THE UNIVERSAL INITIAL MASS FUNCTION IN THE EXTENDED ULTRAVIOLET DISK OF M83

Observations were made in the R_C and NA659 (Hα) bands (Okamura et al. 2002; Yoshida et al. 2002; Hayashino et al. 2003) on 2010 September 7. Two Suprime-Cam fields cover the entire XUV disk of M83, i.e., the whole area with an H i surface density above 1.5 × 10²⁰ cm⁻² (roughly the detection limit in Miller et al. 2009) and a large surrounding area. Figure 1 shows the area coverage and the H i contour (red) on a GALEX FUV image. The two fields are marked with black overlapping solid boxes. The exposure time for each field is 5 × 12 minutes and 5 × 4 minutes in the NA659 and R_C bands, respectively. The yellow contour indicates the edge of the optical disk (roughly, the 25 mag arcsec⁻² isophote). The typical seeing was ∼1''.

Data were reduced in a standard way using the Suprime-Cam reduction software (Yagi et al. 2002; Ouchi et al. 2004). We performed overscan subtraction, flat fielding, distortion correction, background subtraction, and mosaicking. The flux calibration was performed against standard field stars (Oke 1990; Landolt 1992). R_C and NA659 bands are practically at the same wavelength (Hayashino et al. 2003), and we do not expect any spatial variation in the R_C/NA659 ratios of typical foreground field stars. However, residual errors remain at large spatial scales in the ratios (a few percent) which were likely introduced in flat fielding. We made a correction by making an NA659/R_C ratio map using the average ratio of field stars in each 200'' × 200'' grid and by normalizing the NA659 image. The 1σ photometric limits with the ∼5'' aperture (i.e., GALEX resolution) are 24.90 and 25.56 AB mag in the NA659 (Hα) and R_C, respectively.

We use archival GALEX FUV and NUV images (Bigiel et al. 2010). The data are obtained from the GALEX data archive through Galexview in the multimission archive at STScI (MAST). The GALEX observations and data reduction were discussed in Bigiel et al. (2010). The FWHM sizes of the point-spread functions are measured with the IDL software ATV (Barth 2001) and are 47 for FUV and 52 for NUV. The 1σ photometric limits with the ∼5'' aperture are 26.34 and 26.20 AB mag in the FUV and NUV bands, respectively.

Our analysis is guided by the stellar population synthesis model Starburst99 (Leitherer et al. 1999). The Padova stellar evolution tracks with asymptotic giant branch stars are adopted. Most UV-bright objects in the XUV disk of M83 are likely stellar clusters (Thilker et al. 2005; Gil de Paz et al. 2007). Therefore, we adopt an instantaneous burst approximation to model their photometric evolution.

We will show that the standard Salpeter IMF (Salpeter 1955) explains the observations well. Figure 2 demonstrates the differences between the standard and truncated IMFs. The cluster mass is set to 1000 M_☉ for the plot, which is roughly the minimum mass of a cluster to fully populate the IMF up to an O star (see Appendix A). Note that a factor of 10 increase in cluster mass shifts all the magnitude curves in Figure 2 (top) systematically upward by 2.5 mag, but it does not change the color curves. For these models, we assume the Salpeter IMF with a lower cutoff mass of m_l = 0.1 M_☉. The upper cutoff mass is set to m_u = 100, 20, and 3 M_☉, which corresponds to the masses of the most massive O-, B-, and A-type stars, respectively (Cox 2000). In other words, the last two models represent the truncated IMF (or, almost equivalently, the steeper IMF) without O or OB stars. We adopt 20% of the solar metallicity (0.2 Z_☉) from the spectroscopic measurements (Gil de Paz et al. 2007; Bresolin et al. 2009). For reference, the spectra of individual O, B, and A stars are discussed in Appendix B.

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There are quantitative differences between clusters with and without OB stars, i.e., between the standard and truncated (steeper) IMFs. Clusters without OB stars are fainter by 6 mag in FUV for the first 10 Myr and never become as blue as FUV–NUV < 0.2–0.3 mag. Therefore, blue clusters (<0.2–0.3 mag) must have O and/or B stars. The FUV–NUV color is insensitive to the difference between clusters with only B stars (up to m_u = 20 M_☉) and with both O and B stars (100 M_☉). This is primarily because the GALEX bands trace only the Rayleigh–Jeans side of stellar thermal radiation for both O and early-type B stars (Appendix B). The FUV–NUV color is therefore a useful indicator of the presence of O and/or B stars in a cluster.

The NA659 − R_C color differentiates clusters with O stars from those without them, since O stars emit a significantly greater number of ionizing photons than B stars (Sternberg et al. 2003). This is demonstrated in Figure 2 (bottom). Clusters with NA659 − R_C < −1 mag must have O stars, and those with NA659 − R_C < −0.3 mag should have O and/or B stars. For this plot, we calculated the Hα line luminosity L_Hα using the Lyman photon flux Q_Lyc from Starburst99 and the relation L_Hα[erg s⁻¹] = 1.37 × 10⁻¹²Q_Lyc[s⁻¹] from case B recombination with an electron temperature of 10⁴ K (Gavazzi et al. 2002). Case B recombination is perhaps a reasonable assumption even in the low-density environment, since the optical depths in the Lyman resonance lines are very likely quite large (Osterbrock & Ferland 2006) in any star-forming conditions. The NA659 magnitude is based on the stellar continuum luminosity plus L_Hα. We ignore the effect of [N ii] emission since the effect is very small (Gil de Paz et al. 2007; Kennicutt et al. 2008; Goddard et al. 2010; see Section 4.1).

Counting blue clusters in FUV–NUV and NA659 − R_C constrains the IMF at its high-mass end. Clusters become bright in Hα ("blue" in the color NA659 − R_C) predominantly due to O stars, while FUV–NUV is due to both O and B stars. Since O stars have much shorter lives than B stars, NA659 − R_C changes faster than FUV–NUV (Figure 2). Under the assumptions of instantaneous cluster formation and a constant cluster formation rate, the numbers of blue clusters in FUV–NUV and NA659 − R_C (N_UV and N_Hα) should be proportional to the durations that clusters are blue (t_UV and t_Hα, respectively). Thus, we expect N_Hα/N_UV = t_Hα/t_UV if the difference in the populations is due to a simple aging effect starting from the initial populations of the standard IMF. The assumption of a constant cluster formation rate should be approximately accurate when integrated over the large XUV disk and over a short timescale, i.e., the young ages of clusters which can be detected with our color selection criteria (below). In fact, the clusters that we count in Section 5.3 are distributed over the UV disk (Figure 1).

For the standard IMF (m_u = 100 M_☉ and 0.2 Z_☉), a cluster is blue (e.g., FUV–NUV < 0.0 mag) for t_UV = 70.8 Myr and Hα-bright (e.g., NA659 − R_C < −1.0 mag) for 5.8 Myr. Therefore, the number ratio should be N_Hα/N_UV = 0.08 if each population is the consequence of the cluster aging effect. We will compare the observations with this theoretical prediction.

We identify and count stellar clusters at the GALEX resolution (∼5''; ∼ 109 pc at the distance of M83). It is possible that clusters may be blended at this resolution; however, even in that case, our analysis is valid if clusters formed in such proximity are typically coeval.

UV-bright objects are identified based on the FUV image using the SExtractor package (Bertin & Arnouts 1996). Saturated stars and image edges are masked before the identification. Objects within the traditional optical disk (yellow contour in Figure 1) are excluded. We confirmed the very low probability of false detection using the negative image technique. SExtractor is run against the sign-flipped FUV image and detected only one false target at 25.41 mag in FUV. Thus, false detections have a negligible impact on our number counts.

The aperture photometry is carried out in the four bands with the dual image mode of SExtractor using the FUV image as the reference. The 1σ photometric limits with the aperture of the GALEX resolution (∼5'') are 24.90, 25.56, 26.34, and 26.20 mag in the NA659 (Hα), R_C, FUV, and NUV bands, respectively. The sensitivity in NA659 (FWHM = 120 Å) corresponds to a flux of 7.98 × 10³⁴ erg s⁻¹ at a distance d = 4.5 Mpc, which is sufficient to detect an H ii region around a single B star (e.g., 3.44 × 10³⁵ erg s⁻¹ in the case of B0; assuming case B recombination; see Appendix B). We note that the NA659 band includes stellar continuum emission as well as Hα emission.

The contamination from [N ii] λ6548, 6583 in the NA659 photometry is neglected. The line ratio [N ii]/Hα is small (≲ 0.1) in the outskirts of galaxies (Gil de Paz et al. 2007; Kennicutt et al. 2008; Goddard et al. 2010). Even in the extreme case that the stellar continuum has zero contribution to the NA659 flux, the error is only 0.1 mag (and likely less in more realistic conditions).

Figure 1 shows that the Subaru data cover both the inside and the outside of the H i contour (roughly the H i detection limit). Recently formed FUV-bright objects are more likely to reside inside the H i contour as star formation occurs in gas. For the background subtraction in Section 4.4, the objects inside the H i contour (hereafter, IN objects) and outside (OUT objects) are separately cataloged. Note that we intensively used the IMCAT software package (N. Kaiser 2004, private communication)⁸ for the following data analysis.

In Section 5.3, we will discuss a selection of clusters based on their NA659 − R_C color; but in advance, Figure 1 shows the locations of clusters with NA659 − R_C < −1 mag (i.e., bright in Hα). They are distributed over the entire XUV disk, and all are within the H i contour (see Section 4.4).

The extinction curves of Pei (1992) are adopted to correct for Galactic and internal extinctions. The extinctions in FUV, NUV, R_C, and NA659 are (A_FUV, A_NUV, $A_{R_{\rm C}}$, A_NA659) = (2.58, 2.83, 0.81, 0.81)A_V for the Galaxy, (3.37, 2.61, 0.80, 0.80)A_V for the Large Magellanic Cloud (LMC), and (4.18, 2.59, 0.79, 0.79)A_V for the Small Magellanic Cloud (SMC), where A_V is the extinction in V-magnitude. We note that the FUV–NUV color becomes bluer under the Galactic extinction, but redder under the LMC and SMC extinction.

The Galactic extinction correction is made for all objects using A_V = 0.218 mag (Schlegel et al. 1998). We do not apply an internal extinction correction until Section 5, but it will be corrected using A_V = 0.1 mag and the SMC extinction curve for the following reason. The measured metallicity of most outer objects is low (∼0.2 Z_☉; Gil de Paz et al. 2007), and therefore, the extinction curve of the SMC is perhaps the most appropriate. Using E(B − V) values from Gil de Paz et al. (2007), we estimate the amount of internal extinction to be around A_V ∼ 0.1 mag with outliers (e.g., 0.0–1.0 mag). We therefore adopt A_V ∼ 0.1 mag for the statistical correction, and this degree of extinction will be supported by a comparison with a model color in Section 5.2.

The mass detection limit is determined in color–magnitude space with the help of models. Figure 3 shows color–magnitude diagrams for IN objects. The overlaid solid lines are the 3σ and 5σ mag detection limits and model evolutionary sequences for clusters with masses of 10², 10³, and 10⁴ M_☉. The models are for clusters with the standard Salpeter IMF with (m_l, m_u) = (0.1, 100 M_☉) and metallicity 0.2 Z_☉. Models with lower m_u do not reproduce clusters as blue as observed (Figure 2 and see discussion below). Clearly, the mass detection limit changes as a function of color in Figure 3; it decreases as clusters become redder. We note that the R_C and NA659 bands are practically at the same wavelength, and therefore, NA659 − R_C is zero without Hα emission. A negative NA659 − R_C color indicates the presence of associated Hα emission.

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The top panel shows that the Subaru observations detect clusters down to ∼10² M_☉. Clusters become redder and fainter as they age, and those around the detection boundary (10² M_☉) become too faint when they become redder than NA659 − R_C ∼ −0.6 mag. In other words, the sample is complete down to 10² M_☉ in the range NA659 − R_C < −0.6 mag. It is complete down to 10³ M_☉ in NA659 − R_C < 0.0 mag. The extinction is negligible, as shown by the extinction vector (for A_V = 0.1 mag) in the plot.

The bottom panel shows the corresponding color–magnitude diagram in the UV. Again, the mass detection limit is a function of the color range (and thus, the cluster age). The detection limit is ∼10³ M_☉ for the color FUV–NUV < 0.0 mag and is even deeper (∼10² M_☉) for FUV–NUV < −0.2 mag. The extinction is not negligible in FUV and NUV and will be discussed later.

Note that the very blue objects in the bottom panel (FUV–NUV ≲ −0.3 mag and FUV ∼ 22–24 mag) are bluer than any model cluster with the standard IMF can reproduce and are located approximately in the region where single O stars appear (the models of O3 and B0 stars are also plotted). These objects are not included in our number count, since they appear below the mass selection criterion in Section 5.3. We will discuss these objects in Section 5.1.

The contamination of background (and foreground) objects has been an obstacle in identifying the objects within nearby galaxies (Werk et al. 2010; Goddard et al. 2010). The large field of view of Suprime-Cam is a clear advantage as it enables us to remove such contamination statistically. The objects outside the H i gas contour (OUT objects; see Section 4.1) are most likely in the background, whereas IN objects include stellar clusters within M83 as well as background objects.

The IN and OUT objects show different colors statistically. Figure 4 shows the plots of NA659–R_C versus FUV–NUV for the IN and OUT objects above the 5σ mag detection limit and above the 10³ M_☉ threshold line in Figure 3 (bottom). Figure 5 is a histogram of FUV–NUV color for the IN (green) and OUT objects (blue). Clearly, the IN objects are bluer in FUV–NUV than the OUT objects and preferentially have FUV–NUV < 0.2–0.3 mag, while the OUT objects are more likely to have FUV–NUV > 0.2–0.3 mag. Figure 4 shows that virtually all objects with NA659 − R_C < −0.3 mag (OB stars) are IN objects; almost no young stellar clusters exist outside of the H i gas. This clear distinction ensures that the objects outside of the H i gas are not the young clusters in M83 and represent the background population. Note that IN objects are young stellar clusters, not very old clusters with many evolved FUV-bright stars, such as extreme horizontal branch stars, blue stragglers, or planetary nebulae. The old clusters do not become as blue in FUV–NUV as our IN objects (Donovan et al. 2009).

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The background contamination in the IN objects can be removed statistically; we subtract the OUT objects from the IN. In Figure 5, the number of the OUT objects are scaled by the IN/OUT area ratio (55%) and subtracted from that of the IN objects. The derived histogram (red) represents the population of young clusters with mass >10³ M_☉ in the XUV disk.

Virtually all clusters after the subtraction show blue color in FUV–NUV (<0.2–0.3 mag; Figure 5), suggesting that all of these young clusters have O or, at least, B stars (see Figure 2). Thus, massive stars are populated even in the diffuse gas environment. It is also remarkable that almost no red objects (FUV–NUV > 0.2–0.3 mag) exist. This confirms that OUT objects are distributed everywhere across our field of view and represent the background objects; thus, our background subtraction is fairly successful.

There is a possibility that old stellar clusters (i.e., FUV–NUV > 0.2–0.3 mag before extinction correction) exist both in the IN and OUT regions and are removed from the IN population. However, it should not affect our cluster count analysis as we discuss only the young clusters. Such a population, if it exists, must be fairly uniformly distributed both in the IN and OUT regions, since the count after the subtraction is nearly zero in FUV–NUV > 0.2–0.3 mag. We also note that the apparent magnitudes of low-mass clusters (≲ 10³ M_☉) fall below our detection limit after ∼100 Myr (Figure 2, top). Again, this is not a problem with the selection criteria that are adopted in our analysis (Section 5.3).

The presence of ionizing stars (O stars) is evident even in small clusters (<10³ M_☉) in Figure 3, suggesting that the IMF is not truncated. Massive stars do not form under the truncated IMF at all. On the other hand, they should appear occasionally even in small clusters under the stochastic IMF, though they tend not to appear in a small sample due to their low probability of formation in small clusters. Such a stochastic effect becomes particularly apparent when the cluster mass is small (<1000 M_☉). Our Subaru observations detect small clusters (down to ∼10² M_☉) and confirm that even those small clusters show Hα excess (i.e., NA659 − R_C < 0.0 mag); and some even have NA659 − R_C < −1.0 mag, a color which only O stars can produce. Thus, O stars are present in the 10^2–3 M_☉ clusters. The IMF is not truncated even in the low-density and low-metallicity environment.

More precisely, it is necessary to account for the stochastic effects in discussions of very low mass clusters (<10³ M_☉)—and even then, our result still supports the stochastic IMF over the truncated IMF, as we discuss below. We first need to consider the likelihood that a cluster with a given small mass has a massive star. In Appendix A, we estimate that a 10³ M_☉ cluster is likely to have as massive a star as 40 M_☉; the cluster mass must be greater than ∼400 M_☉ to have a high probability of hosting at least one O star (>20 M_☉); a 10² M_☉ cluster likely hosts up to a ∼10 M_☉ star.

The NA659 − R_C color is sensitive to the mass of the most massive star in a cluster when the cluster is young, whereas FUV–NUV does not distinguish O stars from B stars well (Section 3.1; Figure 2; see also Appendix B). If a cluster has no massive star, it should appear redder (NA659 − R_C > −1 mag; Figure 2) than the observed clusters in the range 10^2–3 M_☉; yet some clusters appear in the range NA659 − R_C = −1 ∼ −2 mag. Massive O stars in small clusters should be populated stochastically. In addition, a stochastically populated single O star can outshine a cluster with a small mass (10^2–3 M_☉; Figure 2). This may result in an overestimation of the cluster mass when we apply the standard IMF with m_u = 100 M_☉ to the cluster (as done in Figure 3). Therefore, the masses of small clusters that appear in the range 10^2–3 M_☉ in Figure 3 could be actually even less. This prefers the stochastic IMF, as even the less massive clusters have O stars.

The discussion so far is about clusters of stars. Another possible evidence for the presence of O stars is the population of very blue objects (FUV–NUV ≲ −0.3 mag) in Figure 3 (bottom). They have the apparent magnitude and color similar to those of a single O star. They are possibly isolated, single O stars or small clusters with an O star(s) but without many low-mass stars. Higher resolution images are necessary to confirm them; their presence, if confirmed, may be stronger evidence for O stars that are formed in the low-density environments.

The internal extinction is assumed to be A_V = 0.1 mag from spectroscopic measurements (Section 4.2; Gil de Paz et al. 2007). This degree of extinction on average is also supported by a comparison with the model curve in Figure 4 (top). The extinction vector, corresponding to A_V = 0.1, is also plotted. An extinction correction by this amount creates agreement between the UV data and the model curve, providing additional support for the adopted A_V.

We assume that a stellar cluster (traced in R_C) and the surrounding ionized gas (in NA659) suffer from extinction by the same amount. The two components may have different spatial distributions and a slightly different attenuation (e.g., E(B − V)_continuum ∼ 0.44E(B − V)_gas in case of more active star-forming environments; Calzetti 2001). However, the difference is negligible for our analysis since the extinction is small (A_V = 0.1).

Detected clusters with a color of NA659 − R_C < −1 mag are evidence that some clusters host O stars. Here we test whether their abundance, relative to the ones without O stars, can be explained by a simple aging effect with the standard IMF. Under the assumptions of instantaneous formation of star clusters and a constant cluster formation rate over the XUV disk, the numbers and durations of blue clusters should show the relation N_Hα/N_UV = t_Hα/t_UV, if the relative cluster populations are due to the aging effect.

Consistent sample selection between GALEX and Subaru data is crucial in this analysis. Each of the four photometric bands has its own detection limit (Figure 3), and a bias could be introduced if only magnitude detection limits are taken into account. We therefore use the cluster mass and color as thresholds for cluster counts. As discussed in Section 4.3, both GALEX and Subaru data are complete at ≳ 5σ, in colors NA659 − R_C < −0.3 mag and FUV–NUV< 0.0 mag down to a cluster mass of 10³ M_☉. This is true even after the internal extinction correction (Section 5.2) if a slightly lower detection limit (3.4σ) is adopted. The extinction correction is made for all four bands, which is equivalent to shifting the data points along the extinction vectors in Figure 3. We select the mass-limited sample after the extinction correction using the technique discussed in Section 4.

Almost all of the clusters are in the range FUV–NUV < 0 mag when the extinction is taken into account (Figure 5); thus, we adopt this color range for our analysis. This is the range where B stars definitely, and O stars possibly, exist in the clusters; we count how many of them have O stars below. Clusters are blue, FUV–NUV < 0 mag, for only a short duration. With the standard IMF of (m_l, m_u) = (0.1, 100 M_☉) and 0.2 Z_☉, this is t_UV = 71 Myr (Figure 2). The short t_UV is advantageous, since the assumption of a constant cluster formation rate is likely valid for a short period over the large area (i.e., the entire XUV disk)—no local events likely bias the statistics. On the other hand, clusters with O stars show NA659 − R_C < −1 mag for only 5.8 Myr. The model therefore predicts $t_{\rm {\rm H}{\alpha }}/t_{\rm UV} \sim 0.08$.

The number of blue clusters with FUV–NUV < 0 mag is counted using Figure 5 (red)—after the internal extinction correction, it is N_UV = 88 ± 9. From Figure 3, N_Hα = 9 ± 3 for NA659 − R_C < −1 mag (see Figure 6). The errors are based on the Poisson distribution, and the counts are made after the internal extinction correction. Therefore, the observed ratio is N_Hα/N_UV ∼ 0.10 ± 0.03. This is consistent with the prediction of the standard IMF (within a 1σ deviation). The counts of stellar clusters support the standard IMF with a simple aging effect.

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It is worth noting that the slight deviation does not likely have a statistical significance. However, if anything, it is inclined toward the top-heavy IMF side, as opposed to the previous suggestion of a truncated IMF.

The combination of the parameters we adopt (i.e., low metallicity (0.2 Z_☉), SMC extinction, and A_V = 0.1 mag) is the best to consistently explain the new data, model, and previous spectroscopic studies. The result for the standard IMF does not change even if a higher metallicity (∼0.4 Z_☉), and hence the LMC extinction curve, is adopted. If we ignore the spectroscopic studies, the comparison of the data and model (e.g., Figure 4) provides A_V ∼ 0.2 mag. With this extinction, we count N_UV = 86 ± 9 and N_Hα = 11 ± 3 and obtain N_Hα/N_UV ∼ 0.13 ± 0.04. The model ratio is 0.10 with the metallicity 0.4 Z_☉, where $t_{\rm {\rm H}{\alpha }} = 5.2$ Myr and t_UV = 51.3 Myr. Therefore, the observations and model are consistent even if a different metallicity and extinction are assumed.

The Hα-to-FUV flux ratio (F_Hα/f_ν FUV) over the entire XUV disk is another measure of the high-mass end of the IMF. We find that the observed ratio is consistent with the one predicted from the standard IMF. A lower ratio may suggest a truncated IMF (Meurer et al. 2009; Lee et al. 2009), though an extinction correction introduces an ambiguity (Boselli et al. 2009). We can estimate the ratio more accurately since we derived the extinction of A_V = 0.1 mag statistically (Section 5.2).

In a Starburst99 simulation with a constant star formation rate, a metallicity of 0.2 Z_☉, and the Salpeter IMF with (m_l, m_u) = (0.1, 100) M_☉, the ratio approaches an approximate constant and is, e.g., log (F_Hα/f_ν FUV) ∼ 13.10 in unit of log (Hz) after 1 Gyr assuming a star formation rate of 1 M_☉ yr⁻¹ (though the constant does not depend on these values). Fumagalli et al. (2011) calculate the ratio with their own model using the Kroupa IMF and derive ∼13.22 (from their Figure 1). The scatter between the models is about 30%. Compared to these values, the observed ratios previously reported in LSB galaxies by Meurer et al. (2009)—as low as one-third of the values calculated in these models—deviate at a significant level with respect to the model uncertainties.

We calculate the Hα-to-FUV flux ratio over the XUV disk of M83 by summing up the fluxes of all >3σ detections in the FUV image (Section 4.1). Assuming that OUT objects represent the background population (Section 4.4) and subtracting their total fluxes form those of IN objects (accounting for the IN/OUT area ratio), we obtain F_Hα = 8.36 × 10²⁸ erg s⁻¹ and $f_{\nu \,\rm FUV}=7.23\times 10^{25} \,\rm erg\, s^{-1} \, Hz^{-1}$. Adopting A_V = 0.1 mag and the SMC extinction curve (Section 4.2), the intrinsic ratio after the extinction correction is log (F_Hα/f_ν FUV)_int = 12.93. This value is only ∼30% lower than our model prediction, which is not as much as what the previous study found (Meurer et al. 2009). As the difference between this value and our model calculation is similar to the scatter between the models, we consider a truncated IMF to be unwarranted in the case of M83.