Non-parametric decompositions of disk galaxies

# Non-parametric decompositions of disk galaxies in S${^4}$G using DiskFit

## Abstract

We present photometric models of 532 disk galaxies in 3.6m images from the Spitzer Survey of Stellar Structure in Galaxies ( SG) using the non-parametric DiskFit algorithm. We first test DiskFit’s performance on 400 synthetic  SG-like galaxy images. DiskFit is unreliable in the bulge region, but accurately disentangles exponential disks from Ferrers bars farther out as long as their position angles differ by more than . We then proceed to model the  SG galaxies, successfully fitting 489 of them using an automated approach for initializing DiskFit, optimizing the model and deriving uncertainties using a bootstrap-resampling technique. The resulting component geometries and surface brightness profiles are compared to those derived by Salo et al using the parametric model galfit. We find generally good agreement between the models, but discrepancies between best-fitting values for individual systems are often significant: the choice of algorithm clearly impacts the inferred disk and bar structure. In particular, we find that DiskFit typically assigns more light to the bar and less light to the disk relative to the Ferrers and exponential profiles derived using galfit in the bar region. Given DiskFit’s reliability at disentangling these components in our synthetic images, we conclude that the surface brightness distributions of barred  SG galaxies are not well-represented by these functional forms. The results presented here underscore the importance of validating photometric decomposition algorithms before applying them to real data and the utility of DiskFit’s non-parametric approach at measuring the structure of disks and bars in nearby galaxies.

###### keywords:
galaxies: photometry - galaxies: structure - galaxies: bulges - galaxies: spiral
12

## 1 Introduction

Secular processes dominate the evolution of galaxies at low redshifts, with galactic bars being among the main mechanisms driving evolution (e.g. Kormendy & Kennicutt, 2004; Kormendy, 2013; Athanassoula, 2013; Sellwood, 2014). Bars are long-lived features, initially formed as elongated gravitational instabilities in the plane of the galaxy disk (e.g. Hohl, 1971; Sellwood, 1981; Binney & Tremaine, 1987). As the instability grows and the bar gets stronger it will increase in length and trap more disk stars. This takes angular momentum from the bar, making it thinner and decreasing its rotational pattern speed (Athanassoula, 2003). Absorption of angular momentum by the halo also strengthens the bar (Athanassoula, 2002, 2003). Additionally, bars dissipate angular momentum via gas in the disk, channelling it toward the centre of the galaxy and triggering central star formation (Englmaier & Gerhard, 1997; Athanassoula, 1992; Sellwood, 2013; Tonini et al., 2016). The physical properties of bars are therefore important indicators of the evolutionary states of their host galaxies (Pérez et al., 2017; Kruk et al., 2018; Hoyle et al., 2011; Masters et al., 2011; Athanassoula et al., 2013).

Over the years, a variety of techniques have been adopted to extract bar properties from photometric images of nearby galaxies. Initial attempts focused on applying parametric functions to one-dimensional surface brightness profiles derived by fitting isophotal ellipses (e.g. Kormendy, 1977a, b, c; Kent, 1985; Burstein, 1979), and changes in the ellipticity and position angle of the ellipses themselves can also be used to characterize bars (Wozniak et al., 1995; Erwin, 2005). However, tests show that the latter approach leads to systematic biases in the resulting bar lengths (Gadotti, 2008; Aguerri et al., 2009), while significant parameter degeneracies can emerge from the former approach, particularly near the galaxy centre (e.g. MacArthur et al., 2003; Kormendy, 1977b).

More recently, applying two-dimensional models directly to the imaging data has become the norm for characterizing bars. Several algorithms (e.g. budda, de Souza et al. 2004; gim2d, Marleau & Simard 1998; Simard et al. 2002; imfit, Erwin 2015; galfit/galfitm, Peng et al. 2002, 2010; Vika et al. 2013) decompose galaxy images into parametrized disks, bars, and bulges, and more complex structural components such as arms and rings can also be incorporated (Peng et al., 2010; Ma et al., 2017; Mutlu Pakdil et al., 2017). The reliability and uniqueness of these models is hard to infer, however, since many algorithms don’t return uncertainties on best-fitting values. Bar parameters are thus often presented without uncertainties (Weinzirl et al., 2008; Salo et al., 2015; de Swardt et al., 2015). Although modelling large galaxy samples is an effective means of minimizing the statistical uncertainties on measured values (Blanton et al., 2005), detailed survey- and algorithm-specific tests are required to determine whether or not systematic biases are important (Schombert & Bothun, 1987; Byun & Freeman, 1995; Wadadekar et al., 1999; MacArthur et al., 2003; Gadotti, 2008; Peters & Kuzio de Naray, 2017).

DiskFit is an algorithm for modelling two-dimensional velocity maps or images of nearby disk galaxies (Spekkens & Sellwood, 2007; Sellwood & Spekkens, 2015; Kuzio de Naray et al., 2012). It was designed to measure the kinematic and photometric properties of asymmetries in these systems and to generate robust uncertainties of the best-fitting values using a bootstrap-resampling technique (Sellwood & Sánchez, 2010). In the uncertainty estimation, the residuals from a best-fitting model are randomly scrambled and added to the model to create each bootstrap realization. The standard deviation of the best fitting model values from the ensemble of realizations is then adopted as the uncertainty (Spekkens & Sellwood, 2007). The photometric side of the code differs from many other approaches in that it models the surface brightness distribution of the disk and bar – each assumed to have a fixed centre, position angle and ellipticity – non-parametrically. DiskFit is therefore particularly useful for characterizing the properties of barred galaxies whose bar and disk light distributions may differ from the standard Ferrers and exponential forms, respectively, as suggested both theoretically and observationally in recent studies (Gadotti, 2008; Kim et al., 2016b; Williams & Evans, 2017).

The Spitzer Survey of Stellar Structure in Galaxies ( SG, Sheth et al. 2010) produced 3.6m and 4.5m images for 2331 nearby galaxies in order to map their stellar mass distributions at wavelengths largely immune to dust contamination (Muñoz-Mateos et al., 2013; Querejeta et al., 2015; Muñoz-Mateos et al., 2015). The  SG sample is therefore an ideal testbed for comparing the performance of different photometric decomposition models at recovering disk and bar properties. Salo et al. 2015 (hereafter S15) present multi-component “human-supervised” models of  SG barred and unbarred galaxies using galfit that have been extensively used to constrain their underlying structure and evolution (Muñoz-Mateos et al., 2015; Erroz-Ferrer et al., 2015; Sorce et al., 2016; Bittner et al., 2017). S15 discuss the impact of changing the PSF, sky subtraction, weight smoothing, and model components on the best-fitting galfit models, and also compare to models in the literature for a subset of the sample. However, S15 do not report uncertainties on their final parameters or test galfit’s performance on  SG-like imaging, and the reliability of their decompositions is therefore not quantified. Since DiskFit’s non-parametric approach to characterizing disk and bar components differs from galfit’s parametric one, it is an ideal algorithm to compare to the S15 results to gain a better understanding of the underlying structure of nearby disks and bars and the uncertainties associated with extracting this structure from imaging data (e.g. Peng et al. 2010).

This paper presents non-parametric DiskFit decompositions of  SG disk galaxies for direct comparison with S15’s parametric galfit models. Our goals are to quantitatively test DiskFit’s performance on  SG-like imaging, to determine the conditions under which DiskFit and galfit models of  SG galaxies differ, and to explore the resulting implications for the structure of barred galaxies. §2 describes the  SG subsample adopted for our comparison. §3 describes the synthetic galaxy images that we used to test DiskFit on  SG-like imaging and the corresponding modelling results. §4 presents our DiskFit models of the  SG subsample itself, and a comparison between the best-fitting properties of these models to the corresponding S15 galfit results. We discuss the implications of that comparison for the structure of nearby barred galaxies in §5.

## 2 Sample Selection

There are 2331 galaxies in  SG (Sheth et al., 2010), encompassing all morphological types. Very early and late type galaxies tend not to have distinct disks, and are not well represented by DiskFit’s models. We therefore include only rotationally supported spirals (Hubble types 0 through 7) in our subsample, as listed in the  SG catalogue (Sheth et al., 2010). Since our focus is the characterization of bars in nearby, well-resolved disk galaxies, we exclude high inclination systems ( > 0.7) and low-quality images (quality flag 4 from S15), and require that the scale length of the disk measured by S15 be spanned by at least 15 pixels (1 pixel = 0.75 arcseconds; Sheth et al. 2010). The  SG subsample that meets these selection criteria contains 570 galaxies, some of which are listed in Table 1 (the full table is shown in digital appendix Table A1). We fit the same 3.6m  SG images as modelled by S15. Figure 1 shows the distribution of morphological types included in the subsample, and Figure 2 shows the distribution of structural parameters in that subsample inferred from the galfit models of S15.

## 3 Fitting of Synthetic Galaxies

Validating the performance of a photometric decomposition algorithm on synthetic galaxies before proceeding to interpret fits to real data is essential for disentangling physical effects from software limitations. In this section we describe the simulated  SG-like galaxy images that we use to test DiskFit’s performance (§3.1), as well as the implications of our DiskFit model results on our fitting procedure for real galaxies (§3.2).

### 3.1 Setup and Fitting Procedures

We draw from the statistical properties of the subsample galaxies obtained from the fourth data reduction pipeline of  SG (S15) to create 400 images of synthetic galaxies, each containing a disk, a bar, and a bulge. The goal is to simulate galaxies with idealized structural components and image properties similar to the  SG galaxy subsample in order to quantitatively assess DiskFit’s performance in this regime. For simplicity we adopt parametric surface brightness profiles for the synthetic galaxies, even though DiskFit recovers them non-parametrically.

We adopt exponential surface brightness profiles for the simulated disks:

 Σdisk(r)=Σ0,diske(−r/rd), (1)

with a disk scale length , and a central surface brightness . The simulated surface brightness distribution of the bar is given by the Ferrers function (Ferrers, 1877):

 Σbar(r)={Σ0,bar[1−(r/rbar)2]2r

with a truncation radius , and a central surface brightness . Finally, we adopt a Sérsic function (Sérsic, 1963) for the simulated bulges:

 Σbulge(r)=Σeff exp(−bn[(rreff)1/n−1]), (3)

with a Sérsic index , and surface brightness at effective radius . We use the approximation (Capaccioli, 1989).

The component parameters in the simulated galaxy images are randomly drawn from their distributions in the  SG subsample as determined by S15, so that the real and synthetic samples span comparable ranges. The histograms in Figure 2 show the distribution of , , , , , and in the sample of synthetic galaxies. We also draw from the  SG distributions for the bulge parameters ,   and , imposing constraints on the relative surface brightnesses of the bulge and disk based on ranges from S15.

Once the structural properties of each galaxy are selected, the simulated images are made to be photometrically similar to those of the  SG subsample. We convolve the synthetic images using a Gaussian with full width at half maximum FWHM = 2.1 arcsec (with 0.75 arcsec/px), which closely resembles the IRAC PSF (Sheth et al., 2010). We add Poisson noise to the Gaussian-convolved images to mimic the source and sky background-dominated noise in the  SG images (Sheth et al., 2010). We also create uncertainty maps for each galaxy using an algorithm similar to that adopted by S15. Examples of simulated galaxy images are shown in Figure 3.

After the creation of the synthetic sample, we apply DiskFit to each simulated galaxy and its corresponding uncertainty map. We fit disk, bar, and bulge models for all systems. Input guesses for the disk PA, bar PA, , , Sérsic ,   and are taken to be their true values in order to maximize the chances of recovery. We initially allow all parameters to vary freely in the models to determine the best fitting non-parametric surface brightness profiles for the disk and the bar. However, for reasons that we discuss in §3.2 we leave Sérsic fixed to the true value for all figures following Figure 4. We set DiskFit to correct for seeing using the same Gaussian PSF as adopted in the simulations. We estimate uncertainties on the fitted parameters using 20 bootstrap-resampled realizations of each model using the radial-rescaling method of Sellwood & Sánchez (2010), where the number of bootstrap realizations is limited by the computing resources available through the Centre for Advanced Computing (CAC) at Queen’s University. The next section presents the results of these fits.

### 3.2 Results of Synthetic Galaxy Fits

Figure 4 shows the relationship between the input and recovered bulge properties for the synthetic galaxy images. Panels a), b) and c) show the bulge properties recovered when all bulge parameters are allowed to vary in the fits. It is clear that Sérsic is not reliably recovered, and that there is significant scatter between the input and recovered   and . The situation improves when Sérsic is fixed to the input value, as shown in panels d) and e) in Figure 4. The recovered values for are scattered symmetrically about the 1:1 relation. The recovered   loosely follows the 1:1 line, with the majority of recovered values underestimating the true ones: this is a consequence of DiskFit assigning bulge light to the (non-parametric) disk. The fraction of light in the bulge (a cumulative measure computed from n,   and ) is not recovered by DiskFit regardless of whether or not n is held fixed.

Our simulations imply that DiskFit cannot reliably recover Sérsic in SG-like imaging, i.e simulated galaxy images in which the range of structural parameter values, the resolution, and the image noise resemble that of  SG. We therefore fix this parameter in all subsequent DiskFit models of both simulated and real systems, and have used our simulations to verify that the disk and bar properties are unaffected by this choice beyond the bulge region. Figures 4d) and 4e) imply that, even with fixed to the correct value, the other Sérsic bulge properties are not well-recovered. It is therefore likely that the DiskFit models of the  SG subsample (where the true is unknown) are unreliable in the bulge region of each galaxy, and we do not consider this region further here. All subsequent models of synthetic and real galaxies keep fixed.

A comparison between the input and recovered position angles and ellipticities of the disk and bar in our synthetic galaxy images is shown in Figure 5 and the best fitting values from least-squares linear fits to each trend are given in Table 2. Panels a) and b) of Figure 5 show that for the vast majority of simulated galaxies, the disk and bar PAs are accurately and precisely recovered by DiskFit. We note that synthetic galaxies with outlying values of the recovered disk PA are mostly low-inclination systems with . The relationships between the input and recovered disk and bar ellipticities in Figures 5c) and 5d) show comparatively more scatter, but the correlations remain strong. Table 2 shows that the median absolute deviation normalized to equal the standard deviation for Gaussian distributions (MAD/1.4826) about the best-fitting linear relationship implies an extremely small scatter of the best fitting values from their true ones for most synthetic galaxy fits.

Insight into the nature of the outliers can be gleaned by examining the coloured points in Figure 5, which correspond to the individual galaxies in Figure 3. The red triangles in Figure 5 show an example of a synthetic galaxy, highlighted in Figure 3a), where the recovered properties match the input values within the uncertainties; this system has a relatively bright bar ( 23 px, where the bar comprises 62% of the total galaxy light) at a distinct position angle from the underlying disk.

By contrast, the outlying green circles in Figure 5b) and 5d) illustrate DiskFit’s higher likelihood of failing to recover a weak bar ( 16 px with 0.3% galaxy light) in the synthetic galaxy in Figure 3d); this is perhaps to be expected, since the bar isn’t visible by eye. DiskFit fares better at recovering the longer and slightly stronger bar ( 56 px with 0.9% galaxy light) in the synthetic image in Figure 3c), represented by the blue squares in Figure 5; the bar properties are well-recovered, though is strongly under-estimated. These individual examples illustrate that synthetic galaxies with recovered properties that deviate from the input ones tend to have one structural component that is much brighter than the others.

The yellow triangles in Figure 5, which show the recovered parameters of the synthetic galaxy in Figure 3b), illustrate how DiskFit performs when the disk and bar PA are closely aligned (the two have identical position angles in this specific case). The Disk PA and Disk are well-recovered, but is poorly recovered and the Bar PA is completely lost.

Figure 6 compares the surface brightness profiles of the disk and the bar recovered by DiskFit for the synthetic galaxies, where at the discrete radii selected during modelling. Points with therefore correspond to an overestimation of the light profile by DiskFit, and points with correspond to an underestimation. We normalize the radial axes by and of the (parametrically-constructed) input synthetic galaxies for convenience, but emphasize that these quantities have no meaning in the DiskFit context since the disk and bar are modelled non-parametrically.

The narrow interquartile range of (red shaded regions) in Figure 6a) shows that in general, for , exponential disk surface brightness profiles are reliably recovered non-parametrically by DiskFit. At smaller , the disk and bar surface brightnesses are not well-recovered due to confusion with the bulge (which itself isn’t reliably modelled; see Figure 4). Note that the extreme outliers here consist of galaxies similar to those shown in Figure 3b) - 3d) (coloured yellow, blue, and green in Figures 5 and 6 respectively), where the disk-bar degeneracies are hardest to break. Figure 6b) shows that the bar is also reliably recovered by DiskFit in the range . Note that because DiskFit models the surface brightness profiles of the disk and bar non-parametrically, the two components become degenerate in the model when their position angles are aligned and their ellipticities are similar. This is clearly illustrated by the yellow lines in Figure 6, which show the best-fitting profiles corresponding to the synthetic galaxy in Figure 3b). Our simulations suggest that, for intermediate-inclination disks, DiskFit is unreliable at distinguishing the disk and bar components when (see Holmes et al. 2015 and Randriamampandry et al. 2016 for similar findings in kinematic DiskFit models). Finally, for , the noise in DiskFit’s recovery of the bar increases as the bar light fades sharply (in the Ferrers profile, the bar fades by mag arcsec for ).

The outcome of our DiskFit modelling of the simulated galaxies has important implications for our models of the  SG subsample described in §4.1. We find that bulge properties are not reliably modelled. However, the position angles, ellipticities and surface brightness profiles of galaxies with exponential disks and relatively long, relatively bright Ferrers bars (usually those at least barely distinguishable by eye) are well-recovered beyond the bulge region. The notable exception to these criteria are systems where the disk and bar position angles lie within 5 of one another, which may cause degeneracies in DiskFit’s non-parametric models.

## 4 Fitting of  S4G Galaxies

We now proceed to model the  SG subsample listed in Table 1 with DiskFit, in order to compare the resulting components with those obtained from the human-supervised application of galfit by S15. We use the synthetic galaxy models of §3 to guide the selection of subsample galaxies that we attempt to fit (§4.1), as well as to interpret our results (§4.2).

### 4.1 Setup and Fitting Procedures

For each system in our subsample, we fit for the same combination of disk, bar, and/or bulge as included in the final galfit decomposition presented by S15. The components included in each of the models are listed in column 2 of Table 1.

We attempt to model most galaxies in the subsample with DiskFit, using the disk geometry (, Disk PA) obtained by S15 as input guesses, as well as the S15 bar geometry (, Bar PA) when one is included. We use the exponential disk scale length estimated by S15 to define the radii at which we solve for the surface brightness of each component, which we set to every third pixel from to , and then every fifth pixel out to . The best-fitting model values do not depend strongly on the adopted radial sampling cadence. We estimate uncertainties on the model parameters using 200 bootstrap realizations, a number again constrained by the computing resources available to us through the CAC. As discussed in §3.2 we will not compare models of the bulge because our simulations imply that DiskFit is unreliable in that region. For models including a bulge, we fix Sérsic to the S15 value and allow for and   to vary, using the best-fitting values from S15 as DiskFit initial guesses. Parameters listed as ‘N/A’ in Table 1 were not included in the model for that particular galaxy.

The results of the fits for each galaxy in the  SG subsample are given in Table 1, and the data files containing the resulting surface brightness profiles are available in the electronic version of the paper.

The simulations of §3.2 imply galaxies with |Disk PA - Bar PA| are not reliably modelled by DiskFit. We preemptively exclude the 38  SG subsample galaxies for which this is the case in the S15 models, listing them in Table 1 with flag ‘a’. We therefore attempt to fit a total of 532 galaxies. We note that some galfit models include a nuclear component (144 galaxies) or a second disk (89 galaxies), which we do not include in the DiskFit models; these systems are flagged with a ‘b’ or ‘c’ in the last column of Table 1, respectively.

Additionally, there are a few galaxies for which we struggled to recover the same components as those found by S15 using galfit, with DiskFit getting ‘hung up’ in parameter space during the minimization or after the first few bootstraps. We are able to recover the galfit morphology for some of these systems when we reduce the number of rings used in the DiskFit surface brightness profile to every fifth pixel from to , and then every tenth pixel out to . We give these 19 galaxies an ‘e’ flag in Table 1. For other galaxies that we struggle to fit with the same process, we are able to fit a disk-only model (reporting approximate values), again using fewer surface brightness rings. These 8 galaxies are listed in Table 1 with flag ‘d’. Finally, there are 16 galaxies for which we were not able to use galfit parameters as input at all, with DiskFit failing to minimize for even disk-only models. We flag these galaxies with an ‘f’ in Table 1, and return to them in §5. We omit the  SG subsample galaxies with flags ‘a’, ‘d’, ‘e’, and ‘f’ from our comparisons with the results of S15. This ‘comparison sample’ includes 489 members.

### 4.2 Fits to Real Galaxies: Comparing DiskFit and GALFIT

This section focuses on comparing the best-fitting DiskFit models of the comparison sample to those adopted by galfit in S15. As explained in §4.1, we include the same model components as in the S15 decompositions and use their best fitting values as input guesses for DiskFit. We therefore expect the resulting DiskFit models to resemble the galfit ones as much as possible given the differences in modelling approach.

Figures 7-9 show representative examples of fits to individual galaxies, while Figures 10 and 11 examine the results for the comparison sample as a whole. Since no uncertainties on the S15 models are available, Figure 10 shows only vertical error bars while those in Figure 11 only account for DiskFit uncertainties. For comparison sample galaxies modelled with two disks by S15, we plot the properties of one with the largest in Figure 10. We have verified that the properties of galaxies with nuclear components or second disks (flags ‘b’ and ‘c’ in Table 1), exhibit quantitatively and qualitatively similar behaviour in Figures 10 and 11 as the other comparison sample galaxies. Parameters of the best-fitting linear relationships between our DiskFit fits and those adopted by S15’s models are shown in Table 2.

Figure 7 shows an example of a galaxy, NGC1022, for which the best fitting S15 galfit (panel b) and DiskFit (panel c) disk-bulge-bar models closely resemble each other. The surface brightness profiles of individual components (panel d) are also similar, with DiskFit trading some disk light (solid green line) for bar light (solid blue line) at 10px 30px (7.5 arcsec < < 23 arcsec) compared to galfit (dashed green and blue lines, respectively). NGC1022 is indicated by the red triangles in Figure 10; the DiskFit and galfit disk and bar position angles and ellipticities are similar. We note that the disk ellipticities reported by S15 are derived from the shape of the outer isophotes of the images, and not by galfit itself. Nonetheless, we find good agreement between the DiskFit models and the S15 ones for galaxies without pronounced spiral arms, rings, or other features that are not included in the models.

Figures 8 and 9 illustrate that when such features are present in a galaxy, the best fitting S15 galfit and DiskFit models can differ significantly. By construction, DiskFit uses the entire radial range of the disk to determine the PA (Spekkens & Sellwood, 2007). ESO027-001 in Figure 8 has pronounced spiral arms that pull on the fits differently resulting in disks with discrepant PAs as shown by the blue squares in Figure 10. NGC1452 in Figure 9 exhibits a ring structure at the end of the bar that also produces different galfit and DiskFit models, with the latter returning a much longer, brighter bar than the former with a slightly higher as shown by the green circles in Figure 10. We find that the photometric decompositions of galaxies with spiral arms and rings are the ones most likely to differ significantly when modelled with DiskFit versus galfit.

Figure 10 shows that, on the whole, the two algorithms recover similar disk and bar geometries, with a much less centrally concentrated distribution of points than that seen in the synthetic galaxies (compare to the spread in Figure 5c) and 5d)). The trend lines are consistent with the 1:1 relations within the uncertainties (see Table 2). The agreement between the position angles and ellipticities of the bars and disks recovered by DiskFit and adopted by galfit in S15 is good for the majority of the sample galaxies. There are many more extreme outliers than that seen in the simulated sample (Figure 5a) for the disk PA, resulting in a significantly increased MAD. Many of the points that lie outside of the normalized MAD for all quantities have small error bars, indicating significantly different best-fitting models for the two algorithms (see Figure 8).

Figure 11 compares the difference between the bar and disk surface brightness profiles returned by galfit and DiskFit. Here, represents DiskFit’s best-fitting surface brightness profile minus the profile recovered by S15 using galfit: . Points with correspond to regions where DiskFit attributes more light than galfit, and points with correspond to regions where DiskFit attributes less light (note the units of mag arcsec). We normalize the values radially by and returned by galfit. For simplicity in this comparison, we exclude sample galaxies modelled by S15 using two disks.

There is good agreement between the disks recovered by DiskFit and galfit for in Figure 11a), although DiskFit attributes slightly more light to the disk as increases. For in the sample as a whole, there is more light in the exponential galfit disks than their non-parametric DiskFit counterparts; this is also the case in the individual models shown in Figures 7-9. Figure 11b) shows that this light is being attributed the bar, which has a higher surface brightness for in the DiskFit models compared to the galfit models. A larger is found for , where the non-parametric DiskFit bars are several times brighter than the Ferrers galfit bars (albeit in a region where the bar itself is faint). We note that this behaviour is not seen in the fits to simulated galaxies (c.f. Figure 6), where DiskFit cleanly recovers true exponential disks and Ferrers bars. This suggests that the surface brightness distributions in the  SG galaxies are more complicated than the sum of these two components.

We note that cumulative properties derived from photometric fits are even more uncertain. Figure 12 compares the light fractions implied by our DiskFit and the S15 galfit fits for comparison sample galaxies that include both components: unless the fraction of light in the disk exceeds , the relative brightnesses of the disk and bar components can differ by over .

## 5 Discussion and Conclusions

We have presented non-parametric photometric models of over 500 disk galaxies from  SG using DiskFit. We use a suite of simulated galaxies embedded in  SG-like images to validate DiskFit’s performance on our 570-galaxy  SG subsample (§3.2, Figures 2 and 3), and find that DiskFit non-parametrically recovers the geometry and surface brightness distributions of exponential disks and Ferrers bars as long as their position angles differ by more than 5 (Figures 5 and 6). By contrast, DiskFit does not reliably recover the Sérsic bulge properties of our simulated galaxies (Figure 4) and we ignore the bulge region in our subsequent  SG fits.

We then carry out DiskFit decompositions of the 532  SG subsample galaxies with PAdisk-PAbar as determined by S15 and adopted by the parametric galfit algorithm (Table 1), and compare the best-fitting parameters to the S15 values. While on the whole the DiskFit and galfit models return similar results, we find that discrepancies between the best-fitting disk and bar geometries of some systems well exceed the uncertainties that we estimate using a robust bootstrap resampling technique. Comparing the disk and bar surface brightness profiles, we find that DiskFit attributes more light to the bar and less to the disk than in the S15 galfit models across the extent of the bar (Figure 11). This difference is particularly striking for , where the non-parametric DiskFit bars are several times brighter than the Ferrers galfit bars.

The failure of DiskFit to recover bulges in simulated  SG-like images highlights the importance of validating decomposition algorithms, especially before applying them to large samples of real systems (e.g. Schombert & Bothun, 1987; Byun & Freeman, 1995; Wadadekar et al., 1999; MacArthur et al., 2003; Gadotti, 2008; Peters & Kuzio de Naray, 2017). It is possible that the non-parametric nature of DiskFit makes bulge recovery more difficult than for parametric algorithms such as galfit, though Gadotti (2008) finds that bulges with comparable to the seeing radius are difficult to recover even when both the bulge and the disk are parametrized. We caution against the adoption of bulge parameters derived from 2D decompositions that do not include quantitative estimates of the associated uncertainties and algorithms limitations through simulations (e.g. S15, Wadadekar et al. 1999; Janz et al. 2014; Bittner et al. 2017).

The relatively large scatter between the best-fitting DiskFit parameters and those adopted in the S15 models in our  SG comparison subsample suggests that, unless the (unreported) uncertainties in the S15 galfit fits are considerably larger than those that we derive using DiskFit for the majority of the sample, different photometric decomposition approaches can return significantly different structural properties for disks and bars in nearby galaxies (e.g. Byun & Freeman, 1995; Peng et al., 2010). For  SG disk galaxies in particular, our DiskFit and galfit comparisons suggest that their disk and bar ellipticities are typically constrained to no better than on average, while much larger uncertainties are implied by the outliers in Figure 10.

Our DiskFit models of the  SG comparison sample were constrained to have the same number of components and initial conditions as those reported by S15 using galfit. While a detailed investigation of the impact of structural component and initial guess selection on model uncertainties is beyond the scope of this paper, we speculate that these effects would further widen the gap between parameters derived using different photometric modelling techniques. As explained in §4.1, there are some sample galaxies for which DiskFit failed to converge on even a disk-only model when initiated using the best fitting values from S15 as inputs. We suspect that this stems from the susceptibility of the Levenberg-Marquardt minimization scheme adopted by DiskFit and galfit to local minima in the landscape. Indeed, recent kinematic model tests by Bekiaris et al. (2016) show that the optimization method itself may also affect the best-fitting values obtained from the same modelling algorithm. We therefore conclude that the differences we find between the DiskFit and galfit fits to the comparison sample galaxies likely underestimate the true uncertainties in  SG disk galaxy structural parameters recovered from 2D decomposition algorithms.

In light of our simulations demonstrating that DiskFit accurately disentangles exponential disks from Ferrers bars, the differences between the surface brightness profiles recovered by DiskFit and the S15 galfit models implies that the surface brightness distributions of the  SG comparison sample are not well-represented by these functional forms. The deficit of disk light that we find in the bar region is reminiscent of the shaped features recovered in some decompositions of real galaxies (e.g. Laurikainen et al., 2005; Gadotti, 2008; Kim et al., 2016a), as well as in simulations (e.g. Athanassoula & Misiriotis, 2002). At the same time, the excess of bar light recovered by DiskFit relative to the S15 galfit fits, particularly for , implies that we non-parametrically recover brighter, longer bars than found in comparable Ferrers fits. We therefore concur with Williams & Evans (2017) that real galactic bars may exhibit important differences from the Ferrers function form. This is particularly relevant when a bar’s length is used as a proxy for its evolutionary state (Hoyle et al., 2011; Aguerri et al., 2015; Carles et al., 2016). It is possible that bar lengths derived from non-parametric 2D models such as DiskFit better represent their evolutionary states than do their Ferrers , but a careful validation of this hypothesis using mock and simulated galaxies is required (e.g. Athanassoula & Misiriotis, 2002; Aguerri et al., 2009). We defer such an exploration using DiskFit to future work.

## Acknowledgements

Computations were performed on resources and with support provided by the Centre for Advanced Computing (CAC) at Queen’s University in Kingston, Ontario. The CAC is funded by: the Canada Foundation for Innovation, the Government of Ontario, and Queen’s University.

KS acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC).