Comparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities
Jason E. Young, Caryl Gronwall, John J. Salzer, Jessica L. Rosenberg
aa r X i v : . [ a s t r o - ph . GA ] J u l Comparing Infrared Star-Formation Rate Indicators withOptically-Derived Quantities
J. E. Young , C. Gronwall , , J. J. Salzer , J. L. Rosenberg August 31, 2018
Abstract
We examine the UV reprocessing efficiencies of warm dust and polycyclic aromatic hydrocarbons(PAHs) through an analysis of the mid- and far-infrared surface luminosity densities of 85 nearby H α -selected star-forming galaxies detected by the volume-limited KPNO International Spectroscopic Survey(KISS). Because H α selection is not biased toward continuum-bright objects, the KISS sample spansa wide range in stellar masses (10 –10 M ⊙ ), as well as H α luminosity (10 –10 ergs / s), mid-infrared8.0 µ m luminosity (10 –10 ergs / s), and [Bw-R] color (-.1–2.2). We find that mid-infrared polycyclicaromatic hydrocarbon (PAH) emission in the Spitzer IRAC 8.0 µ m band correlates with star formation,and that the efficiency with which galaxies reprocess UV energy into PAH emission depends on metallicity.We also find that the relationship between far-infrared luminosity in the Spitzer MIPS 24 µ m bandpass and H α -measured star-formation rate varies from galaxy to galaxy within our sample; we do notobserve a metallicity dependence in this relationship. We use optical colors and established mass-to-lightrelationships to determine stellar masses for the KISS galaxies; we compare these masses to those ofnearby galaxies as a confirmation that the volume-limited nature of KISS avoids strong biases. We alsoexamine the relationship between IRAC 3.6 µ m luminosity and galaxy stellar mass, and find a color-dependent correlation between the two. Many lines of evidence now link mid- and far-infrared emission to star-forming activity. For example,observations of star-forming regions in nearby galaxies (e.g., ?? ) show that much of the ultraviolet emissionfrom young stars is absorbed by dust and then re-emitted in the mid- and far-infrared. In particular,because the 7.7 µ m polycyclic aromatic hydrocarbon (PAH) vibrational band falls within the Spitzer 8.0 µ mband pass, ultraviolet-excited IRAC 8.0 µ m PAH emission is believed to track star-formation rate (SFR)(e.g., ?? ). Moreover, ? , ? , and ? find that the luminosities of star-forming galaxies in the Spitzer 8.0 µ mband correlate with SFRs measured through other means.Likewise, thermal emission from warm dust is also tied to star-forming activity because the thermal energybudget of warm dust is dominated by heating from ultraviolet light. Specifically, many works (e.g., ????? )report that luminosity in the Spitzer 24 µ m band tracks SFR since this bandpass is dominated by the thermalspectrum of warm dust. Supporting this correlation, ? find that warm dust, as measured by Spitzer MIPS70 µ m observations, traces out star-forming regions in M81, as opposed to cold dust, observed in Herschel70-500 µ m data, whose thermal budget is dominated by evolved stars and is thus detected throughout M81.However, modern infrared observations indicate that neither 8.0 µ m nor 24 µ m emission is a straightfor-ward SFR indicator. Both of these indicators trace obscured star formation; although the majority of star Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802 Department of Astronomy, Indiana University, Bloomington, IN School of Physics, Astronomy, and Computational Science, George Mason University, Fairfax, VA ? and ? note that 8.0 µ m luminosity is sensitive to both star-formation history andmetallicity since PAH molecules contain carbon. Complicating matters further, the ultraviolet light thatcauses a relationship between PAH emission and SFR also destroys PAHs. ? and ? note that PAH emissionis strongest on the rims of H II regions, and speculate that the radiation environment in the centers ofstar-forming complexes is simply too harsh for PAH molecules to survive. Likewise, silicate dust, the mostprobable source of far-IR thermal emission, is also sensitive to metallicity, and even silicate dust can bedestroyed by sufficiently high temperatures. Additionally, very small grains are subject to stochastic heatingby UV photons, and may be out of equilibrium. Complicating matters further, at low star-formation ratesthe energy contribution from evolved stars can become a significant part of the thermal budget of even warmdust ( ? ). Finally, thermal dust emission alone is ambiguous because dust-enshrouded AGN can also heatinterstellar dust (e.g., ? ).In an effort to relate existing metrics of star-formation rate and characterize the infrared energy budgetsof star-forming galaxies, we present an analysis of mid-infrared (IRAC), far-infrared (MIPS), and opticalphotometry of 85 low-redshift H α -bright star-forming galaxies detected by the KPNO International Spec-troscopic Survey (KISS) (KISS; ? ), a quasi-volume-limited H α selected survey. Because H α selection is notbiased toward continuum-bright objects, the KISS sample effectively characterizes star-forming galaxies byspanning a wide range of properties, such as stellar masses (10 –10 M ⊙ ) and log(O / H) + 12 metallicities(7.8–9.2).While photometry in all four IRAC bands and the MIPS 24 µ m band is tabulated in Table 1, we focus onIRAC 3.6 µ m, IRAC 8.0 µ m, and MIPS 24 µ m because of their relevance to star formation studies. Luminosityin the IRAC 8.0 µ m band comes from a combination of sources (e.g., ? ). The primary contributors in theIRAC 8.0 µ m band are vibrational emission lines of PAHs and the thermal tail of the old stellar population.Luminosity in the MIPS 24 µ m band, on the other hand, samples only thermal dust (e.g., ? ). The IRAC3.6 µ m band is believed to sample primarily the thermal tail of the old stellar population. By studying thesefluxes in tandem, we distinguish these different sources of luminosity. The IRAC 4.5 µ m and 5.8 µ m bandsare less useful for this particular purpose because they contain weaker PAH bands and more contaminationfrom the stellar continuum than the 8.0 µ m band.While similar research has been conducted previously (e.g., ?????? ), KISS has the significant advantagethat it evenly samples galaxies across four orders of magnitude in luminosity with observations that spana factor of 60 in wavelength range. Moreover, unlike other studies sampling small regions within galaxies( ?? ), the objective-prism spectra ensure that KISS SFRs are global SFRs and can be directly compared tointegrated broadband SFR indicator candidates, such as IRAC 8.0 µ m and MIPS 24 µ m luminosities.In Section 2, we describe the observations, basic data processing, and photometry procedures. In Section3, we describe the analysis used to examine the connections and correlations between H α measured SFRs,infrared luminosities, and galaxian stellar masses. In Section 4, we discuss the implications of these relationsand compare our finding to those published in other works. For this work, we assume a ΛCDM cosmologywith H = 67 .
04 km s − Mpc − , Ω m = 0 . Λ = 0 . ? ). α -Selected Sample The KISS field used in this work is located in the NOAO Deep Wide Field Survey (NDWFS; ? ) in Bo¨otes( ? ). The KISS objects were selected from objective-prism spectra to have redshifts < α emission5 σ above their median spectral continua. Objective-prism spectra are preferable to slit spectra for estimatingtotal H α luminosity for extended objects because they capture all of the flux from the object rather thanthe small fraction that would fall on a slit. A redshift (volume) limit rather than a magnitude limit ensuresthat the sample is not biased toward galaxies that are intrinsically bright in the continuum.2n the KISS Bo¨otes field, 131 H α emission line objects were identified. The initial detections were followedup with higher resolution spectroscopy using the Hobby Eberly Telescope (HET), the KPNO 2.1 meter, theMDM 2.4 meter, and the Lick 3 meter telescopes ( ????? ). Using the higher resolution spectra, 28 AGNand LINER galaxies were rejected through an extinction-corrected [N II ] λ α versus [O III ] λ β line diagnostic diagram ( ? ). Even though AGN hosts may be sites of star-forming activity, we are unable todisentangle AGN H α emission from that of star-forming activity, making the SFR measurement from suchgalaxies unreliable. We concentrated on the 98 remaining objects for our study. Metal abundance estimateswere computed for all galaxies using emission-line ratios of strong lines by employing the coarse abundancemethod described in ? and ? ; typical uncertainties in log(O / H) + 12 are 0.12 dex.The H α luminosities referenced in this paper shall hereafter refer to H α luminosities that are mea-sured from objective-prism data and are extinction-corrected using Balmer decrements (c H β ) from follow-upspectra. This correction assumes a single screen model for dust extinction; in this assumption we incur anuncertainty because the Balmer decrement measurements from the follow-up spectra represent the extinctionaveraged over only the regions encompassed by the slit used in the follow-up spectra. Thus, this uncertaintyhas a systematic component in that, for objects of large angular size, where only a smaller fraction of theobject was encompassed in the slit, the correction applied is more likely to deviate from the true value.We incur another uncertainty from the assumption of a flat stellar continuum underneath the H α andH β emission lines. With high resolution spectra, it is sometimes possible to estimate the stellar absorptionand appropriately correct the emission lines; the follow-up KISS spectra are not of sufficient resolution. Theprimary effect is that the computed emission-line strengths are lower than the true values, affecting theBalmer decrements. This issue, and the ramifications of using the method we describe here, are thoroughlydiscussed by ? . They report that our method can underestimate star-formation rates; for the median stellarmass of our objects, this underestimation is 12%, and is much less, even zero, for low mass or low metallicityobjects.Normalizing to the angular sizes of the KISS galaxies in the IRAC 3.6 µ m channel (see below), we list theH α surface luminosity densities and SFR surface densities in Table 1. α Star-Formation Rates
To calibrate mid- and far-infrared broadband photometry as star-formation rate indicators, we use extinction-corrected H α luminosity as a benchmark indicator. Because the stars contributing with any significance tothe ionizing flux have short lifetimes ( <
20 Myr), extinction-corrected H α luminosity is an indicator ofcurrent star formation and is relatively independent of star-formation history. ? provides an H α luminosityto SFR calibration using solar abundances and a Salpeter IMF (0.1 - 100 M ⊙ ):SFR [M ⊙ / yr] = 5 . × − L H α [erg / s] (1)log (SFR [M ⊙ / yr]) = − .
685 + log (L H α [L ⊙ ]) (2) The Spitzer data used in this project came from the Spitzer Deep Wide-Field Survey ( ? ) and The SpitzerProgram to Observe the NDWFS Field in Bo¨otes (Soifer et al. 2004). Spitzer IRAC mosaics from theSpitzer Deep Wide-Field Survey cover 88 of the 98 KISS star-forming galaxies; we detect all 88 of thesegalaxies in IRAC 3.6 µ m and 85 in IRAC 8.0 µ m . Because our photometric uncertainties are dominated bythe uncertainties in the absolute calibration of the IRAC instrument, around 3% , we adopt a 3% uncertaintyfor all our IRAC photometric measurements.The archival MIPS data from Soifer et al. (2004) provide this project with archival Spitzer MIPS µ m band coverage for 81 KISS star-forming galaxies; 74 are detected. The uncertainties in the absolute IRAC Data Handbook: http://ssc.spitzer.caltech.edu/irac/dh/ , and we adopt a 2% uncertainty for ourMIPS photometric measurements as well. Although MIPS 70 µ m and MIPS 160 µ m imaging exists for theKISS galaxies, the object-to-noise contrast is such that the detection rate is less than fifty percent in thesebands. As a result, discussion of MIPS 70 µ m and MIPS 160 µ m photometry is not included in this work.The Spitzer Deep Wide-Field Survey provides IRAC mosaics that are calibrated, co-added, and scienceready. For the MIPS 24 µ m photometry we used archival Post Basic Calibrated Data mosaics. Typically,2-4 Spitzer MIPS observations exist for each object, although a small number have only one observation.We co-added the MIPS observations to construct postage-stamp images after aligning them with centroidingsoftware from the NOAO Image Reduction and Analysis Facility (IRAF). Because the KISS Bo¨otes field was chosen to overlap with the heavily studied NDWFS Bo¨otes field ( ? ),deep optical images exist for the majority of the KISS galaxies in the Bo¨otes field. In particular, this studymakes use of Bw, R, and I band data for 76 of the 88 star-forming galaxies KISS galaxies covered by theSpitzer Deep Wide Field Survey to calculate stellar masses for these galaxies using well-known mass-to-lightrelations ( ? ) (see Section 3.3).As with the objective-prism H α measurements, we corrected the Bw, R, and I band measurements forextinction using a single-screen model along with the Balmer decrements (c H β ) from follow-up spectra. Allreferences to optical photometry hereafter, including the stellar masses, shall refer to the extinction correctedvalues. We calculated luminosity surface densities for each object in each of the NDWFS, Spitzer IRAC, and SpitzerMIPS images discussed in the previous two subsections (when available) using extended source detectionan measurement for each object performed with SExtractor ( ? ). We used the IRAC 3.6 µ m images asSExtractor detection images; the elliptical photometric regions computed by SExtractor based on the IRAC3.6 µ m images were used for photometry in images from all of the other bands, guaranteeing that the fluxescalculated in every band are from the same physical regions within the galaxies. In this fashion we producedextended-source photometric measurements for each object in up to eight bands: the NDWFS Bw, R, and Ibands, all four Spitzer IRAC channels, and the MIPS 24 µ m channel. The NDWFS optical images were binnedand the MIPS 24 µ m images were up-sampled in a flux-conserving manner to match the plate Spitzer DeepWide Field Survey plate scale. In all cases, the SExtractor FLUX AUTO was used. We then converted thesefluxes into luminosity surface densities (Σ λ ) using the angular area of each object in the detection image.After detecting and measuring the KISS objects within these images, we applied aperture corrections toour IRAC and MIPS measurements using aperture corrections derived in the SWIRE data release ( ? ), assuggested by the Spitzer IRAC Handbook . The goals of SWIRE are similar to ours in that they rely in acomparison between the four IRAC and the MIPS 24 µ m channels, and the aperture corrections that theyderive are consistent with those derived by the IRAC and MIPS instrument teams. As a check, we comparedthe IRAC magnitudes determined with this method to those listed in the catalog in ? ; typically, they werewithin two tenths of a magnitude.Although the IRAC 8.0 µ m channel is dominated by PAH vibrational transitions, there is, however,significant contamination from the red tail of the late-type stellar continuum in the 8.0 µ m band pass whichmust removed before any PAH-based SFR metric can be assessed. Because spectral energy distribution(SED) models (e.g., ? ) indicate that the IRAC 3.6 µ m band pass samples the old stellar population almostexclusively, a dust-only 8.0 µ m luminosity can be created by using the 3.6 µ m luminosity to estimate andremove the stellar contribution in the 8.0 µ m band. As in ? , we assume that the flux in the 3.6 µ m bandis dominated by the stellar continuum and, extrapolating this continuum, adopt a coefficient β = 0 .
232 tobe the ratio of the stellar component of the flux density in the 8.0 µ m band to the total flux density in the MIPS Data Handbook: http://ssc.spitzer.caltech.edu/mips/dh/ µ m band. This ratio is derived from the Starburst99 model ( ? ), and as the stellar SED in the mid-infraredregime is not a strong function of stellar age, it is likely to be a reasonable approximation. This techniqueis also used in other work (e.g., ???? ), although the adopted value of β differs between authors, 0.22-0.29 in ? and 0.26 in ? , for instance.Likewise, we remove the stellar continuum from the IRAC 4.5 µ m, 5.8 µ m, and MIPS 24 µ m image mea-surements, using the β values of 0.596, 0.399, and 0.032, respectively ( ? ). Note that, unlike the correctionmade to the 8.0 µ m data, these corrections have very little impact on our analysis since the β value for MIPS24 µ m is fairly small and that our analysis does not utilize the IRAC 4.5 µ m and 5.8 µ m measurements, wherethe contamination is more significant. All references to Σ λ in any of these channels shall hereafter refer todust-only values. Table 1 lists luminosity surface densities for the IRAC 3.6 µ m channel, as well as dust-onlysurface luminosities for the remaining IRAC channels and the MIPS 24 µ m channel.Because we focus on luminosity surface densities, we largely bypass the uncertainty introduced by trans-lating flux into luminosity via the redshift. However, it is still necessary to account for the difference betweenangular diameter distance and luminosity distance; to this end, we have multiplied each of the Σ λ values by(1 + z ) as a final step. All of the values listed in Table 1 and used in our analysis have been corrected inthis way. Because PAH features dominate non-stellar 8.0 µ m flux by more than a factor of 100 above warm dustemission, and nearly a factor of 10 above the stellar continuum ( ?? , see their Figures 8 and 10), severalworks (e.g., ? ) calibrate 8.0 µ m luminosity as an SFR indicator. Using extinction-corrected H α luminosityas a reference indicator, we test these calibrations against the KISS sample of galaxies.To this end, Figure 1 plots H α -measured SFR surface densities against 8.0 µ m luminosity surface den-sities for the KISS galaxies that have 8.0 µ m measurements, along with an error-weighted linear regressiondetermined using the method described in ? . The points have been color coded for log (O / H)+ 12 metallicityfrom follow-up spectroscopy (when available); a typical uncertainty in log (O / H) + 12 is 0.12 dex, and a colorkey is to the right of the plot. The merit of the 8.0 µ m luminosity to SFR calibrations discussed in earlierworks is evident from the correlation in Figure 1. The fitted empirical relationship is shown here, with SFRsand luminosities in units of M ⊙ yr − kpc − and erg s − kpc − , respectively :log Σ SFR = − . ± .
44 + 0 . ± . × log Σ . µ m (3)For the purpose of comparing this relationship to earlier works, we rewrite this relationship in units ofM ⊙ yr − and L ⊙ : log SFR = − . ± . . ± . × log L . µ m (4)We list the fitted coefficients for these relations in Table 2, along with the analogous coefficients fromother work ( ?? ). Different authors generally agree on the power-law coefficient for this relationship, typicallygiving it a value around 0.8–1.0; moreover, these relationships agree in their predicted SFR values over therange that their calibrations overlap. However, it should be noted that the samples were collected by differentmeans. ? use a magnitude-limited sample favoring large galaxies. Acknowledging this, they mention that ifseveral dwarf galaxies had been included in their fit, the slope of their relation would have been different—closer to the one found in this work. ? fit their relations to H II regions in M81, but PAH emission maybe sensitive to filling factors and other physical effects that would make whole galaxy relations differ fromrelations based on individual H II regions.The data presented here exhibit a greater scatter about the trend line than the data presented in earlierworks, with a Spearman rank-order coefficient of 0.52. Because KISS is a more representative sample ofgalaxies, we expect greater variation from the trend line due to galaxy-to-galaxy variation in the physical5rocesses that drive the relationships between infrared luminosities and star-formation rates. Additionally,we also expect deviations from the trend line due to the filling factor phenomenon, as well as randomvariations in the systematic uncertainties in the extinction correction (see below for discussion).Because of the known issues involved in using PAH emission as an SFR indicator, much of the focushas shifted to 24 µ m far-infrared thermal dust emission as an infrared SFR indicator. Many works (e.g., ??? ) suggest that 24 µ m luminosity is linked to ionizing photons both on the galactic scale and on thescale of star-forming complexes. This band is longward of stellar emission, thus mitigating the somewhatmodel-dependent correction needed when examining 8.0 µ m luminosity.We plot in Figure 2 extinction-corrected H α SFR against 24 µ m luminosities for 74 KISS galaxies. Incontrast to earlier works focusing on star-forming clumps within galaxies (e.g., ?? ), or LIRGs rather thannormal galaxies, (e.g., ? ) we find that the data in Figure 2 show only a weak trend of increasing Σ µm withΣ SFR , and have a relatively low Spearman rank-order coefficient of 0.37.These data do not unambiguously indicate any breaks in the luminosity relation seen in other work, suchas the diminished 8.0 µ m and 24 µ m emission from dwarf galaxies seen in ? or the enhanced 24 µ m emissionfrom high luminosity galaxies seen in ? . This is likely due to the greater intrinsic scatter in the KISS sample(as discussed below). Additionally, ? point out that one motivation for a piecewise indicator is the LuminousInfrared Galaxy (LIRG) mode of star formation at the high luminosity end ( L µ m ∼ > × erg / s); thisvolume-limited sample has no LIRGs and only four objects with luminosities in this range, making a piecewiserelation with a break at this luminosity both unwarranted and impossible to constrain in this study.In order to investigate the possibility that the scatter in Figure 2 is driven by systematic uncertaintiesin the H α extinction correction, we compare in Figure 3 the extinction corrected H α measurements toL H α (obs) +0 . × L µ m , the linear combination of uncorrected (observed) H α and 24 µ m luminosities indicatedin ? . They find that this combination of obscured and unobscured SFR indicators best reproduces thecarefully corrected H α values they report, making it an excellent SFR indicator in cases where extinctioncorrections are not available.The cloud of points in Figure 3 is centered around L H α (cor) = L H α (obs) + 0 . × L µ m , indicating thatour extinction corrections produce a corrected H α value that, on average, agrees with the value predictedby the relationship in ? based on our 24 µ m data. There is ∼ ? ) but no systematic variation with c H β (Spearman rank-order coefficient of -0.13), suggestingthat a systematic error in extinction correction is not responsible for the scatter in Figures 2 and 3. One possible explanation for the scatter in Figures 1 and 2 is a variation in the UV to IR reprocessingefficiency from galaxy-to-galaxy. For example, one might suspect that a metallicity enhancement wouldincrease a galaxy’s IR luminosity for a given SFR since both PAHs and silicate grains require elementsheavier than hydrogen. This possibility is decidedly suggested by the metallicity gradient visible in Figure 1,where the objects above the trend line tend to have slightly lower metallicities than objects below the trendline.To explore this idea further, we plot in Figure 4 the 8.0 µ m efficiency; that is, the ratio of the dust-only8.0 µ m surface luminosity density to extinction-corrected H α luminosity surface density, vs metallicity. Thedata in this plot show a positive trend, with a Spearman rank-order coefficient of 0.63, indicating that moremetal rich galaxies are more efficient at reprocessing UV photons into PAH vibrational emission features.The fitted empirical relationship is:log f . µ m f H α = − . ± . . ± . × [log (O / H) + 12] (5)As mentioned above, the extinction correction applied to the H α measurements used in the Σ SFR cal-culation dominates the uncertainty budget in our SFR measurements; if this uncertainty had a systematiccomponent to it, it is possible that, since metallicity and extinction are causally linked, a systematic errorthe extinction correction could artificially create the trend seen in Figure 4. To address this issue, we plotin Figure 5 the 8.0 µ m efficiency (described above) against the c H β Balmer decrement for each object. We6onclude from the lack of correction in Figure 5 (Spearman rank-order coefficient of -0.03) that we can rejectwith high confidence the possibility that the relationship between 8.0 µ m efficiency and metallicity is drivenby systematic errors in the H α extinction correction. ? explore the idea that metallicity affects PAH reprocessing of UV starlight with a sample of galaxiesdesigned to span a wide range in metallicity; their conclusions are similar, indicating that low metallicitygalaxies are PAH deficient, or, at least PAH inefficient. One explanation they suggest is drawn from the ideathat the ISM is enriched with oxygen before carbon-rich asymptotic giant branch stars release the carbonneeded to form PAHs. We explore this idea here by in Figure 6, where we plot 8.0 µ m efficiency againstextinction-corrected Bw-R observed color, a crude indicator of stellar age; the data in Figure 6 show nocorrelation, with a Spearman rank-order coefficient of 0.02.It is important to note that the lowest metallicity galaxies in this sample are more than a dex more metalrich than the lowest in the sample presented by ? , who interpret the link between metallicity and 8.0 µ mproperties as a break in infrared colors around a metallicity of log(O / H) + 12 < ∼
8. The lack of correlationof 8.0 µ m efficiency with Bw-R color in this sample is not in disagreement with the concept of carbon-richasymptotic giant branch stars affecting the PAH content of the ISM, but it does suggest that the the linkbetween metallicity and 8.0 µ m efficiency is more complex than a simple correlation with stellar age in therange sampled by KISS and probed by Bw-R colors. Without greater insight into the nature of the galaxies being studied it is unclear if the correlations presentedabove are physically significant across a range of redshifts. To investigate the properties of the KISS sample,we measured the stellar masses of the KISS galaxies using well-established mass-to-light ratios ( ? ). Themass-to-light ratios in ? that we used are based on Sloan Digital Sky Survey photometry and populationsynthesis models. Specifically, we utilized parameters from Table 7 in ? to write the logarithmic stellar massof a galaxy, in units of M ⊙ , as its logarithmic I band luminosity plus a linear function of [B-R] color:log M = log L I − .
405 + 0 . × [B − R] , (6)We note here that ? report that their optical mass-to-light relations have an uncertainty of ∼ . ? ). These masses were also computedfrom broadband photometry using mass-to-light ratios from ? . As can be seen in Figure 7, the distributionof masses of KISS galaxies follows closely that of the galaxies from ? . Also included in Figure 7 are severalLocal Group galaxies; the KISS mass distribution spans these objects, and we conclude that the surveymethodology behind KISS is effective at sampling typical galaxies.Because λ = 3.6 µ m is well into the Rayleigh-Jeans tail, even for M stars, the mid-infrared colors of stellarpopulations are not a strong function of age or metallicity, and are even less affected by dust obscuration andreddening than H and K bands. For these reasons, 3.6 µ m luminosity is appealing as a stellar mass indicator.While the 3.6 µ m band is contaminated by emission from hot dust and the 3.3 µ m PAH emission feature, thesesources contribute only 5 to 15% of the whole-galaxy luminosity flux in this band ( ? ). In Figure 8 we plotintegrated 3.6 µ m luminosities vs stellar masses for the 76 galaxies for which we have NDWFS photometry.The horizontal (stellar mass) error bars are dominated by the 0.1 dex uncertainty in the ? mass-to-lightrelationships. The relationship between the parameters in Figure 8 is fairly scattered, with a Spearmanrank-order coefficient of 0.47; moreover, it is clearly dependent on Bw-R color, and, upon close inspection,bimodal.The reason is apparent in Figure 9, where we see a bimodal color distribution. Previously, we reported amuch tighter relationship between the 3.6 µ m luminosity and stellar mass for these same galaxies ( ? ), howeverin that analysis our photometry was performed using apertures that were designed to encompass all of theobjects and avoid missing light; the elliptical regions detected by SExtractor are restricted to photometrically7ecure areas, which favors the centers of galaxies over the outskirts. Thus, late-type galaxies that are bulgedominated have much redder colors in the analysis presented here. We interpret the bimodality in Figure9 as a bimodality in the colors of galaxy centers, which is still apparent, though less obvious, in the trendpresented in ? . The mass surface densities, computed via the ? relationship above and the optical luminositysurface densities, are presented in Table 1.As a confirmation, we plot in Figure 10 a histogram of the effective radii of the KISS galaxies, as detectedby SExtractor in the IRAC 3.6 µ m images. Here we define the effective radius to be the geometric mean ofthe semi-major and semi-minor axes. The distribution in Figure 10 peaks at around 1.5 kpc; from this weconclude that the regions which are photometrically secure in the SDWFS IRAC 3.6 µ m images are restrictedto the central portions of the galaxies. Using luminosity surface densities we confirm the correlations directly relating 8.0 µ m luminosities to star-formation rates presented in earlier work ( ?? , see Table 2). Our method has the advantage that it normalizesout galaxy size, unlike results from studies which use whole galaxy luminosities, thereby removing thepossibility that the correlations presented are simply due to larger galaxies being, on average, brighter in allbands. Our use of Σ λ rather than L λ also largely sidesteps additional uncertainty in the redshift to distancecalculation (see Section 2).We find that our data show a much larger relative scatter. Because of its H α selection, KISS samplesa broad range of star-forming galaxies, especially when compared with the samples of earlier authors, suchas ? , who selected bright galaxies, ? , ? , and ? , who studied star-forming regions in nearby galaxies, or ? ,who studied dwarf galaxies. Although the direct relationships presented here have more scatter, they aremore representative of H α -bright galactic populations by virtue of drawing upon an H α -selected volume-limited sample. Moreover, the extinction-corrected objective-prism H α measurements give this sample totalgalaxy-wide SFRs, while other work commonly samples only parts of the target galaxies with slit spectra.The results here are consistent with work to date in reporting that 8.0 µ m PAH emission correlates withSFR with a power-law coefficient slightly less than unity, around 0.9 in this work and in ? . In line with earlierwork (e.g., ??? ), we speculate here that the coefficient value of less than one is driven by the destruction ofPAHs by ultraviolet light. This idea is in-line with observations that PAH emission is predominantly on therims of H II regions ( ?? ). The power-law coefficient of around 0.9 in the PAH to SFR relation is, then, hardlyunexpected as large galaxies with vigorous star formation are more likely to have many H II regions than tohave one monolithic region. Multiple H II regions would increase the surface area to volume ratio, and withit the PAH reprocessing efficiency.As mentioned above, earlier works (e.g., ?? ) note that the carbon content of PAHs make 8.0 µ m luminositysensitive to both star-formation history and metallicity. We speculate, as they suggest, that galaxies withhigher metallicities or richer star-formation histories might be more PAH rich and have larger ultravioletcovering factors, which is in keeping with the findings in ? , and would also explain the trend in Figure4. While neither this work nor ? possess a simple metric for star-formation history, our findings stronglycomplement their sample of galaxies, which were selected to span an extremely wide range in metallicities.In particular, the lack of correlation between 8.0 µ m efficiency and extinction (see Figure 5) suggests that thescatter in the correlation between Σ . µm and Σ SFR is not driven by older galaxies being dustier in general,but rather having a higher proportion of PAHs to silicate dust.Directly comparing our data to the relationships presented in ? and ? , we find that the ? relationshipunder predicts SFR for a given 8.0 µ m luminosity, while the ? relationship over predicts SFR for a given8.0 µ m luminosity; our data and our fitted relationship are logarithmically intermediate. This is consistentwith the metallicity to PAH reprocessing efficiency relationship presented in ? , since ? examined dwarfgalaxies, with low metallicities, and ? focused on bright galaxies, which largely represent the cores of maturegalaxies. Our volume-limited sample shows a larger spread than either of these studies and falls in between.In contrast, we find relatively little correlation between Σ µm and Σ SFR . With a Spearman rank-ordercoefficient of 0.37, we cannot rule out the possibility that there is a weak correlation between these parameters,8owever any such relationship is dominated by galaxy-to-galaxy variation within the mass, metallicity, andluminosity range that this sample covers. Moreover, from the color coding scheme in Figure 2, it is clearthat there is no particular trend with metallicity. Again, by normalizing to galaxy size, we have removedthe effect of larger galaxies being, on average, brighter in all bands.It is important to note that context is critical to the choice and use of SFR indicators. Our study focuseson galaxy-wide correlations, which blend together emission from a range of environments. Since warm dustfar-infrared emission is typically observed deep in H II regions, studies which focus on individual H II regions,or LIRGS, whose luminosities are dominated by monolithic star-forming complexes, may observe correlationswith 24 µ m luminosity which are very strong when applied to star-forming regions within galaxies but areblended together and blurred out in whole-galaxy photometry. Our study suggests that MIPS 24 µ m analogsare not effective as whole-galaxy SFR indicators for typical field galaxies. Using our H α -selected sample of star-forming galaxies, we confirm the calibrations from earlier work (e.g., ????? ) indicating that IRAC 8.0 µ m luminosity tracks SFR as measured by H α emission. The physicalmechanisms for this indicator, ultraviolet-excited PAH vibrational line emission, is well understood. We alsosupport observations linking 8.0 µ m emission to metallicity, with findings that more metal rich galaxies aremore efficient at processing UV photons into PAH emission. This behavior does not appear to be correlatedwith extinction or Bw-R color. Conversely, we find that MIPS 24 µ m warm dust thermal emission is a poorindicator of galaxy-wide star formation.Using optical mass-to-light ratios, we find that the KISS sample of galaxies closely mimics nearby galaxiesin terms of stellar mass distribution. We find that IRAC 3.6 µ m luminosity tracks stellar mass, but notsufficiently well that it can be applied without a color correction.In future work, fitting the SEDs of KISS galaxies will allow us to characterize the typical SEDs of star-forming galaxies. Modern SED models allow the inclusion of far-infrared dust emission. Using the 3.6 µ mband to anchor the stellar mass and the optical bands to calibrate the stellar age, with the KISS samplewe can estimate the PAH and dust contributions to the infrared SEDs of high-redshift star-forming galaxiesobservable with ALMA and Herschel. Acknowledgments
This work made use of images and/or data products provided by the NOAO Deep Wide-Field Survey (Jannuziand Dey 1999; Jannuzi et al. 2005; Dey et al. 2005), which is supported by the National Optical AstronomyObservatory (NOAO). NOAO is operated by AURA, Inc., under a cooperative agreement with the NationalScience Foundation.IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the As-sociation of Universities for Research in Astronomy, Inc., under cooperative agreement with the NationalScience Foundation.This research has made use of the NASA/IPAC Infrared Science Archive, operated by the Jet PropulsionLaboratory, California Institute of Technology, under contract with the National Aeronautics and SpaceAdministration.The Institute for Gravitation and the Cosmos is supported by the Eberly College of Science and theOffice of the Senior Vice President for Research at the Pennsylvania State University.We thank the anonymous referee for many thoughtful comments and suggestions which helped this workachieve its science goals.We are grateful to M. L. N. Ashby for his assistance and suggestions concerning our IRAC measurements.We are grateful to Kristin C. Peterson for editorial work in the preparation of the paper. This workis based [in part] on observations made with the Spitzer Space Telescope, which is operated by the JetPropulsion Laboratory, California Institute of Technology under a contract with NASA.9able 1 Spitzer IRAC & MIPS PhotometryKISS z log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ ) b log (Σ mass ) c log (Σ SFR ) c (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) M ⊙ kpc − (cid:1) (cid:0) M ⊙ yr − kpc − (cid:1) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a Dominated by a 3%. uncertainty in IRAC calibration. b Dominated by a 2% uncertainty in MIPS calibration. c Dominated by a 10% uncertainty in the mass-to-light ratios. . ) a log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ ) b log (Σ mass ) c log (Σ SFR ) c (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) M ⊙ kpc − (cid:1) (cid:0) M ⊙ yr − kpc − (cid:1) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -1002380 0.06 41.070 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -1002388 0.05 41.1820 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -100 a Dominated by a 3%. uncertainty in IRAC calibration. b Dominated by a 2% uncertainty in MIPS calibration. c Dominated by a 10% uncertainty in the mass-to-light ratios. ± ± ? -10.03 ± ± ? -7.9 ± ± The fits are of the form log SFR (M ⊙ ) = a + b × log L (L ⊙ ). Σ µ m [erg s -1 cm -2 kpc -2 ]-3-2-10 l og Σ SF R [ M (cid:12) y r - kp c - ] Σ Star Formation Rate vs. Σ µ m Figure 1 H α -derived SFR surface density vs µ m luminosity surface density, with a line of best fit. Pointsare color coded by log (O / H) + 12 metallicity, with a color key to the right of the plot. Note that metallicityincreases with 8.0 µ m density and SFR density. 13 Σ µ m [erg s -1 cm -2 kpc -2 ]-3-2-10 l og Σ SF R [ M (cid:12) y r - kp c - ] Σ Star Formation Rate vs. Σ µ m Figure 2 H α -derived SFR surface density vs µ m luminosity surface density. Points are color coded bylog (O / H) + 12 metallicity, with a color key to the right of the plot. Compared to Figure 1, there is relativelylittle trend. 14 H β -2-10123 l og ( H α ob s + . × µ m ) - l og ( H α c o r ) Observed H α + 24 µ m vs. Corrected H α Figure 3 A comparison of a linear combination of uncorrected (observed) H α with 24 µ m ( ? ) with extinctioncorrected H α , plotted against the Balmer decrement. The comparison values center around zero, and hasno trend, with a Spearman rank-order coefficient of -0.1315 l og f . µ m - l og f H α Flux µ m per Flux H α vs. Metallicity Figure 4 The ratio of 8.0 µ m flux to extinction-corrected H α flux vs log(O/H)+12 metallicity, along with atrend line; this figure shows a distinct trend, with a Spearman rank-order coefficient of 0.6316 H β l og f . µ m - l og f H α Flux µ m per Flux H α vs. Extinction Figure 5 The ratio of 8.0 µ m flux to extinction-corrected H α flux vs the c H β Balmer decrement; this figureshows no trend, with a Spearman rank-order coefficient of -0.02.17 l og f . µ m - l og f H α Flux µ m per Flux H α vs. Bw-R Color Figure 6 The ratio of 8.0 µ m flux to extinction-corrected H α flux vs Bw-R color; this figure shows no trend,with a Spearman rank-order coefficient of 0.02. 18 (cid:12) ]051015202530 r e l a ti v e nu m b e r Mass Distribution of KISS Galaxies
KISS GalaxiesNearby Galaxies
Figure 7 Distribution of stellar masses of the KISS galaxies (black) and Nearby Galaxies from ( ? ) (red);note that M31 falls near the upper end of the distribution.19 Σ MASS [M (cid:12) kpc -2 ]3940414243 l og Σ . µ m [ e r g s - c m - kp c - ] Σ µ m vs. Σ Stellar Mass -1.0-0.20.51.22.0
Figure 8 3.6 µ m surface luminosity vs to stellar mass surface density relationship. Points are color-codedby Bw-R color with exact values indicated by the key on the right side of the plot. The horizontal (stellarmass) error bars are much larger, and are dominated by the 0.1 dex uncertainty in the mass-to-light ratio.Note the upward trend, the large scatter, and the Bw-R gradient across the trend-line, indicating that 3.6 µ mluminosity cannot be used as a stellar mass indicator without a color correction.20 r e l a ti v e nu m b e r Bw-R Color Distribution of KISS Galaxies
Figure 9 Histogram of Bw-R colors for the 76 KISS galaxies that have reliable optical colors. Note that sincethe detection method used favors galaxy centers, the objects on the red side of the histogram are typicallylate-type galaxies with large bulges. 21 r e l a ti v e nu m b e r Size Distribution of KISS Galaxies
Figure 10 Distribution of effective radii of the KISS galaxies, taken as the geometric mean of the semi-majorand semi-minor axes. Note that the radii represented here correspond only to the areas of the galaxies thatwere detected as photometrically secure in IRAC 3.6 µ m ; the galactic disks likely extend beyond the radiishown here, but at surface brightnesses too low to allow direct comparison in a multi-wavelength analysis.22 r X i v : . [ a s t r o - ph . GA ] J u l Mon. Not. R. Astron. Soc. , 1– ?? (2002) Printed 31 August 2018 (MN L A TEX style file v2.2)
Comparing Infrared Star-Formation Rate Indicators withOptically-Derived Quantities
J. E. Young , C. Gronwall , , J. J. Salzer , J. L. Rosenberg ⋆ Department of Astronomy and Astrophysics,The Pennsylvania State University, University Park, PA 16802 Institute for Gravitation and the Cosmos,The Pennsylvania State University, University Park, PA 16802 Department of Astronomy,Indiana University, Bloomington, IN School of Physics, Astronomy, and Computational Science,George Mason University, Fairfax, VA
31 August 2018
ABSTRACT
We examine the UV reprocessing efficiencies of warm dust and polycyclic aromatichydrocarbons (PAHs) through an analysis of the mid- and far-infrared surface lumi-nosity densities of 85 nearby H α -selected star-forming galaxies detected by the volume-limited KPNO International Spectroscopic Survey (KISS). Because H α selection is notbiased toward continuum-bright objects, the KISS sample spans a wide range in stel-lar masses (10 –10 M ⊙ ), as well as H α luminosity (10 –10 ergs / s), mid-infrared8.0 µ m luminosity (10 –10 ergs / s), and [Bw-R] color (-.1–2.2). We find that mid-infrared polycyclic aromatic hydrocarbon (PAH) emission in the Spitzer IRAC 8.0 µ mband correlates with star formation, and that the efficiency with which galaxies re-process UV energy into PAH emission depends on metallicity. We also find that therelationship between far-infrared luminosity in the Spitzer MIPS 24 µ m band pass andH α -measured star-formation rate varies from galaxy to galaxy within our sample; wedo not observe a metallicity dependence in this relationship. We use optical colors andestablished mass-to-light relationships to determine stellar masses for the KISS galax-ies; we compare these masses to those of nearby galaxies as a confirmation that thevolume-limited nature of KISS avoids strong biases. We also examine the relationshipbetween IRAC 3.6 µ m luminosity and galaxy stellar mass, and find a color-dependentcorrelation between the two. Many lines of evidence now link mid- and far-infrared emis-sion to star-forming activity. For example, observations ofstar-forming regions in nearby galaxies (e.g., Calzetti et al.2005; P´erez-Gonz´alez et al. 2006) show that much of theultraviolet emission from young stars is absorbed by dustand then re-emitted in the mid- and far-infrared. In par-ticular, because the 7.7 µ m polycyclic aromatic hydrocar-bon (PAH) vibrational band falls within the Spitzer 8.0 µ mband pass, ultraviolet-excited IRAC 8.0 µ m PAH emis-sion is believed to track star-formation rate (SFR) (e.g.,Wu et al. 2005; Calzetti et al. 2005). Moreover, Wu et al.(2005), Hong et al. (2010), and Rosenberg et al. (2006) findthat the luminosities of star-forming galaxies in the Spitzer8.0 µ m band correlate with SFRs measured through othermeans.Likewise, thermal emission from warm dust is also tiedto star-forming activity because the thermal energy bud-get of warm dust is dominated by heating from ultravi-olet light. Specifically, many works (e.g., Wu et al. 2005;Alonso-Herrero et al. 2006; P´erez-Gonz´alez et al. 2006; Rela˜no et al. 2007; Calzetti et al. 2010) report that luminos-ity in the Spitzer 24 µ m band tracks SFR since this band-pass is dominated by the thermal spectrum of warm dust.Supporting this correlation, Bendo et al. (2010) find thatwarm dust, as measured by Spitzer MIPS 70 µ m observa-tions, traces out star-forming regions in M81, as opposedto cold dust, observed in Herschel 70-500 µ m data, whosethermal budget is dominated by evolved stars and is thusdetected throughout M81.However, modern infrared observations indicate thatneither 8.0 µ m nor 24 µ m emission is a straightforward SFRindicator. Both of these indicators trace obscured star for-mation; although the majority of star formation takes placedeep in heavily obscured molecular clouds, unobscured ul-traviolet light is not represented in the infrared energy bud-get. For this reason, any galaxy-wide feature which dimin-ishes the effective covering factor will affect the correlationof these infrared luminosities with star-formation rate.For example, Calzetti et al. (2007) andEngelbracht et al. (2005) note that 8.0 µ m luminosityis sensitive to both star-formation history and metallicity c (cid:13) J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg since PAH molecules contain carbon. Complicating mattersfurther, the ultraviolet light that causes a relationshipbetween PAH emission and SFR also destroys PAHs.Helou et al. (2004) and Bendo et al. (2006) note thatPAH emission is strongest on the rims of H II regions, andspeculate that the radiation environment in the centersof star-forming complexes is simply too harsh for PAHmolecules to survive. Likewise, silicate dust, the mostprobable source of far-IR thermal emission, is also sensitiveto metallicity, and even silicate dust can be destroyed bysufficiently high temperatures. Additionally, very smallgrains are subject to stochastic heating by UV photons,and may be out of equilibrium. Complicating mattersfurther, at low star-formation rates the energy contributionfrom evolved stars can become a significant part of thethermal budget of even warm dust (Boquien et al. 2011).Finally, thermal dust emission alone is ambiguous becausedust-enshrouded AGN can also heat interstellar dust (e.g.,Sanders & Mirabel 1996).In an effort to relate existing metrics of star-formationrate and characterize the infrared energy budgets of star-forming galaxies, we present an analysis of mid-infrared(IRAC), far-infrared (MIPS), and optical photometry of 85low-redshift H α -bright star-forming galaxies detected by theKPNO International Spectroscopic Survey (KISS) (KISS;Salzer et al. 2000), a quasi-volume-limited H α selected sur-vey. Because H α selection is not biased toward continuum-bright objects, the KISS sample effectively characterizesstar-forming galaxies by spanning a wide range of proper-ties, such as stellar masses (10 –10 M ⊙ ) and log(O / H)+12metallicities (7.8–9.2).While photometry in all four IRAC bands and the MIPS24 µ m band is tabulated in Table 1, we focus on IRAC 3.6 µ m,IRAC 8.0 µ m, and MIPS 24 µ m because of their relevance tostar formation studies. Luminosity in the IRAC 8.0 µ m bandcomes from a combination of sources (e.g., Wu et al. 2005).The primary contributors in the IRAC 8.0 µ m band are vi-brational emission lines of PAHs and the thermal tail ofthe old stellar population. Luminosity in the MIPS 24 µ mband, on the other hand, samples only thermal dust (e.g.,Wu et al. 2005). The IRAC 3.6 µ m band is believed to sam-ple primarily the thermal tail of the old stellar population.By studying these fluxes in tandem, we distinguish thesedifferent sources of luminosity. The IRAC 4.5 µ m and 5.8 µ mbands are less useful for this particular purpose because theycontain weaker PAH bands and more contamination fromthe stellar continuum than the 8.0 µ m band.While similar research has been conducted pre-viously (e.g., Rosenberg et al. 2006; Calzetti et al.2007, 2010; Wu et al. 2005; Alonso-Herrero et al. 2006;P´erez-Gonz´alez et al. 2006), KISS has the significantadvantage that it evenly samples galaxies across fourorders of magnitude in luminosity with observations thatspan a factor of 60 in wavelength range. Moreover, un-like other studies sampling small regions within galaxies(Calzetti et al. 2005; P´erez-Gonz´alez et al. 2006), theobjective-prism spectra ensure that KISS SFRs are globalSFRs and can be directly compared to integrated broad-band SFR indicator candidates, such as IRAC 8.0 µ m andMIPS 24 µ m luminosities.In Section 2, we describe the observations, basic dataprocessing, and photometry procedures. In Section 3, we de- scribe the analysis used to examine the connections and cor-relations between H α measured SFRs, infrared luminosities,and galaxian stellar masses. In Section 4, we discuss the im-plications of these relations and compare our finding to thosepublished in other works. For this work, we assume a ΛCDMcosmology with H = 67 .
04 km s − Mpc − , Ω m = 0 . Λ = 0 . α -Selected Sample The KISS field used in this work is located in the NOAODeep Wide Field Survey (NDWFS; Jannuzi & Dey 1999)in Bo¨otes (Jangren et al. 2005a). The KISS objects were se-lected from objective-prism spectra to have redshifts < α emission 5 σ above their median spectral continua.Objective-prism spectra are preferable to slit spectra for es-timating total H α luminosity for extended objects becausethey capture all of the flux from the object rather than thesmall fraction that would fall on a slit. A redshift (volume)limit rather than a magnitude limit ensures that the sampleis not biased toward galaxies that are intrinsically bright inthe continuum.In the KISS Bo¨otes field, 131 H α emission line ob-jects were identified. The initial detections were followed upwith higher resolution spectroscopy using the Hobby EberlyTelescope (HET), the KPNO 2.1 meter, the MDM 2.4 me-ter, and the Lick 3 meter telescopes (Wegner et al. 2003;Gronwall et al. 2004; Melbourne et al. 2004; Jangren et al.2005b; Salzer et al. 2005a). Using the higher resolution spec-tra, 28 AGN and LINER galaxies were rejected through anextinction-corrected [N II ] λ α versus [O III ] λ β line diagnostic diagram (Baldwin et al. 1981). Even thoughAGN hosts may be sites of star-forming activity, we are un-able to disentangle AGN H α emission from that of star-forming activity, making the SFR measurement from suchgalaxies unreliable. We concentrated on the 98 remainingobjects for our study. Metal abundance estimates were com-puted for all galaxies using emission-line ratios of stronglines by employing the coarse abundance method describedin Melbourne & Salzer (2002) and Salzer et al. (2005b); typ-ical uncertainties in log(O / H) + 12 are 0.12 dex.The H α luminosities referenced in this paper shallhereafter refer to H α luminosities that are measured fromobjective-prism data and are extinction-corrected usingBalmer decrements (c H β ) from follow-up spectra. This cor-rection assumes a single screen model for dust extinction; inthis assumption we incur an uncertainty because the Balmerdecrement measurements from the follow-up spectra repre-sent the extinction averaged over only the regions encom-passed by the slit used in the follow-up spectra. Thus, thisuncertainty has a systematic component in that, for objectsof large angular size, where only a smaller fraction of theobject was encompassed in the slit, the correction applied ismore likely to deviate from the true value.We incur another uncertainty from the assumption of aflat stellar continuum underneath the H α and H β emissionlines. With high resolution spectra, it is sometimes possibleto estimate the stellar absorption and appropriately correctthe emission lines; the follow-up KISS spectra are not of suf-ficient resolution. The primary effect is that the computed c (cid:13) , 1– ?? omparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities emission-line strengths are lower than the true values, affect-ing the Balmer decrements. This issue, and the ramificationsof using the method we describe here, are thoroughly dis-cussed by Brinchmann et al. (2004). They report that ourmethod can underestimate star-formation rates; for the me-dian stellar mass of our objects, this underestimation is 12%,and is much less, even zero, for low mass or low metallicityobjects.Normalizing to the angular sizes of the KISS galaxies inthe IRAC 3.6 µ m channel (see below), we list the H α surfaceluminosity densities and SFR surface densities in Table 1. α Star-Formation Rates
To calibrate mid- and far-infrared broadband photometry asstar-formation rate indicators, we use extinction-correctedH α luminosity as a benchmark indicator. Because the starscontributing with any significance to the ionizing flux haveshort lifetimes ( <
20 Myr), extinction-corrected H α luminos-ity is an indicator of current star formation and is relativelyindependent of star-formation history. Kennicutt & Evans(2012) provides an H α luminosity to SFR calibration usingsolar abundances and a Salpeter IMF (0.1 - 100 M ⊙ ):SFR [M ⊙ / yr] = 5 . × − L H α [erg / s] (1)log (SFR [M ⊙ / yr]) = − .
685 + log (L H α [L ⊙ ]) (2) The Spitzer data used in this project came from theSpitzer Deep Wide-Field Survey (Ashby et al. 2009) andThe Spitzer Program to Observe the NDWFS Field inBo¨otes (Soifer et al. 2004). Spitzer IRAC mosaics from theSpitzer Deep Wide-Field Survey cover 88 of the 98 KISSstar-forming galaxies; we detect all 88 of these galaxies inIRAC 3.6 µ m and 85 in IRAC 8.0 µ m . Because our photomet-ric uncertainties are dominated by the uncertainties in theabsolute calibration of the IRAC instrument, around 3% ,we adopt a 3% uncertainty for all our IRAC photometricmeasurements.The archival MIPS data from Soifer et al. (2004) providethis project with archival Spitzer MIPS µ m band cover-age for 81 KISS star-forming galaxies; 74 are detected. Theuncertainties in the absolute photometric calibration of theMIPS instrument are around 2% , and we adopt a 2% un-certainty for our MIPS photometric measurements as well.Although MIPS 70 µ m and MIPS 160 µ m imaging exists forthe KISS galaxies, the object-to-noise contrast is such thatthe detection rate is less than fifty percent in these bands.As a result, discussion of MIPS 70 µ m and MIPS 160 µ mphotometry is not included in this work.The Spitzer Deep Wide-Field Survey provides IRACmosaics that are calibrated, co-added, and science ready.For the MIPS 24 µ m photometry we used archival Post Ba-sic Calibrated Data mosaics. Typically, 2-4 Spitzer MIPSobservations exist for each object, although a small number IRAC Data Handbook: http://ssc.spitzer.caltech.edu/irac/dh/ MIPS Data Handbook: http://ssc.spitzer.caltech.edu/mips/dh/ have only one observation. We co-added the MIPS observa-tions to construct postage-stamp images after aligning themwith centroiding software from the NOAO Image Reductionand Analysis Facility (IRAF).
Because the KISS Bo¨otes field was chosen to overlap withthe heavily studied NDWFS Bo¨otes field (Jannuzi & Dey1999), deep optical images exist for the majority of the KISSgalaxies in the Bo¨otes field. In particular, this study makesuse of Bw, R, and I band data for 76 of the 88 star-forminggalaxies KISS galaxies covered by the Spitzer Deep WideField Survey to calculate stellar masses for these galaxiesusing well-known mass-to-light relations (Bell et al. 2003)(see Section 3.3).As with the objective-prism H α measurements, we cor-rected the Bw, R, and I band measurements for extinctionusing a single-screen model along with the Balmer decre-ments (c H β ) from follow-up spectra. All references to opti-cal photometry hereafter, including the stellar masses, shallrefer to the extinction corrected values. We calculated luminosity surface densities for each object ineach of the NDWFS, Spitzer IRAC, and Spitzer MIPS im-ages discussed in the previous two subsections (when avail-able) using extended source detection an measurement foreach object performed with SExtractor (Bertin & Arnouts1996). We used the IRAC 3.6 µ m images as SExtractor de-tection images; the elliptical photometric regions computedby SExtractor based on the IRAC 3.6 µ m images were usedfor photometry in images from all of the other bands, guar-anteeing that the fluxes calculated in every band are fromthe same physical regions within the galaxies. In this fashionwe produced extended-source photometric measurements foreach object in up to eight bands: the NDWFS Bw, R, and Ibands, all four Spitzer IRAC channels, and the MIPS 24 µ mchannel. The NDWFS optical images were binned and theMIPS 24 µ m images were up-sampled in a flux-conservingmanner to match the plate Spitzer Deep Wide Field Surveyplate scale. In all cases, the SExtractor FLUX AUTO wasused. We then converted these fluxes into luminosity surfacedensities (Σ λ ) using the angular area of each object in thedetection image.After detecting and measuring the KISS objects withinthese images, we applied aperture corrections to our IRACand MIPS measurements using aperture corrections derivedin the SWIRE data release (Surace et al. 2005), as suggestedby the Spitzer IRAC Handbook . The goals of SWIRE aresimilar to ours in that they rely in a comparison between thefour IRAC and the MIPS 24 µ m channels, and the aperturecorrections that they derive are consistent with those de-rived by the IRAC and MIPS instrument teams. As a check,we compared the IRAC magnitudes determined with thismethod to those listed in the catalog in Ashby et al. (2009);typically, they were within two tenths of a magnitude.Although the IRAC 8.0 µ m channel is dominated byPAH vibrational transitions, there is, however, significantcontamination from the red tail of the late-type stellar con-tinuum in the 8.0 µ m band pass which must removed before c (cid:13) , 1–, 1–
Because the KISS Bo¨otes field was chosen to overlap withthe heavily studied NDWFS Bo¨otes field (Jannuzi & Dey1999), deep optical images exist for the majority of the KISSgalaxies in the Bo¨otes field. In particular, this study makesuse of Bw, R, and I band data for 76 of the 88 star-forminggalaxies KISS galaxies covered by the Spitzer Deep WideField Survey to calculate stellar masses for these galaxiesusing well-known mass-to-light relations (Bell et al. 2003)(see Section 3.3).As with the objective-prism H α measurements, we cor-rected the Bw, R, and I band measurements for extinctionusing a single-screen model along with the Balmer decre-ments (c H β ) from follow-up spectra. All references to opti-cal photometry hereafter, including the stellar masses, shallrefer to the extinction corrected values. We calculated luminosity surface densities for each object ineach of the NDWFS, Spitzer IRAC, and Spitzer MIPS im-ages discussed in the previous two subsections (when avail-able) using extended source detection an measurement foreach object performed with SExtractor (Bertin & Arnouts1996). We used the IRAC 3.6 µ m images as SExtractor de-tection images; the elliptical photometric regions computedby SExtractor based on the IRAC 3.6 µ m images were usedfor photometry in images from all of the other bands, guar-anteeing that the fluxes calculated in every band are fromthe same physical regions within the galaxies. In this fashionwe produced extended-source photometric measurements foreach object in up to eight bands: the NDWFS Bw, R, and Ibands, all four Spitzer IRAC channels, and the MIPS 24 µ mchannel. The NDWFS optical images were binned and theMIPS 24 µ m images were up-sampled in a flux-conservingmanner to match the plate Spitzer Deep Wide Field Surveyplate scale. In all cases, the SExtractor FLUX AUTO wasused. We then converted these fluxes into luminosity surfacedensities (Σ λ ) using the angular area of each object in thedetection image.After detecting and measuring the KISS objects withinthese images, we applied aperture corrections to our IRACand MIPS measurements using aperture corrections derivedin the SWIRE data release (Surace et al. 2005), as suggestedby the Spitzer IRAC Handbook . The goals of SWIRE aresimilar to ours in that they rely in a comparison between thefour IRAC and the MIPS 24 µ m channels, and the aperturecorrections that they derive are consistent with those de-rived by the IRAC and MIPS instrument teams. As a check,we compared the IRAC magnitudes determined with thismethod to those listed in the catalog in Ashby et al. (2009);typically, they were within two tenths of a magnitude.Although the IRAC 8.0 µ m channel is dominated byPAH vibrational transitions, there is, however, significantcontamination from the red tail of the late-type stellar con-tinuum in the 8.0 µ m band pass which must removed before c (cid:13) , 1–, 1– ?? J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg any PAH-based SFR metric can be assessed. Because spec-tral energy distribution (SED) models (e.g., Li & Draine2001) indicate that the IRAC 3.6 µ m band pass samplesthe old stellar population almost exclusively, a dust-only8.0 µ m luminosity can be created by using the 3.6 µ m lumi-nosity to estimate and remove the stellar contribution in the8.0 µ m band. As in Helou et al. (2004), we assume that theflux in the 3.6 µ m band is dominated by the stellar contin-uum and, extrapolating this continuum, adopt a coefficient β = 0 .
232 to be the ratio of the stellar component of theflux density in the 8.0 µ m band to the total flux density inthe 3.6 µ m band. This ratio is derived from the Starburst99model (V´azquez & Leitherer 2005), and as the stellar SEDin the mid-infrared regime is not a strong function of stellarage, it is likely to be a reasonable approximation. This tech-nique is also used in other work (e.g., Calzetti et al. 2007;P´erez-Gonz´alez et al. 2006; Rosenberg et al. 2006; Wu et al.2005), although the adopted value of β differs betweenauthors, 0.22-0.29 in Calzetti et al. (2007) and 0.26 inWu et al. (2005), for instance.Likewise, we remove the stellar continuum from theIRAC 4.5 µ m, 5.8 µ m, and MIPS 24 µ m image measurements,using the β values of 0.596, 0.399, and 0.032, respectively(Helou et al. 2004). Note that, unlike the correction madeto the 8.0 µ m data, these corrections have very little impacton our analysis since the β value for MIPS 24 µ m is fairlysmall and that our analysis does not utilize the IRAC 4.5 µ mand 5.8 µ m measurements, where the contamination is moresignificant. All references to Σ λ in any of these channelsshall hereafter refer to dust-only values. Table 1 lists lumi-nosity surface densities for the IRAC 3.6 µ m channel, as wellas dust-only surface luminosities for the remaining IRACchannels and the MIPS 24 µ m channel.Because we focus on luminosity surface densities, welargely bypass the uncertainty introduced by translating fluxinto luminosity via the redshift. However, it is still neces-sary to account for the difference between angular diameterdistance and luminosity distance; to this end, we have mul-tiplied each of the Σ λ values by (1 + z ) as a final step. Allof the values listed in Table 1 and used in our analysis havebeen corrected in this way. Because PAH features dominate non-stellar 8.0 µ m flux bymore than a factor of 100 above warm dust emission, andnearly a factor of 10 above the stellar continuum (Dale et al.2005; Li & Draine 2001, see their Figures 8 and 10), severalworks (e.g., Calzetti et al. 2007) calibrate 8.0 µ m luminosityas an SFR indicator. Using extinction-corrected H α lumi-nosity as a reference indicator, we test these calibrationsagainst the KISS sample of galaxies.To this end, Figure 1 plots H α -measured SFR surfacedensities against 8.0 µ m luminosity surface densities for theKISS galaxies that have 8.0 µ m measurements, along withan error-weighted linear regression determined using themethod described in Akritas & Bershady (1996). The pointshave been color coded for log (O / H) + 12 metallicity from follow-up spectroscopy (when available); a typical uncer-tainty in log (O / H) + 12 is 0.12 dex, and a color key is tothe right of the plot. The merit of the 8.0 µ m luminosity toSFR calibrations discussed in earlier works is evident fromthe correlation in Figure 1. The fitted empirical relation-ship is shown here, with SFRs and luminosities in units ofM ⊙ yr − kpc − and erg s − kpc − , respectively :log Σ SFR = − . ± .
44 + 0 . ± . × log Σ . µ m (3)For the purpose of comparing this relationship to earlierworks, we rewrite this relationship in units of M ⊙ yr − andL ⊙ : log SFR = − . ± . . ± . × log L . µ m (4)We list the fitted coefficients for these relations in Ta-ble 2, along with the analogous coefficients from other work(Wu et al. 2005; P´erez-Gonz´alez et al. 2006). Different au-thors generally agree on the power-law coefficient for thisrelationship, typically giving it a value around 0.8–1.0; more-over, these relationships agree in their predicted SFR valuesover the range that their calibrations overlap. However, itshould be noted that the samples were collected by differ-ent means. Wu et al. (2005) use a magnitude-limited samplefavoring large galaxies. Acknowledging this, they mentionthat if several dwarf galaxies had been included in their fit,the slope of their relation would have been different—closerto the one found in this work. P´erez-Gonz´alez et al. (2006)fit their relations to H II regions in M81, but PAH emissionmay be sensitive to filling factors and other physical effectsthat would make whole galaxy relations differ from relationsbased on individual H II regions.The data presented here exhibit a greater scatter aboutthe trend line than the data presented in earlier works, witha Spearman rank-order coefficient of 0.52. Because KISS isa more representative sample of galaxies, we expect greatervariation from the trend line due to galaxy-to-galaxy vari-ation in the physical processes that drive the relationshipsbetween infrared luminosities and star-formation rates. Ad-ditionally, we also expect deviations from the trend line dueto the filling factor phenomenon, as well as random varia-tions in the systematic uncertainties in the extinction cor-rection (see below for discussion).Because of the known issues involved in using PAHemission as an SFR indicator, much of the focus has shiftedto 24 µ m far-infrared thermal dust emission as an infraredSFR indicator. Many works (e.g., Alonso-Herrero et al.2006; P´erez-Gonz´alez et al. 2006; Calzetti et al. 2005) sug-gest that 24 µ m luminosity is linked to ionizing photons bothon the galactic scale and on the scale of star-forming com-plexes. This band is longward of stellar emission, thus mit-igating the somewhat model-dependent correction neededwhen examining 8.0 µ m luminosity.We plot in Figure 2 extinction-corrected H α SFRagainst 24 µ m luminosities for 74 KISS galaxies. In con-trast to earlier works focusing on star-forming clumps withingalaxies (e.g., P´erez-Gonz´alez et al. 2006; Calzetti et al.2005), or LIRGs rather than normal galaxies, (e.g.,Alonso-Herrero et al. 2006) we find that the data in Figure2 show only a weak trend of increasing Σ µm with Σ SFR , c (cid:13) , 1– ?? omparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities and have a relatively low Spearman rank-order coefficient of0.37.These data do not unambiguously indicate any breaksin the luminosity relation seen in other work, such as the di-minished 8.0 µ m and 24 µ m emission from dwarf galaxies seenin Wu et al. (2005) or the enhanced 24 µ m emission fromhigh luminosity galaxies seen in Calzetti et al. (2007). Thisis likely due to the greater intrinsic scatter in the KISS sam-ple (as discussed below). Additionally, Calzetti et al. (2010)point out that one motivation for a piecewise indicator is theLuminous Infrared Galaxy (LIRG) mode of star formationat the high luminosity end ( L µ m ∼ > × erg / s); thisvolume-limited sample has no LIRGs and only four objectswith luminosities in this range, making a piecewise relationwith a break at this luminosity both unwarranted and im-possible to constrain in this study.In order to investigate the possibility that the scatterin Figure 2 is driven by systematic uncertainties in the H α extinction correction, we compare in Figure 3 the extinctioncorrected H α measurements to L H α (obs) + 0 . × L µ m , thelinear combination of uncorrected (observed) H α and 24 µ mluminosities indicated in Kennicutt et al. (2009). They findthat this combination of obscured and unobscured SFR in-dicators best reproduces the carefully corrected H α valuesthey report, making it an excellent SFR indicator in caseswhere extinction corrections are not available.The cloud of points in Figure 3 is centered aroundL H α (cor) = L H α (obs) + 0 . × L µ m , indicating that our ex-tinction corrections produce a corrected H α value that, onaverage, agrees with the value predicted by the relationshipin Kennicutt et al. (2009) based on our 24 µ m data. Thereis ∼ H β (Spearman rank-order coefficient of -0.13), suggestingthat a systematic error in extinction correction is not re-sponsible for the scatter in Figures 2 and 3. One possible explanation for the scatter in Figures 1 and 2is a variation in the UV to IR reprocessing efficiency fromgalaxy-to-galaxy. For example, one might suspect that ametallicity enhancement would increase a galaxy’s IR lumi-nosity for a given SFR since both PAHs and silicate grainsrequire elements heavier than hydrogen. This possibility isdecidedly suggested by the metallicity gradient visible inFigure 1, where the objects above the trend line tend to haveslightly lower metallicities than objects below the trend line.To explore this idea further, we plot in Figure 4 the8.0 µ m efficiency; that is, the ratio of the dust-only 8.0 µ msurface luminosity density to extinction-corrected H α lumi-nosity surface density, vs metallicity. The data in this plotshow a positive trend, with a Spearman rank-order coeffi-cient of 0.63, indicating that more metal rich galaxies aremore efficient at reprocessing UV photons into PAH vibra-tional emission features. The fitted empirical relationship is:log f . µ m f H α = − . ± . . ± . × [log (O / H) + 12] (5)As mentioned above, the extinction correction appliedto the H α measurements used in the Σ SFR calculation dom- inates the uncertainty budget in our SFR measurements;if this uncertainty had a systematic component to it, it ispossible that, since metallicity and extinction are causallylinked, a systematic error the extinction correction could ar-tificially create the trend seen in Figure 4. To address thisissue, we plot in Figure 5 the 8.0 µ m efficiency (describedabove) against the c H β Balmer decrement for each object.We conclude from the lack of correction in Figure 5 (Spear-man rank-order coefficient of -0.03) that we can reject withhigh confidence the possibility that the relationship between8.0 µ m efficiency and metallicity is driven by systematic er-rors in the H α extinction correction.Engelbracht et al. (2005) explore the idea that metal-licity affects PAH reprocessing of UV starlight with a sam-ple of galaxies designed to span a wide range in metallicity;their conclusions are similar, indicating that low metallic-ity galaxies are PAH deficient, or, at least PAH inefficient.One explanation they suggest is drawn from the idea thatthe ISM is enriched with oxygen before carbon-rich asymp-totic giant branch stars release the carbon needed to formPAHs. We explore this idea here by in Figure 6, where weplot 8.0 µ m efficiency against extinction-corrected Bw-R ob-served color, a crude indicator of stellar age; the data inFigure 6 show no correlation, with a Spearman rank-ordercoefficient of 0.02.It is important to note that the lowest metallicity galax-ies in this sample are more than a dex more metal rich thanthe lowest in the sample presented by Engelbracht et al.(2005), who interpret the link between metallicity and 8.0 µ mproperties as a break in infrared colors around a metallicityof log(O / H) + 12 < ∼
8. The lack of correlation of 8.0 µ m effi-ciency with Bw-R color in this sample is not in disagreementwith the concept of carbon-rich asymptotic giant branchstars affecting the PAH content of the ISM, but it doessuggest that the the link between metallicity and 8.0 µ mefficiency is more complex than a simple correlation withstellar age in the range sampled by KISS and probed byBw-R colors. Without greater insight into the nature of the galaxies beingstudied it is unclear if the correlations presented above arephysically significant across a range of redshifts. To inves-tigate the properties of the KISS sample, we measured thestellar masses of the KISS galaxies using well-establishedmass-to-light ratios (Bell et al. 2003). The mass-to-light ra-tios in Bell et al. (2003) that we used are based on SloanDigital Sky Survey photometry and population synthesismodels. Specifically, we utilized parameters from Table 7in Bell et al. (2003) to write the logarithmic stellar mass ofa galaxy, in units of M ⊙ , as its logarithmic I band luminosityplus a linear function of [B-R] color:log M = log L I − .
405 + 0 . × [B − R] , (6)We note here that Bell et al. (2003) report that their opticalmass-to-light relations have an uncertainty of ∼ . c (cid:13) , 1– ?? J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg with a red histogram the stellar masses of galaxies fromthe The GALEX Ultraviolet Atlas of Nearby Galaxies(Gil de Paz et al. 2009). These masses were also computedfrom broadband photometry using mass-to-light ratios fromBell et al. (2003). As can be seen in Figure 7, the distri-bution of masses of KISS galaxies follows closely that ofthe galaxies from Gil de Paz et al. (2009). Also included inFigure 7 are several Local Group galaxies; the KISS massdistribution spans these objects, and we conclude that thesurvey methodology behind KISS is effective at samplingtypical galaxies.Because λ = 3.6 µ m is well into the Rayleigh-Jeans tail,even for M stars, the mid-infrared colors of stellar popula-tions are not a strong function of age or metallicity, andare even less affected by dust obscuration and reddeningthan H and K bands. For these reasons, 3.6 µ m luminosityis appealing as a stellar mass indicator. While the 3.6 µ mband is contaminated by emission from hot dust and the3.3 µ m PAH emission feature, these sources contribute only5 to 15% of the whole-galaxy luminosity flux in this band(Meidt et al. 2012). In Figure 8 we plot integrated 3.6 µ mluminosities vs stellar masses for the 76 galaxies for whichwe have NDWFS photometry. The horizontal (stellar mass)error bars are dominated by the 0.1 dex uncertainty in theBell et al. (2003) mass-to-light relationships. The relation-ship between the parameters in Figure 8 is fairly scattered,with a Spearman rank-order coefficient of 0.47; moreover, itis clearly dependent on Bw-R color, and, upon close inspec-tion, bimodal.The reason is apparent in Figure 9, where we see a bi-modal color distribution. Previously, we reported a muchtighter relationship between the 3.6 µ m luminosity and stel-lar mass for these same galaxies (Young 2012), however inthat analysis our photometry was performed using aperturesthat were designed to encompass all of the objects and avoidmissing light; the elliptical regions detected by SExtractorare restricted to photometrically secure areas, which favorsthe centers of galaxies over the outskirts. Thus, late-typegalaxies that are bulge dominated have much redder colorsin the analysis presented here. We interpret the bimodalityin Figure 9 as a bimodality in the colors of galaxy centers,which is still apparent, though less obvious, in the trendpresented in Young (2012). The mass surface densities, com-puted via the Bell et al. (2003) relationship above and theoptical luminosity surface densities, are presented in Table1. As a confirmation, we plot in Figure 10 a histogramof the effective radii of the KISS galaxies, as detected bySExtractor in the IRAC 3.6 µ m images. Here we define theeffective radius to be the geometric mean of the semi-majorand semi-minor axes. The distribution in Figure 10 peaks ataround 1.5 kpc; from this we conclude that the regions whichare photometrically secure in the SDWFS IRAC 3.6 µ m im-ages are restricted to the central portions of the galaxies. Using luminosity surface densities we confirm the cor-relations directly relating 8.0 µ m luminosities to star-formation rates presented in earlier work (Wu et al. 2005;P´erez-Gonz´alez et al. 2006, see Table 2). Our method has the advantage that it normalizes out galaxy size, unlikeresults from studies which use whole galaxy luminosities,thereby removing the possibility that the correlations pre-sented are simply due to larger galaxies being, on average,brighter in all bands. Our use of Σ λ rather than L λ alsolargely sidesteps additional uncertainty in the redshift todistance calculation (see Section 2).We find that our data show a much larger relative scat-ter. Because of its H α selection, KISS samples a broad rangeof star-forming galaxies, especially when compared with thesamples of earlier authors, such as Wu et al. (2005), who se-lected bright galaxies, Calzetti et al. (2005), Calzetti et al.(2007), and P´erez-Gonz´alez et al. (2006), who studied star-forming regions in nearby galaxies, or Rosenberg et al.(2006), who studied dwarf galaxies. Although the direct re-lationships presented here have more scatter, they are morerepresentative of H α -bright galactic populations by virtue ofdrawing upon an H α -selected volume-limited sample. More-over, the extinction-corrected objective-prism H α measure-ments give this sample total galaxy-wide SFRs, while otherwork commonly samples only parts of the target galaxieswith slit spectra.The results here are consistent with work to date in re-porting that 8.0 µ m PAH emission correlates with SFR witha power-law coefficient slightly less than unity, around 0.9 inthis work and in P´erez-Gonz´alez et al. (2006). In line withearlier work (e.g., Wu et al. 2005; Calzetti et al. 2007, 2010),we speculate here that the coefficient value of less than oneis driven by the destruction of PAHs by ultraviolet light.This idea is in-line with observations that PAH emission ispredominantly on the rims of H II regions (Helou et al. 2004;Bendo et al. 2006). The power-law coefficient of around 0.9in the PAH to SFR relation is, then, hardly unexpected aslarge galaxies with vigorous star formation are more likelyto have many H II regions than to have one monolithic re-gion. Multiple H II regions would increase the surface area tovolume ratio, and with it the PAH reprocessing efficiency.As mentioned above, earlier works (e.g., Calzetti et al.2007; Engelbracht et al. 2005) note that the carbon con-tent of PAHs make 8.0 µ m luminosity sensitive to both star-formation history and metallicity. We speculate, as they sug-gest, that galaxies with higher metallicities or richer star-formation histories might be more PAH rich and have largerultraviolet covering factors, which is in keeping with thefindings in Engelbracht et al. (2005), and would also ex-plain the trend in Figure 4. While neither this work norEngelbracht et al. (2005) possess a simple metric for star-formation history, our findings strongly complement theirsample of galaxies, which were selected to span an extremelywide range in metallicities. In particular, the lack of correla-tion between 8.0 µ m efficiency and extinction (see Figure 5)suggests that the scatter in the correlation between Σ . µm and Σ SFR is not driven by older galaxies being dustier ingeneral, but rather having a higher proportion of PAHs tosilicate dust.Directly comparing our data to the relationships pre-sented in Wu et al. (2005) and P´erez-Gonz´alez et al. (2006),we find that the Wu et al. (2005) relationship underpredicts SFR for a given 8.0 µ m luminosity, while theP´erez-Gonz´alez et al. (2006) relationship over predicts SFRfor a given 8.0 µ m luminosity; our data and our fitted re-lationship are logarithmically intermediate. This is consis- c (cid:13) , 1– ?? omparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities tent with the metallicity to PAH reprocessing efficiencyrelationship presented in Engelbracht et al. (2005), sinceP´erez-Gonz´alez et al. (2006) examined dwarf galaxies, withlow metallicities, and Wu et al. (2005) focused on brightgalaxies, which largely represent the cores of mature galax-ies. Our volume-limited sample shows a larger spread thaneither of these studies and falls in between.In contrast, we find relatively little correlation betweenΣ µm and Σ SFR . With a Spearman rank-order coefficient of0.37, we cannot rule out the possibility that there is a weakcorrelation between these parameters, however any such re-lationship is dominated by galaxy-to-galaxy variation withinthe mass, metallicity, and luminosity range that this samplecovers. Moreover, from the color coding scheme in Figure 2,it is clear that there is no particular trend with metallic-ity. Again, by normalizing to galaxy size, we have removedthe effect of larger galaxies being, on average, brighter in allbands.It is important to note that context is critical tothe choice and use of SFR indicators. Our study focuseson galaxy-wide correlations, which blend together emissionfrom a range of environments. Since warm dust far-infraredemission is typically observed deep in H II regions, studieswhich focus on individual H II regions, or LIRGS, whose lu-minosities are dominated by monolithic star-forming com-plexes, may observe correlations with 24 µ m luminositywhich are very strong when applied to star-forming regionswithin galaxies but are blended together and blurred outin whole-galaxy photometry. Our study suggests that MIPS24 µ m analogs are not effective as whole-galaxy SFR indica-tors for typical field galaxies. Using our H α -selected sample of star-forming galax-ies, we confirm the calibrations from earlier work (e.g.,Calzetti et al. 2007; Wu et al. 2005; Alonso-Herrero et al.2006; P´erez-Gonz´alez et al. 2006; Rela˜no et al. 2007) indi-cating that IRAC 8.0 µ m luminosity tracks SFR as mea-sured by H α emission. The physical mechanisms for this in-dicator, ultraviolet-excited PAH vibrational line emission, iswell understood. We also support observations linking 8.0 µ memission to metallicity, with findings that more metal richgalaxies are more efficient at processing UV photons intoPAH emission. This behavior does not appear to be corre-lated with extinction or Bw-R color. Conversely, we find thatMIPS 24 µ m warm dust thermal emission is a poor indicatorof galaxy-wide star formation.Using optical mass-to-light ratios, we find that the KISSsample of galaxies closely mimics nearby galaxies in termsof stellar mass distribution. We find that IRAC 3.6 µ m lu-minosity tracks stellar mass, but not sufficiently well that itcan be applied without a color correction.In future work, fitting the SEDs of KISS galaxies willallow us to characterize the typical SEDs of star-forminggalaxies. Modern SED models allow the inclusion of far-infrared dust emission. Using the 3.6 µ m band to anchorthe stellar mass and the optical bands to calibrate the stel-lar age, with the KISS sample we can estimate the PAHand dust contributions to the infrared SEDs of high-redshiftstar-forming galaxies observable with ALMA and Herschel. ACKNOWLEDGMENTS
This work made use of images and/or data products pro-vided by the NOAO Deep Wide-Field Survey (Jannuzi andDey 1999; Jannuzi et al. 2005; Dey et al. 2005), which issupported by the National Optical Astronomy Observatory(NOAO). NOAO is operated by AURA, Inc., under a coop-erative agreement with the National Science Foundation.IRAF is distributed by the National Optical AstronomyObservatories, which are operated by the Association of Uni-versities for Research in Astronomy, Inc., under cooperativeagreement with the National Science Foundation.This research has made use of the NASA/IPAC InfraredScience Archive, operated by the Jet Propulsion Laboratory,California Institute of Technology, under contract with theNational Aeronautics and Space Administration.The Institute for Gravitation and the Cosmos is sup-ported by the Eberly College of Science and the Office ofthe Senior Vice President for Research at the PennsylvaniaState University.We thank the anonymous referee for many thoughtfulcomments and suggestions which helped this work achieveits science goals.We are grateful to M. L. N. Ashby for his assistanceand suggestions concerning our IRAC measurements.We are grateful to Kristin C. Peterson for editorial workin the preparation of the paper. This work is based [in part]on observations made with the Spitzer Space Telescope,which is operated by the Jet Propulsion Laboratory, Califor-nia Institute of Technology under a contract with NASA. c (cid:13) , 1– ?? J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg
Table 1.
Spitzer IRAC & MIPS PhotometryKISS z log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ ) b log (Σ mass ) c log (Σ SFR ) c (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) M ⊙ kpc − (cid:1) (cid:0) M ⊙ yr − kpc − (cid:1) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a Dominated by a 3%. uncertainty in IRAC calibration. b Dominated by a 2% uncertainty in MIPS calibration. c Dominated by a 10% uncertainty in the mass-to-light ratios. c (cid:13) , 1– ?? omparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities KISS z log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ . ) a log (Σ ) b log (Σ mass ) c log (Σ SFR ) c (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) erg s − kpc − (cid:1) (cid:0) M ⊙ kpc − (cid:1) (cid:0) M ⊙ yr − kpc − (cid:1) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -1002380 0.06 41.070 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -1002388 0.05 41.1820 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -100 a Dominated by a 3%. uncertainty in IRAC calibration. b Dominated by a 2% uncertainty in MIPS calibration. c Dominated by a 10% uncertainty in the mass-to-light ratios.c (cid:13) , 1– ?? J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg
Table 2.
SFR Calibration CoefficientsSource a bThis Work -8.5 ± ± ± ± ± ± ⊙ ) = a + b × log L (L ⊙ ). c (cid:13) , 1– ?? omparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities
39 40 41 42 43log Σ µ m [erg s -1 cm -2 kpc -2 ]-3-2-10 l og Σ SF R [ M ⊙ y r - kp c - ] Σ Star Formation Rate vs. Σ µ m Figure 1. H α -derived SFR surface density vs µ m luminositysurface density, with a line of best fit. Points are color coded bylog (O / H) + 12 metallicity, with a color key to the right of theplot. Note that metallicity increases with 8.0 µ m density and SFRdensity.
39 40 41 42 43log Σ µ m [erg s -1 cm -2 kpc -2 ]-3-2-10 l og Σ SF R [ M ⊙ y r - kp c - ] Σ Star Formation Rate vs. Σ µ m Figure 2. H α -derived SFR surface density vs µ m luminositysurface density. Points are color coded by log (O / H)+12 metallic-ity, with a color key to the right of the plot. Compared to Figure1, there is relatively little trend. H β -2-10123 l og ( H α ob s + . × µ m ) - l og ( H α c o r ) Observed H α + 24 µ m vs. Corrected H α Figure 3.
A comparison of a linear combination of uncorrected(observed) H α with 24 µ m (Kennicutt et al. 2009) with extinc-tion corrected H α , plotted against the Balmer decrement. Thecomparison values center around zero, and has no trend, with aSpearman rank-order coefficient of -0.13 l og f . µ m - l og f H α Flux µ m per Flux H α vs. Metallicity Figure 4.
The ratio of 8.0 µ m flux to extinction-corrected H α flux vs log(O/H)+12 metallicity, along with a trend line; this figureshows a distinct trend, with a Spearman rank-order coefficient of0.63c (cid:13) , 1– ?? J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg H β l og f . µ m - l og f H α Flux µ m per Flux H α vs. Extinction Figure 5.
The ratio of 8.0 µ m flux to extinction-corrected H α flux vs the c H β Balmer decrement; this figure shows no trend, with aSpearman rank-order coefficient of -0.02. -2 -1 0 1 2Bw-R0123 l og f . µ m - l og f H α Flux µ m per Flux H α vs. Bw-R Color Figure 6.
The ratio of 8.0 µ m flux to extinction-corrected H α flux vs Bw-R color; this figure shows no trend, with a Spearmanrank-order coefficient of 0.02.
M31M33LMCM32 log Stellar Mass [M ⊙ ]05 r e l a ti v e nu m b e r Mass Distribution of KISS Galaxies
KISS GalaxiesNearby Galaxies
Figure 7.
Distribution of stellar masses of the KISS galaxies(black) and Nearby Galaxies from (Gil de Paz et al. 2009) (red);note that M31 falls near the upper end of the distribution. Σ MASS [M ⊙ kpc -2 ]3940414243 l og Σ . µ m [ e r g s - c m - kp c - ] Σ µ m vs. Σ Stellar Mass -1.0-0.20.51.22.0
Figure 8. µ m surface luminosity vs to stellar mass surfacedensity relationship. Points are color-coded by Bw-R color withexact values indicated by the key on the right side of the plot.The horizontal (stellar mass) error bars are much larger, and aredominated by the 0.1 dex uncertainty in the mass-to-light ratio.Note the upward trend, the large scatter, and the Bw-R gradientacross the trend-line, indicating that 3.6 µ m luminosity cannot beused as a stellar mass indicator without a color correction. -2 -1 0 1 2 3Bw-R0102030 r e l a ti v e nu m b e r Bw-R Color Distribution of KISS Galaxies
Figure 9.
Histogram of Bw-R colors for the 76 KISS galaxiesthat have reliable optical colors. Note that since the detectionmethod used favors galaxy centers, the objects on the red side ofthe histogram are typically late-type galaxies with large bulges.c (cid:13) , 1– ?? omparing Infrared Star-Formation Rate Indicators with Optically-Derived Quantities r e l a ti v e nu m b e r Size Distribution of KISS Galaxies
Figure 10.
Distribution of effective radii of the KISS galaxies,taken as the geometric mean of the semi-major and semi-minoraxes. Note that the radii represented here correspond only to theareas of the galaxies that were detected as photometrically securein IRAC 3.6 µ m ; the galactic disks likely extend beyond the radiishown here, but at surface brightnesses too low to allow directcomparison in a multi-wavelength analysis.c (cid:13) , 1– ?? J. E. Young, C. Gronwall, J. J. Salzer, J. L. Rosenberg
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