A Catalog of Galaxies in the Direction of the Perseus Cluster

We established a catalog of sources in the direction of Perseus based on detection with SExtractor⁷ on our WHT V-band mosaic. Prior to detection, we fitted and subtracted the light profiles of most of the bright galaxies and stellar halos using iraf⁸ ellipse. We additionally excluded the inner regions of all subtracted sources, since they often show pronounced residuals, as well as the bright centers of remaining sources that were not subtracted. We therefore masked all regions that were detected with SExtractor in the original Perseus mosaic (where no sources were subtracted) when requiring a detection threshold above 5σ and more than 10,000 connected pixels. We note that this results in a bright V-band magnitude limit of −20 mag for our catalog and a reduced detection efficiency for the larger sources with absolute V-band magnitudes brighter than −19 mag (see Figure 4 and Section 3.3). The masked regions in the partly object-subtracted WHT mosaic are indicated in Figure 1 (top right and bottom panels).

We used a set of model galaxies inserted into our data to tailor the SExtractor parameter configuration especially to the detection of faint galaxies. We generated a set of 69 model galaxies spanning the parameter range of faint low-mass galaxies from compact elliptical to faint low surface brightness galaxies with absolute V-band magnitudes M_V,0 = −10 to −19 mag (m_V,0 = 24.3–15.3 mag), half-light radii r₅₀ = 0.2–7.8 kpc (r₅₀ = 06–230), and effective surface brightnesses $\langle {\mu }_{V,0}{\rangle }_{50}\,=16\mbox{--}27$ mag arcsec⁻² at the distance of Perseus. In the following, we denote extinction-corrected magnitudes by adding the subscript "0". For the model galaxies, we assumed an extinction of A_V = 0.5 mag, which is the average value for the region covered by the WHT mosaic footprint. For all nonartificial sources, we obtained the extinction values at the position of the respective source (see Sections 4.3 and 4.4).

We realized all model galaxies with a one-component Sérsic n = 1 profile and an ellipticity of  = 0.1 and convolved them with a Gaussian kernel adopting our average WHT V-band seeing point-spread function (PSF) FWHM of 09. For each model, we generated one copy of our mosaic where we inserted about 80 duplicates, requiring that they do not overlap with each other or fall on one of the masked regions indicated in Figure 1. The total number of models inserted into 69 different mosaic copies amounts to 5478.

We ran SExtractor several times with varying parameter settings on the mosaics with the inserted model galaxies in order to test which parameter configuration yields the highest detection fractions. In particular, the parameters DT and DMIN, specifying the minimum number of connected pixels (DMIN) above a certain detection threshold (DT) that are required to result in a detection, control which kind of sources will be detected.

Figure 2 shows that with a parameter configuration of DT = 1.3σ and DMIN = 25 pixels, we are able to detect more than 90% of all model galaxies with $\langle {\mu }_{V,0}{\rangle }_{50}\leqslant 24$ mag arcsec⁻². A lower detection threshold of DT = 0.8σ with the same DMIN parameter improves the detection of fainter surface brightness sources with $\langle {\mu }_{V,0}{\rangle }_{50}\gt 24$ mag arcsec⁻². However, although both SExtractor configurations yield similar detection fractions for sources with $\langle {\mu }_{V,0}{\rangle }_{50}\leqslant 24$ mag arcsec⁻², the derived photometry of the DT = 0.8σ detections often turns out to be less reliable. For example, sources with diffuse halos, which would be detected as single objects with the DT = 1.3σ configuration, are frequently split up into multiple detections with the DT = 0.8σ parameter setting. Therefore, we adopted a two-pass detection, where we first ran SExtractor with a detection threshold of DT1 = 1.3σ and then with a detection threshold of DT2 = 0.8σ. We merged the source catalogs of both runs, where we considered all sources from the DT1 run and additional sources from the DT2 run that were not detected with the DT1 SExtractor parameter setting.⁹ In both cases, we ran SExtractor with internal filtering prior to source detection, adopting a Gaussian filter with FWHM = 4 pixels, which is on the order of the average WHT V-band seeing PSF FWHM. To take into account the noise properties of our mosaic during the detection process, we furthermore provided a weight image generated from our data, which is described in Wittmann et al. (2017).

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The detection of faint sources close to or superimposed with brighter sources is very sensitive to the SExtractor deblending parameters, as well as the subtracted background map, which is internally generated by SExtractor. For the deblending, we used a very low deblending contrast (DEBLEND_MINCONT = 0.00001) together with a high number of deblending thresholds (DEBLEND_NTHRESH = 64). This ensures that a bright source is split up into a sufficient number of subdetections, allowing us to recognize superimposed faint sources as separate detections. We note that this may also lead to splitting up extended low surface brightness sources. Multiple detections of a single source were, however, rejected later through visual inspection.

The properties of the subtracted SExtractor background map are regulated by the parameters BACK_SIZE, specifying the size of the region within which the mean background is estimated, and BACK_FILTERSIZE, denoting the width of the filter that is used to smooth the background map. When the size of the background box becomes comparable to the size of a certain object in the data, part of the object flux will be incorporated into the background map and subtracted. Thus, the BACK_SIZE parameter should be small enough to subtract most of the light from extended halos of bright sources, enabling the detection of underlying faint sources, but at the same time larger than the size of the typical sources of interest. We therefore adopted a BACK_SIZE parameter of 64 pixels, corresponding to about 15'' or 5 kpc at the distance of Perseus, and a BACK_FILTERSIZE of 3. We show the mosaic with the subtracted SExtractor-generated background map that we used for source detection in Figure 1 (bottom panel).

A summary of our adopted SExtractor parameters is given in Table 2. In total, we detected 29,111 sources, from which 7899 sources were only detected with the DT1 = 0.8σ SExtractor run. We excluded sources whose centers fall onto a masked region or are located at the edge of our mosaic with centers falling outside of the observed mosaic region.

We cleaned our source catalog from unresolved starlike sources using the SExtractor stellarity index CLASS_STAR. The index can take values between zero and 1, where a value close to zero indicates an extended galaxy-like source and a value close to 1 indicates a compact, starlike source. Figure 3 illustrates the CLASS_STAR distribution of the inserted model galaxies and the real sources as a function of the maximal surface brightness μ_V,0,max measured by SExtractor. The majority (97%) of our inserted model galaxies with an intrinsic $\langle {\mu }_{V,0}{\rangle }_{50}\geqslant 20$ mag arcsec⁻² seem to be well described by CLASS_STAR ≤ 0.3. Among the more compact model galaxies with an intrinsic $\langle {\mu }_{V,0}{\rangle }_{50}\lt 20$ mag arcsec⁻² and r₅₀ > 200 pc, 83% have CLASS_STAR ≤ 0.8. Of the compact model galaxies with r₅₀ = 200 pc, however, 74% have CLASS_STAR > 0.8 and are indistinguishable from unresolved point sources. Thus, for all real detected sources, we consider all sources with SExtractor output parameters in the regime ${\mu }_{V,0,\max }\geqslant 20$ mag arcsec⁻² and CLASS_STAR ≤ 0.3, as well as sources with ${\mu }_{V,0,\max }\lt 20$ mag arcsec⁻² and CLASS_STAR ≤0.8. This reduced our source catalog to a total of 13,132 sources, where 3980 sources were detected by the SExtractor DT2 run.

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We only included sources in our catalog with SExtractor flags ≤ 3, corresponding to unflagged sources, sources with close neighbors, and sources that were originally blended with another object. In total, 15 sources have flags > 3 and were not considered in the catalog. Since for very faint sources, the photometry uncertainties and background contamination significantly increase, we furthermore excluded sources that had an extinction-corrected SExtractor Petrosian magnitude (Petrosian 1976) fainter than ${M}_{V,0,p}=-11$ mag¹⁰ at the distance of Perseus. Our final working sample comprises a total of 7255 sources. The parameter cuts defining the working sample are summarized in Table 3.

Table 3.  Definition of the Working Sample Based on SExtractor Parameters

Parameter Criterion
(μV,0,max ≥ 20 mag arcsec−2 and CLASS_STAR ≤ 0.3) $|$ (${\mu }_{V,0,\max }\lt 20$ mag arcsec−2 and CLASS_STAR ≤ 0.8)
SExtractor flag ≤ 3
${M}_{V,0,p}\leqslant -11$ mag

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Figure 4 displays a completeness estimate of our catalog based on the inserted model galaxies. Shown are the detection fractions, which are the ratios of the number of detected models to the total number of inserted models, as a function of the model input parameters. For the completeness estimate, we extended the parameter range of the inserted models to brighter magnitudes of M_V,0 = −20 mag and smaller sizes of r₅₀ = 50 pc in order to cover the full observed parameter range of our final catalog. In total, 101 models with different parameters contribute to the completeness estimate, where each model type was inserted several times into one copy of the mosaic, amounting to a total of 8015 inserted models.

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In the first row of Figure 4, we show the detection fractions achieved with the combined SExtractor runs with DT1 = 1.3σ and DT2 = 0.8σ. It can be seen that the completeness drops below 50% for models with $\langle {\mu }_{V,0}{\rangle }_{50}=27$ mag arcsec⁻² and M_V,0 = −10 mag. The second row displays the resulting detection fractions after having applied the source rejection criteria to define our working sample (see Sections 3.1 and 3.2). Removing starlike sources by applying the CLASSSTAR parameter cut results in detection fractions lower than 50% for the models with the smallest sizes (r₅₀ < 150 pc) and the brightest surface brightnesses ($\langle {\mu }_{V,0}{\rangle }_{50}\leqslant 17$ mag arcsec⁻²). Excluding sources with M_V,0,p > −11 mag measured by SExtractor implies detection fractions lower than 50% for models with intrinsic M_V,0 = −11 mag, since SExtractor tends to underestimate the magnitudes of the detected models. Rejecting sources that would get masked, and therefore excluded, with the bright object mask displayed in Figure 1 affects the brightest and largest sources with M_V,0 ≤ −19 mag and r₅₀ > 2 kpc, where the average detection fraction is lower than 50%. In summary, the average completeness of our catalog is 92% in the parameter range −12 mag ≥ M_V,0 ≥ −18 mag, $18\,{\mathrm{mag\; arcsec}}^{-2}\leqslant \langle {\mu }_{V,0}{\rangle }_{50}\leqslant 26$ mag arcsec⁻², and $0.2\,\mathrm{kpc}\,\leqslant {r}_{50}\leqslant 7.8\,\mathrm{kpc}$.

For the photometric measurements, we defined the Petrosian radius R_p such that the Petrosian index $\eta ({R}_{p})=\langle I{\rangle }_{{R}_{p}}/I({R}_{p})\,=1/0.3$, where $\langle I{\rangle }_{{R}_{p}}$ denotes the average intensity within R_p, and I(R_p) gives the isophotal intensity at R_p (Graham et al. 2005). We adopted a value of η(R_p) = 1/0.3 instead of the more commonly used η(R_p) = 1/0.2, since the former proved to be more robust for low surface brightness sources to prevent contamination through close neighbor objects or uneven background. We measured the total flux within a circular aperture of 1.5 R_p and derived the corresponding half-light radius from it. We estimated Sérsic indices from the measured concentration values r₉₀/r₅₀, where we matched the observed concentration values to the values calculated for analytic Sérsic profiles with n = 0.5–4.0. For observed concentration values lower or higher than the calculated ones, we adopted a Sérsic index of n = 0.5 or 4, respectively.

As a rough estimate for the local background underlying a source, we used SExtractor-generated background maps. For sources without close bright and extended neighbor sources, we applied a SExtractor background map with a large BACK_SIZE parameter of 256 pixels, corresponding to 607 or 20.6 kpc. For small sources in the vicinity of bright extended sources, we used a background map with a smaller BACK_SIZE parameter of 32 pixels, corresponding to 76 or 2.6 kpc, in order to remove the background gradient of the neighboring source.¹² In the case of larger sources with contaminating neighbors, we fitted and subtracted the light distribution of the respective neighbor source with iraf ellipse in order to avoid the SExtractor background map, which may subtract part of the source flux.

We carefully inspected the measured Petrosian apertures visually for each of the 7255 sources from our working sample in order to identify cases in which the aperture is obviously too large with regard to the visible extent of the source. Most often, problems arose due to imperfect masking, when either the automated unmasking of the source failed, such that large parts of the source were still masked, or neighboring sources contaminated the flux measurement, since they were insufficiently masked. We therefore manually adjusted the masks of all affected sources and measured the Petrosian parameters again.

In the following cases, we entirely excluded a source from any further analysis.

• 1.  
  The source is heavily blended into another source where neither a larger mask nor a SExtractor background subtraction with BACK_SIZE = 32 pixels would result in reliable photometric measurements. We note that the majority of sources in this category appeared very small in size, being possible interlopers suffering from wrong SExtractor photometry and/or CLASS_STAR measurements. In the case of extended galaxy-like sources, we tried our best to fit and subtract the contaminating neighboring source.
• 2.  
  The source is barely visible in our data, although it has been given a SExtractor magnitude of M_V,0,p ≤ −11 mag.
• 3.  
  The source forms part of another source, i.e., the stripped material or spiral arms of luminous cluster galaxies, that is not a subject of this study.
• 4.  
  The source is likely an artifact resulting from reflections or stray light in the data.
• 5.  
  In the case of multiple detections of a single source, we derived Petrosian photometry for the detection that visually appeared best centered on the source and rejected the remaining duplicate detections.

In total, we successfully derived Petrosian photometry for 6038 sources and excluded 1217 sources from further analysis.

In order to run galfit with PSF deconvolution, we first generated a PSF from our data using routines from the iraf package daophot. We ran SExtractor tuned to detect small and compact sources¹³ and selected PSF star candidates by requiring that the sources have CLASS_STAR > 0.9 and not be flagged. We furthermore rejected sources that are superimposed on bright extended sources by excluding all PSF star candidates that overlap with a mask generated with SExtractor.¹⁴ This mask is much larger than the one shown in Figure 1 in order to yield the cleanest possible sample of PSF star candidates. We also excluded PSF star candidates that fall on very low S/N regions in our mosaic, where the pixels have a weight lower than 200, corresponding to σ ∼ 0.07 ADU. We subsequently ran the iraf task phot to perform aperture photometry¹⁵ and selected all stars with apparent V-band magnitudes brighter than m_V = 19 mag that were not saturated. This resulted in a selection of 845 PSF stars in our mosaic. In Figure 5, we display their spatial and FWHM distribution. The FWHM distribution indicates a few outliers among the selected stars with large FWHM values. A visual examination revealed that most of them are partly unresolved double sources. We therefore rejected sources with FWHM > 4.5 pixels. In addition, Figure 5 shows a slight upward trend in FWHM toward brighter magnitudes. As a consequence, we only considered stars with m_V > 16.5 mag. The final sample of PSF stars comprises 797 stars with an average FWHM of 3.86 pixels, as measured by SExtractor. We used this PSF star sample to construct a model PSF with the iraf task psf, which consists of an analytic component obtained by a fit to all of the stars in the sample plus a lookup table quantifying the deviations of the analytic function from the empirical PSF.

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We derived structure parameters with galfit for the 6038 nonexcluded sources from our working sample. We ran galfit for each source with PSF deconvolution, object masks, and a σ image generated from the corresponding weight image of the WHT mosaic, where $\sigma =1/\sqrt{\mathrm{weight}}$. We fitted each source with a one-component Sérsic profile and used the derived Petrosian magnitude, half-light radius, and estimated Sérsic index, as well as the SExtractor source position, axis ratio, and position angle, as first-guess parameters for galfit. We simultaneously fitted the sky component, which can account for both a background offset and a gradient. For sources where we previously subtracted the SExtractor-generated background map with a BACK_SIZE of 32 pixels, we adopted this background instead of fitting the background with galfit, since only the former eliminates small-scale background variations introduced by contaminating neighboring sources (see Section 3.1). For 25 sources, we used the previously subtracted SExtractor BACK_SIZE = 256 pixel background map for galfit, since simultaneously fitting the source and background did not succeed. We specify the applied background subtraction method in the final catalog.

In the first iteration with galfit, we performed the Sérsic fit with seven free parameters¹⁶ but constrained the Sérsic index to n ≤ 4. We note that due to the limited resolution of our data, we are not capable of reliably discriminating between a source with a Sérsic index around n = 4 and a larger value, due to the small change in the profile shape for large Sérsic n (see, e.g., Graham & Driver 2005, Figure 1). We visually examined all fitted models by comparing them to the respective source, as well as the residual images. Some sources showed significant residuals after the subtraction of the model, although the fitted model seemed to provide a good description of the overall shape of the source. We adopted the photometric parameters but flagged the respective sources in the final catalog. For about one-third of the sample, the Sérsic model with free parameters did not provide a good fit, or the fit did not converge.

In these cases, we performed a second iteration with galfit where we held the Sérsic index fixed at the value estimated from the concentration r₉₀/r₅₀ (see Section 4.1) to stabilize the fit. Subsequent visual inspection yielded good solutions for about 1200 of the sources. We also compared the models of all sources that were previously fitted with free parameters but constrained n = 4 and adopted the solution, which yielded less pronounced residuals.

We refitted all sources where our fitting attempts had not succeeded in a third iteration with galfit. In this iteration, we held the x-, y-position fixed, in addition to the Sérsic index. This succeeded for another 19 sources. For the remaining sources, the galfit solutions did not converge, since the half-light radius and/or axis ratio fell below the lowest parameters of r₅₀ = 0.5 pixels and b/a = 0.1 accepted by galfit to fit a source. We therefore ran galfit in a fourth iteration by adopting the fixed lowest values for r₅₀ and/or b/a in addition to the fixed Sérsic index. For sources that were fitted with a fixed r₅₀ = 0.5 pixels, we also adopted a fixed axis ratio of b/a = 1 due to the high uncertainties of the latter at these small sizes.

For 270 sources, it was not possible to obtain a good fit with galfit, but the derived Petrosian parameters seemed to provide a good estimate of the structural parameters. In most of these cases, the affected sources were very faint or showed strong residuals due to a very complex structure where a single Sérsic fit might not be a good approximation. We also adopted Petrosian photometry for 222 sources fitted with galfit but that have statistical uncertainties in m_V,0 and/or $\langle {\mu }_{V,0}{\rangle }_{50}$ larger than 1 mag. These are almost exclusively very faint sources, with 90% of them having M_V,0 > −12 mag. We note that the half-light radii derived from Petrosian photometry only provide upper size limits for small sources, since the measurements did not involve a PSF deconvolution. We entirely excluded sources with absolute V-band magnitudes fainter than M_V,0 = −10 mag from our catalog. For the position angle measurements, we only list values for sources with b/a < 0.9, due to the high uncertainties for nearly round sources. We provide an overview of the photometry processing of our working sample in Table 4 and include the photometric measurements in the final catalog.

We calculated the effective surface brightness $\langle {\mu }_{V}{\rangle }_{50}$ within the half-light radius from the measured parameters and obtained the Galactic foreground extinction A_V at the position of each source from the IRSA Galactic Reddening and Extinction Calculator,¹⁷ with reddening maps from Schlafly & Finkbeiner (2011).

We provide the statistical uncertainties estimated by galfit based on the pixel noise in the final catalog. The uncertainties in $\langle {\mu }_{V}{\rangle }_{50}$ were calculated from error propagation, accounting for uncertainties in m_V,0 and r₅₀. Parameters that were held fixed during a fit have no error estimates, as well as sources where we adopted the Petrosian photometry. We provide an estimate of the typical uncertainties of the Petrosian photometry in Figure 17 in Appendix A.

We derived (g − r) and (r − z) aperture colors from the Subaru data set, which we resampled to match the WHT mosaic pixel scale of 0237. For all sources, we used our previously generated object masks from the WHT data but extended them,¹⁸ since the Subaru data are deeper than the WHT data and object flux becomes visible beyond the masked areas.

We measured the colors as flux ratios within apertures with a radius of r_aper = r₅₀ and a shape defined by the previously derived ellipticity and position angle. For very small sources with r₅₀ < 4 pixels, we adopted circular apertures with r_aper = 4 pixels, since for smaller apertures, seeing effects start to influence the color values. For sources with r₅₀ ≥ 4 pixels, we additionally measured an "outer" color, defined as a flux ratio within an aperture with a radius of r_aper = 2 r₅₀.

Prior to measuring the colors, we determined and subtracted the local background around each source in each of the bands. For the sources with fixed apertures of r_aper = 4 pixels, we calculated the median background level within a circular annulus with an inner radius of 12 pixels and a width of 4 pixels. For sources with apertures scaling with their half-light radius, we adopted a background annulus following the shape of the color aperture and with a width of 1 r₅₀. We set the inner radius of the background annulus depending on the surface brightness of the respective source. Adopting the same background annulus for all sources would result in a background annulus that covers a significant amount of object flux for the high surface brightness sources due to their smaller half-light radii, whereas for the low surface brightness sources, it would be located too far from the source center due to their larger half-light radii. Therefore, we set the inner radius of the background annulus for low surface brightness sources with $\langle {\mu }_{V,0}{\rangle }_{50}\geqslant 24$ mag arcsec⁻² at 3 r₅₀, sources with $22{\mathrm{mag\; arcsec}}^{-2}\leqslant \langle {\mu }_{V,0}{\rangle }_{50}\lt 24$ mag arcsec⁻² at 4 r₅₀, and high surface brightness sources with $\langle {\mu }_{V,0}{\rangle }_{50}\,\leqslant 22$ mag arcsec⁻² at 5 r₅₀.

We calculated statistical uncertainties for the (g − r) and (r − z) colors based on standard error propagation as

$$\begin{eqnarray}&&{\rm{\Delta }}({\text{}}g-{\text{}}r)=\sqrt{{\left(\displaystyle \frac{2.5}{{I}_{g}\mathrm{ln}10}{\rm{\Delta }}{I}_{g}\right)}^{2}+{\left(\displaystyle \frac{2.5}{{I}_{r}\mathrm{ln}10}{\rm{\Delta }}{I}_{r}\right)}^{2}},\end{eqnarray} \tag{ 1 }$$

where I_r and I_g are the aperture flux in the r and g band, respectively, and ΔI_r and ΔI_g are estimated from the Subaru r- and g-band variance image,¹⁹ accounting for the statistical uncertainty in the object and background flux. The same applies for Δ(r − z). We only included sources with Δ(g − r) ≤ 1 mag and Δ(r − z) ≤ 1 mag and without saturated pixels within 3'' from the respective source center in our catalog. We included but flagged all sources that contain pixels with bleeding trails of bright stars within 3'' and may have contaminated colors.

To enable comparison of our measured galaxy colors with data from the literature, we transformed all observed (g − r) and (r − z) colors from the native Subaru HSC system to the standard SDSS system. Color terms were derived synthetically using a set of GALEV stellar population models (Kotulla et al. 2009) as template spectra. These were convolved with both the SDSS filters as presented by Doi et al. (2010) and the HSC filter curves. Based on the derived colors, we computed the following color transformation equations (also see Figure 6 for color comparisons and residuals):

$$\begin{eqnarray}&&{(g\mbox{--}r)}_{\mathrm{SDSS}}=1.111\times {(g-r)}_{\mathrm{HSC}}-0.011,\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{(r\mbox{--}z)}_{\mathrm{SDSS}}=0.967\times {(r-z)}_{\mathrm{HSC}}+0.005.\end{eqnarray} \tag{ 3 }$$

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We performed an extinction correction for all three Subaru bands using the NED extinction calculator, which is based on the reddening maps of Schlafly & Finkbeiner (2011) that we also used for the extinction correction in the V-band data.

We analyzed the dE/ETG cluster candidates for the presence of nuclei based on the Subaru r-band images. We classified a dE/ETG candidate as nucleated if we detected an unresolved high surface brightness point source centered on the respective galaxy. We identified nuclei in 182 of the candidates. In the brighter luminosity regime, 34 of the candidates show possible bulges or bright central sources that appear more extended compared to typical dE nuclei. For 38 dE/ETG candidates, we could not unambiguously classify the source as nucleated or nonnucleated. Four sources show an accumulation of several brighter unresolved point sources near their center or slightly offset from it.²¹ The majority of the uncertain candidates show a central light concentration that could harbor a nucleus, but the potential nucleus does not stand out clearly as a distinct point source. In 242 dE/ETG candidates, we could not identify a nucleus in our data and classified them as nonnucleated. We note, however, that nuclei could be missed in very faint sources or more compact sources with a low brightness contrast between the nucleus and the galaxy main body.

Figure 11 summarizes the nucleation properties of our sample. We found an average nucleation fraction of 47% in the luminosity range −10 mag ≥ M_V,0 ≥ −18 mag when excluding the dE/ETG candidates with unsure nucleation classification. The nucleation fraction increases toward brighter luminosities and surface brightnesses, with a peak at M_V,0 = −15 to −16 mag²² and $\langle {\mu }_{V,0}{\rangle }_{50}=22\mbox{--}23$ mag arcsec⁻². At brighter luminosities and surface brightnesses, the nucleation fraction drops again due to an increase in the fraction of dE/ETG candidates harboring brighter central sources or bulges. The increase of the nucleation fraction with luminosity for faint ETGs is consistent with observations in other nearby clusters, like Fornax, Virgo, and Coma (Sandage et al. 1985; Côté et al. 2006; den Brok et al. 2014; Ordenes-Briceño et al. 2018a; Venhola et al. 2019).

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Figure 14 shows the ${m}_{V,0}-{r}_{50}-\langle {\mu }_{V,0}{\rangle }_{50}$ distribution of morphological subclasses 1–5, defined in Table 5, as well as the dE/ETG candidate fraction with respect to all other sources. It can be seen that the highest dE/ETG fraction, and thus lowest contamination through other sources, is reached at the largest sizes at a given luminosity or surface brightness and at the brightest luminosities. For sources with m_V,0 > 16 mag, the dE/ETG fraction is, on average, above 50% for sources with r₅₀ ≳ 16, with an increasing dE/ETG fraction toward larger sizes. For sources with m_V,0 < 16 mag, the dE/ETG fraction is close to 100%. We note that the fraction of the dE/ETG candidates classified as possible candidates increases toward fainter luminosities and smaller sizes, likely reflecting a more uncertain morphological classification in this parameter regime.

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At the smallest sizes, below r₅₀ ∼ 1'', sources from category 2 dominate, including unresolved sources where the morphological characterization breaks down. The larger sources are likely background ellipticals. A few sources in the parameter range M_V,0 ≲ −14 mag (m_V,0 = 20.3 mag) and r₅₀ ≳ 100 pc ($\widehat{=}\,0\buildrel{\prime\prime}\over{.} 3$) may, however, also be cluster compact elliptical galaxies (e.g., Smith Castelli et al. 2008; Norris et al. 2014). Among the faint and small sources, a few could be Perseus cluster ultracompact dwarf galaxies (Penny et al. 2012, 2014b). Indeed, six of our sources were identified as ultracompact dwarf candidates by Penny et al. (2012) based on HST imaging data. The sources of categories 3–5, including LTGs, galaxies with possibly weak substructure, and edge-on disk galaxies, are mainly found at the intermediate size range. Some of these might be true Perseus cluster members. However, for these categories, it is not possible to discriminate between cluster and background galaxies based on morphology and color alone, requiring spectroscopic confirmation.

It is known that there exists a well-defined relationship between galaxy luminosity and Sérsic index, where brighter galaxies have a higher Sérsic index (e.g., Jerjen & Binggeli 1997; Graham & Guzmán 2003; Gavazzi et al. 2005). For faint galaxies, various studies showed that this relation breaks down, leveling off to a constant value of Sérsic index n ∼ 1 (e.g., De Rijcke et al. 2009; Misgeld et al. 2009; Lieder et al. 2012).

In Figure 15, we display the M_V,0–n distribution of morphological subclasses 1–5, together with the literature M_V,0–n relation. One can see that the vast majority of the sources classified as dE/ETG cluster candidates follow the M_V,0–n relation. At bright luminosities (M_V,0 < −14.6 mag), the dE/ETG fraction is above 50% within an interval of n + 1 from the literature relation, with an increasing dE/ETG fraction toward brighter luminosities. At fainter luminosities, however, the contamination by other sources increases dramatically.

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A relation between Sérsic index and luminosity is also seen for the sources classified as LTGs. This might also indicate that a significant fraction of these are cluster members rather than background galaxies. The sources of the other three morphological categories show no M_V,0–n relation, likely indicating that they are distributed across a wide range of redshifts.

We visually examined the sources classified as dE/ETG cluster candidates in archival HST imaging data in order to check whether we missed intrinsic substructure. In total, we checked 11 HST ACS/WFC3 frames, including 70 of our candidates. The vast majority (59) show a smooth dE-like appearance in the HST images. Five candidates are only barely seen, and four are undetected. Two candidates look suspicious and might be in the background, although clear substructure is not revealed. The generally positive comparison with the HST data further supports our classification of the sources as dE/ETG candidates. We summarize the HST comparison in Table 9 in Appendix D.

We checked which sources in our catalog have available radial velocity measurements. For this, we used NED to compile all sources classified as galaxies that fall on our WHT mosaic footprint (see Section 6). We identified 49 sources that match a source in our catalog. Of the matched sources, 28 have velocities within 2σ of the Perseus cluster mean velocity v_Perseus = 5370 km s⁻¹ (Struble & Rood 1999), where σ =1300 km s⁻¹ (Kent & Sargent 1983). All of these are in the category of likely dE/ETG cluster candidates, thus confirming our morphological classification. Two sources have radial velocities within 2σ–3σ of the cluster mean velocity, of which one source is classified as a likely dE/ETG candidate and the other as a likely background ETG or unresolved source.

The remaining 19 sources are not cluster members, having v > v_Perseus + 3σ km s⁻¹. They fall into the morphological categories of likely background ETGs or unresolved sources (seven sources), cluster or background galaxies with late-type morphology (five sources), cluster or background galaxies with possible weak substructure (four sources), and cluster and background edge-on disk galaxies (one source). Two sources²⁴ were morphologically classified as dE/ETG candidates. They are likely more distant ETGs, although they are characterized by a smooth morphology and lie close to the red sequence in the color–magnitude diagram, with (g–r)₀ = 0.7 and 0.8 mag, respectively.

From the comparison of our visual classification for sources with radial velocity measurements, we can also get a rough estimate of the expected contamination through background galaxies in our dE/ETG candidate sample. Of the sources visually classified as dE/ETG candidates, 28 are confirmed cluster members, whereas two are confirmed background systems. This results in a contamination rate of 7%. Thus, 35 of the 496 sources classified as dE/ETG candidates might be background contaminants.

We also performed an order-of-magnitude comparison to the background galaxy number density for Perseus estimated by Weinmann et al. (2011; see their Appendix A4). The authors derived a background galaxy number density of 45 Mpc⁻² for galaxies with −16.7 mag ≥ M_r ≥ −19 mag by extrapolating the radial number density profile based on SDSS data. Considering sources in the same magnitude regime from our catalog that are not classified as dE/ETG candidates and thus should be dominated by background sources, we derive an average number density of 70 Mpc⁻² within 700 kpc. The value, higher by a factor of 1.6 compared to the one in Weinmann et al. (2011), might be caused by cluster LTGs contaminating our background galaxy number estimate, since we did not visually distinguish between cluster and background systems for LTGs. The order-of-magnitude agreement, however, further strengthens our performed visual classification approach.

8.3.1. Visual versus Automated Detection

8.3.2. New Ultradiffuse Galaxy Candidates

Our dE/ETG sample also includes two candidates in the parameter regime $\langle {\mu }_{V,0}{\rangle }_{50}\geqslant 25$ mag arcsec⁻² and ${r}_{50}\,\geqslant 1.5\,\mathrm{kpc}$ that fall into the category of ultradiffuse galaxies and that were not previously reported. We note, however, that both objects are classified as possible candidates only, due to their not entirely smooth morphological appearance. We show both candidates in Figure 16.

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