Low surface brightness galaxies from BASS+MzLS with Machine Learning

The Tractor catalogue of DR9 for the BASS+MzLS provides valuable properties for the total sample of 364,277,779 extracted sources, including astrometry, photometry, and geometry. Based on some crucial properties in this catalogue, we select the LSBG candiates according to the following procedures step by step.

First of all, most LSBGs are acknowledged to be dominated by an extended disk, so we remove sources with morphological types (type) of PSF, DUP or DEV from the total sample. By this criterion, the point sources, coincident Gaia sources, or elliptical galaxies are excluded and 187,492,198 sources ($\sim 51.470\%$) of the total sample are retained.

Secondly, we require the sources to have half-light radius (as measured via shape_r parameter in the Tractor catalog) $r_{\rm eff}>2.5^{\prime\prime}$ to focus on the extended galaxies, and simultaneously require $r_{\rm eff}<20^{\prime\prime}$ to reject spurious sources or imaging artifacts, following Greco et al. (2018) and Tanoglidis et al. (2021b) where the detections larger than this scale in HSC-SSP or DES images were inspected to be rare and generally spurious. By this criterion, 2,999,940 sources (out of 187,492,198) are retained.

Then, to avoid the sources seriously polluted by the nearby contaminants which would cause unreliable model fitting results, we require our sources to satisfy the following criteria according to Ruiz-Macias et al. (2020):

where X represents the $g$, $r$, or $z$ bands. The fracmasked_X, fracflux_X and fracin_X are parameters in the Tractor catalogue which could probe the quality of the model fitting for the sources. Specifically, the fracmasked_X, the profile-weighted fraction of pixels masked from other observations of the target object, is used to remove sources with a high fraction of masked pixels. The fracflux_X, the profile-weighted fraction of the flux from other sources divided by the target object flux, is used to reject objects with heavily contaminated flux. The fracin_X, the fraction of the flux from the target source within the blob, a group of pixels, is used to select sources with a large fraction to ensure well-constrained model fits. By this criterion, 1,622,986 sources, approximately 0.446% of the total sample, are retained.

Here before the next criterion, we correct the flux for the Galactic extinction and convert it to the magnitude with the prescription (Equation (2)) given by the Legacy Surveys.

where X represents the $g$, $r$, or $z$ bands. $F_{\rm X}$ is the model flux in the X band, measured as flux_X in unit of nanomaggy in the Tractor catalogue, $MW_{\rm X}$ the Galactic transmission of the object position in the X filter, measured as mw$\_$transmission$\_$X in linear units from 0 to 1 in the catalogue, where 1 represents a fully transparent region of the Milky Way and 0 a fully opaque region. $F_{\rm corr,X}$, the Galactic-extinction corrected flux, is further converted to the magnitude, $m_{\rm corr,X}$, based on which the colors of $g$ - $r$ and $g$ - $z$ are obtained.

After that, we request the colors to be within the color box defined by

This color box was empirically determined based on the distribution of the total sample of the BASS+MzLS in the $g$ - $r$ versus $g$ - $z$ diagram, as shown in Figure 1 where the three black solid contours from the inside out, respectively, enclose 68.2$\%$, 95.6$\%$, 99.8$\%$ of the total sample. For determining the color requirements (the red box in Figure 1), our principles are including the majority of the galaxies within the central contour where 68.2$\%$ of the total sample gathers while excluding the high redshift galaxies and spurious objects. By satisfying the color requirements (equation (3)), 994,459 sources ($\sim 0.273\%$ of the total sample) are retained.

Subsequently, we require the ellipticity (1 - b/a) to be less than 0.7 (an axis ratio, b/a, greater than 0.3) to avoid edge-on galaxies, some spurious objects with high ellipticity (e.g., diffraction spikes), or the most obvious lensed galaxies. By this criterion, 772,745 sources (0.212% of the total sample) are retained.

Finally, we calculate the mean surface brightness within the half-light radius, $\bar{\mu}_{\rm eff,X}$, by using Equation (4):

where $r_{\rm eff}$ is the half-light radius, measured as shape_r in the Tractor catalogue. We require the $\bar{\mu}_{\rm eff,X}$ to be within $24.2<\bar{\mu}_{\rm eff,g}<28.8$ mag arcsec^-2 and obtain 344,370 objects (0.095% of the total sample) as the initial sample of the LSBG candidates.

For a clear picture of the process of our selection for the initial LSBG candidates so far, the selection criteria above are listed in Table 1. Up to now, the selection of the initial LSBG candidates were solely via the direct use of the Tractor catalogue, so we furthermore inspected the images of a few thousand initial LSBG candidates and found a large number of the candidates were apparently false LSBGs that are instead the sources of contaminations. So it is necessary to reject those false LSBG candidates from the numerous initial candidates via the machine learning techniques.

From our visual inspection, the most common sources of contaminations for the false LSBGs were:

1. 1.

   Red objects with high ellipticity close to the criterion of 0.7 (e.g., Figure 22(a)).

2. 2.

   Detections that are almost invisible in the images (e.g., Figure 22(b)).

3. 3.

   Diffuse light from the nearby bright stars (e.g., Figure 22(c) and  22(f)).

4. 4.

   Faint, diffuse regions of objects in a larger scale, such as Galactic cirrus (e.g., Figure 22(d)).

5. 5.

   Diffuse light from the arms of large spiral galaxies (e.g., Figure 22(e)).

Aiming to reject the false LSBGs from the initial sample of the LSBG candidates and simultaneously maintain a completeness of the true LSBGs as high as possible, we employed a supervised machine learning classification algorithms.

In this section, we visually inspected the $grz$-composite images of the 57,934 LSBG candidates retained after the machine learning. From the inspection, we found that there are still false LSBGs in the sample whose visual appearances in the images were not like the true LSBGs at all, but the values of their main features listed in Section 3.2.2 given by the Tractor measurements followed the true LSBGs, making it challenging to classify them to be non-LSBGs by our model that were trained solely on learning the main features since we desired a fast learning and classification of the LSBGs in this work. However, in the future, we plan to train a better deep learning classification model using both the features and images of the final LSBG sample selected in this work.

Specifically, these false LSBGs in the current sample still appeared to be like the contaminations shown in Figure 2. Therefore, we rejected them by visual inspection and ultimately resulted in a final sample of 31,825 LSBG candidates with a high purity of the true LSBGs with the half-light radius 2.5^′′ $<r_{\rm eff}<$ 20^′′ and the Galactic extinction-corrected mean effective surface brightness $24.2<\bar{\mu}_{\rm eff,g}<28.8$ mag arcsec^-2. This final sample is so far the largest catalogue of LSBG candidates from the $\sim$ 5500 deg² sky area of BASS+MzLS, more than 1/3 of the entire sky area of the DR9 of the DESI Legacy Survey.

We displayed the distribution of the final sample of the LSBG candidates in the color - color diagram of $g$ - $r$ versus $g$ - $z$ in Figure 5. The sample galaxies (green dots) exhibited a bimodal distribution in the $g$ - $r$ color which naturally required a fitting by a combination of double Gaussian profiles rather than a single Gaussian profile according to our evaluation by the Akaike Information Criterion (AIC / AICc) and the Bayesian Information Criterion (BIC; see details in Section 5.1).

In Figure 5 (the top panel), the best-fitting profile (black solid curve) evaluated by the AIC/BIC is the sum of a blue component represented by a single Gaussian profile with a peak value at a blue $g$ - $r$ color of 0.455 and $\sigma$ of 0.103 (blue solid curve) and a red component represented by a single Gaussian profile with a peak value at a red $g$ - $r$ color of 0.700 and $\sigma$ of 0.070 (red solid curve). Obviously, the blue component is dominated by the blue LSBG candidates of which 97.8$\%$ are bluer than $g$ - $r$ $<$ 0.66 while the red component is dominated by the red LSBG candidates of which 97.8 $\%$ are redder than $g$ - $r$ $>$ 0.56. This means that galaxies between $g$ - $r$ = 0. 56 and 0.66 are the mixture of LSBG candidates from the red end of the blue component ($g$ - $r$ $>$ 0.56) and those from the blue end of the red component ($g$ - $r$ $<$ 0.66). Since the median color of all of the galaxies between 0. 56 and 0.66 is 0.60 in $g$ - $r$, we adopt $g$ - $r$ = 0.60 as the color dividing line (vertical black dashed line) to separate the final sample of LSBG candidates into two subsamples of the blue ($g$ - $r$ $<$ 0.60; 26,672 galaxies) and the red ($g$ - $r$ $>$ 0.60; 5,153 galaxies). The median $g$ - $r$ colors of the blue and red subsamples are 0.44 and 0.67, respectively.

In Figure 6, we show randomly selected LSBG candidates from the the blue (the left) and the red (the right) subsamples for examples. Apparently, the blue LSBG candidates appear disk-like, spiral or irregular while the red ones tend to be spheroidal or elliptical. The former is quite distinguishing from the latter in morphology, implying that the colors of LSBGs correlate with their morphologies. Such a conclusion was also supported by several previous published studies, which would be discussed in Section 5.2.

In Figure 7(a) the distribution of the magnitudes in the $g$-, $r$-, and $z$-band are shown for the final sample of LSBG candidates entirely. In Figure 7(b), the distribution of the $g$-band magnitude is compared between the blue and red subsamples, showing that the blue are slightly brighter than the red in the apparent magnitude in $g$-band. In Figure 7(c), we show the distribution of the mean surface brightness $\bar{\mu}_{\rm eff,g}$ for the blue and red subsamples, respectively. We find that the red subsample shows a bump or an excess at the lower surface brightness tail (fainter than 25.5 $g$ mag arcsec^-2) while the blue subsample has slightly more LSBGs with higher surface brightness (brighter than 25.5 $g$ mag arcsec^-2), implying that the red LSBGs from our sample incline to have lower surface brightness while the blue ones tend to have higher surface brightness. This could be further supported by the statistics that the 16^th, 50^th, and 84^th percentiles of $\bar{\mu}_{\rm eff,g}$ are 24.4, 24.7, 25.5 mag arcsec^-2 for the blue subsample and 24.4, 24.8, 25.8 mag arcsec^-2 for the red subsample.

In Figure 8(a), we present the distribution of ellipticity ($\epsilon$ = 1 - b/a) for the full final sample. It shows that both the blue and the red subsamples have considerable fractions of galaxies with the zero $\epsilon$ from the Tractor catalogue (10% of the blue and 18% of the red). The median $\epsilon$ are $\sim$ 0.31 for the full sample, $\sim$ 0.32 for the blue and $\sim$ 0.28 for the red, respectively. To give a clear picture of the $\epsilon$ distribution for those galaxies without the zero $\epsilon$, we plot a zoom-in picture for them in panel (b), where both subsamples show generally consistent distributions, with the median $\epsilon$ of 0.34 for the blue and 0.31 for the red, respectively. All of these $\epsilon$ distributions demonstrate that the LSBG candidates in our final sample are obviously round between $\epsilon$ = 0.1 and 0.7, which differs from the normal spiral galaxies showing a nearly flat ellipticity distribution between $\epsilon$ = 0.1 and 0.7 (Figure 4 in Rodríguez & Padilla (2013)).

In Figure 9(a), both subsamples are dominated (more than 99%) by galaxies with sizes ranging from 2.5^′′ to 14^′′ in $r_{\rm eff}$, with the medians are 3.5^′′ for the red sample, 4.1^′′ for the blue sample, and 4^′′ for the full sample. It is worth noting that the $r_{\rm eff}$ measurements from the Tractor catalogue for the minority of the large spiral galaxies are all given to be around $\sim$ 13.8^′′, causing a low peak occurs at $r_{\rm eff}$ of $\sim$ 13.8^′′ in the figure. This low peak due to the limitation of the Tractor model measurements has no physical implications, but the galaxies in this low peak all appear blue, large, diffuse, and extended disk LSBGs from our visual inspection. Thus, we still kept these galaxies in our final sample. In Figure 9(b), we plot the S$\rm\acute{e}$rsic index $n$ for the blue and the red subsamples, showing that 95% of the blue subsample have $n<$ 2.5 while 93% of the red subsample have $n<$ 2.5. The distribution of $n$ agrees with each other for both subsamples, with a median of $n$ = 1 for each, showing our final sample is dominated by the disk LSBGs.

In Figure 10 we show the spatial distribution of the blue (top) and the red (bottom) subsamples over the sky area within the the BASS+MzLS footprint (the black solid). We find an obvious discrepancy between the spatial distribution of the two subsamples. The blue LSBGs are more uniformly distributed while the red populations are clustered, showing that red LSBGs preferentially inhabit in denser environments than blue LSBGs. This is found by the studies of Greco et al. (2018) and Tanoglidis et al. (2021b) as well, and we will discuss it in Section 5.2.

In Section 4.1 our LSBG sample was reported to have a bimodal color distribution that could be best fitted by a mixture of double Gaussian models rather than a single Gaussian model. Such a statement is supported by the evaluation of the performance of the single Gaussian model (SGM; grey dashed line in the top panel of Figure 5) and the double Gaussian model (DGM; black line in the top panel of Figure 5) fit according to the AIC/BIC in the equation below (equation (5)) .

where $k$ is the number of fitting parameters, $\hat{L}$ is the likelihood function, and n is the number of samples. When the sample is small in size, AIC should be corrected into AICc. According to Kass & Raftery (1995), the performance of the model improves as the AICc or BIC value decreases.

We derive the BIC or AICc values from fitting the $g$ - $r$ color distribution of our sample with a single Gaussian model as BIC_SGM or AICc_SGM. Similarly, we derive BIC_DGM or AICc_DGM for the fit with the double Gaussian model. Then, the BIC or AICc differences between the SGM and DGM are calculated as $\Delta BIC=BIC_{\rm SGM}-BIC_{\rm DGM}$ and $\Delta AICc=AICc_{\rm SGM}-AICc_{\rm DGM}$. According to Kass & Raftery (1995), if $\Delta BIC$ or $\Delta AICc$ was larger than 10, the DGM would prevail. In our calculation, the $\Delta AICc$ and $\Delta BIC$ values are 235.1 and 227.1, respectively, which are far greater than 10, giving a strong evidence for us to believe that the $g$ - $r$ color distribution is much better fitted by a double Gaussian model than a single Gaussian model. This strongly convinces us of a bimodal $g$ - $r$ color distribution of the final sample of LSBGs. Additionally, such bimodal distributions of the colors of the LSBGs have also been reported for the previously defined sample of LSBGs from Greco et al. (2018) and Tanoglidis et al. (2021b), which would be discussed in detail in Section 5.2.

In this section, we compare our sample of the LSBG candidates with three other LSBG samples from Du et al. (2015)(D15), Greco et al. (2018)(G18) and Tanoglidis et al. (2021b)(T21), respectively. The D15 provides a sample of 1,129 LSBGs selected from the 2800 deg² area of the $\alpha$.40 - SDSS DR7 survey with an imaging depth of $r\sim$ 22.2 mag for point sources of 95% detection (York et al. 2000). This sample is defined on the central surface brightness $\mu_{\rm 0,B}>$ 22.5 mag arcsec^-2, and they are nearby (z $<$ 0.06), blue, Hi-rich, and disk-dominated. The G18 presents a sample of 781 extended LSBGs from the first $\sim$ 200 deg² area of the imaging survey of the Wide layer of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) which has a depth of $g\sim$ 26.8, $r\sim$ 26.4, and $i\sim$ 26.4 mag for point sources at 5$\sigma$ (Aihara et al. 2018a). This sample is defined on the mean surface brightness ($\bar{\mu}_{\rm eff,g}>$ 24.3 mag arcsec^-2) to allow nucleated galaxies into the sample and on galaxy size ($r_{\rm eff}>$ 2.5^′′) as well to be restricted to low redshift. Using the similar selection criteria to the G18, the T21 produces a catalogue of 23,790 extended LSBGs from the $\sim$ 5000 deg² area of the first three years of imaging data from the Dark Energy Survey (DES Y3) with a depth of $g\sim$ 23.52, $r\sim$ 23.10, and $i\sim$ 22.51 mag for point sources at 10$\sigma$ which is corresponding to a surface brightness limit at 3$\sigma$ of $g\sim$ 28.26${}^{+0.09}_{-0.13}$, $r\sim$ 27.86${}^{+0.10}_{-0.15}$, and $i\sim$ 27.37${}^{+0.10}_{-0.13}$ mag arcsec^-2.

In terms of the surface brightness (Figure 11(a)), our sample is highly consistent with the T21, ranging from 24.2 $<\bar{\mu}_{\rm eff,g}<$ 28.8 mag arcsec^-2. The 16^th, 50^th, and 84^th percentiles of $\bar{\mu}_{\rm eff,g}$ are 24.4, 24.7, and 25.5 mag arcsec^-2 for our sample and 24.3, 24.7, 25.3 mag arcsec^-2 for the T21. For the G18 sample, the $\bar{\mu}_{\rm eff,g}$ measurement is not available in its released catalogue, so we are not able to display the G18 sample overplotted in Figure 11(a) to carry out direct comparisons with the three other samples. However, it is clearly stated in G18 that the $\bar{\mu}_{\rm eff,g}$ distribution of their sample is broad with the 16^th, 50^th, and 84^th percentiles are $\bar{\mu}_{\rm eff,g}$ = 24.5 (24.8), 24.8 (25.8), and 25.5 (26.8) mag arcsec^-2 for the blue (red) subsamples. According to such statements, we believe that the G18 sample has quite similar distribution of mean surface brightness to our sample and the T21. In a stark contrast, the Du15 sample has the mean surface brightness distribution with the 16^th, 50^th, and 84^th percentiles of $\bar{\mu}_{\rm eff,g}$ = 23.4, 23.7, and 24.6 mag arcsec^-2, which are much brighter than our the three other samples. This is reasonable because the Du15 sample is from the SDSS imaging survey which has a shallower depth than the BASS+MzLS, DES Y3, and HSC-SSP surveys that our sample, T21 and G18 are, repsectively, based on. This could be furthermore supported by the comparison of magnitude (Figure 11(b)), where our sample, the T21, and the G18 are systematically at least $\sim$ 2 mag fainter than the Du15 sample in the $g$-band apparent magnitude.

In the aspect of the color (Figure 11(c)), the 16^th, 50^th, and 84^th percentiles of $g$ - $r$ are 0.36, 0.47, and 0.60 for our sample, 0.29, 0.43, and 0.60 for the G18 sample, 0.26, 0.38, 0.57 for the T21 sample, and 0.20, 0.30, and 0.41 for the D15. Apparently, our sample generally agrees with the G18 and the T21 in the $g$ - $r$ distribution, albeit the latter two samples are slightly bluer. Among the samples for comparison, the sample of Du15 is the bluest because their galaxies are dominated by Hi-rich and blue LSBGs. Additionally, we reported that our sample has a bimodal distribution of the $g$ - $r$ color in Section 4.1, implying two distinct populations of the blue and the red LSBGs, respectively. Actually, such bimodal distributions of the color has also been found in the G18 and the T21 for their own LSBG samples. Specifically, the G18 sample shows a clear bimodality in both the $g$ - $r$ and $g$ - $i$ colors, and is thus divided into two populations of the red and the blue LSBGs using the median $g$ - $i$ = 0.64 as the dividing line. Similarly, the T21 sample also displays bimodal distribution in both the $g$ - $r$ and $g$ - $i$ colors, and is then separated into two subsamples of the blue and the red LSBGs using the intersection of the two Gaussian model profiles at $g$ - $i$ = 0.60 as the threshold. The color distributions of all the three of our sample, the G18, and the T21 demonstrate that LSBGs, similarly to the galaxies with normal/high surface brightness (normal galaxies), are able to be conventionally divided into two sequences of the blue and the red, with the blue LSBGs dominated by the sprial, disk, or irregular systems in morphology and the red LSBGs by the spheroidal or elliptical morphology.

As for the environments, the blue and Hi-rich LSBGs of the Du15 are mostly in voids or to the edge of the filaments of low densities. For the three of our sample, the G18, and the T21, the LSBGs show consistent spatial distributions, with the blue LSBG populations of each sample more uniformly distributed within the sky footprint and the red populations of each sample highly clustered in the spatial area. This implies that the red LSBGs preferentially inhabit in denser environments than the blue LSBGs.

Furthermore, our sample is consistent with the G18 and the T21 in the ellipticity distribution, with the median around $\epsilon\sim$ 0.3 showing the LSBGs of the three samples are generally round. This is a striking contrast to the almost flat distribution of $\epsilon$ of the normal galaxies between $\epsilon$ = 0 and 0.7.

These comparisons strongly demonstrate that our sample along with the G18 and the T21 have well extended the SDSS-based LSBG samples to a new regime of much lower surface brightness, fainter apparent magnitude and broad properties in a large scale.

The optical colors of galaxies indicate their stellar populations and have a strong correlation with the galaxy morphology and environment. In the frame of galaxies with normal or high surface brightnesses, galaxies in the local universe fall into one of two distinct populations in terms of optical colors: a red sequence and a blue cloud (Strateva et al. 2001; Baldry et al. 2004; Blanton & Moustakas 2009). Besides the color, the bimodal distributions have also been observed and measured in some other parameters, such as metallicity and star formation rate (Kauffmann et al. 2003a, b). The blue cloud is dominated by active, star-forming galaxies while the red sequence is composed of quiescent galaxies. Compared to the blue galaxies which are spiral, disk, or irregular systems in morphology, the red galaxies are ellipticals, spheroidals, lenticulars, and cD galaxies (Blanton & Moustakas 2009). Moreover, red galaxies are more likely to be found in denser environments and more spatially clustered than blue galaxies (Blanton & Moustakas 2009; Das & Pandey 2024). It is proposed that the blue galaxies would evolve onto the red sequence by fading their stellar populations after their star formation was ceased by some quenching mechanisms, such as the natural exhaustion of gas, active galactic nuclei feedback, galaxy harassment, and galaxy mergers, etc.

Similar to the blue cloud and red sequence in the frame of galaxies with normal surface brightnesses, our LSBGs in this work show a bimodal distribution in the optical color, so they fall into two populations in terms of the $g$ - $r$ color: the blue and red LSBGs. In morphology, the blue LSBGs are disk-like or irregular while the red LSBGs are more bulge-dominated or spheroidal. In addition, the red LSBGs are more spatially clustered than the blue LSBGs. So there might be an possible evolutionary path from the blue LSBGs to the red LSBG, and we would investigate this issue in our future work.