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The Nature of the Second Parameter in the IRX-β Relation for Local Galaxies Kathryn Grasha1 , Daniela Calzetti1 , Janice C. Lee2 , Daniel A. Dale3 ABSTRACT We present an analysis of 98 galaxies of low-dust content, selected from the Spitzer Local Volume Legacy (LVL) survey, aimed at examining the dust attenuation relation in normal star-forming galaxies. The infrared-excess (IRX-β) diagram is a technique used to correct star-forming galaxies for dust attenuation solely from observations of the ultraviolet (UV) colors, β. The UV colors are tightly related to the total attenuation as measured by the ratio of the total infrared (TIR) to the UV flux in starburst galaxies. Previous research has, however, indicated that normal star-forming galaxies, when compared to their starburst counterparts, do not follow the same dust attenuation relation and have a much larger spread in the TIR to far-UV (FUV) luminosity for a fixed UV spectral slope. We investigate the reason(s) for which normal star-forming galaxies deviate from the IRX-β starburst attenuation relation, examining the role that the age of the stellar population plays as the “second parameter” responsible for the observed deviation. We model the FUV to far-infrared spectral energy distribution (SED) of each galaxy using Starburst99 synthetic stellar spectra with a wide range of varying parameters, including metallicity, attenuation, age, and we include both constant star formation and instantaneous bursts. We find that, in virtually dust-free galaxies, the stellar population age influences galaxies that are represented with an instantaneous star formation history (SFH), where an increase in β correlates with an increase in the stellar population age at a significance level of 5σ. We also find that dust-free galaxies represented with a continuous star formation rate (SFR) do not appear to have any correlation between the duration of star forming activity with the observed UV color. We use the EW(Hα) as a proxy for the birthrate parameter, where a correlation between the equivalent width (EW) of Hα with both the UV spectral slope and the distance of a galaxy to the starburst IRX relation, is seen for continuous star forming 1 Astronomy Department, University of Massachusetts, Amherst, MA 01003, USA 2 STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA 3 Department of Physics, University of Wyoming, Laramie, WY 82071, USA –2– galaxies at a 4σ confidence level, in agreement with previous results. For both types of galaxies, there is an increase in degeneracy as galaxies with larger contributions from the infrared are considered, i.e. galaxies with increasing amounts of dust. Lack of a simple relationship for all types of galaxies suggests that the UV attenuation in normal star-forming galaxies may not be recovered with UV color alone and is highly influenced by the SFH. As a whole, we find that our galaxies have a tight correlation between the far-UV to near-infrared luminosity and β, suggesting that the scatter from the “second parameter” is better defined in terms of β as opposed to the distance from the starburst IRX relation. Subject headings: galaxies: star formation 1. Introduction Detailed knowledge of the stellar populations of galaxies is one of the ways to gain key insight into the evolution and formation of galaxies in the universe. Studying the stellar populations that give rise to the observed spectral energy distribution (SED) of a galaxy supplies knowledge of the type of stars within the galaxy and gives estimates of the star formation rate (SFR) along with the star formation history (SFH). A major obstacle in studying the intrinsic SED of a galaxy is correcting for the ultraviolet (UV) and optical flux lost to dust attenuation and being re-emitted in the infrared (IR). UV wavelengths, while the most susceptible to the effects of dust, provide insights on the young stellar populations, while longer wavelengths provide information on the older and more evolved stellar populations. Observations from the UV to the far-infrared (160 µm; FIR) constrain the amount of dust attenuation in a galaxy, giving rise to key insights of the physical processes at play in galaxies. Multiwavelength observations allow for an effective means of disentangling the different stellar populations within the observed galaxy SED. A method that allows the recovery of UV flux lost to dust will improve knowledge on the evolution of all types of galaxies at all redshifts. This becomes vitally important as surveys explore deeper into the universe, discovering galaxies that occupy the fainter end of the luminosity function. Understanding the physical properties of how stars form in these high-redshift systems plays a vital role in our knowledge of galaxy evolution. At high-redshift, where multiwavelength information is often limited, correcting for dust attenuation in galaxies is commonly done with the infrared (IR) excess (IRX-β) relation, which relates the observed UV colors (β) to the fraction of UV stellar emission absorbed by dust and re-emitted in the FIR. These two quantities are correlated in local starburst galaxies (Meurer et al. 1999) and in high-redshift systems (Reddy et al. 2010, 2012). The –3– IRX was originally defined by Meurer et al. (1999) as the ratio of the total IR luminosity to the FUV luminosity as LFIR , (1) IRX ≡ log L1600 where LFIR (erg s−1 cm−2 ) is defined as the integrated dust luminosity between 20 − 100 µm from IRAS (Infrared Astronomical Satellite) observations, and L1600 is the luminosity in the FUV from IU E (International Ultraviolet Explorer) data at 1600 Å. The value of the IRX diagram correlates with the UV spectral index β, defined as the power-law f λ ∝ λβ , (2) where fλ is the flux per unit wavelength (erg s−1 cm−2 Å−1 ), used to estimate the attenuation in the UV (Calzetti et al. 1994). This result gives an empirical relationship between β and a correction for dust attenuation, allowing the recovery of the intrinsic UV flux solely from the UV colors and completely independent of the distribution and properties of the dust. Kong et al. (2004) introduced a different definition of the IRX, LTIR IRX ≡ log , LFUV (3) where LTIR (erg s−1 cm−2 ) is the total integrated IR luminosity between 8 − 1000 µm from, e.g., Spitzer (Spitzer Space T elescope) IR observations and the flux in the FUV is from GALEX (GALaxy Evolution eXplorer; Martin et al. 2005) observations. The spectral slope βGLX is found with FUV and NUV photometric data from GALEX as βGLX = log fFUV − log fNUV , log λFUV − log λNUV (4) where fFUV and fNUV (erg s−1 cm−2 Å−1 ) is the flux density per unit wavelength of the FUV (λef f = 1520 Å) and NUV (λef f = 2310 Å) bands. In some literature, the UV spectral slope is given simply as the difference between the FUV and NUV magnitudes; we adopt the GALEX definition of the UV spectral slope in our work from here onward in this paper. We also adopt the IRX definition as defined by Kong et al. (2004), employing the total IR luminosity LTIR , calculated from Spitzer observations. While the IRX relationship provides accurate dust attenuation estimates for starburst galaxies, it does not apply to quiescent, normal star-forming galaxies, where the older stellar population contaminates the observed UV SED (Kong et al. 2004). Since the seminal work of Meurer et al. (1999), defining the relationship between the UV and IR properties for starburst galaxies, a great deal of effort has been dedicated to studying the IRX diagram from the global flux of galaxies (Kong et al. 2004; Siebert et al. 2005; Buat et al. 2005; Johnson et al. –4– 2007; Dale et al. 2007, 2009) and spatially resolved galactic regions (Bell et al. 2002; Gordon et al. 2004; Calzetti et al. 2005; Boquien et al. 2009, 2012; Mao et al. 2012). The quiescent galaxies on the IRX show a considerable amount of scatter compared to the starburst IRX relation. Currently, no single relation for normal star-forming galaxies exists between βGLX the UV attenuation nor is there agreement as to the underlying physical reason that causes the spread. It is necessary to unravel the reasons for which the normal star-forming galaxies deviate from the starburst IRX relation to better understand the nature of the relationship between the UV and IR properties of galaxies. Much work has been done to try and account for this deviation, where Kong et al. (2004) explains the offset of normal star-forming galaxies in terms of the birthrate parameter b, which accounts for present to past-averaged SFRs, where normal star-forming galaxies have a much lower ratio of the b-parameter compared to starburst galaxies. However, the results of Boquien et al. (2009, 2012), and Siebert et al. (2005) do not support the birthrate parameter result; instead, they suggest that the offset may merely be a result of the difference in dust geometry between normal star-forming and starburst galaxies. However, works by Burgarella et al. (2005); Cortese et al. (2006, 2008); Dale et al. (2009), and Reddy et al. (2012) show a connection between the age of the stellar population, and hence the SFH, and the observed spread in the IRX-β, where the b-parameter influences a galaxy on the IRX diagram and lower birthrate systems are generally located further from the starburst IRX relationship. The small aperture of the IU E photometry used in Meurer et al. (1999) for the formulation of the IRX also may have applied a systematic offset, where UV flux densities may have been severely underestimated, resulting in an overestimation of the IRX values for starburst galaxies and further impeding the reconciliation of the relation between normal star-forming and starburst galaxies. Recent work of Takeuchi et al. (2012) has attempted to account for the small aperture size of the IU E to reconcile the deviation of normal star-forming galaxies from that of starburst galaxies. They showed that when the work of Meurer et al. (1999) is corrected for the aperture effect, normal star-forming galaxies have less of an offset from the starburst relation, however, there is still large scatter present and a second parameter is still required to account for the scatter. Work by Burgarella et al. (2005); Johnson et al. (2007), and Boquien et al. (2012) showed that galaxies with a higher β corresponds to steeper attenuation, allowing for the possibility that variations in the adopted attenuation curve could cause the spread in the IRX diagram. A steepening in the attenuation curve as a galaxy moves toward higher β values suggests a transition exists in the attenuation law from highly efficient SFRs (starburst-type galaxies) to more quiescent, normal star-forming galaxies. Work by Calzetti (2001); Boquien et al. (2009), and Reddy et al. (2010, 2012) showed that adopting different extinction curves and dust geometries can impact the IRX diagram, where the age of the recovered stellar population is determined by the adopted –5– extinction curve. Finally, Hao et al. (2011) found that β is a poor predictor of the amount of dust attenuation present in normal star-forming galaxies. The literature so far has not presented a clear case for the “second parameter” in the IRX-β relation that drives most of the scatter. Starburst galaxies are well-fit with a single attenuation relation because they are dominated in the UV wavelengths by the young stellar populations formed in the most recent burst. More quiescent galaxies have a larger presence of older/aging stellar populations, giving rise to a non-negligible flux contribution in the optical, IR and, primarily, the UV regime. It is necessary to disentangle the SEDs of non-starburst galaxies into the young stellar population, dust, and evolved stellar populations in order to tackle the scatter of the IRX relation for normal star-forming galaxies. Multiwavelength data are required in order to properly investigate the parameters responsible for the deviation between the UV attenuation and β in normal, star-forming galaxies. In this paper, we will attempt to address how the age of the stellar population influences the IRX diagram with a combination of UV, optical, and IR photometric data in normal star-forming galaxies that are selected to have virtually no dust effects. This will allow us to quantify whether the mean stellar population age is a viable second parameter, and can be responsible for most of the deviation of normal star-forming galaxies from the starburst dust attenuation relationship. We do not focus on converting LTIR /LFUV into an estimate of the UV attenuation AFUV . Throughout this paper, we adopt a ΛCMD concordance cosmology model of Ωm = 0.27, ΩΛ = 0.73, and H◦ = 70 km s−1 Mpc−1 (Komatsu et al. 2011). All numbers taken from the literature are re-calculated (if necessary) to this cosmological model. 2. Sample Selection Our sources are selected in order to best answer the question of why normal starforming galaxies deviate from the IRX relation for starburst galaxies. With this in mind, we have selected a subset of virtually dust-free galaxies from the Spitzer Local Volume Legacy (LVL; Dale et al. 2009) survey, which has captured predominantly low-metallicity, low-luminosity dwarf and irregular galaxies. All 258 galaxies in the LVL survey are local (D < 11 Mpc) galaxies that avoid the Galactic plane (|b| > 20◦ ), and are brighter than B = 15.5 magnitude (Lee et al. 2011). The LVL sample is built on UV, Hα, and HST (Hubble Space T elescope) imaging from the 11 Mpc Hα and Ultraviolet Galactic Survey (11HUGS; Kennicutt et al. 2008) and the Advanced Camera for Surveys (ACS) Nearby Galactic Survey Treasury (ANGST; Dalcanton et al. 2009), where the galaxies from the ACS data set are |b| > 20◦ and D < 3.5 Mpc and the Hα images are |b| > 30◦ and D < 11 Mpc, providing a statistically robust and complete sample of the nearest galaxies to the Milky –6– Way (MW). The LVL provides an exceptional way to study the star formation activity in a sample of low-mass, low-surface brightness systems that are not flux-limited. We require that all the galaxies in our analysis must have readily available observations at the FUV, NUV, U, B, V, J, H, Ks, IRAC 3.5 µm, 4.5 µm, 5.8 µm, 8.0 µm, MIPS 24 µm, 70 µm, and 160 µm wavelengths. For the FUV and NUV bands, we use GALEX observations. For the optical bands of U, B, and V, we use photometric data from, in order of preference; the Third Reference Catalogue of Bright Galaxies (RC3; de Vaucoulers et al. 1995; Corwin et al. 1994), the Vatican Advanced Technology Telescope (VATT; Taylor et al. 2005), and the Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009). The SDSS u′ , g ′ , r′ photometry is converted to the Johnson U, B, V magnitude system according to Jester et al. (2005). U-band observations are required for each galaxy as the U-band gives the ability to characterize star formation bursts over the age-range of 0.1-1 Gyr. The U − B color is also a strong age discriminator, similar to the D(4000) Å break. J, H, and Ks bands are taken from the 2 Micron All Sky Survey (2MASS; Skrutskie et al. 2006) catalog. 3.6 µm to 160µm photometric observations are taken from the Spitzer/MIPS (Multiband Imaging Photometry for Spitzer; Rieke et al. 2004) and Spitzer/IRAC (Infrared Array Camera; Fazio et al. 2004) archival catalogs. After all the photometry is collected for every galaxy, we correct all the data for foreground Galactic extinction (Schlegel et al. 1998) assuming Aλ /E(B − V ) = 3.1 for all optical and IR data and, corrected as Fλ,corr = Fλ,i × 10−0.4Aλ , (5) where Aλ is the extinction corrections at the wavelengths of U, B, V, J, H, and Ks. For the GALEX filter bandpasses, AF U V = 8.016 E(B − V )M W and AN U V = 8.087 E(B − V )M W . These flux values Fλ,corr are the values that we compare to our models to investigate the best-fit parameters that give rise to the observed SEDs (Section 4.3). We further segregate the galaxies in the LVL sample by excluding all galaxies with a value of log LTIR /LFUV > 0.5, allowing us to study only virtually dust-free galaxies. 175 galaxies in the LVL survey met the requirement of log LTIR /LFUV < 0.5, where 98 of those have the necessary optical band photometry. The galaxies in the LVL survey represent a truly unbiased, representative, and statistically robust sample of nearby star-forming galaxies. Furthermore, by restricting our analysis to galaxies with little dust content, we remove one degree of freedom and can more accurately than in previous studies, pin down the role of stellar population ages and history for normal star-forming galaxies on the IRX-β relation. Some of our photometric data have upper limits as a result of non-detections in the IR bands (J band to 160 µm); we have treated upper limits as appropriate. Non-detections –7– imply that the measures flux density is below the 5σ upper limit. Table 1 lists all 98 sources used in our analysis of the IRX diagram. 3. 3.1. Definitions Bolometric Infrared Luminosity The TIR luminosity is the aggregate emission from all dust grains over the wavelength range 8 − 1000 µm. We estimate the total IR flux emission FTIR from MIPS 24, 70, and 160 µm bands using the recipe in Dale et al. (2002): FTIR = 1.559 ν fν (24 µm) + 0.7686 ν fν (70 µm) + 1.347 ν fν (160 µm), (6) where fν is the measured flux density (Jy) at each wavelength. The total IR luminosity is LTIR = 4πD2 FTIR , (7) where D is the distance to each galaxy and LTIR is used in the IRX calculation for the ratio of the total IR flux to the FUV flux. For each model, the luminosity lost due to dust absorption in the UV and optical regime must be equal to the bolometric luminosity recovered in the IR regime. We assume that the stellar light lost in the UV/optical regime to dust is fully recovered in the IR as dust emission, implying that the galaxy-average dust scattering observed is negligible. For sources that have any combination of upper limits for the flux density of 24, 70, or 160 µm, we treat the estimate of the IR luminosity as an upper limit, with calculated luminosities and their uncertainties listed in Table 1. 3.2. The IRX Diagram Figure 1 shows the IRX relation of log LTIR /LFUV as a function of β for the 98 galaxies in our sample, calculated according to Eq. 3. Meurer et al. (1999) found a correlation between LTIR /LFUV and β (and hence an AFUV and measured SFR) for starburst galaxies, as shown shown in Figure 1, where the scatter greatly increases for the normal star-forming galaxies that make up our sample. The value of β, defined by Calzetti et al. (1994), is derived from a power-law fit of the form fλ ∝ λβ in the range 1268 ≤ λ ≤ 2580 Å. We approximate our UV spectral index value with βGLX (Eq. 4), according to Kong et al. (2004), using GALEX observations. The IRX attenuation relation for starburst galaxies, as determined by Meurer et al. (1999), is log IRX = log(101.77+0.796βGLX − 1) + 0.076 ± 0.044, and can be seen in comparison to our galaxies in Figure 1. (8) –8– Fig. 1.— The IRX diagram, showing the ratio log LTIR /LFUV as a function of βGLX , the UV spectral index. All downward pointing arrows represent galaxies with upper limit values of the total bolometric IR luminosity, LTIR . The solid black line shows the starburst IRX attenuation relation, determined by a least-squares fit to the starburst galaxies from (Meurer et al. 1999). The perpendicular distance dp represents the shortest distance between each galaxy to the starburst attenuation curve. The horizontal dotted line represents the IRX value where we consider all sources below that to be free from dust effects. The angled dashed line in the upper right-hand corner represents the completeness level for sources with dp analysis; the three sources that lie rightward are excluded from all perpendicular distance results. The average error bar size is shown in the bottom right corner. –9– 3.3. Perpendicular Distance dp If the stellar population is a parameter responsible for the observed deviation of normal star-forming galaxies from the starburst IRX relation, the distance of an individual galaxy from the starburst relation should give insight into the role age plays in determining the location of any galaxy on the diagram. The shortest distance from a galaxy to the starburst relation is the perpendicular distance, given as p (9) dp = (xi − xIRX )2 + (yi − yIRX )2 , where (xi , yi ) are the βGLX and IRX coordinates for an individual galaxy, (xIRX , yIRX ) are the βGLX and IRX values of the starburst relationship that is closest to the galaxy coordinates, and dp is a dimensionless distance on the IRX diagram. We will be following the convention as defined in Kong et al. (2004) by assigning a positive dp distance for a galaxy that has a value of LTIR /LFUV lying above the starburst IRX relation and a negative dp for galaxies that lie below the starburst LTIR /LFUV value for a fixed β. All of the galaxies in our sample lie below the starburst IRX relation, giving all of our distances to be negative. Despite having a sample size of 98 galaxies in the range of log LTIR /LFUV < 0.5, there are more dusty galaxies present in the LVL survey that we did not include as they contained too much dust to be considered in our analysis. In order to guarantee complete sampling and sound statistics of any correlation with dp , we exclude galaxies that are right-ward of the dotted line drawn in the right-hand corner of Figure 1. This guarantees that any galaxies above log LTIR /LFUV > 0.5 not present in our sample does not make our dp results incomplete. 4. 4.1. Modeling Generating the Synthetic Spectral Energy Distributions The origin of the IRX scatter demands an understanding of the exact nature and origin of not only the overall dust content of each galaxy, but knowledge on the distribution of the stellar populations ages as well. Since we desire to better understand the underlying parameter that best accounts for the offset and spread of normal star-forming galaxies from the IRX relation for starburst galaxies, we want to explore and examine the parameters of each model that gives rise to the structure in each observed SED. We model the observed SED for each observed galaxy with synthetic models from Starburst99 (Leitherer et al. 1999). Our Starburst99 models draw from a range in metallicities of Z = 0.0004, 0.004, 0.008, and 0.020 using Padova stellar evolutionary model tracks or Padova tracks extended to include thermally pulsating asymptotic giant branch stars to the Starburst99 models. Our – 10 – models cover the age range of 10 Myr to 5 Gyr and are drawn from a Kroupa stellar initial mass function (IMF) from 0.1 M⊙ to 100 M⊙ , with exponents of 1.3 in the mass range of 0.1 − 0.5 M⊙ and 2.3 over the mass range 0.5 − 100 M⊙ for the stellar populations. The SED models use either a continuous SFR of 1 M⊙ yr−1 or a fixed mass (instantaneous burst) SFR with a total stellar mass of 106 M⊙ , using time steps of 0.1 × 106 yr. Our generated SEDs cover the wavelength range from 90 Å to 160 µm. We keep the star formation history very simple on purpose as we need only to divide the galaxies according to the two possible extremes of either instantaneous or constant star formation. Luminosities and colors are determined by convolving the generated synthetic SED with the spectral response function of the filters for all of our passbands from the FUV to 160 µm. The synthetic stellar spectra is convolved with the response function of each passband as R fλ Rλ dλ , (10) fλ,conv = Rλ Rλ dλ λ where Rλ is the filter response function and fλ is the flux density per unit wavelength (erg s−1 cm−2 Å−1 ) of the synthetic spectra at the effective wavelength for each passband, as listed in Table 2. It is these convolved flux values that we compare to the galaxy observations. The IR luminosity is calculated assuming that all attenuated stellar light is re-emitted by dust in the infrared. 4.2. Dust Attenuation Models The observed SED of galaxies in the UV and optical regime is determined by the intrinsic spectrum of the stellar population in addition to any reddening by presence of dust. While we specifically preselected our galaxies to have minimal dust effects, we have applied a range of color excess values from E(B − V ) = [0, 0.10] with steps of ∆E(B − V ) = 0.01 and values of E(B − V ) = [0.1, 0.3] in steps of ∆E(B − V ) = 0.05 to account for any non-negligible dust attenuation effects. We apply the attenuation to our unextinguished models according to the prescription, Fλ = Fλ,i × 10−0.4 k(λ) E(B−V ) , (11) where Fλ is the observed (reddened) flux (erg s−1 cm−2 ), Fλ,i is the intrinsic flux, E(B − V ) is the color excess of the stellar population, and k(λ) is the dust attenuation per wavelength model, where we adopt as a default the starburst attenuation curve (Calzetti et al. 2000). All models with color excess values of E(B − V ) > 0.1 produced too much IR emission that was not recovered in the IR; no model with the coarser sampling of ∆E(B − V ) = 0.05 above E(B − V ) = 0.1 was able to produce the observed IR emission. We do not add intrinsic – 11 – extinction effects to the galaxy observations; instead we use the extinguished models to estimate the dust content of each galaxy. 4.2.1. Variations in the Dust Extinction Models In this section, we explore the effect of adopting different extinction models on the IRX diagram. In addition to the starburst attenuation curve, we adopt a Small Magellanic Cloud (SMC; Bouchet et al. 1985) and a Milky Way (MW, with Rv = 3.1; Cardelli et al. 1989) extinction curve, with both foreground and mixed dust geometry. The foreground case is described by equation 11, while the homogeneously dust/stars mixed case is described as Fλ = Fλ,i 1 − e−τ , τ (12) where τ = 0.921 k(λ) E(B − V ), Fλ,i is the intrinsic flux, and Fλ is the observed (reddened) flux. Figure 2 shows the IRX diagram of a bursting galaxy at four different ages (100, 300, 700, 1000 Myr) with a fixed metallicity of Z = 0.0004, with an adopted starburst, MW, SMC, or a mixed-dust MW/SMC extinction curve. Since we are primarily showing how the value of βGLX changes with the age of the model, we have arbitrarily offset all the data to be consistent with log LTIR /LFUV = −1. Our findings agree with the results of Calzetti (2001); Johnson et al. (2007) that the MW extinction curve does a poor job at recreating the IRX diagram. When adopting the SMC extinction curve, galaxies with the same color excess value E(B − V ), age, and metallicity are both redder in color and have smaller FUV contributions compared to observations using the starburst attenuation curve. This shows the importance of adopting an accurate attenuation; selecting different extinction curves can significantly change the location of a galaxy on the IRX diagram. Changing the assumed extinction model changes the fraction of younger galaxies recovered, as adopting a SMC extinction curve results in more optical to near-IR light contributed from an aging stellar population as opposed to the amount contributed from dust, resulting in older populations recovered. This result is consistent with the work of Reddy et al. (2010, 2012), which showed that adopting a SMC extinction curve, compared to a starburst attenuation curve, does generally yield galaxies with older stellar populations. Mixed dust models trace out the same locations in the IRX diagram as their foreground dust counterparts, however there is smaller range in both βGLX and the IRX values for the mixed dust models. – 12 – Fig. 2.— Top panel: The IRX diagram, showing how a galaxy with a bursting star formation at a fixed metallicity evolves from 100 Myr to 1 Gyr. The shapes of the colors represent the age of the galaxy model, where all blue points represent galaxies with an adopted MW extinction curve, black shapes represent galaxies with an assumed starburst (SB) attenuation curve, red shapes represent galaxies with an adopted SMC extinction curve, pink shapes represent galaxies with a mixed dust (MD) SMC extinction curve, and the purple points represent galaxies with a MD MW extinction curve. The size of each shape represents the color excess value E(B − V ) from 0.0 to 0.07 in steps of 0.01. Each model has been given an offset, normalized to log LTIR /LFUV = −1. Bottom panel: A zoom in of the evolution of 100 Myr with an adopted SB attenuation model, where the colored points represent models with different metallicities, with black representing a metallicity of Z = 0.0004, green representing Z = 0.004, magenta representing Z = 0.008, and cyan representing Z = 0.020. – 13 – Since the UV spectral slope βGLX is dependent on the adopted extinction law, it is expected to find βGLX changing with variations in the extinction curve. Since the FUV flux is predominately supplied by the very young stellar population and the flux in the NUV has a larger contribution from older stars, the UV colors are primarily a measurement of the obscuration of the stellar populations as opposed to supplying information on dust effects, as found by Kong et al. (2004). 4.3. Fitting the SED and Estimations of the Stellar Population Age In order to determine how well the models compare to the observed data, each model is allowed an offset c that minimizes χ2 between the fluxes of the model and the observed data points. The physical properties of the best-fit models allows us to describe the properties of the observed galaxies. Since there are generally at least two stellar populations contributing to the observed SED, we do the fitting of each galaxy from the FUV to Ks bands, where the 3.0-160 µm bands are used purely to estimate the dust luminosity and not the age of the stellar population giving rise to the observed UV and optical stellar continuum. For each galaxy i in our sample, the best-fit model is determined with a χ2 minimization in the following way: X Fobs,B − ci Fmod ,B i 2 , (13) χi = σ(Fobs,B ) B where we sum over the bands FUV, NUV, U, B, V, J, H, and Ks, giving us seven degrees of freedom in determining the scale factor c. Fobs,B is the observed flux at each band pass, σ(Fobs,B ) is accompanying 1σ errors, Fmodi ,B is the flux of each individual model, and ci is the offset that best matches the model and the observed galactic fluxes, calculated as X Fobs,B Fmod ,B . X Fobs,B 2 i . ci = 2 (F σ σ(Fobs,B ) obs,B ) B B (14) The best-fit model is determined by plugging in the value of ci for each model into χ2i . Each χ2i value for each model is then assigned a weight wi = exp(−χ2i /2), giving a probability distribution function (PDF) for the galaxy parameters of interest. We do not automatically assign the physical properties associated with χ2best to describe the observed SED. Instead, the average of the models that lie within a factor of three of χ2best is accepted as an initial estimate of the specific galaxy parameter of interest (age, metallicity, color excess E(B − V ), and star formation type). This process makes sure that we have not selected a single model that fits the galaxy observations by chance. The range of acceptable parameter values for each galaxy, as determined from the PDF, is the range allowed for each parameter and is – 14 – represented as an error bar in all the following figures. Our χ2 routine is performed using YAFITS in the Java programming language. Even with the best-fit model that minimizes χ2 with n input parameters, there is often times an arbitrarily large number of acceptable models that all provide reasonable fits to the data. We further refine the total number of acceptable models for each galaxy through conservation of energy: The total amount of light absorbed due to dust attenuation in the range 912 − 22, 000 Å has to equal the aggregate emission from all the dust grains, LTIR . Any model that does not meet this criterion is rejected. Table 1 lists the best-fit model and range for each galaxy. Some galaxies are satisfied with both bursting and continuous star forming models; these galaxies have both models listed in Table 1 but we only show the bursting model in all of our plots. Figure 3 shows an example of a best-fit Starburst99 model to a set of observations from the FUV to the Ks band for IC 1574. 5. 5.1. Results and Analysis The Color Excess E(B − V ) We apply extinction to the stellar population of our synthetic models according to Eq. 11, where the color excess values range from E(B −V ) = [0, 0.10] with steps of ∆E(B −V ) = 0.01 and coarser sampling, with values of E(B − V ) = [0.1, 0.3] with steps of ∆E(B − V ) = 0.05. Figure 4 shows E(B − V ) as a function of βGLX and Figure 5 shows E(B − V ) as a function of dp ; as expected, galaxies in the range 0 < IRX < 0.5 have a higher average E(B − V ) value than galaxies at IRX< 0. We find no correlation between the color excess of the best-fit model of each galaxy to the UV spectral index βGLX . This leads us to believe that the UV spectral index is not a good indicator of the dust content as traced by the virtually dust-free galaxies in our study. When examining the relation between E(B − V ) with dp , we find that there is a general trend for an increase in the observed color excess of the stellar population as a galaxy lies closer to the starburst IRX relation, as seen in Figure 5. While this suggests a general trend toward redder colors with an decrease in the perpendicular distance (galaxies that are located closer to the starburst IRX relation), the relation is not significant enough for us to conclude that the galaxies with the least amount of dust are located further away from the starburst IRX relation than more dusty galaxies. We have listed both the Spearman rank correlation coefficient ρ and the Kendall correlation coefficient τ for nearly every variable in our study as a function of both βGLX and dp in Table 5 for the entire sample of galaxies, Table 3 for bursting galaxies and Table 4 for continuous galaxies, where the significance of the correlation is generally 3.5σ or smaller. In addition, we separate into subsets on the IRX diagram, where we perform statistics on the galaxies below and above log LTIR /LFUV < 0 for each table. – 15 – Fig. 3.— A best-fit Starburst99 SED from the FUV to the Ks bands for IC 1574. The galaxy observations are represented with crosses and accompanying 1σ error bars. The solid circles represent the convolved flux values at each wavelength. The value of χ2best is 0.5. – 16 – Fig. 4.— The color excess E(B − V ) of the best-fit model for each galaxy as a function of the UV spectral index βGLX . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. – 17 – Fig. 5.— The color excess E(B − V ) of the best-fit model for each galaxy as a function of the perpendicular distance dp . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. – 18 – The Birthrate b-Parameter 5.2. The birthrate parameter (b-parameter) is the ratio of the current star formation to its overall lifetime average (Kennicutt et al. 2008) and is independent of distance. The b-parameter is often also denoted as a measure of the SFR per stellar mass, written as b= SFR SFR t0 (1 − R) = , hSFRipast Mstar (15) where where t0 is the age of the galaxy (usually taken to be ∼12 Gyr), Mstar is the total stellar mass of the of the galaxy, and R is the fraction of gas that stars reinjected through stellar winds into the interstellar medium during their lifetime. We use both the ratio of the FUV to near-IR (NIR) luminosities and the equivalent width (EW) of Hα as proxies for the birthrate parameter to investigate if the age of the stellar population and the SFH is responsible for the deviation of normal star-forming galaxies from the starburst IRX relation. 5.2.1. The FUV to NIR Luminosity Ratio We examine the ratio of the FUV (1520 Å) to NIR (3.6 µm) as a tracer of the bparameter as the FUV traces star formation activity over very recent times (∼100 Myr) while the NIR traces the total stellar mass built up over much longer timescales. The ratio roughly gives the SFR per unit stellar mass, providing a normalized measure of the star formation activity. The FUV/NIR ratio is very sensitive to extinction affects, and we have corrected our observed FUV luminosities for extinction effects according to Eq. 11, where the color excess values E(B − V ) are taken from the best-fit SED models to the galaxy observations. The FUV/NIR ratio is calculated as FUV/NIR = νLν (1520 Å) . νLν (3.6 µm) (16) Figure 6 and Figure 7 shows the FUV/NIR ratio as a function of βGLX and dp , respectively. There is considerable spread between FUV/NIR and dp ; we do not find any correlation between the FUV/NIR ratio and dp , in disagreement with the results of Dale et al. (2009). However, when taking into consideration the b-parameter and βGLX , there is an increasing redness in the UV colors with lower values of the birthrate parameter, where the statistics between the type of galaxy and and FUV/NIR ratio is listed in Table 3 for bursting galaxies, Table 4 for continuous galaxies, and Table 5 for the entire sample of galaxies. The correlation in this case is very significant, especially for bursting galaxies, significant at the 5σ level. – 19 – Fig. 6.— The log of the FUV/NIR ratio of each galaxy as a function of the UV spectral index βGLX . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The size of the circles/squares represents the age for the best-fit models, shown in the right-hand panel. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. – 20 – Fig. 7.— The log of the FUV/NIR ratio of each galaxy as a function of the UV spectral index dp , the perpendicular distance to the starburst IRX relation. The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The size of the circles/squares represents the age for the best-fit models, shown in the right-hand panel. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. – 21 – 5.2.2. Hα Equivalent Width We use the EW(Hα) emission line to estimate the intensity of the current star formation over the past average as another proxy for the b-parameter, where the EW(Hα) is much less sensitive to extinction effects compared to the FUV/NIR ratio. The EW(Hα) is the ratio of the luminosity of the Hα emission line to the continuum luminosity at λHα = 6563 Å, where the emission line is primarily produced by young, massive stars (> 10M⊙ ) over short timescales and the red continuum luminosity at 6365 Å traces the total mass built up from older stars at much longer timescales (Kennicutt et al. 1994). The EW(Hα) measurements are taken from Kennicutt et al. (2008), where the Hα flux is corrected for contamination from [NII] as EW(Hα + [NII]) , (17) EW (Hα) = 1 + [NII]/Hα where we have EW(Hα) measurements for 93 out of our 98 galaxies. The EW(Hα) allows us to circumvent the problem of lack of correlation between the current duration of star formation as a function of βGLX for continuous galaxies. Figure 8 and Figure 9 show the EW(Hα) of our galaxies as a function of βGLX and dp for both continuous and bursting star forming galaxies, respectively. The relation between the EW(Hα) and βGLX is only slightly more significant. The significance of both the Spearman and Kendall correlations are given in Table 3 and Table 4 for both EW(Hα) as a function of perpendicular distance and EW(Hα) as a function of βGLX . In all cases, the correlation is marginally significant, between 3σ and 4σ. It is important to note that an increase in the amount of dust can reduce the observed EW(Hα) if there is differential attenuation in gas emission and stellar continuum (Hao et al. 2011). We would expect an increase in the scatter between the EW(Hα) and dp /βGLX as galaxies with brighter LTIR /LFUV ratios are examined. However, for our low-dust, normal star-forming galaxies, we believe this effect to be negligible. 5.3. Stellar Population Age Estimators We employ the U − B colors to place additional constraints on the effects of the age of the stellar populations on the IRX diagram. We use the log (LU /LB ) color ratio as an age indicator as this ratio is straddles the 4000 Å region, which is sensitive to the age of the galactic stellar populations. The narrow bands of the D(4000) spectral discontinuity, the ratio of the flux densities in the bands of 3850 − 3950 Å and 4000 − 4100 Å, allow it to be fairly insensitive to dust and highly correlates with the b-parameter (Kauffmann et al. 2003). This makes D(4000) a valuable indicator of the mean stellar population age. The log (LU /LB ) colors are more sensitive to dust attenuation than the D(4000) break, but are – 22 – Fig. 8.— The Hα equivalent width (EW) of each galaxy as a function of the UV spectral index βGLX . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The size of the circles/squares represents the age for the best-fit models, shown in the right-hand panel. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The solid black line represent the leastsquares fit to the galaxies best represented with bursting SFRs and the dotted line represents the least-squares fit to the galaxies represented with continuous SFRs. – 23 – Fig. 9.— The Hα equivalent width (EW) of each galaxy as a function of the perpendicular distance dp . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The size of the circles/squares represents the age for the best-fit models, shown in the right-hand panel. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The solid black line represents the leastsquares fit to the galaxies represented with bursting SFRs (N = 33) and the dotted line represents the least-squares fit to the galaxies represented with continuous SFRs (N = 57). – 24 – are still highly sensitive to the mean population age. Figure 10 shows the U − B colors as a function of the UV colors, βGLX . When we divide the sample into bursting and continuous star forming galaxies, the bursting (continuous) galaxies have a Spearman correlation coefficient value of ρ = −0.64 (ρ = −0.48), significant to the 3.9σ (3.7σ) level for our sample size of bursting (continuous) galaxies. A Kendall correlation coefficient gives a significance level of 4.3σ (4.1σ) at ρ = −0.49 (ρ = −0.36). While an increase in the redness of the U − B colors is accompanied with an increase in the redness of the UV colors, we do not consider this correlation to be very significant. The U − B color has a Spearman correlation that is significant at the 2.7σ level to the perpendicular distance dp (Figure 11) from the starburst IRX relation, where we disregard the three galaxies that are above the dp completeness line in Figure 1. A Kendall correlation gives a coefficient that is significant at the 2.9σ level. This leads us to believe that the stellar population, as traced by U − B colors, is not responsible for the perpendicular deviation of normal star-forming galaxies from the starburst attenuation relation. Kong et al. (2004) found a strong correlation (5σ significance) between the D(4000) break and dp . We do not recover this relation between dp and the age of the stellar population. However, D(4000) is largely insensitive to dust, while our estimate of the stellar population age, log (LU /LB ), is largely sensitive to the presence of dust, despite the criterion of our galaxies being largely dust-free. Figure 12 shows the age of each galaxy – determined from a χ2 fitting to our models – as a function of the UV spectral index βGLX , where the range of ages of acceptable models gives the size of the vertical error bars. There is a trend toward increasing age with increasing redness in bursting galaxies, however, there does not appear to be any visible trend in continuous star-forming galaxies. The distribution of stellar age in continuous star forming galaxies seems to show a build up at 5 Gyr, the oldest age value we consider. This occurs because bursting star-forming galaxies pins down an age for the stellar population, while the age for continuous star-forming galaxies gives a duration of the SFH, not revealing any information about the mean age of the stellar population. For the bursting galaxies, we determine the optimal fit to the data with a Levenberg-Marquandt algorithm for non-linear least-squares optimization, where our function is of the form log Age(βGLX ) = log[10A1 βGLX +A2 − 1] + A3 . (18) The statistics between the age and βGLX for the entire sample of bursting and continuous star-forming galaxies can be found in Table 3 and Table 4. We have listed both the Spearman rank correlation coefficient ρ and the Kendall correlation coefficient τ , where we separate out the continuous and bursting star-forming galaxies in addition to separating into subsets – 25 – Fig. 10.— The U − B colors as a function of the UV colors βGLX . U − B is expressed as the ratio of the fluxes of the two bands log (LU /LB ) and the UV colors are expressed as βGLX . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The solid black line represent the least-squares fit to the galaxies best represented with bursting SFRs and the dotted line represents the least-squares fit to the galaxies represented with continuous SFRs. The size of each square/circle represents the age of the best-fit model, shown in the right-hand panel. The average error bar size is shown in the top right-hand corner. – 26 – Fig. 11.— The U −B colors as a function of the perpendicular distance dp . U −B is expressed as the ratio of the fluxes of the two bands log (LU /LB ) and the UV colors are expressed as βGLX . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The solid black line represent the least-squares fit to the galaxies best represented with bursting SFRs and the dotted line represents the least-squares fit to the galaxies represented with continuous SFRs. The size of each square/circle represents the age of the best-fit model, shown in the right-hand panel. – 27 – Fig. 12.— Top panel: The age of each galaxy as a function of βGLX for galaxies that are best-fit with continuous SFRs (open circles). Bottom panel: The age of each galaxy as a function of βGLX for galaxies that are best-fit with bursting SFRs (solid squares). The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The solid black line represent the least-squares fit to the entire sample of bursting galaxies. The vertical error bars represent the range of acceptable model ages for each galaxy. – 28 – on the IRX diagram; the galaxies below log LTIR /LFUV < 0 and the galaxies in the regime 0 < log LTIR /LFUV < 0.5. We find that for the bursting galaxies, the correlation between age and βGLX is very significant > 4σ. The results of age with perpendicular distance dp can also be found in 3 and Table 4. For the bursting galaxies, we find that the perpendicular distance also correlates with the age of the young stellar population (Figure 13). Overall, we find that the relation between age and perpendicular distance, in addition to βGLX , is very sensitive to the presence of dust attenuation, decreasing in significance for increasing attenuation. 5.4. Metallicity We have gathered oxygen (12+log(0/H)) metallicity measurements for 61% of the galaxies in our sample (60/98) from the literature. Since metallicity is a parameter we allow to vary in the Starburst99 spectra, when a galaxy has a measured metallicity value available, we require the generated SED models to match the metallicity of the observed data. If there is no metallicity known a prior, the metallicity of the synthetic SEDs are allowed to accept any metallicity between Z = 0.0004 to 0.02. Figure 14 shows the metallicity as a function of the UV spectral index. Over 93% of the galaxies in our sample with known metallicity measurements lie below the solar metallicity value; LVL galaxies that lie in the bottom region of the IRX diagram are sub-solar metallicity galaxies. Figure 15 shows the metallicity as a function of the perpendicular distance. Again, we fail to recover any correlation between the distance from a galaxy to the IRX relation for starburst galaxies and the metallicity of the galaxy. Since our sample excluded dust-rich galaxies, we can conclude that the correlation between metallicity and β is not a fundamental one. – 29 – Fig. 13.— Top panel: The age of each galaxy as a function of perpendicular distance dp for galaxies that are best-fit with a continuous SFR (open circles). Bottom panel: The age of each galaxy as a function of perpendicular distance dp for galaxies that are best-fit with a bursty SFR (solid squares). The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The vertical error bars represent the range of acceptable model ages for each galaxy. – 30 – Fig. 14.— 12+log(O/H) measurements as a function of the UV spectral slope βGLX for our sample. The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The size of the galaxy symbols represent the best-fit age of each galaxy, represented by the legend on the right-hand panel. The vertical error bars represent the 1σ error for the metallicity values. The solid dotted line represents the solar metallicity value. – 31 – Fig. 15.— 12+log(O/H) measurements as a function of the perpendicular distance dp . The solid squares represent galaxies that are best-fit with bursting SFRs and open circles represent galaxies that are best-fit with continuous SFRs. The colors represent the location of each galaxy on the IRX diagram, where red points represent galaxies with an IRX value of 0 < log LTIR /LFUV < 0.5 and blue points represent galaxies with an IRX value of log LTIR /LFUV < 0. The size of the galaxy symbols represent the best-fit age of each galaxy, represented by the legend on the right panel. The solid dotted line represents the solar metallicity value. – 32 – 6. Discussion Figure 12 shows the main result of our study: We find that examining galaxies by their star formation type (continuous or bursting) gives the best insight on the parameter responsible for the deviation of normal star-forming galaxies from the IRX attenuation relation, where the age of the stellar population increases with increasing values of βGLX for bursttype galaxies. The same age−βGLX trend is not present in continuous galaxies. For bursting galaxies, the age-βGLX relation, either directly derived from SED fittings or approximated with the FUV/NIR color, is the strongest correlation we find for the “second parameter”, with a Kendall τ correlation coefficient significance at the 5.1σ level for bursting galaxies and at the 6σ level for our entire sample of galaxies. This may help alleviate confusion in prior scientific studies that failed to reveal any type of relation between the age of the stellar population and β; studies that are predominantly composed of continuous star-forming galaxies will not reveal a connection between the age and the UV spectral index as determined by SED fitting. The increase in the age of the duration of current star formation for our bursting galaxies is in agreement with Burgarella et al. (2005); Dale et al. (2009) but disagrees with the work of Siebert et al. (2005); Boquien et al. (2009). Figure 13 shows the age as a function of the perpendicular distance from the starburst IRX relation, where we do not see the strong correlation for bursting galaxies as traced by βGLX , suggesting that the “second parameter” may not be determined with the distance from the IRX relation for starburst galaxies. Figure 16 shows the IRX diagram accounting for the type of star-formation and the age that best represents the observed SED for each galaxy from Starburst99 SEDs. The intrinsic ultraviolet spectral slope βGLX is sensitive to the age of the stellar population, where the evolved young stellar population (∼100 Myr) dominates the UV emission in normal star-forming systems. As a result, the increased contamination in the UV spectral slope from evolved stellar populations exhibits itself as a larger dispersion for normal starforming galaxies in the IRX diagram. We do not believe the U − B colors, which serve as a proxy for the D(4000) break and an indicator of the SFH, to be a good indicator of the mean stellar population age for the low-dust, local galaxies of our survey. Dale et al. (2009) found that a majority of the galaxies in the LVL survey showed signs that the outer edges were older than the inner regions of the galaxies. As a result, the observed global total luminosity ratios of the TIR to FUV for normal star-forming galaxies will appear to have a redder stellar population and a mixing of all stellar populations present. They observed that this global flux issue may be why LVL galaxies tend to exhibit older stellar populations than those seen in more active star-forming galaxies, an issue that could be resolved with spatial resolution studies of galaxies. We have also examined the relationship between the metallicity and βGLX (or dp ), where – 33 – Fig. 16.— The IRX diagram, showing the ratio log LTIR /LFUV as a function of βGLX , the UV spectral index. All downward pointing arrows represent galaxies with upper limit values of LTIR . The solid black squares represents galaxies that are best-fit with bursting SFRs and the open circles represent galaxies that are best-fit with a continuous SFR. The solid black line shows the starburst IRX attenuation relation, determined by a least-squares fit to the starburst galaxies from Meurer et al. (1999). The perpendicular distance dp represents the shortest distance between each galaxy to the starburst attenuation curve. The size of each square/circle represents the age of the best-fit model, shown in the right-hand panel. The average error bar size is shown in the bottom right-hand corner. – 34 – we expect metal rich galaxies to present more UV attenuation when compared with metalpoor galaxies. The work of Cortese et al. (2006) found a correlation between βGLX and the 12+log(O/H) value, where the correlation was nearly the same for both starburst and normal star-forming galaxies, significant at the 3σ level. We do not replicate the metallicity−βGLX relation as seen in Cortese et al. (2006); galaxies with redder UV spectral colors do not necessarily represent galaxies with higher metallicities. The correlation found by Cortese et al. (2006) may simply reflect a change in β due to increased dust attenuation in more metal-rich galaxies. Because our sample excludes the dust-rich galaxies as used in the Cortese et al. (2006) sample, it is not surprising that our results fail to find the metallicity−βGLX relation, where we believe the correlation between metallicity and βGLX as seen by Cortese et al. (2006) is an attenuation effect and not driven by metallicity. The strongest correlation for our galaxies described with continuous star formation are the EW(Hα) and FUV/NIR colors versus βGLX ; in this case the EW(Hα) of our normal star-forming galaxies supports the hypothesis that the present to past-averaged SFR may be the second parameter responsible for the deviation of normal star-forming galaxies from the IRX relation as compared to the dust content of the galaxy, in agreement with previous results (Kong et al. 2004; Dale et al. 2009). Both our continuous star-forming galaxies and our instantaneous star-forming galaxies have linear trends of EW(Hα) that correlate with the perpendicular distance, however this correlation is only significant to the 4σ level. The strongest correlation for our entire sample of galaxies is the FUV/NIR colors versus βGLX , with a significance greater than the 6σ level. We believe the “second parameter”, as traced by the FUV/NIR ratio, does suggest that the mean age of the stellar population depends on the UV colors but not on the distance from the starburst IRX relation. 7. Conclusions We present a multiwavelength analysis of a sample of 98 dust-free normal star-forming spiral and compact galaxies from the Spitzer LVL survey. Our work attempts to study normal star-forming galaxies on the IRX diagram, a method used to account for dust attenuation in galaxies from observations solely in the UV (Meurer et al. 1999; Calzetti 2001), where the relationship breaks down for non-starburst galaxies. We focused on investigating the impact that the underlying stellar population age has on the IRX, where we model galaxy observations with a combination of UV, optical, and IR photometric data to better understand if the stellar population mean age or other characteristics are the second parameter responsible for the failure of the starburst attenuation relation to apply to normal star-forming galaxies. To re-construct the full UV through near-IR SED curve for our 98 galaxies, we use – 35 – Starburst99 to produce synthetic model spectra (metallicities of Z = 0.0004 to 0.020, a Kroupa IMF from 0.1 M⊙ to 100 M⊙ , a continuous or bursting SFH having an age range of 10 Myr to 5 Gyr) that are representative of extremes in the SFH of our observations. The comparison between the galaxy observations and our synthetic models are done with a reduced χ2 routine in order to find the best-fit model which produces the best match between the observed SED and the assumed, synthetic SED. In addition, all models must correctly account for the amount of stellar light in the UV and optical that is absorbed by dust and re-radiated away in the FIR. We use both the ratio of the FUV to NIR luminosity and the EW(Hα) to serve as tracers of the birthrate parameter, b-parameter. We find that for galaxies that are best represented with a bursting star formation type, there is a correlation between both the age of the stellar population from direct modeling and the mean stellar population age, as traced by the FUV/NIR colors, and βGLX to the UV attenuation relation for starburst galaxies. This correlation does not hold for galaxies that are best-fit with a continuous SFR, as the age is indicative of the duration of current star forming activity. The strong correlation of the FUV/NIR ratio with βGLX indicates that bursting systems with lower birthrates are associated with redder UV colors, and less significantly, closer to the starburst IRX relationship. This suggests that the SFH does play a role in determining the location of a galaxy on the IRX diagram, where the longest-lasting star forming systems are located further from the starburst IRX curve and/or in the reddest systems. This FUV/NIR color ratio is the strongest when we consider the entire sample of galaxies, suggesting that the mean age of the stellar populations highly depends on the amount of UV reddening of the system, regardless of whether the SFH is bursting or continuous. We also find that for both continuous and bursting star forming galaxies, the U − B colors – which serve as a SFH indicator – do not correlate with the distance from the starburst attenuation curve, however, redder U − B colors are well represented with redder βGLX colors for the entire sample of galaxies, continuous and bursting. We find that the EW(Hα) of galaxies that are well represented with a continuous SFR correlate with the distance from the starburst attenuation relation on the IRX diagram. We also find that the age of the constant SFR galaxies tend to be old (∼5 Gyr), where low and intermediate age ranges are sparse. Galaxies that are well-defined with bursting SFHs, as opposed to continuous SFHs, cover the full age range explored and are generally much younger than the age of continuous star-forming galaxies. This relation between EW(Hα) and dp for continuous galaxies is the only correlation we find with dp in our entire sample of galaxies. The near lack of any correlation to any variable with the perpendicular distance on the IRX diagram suggests that the second parameter responsible for the scatter of normal star-forming galaxies and does not depend on the distance from the starburst IRX relation, – 36 – but instead with increasing redness, as measured with β. Lack of evidence that the scattering parameter scales in the direction of dp indicates that the source of the scatter for normal star-forming galaxies is mainly along the horizontal direction, as probed by β. While the dust content is the predominant driver for the location of galaxies on the IRX diagram (which is especially evident in galaxies with increasing values on the IRX), our results support evidence that the location of normal star-forming galaxies is affected by both dust content and the mean stellar population age. Therefore, the attenuation cannot be determined for normal star-forming galaxies as a simple relation from the UV colors alone as it can for starburst galaxies. The effect of the star formation history on quiescent galaxies is better understood when the galaxies are binned into two groups, represented with bursting or continuous SFRs. Once the galaxies have been separated by types of SFRs, the effect of the stellar population age is then better understood and how that influences their location on the IRX diagram. The large scatter between βGLX and log LTIR /LFUV for normal starforming galaxies implies that a greater care must be used to determine if βGLX is a viable means to recover the intrinsic UV flux lost to dust attenuation, as already supported by Hao et al. (2011). However, as the dust content of a galaxy increases, the dust distribution also plays a role in increasing the scatter in β at a fixed IR/UV ratio, as concluded by prior studies. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Funding for SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the MaxPlanck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. This publication makes use of data products from the Two Micron – 37 – All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. We gratefully acknowledge NASAs support for the GALEX mission, developed in cooperation with the Centre National dEtudes Spatiales of France and the Korean Ministry of Science and Technology. Knock knock! Who’s there?! Cows go. Cows go who? No, silly; cows go moo! 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Jr., & Huchra, J.P. 1994, ApJ, 420, 87 This preprint was prepared with the AAS LATEX macros v5.2. – 41 – Table 1. Galaxy Properties Galaxy R.A. Dec. D (Mpc) SFR Age (Gyr) EW(Hα) (Å) log LTIR (L⊙ ) IRX 12+log(O/H) B C B B B B C C B C C B B C C C B C C C B C C B C B C C C C B C C C C C C B B C C C C C C 0.5+0.2 −0 5+0 −0 0.7+0 −0.2 0.5+0.2 −0 0.7+0 −0.2 0.4+0.1 −0 5+0 −0 5+0 −0 0.5+0.5 −0 +0 5−0 5+0 −0 0.7+0 −0.2 0.3+0.1 −0 5+0 −0 5+0 −0 5+0 −0 +0 0.1−0.13 5+0 −0 5+0 −0 5+0 −0 0.4+0.3 −0 5+0 −0 5+0 −4 0.2+0.5 −0.13 5+0 −0 0.5+0.2 −0 5+0 −0 5+0 −0 5+0 −0 +0 5−0 0.4+0.1 −0.1 1+0 −0 5+0 −0 5+0 −0 0.7+0.3 −0 1+0 −0.3 +0 0.3−0.1 0.4+0.1 −0.12 0.7+0 −0.2 5+0 −0 5+0 −0 2.5+2.5 −1.5 5+0 −0 5+0 −0 0.7+0.3 −0 16.2 31.2 32.8 35.2 8.65 0 9.24(5) 8.87(5) 7.50(4) 8.88(3) <7 <6.5 0.29(2) −0.12(2) 0.238(9) 0.122(16) < −0.11 < −0.19 8.93(11)1 ··· 8.05(10)2,3 8.40(11)4 ··· ··· 20 12.5 20.6 20.5 27.9 29.6 26.9 22.8 33.6 26.1 30.6 50.9 31.3 10.8 55.5 100 25.6 9.31(5) 7.43(6) 7.24(5) 8.50(12) 9.01(2) 7.49(6) 7.50(4) 9.40(4) 7.97(8) 9.02(3) 7.73(4) 8.34(4) 9.37(3) 8.28(4) 8.85(3) 7.84(4) 8.64(9) 0.037(2) −0.50(3) −0.66(2) 0.298(2) 0.416(15) −0.45(2) −0.68(2) 0.204(19) −0.362(15) 0.059(9) −0.194(19) 0.107(14) −0.0030(15) 0.45(2) 0.0761(15) −0.624(17) −0.29(2) 8.73(4)3,5,6 8.20(10)7,8 7.94(5)9,10 8.36(5)11,3,12 8.10(10)13,4 7.97(3)1 7.70(10)14,15,4 ··· 7.7(1)1 8.41(9)3,16 ··· 8.2(2)17,18 8.4(2)19,17 8.56(12)1 8.20(12)20 8.21(5)21,19 ··· 26.5 30.7 35.7 33 24.4 9.35 122.5 17.4 15.5 43.3 31.4 8.65 5.88 4.81 25.7 43.8 54.6 46.9 42.7 35.2 8.32(4) 8.70(4) 8.70(4) 8.14(4) 8.27(7) <7.7 6.98(4) 7.42(5) 6.78(2) 7.51(4) <7.1 6.49(2) <5.5 5.89(6) 6.87(5) 7.34(3) 8.96(4) 8.09(4) 6.88(6) 8.01(4) 0.045(18) 0.173(18) 0.225(17) −0.239(13) −0.112(14) <0.027 −0.328(17) −0.19(4) −0.13(2) −0.572(18) < −0.73 −0.97(3) −0.693(4) −1.28(3) −0.26(2) −0.233(15) −0.066(16) −0.175(13) −0.65(3) −0.514(11) 8.4(2)19,22 ··· 7.71(10)23,24 8.08(19)25,26 8.39(17)26,27 ··· 7.52(8)28,29,27,4 8.2(2)10 ··· 7.83(8)30,31 7.21(3)32,33 8.7(3)56 7.30(5)34,29 7.84(5)29,35,36,37 7.98(10)38 ··· ··· 8.3(3)22,27 7.95(4)7,8,33 8.30(10)7,8 NGC 24 NGC 45 NGC 55 NGC 59 IC 1574 UGCA 15 00 00 00 00 00 00 09 14 14 15 43 49 56.5 04.0 53.6 25.1 03.8 49.2 −24 −23 −39 −21 −22 −21 57 10 11 26 14 00 47 55 48 40 49 54 8.13 7.07 2.17 5.3 4.92 3.34 NGC 300 UGC 891 UGC 1104 NGC 598 NGC 625 UGC 1176 ESO 245−G005 NGC 672 ESO 154−G023 NGC 1313 NGC 1311 NGC 1487 NGC 1510 NGC 1512 NGC 1522 NGC 1705 NGC 1744 00 01 01 01 01 01 01 01 02 03 03 03 04 04 04 04 04 54 21 32 33 35 40 45 47 56 18 20 55 03 03 06 54 59 53.5 18.9 42.5 50.9 04.6 09.9 03.7 54.5 50.4 16.1 07.0 46.1 32.6 54.3 07.9 13.5 57.8 −37 +12 +18 +30 −41 +15 −43 +27 −54 −66 −52 −42 −43 −43 −52 −53 −26 41 24 19 39 26 54 35 25 34 29 11 22 24 20 40 21 01 04 43 02 37 10 17 53 58 17 54 08 05 00 56 06 40 20 2 10.84 7.5 0.84 4.07 9 4.43 7.2 5.76 4.15 5.45 9.08 9.84 9.64 9.32 5.1 7.65 NGC 1800 NGC 2500 NGC 2537 UGC 4278 NGC 2552 UGC 4426 UGC 4459 UGC 4787 CGCG 035−007 UGC 5272 UGC 5340 UGC 5336 UGC 5364 UGC 5373 UGC 5423 UGC 5456 NGC 3239 NGC 3274 UGC 5764 UGC 5829 05 08 08 08 08 08 08 09 09 09 09 09 09 10 10 10 10 10 10 10 06 01 13 13 19 28 34 07 34 50 56 57 59 00 05 07 25 32 36 42 25.7 53.2 14.6 58.9 20.5 28.4 07.2 34.9 44.7 22.4 45.7 32.0 26.5 00.1 30.6 19.6 04.9 17.3 43.3 41.9 −31 +50 +45 +45 +50 +41 +66 +33 +06 +31 +28 +69 +30 +05 +70 +10 +17 +27 +31 +34 57 44 59 44 00 51 10 16 25 29 49 02 44 19 21 21 09 40 32 26 15 14 23 32 35 24 54 36 32 16 35 45 47 56 52 43 49 08 48 56 8.24 7.63 6.9 7.59 7.65 10.28 3.56 6.53 5.17 7.1 5.9 3.7 0.69 1.44 5.3 3.8 8.29 6.5 7.08 7.88 – 42 – Table 1—Continued Galaxy NGC 3344 UGC 5889 UGC 5923 UGC 5918 NGC 3432 NGC 3486 UGC 6457 UGC 6541 NGC 3738 NGC 3741 UGC 6782 UGC 6817 UGC 6900 NGC 4068 NGC 4144 NGC 4163 UGC 7267 CGCG 269−049 NGC 4288 UGC 7408 UGCA 281 UGC UGC NGC UGC 7559 7577 4449 7599 UGC 7605 UGC 7608 NGC 4485 UGC 7690 UGC 7698 UGC 7719 UGC 7774 NGC 4618 NGC 4625 UGC 7866 NGC 4707 UGC 8024 UGC 8091 UGCA 320 UGC 8201 NGC 5023 CGCG 217−018 R.A. Dec. D (Mpc) SFR Age (Gyr) EW(Hα) (Å) log LTIR (L⊙ ) IRX 12+log(O/H) B B B B C C C C C C B B B C C B C C C B B C C B C B B C C B C C B C C C C B B B C C C C B 0.7+0.3 −0.2 0.7+0 −0.2 0.5+0 −0.2 0.4+0.1 −0.1 5+0 −0 +0 5−0 5+0 −0 5+0 −0 5+0 −0 1+4 −0 0.7+0.3 −0.2 0.3+0.1 −0 0.7+0.3 −0.2 5+0 −0 5+0 −0 0.5+0.2 −0 5+0 −0 5+0 −0 5+0 −0 1+0 −0.5 0.03+0.07 −0 0.1+0.2 −0 5+0 −0 0.7+0 −0.2 5+0 −0 +0.3 0.2−0.1 0.1+0.1 −0 0.8+0.2 −0.1 +0 5−0 0.1+0 −0.13 5+0 −0 5+0 −0 0.7+0 −0.2 5+0 −0 5+0 −0 5+0 −0 5+0 −0 0.1+0.1 −0 0.7+0 −0.2 0.07+0.13 −0 1+0 −0 1+0 −0.3 5+0 −4 5+0 −0 0.5+0.2 −0 27 7.34 13 18.1 54.2 34.7 25.2 82.7 23.9 54.9 0 25 9.43 26.2 19.3 6.78 10.5 0 40.5 0 325.2 9.43(5) <7.7 7.45(4) <7.3 9.24(8) 9.37(4) 7.36(6) 6.72(4) 8.16(4) 6.50(2) <7.8 6.37(6) <7.4 7.45(4) 8.83(4) 6.59(5) 7.10(6) <6.3 8.37(4) <7.4 7.49(3) 0.38(2) −0.070(4) 0.233(13) −0.064(4) 0.357(18) 0.22(2) −0.44(3) −0.78(5) −0.029(16) −0.79(2) <0.011 −0.83(3) <0.26 −0.402(17) 0.044(4) −0.56(2) −0.47(3) < −0.42 0.12(2) < −0.18 −0.293(15) 8.76(2)39,40,3 ··· 8.3(2)10 7.84(4)56 ··· ··· ··· 7.82(6)41,26,42,43 8.23(1)44,22,27 8.1(2)45 ··· 7.53(2)1 8.1(3)27 ··· ··· 7.56(14)1 ··· 7.43(6)46 8.5(2)10 ··· 7.80(3)47,42 36.2 8.57 58.5 11.4 6.97(5) 6.60(6) 9.38(3) <7.1 −0.77(2) −0.69(6) 0.142(18) < −0.48 ··· 7.97(6)1 8.31(7)44,40,22,48 ··· 29.8 49.5 <7.56 7.65(4) < −0.62 −0.501(18) 7.66(11)1 ··· 66.7 21.2 40 49.5 21 25.6 16.1 46.2 22.7 26 98.1 50 6.48 17.4 20 8.77(5) 8.06(4) 7.44(5) 7.44(3) 7.43(5) 9.16(4) 8.70(4) 7.01(5) 7.57(5) <6.7 5.99(5) 7.71(4) 6.88(8) 7.96(2) 7.72(4) 0.19(2) −0.157(16) −0.57(3) −0.30(2) −0.16(2) 0.196(11) 0.33(3) −0.80(2) −0.46(2) < −0.94 −0.92(2) −0.801(18) −1.06(6) 0.042(6) −0.150(18) ··· ··· 8.0(2)27 ··· ··· ··· 8.4(2)49 ··· 8.4(2)27 7.67(6)7,50 7.65(6)34,35,51,37 8.1(2)52 7.80(6)55 ··· ··· 10 10 10 10 10 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 43 47 49 49 52 00 27 33 35 36 48 50 55 04 09 12 15 15 20 21 26 31.2 22.3 07.6 36.5 31.1 23.9 12.2 28.9 48.8 06.2 57.4 53.0 39.7 00.8 58.6 09.2 23.7 46.6 38.1 15.0 15.9 +24 +14 +06 +65 +36 +28 −00 +49 +54 +45 +23 +38 +31 +52 +46 +36 +51 +52 +46 +45 +48 55 04 55 31 37 58 59 14 31 17 50 52 31 35 27 10 21 23 17 48 29 20 10 02 50 08 30 41 14 26 01 15 49 07 18 26 09 00 14 30 41 37 6.64 9.3 7.16 7.4 7.89 8.24 10.24 3.9 4.9 3.19 14 2.64 7.47 4.31 9.8 2.96 7.33 3.23 7.67 6.87 5.7 12 12 12 12 27 27 28 28 05.2 40.9 11.1 28.6 +37 +43 +44 +37 08 29 05 14 33 44 37 01 4.87 2.74 4.21 6.9 12 28 38.7 12 28 44.2 +35 43 03 +43 13 27 4.43 7.76 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 +41 +42 +31 +39 +40 +41 +41 +38 +51 +27 +14 −17 +67 +44 +40 7.07 7.73 6.1 9.39 7.44 7.79 8.65 4.57 7.44 4.3 2.13 7.24 4.57 5.4 8.21 30 32 32 34 36 41 41 42 48 54 58 03 06 12 12 31.1 26.9 54.4 00.5 22.7 32.8 52.7 15.1 22.9 05.2 40.4 16.7 24.9 12.6 51.8 42 42 32 01 00 09 16 30 09 08 13 25 42 02 32 04 15 28 09 19 03 26 12 53 59 03 23 25 28 35 – 43 – Table 1—Continued Galaxy UGC UGC NGC NGC UGC NGC UGC NGC R.A. Dec. D (Mpc) SFR Age (Gyr) EW(Hα) (Å) log LTIR (L⊙ ) IRX 12+log(O/H) C C C B C C B C B C B C B C 5+0 −0 5+0 −0 5+0 −0 0.5+0.5 −0 5+0 −0 0.8+0.2 −0.1 0.7+0 −0.2 5+0 −0 0.3+0.2 −0 5+0 −0 +0.2 0.5−0 5+0 −0 0.7+0 −0 5+0 −0 43.4 0 49.6 7.63 11.7 54.2 3.92 24.6 8.76(4) 7.39(7) 8.37(4) 7.75(9) <6.6 7.72(4) <6.1 8.50(4) −0.0101(12) −0.406(19) −0.108(14) −0.09(2) < −0.44 −0.47(2) < −0.43 −0.11(2) ··· 8.29(7)27,51 ··· 8.7(2)52 ··· 8.14(7)53 7.75(5)7,8,29 ··· 8.26 39.7 0 0.98 23.6 6.85(4) 8.67(4) 8.34(4) 5.93(5) 6.85(5) −0.519(18) 0.371(12) −0.368(9) 0.057(8) −0.77(5) 7.95(3)9,51 ··· ··· 7.93(14)54 7.72(3)13,15,52 8313 8320 5204 5264 8760 5477 9128 5585 13 13 13 13 13 14 14 14 13 14 29 41 50 05 15 19 53.9 28.0 36.5 36.7 50.6 33.3 56.5 48.2 +42 +45 +58 −29 +38 +54 +23 +56 12 55 25 54 01 27 03 43 31 09 07 47 09 40 19 45 8.72 4.33 4.65 4.53 3.24 7.7 2.24 5.7 UGC 9240 IC 5052 NGC 7064 UGC 12613 UGCA 442 14 20 21 23 23 24 52 29 28 43 43.4 05.6 03.0 36.3 45.6 +44 −69 −52 +14 −31 31 12 46 44 57 33 06 03 35 24 2.8 5.86 9.86 0.76 4.27 Note. — Columns list the (1) Galaxy name, (2) Right Ascension, (3) Declination in J2000 coordinates, (4) Luminosity distance in Mpc, (5) Instantaneous (B) or continuous (C) SFR of the best-fit model to observations, (6) Age of the best-fit model in Gyr, (7) Hα equivalent width from Kennicutt et al. (2008) in Å, (8) log of the total integrated IR luminosity per solar luminosity L⊙ , (9) IRX values of log LTIR /LFUV , and (10) 12+log(O/H) metallicity values for each galaxy (when available) and respective references. Numbers in parentheses indicate uncertainties in the final digit(s) of listed quantities, when available. In some cases, a galaxy SED can be best-fit with both a continuous and bursting SFR. We have listed both the continuous and bursting model for these select galaxies. Metallicity references: (1) – Moustakas et al. (2010); (2) – Tüllmann et al. (2003); (3) – Zaritsky et al. (1994); (4) – Saviane et al. (2008); (5) – Christensen et al. (1997); (6) – Vila-Costas & Edmunds (1993); (7) – van Zee et al. (1997a); (8) – van Zee et al. (1997b); (9) – van Zee & Haynes (2006a); (10) – Kewley et al. (2005); (11) – Magrini et al. (2007); (12) – Rosolowsky & Simon (2008); (13) – Skillman et al. (2003); (14) – Hidalgo-Gámez et al. (2001); (15) – Miller (1996); (16) – Walsh et al. (1997); (17) – Raimann et al. (2000); (18) – Agüero & Paolantonio (1997); (19) – Storchi-Bergmann et al. (1994); (20) – Masegosa et al. (1994); (21) – Lee & Skillman (2004); (22) – Hunter et al. (1982); (23) – Gil de Paz et al. (2000a); (24) – Gil de Paz et al. (2000b); (25) – Kniazev et al. (2004); (26) – Izotov et al. (2006); (27) – Hunter & Hoffman (1999); (28) – Pustilnik et al. (2003); (29) – Skillman et al. (1989); (30) – Kinman & Davidson (1981); (31) – Hopp & Schulte-Ladbeck (1991); (32) – Pustilnik et al. (2005); (33) – Hunter & Gallagher (1985); (34) – van Zee et al. (2006b); (35) – Moles et al. (1990); (36) – Lee et al. (2005); (37) – Stasińska et al. (1986); (38) – Miller & Hodge (1996); (39) – Moustakas & Kennicutt (2006); (40) – McCall et al. (1985); (41) – Guseva et al. (2000); (42) – Thuan & Izotov (2005); (43) – Buckalew et al. (2005); (44) – Martin (1997); (45) – Gallagher & Hunter (1989); (46) – Kniazev et al. (2003); (47) – Pérez-Montero & Dı́az (2003); (48) – Kobulnicky (1999); (49) – Gil de Paz et al. (2007); (50) – Kennicutt & Skillman (2001); (51) – Hidalgo-Gámez & Olofsson (2002); (52) – Lee et al. (2003); (53) – Izotov et al. (2007); (54) – Skillman et al. (1997); (55) – Berg et al. (2012); (56) – Croxall et al. (2009). – 44 – Table 2. Multi-Wavelength Data Band Wavelength Instrument/Survey FUV NUV U B V J H Ks 3.6 4.5 5.8 8 MIPS 24 MIPS 70 MIPS 160 1520 Å 2310 Å 3660 Å 4410 Å 5540 Å 1.235 µm 1.662 µm 2.159 µm 3.6 µm 4.5 µm 5.8 µm 8 µm 24 µm 70 µm 160 µm GALEX GALEX RC3/VATT RC3/VATT RC3/VATT 2MASS 2MASS 2MASS Spitzer/IRAC Spitzer/IRAC Spitzer/IRAC Spitzer/IRAC Spitzer/MIPS Spitzer/MIPS Spitzer/MIPS Note. — Columns list the (1) Photometric band, (2) Central wavelength of each band, and (3) Instrument or survey the photometric data came from. – 45 – Table 3. Probabilities for Instanteneous Star-Forming Galaxies Total Variables IRX< 0 0 <IRX< 0.5 N Spearman Kendall N Spearman Kendall N Spearman Kendall E(B − V ) vs βGLX 38 FUV/NIR vs βGLX 38 FUV/NIR vs dp 36 EW(Hα) vs βGLX 35 EW(Hα) vs dp 33 U − B vs βGLX 38 U − B vs dp 36 Age vs βGLX 38 Age vs dp 36 12+log(O/H) vs βGLX 24 12+log(O/H) vs dp 22 ρ = −0.013 0.06σ ρ = 0.32 1.6σ ρ = −0.80 3.9σ ρ = 0.59 2.9σ ρ = −0.76 3.7σ ρ = 0.78 3.8σ ρ = −0.68 3.3σ ρ = 0.44 2.2σ ρ = 0.76 3.7σ ρ = −0.77 3.8σ ρ=0 0σ ρ = 0.13 0.5σ τ = −0.03 0.18σ τ = 0.24 1.7σ τ = −0.65 4.5σ τ = 0.41 2.9σ τ = −0.56 3.9σ τ = 0.57 3.9σ τ = −0.51 3.6σ τ = 0.34 2.4σ τ = 0.65 4.6σ τ = −0.61 4.3σ τ =0 0σ τ = 0.03 0.2σ 13 36 τ = 0.15 1.3σ τ = 0.30 2.5σ τ = −0.61 5.4σ τ = 0.04 0.4σ τ = −0.40 3.4σ τ = 0.40 3.3σ τ = −0.49 4.3σ τ = 0.10 0.8σ τ = 0.57 5.1σ τ = −0.38 3.2σ τ = 0.31 2.2σ τ = 0.29 1.9σ 25 E(B − V ) vs dp ρ = 0.23 1.4σ ρ = 0.39 2.3σ ρ = −0.78 4.7σ ρ = 0.11 0.6σ ρ = −0.55 3.2σ ρ = 0.59 3.3σ ρ = −0.64 3.9σ ρ = 0.12 0.7σ ρ = 0.69 4.2σ ρ = −0.49 2.9σ ρ = 0.41 2.0σ ρ = 0.39 1.8σ ρ = 0.34 1.1σ ρ=0 0σ ρ = −0.66 2.3σ ρ = −0.05 0.14σ ρ = −0.11 0.3σ ρ = −0.37 1.0σ ρ = −0.28 1.0σ ρ=0 0σ ρ = 0.58 2.0σ ρ = −0.67 2.1σ ρ = −0.58 1.8σ ρ = 0.73 1.9σ τ = 0.25 1.2σ τ =0 0σ τ = −0.51 2.4σ τ = −0.09 0.4σ τ = −0.018 0.08σ τ = −0.39 1.5σ τ = −0.27 1.2σ τ = 0.02 0σ τ = 0.48 2.3σ τ = −0.52 2.3σ τ = −0.36 1.4σ τ = 0.55 1.9σ 25 25 25 24 24 25 25 25 25 14 14 11 13 11 11 9 13 11 13 11 10 8 Note. — The Spearman (ρ) and Kendall (τ ) rank correlation coefficients for (1) the entire sample of bursting galaxies, (2) the bursting galaxies in the range log LTIR /LFUV < 0, and (3) the galaxies in the range 0 < log LTIR /LFUV < 0.5, where N represents the number of galaxies in each sample for Figure 4 (E(B − V ) vs βGLX ), Figure 5 (E(B − V ) vs dp ), Figure 6 (FUV/NIR vs βGLX ; proxy for the mean age of the stellar population), Figure 7 (FUV/NIR vs dp ), Figure 8 (EW(Hα) vs βGLX ), Figure 9 (EW(Hα) vs dp ), Figure 10 (U − B vs βGLX ), Figure 11 (U − B vs dp ), Figure 12 (Age vs βGLX ), Figure 13 (Age vs dp ), Figure 14 (12+log(O/H) vs βGLX ), and Figure 15 (12+log(O/H) vs dp ). Below the correlation coefficients are the significance of the correlation. – 46 – Table 4. Probabilities for Continuous Star-Forming Galaxies Total Variables IRX< 0 0 <IRX< 0.5 N Spearman Kendall N Spearman Kendall N Spearman Kendall E(B − V ) vs βGLX 60 FUV/NIR vs βGLX 60 FUV/NIR vs dp 59 EW(Hα) vs βGLX 58 EW(Hα) vs dp 57 U − B vs βGLX 60 U − B vs dp 59 Age vs βGLX 60 Age vs dp 59 12+log(O/H) vs βGLX 36 12+log(O/H) vs dp 35 ρ = 0.26 1.7σ ρ = 0.13 0.8σ ρ = −0.65 4.2σ ρ = 0.38 2.5σ ρ = −0.58 3.6σ ρ = 0.61 3.8σ ρ = −0.56 3.6σ ρ = 0.38 2.5σ ρ = 0.46 3.0σ ρ = −0.35 2.3σ ρ = 0.46 2.4σ ρ = −0.14 0.7σ τ = 0.19 1.8σ τ = 0.09 0.9σ τ = −0.47 4.5σ τ = 0.28 2.7σ τ = −0.41 3.7σ τ = 0.44 4.0σ τ = −0.41 3.9σ τ = 0.28 2.6σ τ = 0.37 3.5σ τ = −0.28 2.7σ τ = 0.33 2.4σ τ = −0.12 0.9σ 17 59 τ = 0.15 1.7σ τ = 0.32 3.5σ τ = −0.37 4.2σ τ = −0.02 0.2σ τ = −0.36 4.0σ τ = 0.37 4.1σ τ = −0.36 4.1σ τ = 0.19 2.1σ τ = 0.33 3.7σ τ = −0.13 1.4σ τ = 0.31 2.7σ τ = 0.07 0.6σ 43 E(B − V ) vs dp ρ = 0.21 1.6σ ρ = 0.42 3.2σ ρ = −0.52 4.0σ ρ = −0.05 0.3σ ρ = −0.51 3.8σ ρ = 0.52 3.9σ ρ = −0.49 3.7σ ρ = 0.25 2.0σ ρ = 0.41 3.1σ ρ = −0.15 1.2σ ρ = 0.44 2.6σ ρ = 0.11 0.6σ ρ = −0.010 0.04σ ρ = 0.06 0.2σ ρ = −0.52 2.1σ ρ = 0.40 1.5σ ρ = −0.33 1.3σ ρ = 0.48 1.9σ ρ = −0.25 1.0σ ρ = 0.20 0.8σ ρ=0 0σ ρ=0 0σ ρ = 0.20 0.6σ ρ = −0.19 0.5σ τ =0 0σ τ = 0.04 0.2σ τ = −0.38 2.1σ τ = 0.27 1.4σ τ = −0.25 1.5σ τ = 0.34 1.9σ τ = −0.26 1.4σ τ = 0.18 0.9σ τ =0 0σ τ =0 0σ τ = 0.06 0.2σ τ = −0.14 0.5σ 43 43 43 40 40 43 43 43 43 27 27 16 17 16 18 17 17 16 17 16 9 8 Note. — The Spearman (ρ) and Kendall (τ ) rank correlation coefficients for (1) the entire sample of continuous star-forming galaxies, (2) the continuous galaxies in the range log LTIR /LFUV < 0, and (3) the galaxies in the range 0 < log LTIR /LFUV < 0.5, where N represents the number of galaxies in each sample for Figure 4 (E(B − V ) vs βGLX ), Figure 5 (E(B − V ) vs dp ), Figure 6 (FUV/NIR vs βGLX ), Figure 7 (FUV/NIR vs dp ), Figure 8 (EW(Hα) vs βGLX ), Figure 9 (EW(Hα) vs dp ), Figure 10 (U − B vs βGLX ), Figure 11 (U − B vs dp ), Figure 12 (Age vs βGLX ), Figure 13 (Age vs dp ), Figure 14 (12+log(O/H) vs βGLX ), and Figure 15 (12+log(O/H) vs dp ). Below the correlation coefficients are the significance of the correlation. – 47 – Table 5. Probabilities for Entire Sample of Star-Forming Galaxies Total Variables IRX< 0 0 <IRX< 0.5 N Spearman Kendall N Spearman Kendall N Spearman Kendall E(B − V ) vs βGLX 98 FUV/NIR vs βGLX 98 FUV/NIR vs dp 95 EW(Hα) vs βGLX 93 EW(Hα) vs dp 90 U − B vs βGLX 98 U − B vs dp 95 Age vs βGLX 98 Age vs dp 95 12+log(O/H) vs βGLX 60 12+log(O/H) vs dp 57 ρ = 0.15 1.3σ ρ = 0.19 1.6σ ρ = −0.69 5.6σ ρ = 0.47 3.8σ ρ = −0.59 4.7σ ρ = 0.65 5.1σ ρ = −0.55 4.5σ ρ = 0.41 3.4σ ρ = 0.27 2.2σ ρ = −0.18 1.5σ ρ = 0.30 1.9σ ρ = −0.07 0.4σ τ = 0.10 1.2σ τ = 0.15 2.1σ τ = −0.51 6.1σ τ = 0.33 4.0σ τ = −0.41 4.8σ τ = 0.46 5.3σ τ = −0.40 4.8σ τ = 0.29 3.5σ τ = 0.21 2.5σ τ = −0.13 1.5σ τ = 0.22 2.0σ τ = −0.05 0.5σ 30 95 τ = 0.15 2.2σ τ = 0.46 4.6σ τ = −0.45 6.6σ τ = 0.016 0.2σ τ = −0.36 5.1σ τ = 0.37 5.1σ τ = −0.39 5.7σ τ = 0.16 2.3σ τ = 0.12 1.7σ τ = −0.05 0.7σ τ = 0.21 2.4σ τ = 0.15 1.6σ 68 E(B − V ) vs dp ρ = 0.22 2.1σ ρ = 0.42 4.0σ ρ = −0.62 6.1σ ρ = 0.02 0.2σ ρ = −0.51 4.9σ ρ = 0.52 4.9σ ρ = −0.53 5.3σ ρ = 0.22 2.2σ ρ = 0.15 1.5σ ρ = −0.07 0.6σ ρ = 0.31 2.3σ ρ = 0.20 1.5σ ρ = −0.05 0.2σ ρ = 0.11 0.6σ ρ = −0.64 3.4σ ρ = 0.28 1.5σ ρ = −0.35 1.8σ ρ = 0.31 1.6σ ρ = −0.41 2.2σ ρ = 0.24 1.2σ ρ = −0.13 0.7σ ρ = 0.15 0.7σ ρ = −0.20 0.9σ ρ = 0.18 0.7σ τ = −0.03 0.2σ τ = 0.09 0.6σ τ = −0.46 3.6σ τ = 0.19 1.4σ τ = −0.25 1.9σ τ = 0.22 1.6σ τ = −0.33 2.5σ τ = 0.19 1.4σ τ = −0.09 0.7σ τ = 0.10 0.7σ τ = −0.12 0.7σ τ = 0.12 0.6σ 68 68 68 64 64 68 68 68 68 41 41 27 30 27 29 26 30 27 30 27 19 16 Note. — The Spearman (ρ) and Kendall (τ ) rank correlation coefficients for (1) the entire sample of star-forming galaxies (continuous and bursting), (2) the galaxies in the range log LTIR /LFUV < 0, and (3) the galaxies in the range 0 < log LTIR /LFUV < 0.5, where N represents the number of galaxies in each sample for Figure 4 (E(B − V ) vs βGLX ), Figure 5 (E(B − V ) vs dp ), Figure 6 (FUV/NIR vs βGLX ), Figure 7 (FUV/NIR vs dp ), Figure 8 (EW(Hα) vs βGLX ), Figure 9 (EW(Hα) vs dp ), Figure 10 (U − B vs βGLX ), Figure 11 (U − B vs dp ), Figure 12 (Age vs βGLX ), Figure 13 (Age vs dp ), Figure 14 (12+log(O/H) vs βGLX ), and Figure 15 (12+log(O/H) vs dp ). Below the correlation coefficients are the significance of the correlation.