KMTNet Nearby Galaxy Survey III. Deficient H$\alpha$ flux in the Extended Disks of Spiral Galaxies

NGC 1512. This galaxy has prominent features with inner and outer spiral structures. In Thilker et al. (2007), it was classified as a Type 1 XUV-disk galaxy that shows structured UV-bright complexes beyond the SF threshold, corresponding to $\mu_{\mathrm{FUV}}\sim 27.25$ AB mag arcsec^-2. This galaxy has been considered an interacting system with a blue compact dwarf galaxy NGC 1510, located in the south-west direction. The disturbed spirals in the north-west region and filamentary structure between the two galaxies clearly indicate the signs of interaction. Koribalski & López-Sánchez (2009) reported a tight correlation between the dense neutral gas and UV-bright clumps, and discovered two probable tidal dwarf galaxies. These indicate that the interaction between NGC 1512 and NGC 1510 may have triggered the recent star formation activity in NGC 1512.

NGC 2090. This galaxy might be less fascinating than NGC 1512 as it consists of clumpy flocculent spirals. Since it has only minimal UV emission beyond the SF threshold, Thilker et al. (2007) classified this galaxy as a Type 2 XUV-disk galaxy, which has blue FUV$-$NIR color in a large and faint outer disk. They also described that NGC 2090 is likely to reside in an isolated environment.

Thilker et al. (2007) claimed that XUV-disk galaxies tend to be gas-rich systems, in which Type 1 features may be induced by some external perturbations. A spatially resolved analysis of these two types of XUV-disk galaxies will be crucial to not only inspect the cause of the deficient H$\alpha$ flux in the low SFR regime but also provide insight into the mechanism triggering the recent SF in the extended disks. The major properties of the galaxies are summarized in Table 1.

The data reduction was carried out in the same way described in Byun et al. (2018). In brief, we followed the standard IRAF procedures, which include overscan correction and flat-field correction using a dark-sky flat. We performed background subtraction for individual images using modeled planes with PYTHON. Using SExtractor (Bertin & Arnouts, 1996) and SCAMP (Bertin, 2006), we solved astrometric calibrations as instructed by the KMTNet team.¹¹1http://kmtnet.kasi.re.kr Finally, we created co-added images using SWarp (Bertin et al., 2002). From the RMS noise per pixel, the 1$\sigma$ depths of surface brightness in the optical broadbands were calculated as low as $\sim$27–29 mag arcsec^-2.

Since the H$\alpha$ narrowband image contains both stellar continuum and nebular emission, continuum subtraction is necessary. To subtract the scaled $R$-band image from the H$\alpha$ image, we firstly calculated a scale factor defined as $\mathrm{BNCR}\equiv c_{B}/c_{N}$, where $c_{B}$ and $c_{N}$ are the fluxes of the field stars measured in the broad- and narrow-band images, respectively. Note that most of the field stars were assumed to have no H$\alpha$ emission.

Figure 2 shows the calculated BNCR distribution of NGC 1512 data as a function of the $g-r$ color of the field stars, which were obtained from the AAVSO Photometric All-Sky Survey (APASS) DR9.²²2https://www.aavso.org/apass It reveals that the BNCR depends on the color, showing a large scatter of $\sigma\simeq 0.4$. We note that NGC 1512 showed a color variation of $B-R\sim 0.45$–1.45 mag (see Figure 5), corresponding to $g-r\sim$ 0.10–0.75 mag.³³3It is transformed by using the equations from https://www.sdss.org/dr16/algorithms/sdssubvritransform/#Lupton(2005) Using a high BNCR when subtracting the continuum can be risky, because it can introduce a false H$\alpha$ emission in the regions dominated by old stellar populations. Therefore, we adopted the minimum BNCR, corresponding to the reddest color of each galaxy, even though it may result in an over-subtraction of the stellar continuum. Indeed, this choice mostly raised uncertainties in the regions that have lower $g-r$ colors. Systematic uncertainty due to the use of a single BNCR will be discussed in Section 5.5.

We estimated the H$\alpha$ flux using a continuum-subtracted H$\alpha$ image, adopting the method described in Appendix A of Kennicutt et al. (2008). In brief, we firstly computed the photometric zero point of the $R$-band image, which is expressed as

where $f_{\lambda}$ is the mean flux density of $217.7\times 10^{-11}$ erg s^-1 cm^-2 Å^-1 in the $R$-band (Bessell et al., 1998), and CR is the measured count rate [count s^-1] of the field stars. Then, we calibrated the H$\alpha$ flux using the equations

where FWHM_Hα is an H$\alpha$ bandwidth of 80Å, and CR_Hα is the measured count rate of the source in the continuum-subtracted H$\alpha$ image. Since the photometric zero point was computed using the $R$-band image, we multiplied CR_Hα by BNCR to adapt to the same zero point. Note that all the single images taken with KMTNet have the identical exposure time of 120 sec, so the count normalization by exposure time does not affect the above calibration in practice. Finally, transmission correction for the KMTNet filter set was applied. The surface brightness limit was calculated to be $\sim$$7\times 10^{-18}$ erg s^-1 cm^-2 arcsec^-2, which is comparable to the depth in Kennicutt et al. (2008). We note that the H$\alpha$ flux in this study is a composite of H$\alpha$ and [Nii] lines, so our measurements for the H$\alpha$ flux can be considered as an upper limit.

Prior to performing the photometry, we carried out a background subtraction for all of the FUV-to-MIR data. Then, we placed adjacent circular apertures that covered the entire galaxy, as shown in Figure 3. This hexagonal placement allowed us to perform spatially resolved photometry while minimizing the loss of flux. The aperture size was set to be 6 arcsec in radius, corresponding to 300 pc at a distance of 10 Mpc. This aperture seemed adequate to cover the physical size of typical Hii regions (see Hunt & Hirashita, 2009, and references therein).

It is worth mentioning that a resolution bias can occur when determining properties within apertures in spatially resolved analyses (see Smith & Hayward, 2018; Sorba & Sawicki, 2018). A smaller aperture size may introduce an incorrect flux measurement due to contamination by the light of neighboring sources. We found that the SED fitting results, especially internal attenuation, tended to be inaccurately derived in crowded regions when using an aperture size smaller than 6 arcsec.

Such grid-shaped apertures with a radius of 6 arcsec are quite dense, so it enabled significant statistical sampling. Furthermore, it minimized the effect of aperture correction. The FWHM of the point spread functions of the GALEX, KMTNet, and IRAC data are smaller than 5 arcsec, while that of MIPS data is about 6 arcsec. We computed the aperture correction factors corresponding to the aperture size of 6 arcsec by referring to the descriptions of each instrument.⁴⁴4 http://www.galex.caltech.edu/ and https://irsa.ipac.caltech.edu/ Consequently, the measured fluxes were scaled up by $\lesssim$10% for FUV-to-IRAC 8.0$\mu$m, and $\sim$80% for MIPS 24$\mu$m.

We corrected the fluxes for the foreground reddening $A_{V}$, which was derived from the maps of Schlafly & Finkbeiner (2011) and the extinction law of Cardelli et al. (1989) with $R_{V}=3.1$. It yielded the correlations of $A_{\mathrm{FUV}}=2.7A_{V}$, $A_{\mathrm{NUV}}=3.2A_{V}$, $A_{B}=1.3A_{V}$, $A_{R(\mathrm{H\alpha})}=0.8A_{V}$, and $A_{I}=0.5A_{V}$. Indeed, we designed the survey avoiding galaxies in the low Galactic latitudes to minimize contamination from the Galactic cirrus, so the foreground reddening appears to be weak or negligible.⁵⁵5https://irsa.ipac.caltech.edu/applications/DUST/

Since the image conditions for the two galaxies were slightly different, it was hard to select the star-forming regions using a single common threshold in FUV (or H$\alpha$) flux. Therefore, we firstly limited the FUV fluxes to $\mathrm{log}\ f_{\mathrm{FUV}}\geq-28.4$ and $-$28.1 erg s^-1 cm^-2 Hz^-1 for NGC 1512 and NGC 2090, respectively. Then, we empirically eliminated the sky background and non-astronomical objects with the combination of H$\alpha$-to-FUV flux ratio, and optical colors. In addition, we removed the pixels contaminated by foreground stars and saturation trails. Note that the pixels in nuclear regions of the galaxies were also discarded to minimize contaminations by spheroidal components and latent active galactic nucleus (AGN). As a result, a total of 387 and 377 regions were selected as star-forming clumps in NGC 1512 and NGC 2090, respectively. The error budgets of the flux measurements for star-forming regions were computed by taking the RMS within each aperture and background scatter into account.

The placement of the grid-shaped apertures is simple and allowed us to directly reproduce the properties of galaxies as a 2-D maps. However, some star-forming clumps may not be exactly centered in the aperture, introducing an incorrect flux measurement. Meanwhile, SExtractor is a widely used tool, which finds the center of the source and measures the flux. In order to assess whether the grid-shaped apertures measured the fluxes correctly, we independently carried out photometry using SExtractor, and compared the measured fluxes. The aperture size was fixed to the same radius of 6 arcsec, using FLUX_APER in SExtractor.

Figure 4 shows the FUV and H$\alpha$ flux distributions of the star-forming regions in NGC 1512 measured using the two photometry methods. The result of grid-shaped aperture photometry was found to be broadly consistent with the result from SExtractor, even though there is no guarantee that the samples were identical to each other. This implies that there was no critical defect in the flux measurement with the grid-shaped aperture photometry. Note that there were some deviations between the results derived by the two methods in regions of low H$\alpha$ flux. This mainly originated from cavities in the H$\alpha$ image created when the continuum of saturated stars was subtracted.

Interestingly, the H$\alpha$-to-FUV flux ratio decreased as the flux decreased. This finding is in good agreement with previous studies (e.g., Lee et al., 2009) that showed a deficient H$\alpha$ flux in low luminosity systems such as dwarf galaxies. The only difference is that we are dealing with the spatially resolved fluxes for a single galaxy. We estimated the total fluxes by summing the fluxes of the star-forming regions, shown as a black star in Figure 4. If we had estimated the total flux of such a galaxy, a deficient H$\alpha$ flux would not have been discovered.

We performed a spatially resolved SED fitting with the Code Investigating GALaxy Emission (CIGALE; Boquien et al., 2019) in order to investigate the local properties of individual star-forming regions, such as their internal attenuations and star formation histories (SFHs). This software contains various modules, which permit detailed adjustments to create SED models, and perform an energy balanced fitting with dust absorption in the shorter wavelengths and re-emission in longer wavelengths, simultaneously. Note that many SED modeling codes have been developed, such as MAGPHYS (da Cunha et al., 2008). We expect that the result is unlikely to significantly change regardless of which code we use (see Hunt et al., 2019).

To avoid a waste of computing time by excessive iteration when creating SED models, we constrained the optimized parameter ranges, yielding a total of $\sim$500,000 models. We adopted the single stellar population model of BC03 (Bruzual & Charlot, 2003) with Chabrier IMF (Chabrier, 2003). The metallicity was fixed to $Z=0.02$, which is the same as the solar metallicity. Note that this choice did not significantly affect the fitting result for the extended disks, which are expected to have lower metallicities (see details in Section 5.2). We allowed the Lyman continuum (LyC) escape fraction in the range of $f_{esc}=0.0$–0.3, which was recently suggested as a feasible boundary condition in individual star-forming clumps (see Choi et al., 2020; Östlin et al., 2021). We selected a delayed double-exponential SFH model, which consists of the main (old) stellar population and late starburst population. Since this study is focused on recent SF events, we assigned the main population to have relatively simple SFHs with the oldest stellar age of 13 Gyr and e-folding times with large sampling intervals (1, 3, 5, and 7 Gyr). On the other hand, the late burst population was allowed to have more various histories, which were somewhat biased to the timescales of H$\alpha$ and FUV radiations. We adopted the dust attenuation model of Charlot & Fall (2000), which considers the environment of the interstellar medium (ISM) and birth clouds (BC). These were separately applied to stars older and younger than 10 Myr, respectively. In addition, based on many observational studies (e.g., Calzetti, 1997; Wuyts et al., 2011; Erb et al., 2006; Bassett et al., 2017), we assumed that the attenuation ratio between ISM and BC environments can vary within a range of $\mu=0.44$–1.00. Note that the attenuation for H$\alpha$ emission cannot be directly estimated from the CIGALE fitting since we used the total flux of H$\alpha$ narrowband for the fit. Instead, we computed it using the empirical relation between the attenuation in stellar continuum and that in nebular emission (see details in Section 5.1). The dust emission model of Dale et al. (2014) was adopted, and no AGN effect was considered. All the parameters used in the SED fitting are summarized in Table 2.

It is worth mentioning that the CIGALE fitting provides average SFRs over the last 10 and 100 Myr (SFR₁₀ and SFR₁₀₀). However, we did not use them for any SFR analyses, including a direct comparison to SFRs derived from H$\alpha$ and FUV fluxes, because there is no guarantee that the entire H$\alpha$ and FUV fluxes are originated from the stars exactly formed over the last 10 and 100 Myr, respectively. Instead, we used them to investigate the existence of late bursts (see Section 5.4).

Even though each flux might be affected by the internal characteristics of the star-forming regions, it is meaningful to examine the photometric properties before analyzing the SED fitting result. Note that NGC 1510, which was not our interest, is not shown in the figures hereafter.

Figure 5 shows several properties of the star-forming regions in two galaxies measured with the grid-shaped aperture photometry. It reveals that the selection criteria for the star-forming regions were appropriate, given that the structures of the galaxies were well reproduced. While a portion of the data in the disk of NGC 2090 was discarded, it still seems enough to investigate the galaxy’s properties.

The left panels in Figure 5 show the spatial distributions of the $B-R$ colors in galaxies. NGC 1512 shows a negative radial color gradient as expected from the existence of UV-bright extended spirals, which are likely to be less affected by dust attenuation. On the other hand, NGC 2090 shows a nearly constant color distribution in the disk, with an average of $B-R\sim 0.95$ mag.

We examined the correlation between H$\alpha$-to-FUV flux ratio and radial distance as shown in the middle panels of Figure 5. Note that NGC 2090 has large ellipticity, so we converted the projected distance into major axis distance using an axis ratio of $a/b=2$. In NGC 1512, the H$\alpha$-to-FUV flux ratio appears to first decrease on average with the radial distance and then increase later. In contrast, NGC 2090 shows a slight correlation between the flux ratio and radial distance. However, both galaxies show large scatters in the H$\alpha$-to-FUV flux ratio at a given radial distance. This indicates that the individual star-forming regions may have various characteristics regardless of their radial distance from the center of the galaxies. The central regions of the galaxies tend to have slightly higher H$\alpha$-to-FUV flux ratios on average compared to the areas beyond, possibly due to higher dust attenuation and/or [Nii] contamination.

The right panels in Figure 5 show a comparison of the FUV and H$\alpha$ fluxes in star-forming regions. As mentioned in Section 3.1, the H$\alpha$-to-FUV flux ratio decreases with decreasing flux. Although the fluxes were measured by using apertures of a similar physical size, the flux distributions of the galaxies appear to be different. This may be explained by two causes: inherently different SFRs and/or diverse contaminations including dust attenuation. In the next section, we will attempt to present more straightforward comparisons using the converted SFRs, which were corrected for several factors obtained from the SED fitting.

The spatially resolved SED fitting of the two galaxies worked reasonably well, with the result showing the reduced $\chi^{2}$ in almost all regions estimated to be less than 5, with a median of $\sim$0.5. Figure 6 shows examples of the best-fit SEDs for three representative regions in NGC 1512: the outer spirals, inner spirals, and central regions. We note that the SEDs in the inner and outer spirals are not fitted well at long wavelengths. Indeed, the IR data in most regions of the extended disks were not available due to the signal-to-noise ratio lower than 3 or the limited FoV of the utilized data set (Figure 1). Meanwhile, the outer regions of the spiral galaxies are expected to exhibit relatively weak dust emissions (see Casasola et al., 2017), implying there are insignificant attenuations. Therefore, we expect that we do obtain reasonable results even though SED fitting for the extended disks was mainly performed with stellar continuum only.

In order to estimate the inherent SFRs, we corrected the H$\alpha$ and FUV fluxes for the internal attenuation derived from SED fitting. The upper panels in Figure 7 show the 2-D distribution of $E(B-V)_{\mathrm{gas}}$, corresponding to $E(B-V)_{\mathrm{BC}}$, as will be discussed in Section 5.1. These were determined by using $A_{V}^{\mathrm{ISM}}$ and an attenuation ratio between ISM and BC with an assumption of $R_{V}=3.1$. Overall, $E(B-V)_{\mathrm{gas}}$ were revealed to be lower than 0.3 mag in most regions of both galaxies, while NGC 2090 has a median value slightly higher than NGC 1512. For NGC 1512, we confirmed that the results were broadly consistent with the results of the spectroscopic analyses in Bresolin et al. (2012) and López-Sánchez et al. (2015). Furthermore, these results are also similar to that of another XUV-disk galaxy, M83 (Gil de Paz et al., 2007), indicating that our estimates are reliable.

We calculated the SFRs using the equations in Kennicutt (1998) as follows

with the conversion factors from Salpeter IMF (Salpeter, 1955) to Chabrier IMF (Chabrier, 2003) found in Kennicutt & Evans (2012). The H$\alpha$ and FUV fluxes were corrected for the attenuations derived from the SED fitting. We assumed that the ionizing photon escape fraction of each star-forming clump can reach up to 30% in the SED fit, and accordingly the loss in H$\alpha$ flux was also recovered by using $L_{\mathrm{H\alpha}}^{\mathrm{int}}=L_{\mathrm{H\alpha}}^{\mathrm{corr}}/(1-f_{esc})$, where $L_{\mathrm{H\alpha}}^{\mathrm{int}}$ and $L_{\mathrm{H\alpha}}^{\mathrm{corr}}$ are the intrinsic and attenuation-corrected H$\alpha$ luminosities, respectively.

The middle and bottom panels in Figure 7 show the SFRs derived from the FUV and H$\alpha$ fluxes after the corrections in attenuation and LyC escape. The two SFRs for most regions of the galaxies appear to be clearly different, in the sense that the SFR_Hα tends to be systematically lower than SFR_FUV.

As shown in Figure 8, we compared the SFRs with each other to highlight the correlations between them. It is obvious that both galaxies show a decline in SFR_Hα/SFR_FUV as the SFR decreases. Note that the choice of IMF hardly affect the results, since all the points move in the same direction, by as much as 0.2 dex. We also denoted galactocentric radial distance in color to reveal the radial dependence of the discrepancy. While the correlation between radial distance and the discrepancy in SFRs is not entirely clear, it can be roughly divided into two regions. The central regions of galaxies are distinguishable from the rest, as they have higher SFRs and tend to deviate less from a one-to-one relation between the SFRs. In contrast, the outer regions exhibit lower SFRs and SFR_Hα/SFR_FUV, and large deviations between SFRs, on average. However, interestingly, the outermost regions (light green) deviate less from a one-to-one relation compared to the adjacent inner regions (dark green), resulting in significant scatters. The possible cause of this trend will be discussed in Section 5.4.

Figure 9 shows the ratio of SFR_Hα to SFR_FUV as a function of the SFR_Hα. These were converted into SFRs corresponding to Salpeter IMF in order to directly compare with the results of Lee et al. (2009). They claimed that the discrepancy between the SFRs became significant at SFR${}_{\mathrm{H\alpha}}\lesssim 0.003$ M_⊙ yr^-1. Our results extend this finding to a much lower SFR regime. Consequently, a deficient H$\alpha$ flux intrinsically exists in low SFR regimes. The possible causes of the H$\alpha$ deficit will be discussed in the following section.

To estimate the intrinsic SFR using a specific flux, the internal attenuation for that wavelength must be corrected properly. From the CIGALE results, we could obtain the attenuation for FUV, but not H$\alpha$. Therefore, we calculated the attenuation for H$\alpha$ as follows.

The classical ratio between the two attenuations measured by stellar continuum and nebular emission is $\mu=0.44$ (Calzetti, 1997; Wuyts et al., 2011). However, it has been recently reported that the ratio in highly star-forming galaxies can be higher, up to 1 (e.g., Erb et al., 2006; Reddy et al., 2010; Kashino et al., 2013; Reddy et al., 2015; Pannella et al., 2015; Bassett et al., 2017). Here, we can regard the attenuations for stellar continuum and nebular emission as the attenuations in ISM and BC, respectively (see Yuan et al., 2018). Since we allowed various ISM-to-BC attenuation ratios between 0.44 and 1 in the SED fitting, the attenuation for H$\alpha$ was calculated by using the equation $A_{\mathrm{H\alpha}}=A_{R}/\mu$ for each star-forming region. As a result, $A_{\mathrm{FUV}}/A_{\mathrm{H\alpha}}$ varied from 1.2 to 3.0, while this ratio in the extended disks tended to be higher than that in central regions of galaxies.

Alternatively, one of the simplest ways to estimate the attenuation for H$\alpha$ is using the correlation of $A_{\mathrm{FUV}}/A_{\mathrm{H\alpha}}=1.8$, which is expected from the Calzetti extinction curve and differential extinction law (Calzetti, 2001). Although it is apparently different from the ratio calculated above, it would be instructive to check the difference in the resultant SFR_Hα. Consequently, we found that there is good consistency between the two SFR_Hα obtained with different $A_{\mathrm{H\alpha}}$, showing a scatter of $\sim$0.06 dex. This result indicates that the deficiency of H$\alpha$ flux in the extended disks of galaxies is unlikely to be caused by the incorrect estimation of internal attenuation.

When we allowed metallicity to be free, the SED fitting results appeared to be biased to high metallicity values. Therefore, we fixed metallicity to $Z=0.02$ when creating the SED models for the sake of simplicity. This seemed a proper assumption since the SFR conversion recipes in Kennicutt (1998) assume a solar abundance with continuous SFH. However, the outer regions of late-type galaxies are expected to have lower metallicity than the inner regions due to the low efficiency of star-forming activity. Indeed, a negative radial gradient of metallicity has been observed in NGC 1512 via spectroscopic studies (e.g., López-Sánchez et al., 2015). Furthermore, the XUV-disk galaxies have been found to have metallicities in a range of $Z/Z_{\odot}=$ 1/10–1 (e.g., Gil de Paz et al., 2007; Bresolin et al., 2009; Werk et al., 2010; Bresolin et al., 2012). For these reasons, we attempted SED fitting with lower metallicities.

The stellar opacity decreases with decreasing stellar metallicity, and thereby low metallicity increases the ionizing flux. Therefore, it may be inappropriate to adopt sub-solar metallicity, as it will lead to even lower SFR_Hα/SFR_FUV. Despite this concern, we performed independent additional SED fittings with fixed metallicities of $Z=0.004$, 0.008, and 0.02.

As a result, the attenuation, especially in central regions, appeared to slightly increase with decreasing metallicity. However, as discussed earlier, a slight deviation in attenuation barely affects SFR_Hα/SFR_FUV.

To quantitatively compare the results, we carried out the Kolmogorov–Smirnov test for the distributions of SFR_Hα and SFR_FUV inferred from different metallicities. It suggested that the null hypothesis that they are drawn from the same population cannot be rejected ($p$-value $\gtrsim 0.98$).

Young, star-forming galaxies emit LyC radiation ($\lambda<912$Å), and the escape of these ionizing photons is considered to be one of the main contributors to the re-ionization of the early universe (see Ouchi et al., 2009; Wise & Cen, 2009; Yajima et al., 2011; Bouwens et al., 2015; Paardekooper et al., 2015). However, it is still debated how much of these photons escape from their host galaxies. Most studies have suggested that the LyC escape fraction of galaxies converges to below 0.15 (e.g., Leitet et al., 2013; Borthakur et al., 2014; Izotov et al., 2016; Leitherer et al., 2016; Bassett et al., 2019). In contrast, a few cases have been reported with high LyC escape fractions, up to 0.73, that might have originated from highly star-forming dwarf galaxies (e.g., Bian et al., 2017; Izotov et al., 2018; Fletcher et al., 2019).

The aforementioned studies were dealing with the entire light of individual galaxies, unlike this study focusing on local star-forming clumps. The ionizing photons are produced by very young stars surrounded by complex ISM structures (e.g., Witt et al., 1992; Dove et al., 2000). Stellar feedback can affect the dynamical state and morphology of the ISM, thereby instantaneously increasing the LyC escape fraction (e.g., Weilbacher et al., 2018; Barrow et al., 2020; Choi et al., 2020).

Since the leakage of ionizing photons can result in an underestimation of SFR_Hα, the observed H$\alpha$ flux must be corrected by the amount of loss using $f_{\mathrm{H\alpha}}^{\mathrm{int}}=f_{\mathrm{H\alpha}}^{\mathrm{obs}}/(1-f_{esc})$, where $f_{\mathrm{H\alpha}}^{\mathrm{int}}$ and $f_{\mathrm{H\alpha}}^{\mathrm{obs}}$ are the intrinsic and observed H$\alpha$ fluxes, respectively.

The main results in this study were obtained using a LyC escape fraction of $f_{esc}=0.0$–0.3, but it is worthwhile to check whether the higher fractions can eliminate the discrepancy between the SFRs. We carried out additional SED fittings by allowing the upper limits of LyC escape fraction to vary up to 0.9 while fixing the remaining parameters unaltered.

Figure 10 shows the distributions of derived SFR_FUV and SFR_Hα when the loss of H$\alpha$ flux is fully recovered. For a better comparison, we applied the contours of different colors with a threshold containing $\gtrsim$90% data. It is obvious that the contours approach a one-to-one relation between the SFRs as the LyC escape fraction increases. In addition, the contours gradually move to the top right direction as the attenuation from the newly-performed SED fitting is yielded to be slightly higher. When the LyC escape fraction is higher than 0.8, the discrepancy between the SFRs is marginally eliminated. However, it seems unlikely that most of the star-forming clumps have such an extremely high LyC escape fraction. This suggests that LyC escape alone cannot explain the low SFR_Hα/SFR_FUV in the extended disks of galaxies.

We also note that LyC photons can also be lost via dust absorption in ionized regions. However, the dust-to-gas mass ratio in ionized gas is likely to be substantially less than in neutral gas (by a factor of 2 to 10; Akimkin et al., 2017). It has also been found that dust has little effect on the nebular spectrum (Mathis, 1986). Scattering of H$\alpha$ can also lower the H$\alpha$ fluxes measured at star-forming regions, giving rise to the same effect as the LyC escape. However, the effect by dust scattering is, in general, more prominent at the FUV wavelengths, reducing the FUV flux more strongly. Most, if not all, of the single scattered light, will be lost from the aperture. On the other hand, some fraction of multiply scattered light can enter the aperture that is under consideration. However, the fraction of multiple-scattered light is reduced by a factor of $a^{n}$, where $a$ and $n$ are the dust albedo ($a<1$) and number of scatterings, respectively. Thus, the net effect of dust scattering is the loss of light, unless the dust optical depth is so high that the observed flux is dominated by scattered light. As a result, it can further lower the H$\alpha$-to-FUV flux ratio when the amounts of loss in the H$\alpha$ and FUV fluxes are corrected, making the issue of the H$\alpha$ deficiency worse. Therefore, the dust absorption/scattering effects are not likely to significantly alter our results.

Since the H$\alpha$ and FUV fluxes trace star formation on different timescales, consistency between the estimated SFR_Hα and SFR_FUV can only be achieved when a constant SFR persists for at least 100 Myr. In other words, SFR variation in a shorter timescale may induce a discrepancy between SFR_Hα and SFR_FUV.

Alberts et al. (2011) investigated the stellar populations of five nearby XUV-disk galaxies using UV and NIR images. They found that the UV-bright sources in the outer disks of galaxies tended to have relatively old ages with a median of $\sim$100 Myr. Such a relatively old stellar population can lead to deficient H$\alpha$ emission in the outer disks. They also mentioned that this finding may be affected by biased sample selection since more than half of the sources had no H$\alpha$ emission. In contrast, we selected star-forming regions using both FUV and H$\alpha$, making our sample less biased compared to that of Alberts et al. (2011). Nevertheless, a deficit in H$\alpha$ flux in the extended disks of galaxies still appeared.

A similar correlation between the H$\alpha$-to-FUV ratio and the H$\alpha$ (or FUV) intensity has been found in the diffuse regions outside of star-forming regions in external galaxies and our Galaxy (e.g., Hoopes & Walterbos, 2000; Hoopes et al., 2001; Seon et al., 2011). They interpreted the trend using a scenario wherein the diffuse H$\alpha$ photons originate from relatively late-type stars (late O- and B-stars). Their interpretation (for the diffuse regions) is consistent with the present scenario (for the star-forming clumps) since the lifetime of early-type stars is shorter than that of late-type stars.

Recently, Emami et al. (2019) described that starbursts with rising/falling phases can introduce a decline in the H$\alpha$/FUV luminosity ratio, and that this tendency is more distinct when the burst has a large amplitude and short duration. Indeed, the outer regions of XUV-disk galaxies are likely to have intermittent star-forming events because they have less gas and are vulnerable to stellar feedback. Hence, it would be useful to investigate when and where recent starbursts have occurred in understanding the origin of the deficient H$\alpha$ flux.

To determine the phase of SFHs of late bursts, we adopted the CIGALE parameters of SFR₁₀ and SFR₁₀₀. This represents the average SFRs over the last 10 Myr and 100 Myr, respectively. We note that these are only tracers to check the SFHs, including recent starbursts, not proxies of SFR_Hα or SFR_FUV. For a given e-folding time of the burst, we can expect SFR₁₀/SFR₁₀₀ to be lower than 1 if the burst had started at a lookback time between 10 Myr and 100 Myr. Conversely, if the burst started within the last 10 Myr, the ratio would be higher than 1. Indeed, we allowed the age of the late burst to have sparse intervals (5, 15 Myr, and the rest) in the SED fitting to robustly distinguish the burst phase. Note that we attempted extra fittings with denser intervals. We found that even the detailed characteristics of late bursts vary, the overall trend almost matches the following descriptions.

The upper panels in Figure 11 show the 2-D distributions of SFR₁₀/SFR₁₀₀ for the star-forming regions in the galaxies. Although SFR₁₀/SFR₁₀₀ are slightly mixed, it can be roughly divided into three groups according to the radial distance: the central regions, inner disk, and outer disk. The central regions seem to have SFR₁₀/SFR${}_{100}\sim 1$, indicating no or weak late bursts. The ratios of the inner disk appear to be lower than 1, while the outer disk has higher values. This implies that the burst populations in the inner disk tend to be older than those in the outer disk. Alternatively, the e-folding time of the inner disk might be shorter than that of the outer disk if the bursts had started simultaneously.

In the bottom panels of Figure 11, we present the distributions of SFR_FUV and SFR_Hα, which are color-coded by SFR₁₀/SFR₁₀₀. The three groups defined above are clearly distinguishable on the 2-D planes. Note that not all data, roughly separated by three different color ranges, actually belong to three individual groups, but most of them do. We highlight that the discrepancy between the SFRs is maximized in the inner disk, where SFR₁₀/SFR₁₀₀ is the lowest.

To investigate the overall SFHs for the three groups, we adopted a T-shaped boundary consisting of the linear fit and its orthogonal function. Each intersection was determined arbitrarily by visual inspection. Figure 12 shows the SFHs reproduced with the CIGALE results for three groups in NGC 1512. In order to emphasize the representative trend in each group, we normalized the SFRs by the highest value in each SFH, and applied translucent colors. As we mentioned above, the central regions were dominated by the main populations, which can be described as an exponential SFH with insignificant late bursts over the last 100 Myr. In contrast, the inner and outer disks clearly appear to have had late bursts. Interestingly, almost all of these late bursts started at the same time ($t_{\mathrm{lookback}}=15$ Myr), but they have evolved with different e-folding times.

We also note that the maximum amplitudes of the main populations in the inner disk tend to be smaller than those of the outer disk. In summary, the late bursts in the disks occurred in two different types: (1) bursts with strong amplitude and short e-folding time in the inner disk, and (2) bursts with moderate amplitude and long e-folding time in the outer disk. Together with the descriptions of Emami et al. (2019), we conclude that the strong discrepancy between SFR_Hα and SFR_FUV in the inner disk could be induced by the rapidly decreasing SFR over the last 10 Myr.

As we mentioned in Section 2.1, the two galaxies are thought to reside in different environments. This leads to the inference that the mechanisms triggering SF in the extended disks might also be different. For example, NGC 1512 was expected to exhibit signs such as asymmetric and delayed SF. However, the SFHs, including late bursts in the extended disks of both galaxies, were revealed to show quite azimuth-symmetric distributions. In other words, the late bursts in the extended disks had started simultaneously, and then underwent an “inside-out” suppression. Consequently, these findings suggest that the internal processes of galaxies or gas accretion from the intergalactic medium might be responsible for the recent SF in the extended disks of galaxies. This interpretation is still inconclusive because of the small sample size. We expect that larger samples of XUV-disk galaxies would be helpful to understand the origin of recent SF in galaxy outskirts.

All of the above results are based on H$\alpha$ fluxes measured from continuum-subtracted H$\alpha$ images. These images were created by ‘image-to-image’ subtraction of the $R$-band images scaled by a single BNCR from the H$\alpha$ narrowband images. In Section 2.2, we demonstrated that BNCR depends on the $g-r$ color of objects, and the individual star-forming clumps in galaxies have various colors. For this reason, we may concern that using a single BNCR would cause an inaccurate continuum subtraction. That is, the choice of a minimum BNCR can give rise to an over-subtraction of the continuum in the regions with bluer colors.

Alternatively, the H$\alpha$ fluxes can be estimated using ‘aperture-to-aperture’ subtraction for the H$\alpha$ narrowband and $R$-band fluxes measured in individual apertures. In this approach, each $R$-band flux is scaled by the corresponding BNCR for each aperture. In order to examine whether this method resolves the discrepancy between the SFRs, we attempted to re-analyze using the H$\alpha$ fluxes measured in this way.

Figure 13 compares the results of ‘image-to-image’ and ‘aperture-to-aperture’ continuum subtraction. Here, the contours represent a threshold containing $\gtrsim$90% data. The results for low SFR regions changed significantly depending on the adopted subtraction method, while it was not significantly altered in high SFR regions. This is a natural consequence as the regions with high SFRs, especially the central regions, tend to have redder colors. However, the discrepancy between the SFRs still exists even if ‘aperture-to-aperture’ subtraction is an appropriate method for estimating the H$\alpha$ flux. This suggests that the lack of H$\alpha$ flux in the extended disks of galaxies is an intrinsic phenomenon, rather than introduced by incorrect flux measurement.