Deep K -band surface brightness photometry of dE galaxies

Context. Dwarf elliptical galaxies (dEs) are the most abundant in the Universe. Research into these objects in connection with late-type dwarf galaxies is important for evaluating theories of dwarf galaxy formation and evolution. Aims. Our past studies (2000–2010) suggested a possible evolutionary link between early-and late-type dwarf galaxies. These results are based on deep near-infrared (NIR) surface photometry data of dwarf irregulars (dIs), blue compact dwarfs (BCDs), and a small sample of Virgo dEs. As a continuation of those works, in 2017 we embarked on a study of dEs using the same surface photometry methods, with the aim being to compare early-and late-type dwarfs based on homogeneous datasets. Methods. We selected 74 dEs from two different environments for which we obtained deep images. Isophotal analysis was performed on the images to obtain surface brightness profiles. The two sampled environments were the Local Volume and Virgo cluster, which provide the possibility to compare isolated evolution against evolution in crowded environments. To compare dwarf datasets homogeneously, we used the NIR Ks band which is known to be a better gauge of galaxy mass, with reduced extinction compared to visible bands. Results. In this first paper, we derive apparent physical parameters for 72 dEs from deep NIR imaging and provide preliminary fitting results of their surface brightness profiles. Two targets were undetected in the Ks images, indicating possible misclassification. Physical parameters of 16 dEs are measured for the first time and the parameters of the remaining 56 dEs are compared with the literature. We obtain a mean difference between the measured physical parameters and the results from prior studies of about 0.2 ′′ for the galaxy center coordinates, ≈ 20 ′′ for the semi-major axis, ≈ 0.4 mag for the total apparent magnitude, ≈ 0.11 for the ellipticity, and ≈ 14 ◦ for the position angle. We find well-fitting surface brightness profiles for the dEs using the hyperbolic secant (sech) model combined with an exponential component. Alternatively, we find good agreement with observations for a sech plus a de Vaucouleurs law.

Based on their classic Hubble morphological classification, dwarf galaxies are categorized as either early-or late type. Earlytype dwarfs are gas-poor and include dwarf elliptical galaxies (dEs) and dwarf spheroidal galaxies (dSphs), while late-type dwarfs are gas-rich and include quiescent dwarf spirals (dS), dwarf irregulars (dIs), and star-forming blue compact dwarfs (BCDs).
⋆ The physical parameters calculated in this paper and the reduced images are only available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https:// cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/675/A90 Possible evolutionary links between early-and late-type dwarfs have been suggested through stripping mechanisms (e.g., Lin & Faber 1983;Kormendy 1985;Thuan 1985;Davies & Phillipps 1989;Ferguson & Binggeli 1994;Grebel 2001;Penny et al. 2014), while other authors argue against any direct evolutionary links between the two classes (e.g., Thuan 1985;James 1991). Other studies reach or review different uncertain conclusions, which suggest other evolutionary links, such as giant galaxy stripping, galaxy-galaxy interactions, or formation in the early Universe (e.g., Gerola et al. 1983;Aguerri & Gonzalez-Garcia 2009;Lisker 2009;Jerjen 2012;Meyer et al. 2014). Some authors highlight the importance of their environment's density and suggest different origins based on the environment (e.g., Lisker 2009;Jerjen 2012;Meyer et al. 2014;Penny et al. 2014). Still, the connection between the two classes of dwarfs remains poorly understood. This could be due to three main factors: the small samples, shallow observational limits, and environmental influences.
Based mostly on surface brightness photometry derived from deep near-infrared (NIR) imaging plus spectroscopic data, over the last two decades, our group has studied late-type dwarf galaxies based on a sample consisting of approximately 150 dIs and BCDs located in the Local Volume (LV) and eight nearby clusters (Vaduvescu et al. , 2006(Vaduvescu et al. , 2007(Vaduvescu et al. , 2011(Vaduvescu et al. , 2014(Vaduvescu et al. , 2018Vaduvescu & McCall 2008;Fingerhut et al. 2010;McCall et al. 2012). Among other results, these studies have uncovered evidence for evolutionary links between dIs and BCDs, while also hinting at links between early-and late-type dwarfs . The evolutionary links found in previous studies match the recent conclusions of Ivkovich & McCall (2019), who show that early-type dwarf spheroidal galaxies (dSphs) lie on the dwarf potential plane, as defined by late-type dwarfs (McCall et al. 2012). This suggests that the early-type dwarfs could emerge from late-type dwarfs that have converted most of their gas into stars. These prior works, using absolute magnitudes (which are sometimes prone to uncertain distances), suggest it would be worthwhile to to check for further evolutionary links between early-and late-type dwarfs via deep surface photometry studies.
As a continuation of prior studies that used the same photometric techniques, we embark on a study of physical properties of dEs via deep NIR Ks-band imaging (1.99-2.31 µm). This regime is known to be a better gauge of the galaxy mass and to minimise the dust extinction (galactic and internal) compared to visible bands; however, it has not been widely studied (e.g., James 1991;Thuan 1985). In this first paper, we derive the physical parameters (RA, DEC, apparent magnitude, semi-major axis, ellipticity, position angle) of a sample of 72 dEs, obtaining their surface brightness profiles (SBPs) based on deep NIR K-band archival and newly obtained imaging. In further works, we will derive fitting parameters of the selected sample and determine their correlations with the dwarf fundamental plane.
We selected our dE sample from two different environments in order to investigate the perturbations on galaxy profiles caused by varying object densities. First, 39 dEs were selected from the LV, which is defined as a region centered between the Milky Way and the Andromeda galaxy in a sphere with a radius of around 10 Mpc containing more than 500 known galaxies (Koribalski et al. 2018). The LV plays an important role in our work; it is a nearby and low-density environment, and is therefore an ideal laboratory for studying galactic entities more accurately. In addition to the LV sample, 35 dEs were selected from the Virgo cluster, the largest and closest galaxy cluster in our local Universe, centered around 16 Mpc away with a radius of about 6 Mpc, and containing on the order of 2000 galaxies (Binggeli et al. 1985). Virgo is still in formation, showing a complex geometry and important substructure (Boselli et al. 2014). Both the LV and Virgo allow the comparison of objects in isolation with objects located in clusters, the two being known to experience different perturbation effects (Boselli et al. 2014;Binggeli et al. 1987). The combined sample of 74 dEs was built based on preclassification in visible bands by other authors (e.g., Janz et al. 2017; Karachentsev et al. 2004;Ivkovich & McCall 2019). This sample includes available deep Ks archival images of 44 targets, in addition to our own observations of 30 objects. The paper is organized as follows. In Sect. 2, we present the selection criteria for our dE sample, including the origin of the data. In Sect. 3, we present the image-reduction method followed by the star-subtraction and zero-point calculation. In Sect. 4, we present the method used to derive the surface photometry. Our results are presented in Sects. 5 and 6. In Sect. 7, we summarise the planned upcoming work.

Sample selection
We selected 87 dwarf elliptical galaxies from which 74 had available data; see Table 1. We used three methods for sample selection (in some cases, the same galaxies were identified with more than one of the methods): 1. The first method entails querying NED 1 for the categories "dE, dS0" in the classic interface "By Classification" menu item. The membership of the returned galaxies was verified in the associated literature. We identify only a few dEs using this method (5 LV objects). 2. The second method is a search of NASA/SAO ADS 2 with the aim of finding articles with large samples of classified dEs. The resulting papers were cross-checked and we kept only those that had the largest number of galaxies with the most overlap. This search resulted in the identification of 57 objects originating from three papers: "Catalog of Neighboring Galaxies" (CNG; Karachentsev et al. 2013), Janz et al. (2017, and Ivkovich & McCall (2019). 3. The third method was a search through the sample selected by Vlad Tudor (priv. comm., former ING student). This source resulted in 30 objects. The joined sample resulted in 74 galaxies, and their observational data are presented in Table A.1 and Table A.2 for the LV and Virgo objects, respectively.

Archival images
The archives of several observatories hosting NIR instruments on 2-8 m class telescopes were queried to return Ks imaging data using the MASFO 3 online tool. As data from different telescopes and instruments can be challenging to combine, the selected telescope-instrument combinations were limited to the deepest dataset available for a given target. This condition restricted the data to either VISTA/VIRCAM (retrieved via ESO Science archive facility) or CFHT/WIRCam (available via the Canadian Astronomy Data Centre). Raw images for 44 targets could be retrieved from the two archives, resulting in 40 objects from VISTA/VIRCAM and 4 from CFHT/WIRCam.

Observations
To complete the LV sample, we were awarded four nights at the William Herschel Telescope (WHT) 4 using the LIRIS instrument in two observing modes. The observations were split into two service nights for observing 11 targets, and two regular visiting nights 5 to observe 19 targets, observing 30 targets in total.
The observations were obtained using the Ks band filter and we aimed to reach a surface brightness of K s ≈ 24 mag arcsec −2 (Vaduvescu & McCall 2008). A total of 120 images were taken for each object with 15 s exposure time per science image, resulting in a total of 30 min integration time per target. The 15 s individual exposure time was limited by the detector linearity limit and the moon brightness (>80% illumination). For targets smaller than 1 arcmin, a four-point dithering pattern was used to cycle the target between the four quadrants of the detector, allowing small dithering. For larger objects, we kept the target close to the detector center and the sky images were taken by nodding outside the galaxy field. In order to reduce the overhead time, two consecutive science images were taken at each point (e.g., AA-BB-CC-DD 6 ).

Image reduction
The IRAF 7 (Tody 1986(Tody , 1993 data-reduction technique was used by Vaduvescu & McCall (2004) and . As part of this work, we compared the data reduction using the IRAF REDNIR.CL script presented in  with automatic data-reduction software THELI GUI 8 (Schirmer 2013;Erben et al. 2005), first v2.10.5 and later v3.
The IRAF versus THELI comparison is based on 12 VISTA/VIRCAM images ("pawprints") from two different observing periods. The resulting combined images are presented in Fig. 1 and we identified THELI as a better option. These results show that there is comparable image quality between IRAF and THELI v2, while THELI v3 shows an improvement. In addition to the comparable image quality, THELI also provides a faster and easier workflow for obtaining field-and sky-corrected co-added images in an automated way. The main advantage of the automatic field distortion correction is the large mosaic image, which improves the absolute photometric result by allowing more reference stars to be used, while opening the possibility for further research. A downside of THELI is that it is computationally heavy, which causes issues for a normal PC if combined with a large dataset. For reducing 140 VISTA/VIRCAM pawprints, a minimum of 300 GB free disk space and more than 32GB of RAM are needed. Therefore, in the case of larger 4 The WHT is operated on the island of La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. 5 LIRIS photometry was obtained as part of C171/2019B. 6 The different letters refer to the four quadrants. 7 IRAF is widely used astronomical software. It was designed in 1981 by the National Optical Astronomy Observatories and is suitable for a wide range of astronomical image-processing tasks. 8 THELI is an automated astronomical image-reduction tool suitable for processing large amounts of single-and multi-chip CCD camera images and is designed to produce an astrometrically and photometrically calibrated co-added image, https://www.astro.uni-bonn. de/theli/ Fig. 1. Comparison of the results of three image-reduction methods using 12 individual images, for the galaxy SUCD1. All three crops have a FOV of 2.4 ′ × 2.4 ′ and normal sky orientation. The IRAF result is shown in the upper left, THELI v2 in the upper right, and THELI v3 in the second row. The foreground stars in these frames have a FWHM variation of ±0.1 ′′ while the S/N shows an increase by more than 10% and 50% for the THELI v2 and THELI v3, respectively, compared to IRAF. The actual reduced IRAF image size is approximately three times larger than the presented crop, while for THELI it is 20 times larger. Fig. 2. SUCD1, an example galaxy for testing the effect of the sky flatfield image using 12 individual frames. The pictures have a FOV of 2.4 ′ × 2.4 ′ and normal sky orientation. The flat field correction was not used for the first (left) image, but was used for the second (right) image. In both cases, the standard deviation of the background level is 0.6 ADU, total apparent magnitude 14.43 ± 0.01, and semi-major axis length 2.8 ′′ ± 0.13. datasets (17 of 74 dEs), the images had to be split and reduced in smaller batches.
The THELI data-reduction instructions can be found online 9 , but our data consist only of science frames and in some cases sky frames. The effect of the skyflat images was verified (see Fig. 2) and in our case it did not provide improvement. This lack of improvement with or without applying the flat images can be explained by the large gaps in the observing periods and by the masks applied in the image section with outstanding pixel-to-pixel sensitivity fluctuation. Therefore, in the THELI calibration tasks, after preparing the raw data for usage, we skipped the bias, dark, and flat calibration steps and jumped to the background correction step, which calculates and subtracts the background model. The background models are constructed from three to seven frames observed closest in time to the science frame(window size). If the data originated from the WHT/LIRIS observations, two images were taken at every dither point and the images were split in two groups (split sequence section: 2 groups with a sequence length of 2). The collapse correction step was mainly used to correct the LIRIS reset anomaly. During the THELI coaddition tasks, we skipped the separate target groups task. The automatic astrometry/ relative photometry failed in three cases, for which we manually updated the header "WCS" information using the THELI iView tool. In this image viewer, the user has an overlap of the image and star catalog with a possibility of manual alignment. Using the images with the new header information, we repeated the create catalogs and astrometry/ relative photometry steps. In the coaddition task, we used the median combining method, and in cases of larger data sets, the images were separately reduced. The resulting images can be merged together for the last step. In the case of ten Virgo objects located in the same mosaic field, the images were reduced and co-added individually. The final frames were aligned with external tools (e.g., IRAF/ Python "astroalign"), and then combined with IRAF.

Image cropping
To reduce the processing time, the final reduced images were cropped. We used a 2 ′ × 2 ′ crop for targets with literature diameters of smaller than 1 ′ , while for larger ones we set the crop size to more than twice the diameter of the galaxy found in the literature. For cropping the images, a Python script was used, which reads a list of galaxy center coordinates (RA, DEC) from a file, and then searches for the target in the available reduced images before creating a crop of the FITS image while keeping the galaxy centered in the crop image.

Photometric zero point
The zero point (zp) was resolved automatically using THELI GUI v3 and in some cases the Photometry Pipeline (PP) 10 , using all the available stars from the field. The results in both cases were verified manually for at least three galaxies with IRAF using the PHOT task on ten 2MASS stars (Skrutskie et al. 2006) selected via Aladin Lite 11 (Boch & Fernique 2014;Bonnarel et al. 2000). During the zp verification, we obtained a maximum of ±0.2 mag difference between the automatic and manual methods, with a typical uncertainty of around ±0.05 mag. This difference can be explained by the errors in the catalog values and by the number of sources contributing to the calculations. For the VISTA/VIRCAM mosaic images, a smaller crop (typically 10 ′′ × 10 ′′ , in some cases 25 ′′ × 25 ′′ ) was used for the zp calculation to minimize the effect of the accumulated exposure-time variations in different parts of the mosaic image.

Masking
The close-by objects around each target (foreground stars, resolved stars, and other galaxies) can produce additional flux and introduce noise in the isophotal profiles of the galaxies; see  Science Data Analysis System (IRAF/STSDAS) isophote package (used in later steps), offers the possibility to remove these extra flux effects; however, these packages have not been optimized for this task. Therefore, the IRAF imedit task was used to manually remove foreground objects from all images, except four galaxies (NGC 59,M 110,M 32,NGC 3077). In these four cases, a more sophisticated IRAF-based tool KILLALL (Buta & McCall 1999) was used; see the results in Fig. 4. For M 32 and M 110, one can observe a shift in the two magnitude profiles (with or without close-by objects), which suggests an incorrect galaxy flux estimation caused by the overcrowded field or the aggressive star-removal algorithm (see Fig. 4). The effect of the foreground star removal on the physical parameters is also presented in Table B.1 for three tested objects, where the galaxy name (in these three cases) is annotated with no close object ( n Co) in the case where the results were obtained from the starremoved image, and close objects (_Co), where the original images were used for the analysis.

Surface photometry
The surface photometry was extracted using the Python program "Galaxy Photometry v2" (GPv2) 12 , which performs elliptical isophote analysis, returns galaxy apparent physical parameters, performs preliminary SBP fitting, and provides extra information for verifying the results.

Isophotal analysis
GPv2 is a wrapper built around the "photutils.isophote" 13 package, which is the Python equivalent of the IRAF ellipse task. This IRAF task is used for computing the SBPs of galaxies (e.g., Fig. 4. Surface brightness profiles for four targets masked with KILALL. In all cases, we present the SPBs either with close objects (Co) without using KILLALL, or no close objects (nCo) when we used KILLAL. In the cases of M 32 and NGC 205, a larger deviation can be observed in the SBPs. In these two cases, we provide the inserts of the galaxy images in the left without removing the surrounding objects and in the right the same field after KILLALL object removal. In the cases of M 32 and NGC 205, we can observe the effect of an overestimation of the isophotal flux values due to the number of resolved objects and the aggressive star removal during the masking, respectively. Aguerri et al. 2005;Vaduvescu et al. 2006) and was implemented in the method used by Vaduvescu et al. (2006) and Lian et al. (2015). These methods are based on an iterated execution of the IRAF ellipse task with adjusted input parameters. The GPv2 provides an automation of the procedures described by Vaduvescu et al. (2006) and attempts a four-step technique as opposed to two.
In the first step, the script generates an estimation of the fitting ellipses using predefined parameters (see Sect. 4.3), allowing variable centers, ellipticity, and position angle (PA). Based on these results, more accurate parameters can be defined. In the second step, the ellipses are re-fitted with fixed central coordinates. In the last two steps, the calculations for step two are repeated while attempting to add additional constraints, fixing the ellipticity and later the PA.
The importance of the GPv2 lies in providing an automatic way to apply a widely used technique and in providing an alternative to the IRAF/STSDAS package, which was recently made publicly unavailable and included the ellipse task.

Background modeling
Using the THELI sky subtraction, the background of the reduced images can remain lower or higher than the desired average zero value. The images can also contain unwanted artefacts, such as darker regions or brighter stripes due to imperfect data reduction or a remaining bright companion. To correct these artefacts, before starting to compute the SBPs, the GPv2 uses the "photutils.background" 14 package for background estimation, and the newly obtained background model is subtracted from the original science frame; see Fig. 5.

Automatically defined parameters
In Sect. 4.1, we mention that, for the first step of the GPv2 isophotal analysis, we use predefined parameters and in the further steps we recalculate them. The predefined parameters are: the galaxy center coordinates x and y (whose values match the central coordinates of the cropped frame; see Sect. 3.2), the ellipticity (whose default value is 0.2), and the PA (whose default value is 0).
After the first estimation of fitting the isophotal ellipses, the semi-major axis (a T ) of the galaxy is calculated. When the flux value inside a few consecutive ellipses reaches the background level (given by the maximum value of the background model) and starts to fluctuate around it, we consider that we have reached the size limit for the galaxy given the observed depth. This galaxy size is denoted a T ; see Fig. 6.
In the further steps, the new center, ellipticity, and PA values are weighted averages of the individual isophotal ellipses within the a T limit. For the PA, the following circular mean formula 15 was used: PA = arctan 2(sin(PA), cos(PA)). (1) The weight values are the inverse values of the error of the respective parameter for the individual isophote measurements.
Using the weighted average instead of the median raises the importance of the central part of the galaxy.

Intensity-to-magnitude conversion
Using "photutils.isophote", we obtain the total flux intensity and the isophotal intensity (I) of the dEs. To convert intensity to magnitude, we used the classic formula: where m surf = 2.5 × log 10 ps 2 , where ps is the pixel scale. To convert the intensity errors (σ I ) to magnitude uncertainties (σ m ), we used the error propagation formula:

Verification
The results of the GPv2 were verified by comparison and black box testing. Firstly, we compared the SBP returned by the GPv2 and the IRAF ellipses task. These comparison results are presented in Fig. 7, and we can observe a good overlap. Secondly, before accepting the results of any elliptical isophote analysis, three criteria needed to be fulfilled: 1. The final isophote analysis needs to have the central coordinate (x0, y0) fixed. Fixing the ellipticity or PA is not required, but at least one of the two is preferable. 2. The allowed tolerance of the galaxy size calculated by GPv2 until the noise level, determined visually, must be less than 10%. This criterion is illustrated in Fig. 7, in which the blue error bars in the isophotal magnitudes start after the magenta line, which indicates the calculated galaxy size.  The magenta line illustrates that the adopted size of the galaxy is slightly larger than the limit where the noise starts to dominate the isophots.
3. The residuals, that is, the difference between the galaxy image and its surface model, must be comparable with the background noise level. When satisfactory models could not be obtained, the automatic initialization was skipped and manual input was used in order to try other input parameters. This could mean an extra three to five iterations. The most typically modified input variables during the execution are as follows: 1. "box_size": The "photutils.background" package requires a box_size parameter in order to define the sampling step size. This parameter must be adjusted properly to the size of the galaxy, to be small enough to minimize the effect of the galaxy in the model and big enough to reduce the desired artifacts. This modification was needed for 65% of the galaxies from the total cases. 2. First semi-major axis length: If the galaxies were larger than 0.2 ′ in diameter or were non-nucleated, the semi-major axis of the first ellipse had to be increased. This modification was needed for 40% of the galaxies from the total cases. 3. Center coordinates: The center of the galaxy taken from the literature and WCS from the fits header are not guaranteed to be correct and can be shifted relative to the apparent position of the galaxy. When this is the case, the x0 and y0 central coordinates need to be adjusted slightly before the execution of GPv2. This modification was needed for 35% of the galaxies from the total cases.

GPv2 results
In this section, we present the results of the GPv2 surface photometry modelling tool. These results can be separated in three sections: obtaining the SBPs, recalculating the physical parameters, and obtaining the residual files.

Surface brightness profiles
The isophotal analysis was performed for 72 galaxies. The obtained SBPs are presented in Appendix C, where the error bars A90, page 6 of 38 are plotted with 2σ uncertainty. These profiles represent observational data; they are not based on fitting models, and therefore they can be used in searches for new fitting laws. From the original sample of 74 galaxies, VCC 1538 (with an accumulated exposure time of 34 min, VISTA/VIRCAM) and VCC 1405 (with 56 min total exposure time, VISTA/VIRCAM) were not detected in the reduced K s band images for the available deepness (see Fig. 8). This suggests a possible misclassification of these galaxies.

Physical parameters
Physical parameters of the 72 galaxies were calculated and presented in Table B.1 for the LV objects, and Table B Where these values cannot be fixed, we also present their interval (in columns σ b/a and σ PA ). -The magnitude uncertainty (σ m ) derived from the mean isophotal surface intensity error. Thus, the uncertainty in the ellipticity (σ b/a ) and PA (σ PA ) are based on the mean error values along the isophotal analysis. The semi-major axis uncertainty is σ a = a T − a σm , where a σm is the semimajor axis length at which the isophotal intensity is equal to the final isophotal intensity (I T ) minus the mean intensity error. We searched the 2MASS and CNG catalogs in order to compare with our results. This search shows that we obtained first-time 16 physical parameters for 13% of the LV sample and 33% of our Virgo sample. The remaining 78% of our galaxies were used for test purposes and to provide improved parameters thanks to deep imaging. The 2MASS catalog uses a standard aperture for the physical parameter measurements, which was derived from the isophote at K s = 20 mag arcsec −2 (Jarrett et al. 2003). To be able to compare our data more accurately, we also calculated the K s = 20 mag arcsec −2 semi-major axis (a 20 ) and the total apparent magnitude (m 20 ). Additionally, the 2MASS catalog also provides total magnitudes, which are 16 Galaxies that do not have physical parameters measured in the 2MASS or CNG catalogs, or which were incorrectly classified.   10. Comparison of our calculated semi-major axes (X axis) with published catalog data (Y axis). The orange upper-left number in each subplot is the median deviation between the respective catalog and measured values. The orange line marks the ideal linear correlation, this function having a slope of one and intercept equal to the median deviation value. For the LV galaxies with crowded surroundings, we note higher catalog values due to the unremoved surrounding objects. For the Virgo galaxies a T , we observe that the literature data have not been sufficiently deep to detect outer regions of the galaxies. calculated using different techniques; for example, with extrapolation (Jarrett et al. 2003). We marked these extended 2MASS magnitudes as m 2MASSext .
The comparison between our results and the existing catalogs were performed for the parameters of galaxy center positions, apparent magnitude, semi-major axis, ellipticity and PA. We obtained an 0.2 ′′ median deviation between the galaxy center positions, 0.4 mag for the apparent magnitude, 20 ′′ for the semi-major axis, 0.11 for the ellipticity and 13.8 • for the PA values.
A more detailed analysis of the comparison of the apparent magnitude median deviation values can be found in Fig. 9. This figure also contains the expected linear correlation function using the y = x + b formula, where b represents the mean difference between the catalog values and our results (e.g., (|m T LV − m 2MASS |) = 0.44), y represents the catalog values (e.g., m 2MASS ), and x represents our values (e.g., m T LV ). The obtained median differences (b values) are also shown in the figures. The expected linear correlation overlaps with our data, suggesting its systematic improvement in the magnitude values for which we obtained an average 0.1 mag improvement for the LV targets and 0.2 mag improvement for the Virgo targets. Figure 10 shows the results of a comparison of the semimajor axis values, where we present the expected linear correlation and the mean difference value in arcsec. In this case, A90, page 7 of 38 A&A 675, A90 (2023) Fig. 11. Comparison of the depth of our result (left) with the 2MASS K band image (right) for the VCC 781. The size of the field is 3.41 ′ × 2.65 ′ in normal sky orientation. We highlight the fact that the 2MASS image loses most of the details in the outer parts of the galaxy. we can observe a linear correlation between the a 20 values and the 2MASS catalog values, suggesting our workflow is correct; however, a large deviation can be seen between the a T and 2MASS values. Verifying the available images for the sample in the catalogs suggests that the 2MASS values sample mainly the central part of the galaxy, losing information about the outer regions (see Fig. 11). The comparison with the CNG suggests an underestimation in our results. This could be caused by the unremoved foreground stars and background galaxies especially for the objects M 32 and M 110, which are located in crowded fields.
The comparison results of the ellipticity and PA values are presented in Figs. 12 and 13 respectively. In both of these cases, we observe scatter in our data. For the ellipticity values, we observe a larger scatter for LV values and more precise catalog measurements for the Virgo values. For the PA values, the main tendency shows that the measured PA values are consistent with the catalog values.

Residual images
The residual images (see Sect. 4.5 for further explanation or Appendix C for images) can reveal hidden features about the inner parts of galaxies and can be used to decide whether or not further examination of these targets is necessary. In Appendix B, we categorize our galaxies based on visual examination of the residual images. We assign flag 0 to the galaxies in which we observe a single nucleated core, flag 1 for the galaxies that have a second knot close to their center or multiple cores, flag 2 for the ones showing late-type structures (e.g., spiral or jet-like), flag 3 for the ones with multiple objects overlapping (suggesting unresolved clusters), and flag 4 for the ones with a non-nucleated core. From the sample, we highlight VCC 745, an apparent merger; LEDA 1690666, NGC 59, and VCC 523, which have multiple cores, and the globular cluster Bol 520, incorrectly classified by Karachentsev et al. (2013) as a dE, but later corrected by Kaisin & Karachentsev (2013).

Surface-brightness-profile modeling
In the GPv2, three classical fitting models are implemented: exponential Ivkovich & McCall 2019), de Vaucouleurs (de Vaucouleurs 1948Ferguson & Binggeli 1994), and Sersic (Sérsic 1963;Vitral & Mamon 2020). We obtained good fitting results for dEs with all of them; however, there is room for improvement of each of them. Therefore, we extended our search and carried out a more detailed examination, also verifying other models: the hyperbolic secant (sech), Gaussian function (Vaduvescu et al. 2006), King model (King 1962); and combined functions of an exponential plus de Vaucouleurs, exponential plus sech, exponential plus Gaussian, de Vaucouleurs plus sech, de Vaucouleurs plus Gaussian, and Gaussian plus sech.
The model fitting was done using a Python script based on the "scipy.optimize" package curve_fit task with the default Levenberg-Marquardt fitting algorithm (Virtanen et al. 2020). The following constraints were used for the variables: the flux intensity values were allowed to vary between 0.1 counts and twice the central intensity; the scale length between 0.1 ′′ and twice the galaxy size; and the power variable between 0.5 and 10. The fitting was done on the isophotal intensity profiles to maximise the precision close to the galaxy core. For better representation, the results were converted into magnitudes and shown in isophotal magnitude plots (Fig. 14 ).
The goodness of the fit was verified using the chi-square test. First, we choose the best three functions for each galaxy and the best results were obtained for the combined functions exponential plus sech, de Vaucouleurs plus sech, and Gaussian plus sech. Secondly, we examined these three models and we chose the best fit for each galaxy. In conclusion, we find that from the 12 different fitting models, the best fitting was the exponential plus sech for 44% of the LV targets and 52% of the Virgo sample.
Based on previous results Vaduvescu et al. ( , 2006, the expectation would be that the sech component fits the outer regions of the dEs while the exponential component describes the galaxy center. However, for some of our data, the two functions can swap roles. An example of this is shown on the left of Fig. 14. The expected case when the sech function models the outer region of the galaxy is shown on the right of Fig. 14. This latter case is an example of a fit of the de Vaucouleurs plus sech function, which follows the outer region of the galaxy within the errors but fails at the galaxy center. A90, page 8 of 38 Pinter,V.,and Vaduvescu,O.: A&A proofs, 14. Example for the sech component (dash-dotted) contribution for fitting dEs, VCC 781 (main, big plots).The left plot shows the fit of the exponential plus sech functions, which overlay perfectly over the measured profile. The right plot shows the fit of the de Vaucouleurs plus sech functions, which follows the outer region of the galaxy within the errors but fails at the galaxy center. The fitting was done for isophotal intensities, see lower left inserts, however for better examination of the fit we convert the fitting function into magnitudes. The bottom plot shows the residuals for the model subtracted from the data. The upper right inserts show the distribution of the residuals fitted with normal distribution probability density function. Therefore, as a second-best option, we cannot neglect the combination of the de Vaucouleurs plus sech model (see Fig. 14), which is the best fit for 25% of the LV and 12% of VIRGO data. The remaining 31% of LV and 36% of VIRGO targets were fitted with the Gaussian plus sech, which suggest their blue compact dwarf nature based on previous results (Vaduvescu et al. 2006).

Conclusions and future work
During this work, we collected and reduced deep K s imaging for 74 dEs based on available image archives (VISTA and CFHT/WIRCAM) adding our own WHT observations. We obtained SBPs reaching as deep as K s ≈ 23.8 mag arcsec −2 in median for LV targets and K s ≈ 24.8 mag arcsec −2 for Virgo targets, from which we derived apparent physical parameters for 72 dEs (two targets remaining undetected in the Ks images). In the case of the Virgo sample, our physical parameters suggest that deeper imaging is necessary in order to approach the size limit for the galaxy; however, in the case of the LV targets, we confirm the literature results that already sampled the outer regions of the galaxies.
The SBPs were tested against classical fitting laws and combinations thereof. We obtained best fitting models for dEs using the exponential plus sech, and de Vaucouleurs plus sech models. Alongside previous works (Vaduvescu et al. , 2006, our results could be used to classify most dwarf galaxies. However, our selected dE SBP models require further examination in the near future; for example, using GALFIT 17 modeling. As a continuation of this work, we will further examine the outcome of using exponential plus sech, and de Vaucouleurs plus sech functions for fitting dEs. After adopting the best fitting model for the entire sample, the fitting parameters of these functions will be used to search for physical correlations between early-and late-type dwarfs. This examination will be completed using the fundamental plane defined by ), McCall et al. (2012 or the potential plane defined by Ivkovich & McCall (2019).