A Nonparametric Morphological Analysis of H$\alpha$ Emission in Bright Dwarfs Using the Merian Survey

To estimate the continuum emission through N708, we take advantage of the fact that the continuum in this region of the spectrum can be well approximated by a power law. Because this assumption only holds locally around H$\alpha$, we do not include HSC $g$ or $y$ bands in our fitting. The 4000 Å break falls into the $g$ band within our redshift range, and so including $g$ band photometry would complicate the shape of the SEDs and invalidate our power law assumption. The $y$ band photometry is shallower and often unreliable for our sources, so we would be disadvantaged if we included it in our modeling.

In addition to our power law assumption for the continuum, we also assume that the increase in emission through a photometric band – as compared to the emission we would expect from the continuum only – is a function of the H$\alpha$ EW, [O III] EW, and redshift. In other words, the increase in emission from continuum only to emission with nebular lines (also including lines other than H$\alpha$ and [O III], such as [N II] and [S II]) is largely determined by the strength of H$\alpha$ and [O III] and their observed wavelength. We estimate the value of this increase in emission as a scale factor $\eta$, which we derive empirically using a library of simulated spectra and synthetic photometry based on the SED-fitted parameters of low-mass GAMA galaxies and created using the Flexible Stellar Population Synthesis (FSPS) code (Conroy et al., 2009; Conroy & Gunn, 2010; Johnson et al., 2021). We describe the model in Section 3.1.1 and the calculation of the scale factor $\eta$ in Section 3.1.2.

We fit the observed photometry using the power-law model and scale factor to estimate the continuum power-law index. With the shape of the continuum, we can calculate its contribution through N708, correct for it, and measure H$\alpha$ EW and flux. Details of this method follow below.

While we did not apply a correction for dust extinction when comparing to similarly uncorrected values in Section 3.2, it is necessary to correct for extincted emission before using $L_{{\rm H}\alpha}$ to compute the SFR. We correct for foreground extinction using the SFD dust maps of Schlegel et al. (1998) and Schlafly & Finkbeiner (2011). For maximum consistency and to avoid introducing additional significant scatter, we derive a mass-dependent average correction for internal attenuation based on the SED fits to the GAMA sources (Taylor et al., 2011). We found corrections based on the Balmer decrement from the spectra to be unreliable for the GAMA sources. Details of this approach are provided in Appendix B.

Using the extinction-corrected total H$\alpha$ flux integrated from the H$\alpha$ maps, we calculate the galaxies’ SFR according to Hao et al. (2011); Murphy et al. (2011), and Kennicutt & Evans (2012):

We also calculate the specific star formation rate of the galaxies and show the distribution with $\log(M_{\star}/M_{\odot})$ in the top panels of Figure 5. We fit a line to our star-forming main sequence (SFMS), which we note is not based on a complete sample and does not represent a thorough computation of the SFMS for the Merian sample. We defer this analysis to future work and use the SFMS only in a relative sense to identify which galaxies are particularly active in star formation relative to our sample.

We use the publicly available Python package statmorph (Rodriguez-Gomez et al., 2019) to calculate the nonparametric morphology statistics for the H$\alpha$ maps and for the $z$-band images, which we take to be representative of the stellar continuum. However, due to the irregularity of the H$\alpha$ maps, we manually fix the centers and segmentation maps (determined as described in Section 3.1.3) for the H$\alpha$ map calculations to those obtained from the $z$-band images. This enables us to conduct a better comparison of the morphological statistics of the two image types.

There are several groups of widely used nonparametric morphological parameters calculated by statmorph. We focused our analysis on the concentration-asymmetry-smoothness (CAS; Conselice, 2003) and Gini-$M_{20}$ (Abraham et al., 2003; Lotz et al., 2004) statistics, all of which are described in greater detail in Rodriguez-Gomez et al. (2019).

While the CAS parameters are among the most commonly used, they are sensitive to resolution and noise effects. Others have shown that the smoothness statistic especially is unreliable at resolutions below 1000 pc (Lotz et al., 2004; Nersesian et al., 2023) and Pović et al. (2015) argued that it is not reliable at all for ground-based data. Our resolution ($\gtrsim$ 1 kpc) is too low to calculate meaningful values, and accordingly we have not included smoothness in our results. The concentration parameter is generally more stable, but we similarly do not include it in our analysis, due to the required assumption of circular symmetry and the different surface brightness limits of the medium-band and broadband images.

While the asymmetry index ($A$) is also affected by resolution and noise, it is not as sensitive as the smoothness parameter (Lotz et al., 2004). Calculations of the smoothness parameter yielded values that were clearly nonphysical, but we found the asymmetry values to be more reasonable – at least for relative comparison within our sample. We therefore calculate and report the value of the asymmetry index. It quantifies the rotational symmetry of the galaxy and is obtained by rotating the image 180^∘ and subtracting it from the original unrotated image. In order to obtain a reliable value, the asymmetry of the background (calculated from an empty region of the image) is also subtracted off. It is calculated as

where $I_{ij}$ is the flux value of pixel $i,j$ in the original image, $I_{ij}^{180}$ is the flux value in the rotated image, and $A_{\text{bgr}}$ is the background asymmetry, calculated from a source-free region of the image. The asymmetry is calculated using all pixels within 1.5 Petrosian radii of the asymmetry center, which is defined as the center that minimizes the asymmetry. Again, because we fix the center for the H$\alpha$ images to that of the $z$ band, we note that the H$\alpha$ asymmetry center is the point that minimizes the $z$-band asymmetry and the H$\alpha$ asymmetry is calculated within 1.5 $z$-band Petrosian radii. Using the true H$\alpha$ asymmetry center results in a lower value of $A$ by definition, but the chosen center is frequently far from the continuum center, due to the irregular H$\alpha$ map morphologies. Aside from this one adjustment, the asymmetry of the stellar continuum and the H$\alpha$ maps are calculated identically following the approach described above.

The Gini coefficient was originally developed by economists to measure the wealth inequality of a population but has been applied to galaxy morphology in order to quantify the homogeneity of the flux distribution. Abraham et al. (2003) and Lotz et al. (2004) were among the first to adapt the Gini coefficient for astronomical applications, accounting for the unreliability of the statistic at low signal-to-noise ratio and presenting a method for constructing a segmentation map that depends on the Petrosian radius. The Gini coefficient is calculated as

where $X_{i}$ is the flux of the $i$th pixel sorted in ascending order by brightness and $\bar{|X|}$ is the mean of the absolute values of all fluxes associated with the sources as determined by the $z$-band segmentation map. A Gini coefficient of 1 corresponds to a galaxy with all of its flux in a single pixel, and a Gini coefficient of 0 represents perfectly evenly distributed flux.

The last morphological parameter we consider is the $M_{20}$ statistic, also presented by Lotz et al. (2004). $M_{20}$ measures the second moment of the brightest 20% of the galaxy’s flux relative to its total second moment. It is calculated as

where $I_{\rm tot}$ is the total flux of the pixels associated with the source as determined by the segmentation map and $\mu_{\rm tot}$ is the total second moment:

The center coordinate ($x_{c},y_{c}$) is found as the point that minimizes $\mu_{\rm tot}$ for the continuum image and, as for the other parameters, is fixed to the $z$-band value for the H$\alpha$ maps. While $M_{20}$ is similar to the concentration parameter, it is more flexible. It does not assume circular symmetry and is more influenced by the brightest regions of the galaxy. It is therefore useful for identifying features like bright nuclei or off-center clusters.

The Gini coefficient and $M_{20}$ statistic are frequently used together to identify mergers or characterize bulge strength (Lotz et al., 2004, 2008). Under this scheme, sources whose broadband morphological statistics fall in the high-Gini, high-$M_{20}$ region of this parameter space are classified as merger candidates. We show the distribution of $G$ versus $M_{20}$ measured from the continuum images in the right panel of Figure 6 along with the merger-separating lines presented in Lotz et al. (2008). We also show the distribution of the H$\alpha$ parameters in the left panel of this figure, which cover a broader range of the parameter space. We discuss the implications of this difference further in Section 5.1. The Gini coefficient and $M_{20}$ statistic are also useful for quantifying the H$\alpha$ homogeneity (or lack thereof) and the degree of central concentration of bright H$\alpha$ clumps. Figure 7 shows four galaxies with H$\alpha$ maps with extreme values of $G$ and $M_{20}$ to demonstrate the use of these values in identifying, for example, multiple bright clumps and central nuclei.

To ensure that we only consider galaxies with reliably calculated morphological parameters, we impose the selection criteria proposed in Rodriguez-Gomez et al. (2019). We apply the built-in quality selection from statmorph, removing all sources with flag > 0 with flag as defined in Rodriguez-Gomez et al. (2019) to indicate a poor-quality measurement. We also remove sources with mean signal-to-noise ratio per pixel below 2.5 and sources with $r_{20}$ (the radius containing 20% of the galaxy’s flux) less than half the FWHM of the PSF. Lastly, we remove any sources that pass all of the above criteria but have unphysical values for asymmetry (i.e. negative). After imposing these selections, we removed 277 sources, yielding a sample of 1,250 galaxies with reliable continuum fits, active star formation, good-quality images, and reasonable morphological calculations. We report the values of the asymmetry index, Gini coefficient, and $M_{20}$ statistic measured from the $z$ band and H$\alpha$ images for these sources in Table 2.

The majority of sources removed owing to the morphology quality cut are low-mass (with a median $\log(M_{\star}/M_{\odot})\approx 9.3$), have low surface brightness and low SSFR for their mass, and are physically small. Because they do not have reliable morphological measurements by definition, it is challenging to quantify the bias introduced by this quality cut, but from visual inspection the majority of the sources appear dim and diffuse. To assess the impact of excluding these sources, we analyzed the sample with the “poor-quality” morphological measurements included and found that it had little effect on our results as described in Section 5.

The main impact of this selection is in removing the majority of extremely low-mass sources from our sample – all but one of the 21 sources with $\log(M_{\star}/M_{\odot})<8$ are removed. As discussed previously, our sample is not complete at the low-mass end, as it is exceedingly difficult to get spectroscopic measurements for these low surface brightness objects. Probing such faint sources is beyond the scope of our data and in fact represents a different physical regime – one characterized by low stellar density and thus less active star formation (Kado-Fong et al., 2022b). In the analysis that follows, we restrict our sample to sources with $\log(M_{\star}/M_{\odot})\geq 8$, removing the remaining source below this threshold.

Additionally, as discussed above, nonparametric morphological parameters can be sensitive to resolution. As our sample spans a range of redshifts, one might be concerned about the impact of variable resolution on subsequent analysis of the galaxies’ morphology. Our H$\alpha$ maps have a typical PSF FWHM of $\sim$ 5 pixels, which corresponds to a physical scale of 1.03 kpc at $z=0.064$ and 1.5 kpc at $z=0.1$. Despite the moderate change in resolved physical scale, we find no significant morphological trends with redshift for any of our parameters, providing confidence that any observed trends are representative of intrinsic differences among the galaxies and not simply a result of resolution effects.

Another challenge is that at lower star formation rates, we may be unable to detect H$\alpha$ emission owing to surface brightness incompleteness, potentially biasing trends between morphology and SFR. To assess the potential significance of this effect, we binned our sources by mass and redshift. We found that in the high-mass galaxies the lowest SFR surface density pixels are $\sim$1000 times fainter than the highest SFR surface density pixels and we achieve a similar dynamic range in the low-mass galaxies at the same redshift. Hence, we do not believe that the morphological trends in our maps can be attributed to differential incompleteness due to surface brightness.

While we find no mass- or SSFR-dependent impacts of surface brightness limitations, it is likely that some amount of diffuse emission in our galaxies drops below our detection limits. While we have shown that this would have no relative impact on our measurements, it might result in slightly inflated values of the Gini coefficient overall as compared to what would be measured with deeper imaging.

Lastly, it is important to consider the potential impact of spatially dependent dust attenuation on our measured morphological parameters for the H$\alpha$ maps. Without high-resolution infrared imaging or integral field spectroscopy, it is not possible to explicitly correct for spatially varying attenuation in our images. Previous work has shown that dust attenuation is typically higher toward the center of galaxies (Boissier et al., 2004, 2007; Nelson et al., 2016; Kahre et al., 2018; Jafariyazani et al., 2019), but has found that both the overall attenuation and the gradient decrease with mass and that there is little attenuation at any radius for the lowest-mass sources ($\log(M_{\star}/M_{\odot})<9.2$). Given that dust attenuation is correlated with metallicity (Boissier et al., 2004, 2007) and dwarfs typically do not have significant metallicity gradients (Croxall et al., 2009), it is unlikely that dust would impact the measured morphological parameters of the dwarf galaxies in our sample.

For the higher-mass sources, the gradient in attenuation is potentially more significant, with the H$\alpha$ attenuation reaching up to $\sim$2–3 mag in the central 1 kpc, but declining rapidly to less than 1 mag beyond 1 kpc and becoming negligible beyond 3 kpc (Nelson et al., 2016). We note that this value is an upper limit, as the analysis from Nelson et al. (2016) is based on star-forming galaxies at $z\approx 1.4$, which have higher SSFRs (by nearly an order of magnitude) and are dustier than our galaxies at $z<0.1$.

To approximate the impact of radially dependent attenuation on our measured morphological parameters for the higher-mass galaxies in our sample ($\log(M_{\star}/M_{\odot})>9.8$), we conducted a simplified experiment using the parameterization of H$\alpha$ attenuation from Nelson et al. (2016), the details of which are presented in Appendix C. Ultimately, we find that the asymmetry is not strongly affected by dust but that $G_{{\rm H}\alpha}$ and $M_{20,{\rm H}\alpha}$ could be biased by at most $10-20\%$ for the highest-mass galaxies in our sample. These estimates represent extreme upper limits for the galaxies in our sample, as they are based on galaxies with higher SFRs and our toy model for dust correction is very simplified. These caveats are discussed further in Appendix C. A true characterization of the morphological bias would require additional information.

The Merian medium-band photometry and imaging provide an exciting opportunity to isolate the two-dimensional distribution of H$\alpha$ emission in the observed galaxies and to compare this distribution to the emission of the stellar continuum for a large and consistently processed sample. In Figure 8 we show a comparison of the distribution of morphological parameters measured from the H$\alpha$ maps to those measured from the continuum images (the scaled $z$ band) binned by mass. In every mass bin, the H$\alpha$ maps have significantly higher values of $G$, $M_{20}$, and asymmetry than the continua. The H$\alpha$ maps are overall much less homogeneous and much more asymmetric, with their brightest regions less centrally concentrated. The H$\alpha$ maps also exhibit a larger spread in the distribution of their values of $G$, $M_{20}$, and $A$. Compared to the continua, the H$\alpha$ maps are overall more morphologically diverse and much more irregular.

The difference in the distribution of morphological parameters between the H$\alpha$ maps and the continuum images is also evident in Figure 6, which shows the distribution of the Gini coefficient and $M_{20}$ statistics for the two sets of images, colored by asymmetry. Using broadband morphologies, Lotz et al. (2008) found that merger candidates fall into the upper right quadrant of this parameter space - as defined by the lines shown in the figure. The irregular morphologies of the H$\alpha$ map are sufficiently distinct from their continuum images, and so their $G$-$M_{20}$ distribution cannot be interpreted in this way; the distribution of $G_{{\rm H}\alpha}$ and $M_{20,{\rm H}\alpha}$ covers a larger area of the parameter space than the continuum statistics. Rather than being sensitive to mergers, the H$\alpha$ maps are sensitive to the distribution of star formation surface density.

We find a significant correlation between asymmetry and SSFR, a trend that has been previously well established for higher-mass galaxies in both observations and simulations (Yesuf et al., 2021; Bottrell et al., 2023). In the top panels of Figure 5, we show the distribution of SSFR versus stellar mass, colored by asymmetry ($A_{{\rm H}\alpha}$ and $A_{{\rm cont}}$ respectively). In the bottom panels, we show $A_{{\rm H}\alpha}$ and $A_{{\rm cont}}$ as a function of distance from the SFMS ($\Delta$MS) using the fit to our sample as described in Section 3.3. There is a clear and significant correlation between $\Delta$MS and both $A_{{\rm H}\alpha}$ and $A_{{\rm cont}}$, with asymmetry increasing with distance above the MS. This trend holds for both the H$\alpha$ maps and the continuum maps, with the H$\alpha$ maps being more asymmetric overall.

In addition to the unique contribution of our H$\alpha$ distributions, our sample is also novel in its mass range – namely in the large number of galaxies below $\log(M_{\star}/M_{\odot})\lesssim 9.3$. In Figure 8, we show the distribution of the measured morphological parameters for the H$\alpha$ maps and the continua binned by mass. There is little difference among the distributions for the three highest-mass bins, except for a slight decrease in $M_{20,{\rm cont}}$ and in $G_{{\rm H}\alpha}$ and a slight increase in $A_{{\rm H}\alpha}$ with increasing mass. The values of $G_{{\rm cont}}$, $A_{{\rm cont}}$, and $M_{20,{\rm H}\alpha}$ are otherwise similarly distributed for the higher mass bins.

The lowest-mass bin, however, on average has a larger value of $G_{{\rm H}\alpha}$ – i.e. the H$\alpha$ emission of the lowest-mass galaxies is less homogeneously distributed than for the higher-mass galaxies. The lowest-mass galaxies also have lower values of $A_{{\rm H}\alpha}$ on average; they are more symmetric. The main difference between the H$\alpha$ emission of the lowest-mass galaxies and that of the higher-mass galaxies is the lack of diffuse emission and the high concentration (but not necessarily central concentration) of the emission. As discussed in Section 4.2, the majority of sources removed from the sample owing to unreliable morphological measurements were in the lowest-mass bin and appear to have diffuse emission. It is possible that the Gini coefficient for the low-mass values could be slightly inflated by this cut, but not sufficiently so as to account for the observed trend.

We also investigate morphological trends with SSFR as shown in Figure 9. Once again, the increase in asymmetry with SSFR is clear, both in the continuum and in the H$\alpha$ maps. The lack of strong asymmetry trends with mass as discussed above indicates that, despite the correlation between SSFR and stellar mass, asymmetry is independently correlated with SSFR.

We see an increase in the Gini coefficient of the H$\alpha$ maps in the highest SSFR bin. We also see a trend of increasing $M_{20}$ for the H$\alpha$ maps, except in the highest SSFR bin, which has a significantly lower median $M_{20}$. There are no trends in these parameters with SSFR for the continuum images. The objects with the highest SSFR tend to be less homogeneous and to have their brightest regions more centrally concentrated. We find that these trends with SSFR are driven primarily by the lowest-mass galaxies, which we investigate more below. Unlike the trends with mass, the quality cuts discussed in Section 4.2, which preferentially remove diffuse, low SSFR objects that appear to be more symmetric, would likely lead to the underestimation of the observed trends with SSFR.

It is possible that the trends with mass discussed above are affected by the mass-dependent H$\alpha$ attenuation discussed in Section 4.3. A correction for dust attenuation in the high-mass galaxies would likely result in an increase in the measured values of $G_{{\rm H}\alpha}$ and a decrease in $M_{20,{\rm H}\alpha}$. While we cannot precisely quantify this bias, as described in Section 4.3 and Appendix C, we believe it is below $10\%-20$%. The mass dependence of dust attenuation could be contributing to the observed trend in $G_{{\rm H}\alpha}$ with mass or masking a trend in $M_{20,{\rm H}\alpha}$ with mass, but we found that applying our derived morphological corrections for dust (see details in Appendix C) did not significantly impact the observed trends with SSFR.

In addition to the aggregate trends with mass and SSFR discussed above, we investigate trends of morphological parameters with SSFR for our galaxies binned by mass. We show the trends in morphological parameters for the H$\alpha$ maps with SSFR for two different mass bins in Figure 10. The bins are selected in order to compare galaxies with distinct physical properties. Galaxies do not begin to form coherent thin disks or spiral arms until at least $\log(M_{\star}/M_{\odot})\gtrsim 9.0$ (Sánchez-Janssen et al., 2010; Kado-Fong et al., 2020b; Dekel et al., 2020) and below this mass are puffier and more spheroidal. We therefore choose our low-mass bin to include all galaxies with $\log(M_{\star}/M_{\odot})\leq 9.3$, which accounts for about 25% of our total sample. Our higher mass bin includes galaxies with $\log(M_{\star}/M_{\odot})\geq 9.7$, well into the regime of thin disks. We note that while the choice of bins is arbitrary, the trends presented below are not sensitive to small changes in the bin limits.

The SSFR-asymmetry correlation holds in both the H$\alpha$ maps and the continuum maps for the lowest-mass galaxies, but we also find that the Gini coefficient of the H$\alpha$ maps increases with SSFR for the lowest-mass galaxies while $M_{20}$ decreases. This trend is not evident for the higher mass sources, which show no significant trend in $G_{{\rm H}\alpha}$ or $M_{20,{\rm H}\alpha}$ with SSFR. For the higher mass sources, we do not span a sufficient range in SSFR to conclusively evaluate whether these morphological trends hold for high-mass sources with extremely high SSFR. We note that this class of galaxies is rare locally and it would be challenging to find a large sample with these properties. As discussed in Section 4.2, for galaxies in the higher mass bin, the H$\alpha$ emission is likely most strongly attenuated near the center of the galaxies (up to $\sim$ 2-3 mag) and minimally affected beyond $\sim$ 1-3 kpc. While it is possible that our measured morphological parameters are slightly impacted by extinction, we expect this effect to be minimal in our mass and SSFR regime.

For the lowest-mass galaxies, as SSFR increases, their H$\alpha$ emission becomes both more asymmetric, less homogeneous, and more centralized. Their H$\alpha$ emission – and therefore their sites of recent star formation – is highly compact, and somewhat nuclear but slightly off-center. This trend is not present in the distribution of continuum morphological parameters or in the distributions for the higher-mass galaxies. This result highlights the strength of our sample’s unique ability to trace H$\alpha$ emission independently and to probe galaxies at lower masses.

While no previous studies have probed H$\alpha$ morphologies at precisely the same mass and redshift range as our sample, the body of research studying two-dimensional H$\alpha$ emission and the relationship between star formation and morphology is substantial. In this section, we highlight some key results from the literature and demonstrate how our results agree with and extend previously established trends.

One of our main results discussed in Section 5.1 is the finding that the H$\alpha$ maps in our sample are overall more asymmetric and less homogeneous than the continuum images, with broader distributions of their morphological parameters. A number of other studies – some comparing broadband images to narrowband H$\alpha$ (Fossati et al., 2013; Boselli et al., 2015) and some using integral field spectroscopy (Nersesian et al., 2023) – have also found H$\alpha$ emission to be significantly more asymmetric than the stellar continuum with larger scatter. Fossati et al. (2013) and Boselli et al. (2015) report mean broadband asymmetries of $\sim$0.1 with a standard deviation of $\sim$0.08 and mean H$\alpha$ asymmetries of $\sim$0.2-0.35 with a standard deviation of $\sim$0.2 in near-perfect agreement with our sample, which has a mean broadband asymmetry of 0.1 with $\sigma=0.08$ and a mean H$\alpha$ asymmetry of 0.26 with $\sigma=0.2$ (see Figure 8). We do note that most of these studies are focused on local galaxies, typically with larger masses than we consider in our sample.

While not all such studies have explicitly considered the Gini coefficient, given their more local samples and therefore higher spatial resolution, some have included the CAS smoothness parameter in their analysis (Boselli et al., 2015) and find that H$\alpha$ emission is significantly clumpier than the continuum, again with a broader distribution. This is conceptually similar to our finding for the Gini coefficient, indicating that H$\alpha$ emission is less smooth and homogeneous than the stellar continuum. We note that Nersesian et al. (2023) find a lower value of the Gini coefficient for H$\alpha$ as compared to the continuum, but it is likely that this difference is reflective of our different mass ranges, our different physical resolution, or of our decision to fix the Gini segmentation maps of the H$\alpha$ images to those derived for the continuum images.

In addition to confirming the general morphological characteristics of the H$\alpha$ maps, previous studies have presented similar findings for trends with mass and SSFR. In particular, a lack of change in asymmetry (both for the H$\alpha$ and for the continuum) with mass has been seen in narrowband surveys (Fossati et al., 2013; Boselli et al., 2015). These studies have also found a correlation between asymmetry and SSFR – both for the continuum and for H$\alpha$. Again, while few studies have specifically investigated trends with the Gini coefficient for H$\alpha$, Boselli et al. (2015) did find that the smoothness parameter of the H$\alpha$ maps increases with SSFR; H$\alpha$ emission becomes clumpier as SSFR increases.

Yesuf et al. (2021) conducted a thorough mutual information analysis and determined that, out of their chosen set of physical parameters, asymmetry is most strongly correlated with $\Delta$MS. Their sample covered a similar redshift range to our sample but did not extend to masses below $\log(M_{\star}/M_{\odot})\approx 9.5$. Their morphological parameters were calculated based on broadband imaging and not H$\alpha$ imaging. Yesuf et al. (2021) proposed that the asymmetry-$\Delta$MS relation can perhaps be explained by asymmetric cold accretion leading to elevated star formation or by structural asymmetries induced by interactions or minor mergers.

Bottrell et al. (2023) further investigated the physical explanations for the observationally established relationship between asymmetry and high SSFR using simulated HSC-SSP imaging from IllustriusTNG. They created synthetic $i$-band imaging for galaxies at redshifts similar to and higher than our sample, with typical masses higher than what we cover. They were able to reproduce the asymmetry-$\Delta$MS trend with their simulated galaxies and argue that mini mergers are the dominant source of enhanced asymmetry and SSFR. They find that mini mergers are more common and lead to smaller but more prolonged boosts in SSFR and asymmetry than minor or major mergers.

Overall, our main findings agree with existing results surrounding nonparametric morphology of H$\alpha$ emission as compared to continuum emission. They also generally agree with morphological trends with mass, SSFR, and $\Delta$MS, particularly trends in asymmetry. Our sample extends to lower masses than previous studies at comparable redshifts. We consider the implications of this new mass bin below.

The correlation between asymmetry and SSFR (or between asymmetry and $\Delta$MS) has been previously established both in observations and in simulations, as described above (Fossati et al., 2013; Boselli et al., 2015; Yesuf et al., 2021; Bottrell et al., 2023). The physical explanations for this relationship focus on two main phenomena: galaxy-galaxy interactions and cold gas accretion. But what is the relative importance of each of these processes, and how do they change at low mass?

It is largely agreed upon that mergers lead to morphological asymmetry, with the lower mass companion being more strongly affected by the interaction if it survives (De Propris et al., 2007; Casteels et al., 2014). Mergers are also known to lead to strong enhancements in star formation (Keel et al., 1985; Ellison et al., 2013; Kaviraj, 2014). However, major mergers occur relatively infrequently (Lin et al., 2004; Patton & Atfield, 2008; López-Sanjuan et al., 2009), and certainly not frequently enough to explain the ubiquity of the SSFR-asymmetry trend. Bottrell et al. (2023) found that major and minor mergers were far too rare to cause observed asymmetry and SFR enhancements, but mini mergers (mergers with companions with greater than a 1:10 ratio of stellar masses) occurred sufficiently frequently. They also found that a more dramatic mass ratio in a merger led to a longer-lived increase in asymmetry and SFR. Overall, they concluded that in their simulations mini mergers accounted for twice as much asymmetry as minor and major mergers combined.

Can this same explanation be applied to dwarfs? The merger-asymmetry boost has been shown to hold at lower masses (Starkenburg et al., 2016; Guzmán-Ortega et al., 2023), but Martin et al. (2021) showed that mergers can only account for a small amount of the observed morphological disturbances in dwarf galaxies. Rather, they argue that nonmerger interactions are more important in shaping the morphologies of dwarf galaxies. Besla et al. (2018) found that while the major merger rate decreases with decreasing stellar mass for dwarf galaxies, the fraction of dwarfs with a close companion of comparable mass increases with decreasing mass. Hence, for dwarfs, major mergers are likely not a dominant process in creating asymmetry. Instead, less dramatic but more common interactions with nearby galaxies could play a significant role. Similarly, the connection between mergers/interactions and enhanced star formation has been shown to hold for dwarf galaxies (Stierwalt et al., 2015; Starkenburg et al., 2016; Kado-Fong et al., 2020, 2023). It therefore seems reasonable that the same class of interaction-related explanations should hold for the asymmetry-SSFR trend at low mass.

The second important physical phenomenon invoked to explain the asymmetry-SSFR correlation is cold accretion. Higher-mass galaxies, which have lower gas fractions than dwarf galaxies, require additional material to fuel sustained star formation. Galaxies are thought to obtain this extra gas by cold accretion along dark matter filaments (Sancisi et al., 2008; Sánchez Almeida et al., 2014), which has been shown to lead to asymmetries in galaxy morphologies and is well associated with an increase in SSFR.

It is important to note that the accretion explanation is not completely independent of the merger explanation; it is challenging to determine exactly how many mini mergers occur independently of cold accretion along filaments. Low-mass galaxies could be accreted along preexisting streams of material, as opposed to being independently gravitationally attracted to merge with the primary galaxy. This distinction is especially unclear for dwarf galaxies, for whom mini mergers would involve systems of very low mass, possibly even individual clumps of cold gas with no stars at all.

Additionally, because dwarf galaxies are gas-rich (Bradford et al., 2015), the addition of fuel (Hallenbeck et al., 2012; Richtler et al., 2018; Ju et al., 2022) may be less important in dwarfs than any accompanying dynamical disturbance. It is likely that the accretion-enhanced asymmetry and SSFR explanation for dwarf galaxies is less conceptually distinct from the impact of mergers.

One of the most striking results of our study is that the H$\alpha$ emission occurs in a small number of marginally resolved regions in the high-SSFR, low-mass galaxies. (No such trend is observed in the higher-mass galaxies, but we note that our sample does not probe the same SSFR regime for these sources.) Few if any of the rigorously star-forming low-mass galaxies have anything resembling a diffuse H$\alpha$ map as demonstrated quantitatively in Figure 10 and shown qualitatively with the maps themselves in Figure 11 (an extension of Figure 11 with complete samples of H$\alpha$ maps for the groups shown is included in Appendix D). What can this trend tell us about bursting dwarf galaxies and the processes that lead to dramatic star formation enhancements?

We should first note that while H$\alpha$ emission does not explicitly trace the presence of molecular gas, such material is a necessary prerequisite for recent star formation. Though in dwarf galaxies it is very challenging to detect CO directly (Leroy et al., 2005), recent high-resolution studies of higher-mass galaxies have shown that on the scale of our physical resolution ($\gtrsim$1 kpc) the distribution of CO is very similar to the H$\alpha$ emission (Pan et al., 2022). Hence, we can reasonably conclude that there is dense molecular gas at the sites of highly concentrated H$\alpha$ emission.

Dwarf galaxies differ fundamentally from larger galaxies, not only in their aggregate mass but also in their structure. While galaxies with $\log(M_{\star}/M_{\odot})>9.3$ have coherent large-scale structures including thin disks, spiral arms, or galactic bars, dwarf galaxies are typically puffy with shallow potentials and no such coherent large-scale features (Sánchez-Janssen et al., 2010; Kado-Fong et al., 2020b; Dekel et al., 2020). These structural distinctions help explain observed differences in composition and in star formation behavior between dwarfs and high-mass galaxies. Under the pressure-regulated, feedback-modulated (PRFM) model of star formation (Ostriker & Kim, 2022), the rate at which a galaxy forms stars is set by its midplane pressure. Due to their lower mass surface densities and larger scale heights, dwarfs tend to have lower star formation efficiencies and so form fewer stars and retain a larger fraction of their gas.

Given these differences, is it surprising that we do not see evenly distributed H$\alpha$ emission – i.e. evenly spatially distributed star formation and molecular gas – in the most active low-mass galaxies? As discussed above, enhanced star formation is most often thought to result from interactions with other galaxies and/or from accretion of cold gas. For a typical Milky Way-like galaxy, a mini merger or an interaction may cause enhanced star formation via compression in molecular clouds in the disk but is unlikely to cause a galaxy-scale instability - leading to spatially distributed star formation. (We note that in massive galaxies with higher SSFRs than what we probe in our sample, highly concentrated central star formation has been observed – as in ultraluminous infrared galaxies.) Conversely, for a low-mass galaxy without any such stabilizing structure and a much shallower potential, the same interaction could destabilize the disk, causing the galaxy’s gas reservoir to collapse toward its center. This type of rapid compression would result in highly concentrated molecular gas and star formation. It is therefore unlikely that we would see a low-mass galaxy with extremely active star formation evenly distributed over the galaxy.

It is also unlikely that a galaxy in this mass range could sustain such a high SSFR concentrated in a small central area if it were in dynamical equilibrium because the implied gas surface densities would be much higher than expected in dwarfs. Specifically, given their implied star formation rate surface densities, the extended Kennicutt-Schmidt relation (see, e.g., de los Reyes & Kennicutt, 2019) implies extremely high molecular gas fractions ($>\!0.9$) for these galaxies; such high molecular gas surface densities significantly exceed the surface densities expected in low-mass galaxies (see, e.g., Leroy et al., 2008; de los Reyes & Kennicutt, 2019; Kado-Fong et al., 2022b). We elaborate on this estimate and sketch out a toy model in Appendix E to demonstrate that it is highly unlikely that these sources are in dynamical equilibrium and to further support our interpretation of an external nonequilibrium process for starbursts in the low-mass sample.

The prevalence of a near-central clump of H$\alpha$ emission in the lowest-mass galaxies fits well within the larger picture of star formation in dwarf galaxies. In addition to their lower star formation rate surface densities, dwarfs have also been shown to have significantly burstier star formation histories, forming large fractions of their stellar populations in discrete episodes of star formation rather than forming stars at a constant rate for a prolonged period of time. In fact, the burstiness of a galaxy’s star formation history is believed to be a function of its stellar mass (Weisz et al., 2012; Guo et al., 2016; Sparre et al., 2017; Emami et al., 2019; Atek et al., 2022; Pan & Kravtsov, 2023). Starbursting dwarf galaxies are typically dominated by a small number of large H II regions (Lee et al., 2009a; Zick et al., 2018), sometimes even a single H II region for the lowest-mass galaxies. While our imaging cannot resolve individual H II regions, it is likely that the high heterogeneity of the H$\alpha$ maps for the low-mass, high-SSFR galaxies is driven by this phenomenon.

This also helps explain why we do not see the $G_{{\rm H}\alpha}$-SSFR or $M_{20,{\rm H}\alpha}$-SSFR trends for higher mass. They tend to be less bursty and more efficient in their star formation, with sites of star formation more spatially distributed. We note that our sample does not include any high-mass objects with extremely high SSFRs, so we are unable to comment on the morphology of this class of rare and extreme objects.

Our finding that nearly all of the low-mass, high-SSFR galaxies in our sample have H$\alpha$ distributions dominated by a small number of marginally resolved clumps can also shed light on questions about the physical interpretations of existing dwarf galaxy classifications. For decades, there has been much interest in identifying, classifying, and understanding blue compact dwarfs (BCDs, e.g., Thuan & Martin, 1981; Gil de Paz et al., 2003), which, as their name implies, are characterized by their blue color and compact light distribution. Do BCDs constitute an independent population of objects, or do they represent a transient stage in the life cycle of a typical dwarf galaxy? How do these galaxies fit into the larger narrative of dwarf galaxy evolution? Significant evidence exists that BCDs are triggered by interactions with their environment (e.g., Taylor, 1997; Bekki, 2008; Ashley et al., 2017) – interactions that are similar to the proposed triggering scenarios described above. Our results provide further evidence for these theories, supporting the interpretation that BCDs represent a transient stage in a dwarf galaxy’s life cycle – one of active star formation that is triggered by interactions with its environment.

Dwarf galaxies are bursty, and our analysis shows that bursting dwarf galaxies are often if not always highly concentrated, with a small number of compact star formation sites near, but slightly offset from, the center of the galaxy. Nonbursting low-mass galaxies – those with lower SSFRs – are less compact and more homogeneous. It is reasonable to conclude that most typical dwarf galaxies go through stages where they are blue and compact (the same stages where they are highly star-forming) and then settle down to a more diffuse morphology. Dwarf classifications based on compactness – especially those using broadband imaging that contains emission representative of star formation – may therefore fundamentally represent cuts based on SSFR.