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ApJ,accepted PreprinttypesetusingLATEXstyleemulateapjv.6/22/04 OPTICAL STAR-FORMATION RATE INDICATORS John Moustakas1, Robert C. Kennicutt, Jr.1,2, & Christy A. Tremonti1 ApJ, accepted ABSTRACT Usingintegratedopticalspectrophotometryfor412star-forminggalaxiesatz ∼0,andfiber-aperture spectrophotometry for 120,846 SDSS galaxies at z ∼ 0.1, we investigate the Hα λ6563, Hβ λ4861, [O ii]λ3727,and[Oiii] λ5007nebular emissionlines andtheU-bandluminosityas quantitativestar- formationrate (SFR) indicators. We demonstrate that the extinction-correctedHα λ6563luminosity is areliable SFRtracereveninhighly obscuredstar-forminggalaxies. We findthat variationsin dust 6 reddening dominate the systematic uncertaintyin SFRs derivedfrom the observedHβ, [O ii], andU- 0 band luminosities, producing a factor of ∼1.7,∼2.5, and ∼2.1 scatter in the mean transformations, 0 respectively. Weshowthat[Oii]dependsweaklyonvariationsinoxygenabundanceoverawiderange 2 inmetallicity,12+log(O/H)=8.15−8.7dex(Z/Z⊙ =0.28−1.0),andthatinthismetallicityinterval n galaxiesoccupyanarrowrangeinionizationparameter(−3.8.log U .−2.9dex). Weshowthatthe a scatterin[Oiii]λ5007asaSFRindicatorisafactorof3−4duetoitssensitivitytometalabundance J andionization. WedevelopempiricalSFRcalibrationsforHβ and[Oii]parameterizedintermsofthe 8 B-band luminosity, which remove the systematic effects of reddening and metallicity, and reduce the SFR scatter to ±40%and±90%,respectively,althoughindividual galaxiesmaydeviate substantially 2 from the median relations. Finally, we compare the z ∼ 0 relations between blue luminosity and v reddening, ionization, and [O ii]/Hα ratio against measurements at z ∼1 and find broad agreement. 0 We emphasize, however, that optical emission-line measurements including Hα for larger samples of 3 intermediate-andhigh-redshiftgalaxiesareneededtotesttheapplicabilityofourlocallyderivedSFR 7 calibrations to distant galaxies. 1 Subject headings: galaxies: abundances—galaxies: evolution—galaxies: formation—galaxies: ISM 1 5 0 / 1. INTRODUCTION of the cosmic SFR, and to investigate the physical h processes responsible for this evolution. In this paper Over the past twenty years many techniques have p we carry out a detailed empirical analysis of rest-frame been devised to estimate the global star-formation rates - optical SFR indicators. o (SFRs) of galaxies. The first quantitative analysis One of the most well-understood SFR indicators r of SFRs using the Hα λ6563 nebular recombination t is Hα λ6563. The Hα luminosity is directly propor- s line was undertaken by Kennicutt (1983). Today, a with the advent of large, multi-wavelength surveys of tional to the hydrogen-ionizing radiation from massive v: galaxies, virtually every part of the electromagnetic (& 10 M⊙) stars, and therefore provides a near- instantaneous (. 10 Myr) measure of the SFR with i spectrum has been explored as a means of deriving X minimal dependence on the physical conditions of the SFRs (e.g., Kennicutt 1983; Buat et al. 1989; Condon ionized gas (Kennicutt 1998). Unfortunately, Hα is only r 1992; David et al. 1992). Two indicators directly asso- a observablefromthegroundatz .0.4intheoptical,and ciated with massive star formation are the ultraviolet (UV; λλ1200 − 2500 ˚A) and nebular recombination at 0.7 . z . 2.5 through the near-infrared atmospheric windows (Fig. 1). Given the observational difficulties of line luminosities. These techniques were particularly observingHαathighredshift,therefore,the[Oii]λ3727 important in establishing the order-of-magnitude rise in nebular emission line has been suggested as an alter- the SFR density of the universe from the present day to native SFR indicator (Gallagher et al. 1989; Kennicutt z = 1 and beyond (Lilly et al. 1996; Madau et al. 1996; 1992b; Guzman et al. 1997; Barbaro & Poggianti Cowie et al. 1997; Glazebrook et al. 1999; Steidel et al. 1997; Jansen et al. 2001; Aragon-Salamancaet al. 1999; Hopkins 2004). Despite considerable progress 2002; Rosa-Gonza´lez et al. 2002; Hopkins et al. 2003; in measuring SFRs of distant galaxies, however, their Kewley et al. 2004; Mouhcine et al. 2005). Its intrinsic accuracy remains limited by a wide range of system- strength and blue rest-frame wavelength allow it to atic uncertainties (Cram et al. 1998; Glazebrook et al. be measured even in low signal-to-noise (S/N) spec- 1999; Bell & Kennicutt 2001; Sullivan et al. 2001; tra at z . 1.5 in the optical, and at 2 . z . 5.2 Hopkins et al. 2001, 2003; Charlot et al. 2002; in the near-infrared (Fig. 1). However, the [O ii] Rosa-Gonza´lez et al. 2002; Kewley et al. 2002, 2004; luminosity depends explicitly on the chemical abun- Hirashita et al. 2003; Bell 2003). Well-calibrated SFR dance and excitation state of the ionized gas, and diagnostics with well-understood systematic uncertain- suffers a larger amount of dust extinction than Hα. ties are needed to improve constraints on the evolution Therefore, unlike the Balmer recombination lines, 1 Steward Observatory, University of Arizona, 933 N Cherry [O ii] is not directly proportional to the SFR and Ave.,Tucson,AZ85721,USA must be calibrated either empirically (Kennicutt 2 Institute of Astronomy, University of Cambridge, Madingley 1992b; Rosa-Gonza´lez et al. 2002; Kewley et al. Road,CambridgeCB30HA,UnitedKingdom 2004), or theoretically (Barbaro & Poggianti 1997; 2 Moustakas, Kennicutt, & Tremonti Charlot & Longhetti 2001). high S/N optical spectrophotometry (3600−6900 ˚A at Gallagher et al. (1989) presented the first quantita- ∼ 8 ˚A FWHM resolution) for a diverse sample of 417 tive analysis of [O ii] as a SFR indicator using [O ii] nearby galaxies (Moustakas & Kennicutt 2005a, here- and Hβ measurements of a sample of 75 blue-irregular after MK05). This survey targets objects that repre- galaxies. Kennicutt (1992b) improved upon this study sent a small fraction of the galaxy population today, by obtaining integrated optical (3650 − 7150 ˚A) spec- but which may be more typical of high-redshift sam- tra of 55 galaxies spanning the Hubble sequence, in- ples, including starbursts, interacting/merging systems, cluding a handful of peculiar objects, and derived the and dusty, infrared-luminous galaxies; the sample also first empirical calibration of [O ii] relative to Hα. includes a large number of normal star-forming galax- Previously, the equivalent width of [O ii] was used ies. We utilize the long-slit drift-scanning technique de- only indirectly to infer ongoing star formation (e.g., veloped by Kennicutt (1992a) to obtain spatially inte- Broadhurstet al.1988;Colless et al.1990;Dressler1984; gratedspectraatintermediatespectralresolution,which Couch & Sharples 1987). Subsequently, Jansen et al. makesourobservationswell-matchedtotraditionallong- (2001) and Kewley et al. (2004) used the Nearby Field slitspectroscopyof distantgalaxies. We supplement our Galaxy Survey (NFGS; Jansen et al. 2000a,b), an imag- newobservationswiththe NFGSto increasethenumber ing and spectrophotometric survey of a representative ofnormalgalaxies,andtoidentifyanyselectionbiasesin sample of ∼ 200 nearby galaxies, to quantify how vari- our diverse sample of galaxies. In addition, we compare ations in reddening and chemical abundance affect the our analysis of optical SFR diagnostics againsta sample observed [O ii] luminosity, and to improve the [O ii] of ∼120,000star-forminggalaxies fromthe SDSS in or- SFR calibration. Jansen et al. (2001) showed that the der to assessthe effects of statisticalincompleteness and observed [O ii]/Hα ratio varies by a factor of ∼ 7 near aperturebias inourintegratedgalaxysampleandin the M∗, predominantly due to variations in dust redden- SDSS, respectively. B ing, and that the [O ii]/Hα ratio is inversely propor- Weusethesedatatostudythe[Oii]λ3727,Hβ λ4861, tional to galaxy luminosity (see also Carter et al. 2001; and [O iii] λ5007 nebular emission lines as quantitative Aragon-Salamancaet al. 2002). Comparing the NFGS SFR diagnostics by comparing them against SFRs de- observations to photoionization models, Kewley et al. rived from the extinction-corrected Hα luminosity. We (2004)concludedthatthe[O ii]/Hαratioisalsostrongly also investigate the U-band luminosity as a SFR indica- dependent on the heavy element abundance and varies tor in an effort to determine whether far-optical broad- weakly with the strength of the ionizing radiation field. band photometry offers comparable precision to empir- However,allthesestudieshavebeenbasedonrelatively ically calibrated emission-line diagnostics for deriving small samples of optically selected normal galaxies ex- SFRsofdistantgalaxies. In§2wepresentourintegrated hibiting modest current-to-past-averagedstar-formation and SDSS samples. In §3 we explore empirical correla- rates, normal morphologies, and typical or lower-than- tions between optical SFR diagnostics and global prop- average infrared luminosities. From models of hierarchi- erties such as luminosity, dust extinction, and chemical cal galaxy formation (e.g., Somerville & Primack 1999), abundance in order to understand the dominant sources weanticipateahigherincidenceofextremeorburstystar of uncertainty that limit the application of these diag- formation at high redshift due to a greater frequency of nostics. In §4 we derive new empirical SFR calibra- mergers/interactionsand larger reservoirsof neutral gas tions. Finally, §5 we discuss the applicability of our (e.g., Hammer et al. 2005). Therefore, SFR calibrations new calibrations to intermediate-redshift galaxy sam- basedonlocalsamplesofnormalgalaxiesmaynotapply ples, and present our conclusions in §6. To compute at high redshift. distances and absolute magnitudes (always on the Vega Large spectrophotometric surveys of the nearby uni- system) we adopt Ω +Ω = 1, Ω = 0.3, and H = 0 Λ 0 0 verse such as the Sloan Digital Sky Survey (SDSS; 70 km s−1 Mpc−1 (Spergel et al. 2003; Freedman et al. York et al. 2000) provide the opportunity to study 2001). Following convention, we give both emission- the emission-line properties of galaxies with unprece- and absorption-line equivalent widths as positive num- dentedstatisticalprecision(e.g.,Brinchmann et al.2004; bers in the rest frame-of-reference. Finally, we adopt Tremonti et al. 2004). Hopkins et al. (2003) present a 12+ log(O/H)⊙ = 8.7 dex as the solar oxygen abun- thorough analysis of multi-wavelength SFR diagnostics dance (Allende Prieto et al. 2001; Holweger 2001). intheSDSS.However,thefractionoflightsubtendedby the3′′ fiber-opticapertureutilizedbythe SDSSdepends 2. THEDATA on the distance and intrinsic properties (size, bulge-to- 2.1. The Integrated Galaxy Sample disk ratio, surface-brightness distribution, etc.) of each individual galaxy. For example, in the star-forming Our integrated galaxy sample consists of our own galaxysample studied byTremonti et al.(2004) the me- spectroscopic observations (MK05) and the NFGS dian light fraction is only ∼ 25%. Furthermore, the (Jansen et al. 2000a,b). We briefly summarize the rel- SDSS’sstrictmagnitude-limitedselection(r <17.7mag) evant details of each survey, and refer the reader to the targets primarily the most luminous present-day galax- original papers for more information regarding the sam- ies, which are unlikely to be representative of high- pleselectionanddatareductions. TheMK05surveypro- redshift star-forming galaxies. Therefore, empirical SFR vides high S/N optical (3600−6900 ˚A) spectrophotom- calibrations based on SDSS observations should not be etry at ∼ 8 ˚A FWHM resolution for 417 nearby galax- applied blindly to distant samples. ies. Based on a variety of internal and external com- As part of a larger effort to characterize the physi- parisonsMK05findthatthe relativespectrophotometric calproperties ofstar-forminggalaxies,we haveobtained precision of the data is ∼ 4%. The survey roughly di- vides into four major subsamples: (1) ∼ 125 galaxies Optical SFR Indicators 3 selected from the First Byurakan Survey of UV-excess grams to differentiate galaxies with nebular emis- galaxies (Markarian et al. 1989); (2) ∼ 100 infrared- sion powered by star formation versus galaxies with luminous galaxies selected from the IRAS Warm and an admixture of star formation and AGN activ- Bright Galaxy Surveys (Kim et al. 1995; Veilleux et al. ity (Baldwin et al. 1981; Veilleux & Osterbrock 1987; 1995, 1999); (3) ∼ 35 morphologically selected inter- Ho et al. 1997; Kewley et al. 2001a). In Figure 2 acting/merging systems drawn from the Ph. D. thesis we plot the observed [O iii]/Hβ line-ratio as a func- sample of Turner (1998); and (4) ∼ 130 normal galax- tion of [N ii]/Hα for the MK05 data (squares) and ies selected from a volume-limited Hα- and UV-imaging the NFGS (triangles). For comparison with the in- survey of the 11 Mpc local volume (R. C. Kennicutt tegrated line-ratios, we overplot the emission-line se- et al., 2006, in preparation), and the Ursa Major clus- quencetracedbyindividualHiiregions(smallpoints)in ter (Tully et al. 1996). These samples are intentionally spiral galaxies (McCall et al. 1985; Zaritsky et al. 1994; chosen to span the diverse range of galaxies in the lo- van Zee et al. 1998) and dwarf galaxies (Izotov et al. cal universe with active star formation, both to improve 1994, 1997; Izotov & Thuan 1998). The solid curve ourunderstandingofgalacticstarformationandtoserve in Figure 2 empirically segregates normal star-forming as a more comprehensive reference sample for lookback galaxies from AGN based on an analysis of ∼ 105 studies. To provide a more representative, complemen- SDSSgalaxiesbyKauffmann et al.(2003a). Thedashed tary sample of nearby galaxies we turn to the NFGS. curve defines the theoretical boundary between AGN The NFGS is a photometric and spectroscopic survey and star-forming galaxies presented by Kewley et al. of 196 galaxies selected to reproduce the B-band lumi- (2001b). We conservatively adopt the Kauffmann et al. nosity function (Jansen et al. 2000a). The wavelength (2003a) curve to remove objects with AGN activ- coverage (3600 − 7100 ˚A), spectral resolution (∼ 6 ˚A ity, although in §4 we explore the effect of includ- FWHM), relative spectrophotometric precision (∼ 6%), ing AGN on our results. Finally, we classify ob- and S/N of the NFGS are well-matched to our own objects without 1σ [O iii] λ5007 or [N ii] λ6584 detec- servations. Excluding several broad-line AGN and one tions as star-forming galaxies using either the condition BL Lac, the combined integratedgalaxysample consists log([N ii]/Hα) < −0.4 (Tremonti et al. 2004), or using of spectrophotometry for 589 galaxies. the [S ii] λλ6716,6731/Hα and [O i] λ6300/Hα versus To measure fluxes and equivalent widths of the nebu- [O iii] λ5007/Hβ diagnostic diagrams and the theoreti- laremissionlinesweutilizeispec1d,aspectralsynthesis cal boundaries defined by Kewley et al. (2001b). After fitting code describedin detail inMK05. Using ispec1d rejecting another 9 objects that cannot be classified us- we find the non-negative linear combination of popula- inganyoftheabovemethods,ourfinalintegratedsample tionsynthesismodels(Bruzual & Charlot2003)thatop- consists of 412 star-forming galaxies. timally reproducesthe observedstellar continuum. Sub- Figure 2 shows that the sequences formed by H ii tracting the model continuum from the data results in a regions and star-forming galaxies overlap across the full purenebularemission-linespectrumself-consistentlycor- range of emission-line ratios in the [N ii]/Hα versus rectedforunderlyingstellarabsorption. Wemeasurethe [O iii]/Hβ plane (Kennicutt 1992b; Lehnert & Heckman emission-line fluxes and equivalent widths of the strong 1994; Kobulnicky et al. 1999; Charlot & Longhetti nebular lines, tabulated in MK05, using simultaneous, 2001). Therefore, to first order, techniques devel- multi-Gaussian profile fitting with physically motivated oped to analyze the physical properties of individual constraints onthe intrinsic velocity widths and redshifts H ii regions may be used to interpret the integrated of the Balmer and forbidden lines. For consistency we spectral properties of galaxies (e.g., Kobulnicky et al. re-measure the emission-line fluxes in the NFGS spectra 1999; Stasin´ska & Sodré 2001; Pilyugin et al. 2004a; using ispec1d. We find our measurements broadly con- Moustakas & Kennicutt 2005b). sistent with Jansen et al. (2000b), except at low equiv- In Figure 3 we compare the spectrophotometric alent widths where we argue that our technique is more properties of the MK05 and NFGS samples. We reliable. plot the distributions of the combined sample as To define a sample of star-forming galaxies and to en- dashed, unshaded histograms. We collect B-band sure that we canmeasure reliably the nebular reddening photometry for both samples, listed in order of (§3.1), we impose a 3σ S/Ncut onthe Hα and Hβ emis- preference, from de Vaucouleurs et al. (1991), LEDA3 sion lines, which removes 28 objects from the integrated (Prugniel & Heraudeau 1998), or by synthesizing pho- sample. We verify that most of these objects are early- tometry directly from the spectra, as described in type(E/S0)galaxieswitheffectivelyzerostarformation. MK05. These magnitudes have been corrected for fore- However, three galaxies (NGC 1266, UGC 05101, and ground Galactic extinction (RV = 3.1; O’Donnell 1994; CGCG 049-057) fail our S/N criterion on Hβ because Schlegel et al.1998),butnotfornebularemissionlinesor they are dusty, infrared-luminous galaxies. All three ob- inclination effects since these correctionsare challenging jects havewell-detectedHα emission,andinonlyonedo orimpossible tomakeathighredshift. Distancesfor the wemarginallydetect[Oii]. Sincethesegalaxiescomprise MK05 sample are based on either primary or secondary < 1% of the full integrated sample, and just 4% of ob- measurementswhenavailable,ortheMould et al.(2000) jects with L(IR)>1011 L⊙ (§3.2), we do not expect our multi-attractor linear infall model. Distances for the conclusions to be biased with respect to highly obscured NFGS sample are based exclusively on the infall model. galaxies. However, these types of objects emphasize the We assign a fixed 15% uncertainty to objects without a need for either Hα or infrared observations to ensure a published distance error. complete census of star formation in galaxies. In Figure 3a we plot the B-band luminosity distribu- We use traditional emission-line diagnostic dia- 3 http://leda.univ-lyon1.fr 4 Moustakas, Kennicutt, & Tremonti tions for the MK05 and NFGS samples, using M⊙,B = ture bias, while preserving the approximate magnitude- +5.42 mag to convert between L(B)/L(B)⊙ and MB. limited nature of the sample (see also Tremonti et al. Despite the significantly different selection criteria, we 2004). The 10% cut on light fraction removes less than findtheluminositydistributionsofthetwosamplesqual- 4% of the sample, whereas a cut at 30% removes over itatively similar. The MK05 survey includes a larger half of the sample and introduces biases which are dif- number of faint dwarf galaxies (M & −16 mag) and ficult to quantify. The above requirements result in a B galaxies more luminous than M ≃ −20 mag relative parent sample of 360,902 SDSS galaxies. B to the NFGS. The combined distribution, however, is Emission-line fluxes and equivalent widths for these fairly uniform between M ≃ −16 and −22 mag, and galaxies have been measured4 using a customized con- B spans the range between ∼−12 mag and ∼ −22.5 mag. tinuum fitting code based on the Bruzual & Charlot In Figure 3b we plot the distribution of dust extinction (2003) populations synthesis models and described by at Hα, A(Hα) = 2.52E(B−V), as determined from the Tremonti et al. (2004) (§2.1). We have compared the Balmerdecrement(§3.1). Themedian(mean)extinction results of this code and ispec1d and we find excellent for the combined sample is 0.51 mag (0.59±0.50 mag), agreement among the resulting emission-line flux and ranging from zero to 2.62 mag in IC 0750, a highly equivalent width measurements. To define a sample of reddened Sab galaxy in the MK05 sample. Figure 3c star-forminggalaxieswe impose 3σ detections ofthe Hα characterizes the metallicity distribution of these sam- and Hβ emission lines, which eliminates ∼ 50% of the ples, using the methodology in §3.4.2 to estimate the parentsample(allearly-type),leaving173,540emission- gas-phase abundance. The median (mean) metallic- line galaxies. Finally, we remove objects contaminated ity is 8.54 dex (8.50±0.21 dex), and spans the range by AGN activity using the methodology described in 7.77 < 12+log(O/H) < 8.84 dex (0.12 . Z/Z⊙ . 1.4). §2.1,resultinginasampleof120,846star-forminggalax- The metallicity distribution of the MK05 sample ex- ies. The mean r-band light fraction for this sample is tends to lower values than the NFGS due to the inclu- 25±9%. sion of a larger number of low-luminosity galaxies. Fi- In Figure 4 we compare the distributions of spec- nally, in Figure 3d we plot the distribution of observed trophotometric properties for the SDSS and integrated [O iii] λ5007/[O ii] λ3727 flux ratios for both samples. galaxy samples. To facilitate a direct comparison we The [O iii]/[O ii] ratio characterizes the hardness of plot the distributions normalized to the total number the ionizing radiation field, or the ionization parameter of galaxies in each sample. For the SDSS we compute of the photoionized gas (Shields 1990; Kewley & Dopita M using the Petrosian g -band magnitude and B,Vega AB 2002). Inthe MK05samplethemedian(mean)logarith- (g−r) color, and the following relation (M. R. Blan- AB mic [O iii]/[O ii] ratio is −0.33 dex (−0.27±0.32 dex), ton et al. 2006,in preparation): but spans a factor of ∼ 65 in excitation, whereas the NFGS distribution peaks in a narrow range around B =g +0.3915(g−r) +0.087, (1) Vega AB AB −0.45±0.20 dex. Although in the local universe low- wheretheg-andr-bandmagnitudeshavebeencorrected massgalaxiesundergoingastrongburstofstarformation for foreground Galactic extinction (Schlegel et al. 1998) typicallyexhibitthehighest[Oiii]/[Oii]ratios,stronger and k-corrected5 to z = 0 (Blanton et al. 2003). The ionizing radiation fields may be much more common in standard deviation of the color term in equation (1) is high-redshift, massive galaxies(e.g., Pettini et al. 2001). 0.15 mag, which we add in quadrature to the measured Insummary,wefindthatbycombiningoursurveywith photometric uncertainties. the NFGS we achieve wide coverage of the physical pa- Figure 4a shows that the SDSS galaxies provide com- rameter space spanned by the z = 0 population of star- plete coverage of the bright end of the B-band luminos- forminggalaxies,fromnormalgalaxiesthatdominatethe ity distribution, centered on −20.1 mag. By compari- mass density, to dwarfs and optical/infrared starbursts son, the integrated sample spans a much broader range that likely dominate at high redshift (e.g., Flores et al. inabsolute magnitude, uniformly rangingfromthe most 1999; Hammer et al. 2005; Bell et al. 2005). In §5 we luminous objects in the SDSS to M ≃ −16 mag, in- show that the diversity of this sample allows us to con- B cluding a handful of M > −16 mag dwarf galaxies. struct SFR diagnostics that may be applied at high red- B Throughout our analysis we will attribute many of the shift. differences in physical properties between the integrated 2.2. The SDSS Sample and SDSS samples to the different luminosity distributions, although aperture bias in the SDSS observations To complement our sample of galaxieswith integrated are also important, as we discuss below. spectra we culled the SDSS fourth data release (DR4; Figure 4b compares the distributions of A(Hα) in Adelman-McCarthy 2005) to define a complete sample the SDSS and integrated galaxy samples. The median of nearby star-forming galaxies. We use DR4 galaxies (mean) extinction in the SDSS is 0.83 mag (0.85 ± in the SDSS Main Galaxy Sample (Strauss et al. 2002), 0.41 mag), whereas in the integrated sample A(Hα) which have Petrosian r magnitudes between 14.5 < r < peaks at zero and decreases almost monotonically to 17.77magandr-bandPetrosianhalf-lightsurfacebright- nesses µ ≤ 24.5 mag arcsec−2 (corrected for fore- A(Hα)≃2.6mag. We attributethe observeddifferences 50 in these distributions to two effects. First, in the lo- ground Galactic extinction; Schlegel et al. 1998). We caluniversethereexistsacorrelationbetweenluminosity only include galaxies having z > 0.033 to ensure that and dust extinction, whereby luminous galaxies contain [O ii] λλ3726,3729 lies within the spectral range of the SDSS spectrograph. In addition, we elect to remove 4 http://www.mpa-garching.mpg.de/SDSS galaxies where less than 10% of the r-band light falls 5 Using k-correct version 4.1.3, which is available at in the fiber in order to remove cases of extreme aper- http://cosmo.nyu.edu/blanton/kcorrect. Optical SFR Indicators 5 moredust,onaverage,thanlessluminousgalaxies(§4.1; To summarize, we find significant differences among Buat & Xu 1996; Wang & Heckman 1996; Tully et al. the SDSS and integrated samples, which is not surpris- 1998; Adelberger & Steidel 2000; Jansen et al. 2001; ing given the different selection criteria. Although the Stasin´ska et al.2004). Consequently,A(Hα)intheSDSS integrated sample contains < 1% the number of objects peaks at higher values both because the mean luminos- in the SDSS sample, it intentionally spans a broader ity of the SDSS sample is larger, and because the SDSS range of physical properties such as luminosity, metal- misses less-extincted, lower-luminosity galaxies. In ad- licity, dust extinction, and ionization. By comparison, dition, aperture bias in the SDSS may be important. If the strength of the SDSS sample is its statistical com- the centers of spiral galaxies have higher optical depths pleteness of the bright end of the luminosity function, to dust comparedto the optical depth averagedoverthe althoughaperture bias must be carefully treated. In the whole galaxy (e.g., Valentijn 1994; Jansen et al. 1994), following analysis of optical SFR diagnostics we discuss then the mean extinction in a fiber-optic survey of star- all these effects in detail. forming galaxies will be higher, on average, than the mean extinction of an integrated spectroscopic survey. 3. ANALYSIS Kewley et al. (2005), however, find that extinction does 3.1. Nebular Reddening not depend on enclosed light fraction based on a com- Toquantifythe amountofdustreddeningwecompute parison of integrated and nuclear spectra in the NFGS. the Balmer decrement, Hα/Hβ, where all the Balmer In Figure 4c we compare the metallicity distributions emission lines have been corrected for underlying stellar of the two samples, adopting the empirical abun- absorptionasdiscussedin§2. We define the colorexcess dance calibrations given in §3.4.2. Relative to the due to dust reddening, E(Hβ-Hα), using the relation integrated galaxy sample, the distribution of oxygen abundances in the SDSS peaks strongly at higher (Hα/Hβ) int abundance. The median metallicity in the SDSS is E(Hβ-Hα)≡−2.5 log , (2) (cid:20)(Hα/Hβ) (cid:21) 12 + log(O/H) ≃ 8.70 dex (Z/Z⊙ ≃ 1), compared obs to ∼ 8.54 dex (Z/Z⊙ ≃ 0.7) in the integrated sam- where (Hα/Hβ)obs is the observed decrement and ple. We attribute these differences to a combination (Hα/Hβ) is the intrinsic Balmer decrement. We as- int of two effects: the luminosity-metallicity correlation sume the case B recombination value (Hα/Hβ) = int and aperture effects. Locally, and at high redshift, 2.86, which is appropriate for an individual H ii re- luminous star-forming galaxies obey a luminosity- gion at a typical electron temperature and density metallicity correlation, whereby luminous galaxies are (Storey & Hummer1995). Toaccountforthesmallvari- more metal-rich than low-luminosity galaxies (J. Mous- ationin (Hα/Hβ) with electrontemperature we prop- int takas et al. 2006, in preparation; Skillman et al. 1989; agate a 5% systematic uncertainty in (Hα/Hβ) into int Zaritsky et al. 1994; Richer & McCall 1995; Garnett the total error in E(Hβ-Hα). To relate E(Hβ-Hα) to 2002; Melbourne & Salzer 2002; Tremonti et al. 2004; the broad-band color excess, E(B−V), we introduce an Kobulnicky et al. 2003; Kobulnicky & Kewley 2004). attenuationcurve,k(λ)≡ A(λ)/E(B−V),toobtainthe The median MB magnitude difference of the two expression samples is −1.33 mag. Adopting the slope of the B-band luminosity-metallicity correlation found by E(Hβ-Hα) Tremonti et al. (2004), −0.185 dex mag−1, we predict E(B−V)≡ k(Hβ)−k(Hα), (3) a median metallicity difference of +0.25 dex. This value has the correct sign, and, given all the uncertain- wherek(Hβ)andk(Hα)arethevaluesofk(λ)at4861˚A ties, is roughly consistent with the measured median and 6563 ˚A, respectively (e.g., Calzetti 2001). metallicity difference of +0.16 dex. Aperture effects In order to de-redden our integrated emission-line may also drive the SDSS metallicities to higher values, fluxes we must assume a functional form for k(λ). The since the centers of spiral galaxies are typically more mostcommonpracticeis toneglectradiativetransferef- metal-rich than their outskirts (e.g., McCall et al. fects due to variations in geometry (which, in general,is 1985; Oey & Kennicutt 1993; Zaritsky et al. 1994; notagoodassumption:Witt et al.1992;Witt & Gordon Kennicutt & Garnett 1996; van Zee et al. 1998; 2000), and adopt a Milky Way or LMC/SMC extinc- Pilyugin et al. 2004b). Tremonti et al. (2004) esti- tion law. Alternatively, Charlot & Fall (2000) advocate mate that aperture bias in the SDSS may lead to an a power-law attenuation curve, k(λ) ∝ λ−0.7, based on overestimate of the globally averaged metallicity by at a multi-wavelength analysis of nearby starburst galaxies least +0.1 dex (see also Kewley et al. 2005). and simple radiation transfer arguments. Because opti- Finally, in Figure 4d we compare the distributions of cal extinction and attenuation curves are similar (un- theobserved[Oiii]λ5007/[Oii]λ3727ratiosintheSDSS like in the ultraviolet), we opt for the simplest solu- and integratedgalaxysamples. The median (mean) ion- tion and adopt the O’Donnell (1994) Milky Way ex- ization parameter of the SDSS galaxies is −0.54 dex tinction curve. Equation (3) then becomes E(B−V) = (−0.52±0.15 dex), lower on averageand more narrowly 0.874E(Hβ-Hα). peaked than the distribution of ratios in the integrated In§4 we alsoconsiderusing the Hβ/Hγ Balmer decre- galaxy sample. The observed differences are consistent ment to account for dust extinction, since Hγ λ4340 with the higher mean luminosity and metallicity of the is observationally accessible across the same range of SDSS galaxies(Dopita et al.2000; Kewley et al.2001a), redshifts as the emission-line SFR diagnostics consid- and with the inclusion of a larger number of extreme ered in this paper (Fig.1). However, obtaining a reli- starburstswith hardionizing radiationfields inthe inte- able measurement of Hγ is challenging because of its grated galaxy sample. intrinsic weakness and the combined effects of stellar 6 Moustakas, Kennicutt, & Tremonti absorption and dust extinction. In the following, we respectively. Equation (4) also assumes that no Lyman- adopt an intrinsic Hβ/Hγ ratio of 2.14 assuming an continuum photons are absorbed by dust, a point that electron temperature of 10,000 K; this ratio varies by we return to below. just ±3% across a broad range of nebular conditions In this paper we adopt the extinction-corrected Hα (Storey & Hummer 1995). Using the O’Donnell (1994) luminosity as our fiducial SFR tracer. However, it is Milky Way extinction curve, the analogous relations instructive to assess the absolute accuracy of Hα as a to equations (2) and (3) for the Hβ/Hγ ratio become SFRindicatorbycomparingitagainstotherindependent E(Hγ−Hβ) = −2.5 log(2.14/Hβ/Hγ) and E(B−V) = indicators. Several authors have carried out this exer- 2.05E(Hγ−Hβ), respectively. cise using the ultraviolet, infrared, and radio luminosity InFigure5wecomparethe reddeningsdeterminedus- (Buat & Xu 1996; Cram et al. 1998; Glazebrook et al. ingHα/HβandHβ/HγfortheMK05andNFGSsamples 1999; Bell & Kennicutt 2001; Sullivan et al. 2001; (squaresandtriangleswitherrorbars,respectively),and Hopkins et al.2001;Kewley et al.2002;Buat et al.2002; the SDSS (small points without error bars). The solid Hopkins et al. 2003; Hirashita et al. 2003; Bell 2003). lineistheline-of-equalityforthetwomeasurements. For Thesestudies revealthe numerouschallengesofderiving thiscomparisonweapplya7σS/NcutonHγ,andwere- absolute SFRs because each indicator is coupled to the quire that EW(Hβ)>10 ˚A in emission. We impose this true SFR by different physical processes, and they each minimum equivalentwidthbecause the Hγ emission-line sufferavarietyofsystematicuncertainties. Nevertheless, measurement is very sensitive to the quality of the con- wechoosetocompareψ(Hα)totheSFRderivedfromthe tinuum subtraction. For the SDSS galaxies we find no bolometricinfraredluminosity,L(IR)≡L(8−1000µm). median systematic offset and a dispersion of 0.15 mag. The infrared luminosity measures the amount of stellar The E(B−V) measurements based on Hβ/Hγ for the radiation absorbed and re-emitted by dust grains. As- MK05 and NFGS samples are displaced systematically suming solar metallicity, that the dust re-radiates 100% toward higher reddening by 0.08 and 0.15 mag, respec- ofthebolometricluminosity,andthatstarformationhas tively, and the residual scatter is significant: 0.22 and been continuous for the past 10−100 Myr, Kennicutt 0.38 mag, respectively. We attribute the larger discrep- (1998) provides the following transformation given the ancybetweenE(B−V)usingHβ/HγandE(B−V)using same IMF used in equation (4): Hα/Hβ in the integrated samples to their lower spectral preasroelduttioonth(e∼S8DSaSnd(∼∼46˚A˚A).FLWiaHngMe,traels.p(e2c0t0iv4ebl)y)d,isccoumss- ψ(IR)=4.5×10−44 eLrg(IsR−)1 M⊙ yr−1. (5) in detail the biases inherent to low spectral resolution Thecoefficientinequation(5)willbedifferentingalaxies spectroscopy. Thus, while Hβ/Hγ offers a direct mea- withsignificantdustheatingfromoldstellarpopulations, surement of the reddening in the absence of Hα, the er- orloweroveralldustcontent(Kennicutt1998;Bell2003; rors are formidable (& 50%), even in the best case sce- Hirashita et al. 2003). nario when detailed continuum subtraction can be used We estimate L(IR) for our integrated galaxy sample and the line S/N and equivalent width are moderately using the following procedure. Fluxes from IRAS at 12, high. Fortunately, at high redshift galaxiesare more gas 25,60and100µmforoursurveyhavebeentabulatedby richandline equivalent widths aregenerallylarger(e.g., MK05. Ranked in order of preference, these fluxes are Kobulnicky et al. 2003). Thus, using Hβ/Hγ as a red- from the large optical galaxy catalog (Rice et al. 1988), deningdiagnosticinhigher-redshiftsamplesmaybemore the IRAS Bright Galaxy Survey (Soifer et al. 1989), or reliable (e.g., Flores et al. 2004). the Faint Source Catalog (Moshir et al. 1990). IRAS 3.2. Hα λ6563 Star-Formation Rates fluxes for the NFGS have been gathered from the same references. If no detection is reported at 12 or 25 µm, The Hα λ6563 nebular emission line is one of the we use the empirical ratios (correct to ±30%) given primary diagnostics used to estimate the SFRs of in Bell (2003): S (12 µm)/S (100 µm) = 0.0326 and galaxies in the local universe (Kennicutt 1983, 1992b; ν ν S (25 µm)/S (60 µm) = 0.131. We confirm the va- Gallego et al. 1995; Kennicutt 1998; Nakamura et al. ν ν lidity of these ratios for the subset of our sample with 2004; Brinchmann et al. 2004). The largest uncertain- detections in all four IRAS bands. To extrapolate the ties affecting Hα-based SFRs are due to dust absorp- infraredspectralenergy distribution beyond 100 µm, we tion of Lyman-continuum photons within individual constructamodifiedblackbodywithdustemissivitypro- H ii regions, dust attenuation in the general interstellar portionaltoλ−1 (Gordon et al.2000;Bell2003). Wede- medium of the galaxy, and uncertainties in the shape of termine the temperature and normalization of the mod- the initial mass function (Kennicutt 1998). Throughout ified blackbody using the S (60 µm)/S (100 µm) flux this paper we adopt the theoretical calibration between ν ν ratio for each object. Finally, we integrate numerically the Hα luminosity, L(Hα), and the SFR, ψ, given by between 8−1000 µm to obtain L(IR). On average, our Kennicutt (1998): L(IR) estimatesareafactorof1.84±0.22(rangingfrom L(Hα) factors of 1.28−3.19) larger than the far-infrared lumi- ψ(Hα)=7.9×10−42 erg s−1 M⊙ yr−1, (4) nosity,L(FIR)≡L(40−120µm)(Helou et al.1988). We assume a systematic uncertainty of 15% in L(IR) (Bell where L(Hα) has been corrected for underlying stellar 2003),whichweaddinquadraturetothereportedIRAS absorption and interstellar dust attenuation (see also flux uncertainties. Kennicutt et al. 1994). This transformation has been To verify our technique for estimating L(IR), which computed for solar metallicity, the Salpeter (1955) IMF uses flux measurements in all four IRAS bands, with lower- and upper-mass cutoffs of 0.1 and 100 M⊙, we compare our results against the methods devel- Optical SFR Indicators 7 oped by Dale et al. (2001), Dale & Helou (2002), and face value, this agreement may seem surprising, given Sanders & Mirabel (1996). Dale et al. (2001) present a the simple assumptions built into equations (4) and (5). semi-empirical technique for estimating L(3−1100 µm) Forexample,ourHαSFRcalibrationassumesthatnone by arguing that the infrared spectral energy distribu- of the Lyman-continuum radiation from massive stars is tions of dusty galaxies can be parameterized in terms absorbed by dust. Including this effect, which may be a of a single parameter, the S (60 µm)/S (100 µm) ratio, significant correction (e.g., Inoue et al. 2001), would in- ν ν which characterizes the relative level of star formation crease the inferred SFR at a given Hα luminosity. How- activity in galaxies. Subsequently, Dale & Helou (2002) ever, the agreement between ψ(IR) and the extinction- use new submillimeter observations to show that their correctedψ(Hα)suggeststhatLyman-continuumextinc- original model over-predicts the amount of cold dust tion is not significant for our sample. We note, how- emission in quiescent galaxies, and they present an up- ever, four infrared-luminous galaxies in the MK05 sam- datedsemi-empiricalrelationforderivingL(3−1100µm) ple (CGCG239-011 W, IRAS 17208-0014, NGC 3628, based on IRAS fluxes at 25, 60, and 100 µm. Finally, and UGC 09618 N) which fall significantly below the Sanders & Mirabel (1996) present an empirical relation ψ(Hα) = ψ(IR) line in Figure 6b. Assuming ψ(IR) rep- forderivingL(8−1000µm)basedonallfourIRASbands. resents the actual SFR in these objects, the extinction- However,becausethisrelationisoptimizedforluminous- corrected ψ(Hα) would underestimate the SFR by up and ultra-luminous infrared galaxies, it tends to over- to an order-of-magnitude. In addition, ψ(IR) is suscep- predict L(IR) in galaxies with a larger amount of cold tible to several simplifying assumptions which we have dust (Dale et al. 2001). With these caveats in mind, we neglected in our comparison. The most important as- findthatourL(IR)valuesare19%,16%,and7%smaller, sumption may be that 100% of the bolometric luminos- respectively,thanthethreecalibrationsdescribedabove. ity associated with the current star formation episode is We attribute part of the difference with the Dale et al. absorbed by dust and re-emitted into the infrared. In (2001) and Dale & Helou (2002) estimates to the differ- fact, at low luminosity (M & −19 mag), we find that B entdefinitionsofL(IR). Forexample,asmuchas∼10% ψ(Hα)/ψ(IR) > 1 for our sample in a systematic sense. of the total infrared energy budget in quiescent systems Iftheextinction-correctedψ(Hα)reflectstheactualSFR is emitted at 3 −8 µm (Dale & Helou 2002, their Ta- in these objects, then ψ(IR) would under-estimate the ble 2). Because we adopt a systematic uncertainty of SFR by factors of 1.5−5. 15% in our estimate of L(IR), we conclude, therefore, Clearly,alltheseeffects warranta morein-depthanal- thatourresultsareconsistentwiththeseothermethods. ysis. However, our emphasis in this paper is to ex- In Figure 6 we plot the ψ(Hα)/ψ(IR) ratio against plore rest-frame optical emission-line diagnostics. Con- L(B) for our integrated sample, using the observed Hα sequently, in the remainder of this paper we adopt the luminosity in panel (a) and the extinction-corrected Hα Hα luminosity, suitably corrected for stellar absorption luminosity in panel (b). The solid line indicates equal- and extinction using the observed Balmer decrement, as ity of the two SFR measurements. Here and throughout our fiducial SFR tracer, and we assume equation (4) is much of our analysis we adopt the B-band luminosity the appropriatetransformationfrom luminosity to SFR. as our preferred independent variable. As we discuss in §4.1, the two dominant sources of scatter in optical 3.3. Hβ λ4861 Star-Formation Rates SFR diagnostics, dust extinction and metallicity, corre- Above z ∼ 0.4, Hα becomes inaccessible to ground- late strongly with L(B). Furthermore, L(B) serves as based optical spectrographs. In the search for reliable, an observationally convenient surrogate for stellar mass self-consistent SFR measurements at all redshifts, the that is available for both our local samples and most higher-order Balmer lines such as Hβ offer a promising high-redshift samples. In panel (b) we also plot the dis- alternative. The advantages and disadvantages of us- tributionof Sν(60 µm)/Sν(100µm) ratiosfor the MK05 ing Hβ to measure the SFR were originally discussed by and NFGS samples, illustrating the higher average level Kennicutt (1992b), who discouraged its use due to the of star formation activity in the MK05 sample. difficulty of accounting for underlying stellar absorption Tofirstorderwefindthatψ(Hα)basedontheobserved from moderate-resolution spectroscopy of galaxies with Hα luminosity is systematically offset from ψ(IR) by a EW(Hα+[N ii]).50 ˚A. However,population synthesis median(mean)amount−0.27dex(−0.26dex),andthat modeling of the stellar continuum ensures accurate re- the scatter in the ratio is 0.37 dex, or a factor of ∼ 2.3 movalof the absorptionunderlying the nebular emission (Fig. 6a). To second order, we observe a strong system- lines (§2; MK05; Tremonti et al. 2004). aticdependence onL(B)inthe sensethatψ(Hα)/ψ(IR) As a SFR diagnostic,Hβ, like all the Balmer lines, in- decreases by a factor of ∼ 100 over a factor of ∼ 3000 herits the same strengths and weaknesses of Hα: it is increase in L(B). In Figure 6b we show the effect of equallysensitiveto variationsin the IMFandto absorp- correcting Hα for extinction using the observed Balmer tion of Lyman-continuum photons by dust within star- decrement. Themedian(mean)systematicdifferencere- formingregions. Inaddition,Hβ suffersmoreinterstellar duces to 0.00 dex (0.02 dex), and the scatter decreases dustattenuationandisfractionallymoresensitivetoun- to0.22dex. Moreover,extinction-correctingHαremoves derlying stellar absorption. For example, assuming that much of the second-order trend seen in panel (a). Hα experiences one magnitude of extinction and that Consequently, we find that correcting Hα for extinc- stellar absorption is a 20% correction, the observed Hβ tion using a simple Milky Way extinction curve and the line will be 0.18times the strengthof Hα. Despite these observedBalmerdecrementgivesHαSFRsthatarecon- uncertainties,whenavailable,Hβ maybeasuperiorSFR sistent with ψ(IR) with a precisionof ±70%and no sys- diagnostic than the more commonly used [O ii] λ3727 tematic offset, even in many of the most dust-obscured nebular emission line (§3.4). galaxies in our sample (see also Kewley et al. 2002). At In Figure 7 we explore the systematic effects of stellar 8 Moustakas, Kennicutt, & Tremonti absorptionanddustreddeningonHβ asaprecisionSFR absorptioncorrectionfortheSDSSsampleis2.4±0.6˚A. indicator. This comparison includes all objects having The median (Hβ/Hα) ratios in Figures 8a and 8b are obs EW(Hβ) > 5 ˚A in emission. Below this limiting equiv- systematically lower by 0.07 dex than the correspond- alent width, Hβ measurements are very uncertain, even ing panels in Figure 7 due to the higher mean extinc- when using population synthesis to subtract the stellar tionandnear-absenceofanygalaxieslessluminous than continuum. For reference, in the MK05 and NFGS sam- M ≃ −18 mag in the SDSS sample (Fig. 4). Finally, B plesthemeanstellarabsorptionunderlyingtheHβ emis- Figure 8c shows the transformation between L(Hβ) obs sion line is 4.4±0.6 ˚A and 3.9±0.5 ˚A, respectively. andψ(Hα)asafunctionofL(B). Themedianconversion Figure7a plotstheobservedHβ/Hαratiowithoutcor- factor varies from −0.65 dex around ∼ 3×109 L(B)⊙, rections for dust reddening or stellar absorption at Hβ. to −0.95 dex near ∼ 1011 L(B)⊙, while the dispersion Thedashed lineinpanels(a)and(b)indicatestheintrin- at fixed luminosity is fairly constant at ∼ 0.23 dex, or sic Balmer decrement, log(Hβ/Hα) = −0.46 dex (see ±70%. int §3.1). By definition, galaxies whose Hα and Hβ fluxes In conclusion, we find that both variations in dust have been corrected for reddening using the Hα/Hβ ra- reddening and stellar absorption limit the precision of tio would lie along this line, and Hβ would mirror Hα L(Hβ) as a quantitative SFR indicator. Correcting obs as a star formation tracer. We find that the observed Hβ for underlying stellar absorption either statistically Hβ/Hα ratio varies systematically with L(B) due to or using population synthesis modeling reduces the un- the combined effects of stellar absorption and redden- certainty in ψ(Hβ) substantially and should not be ne- ing, and that the median (mean) ratio is −0.84 dex glected. Finally, we find that dust reddening introduces (−0.86±0.22dex). InFigure7b weshowtheeffectofcor- an average error of 0.1−0.25 dex in ψ(Hβ), depending recting Hβ for underlying stellar absorption. The data on the luminosity distribution of the sample. In §4.2 we shifttowardtheintrinsicratioinaluminosity-dependent attempt to improve the statistical precision of L(Hβ) obs waybecause,locally,luminous/massivegalaxieshave,on as a SFR indicator by parameterizing L(Hβ) /ψ(Hα) obs average, lower emission-line equivalent widths. The de- in terms of L(B). pendence onL(B) becomesless pronounced,the median (mean)ratioincreasesto−0.53dex(−0.54dex),andthe 3.4. [O ii] λ3727 Star-Formation Rates scatterreducestojust0.07dex. Theresidualdependence As we discuss in §1, the [O ii] λ3727 nebular of (Hβ/Hα) on L(B) reflects the luminosity-dust cor- emission line is frequently used as a qualitative and obs relation, which we discuss in more detail in §4.1. The quantitative tracer of star formation in galaxies (e.g., low scatter in this figure is due to the Hα/Hβ ratio’s Songaila et al. 1994; Hammer et al. 1997; Hogg et al. sensitivity to variations in reddening. 1998; Hippelein et al. 2003; Teplitz et al. 2003). SFRs Finally, in Figure 7c we plot the ratio of the ob- basedon[Oii],however,aresubjecttoconsiderablesys- served Hβ luminosity, L(Hβ) , corrected for stellar tematicuncertaintiesduetovariationsindustreddening, obs absorption, to ψ(Hα), versus L(B). Below L(B) . chemical abundance, and ionization among star-forming 3×109 L(B)⊙, the median ratio is nearly constant at galaxies. In this section we explore these systematic ef- ∼−0.4dex,andthescatterrangesfrom0.06to0.13dex, fects using empirical correlations in order to understand or 15 − 35%. Toward higher luminosity, the median the limitations of [O ii] as a SFR indicator. ratio decreases progressively (reaching a minimum of ∼ −0.9 dex), while the scatter increases systematically 3.4.1. Variations in Dust Reddening from0.13dexnear∼3×109 L(B)⊙,to0.20dex(±60%) We begin our analysis by studying the effects of dust at ∼1011 L(B)⊙. In §4.2 we parameterize the observed reddening on the [O ii]/Hα flux ratio. In Figure 9 we non-linear dependence of L(Hβ)obs/ψ(Hα) on L(B) and plot [O ii]/Hα versus L(B) for the integrated spectro- discuss it in more detail. Finally, we note that if we do scopic sample. Figure 9a shows the observed [O ii]/Hα not correct Hβ for stellar absorption in Figure 7c, the ratio,([O ii]/Hα) ,uncorrectedfordustreddening. As obs trend with luminosity steepens (since the correction is shown by Jansen et al. (2001), the observed ratio varies more important for luminous galaxies), the median Hβ systematically with luminosity in the sense that more SFR conversion factor is ∼ 70% lower, and the scatter luminous galaxies have, on average, lower [O ii]/Hα ra- increases to 0.36 dex, or ±130%. We find that even ap- tios. We find a median (mean) logarithmic ratio of plying a simple statistical correction of 4±1 ˚A reduces −0.17 dex (−0.21±0.22 dex), corresponding to a linear the scatter in L(Hβ)obs/ψ(Hα) to ∼ 0.24 dex, although ratio ([O ii]/Hα)obs ≃ 0.68 and a scatter of ±65%. For the systematic trend with blue luminosity remains. comparison, Kennicutt (1992b) obtains a median line- The SDSS sample provides the opportunity to investi- ratio of 0.45±0.26 based on a smaller sample of nor- gate the same empirical correlations explored above us- mal luminous galaxies. Figure 9b shows the reddening- ing more than two orders-of-magnitude more galaxies. corrected [O ii]/Hα ratio, ([O ii]/Hα) , versus L(B). cor In Figure 8 we plot the Hβ/Hα ratio as a function of Correcting both [O ii] and Hα for dust reddening re- L(B) for the SDSS. In order to accomodate the large moves almost all the luminosity dependence seen in number of data points, each panel displays the loga- panel(a), increasesthe median (mean) ratioto 0.00dex rithm of the number of galaxies in a 100×100 square (−0.01 dex), and reduces the scatter to 0.12 dex. Con- grid. The trends exhibited by the SDSS galaxies are sequently, we find that even with an optimal reddening verysimilartothoseobservedinFigure7using theinte- correction (i.e., using Hα/Hβ), the scatter in [O ii]/Hα grated sample. Once again, we find that correcting Hβ is ∼ 32%, which, in the absence of any other correc- for stellar absorption reduces both the luminosity de- tions, places a lower limit on the uncertainty in [O ii] pendence and the scatter in the observed Hα/Hβ ratio SFRs. However, if Hα were available to make this dust (compare Figs. 8a and 8b). For reference, the mean Hβ correction then Hα should be used in place of [O ii] to Optical SFR Indicators 9 derive the SFR. A Spearman rank correlation test on compared to a factor of ∼ 3.5 in the integrated sample. the data in Figure 9b yields a correlation coefficient of In §3.4.2 we show that these differences arise because −0.18; the probability of obtaining this coefficient by the reddening-corrected [O ii]/Hα ratio correlates with chance is < 1%. In §3.4.2 we show that metallicity, oxygen abundance, which affects the SDSS sample to a which also correlates with luminosity (see §4.1), drives greater extent. this residual correlation. Finally, in Figure 9c we plot Beforeinvestigatingthemetallicitysensitivityof[Oii], the L([O ii]) /ψ(Hα) ratio versus L(B). We find that we turn our attention to an interesting set of outliers in obs the median [O ii] SFR transformation varies systemat- Figure 11 (left). In the integrated sample we find galax- ically with blue luminosity, from 0.02−0.05 dex below ies with widely varying [O ii]/Hα ratios, −0.8 dex . 3×109 L(B)⊙, to −0.67 dex near ∼ 1011 L(B)⊙. This log([O ii]/Hα)obs .0.1 dex, but verylittle dust redden- luminosity dependence is driven by the combined effects ing, E(Hβ-Hα) . 0.2 mag. These objects are the low- of reddening and metallicity, which we discuss in detail luminosity,low-metallicitygalaxiesinour sample,which below, and parameterize in §4.3. In the absence of any exhibit low [O ii]/Hα ratios because they are deficient otherinformation,however,SFRs basedonthe observed in heavy elements such as oxygen. Although obtaining [O ii] luminosity are susceptible to a ∼ 0.39 dex uncer- high-quality spectroscopy of the high-redshift counter- tainty, or a factor of ∼2.5. partstotheselow-luminosityobjectsisverydifficult(see, Figure 10 plots the correlationbetween [O ii]/Hα and e.g., §5), their existence indicates that any [O ii]-based L(B)fortheSDSSsample. Themeanandmedianratios SFR calibration must be applied carefully to chemically of the SDSS galaxies are systematically lower than the unevolvedobjects,whichmaybe muchmorecommonat corresponding ratios for the integrated sample (Fig. 9). high redshift (e.g., Maier et al. 2005). We do not iden- These differences are partly due to the narrower optical tify a corresponding branch of extremely low-metallicity luminosity distribution in the SDSS sample (Fig. 4a): galaxiesintheSDSSsample,whichisconsistentwithits the low-luminosity galaxies in the integrated sample act luminositydistributionandthe study byTremonti et al. to elevate the median ratio. However, even at fixed (2004). luminosity the distribution of [O ii]/Hα in the SDSS is shifted to lower values. For example, the median 3.4.2. Variations in Oxygen Abundance (mean)([O ii]/Hα)cor ratioaround(2−5)×1010L(B)⊙ In the preceding analysis we have shown that the ob- is −0.22dex (−0.22±0.15 dex), comparedto −0.04dex served [O ii]/Hα ratio correlates very tightly with red- (−0.06 ± 0.12 dex) in the integrated sample. Finally, deningintheintegratedsampleandlesswellintheSDSS comparing Figures 9b and 10b, we find that the red- sample. To investigate this difference and the origin of dening correction applied to the SDSS galaxies is much the residual scatter, we study how variations in metal- less effective at removing the luminosity dependence of licity affect the [O ii]/Hα ratio. One widely used abun- the [O ii]/Hα ratio than for the galaxies with integrated danceindicatoristheR parameter(Pagel et al.1978), spectroscopy. We explore this point next. 23 given by In Figure 11 we show the observed [O ii]/Hα flux ratio as a function of E(Hβ-Hα) for the integrated sam- [O ii] λ3727+[O iii] λλ4959,5007 ple and the SDSS. Confirming Jansen et al. (2001), we R ≡ , (6) 23 Hβ λ4861 findthat([O ii]/Hα) correlatestightlywithreddening obs (see also Aragon-Salamancaet al. 2002; Kewley et al. where eachemission line must be correctedfor dust red- 2004). In the integrated sample ([O ii]/Hα) de- obs dening (but see Kobulnicky & Phillips 2003). Observa- creases by an order-of-magnitude over a factor of ∼ 2.5 tionsof Hiiregionsandphotoionizationmodelingreveal change in E(Hβ-Hα). Following Jansen et al. (2001), thatR dependsontheoxygenabundance,althoughthe 23 we overplot the predicted reddening at [O ii] and Hα relationship is not monotonic (Edmunds & Pagel 1984; forthe O’Donnell(1994)Galacticextinctioncurve(solid Skillman 1989; McGaugh 1991; Kobulnicky et al. 1999; line), and the Charlot & Fall (2000) attenuation curve Pilyugin 2000, 2001; Kewley & Dopita 2002). In addi- (dashed line). Other reddening curves in this wave- tion, R depends on the ionization parameter, partic- 23 length regime (e.g., for the Small Magellanic Cloud; ularly at low metallicity (e.g., Kobulnicky et al. 1999), Gordon et al. 2003) are very similar to the two curves and possibly even at high metallicity (Pilyugin 2001). plotted. We define the intercept of these curves to be Recent observations have also shown that the theoret- log([O ii]/Hα) = 0.0 dex for the integrated sam- obs ical calibration of R is discrepant by 0.2 − 0.5 dex 23 ple, corresponding approximately to the intrinsic (de- relative to electron-temperature abundance measure- reddened) flux ratio of the data (see Fig. 9b). The slope ments, and may require revision to lower abundances of the relation between ([O ii]/Hα) and E(Hβ-Hα) obs (J.Moustakasetal.,2006,inpreparation;Pilyugin2001; is remarkably consistent with the expected reduction in Kennicutt et al.2003;Garnett et al.2004;Bresolin et al. flux between 3727 ˚A and 6563 ˚A due to a simple fore- 2004). Unfortunately, we cannot use R to probe the 23 ground extinction curve. The SDSS galaxies, by com- metallicitysensitivityof[Oii]becauseitdependsexplic- parison, exhibit a more complex relationship between itly on the [O ii] intensity. To emphasize this point, we reddening andobserved[O ii]/Hα] ratio (Fig.11, right). adopt Hα/Hβ = 2.86 as the de-reddened Balmer decre- The solid and dashed lines show the same two extinc- ment and rewrite equation (6) as tion curves described above, this time normalized to log([O ii]/Hα) =−0.16dex(seeFig.10c). TheSDSS obs sample exhibits a much larger range in [O ii]/Hα ratio log [O ii] λ3727 =log(R )− atfixedreddening. Within E(Hβ-Hα)=0.4±0.05mag, (cid:16) Hα (cid:17) 23 (7) the total range in ([O ii]/Hα) spans a factor of ∼11, log 1+ [O iii] λλ4959,5007 −log(2.86). obs (cid:16) [O ii] λ3727 (cid:17) 10 Moustakas, Kennicutt, & Tremonti This equation shows that log([O ii]/Hα) and log(R ) regime we find ∼ 75% of the integrated spectroscopic 23 are linearly proportional with a slope of unity and an sample and ∼ 50% of the SDSS galaxies. The weak intercept that depends weakly on the [O iii]/[O ii] ra- metallicity dependence and small scatter (±15−35%) tio. Due to this covariance,therefore,we arguethat R of the reddening-corrected [O ii]/Hα ratio in the metal- 23 should not be used to quantify the [O ii] metallicity de- licityinterval12+log(O/H)=8.15−8.7dexconstitutes pendence. one of the principal results of this paper. Finally, above Fortunately, there are several other strong-line 12 + log(O/H) = 8.7 dex we find that ([O ii]/Hα) cor abundance diagnostics that do not rely on the decreases by a factor of ∼ 1.6 in the integrated sam- [O ii] emission-line flux. One such indicator is ple and by more than a factor of ∼ 3 in the SDSS over the ([O iii]/Hβ)/([N ii]/Hα) ratio (Alloin et al. 1979; a very short interval in metallicity, ∼ 0.2 dex. In this Pagel et al. 1979; Dutil & Roy 1999; Pettini & Pagel regimethe median(mean)ratiooftheintegratedsample 2004). A recent empirical calibration between is−0.13dex(−0.12±0.11dex)comparedwith−0.24dex ([O iii]/Hβ)/([N ii]/Hα) and the oxygen abundance is (−0.24±0.13 dex) in the SDSS. We conclude, therefore, given by Pettini & Pagel (2004): thatcorrecting[O ii]/HαforextinctionintheSDSSsam- ple (Fig. 10b) marginally decreases the scatter because of the steep metallicity dependence of ([O ii]/Hα) for [O iii] λ5007/Hβ λ4861 cor 12+log(O/H)=8.73−0.32 log . 12+log(O/H)>8.7 dex. (cid:18)[N ii] λ6584/Hα λ6563(cid:19) To better understand Figure 12 we turn to photoion- (8) ization models. Recently, Kewley et al. (2001a) have Equation (8) is only appropriate in the range −1.0 . studied the variation of optical emission-line ratios as log{([O iii]/Hβ)/([N ii]/Hα)}.1.9 dex, or 8.12.12+ a function of metallicity, ionization parameter, ioniz- log(O/H)<9.05dex. Below 12+log(O/H)≃8.12 dex, ing spectral energy distribution, and star-formation his- therefore,weadoptanempiricalcalibrationbasedonthe tory using a large grid of photoionization model cal- [N ii] λ6584/Hα ratio (Pettini & Pagel2004): culations. We use these models to plot in Figure 12 the theoretical [O ii]/Hα ratio as a function of oxygen abundance for six values of the ionization parameter, 12+log(O/H)=8.9+0.59log([N ii] λ6584/Hα). (9) U ∝ (n f2Q)1/3, where n is the electron density, f is e e Note that equation (9) should not be applied at high the filling fraction, and Q is the rate of photoionizing metallicity because [N ii]/Hα converges to an approxi- photons injected into the gas by massive stars. These mately constant value in star-forming galaxies (see, e.g., theoreticalcurveshavebeencomputedusing inputspec- Fig. 2). Due to their small wavelength separation, both tral energy distributions for evolved star-clusters from ([Oiii]/Hβ)/([Nii]/Hα)and[Nii]/Hαareinsensitiveto STARBURST 99 (Leitherer et al. 1999), which are them- dust reddening, and therefore equations (8) and (9) can selves based on the metallicity-dependent stellar atmo- be applied to the observed emission-line fluxes. spheresfromLejeune et al.(1997) andthe Geneva6 stel- InFigure12weplotthereddening-corrected[O ii]/Hα lar evolutionary tracks. For this comparison we have ratio as a function of oxygen abundance for the inte- adopted the 8 Myr continuous star-formation history grated sample, H ii regions, and the SDSS sample. The modelsfromKewley et al.(2001a)basedontheSalpeter H ii region comparison is valuable because H ii regions (1955) IMF, evaluated between 0.1 and 120 M⊙. span a broader range of [O ii]/Hα flux ratios and abun- We find very good correspondence between the ob- dances relative to both our galaxy samples. Not unex- served and the theoretical metallicity dependence of pectedly,wefindthat([O ii]/Hα) varieswithmetallic- [O ii]/Hα. In the metal-poor regime, the models show cor ity. Heavy elements, particularly oxygen, are an impor- that both a reduction in the heavy-element abundance tant source of radiative cooling in H ii regions because and a hardening of the ionizing radiation field, toward theyhavecollisionallyexcitedenergylevelsthatarewell- higher values of U, drive the rapid decline in [O ii]/Hα. populated at ∼10,000 K (Osterbrock 1989). Figure 12, The plateau in the intermediate-metallicity regime, and therefore, reflects the behavior of oxygen cooling with thesubsequentdeclinein[O ii]/Hαathighmetallicity,is metallicity. due to the increasing importance of nebular cooling via In order to characterize the dependence of [O ii]/Hα the infrared fine-structure lines and a consequent weak- on oxygen abundance we divide Figure 12 into a metal- ening of the [O ii] line-flux. Finally, according to the poorregime,12+log(O/H)<8.15dex,anintermediate- models,thescatterin[O ii]/Hαatfixedmetallicityarises metallicity regime,8.15<12+log(O/H)<8.7 dex,and from differences in ionization parameter. For example, a metal-rich regime, 12+log(O/H)>8.7 dex. In §3.4.1 around12+log(O/H)=8.4±0.1dexthetotalvariation we identified the most metal-poor galaxies in the inte- inionizationparameterintheintegratedsampleisafac- grated spectroscopic sample as outliers in the correla- tor of ∼10 (−3.8.log U .−2.9 dex), which results in tionbetween([O ii]/Hα) anddustreddening(Fig.11, the measured ∼ 15% scatter in the observed [O ii]/Hα obs left). In Figure 12 (left) we see that their ([O ii]/Hα) ratio at fixed metallicity. cor ratiosobeyanalmostlineardependenceonoxygenabun- dance, rising by a factor of ∼ 5 over a factor of ∼ 2.5 3.4.3. Summary of Physical Sources of Scatter in increase in metallicity. In the SDSS there are only 57 [O ii]/Hα galaxies in this part of the diagram, all with metallici- The empirical correlations shown in Figures 9-12 en- ties around ∼ 8.1 dex. In the intermediate-metallicity able us to evaluate the importance of dust extinction, regime([O ii]/Hα)cor plateaustoamedian(mean)value metallicity, and ionization on the L([O ii])obs/ψ ratio. of 0.04 dex (0.03±0.07 dex) in the integrated sample, and to 0.01 dex (0.00±0.11 dex) in the SDSS. In this 6http://obswww.unige.ch/~{}mowlavi/evol/stev_database.html