the total LIR,PACS to LIR,PACS,beam (dotted), for the subsample of ourextended (U)LIRGs tigated, i.e. −0.9 ≤ log(f /f ) ≤ 0.4. An uncer- log(f /f ) >−0.2. Therefore,it stillworthusinga 70 160 70 160 out tainty of 0.23 dex should be adopted if this best-fit rela- color-dependentL /L relationtodotheaper- [Nii]205µm IR tion is used to compute L /L from f /f . ture correction since the underestimation is systematic. [Nii]205µm IR 70 160 As seen in Figure 3, there is a strong relation between L /L and FIR color for log(f /f ) > 3. RESULTSANDDISCUSSION [Nii]205µm IR 70 160 out −0.2. Giventhataboutonethirdofourextendedsources 3.1. The [Nii]205µm Emission as a SFR Indicator have log(f /f ) >−0.2 (see Figure 2a) it is neces- 70 160 out 3.1.1. L −SFR Correlation sarytouseacolor-dependentaperturecorrectionforthe [NII] [Nii]205µm emission. To estimate the SFR of our sources we used the al- The aperture-corrected, total L gorithm of Dale et al. (2007), e.g. SFR(M yr−1) = [Nii]205µm ⊙ for the extended GOALS-FTS sources were, 4.5×10−37L (W)+7.1×10−37νL (1500˚A)(W),which IR ν L[Nii]205µm = L[Nii]205µm,beam + L[Nii]205µm,out, takes into account dust obscuration by combining the where L[Nii]205µm,beam and L[Nii]205µm,out representthe IRAS IR and GALEX FUV fluxes. Here LIR was cal- [Nii]205µm luminosities measured inside and outside culated with the IRAS four-band data. Without tak- the SPIRE/FTS beam, respectively. L ing into accountthe dependence of SFR on the assumed [Nii]205µm,beam was measured directly from the SPIRE/FTS spectrum, initial mass function, the uncertainty in SFR from this while L was obtained using L composite calibrator is dominated by the uncertainty in [Nii]205µm,out IR,PACS,out and (f /f ) . As shown in Figure 2a, most of our the coefficient of the first term on the right side of the 70 160 out galaxies have log(f /f ) < −0.2, so the aperture equation. Here we adopted an uncertainty of 40% (e.g. 70 160 out correction for these sources should not be very sensitive Kennicutt & Evans 2012), and it was propagated to the to the FIR color as indicated by Figure 3 (and equation final SFR after taking a quadratic sum of all errors. For 1). The solid histogram in Figure 2(b) shows the the GOALS-FTS sample, the FUV data were adopted distribution of the L /L ratios from Howell et al. (2010), while for the normal galaxy [Nii]205µm [Nii]205µm,beam (≡f ) for the extended sources. For about 70% of all andISOsamples, the FUV data werecompiled fromthe corr literature(mainlyfrom,e.g. Daleetal. 2007;GildePaz the cases, f is less than 2, i.e. the SPIRE/FTS beam captured mcoorrre than a half of the total [Nii]205µm et al. 2007) and the GALEX data release GR719. Since our SFR estimate relies on the availability of UV obser- emission from a galaxy. To further examine whether the color-dependent vations, we restricted our sample to 121 galaxies with aperture correction is essential, we also plotted available UV photometric data (hereafter SFR sample). the L /L distribution (dotted line) Before further analysis, however, it is instructive to IR,PACS IR,PACS,beam in Figure 2b. The median values of f and check whether our dataset is capable of exploring a rela- corr tionbetweenL andSFR.Thisisduetothefact LIR,PACS/LIR,PACS,beam are 1.66 and 1.44, respec- [Nii]205µm tively,whichindicatesthatthe overallL would that (1) for the GOALS-FTS sample, the aperture cor- [Nii]205µm be underestimated by about 12% if we used a con- rectionisessentialtheconversionofLIRintoL[Nii]205µm; stant L /L ratio to do the aperture correc- (2) The SFRs for the GOALS-FTS galaxies are domi- [Nii]205µm IR tion. This is insignificant compared to the scatter nated by LIR. Therefore, L[Nii]205µm and SFR may ar- of the L /L -FIR color relation. However, tificially correlate with each other even if they do not [Nii]205µm IR the underestimation will reach 30% for sources with 19 http://galex.stsci.edu/GR6/#5 The [Nii] 205 µm Emission in Local LIRGs 7 Fig. 3.— Correlation between the [Nii]205µm to IR luminosity (see the text for the derivation of the IR luminosity used here) ratio and FIR color. For (U)LIRGs, L[Nii]205µm, LIR,PACS and FIR color were measured within the SPIRE beam, whereas for other labelled individual galaxies, we used the SPIRE mapping observations and stacked spectra for similar FIR colors to measure L and [Nii]205µm LIR,PACS withintheregionofthemappedpixel(seethetextformoredetails). Thedashed(red)lineshowsthebestpolynomialfittothe resultsshownbythesolid(black)line,whichwerecomputedusingthelocfit.censorfunction. have an intrinsic relationship. As shown in Figures 4a L -SFR relation(s). [Nii]205µm and 4b, sources with f ≤ 1.5 and f > 1.5 for From Figure 5 we can see that the scatter in corr corr ourGOALS-FTS sample residein similar phase spaceof L −SFR relation becomes larger with the in- [Nii]205µm L[Nii]205µm and LIR. In addition, very extended sources crease of SFR, consistent with Zhao et al. (2013). In with f > 2.0 only occupy a small fraction (∼17%) this figure we demonstrate that the increase in scatter corr of the SFR sample. Therefore, we conclude that our is traced to the individual galaxy colors (f /f ). To 60 100 dataset will not artificially make a correlation between isolate the color-dependence (and thus reduce the scat- L and SFR. ter)oftheL −SFRrelation,wedivideoursam- [Nii]205µm [Nii]205µm In Figure 5, we plot SFR against L for both ple galaxies into three sub-samples according to their [Nii]205µm (U)LIRGs and normal galaxies. Squares represent the f60/f100, i.e. a “cold” one with 0.2 ≤ f60/f100 < 0.6 (U)LIRGsintheGOALS-FTSsample. Circlesshownor- (i.e. a blackbody temperature of 30 . T . 50 K); a malgalaxiesobservedbyHerschel,whereasdiamondsare “warm” one with 0.6≤f60/f100 <0.9 (50.T .60 K), the ISO sources from Brauher et al. (2008). The solid and a “hot” one with 0.9≤f60/f100 <1.4 (60.T .90 symbolsinFigure5indicatethatthefractionalcontribu- K). These color bins were chosen according to the FIR tionfromapossibleactivegalacticnucleus(AGN)tothe color distribution (three peaks in Figure 4c) of our sam- bolometric luminosity, f , is greater than 0.35. Here ple galaxies. Additional considerations for the separa- AGN f was derived from a set of the mid-IR diagnostics tionofcoldandwarm/hotsamplesarethat(1)Starburst AGN based on [Nev]/[Neii], [Oiv]/[Neii], continuum slope, galaxiesusuallyhavef60/f100 >0.55(Buat&Burgarella polycyclic aromatic hydrocarbon equivalent width, and 1998); (2) The turnover of the L[Nii]205µm/LIR-f60/f100 the diagram of Laurent et al. (2000), following the pre- relation happens at f /f ∼0.5. 60 100 scriptions in Armus et al. (2007; see also Veilleux et al. ToinvestigatetherelationshipbetweenL and [Nii]205µm 2009; Petric et al. 2011; Stierwalt et al. 2013). These SFR, we fitted each sub-sample using a least-squares, galaxiesare excluded from our fitting procedures for the geometrical mean functional relationship (Isobe et al. 8 Zhao et al. Fig. 4.—Distributionsof(a)and(b): L[Nii]205µm andLIR fortheGOALS-FTSsample,respectively;(c): FIRcolorfortheSFRsample. Thesolidanddotted histogramsinpanels(a)and(b)showtheresultsforthefcorr ≤1.5andfcorr>1.5subsamplesrespectively. 1990) with a linear form, i.e. The nearly linear relation between L and SFR [Nii]205µm log SFR(M yr−1)=a+blog L (L ). (2) indicatesthatthe powersourceofthe [Nii]205µmemis- ⊙ [Nii] ⊙ sion may be related to the details of the star formation to all galaxies except those having f > 0.35. Using AGN processes that take place in each galaxy. Given such thesamemethod,wealsofittedthewholegalaxysample. a strong correlation, and to reduce any systemic uncer- TotakeintoaccounttheuncertaintiesbothinL [Nii]205µm tainties caused by the sample itself (such as sample size, and SFR, we used two independent approaches, which dynamic range,etc), we alsofitted the L −SFR allow us to evaluate their reliabilities, to estimate the fi- [Nii]205µm relation with a fixed slope of 1. These results are also nal coefficients (a, b) and associated errors in equation given in Table 2, and plotted in Figure 5 as a dashed 2. The first method (M1) was carried out by using a line for each sample. The reduced χ2 from both fixed Monte Carlo simulation described as follows. Firstly, we and varying slopes, as listed in 2, agree with each other generated a simulated sample by assuming a Gaussian within < 15%, and thus the fitted results with a fixed error using the measured data points and uncertainties. slope of 1 are recommended to be used for computing Secondly, we fitted this sample using equation2 and the SFRs. geometricalmeanmethod. Thirdly,werepeatedthepre- Are the fitted relations sensitive to R for our vioustwosteps10000times. Thedistributionsofthefit- 122/205 (sub-)samples? To further check this, we fitted the ted results from this process are shown in Figure 6. The L −SFR relations for the (sub-)samples by ex- second method (M2) is that the observed data points [Nii]205µm cluding the ISO galaxies and using the method M2. We werefittedbyusingaweightedleast-squares,geometrical found that the resultant slopes and intercepts only have meanregression. TheweightingisdefinedafterWilliams etal. (2010),namely,1/σ2 ≡1/(b2σ2 +σ2 ),where tiny changes, as shown in Table 2. Therefore, we con- L[NII] SFR clude that our results are not affected substantially by σ2 and σ2 are the errors in L and SFR, L[NII] SFR [Nii]205µm including the ISO galaxies. respectively. Table 2 lists the number of objects in each sample, 3.1.2. The Scatter in the L[Nii]205µm−SFR Relation the fitting coefficients, 1σ errors and scatters from both Table 2 shows that the scatter of each sub-sample is methods, for the L −SFR relation. From the a factor of ∼1.5 smaller compared to that of the full [Nii]205µm table wecansee thatM1andM2 giveconsistentresults. sample. This suggests that the color-dependence of the Hence, we only discuss the results from M2 hereafter. [Nii]205µmemission contributes significantly to the to- In Table 2 we also show the Spearman’s rank correla- tal scatter of the L −SFR relation. This is fur- [Nii]205µm tioncoefficient(ρ,assessinghowwellanarbitrarymono- therconfirmedbythefollowingtwochecks: (1)Aprinci- tonic function could describe the relationship between pal component analysis indicates that the FIR color ac- two variables), and the level of significance (Sig), which countsfor41%ofthetotalvarianceofthe entiresample; was computed from the p-value using a Student’s t dis- (2) We simply normalized the L by the galaxy [Nii]205µm tribution. These ρ and Sig indicate that there exists a FIR color, i.e., log L = log L + [Nii]205µm,norm [Nii]205µm very strong correlationbetween L[Nii]205µm and SFR. log(f60/f100), and then fitted the log L[Nii]205µm,norm− Onaverage,SFRscaleswithLb withbbetween0.62 SFR relations with method M2 (varying slope) and cal- [Nii] and 1.34 at 3σ significance. The slopes in the current culated the scatters, which are 0.15, 0.23, 0.20 and 0.26 work are consistent with the result (0.95±0.05) found dex for the “Cold”, “Warm”, “Hot” and “All” samples, in Zhao et al. (2013) within 1−2σ uncertainty ranges. respectively. For the former three samples, these values The [Nii] 205 µm Emission in Local LIRGs 9 Fig. 5.—Correlationbetween the [Nii]205µmluminosityandSFR.Thesquares andcirclesaregalaxies havingHerschelobservations; while the diamonds are galaxies from Brauher et al. (2008), whose L were derived with the [Nii]122µm emission. The solid [Nii]205µm symbol indicates that the AGN contributes morethan 35% tothe total bolometricluminosity, and areexcluded fromthe fit. The points arecolor-codedaccordingtotheirf60/f100. ForeachFIRcolorbin,thebest-fitrelation(slopeof1)isshownbythedashed-line,withthe blacklineshowingtherelationfortheentiresample. are almost the same as those for the L −SFR of ionization conditions in different galaxies. This is be- [Nii]205µm relation, while for the “All” sample, it is reduced by a cause the FIR color is tightly correlated with the ion- factor 1.3. If we “corrected” the L using the ization parameter, U (Abel et al. 2009; Fischer et al. [Nii]205µm dotted lines in Figure 7a, i.e. 2014; Comier et al. 2015). Adopting the [Oiii]88µm- to-[Nii]205µmflux ratioasanindicatorofthe hardness 6.07 if x≤−0.29 of the radiation field, Zhao et al. (2013) also suggested y = (3) (cid:26)5.20−3.00x otherwise that the hardness variation can largely account for the scatter. However, the [Oiii]88µm/[Nii]205µm ratio is where y = log(L[Nii]205µm/SFR), in units of sensitive to electron density (Rubin 1985) since the lev- L⊙/(M⊙yr−1), and x = log(f60/f100), their scatters els emit these two lines have their critical densities dif- would become 0.15, 0.21,0.22 and 0.18 dex respectively, fering by a factor of >10. Therefore, here we used the and are comparable to the measurement uncertainty of [Oiii]88µm/[Nii]122µm ratio, which is insensitive to 0.19 dex (median value of the entire sample). density, as a hardness indicator (Ferkinhoff et al. 2011) As discussed in detail in Zhao et al. (2013), the scat- to further check the hardness effect. ter and/orcolordependence inthe L −SFR(or However, we note that the [Oiii]88µm/[Nii]122µm [Nii]205µm L −L ) relation is mainly due to the variation ratio is only a good hardness indicator for a fixed [Nii]205µm IR 10 Zhao et al. Fig. 6.—Distributionsofthefittedinterceptsandslopes,whichwereobtainedthroughtheMonteCarlosimulations(seetextfordetails), foreach(sub-)samples. Ineachpanel,thenumbersinparentheses givethebest-fitparametersforaGaussianfunction. U. It is correlated with U at a given hardness and (Cormier et al. 2015). Therefore, for the sample hav- log(L /L ) =y −(1.2+3.1x) (5) [Oiii]88µm [Nii]122µm corr 1 ing both [Oiii]88µm and [Nii]122µm data (hereafter “OIII sample”) we correct log(L[Nii]205µm/SFR) (then where y = log(L[Nii]205µm/SFR), y1 = the scatter changed from 0.36 dex to 0.28 dex), and log(L[Oiii]88µm/L[Nii]122µm), and x = log(f60/f100). the [Oiii]88µm/[Nii]122µm ratios using the following Equation (5) is the result of a least-square fit to the equations, respectively: [Oiii]88µm/[Nii]122µm−f60/f100 relation (see Figure 7b). In this way, we may eliminate/reduce the effect of U on both parameters. As shown in 7c, there exists y if xa≤w−e0a.k29correlation between log(L /SFR) and log(L /SFR) = [Nii]205µm [Nii]205µm corr (cid:26)y−(5.20−3.00x)+6.07 othelrowgi(sLe /L ), with the Spearman’s rank [Oiii]88µm [Nii]122µm (4) coefficient ρ = −0.5 at a 2.1σ level of significance. The