STAR-FORMING OR STARBURSTING? THE ULTRAVIOLET CONUNDRUM

We have obtained far- and near-ultraviolet processed count and intensity maps from the GALEX archives. Thanks to its large field of view of 124, it can encompass the full extent of the selected galaxies with a single pointing. The far ultraviolet band is centered on λ_eff = 151 nm whereas the near ultraviolet one is centered on λ_eff = 227 nm. Detailed information about the instruments are provided in Martin et al. (2005).

Galaxies have been observed as part of the Nearby Galaxy Survey (NGC 0628, NGC 2403, NGC 5055, NGC 5194, NGC 5457 and NGC 7793) and Guest investigators programs (program 71 cycle 1 for NGC 3031 and program 5 in cycle 3 for NGC 5236).

Ground-based optical images consist of narrowband Hα observations as well as broadband U, B, and R observations.

Most Hα images have been obtained from the Spitzer Infrared Nearby Galaxies Survey (SINGS; Kennicutt et al. 2003) archives, fifth delivery, final enhanced products released on 2007 April 10. Observations have been carried out at the National Optical Astronomy Observatory, in 2001 on the Kitt Peak National Observatory (KPNO) 2.1 m and Cerro Tololo Inter-American Observatory (CTIO) 1.5 m telescopes. More details are available in the SINGS "User's Guide."⁸ For NGC 5236, the data were obtained on the Bok 2.3 m telescope on 2005 May 10.

Continuum emission has been subtracted from the Hα image using the corresponding scaled R-band image following the method described in S. Hong et al. (2010, in preparation).

SINGS spectroscopic observations (J. Moustakas et al. 2010, in preparation) have been used to infer the mean [N ii]/[Hα] ratio within the galaxies. The measured fluxes have been corrected for contamination by the [N ii] lines accordingly. As no spectrum was available for the high-metallicity galaxy NGC 5236, we have assumed [N ii]/[Hα] = 0.5, close to 0.53 found by Kennicutt et al. (2008) that has been estimated based on a scaling relationship between M(B) and [N ii] as described in Appendix B of that paper. Although the relative strength of the [N ii] lines can change from one H ii region to another and can evolve as a function of the radial distance, we have assumed a constant ratio for each galaxy. Indeed very super-metallic and sub-metallic star-forming regions—in which the relative strength of the [N ii] lines may deviate significantly from the mean observed values—are less likely to be detected in the UV for the former and in the mid-infrared for the latter.

Images in the U, B, and R bands have been obtained either from the SINGS archives—as mentioned in the previous section—or observed in the context of the Steward Nearby U-band GaLaxy (SNUGL) survey, using 90prime (Williams et al. 2004).

Spitzer is a key observatory to estimate the total infrared luminosity. Indeed its two imagers cover a large range of infrared emission, from 3.6 μm to 8.0 μm for IRAC and 24 μm to 160 μm for MIPS. The relations to estimate the bolometric infrared luminosity routinely use the IRAC 8.0 μm and the MIPS 24 μm bands (see for instance Calzetti et al. 2005; Pérez-González et al. 2006; Boquien et al. 2009, and references therein). All galaxies but two have been observed as part of SINGS. We used the processed legacy data provided by the SINGS team. The only galaxies that are not observed by SINGS are NGC 5236 (also observed by Engelbracht et al. 2008) and NGC 5457 (observed by Gordon et al. 2008) are part of the Spitzer Local Volume Legacy Survey (Dale et al. 2009).

Images of the galaxies in FUV, Hα, and 24 μm are presented in Figures 1 and 2. For NGC 5236, the missing Hα image has been substituted with the R-band one.

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A summary of the bands, telescopes used, observing dates, exposure times, and sensitivities of all observations are presented in Table 2.

Given the multi-wavelength nature of this study, we have selected the star-forming regions using the GALEX FUV and the Spitzer MIPS 24 μm images. Indeed, not only do those wavelengths trace star formation but they also have a similar resolution (∼5''–6''), which ensures that the totality of the region is encompassed in other wavelengths that provide a better resolution such as the IRAC 8.0 μm and the optical bands. Given that they offer a complementary view of star formation—far ultraviolet emission absorbed by the dust is re-emitted in the infrared—the selection of the star-forming regions has been performed independently in those bands. This allows us not to miss regions that have a very low or a very high extinction, the former being mainly visible in FUV while the latter are primarily detected in the infrared.

Even at a resolution of ∼5''–6'', star-forming regions complexes are sufficiently resolved such that their shape have to be taken into account using polygonal apertures. Visual inspection shows that the irregular shapes are mainly due to the overlap of very close star-forming regions. The apertures have been made as small as possible to reduce the number of star-forming regions inside an individual aperture to limit the contamination by nearby sources. The goal is to select star-forming regions as simple as possible, and to avoid the most complex ones composed of stellar populations of different ages. To achieve this goal, we have defined apertures using polygons. Each polygon is defined manually to encompass as few star-forming regions as possible within a single aperture as well as to avoid artifacts, and background and foreground objects.

Even if some regions are most likely selected in the UV and in the IR but with different apertures, no attempt has been made to make a link between the two. This is made difficult by the fact that for a given region the apertures can be quite different, cover only a part of the region, or be split into several apertures. However, a visual inspection of the apertures shows that some regions have an aperture defined only from either UV or IR even if it is visible in both bands. This is due to the fact that the apertures for each band are built mainly for the most prominent regions.

The background flux is defined on a per-aperture basis using an annulus around the aperture. The radius and the width of this annulus is defined for each galaxy depending on the surface density of star-forming regions. Local background subtraction has been performed in all bands. The background level is then calculated using the mode of the pixels enclosed in the background annulus. To improve the determination of the galactic background level, for some wavelengths we have invalidated emission above a given threshold in the background annulus. This threshold has been manually determined to eliminate as much emission as possible from the nearby sources while keeping the genuine background emission. This was done for the GALEX bands as well as the Spitzer IRAC 8.0 μm and MIPS 24 μm bands. This threshold was not applied to broadband optical images where young star-forming regions are much less prominent; in the U, B, and R bands, the local background is dominated by an evolved stellar population.

The raw fluxes and the errors have been calculated using the IRAF procedure polyphot.

Following the aforementioned criteria, we have selected a total of 1146 star-forming regions in the eight galaxies constituting the sample. In order to increase the significance of the results we have subsequently selected only star-forming regions that have flux uncertainties of at most 20% in the GALEX FUV, NUV, and the Spitzer MIPS 24 μm band, leaving us with a total sample of 324 regions. The number of UV-selected and infrared-selected regions is presented in Table 3, for each galaxy in our sample.

We have performed an aperture correction on the infrared fluxes. As the method routinely used is not tailored for non-circular apertures, we have proceeded as described in Boquien et al. (2007). We have calculated an "equivalent radius": $r = \sqrt{S/\pi }$, r being the equivalent radius and S the surface of the aperture in units of pixels. The flux has then been corrected using this equivalent radius combined with the formulas provided in the Spitzer handbook for extended sources for IRAC⁹ and in Engelbracht et al. (2007) for MIPS. For the 8.0 μm (24 μm) band, the average correction factor was 0.94 ± 0.17 (resp. 1.70 ± 2.11). No aperture correction has been performed neither on UV images—as the corrections are very small—nor on optical images, thanks to their higher angular resolution.

We have corrected our UV and optical data for the effect of foreground Galactic extinction using the Cardelli et al. (1989) attenuation curve along with the differential extinction E(B − V) provided by the NASA/IPAC Extragalactic Database.

The observed fluxes in all bands are presented in Table 4. The luminosities of the star-forming regions span a factor ∼200 in FUV (5.15 × 10³²–1.00 × 10³⁵ W) and a factor ∼2000 in 24 μm (5.81 × 10³¹–1.23 × 10³⁵ W). We can see in Figure 3 that those two star formation tracers are strongly correlated with a Pearson correlation coefficient r = 0.75 between log(L(24)) and log(L(FUV)).

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We observe that especially at higher luminosities, the 24 μm luminosity increases faster than the FUV one. This is most likely an extinction effect, as can be seen in infrared luminous galaxies for instance. The fit of the sample gives log L(FUV) = 16.55 ± 0.85 + (0.52 ± 0.03) × log L(24). The slope is as expected, significantly smaller than 1.

While the correlation between the FUV and the 24 μm star formation tracers is good, the UV bands are impacted by the dust. The distribution of UV colors is presented in Figure 4.

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There is a clear distinction in the UV colors distribution among the galaxies. The bluest one NGC 5457 peaks 0.2 dex bluer than the reddest one, NGC 5236. This may be a consequence of the presence of older UV-emitting stars unrelated to the current star formation episode or the extinction, which affects UV luminosities (a range of 0.2 dex corresponds to an extinction range A_V ≃ 1 for the stellar component assuming a starburst attenuation curve). This is supported by the fact that very few star-forming regions have an UV color that is compatible with an ionizing population even though Hα is detected in most of them, which indicates a reddening unrelated to the age of the current episode. Indeed, assuming a Kroupa (2001) IMF, and a solar metallicity, a simple stellar population will still have EW(Hα)≃ 1 Å after 20 × 10⁶ years.

Among the 324 selected star-forming regions, we have suitable Hα imaging information for 228 and we measure their fluxes. The lack of Hα observations for NGC 5055 (we do not have the corresponding suitable R-band image to perform continuum subtraction making the Hα fluxes too unreliable to be used here) and NGC 5457 is responsible for this difference. Among those regions, 213 (respectively 184) are detected with S/N>3 (resp. S/N>5). It shows that the star-forming regions are young and have recently formed stars. Indeed, the Hα equivalent width is a good tracer of the age of a single star-forming episode for the first ∼10–5 × 10⁶ years. We will see in Section 6.2 that the U − B color is also a good tracer of the age.

In order to estimate attenuation values for our regions, we have made use of the 24 μm and the Hα images. Indeed Calzetti et al. (2007) showed that there is a very good correlation between the extinction-corrected Paα and a combination of the 24 μm and dust-obscurated Hα leading to an estimate of the intrinsic Hα luminosity:

$$\begin{equation} L\left({\rm H}\alpha \right)_{\rm intrinsic} = L\left({\rm H}\alpha \right)_{\rm observed}+0.031\times L\left(24\right). \end{equation} \tag{ 1 }$$

This permits to derive the extinction of the gas:

$$\begin{equation} A_V^{\rm gas} = 3.06\times \log \left[1+\frac{0.031\times L\left(24\right)}{L\left({\rm H}\alpha \right)_{\rm observed}}\right]. \end{equation} \tag{ 2 }$$

As the extinction of the stars is smaller, we assume here that A_V = 0.44 × A^gas_V (Calzetti et al. 2000). We obtain an extinction ranging from A_V = 0.06 to A_V = 1.28 with a mean <A_V> = 0.44 ± 0.28.

Note that as this method, to estimate the extinction, is dependent on the Hα, NGC 5055 and NGC 5457 fluxes cannot be corrected for the extinction and are therefore excluded from any subsequent analysis involving extinction correction.

To model the SED of individual star-forming regions, we have used the Pégase ii evolutionary spectral synthesis code (Fioc & Rocca-Volmerange 1997). We have assumed an instantaneous starburst having an age ranging from 1 × 10⁶ years to 300 × 10⁶ years with a constant metallicity of Z = 0.02 and a Kroupa (2001) IMF from 0.1 M_☉ to 120 M_☉. The impact of assuming solar metallicity in the models on our results will be examined in Section 6.2.

Fluxes and colors are determined convolving the generated SED—taking into account the nebular emission lines as well as the nebular continuum, which is important for young regions (Anders & Fritze-v. Alvensleben 2003)—with the spectral response function of the filters for the FUV, NUV, U, and B bands. The infrared luminosity is obtained calculating the absorbed flux by the dust. See the section hereafter for details about the dust models.

We use different dust models in order to probe the effect of dust–stars geometry: (1) the starburst attenuation curve (Calzetti et al. 2000): classically used in deep surveys with the IRX–β relation; (2) the foreground dust screen Small Magellanic Cloud attenuation curve (Gordon et al. 2003); and (3) the mixed stars and dust Small Magellanic Cloud attenuation curve using the relation: I_observed/I_intrinsic = 0.921 × (1 − 10^−0.4A(λ))/A(λ) adapted from Natta & Panagia (1984).

The dust extinction is applied to the unextinguished SED with A_V ranging from 0 to 3 by steps of 0.1. In this paper, conventionally, A_V designates the extinction of the stars. The extinction of the gas is noted A^gas_V. The nebular emission accounts for a small fraction of the total flux in the broad bands, and the same extinction law has been applied to the stellar and the nebular emissions in these cases.

A comparison with the models generated by Calzetti et al. (2005) using Starburst99 shows that the results are nearly identical.

In order to determine the total infrared emission of the selected star-forming region, we use the Spitzer IRAC 8.0 μm and MIPS 24 μm emission. While the exploitation of the MIPS 70 μm and 160 μm bands would yield better results, their resolution (17''and 38'') is too low to separate individual star-forming regions. For this study, we estimate the total infrared emission using the Calzetti et al. (2005) relation that was derived in a preliminary study on NGC 5194:

$$\begin{equation} \log L\left({\rm IR}\right) = \log \left[L\left(24\right)\right]+0.908+0.793\log \left[L_\nu \left(8\right)/L_\nu \left(24\right)\right]. \end{equation} \tag{ 3 }$$

The scatter around the relation within a galaxy is about 40% (Calzetti et al. 2005), which is the accuracy level we can expect for the determination of the total infrared flux of individual star-forming regions. Pérez-González et al. (2006) also derived a similar relation. Practically, the difference between the Calzetti et al. (2005) and the Pérez-González et al. (2006) IRX estimates for the selected star-forming regions is −0.07 ± 0.03 dex, which is only a few percent of the total range and does not alter the results presented in this study.

To test if the age is the "second parameter" we are looking for, an accurate determination of the stellar population ages is needed. Given the large number of star-forming regions involved, a direct spectral observation of the age sensitive 4000 Å break, as measured by the D₄₀₀₀ parameter, is not available for the majority of regions in our sample. We have decided to exploit the U − B color as a proxy to the 4000 Å break. Indeed the U-band is centered around 360 nm while the B-band is centered around 440 nm, on each side of the break. A simple Pégase II model using a Kroupa (2001) IMF from 0.1 M_☉ to 120 M_☉ and a metallicity of Z = 0.02 shows that for an instantaneous burst, the U − B color ranges from −1.18 after 1 × 10⁶ years to 0.04 after 300 × 10⁶ years (Figure 5, left panel).

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While the D₄₀₀₀ parameter is essentially extinction free thanks to the narrow wavelength range probed, extinction is strong at short wavelengths, inducing an important uncertainty regarding the broadband U and B fluxes. However, this problem is mitigated on using the U − B color. Indeed, when averaged on a number of dust geometries and extinction curves, an extinction of A_V = 1 yields only E(U − B) ∼ 0.1 × A_V mag. We will see in Section 6.3 that the stellar extinction—assuming A^stars_V = 0.44 × A^gas_V—ranges from A_V = 0.06 and A_V = 1.28, with a mean extinction of 0.44 magnitude, which yields an average uncertainty of 0.04 mag (0.1 mag if we assume a starburst attenuation law).

Young star-forming regions are the main source of Hα emission in star-forming galaxies. As the population ages, the Hα drops dramatically as stars emitting ionizing photons have a life expectancy typically under 20 × 10⁶ years. A standard way to estimate the age is the equivalent width of the Hα emission line, which decreases as the most massive stars die. The exact estimation would necessitate spectroscopic observations. Indeed, even if the R-band emission is not only constituted of the continuum—it is "polluted" by the Hα and [N ii] lines and the nebular emission in general—it is the best possible approximation with the available data. Another advantage is to limit the differential extinction as the Hα line and the R-band central wavelength are close.

A comparison of the evolution of U − B and Hα equivalent width age tracers against time is plotted in Figure 5, left panel, and they are compared with observations in Figure 5, right panel.

We see in Figure 5, right panel, that for all star-forming regions, the Hα equivalent width is reasonably high, ranging typically from ∼15 Å to ∼600 Å. This indicates a young age, typically less than 10 × 10⁶ years. The U − B color ranges typically from −1.3 to −0.1. There is a clear correlation between the Hα equivalent width and the U − B color with a Pearson correlation coefficient r = −0.52. NGC 5194 star-forming regions are significantly offset from the mean correlation, having a much lower Hα equivalent width for their U − B color (or having a much bluer U − B color for their Hα equivalent width). The instantaneous burst model with a Kroupa (2001) IMF and a metallicity of Z = 0.02 can reproduce most star-forming regions that have a U − B color redder than −0.9 assuming an extinction such as E(U − B) = 0.24 × A_V mag and ${\rm EW}\left({\rm H}\alpha \right)\propto 10^{-0.4\times 0.68\times A_V}$ with 0.04 < A_V < 1.28. This shows that while the U − B color is only weakly sensitive to the extinction, the inclusion of extinction effects is nevertheless needed to reproduce most of the observations. However, for the bluest U − B star-forming regions, the model significantly overpredicts the observations of the Hα equivalent width. One possible explanation is an insufficient background removal in the R-band image within each region, artificially decreasing the EW(Hα) values for blue U − B colors. An alternative explanation is a strong contamination of the R band by the Hα and [N ii] lines, which would lead to significantly overestimate the continuum in the R band. However, the mean EW(Hα) is 195 ± 193 Å and the typical width of a R-band filter is ∼1500 Å. This means the contamination is at most about 25%, insufficient to reproduce the observations. In Section 6.3, we will see that the characteristics of most of the star forming can be reproduced by a simple model in the IRX–β diagram. An important fraction of them, however, should not present any significant Hα emission—73% (resp. 60%) should be older than 12 × 10⁶ years (resp. 20 × 10⁶ years)—if the underlying hypotheses (the star formation history can be modeled as an instantaneous burst and the trend observed as a function of the perpendicular distance is an age effect) are correct.

A parameter that may affect the age estimate is the metallicity. Indeed, higher metallicity stars have a significantly redder U − B color due to the presence of a high number of metallic absorption lines in their atmosphere. An illustration of this effect on the U − B and the ultraviolet colors is presented in Figure 6.

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While the metallicity has an influence, it is small as the oxygen abundances are typically in the relatively narrow range 12 + log O/H= 8.6–9.2, except NGC 5457 whose outermost regions have a metallicity down to 8.2. As a reference, Asplund et al. (2005) determined the solar metallicity as Z = 0.0122 or 12 + log O/H = 8.66.

Another uncertainty is due to the synthesis of the U-band luminosities. Indeed, even in simple U − B, B − V color–color diagrams, the model tracks are not consistent with integrated photometry of dwarf galaxies (see Lee 2006, for more details).

In Figure 7, we present the IRX–β diagram of the selected star-forming regions compared with the model presented in Section 5.

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Several results have to be noted. We see that most of the star-forming regions are in general agreement with the models though a number of regions have a conspicuously blue UV color or a particularly low IRX. We also see that the selected star-forming regions describe a clear envelope mostly circumscribed in its upper part by the modeled starburst IRX–β relation of a very young starburst. We retrieve here the well-known result that quiescent star-forming galaxies lay under the starburst IRX–β curve.

A visual inspection shows an expected qualitative trend to have younger regions where the UV color is the bluest while on the right part there are predominantly older regions which have a redder UV color. Interestingly, the younger regions have a trend closer to the modeled IRX–β starburst relation. One explanation could be that it marks the locus of both constant star formation and young stellar regions. Indeed, in addition to their young age, the dust–stars geometry is likely to be similar to that of starburst galaxies (star-forming regions inside a dust shell). Another explanation could be that those regions are still relatively enshrouded in their birth cloud. However, as shown by Prescott et al. (2007), only 3% of regions are completely enshrouded in dust.

Here we quantify whether age may be the parameter accounting for the deviations of our regions from the starburst attenuation curve in the IR–β diagram.

A standard tool to evaluate the distance of a star-forming region (or a galaxy as a whole) from the standard starburst attenuation law is the perpendicular distance in the IRX–β diagram (Kong et al. 2004, for instance). The distance is simply defined as the Euclidean distance:

$$\begin{equation} d = \sqrt{\left(x-x_{\rm EL}\right)^2+\left(y-y_{\rm EL}\right)^2}, \end{equation} \tag{ 4 }$$

where x (resp. x_EL) and y (resp. y_EL) are the β and IRX values of the individual star-forming regions (resp. of the extinction law locus that is the closest to the observed value) and d is the dimensionless distance in the IRX–β plot. The starburst and SMC IRX–β relations are obtained from the model presented above. The SMC extinction law will be studied more in detail in Section 7. We assume an age of 6 × 10⁶ years, which gives an intrinsic log F_λ(FUV)/F_λ(NUV) = 0.37. The IRX–β relation is obtained varying the extinction applied to this population. Following the Kong et al. (2004) convention, star-forming regions which have a higher (resp. lower) than expected IRX given their UV slope will have d>0 (resp. d < 0).

In Figure 8, we plot the equivalent width as the ratio between the Hα flux and the R-band flux density corrected for the extinction using the formula in Section 6.2 against the perpendicular distance.

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As expected, the mean Hα equivalent width increases as a function of the perpendicular distance with a slope of 385 and a large 1σ scatter around the linear fit: 150 Å. The perpendicular distance and the Hα equivalent width are weakly correlated with a Pearson correlation coefficient r = 0.18. The most surprising result is that even at large negative perpendicular distances, a significant Hα emission is detected. This result shows that the age as measured by the Hα equivalent width is not the "second parameter" we are seeking. From the point of view of star formation, it could mean that the assumption of an instantaneous starburst is not valid. We will explore if variations of the star formation history can explain the observations in Section 6.5.

In Figure 9, the extinction-corrected U − B—assuming a starburst attenuation law: E(U − B) = 0.24 × A_V mag—is plotted as a function of the perpendicular distance.

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While a trend of the U − B color as a function of the perpendicular distance could be expected, it is particularly weak, with a slope of only −0.62 ± 0.20. The perpendicular distance and the U − B color are correlated with a Pearson correlation coefficient r = −0.17. The weakness of the trend combined with the important scatter hints that another physical phenomenon than the age plays a much more important role.

We have shown here that the age, which was a prime candidate to explain the deviation from the starburst attenuation law in the IRX–β diagram does not seem to play a major role. Indeed, using two different age tracers, the U − B color and the Hα line equivalent width, the large dispersion around the relation shows that the influence of the age is at most minimal under the current assumptions and for the timescales probed by those two tracers.

We have shown that an instantaneous starburst cannot simultaneously reproduce the large perpendicular distances and a non-negligible Hα emission. In particular, there are a number of regions in our sample that are too red in UV colors. We now consider the possibility that the stellar populations in those star-forming regions are more complex than a simple instantaneous burst description. We thus introduce a model of the stellar population of a galactic disk that considers an exponentially decreasing SFR of the form:

$$\begin{equation} {\rm SFR}\left(t\right) = a\times \exp \left(-t/\tau \right), \end{equation} \tag{ 5 }$$

where a is an arbitrary normalization constant in units of M_☉ yr⁻¹, t is the time in years, and τ is the time constant in years.

First of all, we want to see if an exponentially decreasing SFR is able to reproduce the observations. To take into account different cases of star formation history, we test three models which differ by the ratio SFR(12 × 10⁹)/SFR(0). SFR(0) is the SFR at t = 0 year and SFR(12 × 10⁹) is the SFR at t = 12 × 10⁹ years, both from Equation (5). The values of this ratio are 1/10, 1/100, and 1/1000 (which correspond to a birthrate parameter of 2.6 × 10⁻¹, 4.7 × 10⁻², and 6.9 × 10⁻³ and a timescale of 5.2 × 10⁹ years, 2.6 × 10⁹ years, and 1.73 × 10⁹ years, respectively). It turns out that this star formation history can be readily excluded as it cannot reproduce at all the observations. The reason is that even for SFR(12 × 10⁹)/SFR(0) = 1/1000, the current SFR is high enough to overwhelm ultraviolet emission from older stellar populations.

A more realistic model for a galactic star-forming region is a small burst on top of the galactic stellar population. To model the galactic stellar population, we use an exponentially decreasing SFR as described in Equation (5) for 0 ⩽ t ⩽ 11.95 × 10⁹ years, no star formation for 11.95 × 10⁹ < t < 12 × 10⁹ years and an instantaneous burst at t = 12 × 10⁹ years. The rationale is that in the area of the star-forming region, due to the diffusion of the stars over time, the stellar population is made of stars born in different regions of the galaxy subsequently mixed. However, stars younger than a few 10 × 10⁶ years are too young to have migrated long distances. In addition, we assume that in the last 50 × 10⁶ years, no star formation has taken place at the location of the current star-forming region and no significant migration from nearby star-forming regions has occurred. The mass of the instantaneous starburst at t = 12 × 10⁹ years is defined as M_stars/300 following Calzetti et al. (2005), were M_stars is the mass of the stars constituting the background galactic population. The model is plotted in Figure 10 along with the observations in an IRX–β diagram.

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While this model reproduces a much larger range of ultraviolet colors as a whole, it still cannot explain the Hα emission of such regions. Indeed, initially the instantaneous starburst emission dominates over the older population until it fades away after a few tens of millions years, after which the older population dominates and is responsible of the redder ultraviolet colors compared to the model presented in Section 5.

While a continuous star formation does not account for the observations, we can take into account a more stochastic nature of the star formation history by considering a single, still UV emitting, older burst. Indeed, the presence of a significant old stellar population can have an influence on the UV color. Individual star-forming regions with local backgrounds subtracted are less affected by this effect than integrated galaxies. Some of the observed regions are redder than what can be reproduced by an ionizing population and a SMC extinction law (see Figure 7 and Section 7, the SMC extinction law is already extreme in that it has a very steep slope in the UV, this means that for a given IRX, it reddens the UV color more than any other extinction law considered in this study). That there are some regions, which have an even redder color, hints about the possibility of a dilution by older stellar populations. In order to test this, we have made a simple model assuming two instantaneous bursts, the one we are currently observing and another one which is 300 × 10⁶ years old. The star formation history is undoubtedly more complex but cannot be precisely retrieved with the current observations. However, NUV emitting populations have a life expectancy of about 10⁹ years. We take here a 300 × 10⁶ years old instantaneous burst as an approximation of the real star formation history. The mass ratio of the more evolved stellar population to the younger one varies from 0 to 300. We have selected all star-forming regions that have a redder UV color than a 20 × 10⁶ years old starburst extincted with the SMC extinction law. We then have calculated what dilution would be necessary to redden the UV color, if those regions were actually 20 × 10⁶ years old to account for the fact that they still emit in Hα. There is a total of 67 star-forming regions which have a UV color redder than a SMC-extincted 20 × 10⁶ years old burst. The model shows that the mean mass ratio is 7.8 ± 7.1 with a median of 5. This is much smaller than the ratio for integrated galaxies which reach up to few hundreds. This corresponds to a mean flux ratio of 0.15 in FUV and 0.29 in NUV. Note however that 64% of those star-forming regions have flux uncertainties such that the observations could be reproduced without needing an older stellar population.

The dilution by an old stellar population has an influence not only on the UV color but also simultaneously on the U − B color, as we can see in Figure 11.

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We see that even a relatively small mass ratio can have a significant influence on the colors. The influence fades away as the older population gets older. Indeed, the intrinsic UV luminosity drops quickly with age. Hence, even if the older population gets redder, a higher mass ratio is needed to offset its smaller UV luminosity. On the other hand, the life expectancy of U- and B-emitting stars is much longer than those which predominate the UV luminosity. That is why an older population has significantly more influence on the U − B color than on the UV color.

We have shown in Section 6.4 that there is a weak correlation between the perpendicular distance from the IRX–β relation and the age as traced by the Hα equivalent width and the U − B color. In all cases, the trends with the age are too weak relative to the scatter in the data to support the notion of aging stellar populations as an important "second parameter," at least for the timescales probed by the U − B color and the Hα equivalent width. We have seen in Figures 8 and 9 that neither the U − B color nor the Hα equivalent width strongly correlate with the perpendicular distance. The absence of correlation is independent of the "reference" attenuation curve, be it the starburst or the SMC extinction law. The reddening of the SED is therefore not due to age effects but is a consequence of another parameter.

It appears that, contrary to what has been found studying integrated galaxies by Kong et al. (2004) for instance—but in agreement with Johnson et al. (2007)—there is no obvious trend between the perpendicular distance and the age in the case of individual star-forming regions.

In this study we have tested three different kinds of extinction laws: starburst (Calzetti et al. 1994, 2000; Meurer et al. 1999), foreground SMC (Gordon et al. 2003), and mixed SMC. Conventionally, the perpendicular distance is derived from the IRX–β starburst relation (Kong et al. 2004; Cortese et al. 2006, for instance). There are several indications that there is a range of extinction laws at work in quiescent star-forming galaxies.

As inferred from Figures 7, 12, and 14, both a starburst attenuation curve and an SMC extinction curve with foreground dust are required to span the locus occupied by the data points. Neither curve individually is a perfect match to the data, and both (plus combinations of the two) are required to span a large range of the data locus. Likely this indicates a variation in the applicable dust geometries to the individual regions.

In Section 7, we have shown that assuming a range of models (starburst, foreground SMC assuming A_V = A^gas_V or A_V = 0.44 × A^gas_V—this ratio is prominently dependent on the dust–stars geometry—and mixed SMC), it is possible to reproduce simultaneously the UV color and the Hα emission of most star-forming galaxies. We assume that the starburst and foreground SMC are the two most "extreme" laws at work in quiescent star-forming galaxies and that there is a range of dust–stars geometries in between. The two curves (and the SMC needs to be implemented with differential extinction between stellar and nebular emission) bracket most of the range of observed values. A variation of the extinction curve has also been detected for UV-luminous galaxies at z ∼ 2 by Noll et al. (2009).

Dilution of actively (Hα emitting) star-forming regions by an older (∼300 × 10⁶ years) instantaneous burst population is a necessary requirement for a few of the reddest (in UV colors) regions but not for all.

We remove local background from all our star-forming regions, thus removing Hubble-time-averaged stellar populations. However, the typical region sampled by our apertures is around 300–500 pc. In this physical region, we can expect multiple populations to be present and possibly contribute to the observed colors. Indeed for the reddest UV color regions, the required mass ratio between an ionizing stellar population and an older, 300 × 10⁶ years old stellar population is about 1/5. This indicates the possibility of five to six generations of stars over the past 300 × 10⁶ years, within a 500 pc region. However, our data cannot discriminate between this possibility and the alternative of yet more complex star–dust geometries and extinctions than what considered here.

Interestingly, we note that very few regions that are detected in the UV do not have any Hα counterpart. One of the possible reasons is that regions that are sufficiently old do not emit in Hα anymore and tend to dissolve to become part of the diffused UV emission from the galaxy. Hence, they were not selected and only acted as a contaminant. The fact that we do not find the trend that can be found in integrated galaxies hints that it may be due, in reality, to the contamination by older stellar populations. Indeed, as we have seen in this paper, the age or the latest generation of stars does not seem to play any significant role. We think the birthrate parameter is not appropriate either in the sense that it is inaccurate as it averages the SFR over the life of the galaxy whereas the typical lifespan of the UV is about 10⁹ years. We therefore think that the fact that few regions are not detected in Hα hints in favor of the scenario of the contamination.

Finally, it can be noted that Dale et al. (2009) found a trend between the perpendicular distance and the Hα equivalent width calculated using the same method as the one described in this paper. The most likely explanation is that the trend is due to the pollution of the underlying continuum by evolved stellar populations. Indeed, their average Hα equivalent widths are averaged over the galaxy. If we assume that the mean age of star-forming regions is the same in all galaxies—which is a reasonable assumption for quiescent star-forming galaxies—the differing amount of underlying stellar populations can create such a correlation: they simultaneously increase the perpendicular distance reddening the UV color and lower the Hα equivalent width by increasing the flux of the continuum. In addition, as the R-band emitting and the UV-emitting stars have a different life expectancy, it induces some scatter in the relation.

From what we have shown previously, the usual SFRs estimates based on the assumption of the starburst IRX–β relation are unreliable in the case of quiescent star-forming galaxies. To estimate the SFR, one approach can be to derive an empirical law from a sample of galaxies, like has been done by Cortese et al. (2006), for instance; however the scatter remains important.

To determine accurately the actual law, it is crucial to estimate the fraction of the UV color that is contributed by an older population as we have shown in Section 6.5. Taking into account the age of the stellar population, Cortese et al. (2008), for instance, have provided some recipes to correct for the UV extinction, assuming a Large Magellanic Cloud extinction law. Another critical point to derive the actual SFR is the choice of an extinction law. Indeed, as we have already mentioned, the effect of the extinction is much more dramatic on the UV color in the case of a SMC law. This can be seen in Figure 12 for instance. In Figure 16, we plot the ratio of the estimated SFR assuming a starburst attenuation law to the estimated SFR assuming a SMC extinction law as a function of the UV color.

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We see that indeed the effect on the derived star formation law can be quite dramatic. If we assume a starburst attenuation law, for A_V = 1 we can overestimate the SFR by a factor up ∼7 if the actual extinction law is foreground SMC-like. Conversely, a similar error, but in the sense of underestimating the SFR, will be made if the foreground SMC extinction is adopted, but the actual extinction is described by a starburst attenuation curve.

As we have shown, the age seems to be only a minor factor regarding the location on the IRX–β diagram. However, standard SFR estimators are significantly age-dependent. Indeed, the Kennicutt (1998) estimators for instance are based on the assumption of a constant SFR during 100 × 10⁶ years. However, if it is sensible for a galaxy-averaged luminosity, it is unlikely that small individual star-forming regions undergo such a star formation history. If we assume a foreground SMC, the best-fit age is 6 × 10⁶ years.

Even if we have selected over 300 star-forming regions, the location of each of the region is dependent on the galaxy metallicity, for instance. As no such study has been performed before, we can only compare to samples of integrated galaxies. In Figure 7, we plot the IRX–β diagrams along with data points from SINGS and LVL (Dale et al. 2009).

We see that the IRX range is very similar to that of individual star-forming regions in galaxies. Regarding the UV color, it tends to be redder. This is particularly striking for galaxies which have a small IRX lower than −0.3, but have red UV colors of 0.24 ± 0.07 compared to 0.37 ± 0.05 for galactic star-forming regions. This can be explained by the influence of an older stellar population. Indeed, photometry of integrated galaxies is particularly influenced by a near-ultraviolet emitted older stellar population which reddens the UV color. Conversely, individual star-forming regions are relatively less affected by older populations as (1) the specific SFR in a star-forming region is higher than for an integrated galaxy hence lowering the relative luminosity of any older population; and (2) the way the background level is measured naturally subtracts the contribution of an older populations in the aperture (see Section 4.1). Therefore, rather than an undersampling of the parameter space, the fact that we have not detected regions, which have simultaneously a red UV color and a low IRX, is a consequence of a bias introduced by the emission of older stellar populations in the case of integrated galaxies. As we can see in Figure 7, the envelope of SINGS and LVL galaxies is shifted toward redder colors compared to the individual star-forming regions; and there is a significant number of galaxies with extremely red UV colors: 9.6% of the galaxies in the combined LVL and SINGS sample and 1.2% of the individual star-forming regions have a log F_λ(FUV)/F_λ(NUV) redder than 0.