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Appendix A: Comparison between different SFR tracers for the DGS sample

Appendix A.1: Limitations of SFR tracers in metal-poor dwarf galaxies

In this work, we rely on the most recent calibrations reported in Kennicutt & Evans (2012), which are calibrated for an initial mass function (IMF) characterized by a broken power law with a slope of −2.35 from 1 to 100 M_⊙ and −1.3 between 0.1 and 1 M_⊙ (Kroupa & Weidner 2003). Table A.1 gives an overview of the reference SFR calibrations used in this work. The SFR calibrations based on single tracers in the first part of Table A.1 predict the SFR in M_⊙ yr^-1 following the prescription log  SFR = log  L_x − log  C_x, where L_x is the SFR indicator in units of erg s^-1 and C_x represents the calibration coefficients for a specific SFR diagnostic. The second part of Table A.1 provides the calibrations to correct unobscured SFR indicators for extinction.

The empirically derived SFR calibrations from Table A.1 assume a constant star formation rate over timescales comparable to or longer than the lifetime of stars to which the SFR tracers are sensitive. The age range for the SFR tracers used in this analysis are summarized in the second column of Table A.1 and were adopted from Kennicutt & Evans (2012), with the first, second, and third number representing the lower age boundary, the mean age, and the age of stars below which 90% of the emission is contributed, respectively. For observations covering an entire galaxy, we sample a wide range in age across the different star-forming complexes, sufficient to maintain a constant level of star formation activity when averaging out over different galaxy regions. With low-mass galaxies being dominated by one or only few Hii regions and furthermore characterized by bursty star formation histories (e.g., Mateo 1998; Fioc & Rocca-Volmerange 1999), the assumption of constant star formation rate might not be valid because of the insufficient sampling of different ages. The SFR calibrations might, therefore, no longer hold. In particular, on spatially resolved scales (i.e., few hundreds of parsec or the size of a typical Hii region for nearby DGS sources achieved in Herschel observations), the sampling of different ages will not suffice to sample the entire age range to maintain a constant star formation activity (i.e., constant SFR across the entire age range) and the SFR calibrations might break down. Therefore, we caution the interpretation of the SFR in the analysis of metal-poor dwarf galaxies, in particular for the spatially resolved analysis in Sect. 3, in the sense that the unobscured SFR obtained from GALEX FUV might underestimate the “true” level of star formation activity throughout the galaxy.

Other than the constant SFR, empirical SFR calibrations assume the universality of the initial mass function (IMF). Pflamm-Altenburg et al. (2007) question this universality of the IMF on global galaxy scales, especially in dwarf galaxies, arguing that the maximum stellar mass in a star cluster is limited by the total mass of the cluster with the latter being constrained by the SFR. Neglecting this effect could result in an underestimation of the SFR by up to 3 orders of magnitude. Since the data currently at hand do not allow a proper investigation of any possible deviations from universal IMF, we apply and derive SFR calibrations in this paper under the assumption of universality of the IMF, but keep in mind that possible systematic effects might bias our analysis. The extendibility of SFR calibrations to the early Universe might furthermore be affected by deviations from this universal IMF, with indications for a top heavy IMF at high-redshift (Larson 1998; Baugh et al. 2005; Davé 2008; Lacey et al. 2008; Wilkins et al. 2008).

Appendix A.2: Comparison of unobscured SFR tracers: GALEX FUV and Hα

The FUV and Hα fluxes are commonly-used tracers of the unobscured star formation. The applicability of FUV as a star formation rate tracer might, however, be affected by the recent star formation history in dwarfs, which is often bursty and dominated by few, giant Hii regions (e.g., Mateo 1998; Fioc & Rocca-Volmerange 1999). With Hα being sensitive to the emission of OB stars with mean ages ~10⁷ yr and FUV tracing the emission of massive A stars with ages ~10⁸ yr (Lequeux 1989), Hα might be more appropriate as SFR tracer in dwarf galaxies with a particular bursty star formation history.

In Fig. A.1, we compare the ratio of the SFR as obtained from the SFR calibrators FUV + MIPS 24 μm and Hα + MIPS 24 μm (see SFR relations in Table A.1) as a function of oxygen abundance. Total Hα fluxes are taken from Gil de Paz et al. (2003); Moustakas & Kennicutt (2006); Kennicutt et al. (2008); Östlin et al. (2009). We determine the best fit to the data points based on linear regression fits using the IDL procedure MPFITEXY, which is based on the nonlinear least-squares fitting package MPFIT (Markwardt 2009). The best-fit line and a perfect one-to-one correlation are indicated as dotted red, and dashed black lines. The dispersion around the best fit is indicated in the bottom right corner.

For galaxies with oxygen abundances 12 + log  (O/H) ≥ 8.1, the two composite SFR tracers seem to provide consistent estimates of the SFR, while below 12 + log  (O/H) < 8.1 galaxies start to deviate from a perfect one-to-one correlation. Due to the lower stellar masses of metal-poor dwarfs, their star formation history is dominated by only few giant Hii regions and, thus, heavily dependent on the time delay since the last burst of star formation. With FUV tracing the unobscured star formation over a timescale of 10 to 100 Myr (Kennicutt 1998; Calzetti et al. 2005; Salim et al. 2007), the SFR derived from FUV emission will be lower compared to Hα in galaxies characterized by a single recent burst of star formation (<10 Myr) over a timescale of 100 Myr. Therefore, Hα is considered a better SFR calibrator in low-mass dwarfs, which are dominated by single Hii regions. The correspondence between SFR estimates from FUV and Hα emission for galaxies with 12 + log  (O/H) ≥ 8.1 might indicate an age effect, where the latter objects are rather in a post-starburst phase and the most recent starburst occurred more than 10 Myr ago. The unavailability of Hα maps (only global Hα fluxes could be retrieved from the literature for most galaxies) prevents us from using Hα as reference SFR tracer, since we are unable to recover the Hα emission that corresponds to the areas in galaxies covered by our Herschel observations. Therefore, FUV is used as reference SFR tracer for this analysis, bearing in mind that the conversion to SFR might break down for low-mass metal-poor dwarfs where FUV will on average underestimate the SFR derived from Hα by 50% (see Fig. A.1).

Fig. A.1 Comparison between the ratio of the SFR as obtained from the SFR calibrators FUV + MIPS 24 μm and Hα + MIPS 24 μm as a function of oxygen abundance. Galaxies are color-coded according to metallicity with increasing oxygen abundances ranging from black then blue, green and yellow to red colors. The dotted red, and dashed black, lines represent the best fit and a perfect one-to-one correlation, respectively. The dispersion around the best fit is indicated in the bottom right corner.

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Appendix A.3: Comparison of obscured SFR tracers: IRAC8 μm, MIPS 24 μm, L_TIR, and 1.4 GHz

Different monochromatic and multiband data in the infrared and radio wavelength domain can be used to trace the obscured star formation component. Here, we compare IRAC 8 μm, MIPS 24 μm, PACS 70 μm, the total infrared luminosity, and radio continuum emission at 1.4 GHz. Total IRAC 8 μm flux densities have been adopted from Rémy-Ruyer et al. (in prep.). The DGS sample has been observed by the Herschel PACS (70, 100, 160 μm) and SPIRE (250, 350, 500 μm) photometers in all continuum bands. Details about the observing strategy, the applied data reduction techniques and aperture photometry results are presented in Rémy-Ruyer et al. (2013). Total infrared luminosities L_TIR are taken from Madden et al. (2013), as determined from Spitzer bands using the prescriptions in Dale & Helou (2002). Radio continuum measurements are retrieved from the NRAO VLA Sky Survey (NVSS) catalog (Condon et al. 1998), Cannon & Skillman (2004), Thuan et al. (2004), and Hunt et al. (2005).

The emission from PAHs usually dominates the IRAC 8 μm band in metal-rich galaxies. In low-metallicity galaxies, the IRAC 8 μm band might also contain an important contribution from the warm continuum emission from very small grains. Since the PAH emission has been observed to be under-luminous below 12 + log  (O/H) ~ 8.1 (Boselli et al. 2004; Engelbracht et al. 2005; Jackson et el. 2006; Madden et al. 2006; Draine et al. 2007; Engelbracht et al. 2008; Galliano et al. 2008), in combination with the uncertainty to quantifying the 8 μm band in terms of PAH and VSG contribution, the IRAC 8 μm band is considered an unreliable SFR calibrator for the DGS sample covering a wide range in metallicity. Calzetti et al. (2007) could indeed identify that the sensitivity of the IRAC 8 μm band to metallicity is about one order of magnitude worse compared to MIPS 24 μm. The weak PAH emission toward lower metallicities is not directly related to the lower metal abundance but rather emanates from the generally strong and hard radiation fields in low-metallicity systems destroying and/or ionizing PAHs (e.g., Gordon et al. 2008; Sandstrom et al. 2012). Other than its dependence on metallicity (or thus radiation field), PAH emission tends to be inhibited in regions of strong star formation activity while it can be several times more luminous compared to other star formation rate tracers in regions with relatively weak or nonexistent star formation (e.g., Calzetti et al. 2005; Bendo et al. 2008; Gordon et al. 2008). Prior to any conversion of IRAC 8 μm emission to SFR, the band emission needs to be corrected for any stellar contribution. Given that the contribution from the stellar continuum could be substantial in low-abundance galaxies, this will make the correction using standard recipes (e.g., Helou et al. 2004) highly uncertain. All together, we argue that the IRAC 8 μm is not appropriate as SFR indicator in our sample of dwarf galaxies with widely varying metallicities.

The most common monochromatic tracer of obscured star formation is MIPS 24 μm emission, which generally originates from a combination of stochastically heated very small grains (VSGs) and large grains at an equilibrium temperature of ~100 K. For a grain size distribution similar to our Galaxy, we expect large equilibrium grains only to start dominating the MIPS 24 μm emission above a threshold of G₀ ~ 100, where G₀ is the scaling factor of the interstellar radiation field, expressed relative to the FUV interstellar radiation field from 6 to 13.6 eV for the solar neighborhood in units of Habing flux, i.e., 1.6 × 10^-3 erg s^-1 m^-2. The emission in the MIPS 24 μm band has been shown to be well-correlated with other star formation rate tracers on both local scales (Calzetti et al. 2007; Leroy et al. 2008) and global scales (e.g., Calzetti et al. 2005, 2007; Wu et al. 2005; Alonso-Herrero et al. 2006; Pérez-González et al. 2006; Zhu et al. 2008; Kennicutt et al. 2009; Rieke et al. 2009; Hao et al. 2011) and directly traces the ongoing star formation over a timescale of ~10 Myr (Calzetti et al. 2005; Pérez-González et al. 2006; Calzetti et al. 2007).

Since the grain properties and size distribution has been shown to be sensitive to the metallicity of galaxies (Lisenfeld et al. 2002; Galliano et al. 2003, 2005), we need to verify whether MIPS 24 μm is an appropriate SFR tracer for the DGS sample. In low-metallicity objects, small grain sizes (≲3 nm) start to dominate the 24 μm emission compared to larger dust grains (Lisenfeld et al. 2002; Galliano et al. 2003, 2005), due to the fragmentation of these larger dust grains through shocks experienced in the turbulent ISM. The hard radiation field in low-metallicity galaxies (see Sect. 4.3) furthermore increases the maximum temperature of stochastically heated grains and shifts the peak of the SED to shorter wavelengths, boosting the MIPS 24 μm flux (e.g., Thuan et al. 1999; Houck et al. 2004; Galametz et al. 2009, 2011). To verify the influence of metallicity on the MIPS 24 μm band emission, we compare the estimated star formation rates obtained from MIPS 24 μm to other SFR indicators, which should not be biased (or at least less) by variations in the dust composition across galaxies with different metal abundances.

Fig. A.2 Comparison between the ratio of the SFR as obtained from the SFR calibrators MIPS 24 μm and PACS 70 μm (top), FUV+MIPS 24 μm and FUV+TIR (middle) and FUV+MIPS 24 μm and FUV+1.4 GHz (bottom) as a function of oxygen abundance. Galaxies are color-coded according to metallicity with increasing oxygen abundances ranging from black then blue, green and yellow to red colors. The dotted red and dashed black lines represent the best fit and a perfect one-to-one correlation, respectively. The dispersion around the best fit is indicated in the bottom right corner.

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Toward longer wavelengths (70, 100, 160 μm), the band emission is dominated by larger dust grains and should not depend strongly on the abundance of very small grains. For larger dust grains a significant fraction of the dust heating might, however, be attributed to more evolved stellar populations, making the link between FIR continuum emission and star formation more dispersed (Bendo et al. 2010; Calzetti et al. 2010; Boquien et al. 2011; Bendo et al. 2012a; Groves et al. 2012; Smith et al. 2012). In a similar way, the total infrared luminosity might be subject to heating from old stars and, therefore, only linked to star formation on much longer timescales. Some individual studies argue that most of the dust heating is provided by star-forming regions in dwarfs (e.g., Galametz et al. 2010; Bendo et al. 2012a), even at wavelengths longward of 160 μm, suggesting that the longer wavelength data (70, 100, 160 μm) could potentially be reliable star formation rate tracers. More detailed analyses of the dominant heating sources for dust in dwarfs however might be required to conclude on the applicability of FIR continuum bands to trace the SFR. In Fig. A.2, we compare the SFR as estimated from the single continuum bands MIPS 24 μm and PACS 70 μm (see top panel). The best-fit line and dispersion (0.28 dex) in this plot is mainly dominated by three galaxies (SBS 0335-052, Tol 1214-277, Haro 11), which have the peak of their SED at very short wavelengths and, therefore, the 24 μm band will overestimate the SFR while the 70 μm emission will underestimate the SFR. The other galaxies seem to follow the one-to-one correlation better with a dispersion of 0.18 dex around the one-to-one correlation (or difference between the two SFR estimates up to 51%).

In the central panel of Fig. A.2, we make a similar comparison between the composite SFR tracers FUV + 24 μm and FUV+TIR. The best-fit line (with slope α = 0.15) diverges from the one-to-one correlation with the combination of FUV and MIPS 24 μm providing higher SFR than inferred from FUV+TIR. We argue that this discrepancy is mainly caused by the fact that the SFR relations for the total infrared luminosity were calibrated based on galaxy samples of normal star-forming galaxies with close to solar abundances. They might, therefore, be less appropriate for metal-poor dwarfs, which are typically characterized by steeply rising mid-infrared (MIR) to far-infrared (FIR) slopes and overall SEDs peaking at wavelengths lower than ~60 μm (e.g., Thuan et al. 1999; Houck et al. 2004; Galametz et al. 2009, 2011).

Radio continuum emission at 1.4 GHz is dominated by nonthermal synchrotron emission associated with the acceleration of electrons in a galaxy’s magnetic field, and, therefore, independent of the grain composition in a galaxy’s ISM. The emission at 1.4 GHz is often used as a tracer of star formation, since the optically thin radio synchrotron emission correlates well with the FIR emission (i.e., the FIR-radio correlation; e.g., de Jong et al. 1985; Helou et al. 1985). However, the 1.4 GHz is not really a tracer of obscured star formation since it probes the energy from supernovae associated with star-forming regions and, therefore, rather correlates with the total energy output from star-forming regions, including both obscured and unobscured star formation. Figure A.2 (bottom panel) shows the ratio of SFR estimated from FUV + 24 μm and FUV + 1.4 GHz as a function of oxygen abundance (or metallicity), with the black dashed line representing the one-to-one correlation. In general, the SFR obtained from the composite tracer FUV+MIPS 24 μm is higher than the SFR estimated from FUV+1.4 GHz. We argue that this deviation can again be attributed to the bursty star formation history in dwarf galaxies. Although the emission at 24 μm and 1.4 GHz is sensitive to stars of ages up to at least 100 Myr (see Table A.1), the MIPS 24 μm band is dominated by the emission of stars younger than 10 Myr. In view of the recent trigger of star formation that characterizes most dwarf galaxies in our sample, the 1.4 GHz emission will typically underestimate the SFR since it was calibrated for models of constant SFR (or supernova rate) over the past 100 Myr. One exception is galaxy HS 0822+3542, for which the SFR seems to be underestimated based on FUV+MIPS 24 μm data. The strange behavior of this galaxy in the PACS wavebands (Rémy-Ruyer et al. 2013) supports the peculiarity of this object. Another outlier is Haro 11, which shows the highest ratio based on the composite tracer FUV+24 μm. We believe that the warmer dust temperatures with a peak in its SED at very short wavelengths (~40 μm, Galametz et al. 2009) in this LIRG causes an overestimation of the SFR based on MIPS 24 μm.

Based on the above comparison between different tracers of obscured star formation, we opted to use the reference SFR tracers FUV and MIPS 24 μm for the analysis of the DGS sample. By estimating the SFR from FUV and MIPS 24 μm emission, we should be tracing the emission of young stars with ages up to 100 Myr. It is possible, however, to get diffuse emission that is not locally heated by star-forming regions in both FUV and MIPS 24 μm bands originating from heating by the diffuse interstellar radiation field. This could potentially cause an overestimation of the SFR in diffuse regions and might bias the interpretation of the observed relations between the SFR and FIR line emission, in particular for the spatially resolved analysis of Sect. 3. With the Dwarf Galaxy Survey often not mapping the nearby galaxies completely in the FIR lines but rather focusing on the brightest star-forming regions, we argue that the contribution from diffuse regions and the heating by evolved stellar populations most likely will be limited in many cases. Although, we should keep in mind the possible contribution of diffuse FUV and 24 μm emission to the SFR estimates upon analyzing the SFR relations. Similarly, the FUV band might contain residual starlight from evolved stellar populations due to the low level of obscuration in some of the dwarfs. The presence of only few evolved stars in dwarfs (compared to more massive early-type galaxies with large spheroids), however, makes it unlikely that residual starlight of old stars will contribute significantly to the FUV emission.

Fig. A.3 Comparison between the Herschel and ISO line fluxes, i.e., the ratio of the Herschel and ISO measurements for [Cii] (top), [Oi]63 (middle), and [Oiii]88 (bottom) as a function of Herschel line luminosities. The mean and standard deviation of the Herschel-to-ISO flux ratio is indicated in the top left corner of each panel. The best-fit line and a perfect one-to-one correlation are indicated as solid red and dotted black lines, respectively.

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Appendix A.4: Comparison ISO-Herschel

Since the literature sample is composed of Herschel and ISO fluxes, we need to verify whether the spectroscopic flux calibration of the Herschel PACS and ISO LWS instruments are compatible. Hereto, we assemble the ISO fluxes from the Brauher et al. (2008) catalog for galaxies in our literature sample with Herschel measurements. We only consider galaxies that are classified as unresolved with respect to the LWS beam in Brauher et al. (2008) to minimize the influence of different beam sizes in our comparison. We gather a sample of 44, 19, and 10 sources with [Cii], [Oi]₆₃ and [Oiii]₈₈ fluxes from both Herschel and ISO observations. Those galaxies are indicated with a dagger behind their name in Tables B.3, B.4 and B.5. Figure A.3 presents the Herschel-to-ISO line ratios for [Cii] (top), [Oi]₆₃ (middle) and [Oiii]₈₈ (bottom). Based on the 44 measurements for [Cii], we find that the Herschel fluxes are on average 1.19 ± 0.43 higher compared to the ISO measurements. The best-fit line (see solid red line in Fig. A.3, top panel) lies close to the one-to-one correlation. Overall, the Herschel and ISO [Cii] fluxes are consistent with each other within the error bars, in particular for the higher luminosity sources. Based on the 19 [Oi]₆₃ and ten [Oiii]₈₈ measurements, we infer that the Herschel measurements are on average lower by a factor of 0.86 ± 0.16 and 0.69 ± 0.18, respectively, compared to the ISO fluxes. For the [Oi]₆₃ line, the Herschel PACS and ISO LWS measurements still agree within the error bars, but for the [Oiii]₈₈ line the discrepancy between Herschel and ISO measurements is considered significant. Although the larger ISO LWS beam (~80″) could collect more flux compared to the PACS beam for the [Oi]₆₃ and [Oiii]₈₈ lines (FWHM ~ 9.5″), we would expect to see similar behavior for the [Cii] line

(PACS FWHM ~ 11.5″) if the difference in beam size is driving the offset between Herschel and ISO fluxes. The absence of any beam size effects for [Cii] makes us conclude that the discrepancy between Herschel and ISO for [Oiii]₈₈ can likely be attributed to a difference in calibration. Given the significant difference in [Oiii]₈₈ line fluxes, we will only take the [Oiii]₈₈ measurements derived from Herschel observations into account for the SFR calibrations.

Appendix B: Tables

© ESO, 2014