Introducing the FLAMINGOS-2 Split-K Medium Band Filters: The Impact on Photometric Selection of High-z Galaxies in the FENIKS-pilot survey

To understand the impact of adding the $K$-split photometry to an existing multi-wavelength catalogue in determining photometric redshifts, a mock galaxy catalogue was simulated. The synthetic photometry of the catalogue was generated to have similar depths and broad-band filter sets as the UltraVISTA catalogues in the COSMOS field ($u$, $B$, $V$, $g$, $r$, $i$, $z$, $J$, $H$, $K_{s}$, and the four SPITZER/IRAC channels at 3.6, 4.5, 5.8 and 8.0 micron), because these are representative of the current state of the art in deep fields. The depths for the $K$-split filters are $K_{\mathrm{blue}}$ 5$\sigma$ depth = 25 mag, set to approximately match the $K_{s}$ depth in the UltraVISTA catalogue (based on the total flux), and the $K_{\mathrm{red}}$ depth set to 5$\sigma$ depth = 24.3 mag, to reproduce similar observational constraints associated with this filter such as the comparatively lower observational efficiencies achieved on the F2 instrument and brighter sky backgrounds. These $K$-split depths are similar to the observed depths of the pilot survey shown in Section 4.

The mock galaxy catalogues are comprised of several different aged SSPs, spanning a range of SNR to produce the expected range of galaxies one might observe in deep photometric surveys. A total of five galaxy types were simulated: four SSPs with 0.1, 0.3, 0.6 and 0.9 Gyr ages (assuming solar metallicity and no dust attenuation) giving a range of Balmer/4000 Å  break amplitudes, and a dusty constant star-forming galaxy with strong emission lines. The emission line galaxy has an ionisation potential, log(U)$=-2$, for strong [OIII] emission and a A_V = 2 mag attenuation, (using the Calzetti, 2001, dust law) to flatten the UV spectral slope and thus highlight the effect that the $K$-split filters can have on tracing emission line color signatures. To establish which types of galaxies, and at what redshifts, are impacted most by the $K$-split filters, the mock catalogues are created with galaxies randomly drawn from a uniform distribution, over a large redshift range.

These galaxy models were generated using Bayesian galaxy modelling software: Bayesian Analysis of Galaxies for Physical Inference and Parameter EStimation (BAGPIPES Carnall et al., 2017) which uses Bruzual & Charlot (2003) stellar population models and emission line modelling with Cloudy (Ferland et al., 2017). Examples of two galaxy models are shown in Fig. 3 at a range of redshifts to illustrate how the $K$-split filters move through the SEDs as they are redshifted.

To simulate a range of SNR, each galaxy has its flux scaled such that the $K_{\mathrm{red}}$ band has a specific SNR (which was chosen as it has the shallowest depth in the $K$-band for these simulations). Scaling the flux by the $K_{\mathrm{red}}$ filter essentially produces a similar SNR profile across the multi-wavelength filters irrespective of redshift. A consequence of the scaling is that it produces slightly different mass ranges at different redshifts (i.e. lower masses at low redshifts and higher masses at high redshifts). As a point of reference, a 0.9 Gyr SSP at $z\sim 5$ with a SNR=5 in the $K$-split filters has a log(M*/M_⊙)=11.

To test the $K$-split filters impact on recovering the redshifts of the simulated galaxies, we used the photometric redshift fitting software EAzY (Brammer et al., 2008). EAzY uses linear combinations of multiple template spectra to find the minimum chi-squared description of the observed SED, in order to construct a redshift probability distribution, P(z). EAzY has been widely used to determine photometric redshift catalogues for multi-wavelength surveys including NMBS (Whitaker et al., 2011), UltraVISTA (Muzzin et al., 2013), 3D-HST (Momcheva et al., 2016), and ZFOURGE (Straatman et al., 2016). The template set is from ZFOURGE (see Section 4.4) and includes standard EAzY templates plus a strong emission line galaxy template and an old and dusty galaxy template. These two additional templates help demonstrate how the $K$-split filters can distinguish between galaxy SEDs that can resemble massive quiescent galaxies. EAzY was run both with and without the new $K$-split medium bands to compare the impact on the recovered photometric redshifts.

There are two key metrics that we consider in our analysis of the EAzY results: photometric redshift precision and outlier fractions, both of which relate to the photometric redshift accuracy: $|z_{\mathrm{input}}$ - $z_{\mathrm{recovered}}|$ / ( 1 + $z_{\mathrm{input}}$ ) (hereafter $\Delta z/(1+z)$). The photometric precision metric is measured by the spread in the $\Delta z/(1+z)$ for which we use the normalised median absolute deviation (NMAD), normalised by a factor of 1.48 (hereafter $\sigma_{\textsubscript{NMAD}}$). The outlier fraction is defined as the number with $\Delta z/(1+z)>$ 0.1 relative to the number of galaxies in the sample. These two metrics show the overall improvement in photometric precision and accuracy achieved by including the $K$-split filters. The results for the 0.6 Gyr SSP mock galaxy catalogue are shown in Fig. 4 where the upper panels show the input versus recovered redshift without and with the $K$-split filters (left and right respectively). The lower panels show the $\Delta z/(1+z)$ versus redshift and include running median curves shown for each SNR bin. The outlier fraction and $\sigma_{\textsubscript{NMAD}}$ are displayed for the full SNR population and for the redshift range $4.2<z<5.2$ where we see the most improvement from the $K$-split filters. With the $K$-split filters, the outlier fraction is reduced by a factor of 2.4 and $\sigma_{\textsubscript{NMAD}}$ improves by a factor of 2.3. The full set of diagnostic plots for the 4 other galaxy models are shown in Appendix B.

To investigate the redshift ranges impacted by $K$-split filters, one can take the ratio of the running median $\Delta z$ lines with and without the $K$-split filters. This is shown for the 0.6 Gyr SSP population in Fig. 5. We can see here that the improvement in $\Delta z/(1+z)$ for SNR$>$10 can be as high as a factor of 10 at a $z\sim 4.6$, whereas this improvement is less at $z\lesssim 4.2$ and $z\gtrsim 5.2$. Finally, one can see that there are minimum SNR requirements for the photometry to achieve photometric precision and accuracy improvement. In the 0.6 Gyr SSP, SNR$\lesssim$5 produces minimal impact on the photometric precision. It should be emphasised that for each increment in SNR, the SNR of all the filters are improved and so do not describe the minimum SNR required in the $K$-split filters. An investigation varying the $K$-split SNR whilst keeping the other photometric errors constant is shown in the Section 3.2.

Figure 6 summarises the $\sigma_{\textsubscript{NMAD}}$ and outlier fractions for the simulations for each of the SNR bins and the five galaxy types. Note that these metrics are quoted for the redshift range $2<z<4$ for the dusty star-forming galaxy (labelled dusty SF in Figure 6) and the remaining 4 SSPs for the redshift range $4.2<z<5.2$, highlighting the areas where the most improvement is seen from the $K$-split filters. All galaxy types see at least some improvement in the outlier fraction and $\sigma_{\textsubscript{NMAD}}$, with the exception of the 0.1 Gyr SSP population, which has no strong Balmer/4000 Å  break and whose photometric redshift performance is dominated by the strong Lyman break. In general, the most improvement is seen for the 0.6 Gyr and 0.9 Gyr SSP populations. The $\sigma_{\textsubscript{NMAD}}$ for the 0.6 Gyr and 0.9 Gyr SSP galaxies at SNR=10 are both reduced a factor of 2.4 and the outlier fraction is reduced by a factor of 11 and 2.3, respectively. While there are similar relative improvements for the 0.3 Gyr SSPs at SNR=10 (factor of 2.4 improvement in $\sigma_{\textsubscript{NMAD}}$ and 100$\%$ reduction in outliers), the outlier fraction and $\sigma_{\textsubscript{NMAD}}$ values are significantly lower even without the $K$-split filters. Interestingly, the impact of the $K$-split filters on the 0.3 Gyr SSP is most prominent at SNR=5, with large improvements to $\Delta z/(1+z)$ impacting the $\sigma_{\textsubscript{NMAD}}$ despite relatively unchanging the outlier fraction. Finally, for the dusty star-forming galaxy we use the redshift range $2<z<4$, where the emission lines for [OIII] and H$\alpha$ enter the $K$-split filters. Here the outlier fraction is reduced by a factor of 2 and the $\sigma_{\textsubscript{NMAD}}$ is improved by a factor of 1.5, although these quantities are aggregated over a broad redshift range and individual improvement in $\Delta z/(1+z)$ can be as high as a factor of 4.

The results of these simulations indicate that at sufficient SNR, the most impact from the $K$-split filters is apparent for the older SSP populations, where there is very little rest-frame UV flux and the photometric redshift is strongly influenced by identifying the Balmer/4000 Å break. It should be noted here that the outlier fraction and $\sigma_{\textsubscript{NMAD}}$ quoted in this section is dependent on the photometric filter sets and the depths used. Therefore, while quantitative comparisons are still relevant, their absolute value may change accordingly.

The simulations in the previous section included varying the SNR for all the photometric filters, however it also useful to assess the sensitivity of the SNR of the $K$-split filters given an existing photometric catalogue at fixed depths. As an additional outcome, we can determine the ideal depth of the $K$-split photometry given existing photometric catalogues. To investigate the impact of the $K$-split photometry SNR on the photometric redshift probability distribution function, P(z), we conducted the following simulations. We simulate photometry for two different galaxy SEDs, fixed at $z=4.6$, where the $K$-split filters sample the largest color signature for an evolved galaxy with a Balmer/4000Å break, and incrementally increase the SNR of the $K$-split photometry while maintaining the SNR of the other bands at the same depths as those used in Section 3.1.

The two galaxy SEDs are simulated using BAGPIPES with (1) a massive post starburst galaxy with residual star-formation and strong dust attenuation and (2) a massive quiescent galaxy based on the same 0.9 Gyr SSP model used in Section 3.1. These two galaxy SEDs are chosen to be representative of the type of quiescent and quenching galaxies one might expect at $z>4$. The filter set and depths used are the same as Section 3.1. Galaxies are modelled with various stellar masses such that their $K_{s}$ band luminosities are the same. Photometry is generated from the model galaxy with a scatter consistent with the photometric errors. In the simulation, the $K$-split photometry SNR is incrementally increased and EAzY is used to derive a P(z) using the full template set described in 3.1.

Fig. 7 shows the results of the test, for which there are two key takeaways. The first is that the galaxy SED shape is important in determining the contribution of $K$-split photometry to P(z). The narrowing of the P(z) (seen from the 95th percentile lines shown as red dashed lines in the right panel of Fig. 7) for the massive quiescent galaxy SED in the top row is more significant than for the post starburst galaxy in the bottom row, with a decrease in the width of the P(z) by a factor of $\sim$ 6 and $\sim$ 2 respectively. This is in part due to the substantial Lyman-break which is sampled by observer-frame optical bands, which already constrains the redshift of the massive Lyman-break galaxy well. Secondly, from the steep rise in the 95th percentile line in the top-right panel of Fig 7 at a $K$-split SNR$\sim$10, it is evident that there is a critical SNR where the impact of the $K$-split filters starts to emerge. Conversely, consistent with Section 3.1, it appears that there is no substantial improvement to the photometric redshift with a $K$-split SNR$\lesssim$5 in either galaxy model.

The marked improvement in photometric redshift precision of the 0.9 Gyr SSP model at SNR $\sim$ 10 can be understood by looking at the massive quiescent galaxy SED in the top row of Fig. 7. This suggests constraining the steep Balmer and 4000 Å break with the $K$-split filters requires a minimum SNR of $\sim 10$. At this SNR the simulation results indicate we can likely distinguish between the two different SEDs shown in the top-left panel (a quiescent galaxy at $z=4.6$ in black and secondary solution of a dusty galaxy at $z=3$). Once this threshold SNR is achieved in the $K$-split photometry, the bi-modal P(z) collapses to the correct redshift of the simulated galaxy. In this way, the gain in photometric precision can also be considered synonymous with discriminating between two different galaxy SED types. For the 0.9 Gyr SSP case, the redshift probability without $K$-split filters is not well-constrained and cannot distinguish between a $z\sim 3$ dusty, old galaxy and a $z\sim 5$ quiescent galaxy. The inclusion of the $K$-split filters with sufficient SNR effectively excludes the $z\sim 3$ solution.

A final point to take from this simulation is with respect to the interpretation of the P(z) and the chosen redshift estimate. While it is often standard practice to choose a redshift weighted mean, with a luminosity prior ($z_{\bar{x},K}$) to avoid selecting a lower probability density peak, the upper-right panel of Fig. 7 shows the prior may not be appropriate when there are potential SED degeneracies. In this case $z_{\bar{x},K}$ value falls between the two bi-modal peaks suggesting a solution that has a low likelihood. Therefore, in this instance, the mode of the P(z), $z_{mo,K}$, is more robust. The lesson is that large disagreements between $z_{mo,K}$ and $z_{\bar{x},K}$ should be treated with caution.

Using the same mock catalogues from Section 3.1, we conducted stellar population modelling using FAST (Kriek et al., 2009) to investigate the impact of the $K$-split filters on determining stellar mass and age, two key characteristics of massive quiescent galaxies. FAST was run using the 0.6 Gyr and 0.9 Gyr mock galaxy catalogues both with and without the $K$-split filters and fixing the redshift to the simulated values. Comparisons were made to the recovered masses and ages at the redshift ranges where the expected impact from the $K$-split filters is the most i.e. $4.2<z<5.2$. The results are that the standard deviation in the residuals with and without the $K$-split filters are mostly unchanged for the stellar masses and ages in both the 0.6 Gyr and 0.9 Gyr SSP models. There is a low overall scatter in the residuals for both age and mass without the $K$-split filters ($\lesssim$0.1 dex for all SNR). This shows that, given the correct redshift, the overall SED shape, and hence age and mass-to-light ratio, is well constrained by the broad-band filters. This highlights that the main impact the $K$-split filters have in selecting quiescent galaxies is from correctly determining photometric redshifts, without which the masses and ages cannot be constrained meaningfully.

For a wide area survey, there is the opportunity to better constrain the quiescent galaxy stellar mass function (GSMF) at $z>4$, with more robust photometric redshifts using the $K$-split filters. To date, various measurements of the GSMF have been made at $z\gtrsim 4$, however given the challenges in photometrically selecting quiescent galaxies at high redshift, there are a wide range of values. The left panel of Fig 8 shows a selection of quiescent GSMF published in recent years at the highest redshifts. It is noted that while these GSMFs do not all span the same redshift ranges and have different selection methods, the shape, normalization and evolution of the quiescent GSMF at high-redshift is currently not well constrained and therefore provides the range of possible values. Given the large range in the GSMFs, spanning 2 orders of magnitude at log(M*/M_⊙)=11, there is clearly substantial motivation to further constrain them.

A wide area survey using the $K$-split filters is already underway with the FENIKS Large and Long program (PI Papovich). This survey will cover a large area, $\sim$0.6 deg², and 5$\sigma$ depths of 24.3 mag in $K_{\mathrm{blue}}$ and 23.3 mag in $K_{\mathrm{red}}$, aimed at maximising the number of candidates (see Papovich in prep. for more details).

To predict the numbers of quiescent galaxies identified in such a survey, we ran the following analysis. To determine the likely numbers of quiescent galaxies, we integrated the GSMFs in the left panel of Fig 8 at log(M*/M_⊙)$>$10.9 in numerous mass bins and converted them to a distribution of masses by using the survey area and converting to a volume assuming a redshift range of $4.2<z<5.2$. We then converted these to $K$-band luminosities by modelling a passively evolving galaxy with $z\textsubscript{form}\sim 7$, and then calculated their SNR based on the $K$-split photometry using the proposed large area survey depths. The right panel of Fig 8 shows the expected number of quiescent galaxies for which we would be able to make $K_{\mathrm{blue}}$-$K_{\mathrm{red}}$ color measurements at a certain SNR.

At the redshift range of $4.2<z<5.2$, the passively evolving galaxy has a $K_{\mathrm{blue}}$-$K_{\mathrm{red}}>$ 0.4 mag. Given the effective selection of quiescent galaxies with a SNR$\sim$10 in the $K$-split photometry (as demonstrated in Section 3.1 and 3.2) one can infer a $K_{\mathrm{blue}}$-$K_{\mathrm{red}}>0.4$ at 3$\sigma$ significance should be sufficient to identify quiescent galaxies. Using this selection criteria the wide area survey could robustly identify anywhere between 1 and 120 quiescent galaxies, based on the variation in quiescent GSMF present in the literature. This survey would therefore provide strong constraints for the quiescent GSMF at $z>4$.

To test the capabilities of the $K$-split filters on a smaller pilot survey we consider a smaller survey area of 100 arcmin² and target depths motivated by the analysis in Section 3.2. Based on the SNR analysis, a galaxy with log(M*/M_⊙)=11 and SNR$\sim$10 in the $K$-split filters translates into a target 5$\sigma$ depth for a survey of 24.0 AB magnitude in $K_{\mathrm{red}}$ and 24.8 AB magnitude in $K_{\mathrm{blue}}$.

Scaling the numbers of identified quiescent galaxies from the GSMF analysis above, down to match the area of the pilot survey would mean identifying between 0 and 6 quiescent galaxies. Here we also consider direct measurements of number densities from literature. Using the number densities from Alcalde Pampliega et al. (2019), which probe a $4<z<5$ sample with stellar mass of log(M*/$M_{\odot}$)$>$11, we expect to encounter 0.9$\pm$0.5 massive quiescent galaxies. As a comparison, the number of quiescent galaxies identified based on existing literature values could be as high as 2.9$\pm$1.4 (based on Santini et al., 2021) or as low as 0.5$\pm$0.2 (based on Marsan et al., 2020), both of which include consideration for cosmic variance. In contrast if there is no evolution of the massive quiescent galaxy number densities from $3<z<4$, using the value from Straatman et al. (2014), one might expect 4.6$\pm$1.8 massive quiescent galaxies per pilot survey area. While a larger survey area is ideal to identify many candidates that are not subject to field-to-field variance, a small pilot survey area such as this could be considered the minimum area to be covered to in order to identify quiescent galaxies at $z>4$.

After the design and commissioning of the $K$-split filters, a pilot survey was carried out to test the impact of the $K$-split filters using real data. The FENIKS pilot survey (Co-PIs: C. Papovich, E. Taylor, C. Marsan) is an eight night survey with the F2 instrument on the 8.1 m Gemini South Telescope at Cerro Pachón observatory, Chile. The observations were undertaken predominantly in queue mode starting in November 2017 and finishing April 2019 (programs GS-2017A-Q-10, GS-2017B-C-2, GS-2017B-FT-16, GS-2018A-Q-212, GS-2018A-Q-213, GS-2018A-DD-101, GS-2018B-Q-124, GS-2019A-FT-101). Seeing conditions were generally excellent with 50th percentile seeing of 0.45” in $K_{\mathrm{red}}$ (0.37” and 0.65” upper and lower quartiles) and 0.49” in $K_{\mathrm{blue}}$ (0.38” and 0.74” upper and lower quartiles).

The strategy for this survey is to add the $K_{\mathrm{blue}}$ and $K_{\mathrm{red}}$ photometry to existing, deep photometric catalogues: UltraVISTA (Muzzin et al., 2013) DR3 (private communication) and ZFOURGE (Straatman et al., 2016) catalogues, reaching depths consistent with those in section 3.4, and in doing so, push the limits of these surveys to explorations of higher redshifts, in particular at $z>4$. Three fields in total were chosen across COSMOS and CDFS from pre-selected catalogues to maximize the discovery of potential $z\textsubscript{phot}>4$ massive galaxies. A summary of the exposure times and image depths are shown in Table 1. The F2 circular FOV is 6.1’ diameter (29.2 arcmin² per field) making up a total survey area of 87.6 arcmin². This survey area is $\sim$ 25$\%$ of the ZFOURGE survey area and $\sim$ 1$\%$ of the UltraVISTA deep survey area.

The F2 $K_{\mathrm{blue}}$ and $K_{\mathrm{red}}$ data were reduced using a custom IDL pipeline, written by one of the authors (I. Labbé), used in the ZFOURGE (Straatman et al., 2014) and NMBS (Whitaker et al., 2011) surveys. The pipeline utilizes a two-pass sky subtraction method based on the methodology of the IRAF package (Tody, 1986) xdimsum, which produces sky subtracted images from sets of dithered observations. Our final reduced images are flat fielded, point-spread-function (PSF) and pixel matched to the $K_{s}$ detection images (both legacy catalogue detection images have pixel scales of 0.15” per pixel) and photometrically calibrated using a nearby NIR spectro-photometric standard star (selected from the Calibration Database System ²²2https://www.stsci.edu/hst/instrumentation/reference-data-for-calibration-and-tools/astronomical-catalogs/calspec). Our standard stars were observed in conjunction with our science fields to achieve $\sim$1$\%$ precision on our zero points. A series of secondary standards were selected in each field to calibrate observations on different nights to the zeropoint of our primary calibrated science observations. Some custom reduction methods were utilized to deal with thermal radiation from the on-instrument wave-front sensor (OIWFS) illuminating the F2 detector. A more detailed treatment of the data reduction can be found in an upcoming paper (Esdaile et al. in prep).

The FENIKS pilot survey catalogues are created by adding the F2 photometry to the existing legacy catalogues, which are based on the $K_{s}$ band detections. Photometry is undertaken by placing fixed apertures at the same RA/Dec locations for each corresponding legacy catalogue object. As the legacy catalogues use large apertures for their photometry (1.2” and 2.1” diameter in ZFOURGE and UltraVISTA catalogues respectively) and the $K_{s}$ images for these catalogues are deeper than the F2 images, matching aperture sizes would produce lower SNR $K$-split photometry and diminish their impact on determining photometric redshifts. Taking advantage of the exceptional seeing conditions for the F2 images, we can improve the SNR of the F2 photometry by selecting smaller, ‘optimal’ apertures. Optimal apertures were selected by investigating the SNR curve of growth for a star in the PSF matched F2 images. By limiting the aperture sizes to the PSF of the $K_{s}$ images (0.9” and 1.05” in ZFOURGE and UltraVISTA respectively) we were able to increase the SNR by up to 58$\%$. Limiting the aperture to the PSF avoids introducing any systematic errors such as from centroiding or from limited knowledge of the PSF curves of growth.

Using optimal apertures however presents the problem of having different aperture sizes from the legacy catalogues, meaning color measurements would be made without the same fraction of light within an aperture. This is particularly important to address as colors are used in determining photometric redshifts. Therefore in order to be consistent with the aperture fluxes in the legacy catalogues, we scale our fluxes such that the ratio of the fluxes, or colors i.e. $K_{s}$ - $K$x, are consistent irrespective of aperture size. This is done using Equation 1 below which shows the scaling as a ratio of the optimal aperture fluxes to catalogue aperture fluxes.

It is noted that these corrections assume that there is a negligible color gradient, which is reasonable for the compact sizes of massive quiescent galaxies at $z>4$. Errors are calculated by placing random, empty, non-overlapping apertures over the field and calculating the standard deviation of these aperture fluxes. These errors are also scaled to catalogue aperture sizes as per Equation 1. Additionally, the errors are scaled by the inverse square-root of the relative exposure time at each objects location. This ensures objects on the periphery of the field have larger errors consistent with lower per pixel exposure time due to dithering.

The K-split fluxes are scaled to total, or left as fixed aperture fluxes, consistent with the format of the respective legacy catalogues. We note that while the legacy catalogues have their own contamination flags, we simply inspected image cut-outs of F2 images with galaxies of interest to ensure no contamination from nearby sources was present. Finally, the fluxes and errors are normalised to match the corresponding zero points of the catalogues which are both 25 AB magnitude for UltraVISTA and ZFOURGE catalogues (corresponding to a flux density of 3.631$\times 10^{-30}$erg s^-1Hz^-1cm^-2 or 0.3631 $\mu$Jy).

Photometric redshifts are determined using EAzY. The templates used are the same as UltraVISTA and ZFOURGE (and in the simulations of 3.1), which are both comprised of PEGASE stellar population synthesis models (Fioc & Rocca-Volmerange, 1999), along with some additional SEDs to supplement the standard EAzY template set by including old and dusty galaxies and strong emission line galaxies.

Stellar population modelling was done using FAST (Kriek et al., 2009). Stellar mass, SFR, dust extinction and age are all derived by fitting Bruzual & Charlot (2003) models assuming Chabrier (2003) initial mass function (IMF) and exponentially declining SFH with timescale $\tau$, solar metallicity and Calzetti (2001) dust attenuation law. FAST was run using photometric redshift outputs from EAzY which is a standard technique also employed by the ZFOURGE and UltraVISTA catalogues.

In our FENIKS pilot survey we select galaxies in the redshift range $4<z<5.5$ where the $K$-split filters straddle the Balmer and 4000 Å break. We select galaxies with $K_{s}$ SNR $>$ 7, for which we estimate our catalogs are complete to log(M*/$M_{\odot}$) = 10.7 for a passively evolving stellar SED, with a formation redshift of $z\textsubscript{form}\sim 7$ from the Bruzual & Charlot (2003) models and a Kroupa (2001) IMF. Our final candidate list comprises 12 massive galaxies, from which a subset is shown in Fig. 9.

The photometric redshift probability distribution function, P(z), is shown in the right hand panels of Fig. 9 for each galaxy with the $K$-split photometry (blue histogram) and without (grey histogram). The P(z)s for the 12 selected massive galaxies at $z>4$ are consistent between the original legacy catalogues and the FENIKS survey including the $K$-split photometry. Additionally there are no substantial changes to the best-fit SEDs with and without the $K$-split photometry. This supports the idea that the z_phot estimates are robust, as the $K$-split filters provide additional confidence in the SED fit. The additional confidence is significant given the potential for emission line galaxies contaminating the selection (e.g. Merlin et al., 2019; Marsan et al., 2020). Furthermore, the consistency of the photometry with the legacy catalogue best-fit SEDs reinforces that these galaxies host old stellar populations, such as the case for FENIKS-COS352-11539.

While our sample generally does not appear to show a substantial increase in P(z) precision using the $K$-split photometry, there are indications that the P(z) is changing with their inclusion. This can be seen for FENIKS-COS352-11539, which shows a truncation of the P(z), narrowing the range of potential redshift solutions. Considering the results of the simulations in Section 3, the limited improvement in precision is likely driven by three factors. Firstly, the galaxy SED shape impacts the P(z) significantly (as seen in simulations in Sections 3.1 and 3.2). Most of the massive galaxies identified have at least some rest-frame UV flux, corresponding to a detectable Lyman-break, which substantially constrains the P(z) to $z>4$, even in the absence of the $K$-split filters. Secondly, the relatively low SNR ($\lesssim$ 5) of the $K$-split pilot survey photometry limits the constraints on the P(z) for these faint galaxies. In particular this is seen for FENIKS-COS352-13117, which has low rest-frame UV flux but also low SNR for the $K$-split photometry. Lastly the redshift range for the galaxies with lower rest-frame UV flux are at redshift ranges where the $K$-split filters have less of an impact ($z\lesssim 4.3$), consistent with the simulations. This highlights the serendipity of our selected galaxies and the potential field-to-field variability contributing to a lack of decisive contribution to the P(z). For example, if a galaxy like FENIKS-COS352-13117 was present at a slightly higher redshift, the $K$-split filters would sample a brighter portion of the Balmer break, resulting in higher SNR measurements. As an additional check, we note that there are no galaxies in our catalogues with $z\textsubscript{phot}>4$ with $K_{\mathrm{blue}}$-$K_{\mathrm{red}}>0.4$ at $>3\sigma$ significance, which reinforces the idea that there are no galaxies for which the $K$-split filters would have had an impact in our observed pilot fields.

Any changes to the P(z) and/or the best-fit SED will have consequences for the derived physical properties, such as stellar mass and also rest-frame colors typically used to select quiescent galaxies. Given the limited change to both the P(z) and best-fit SED from the added $K$-split filters, these quantities do not change significantly for the selected 12 massive galaxies in the FENIKS survey catalogue. The analysis below on quiescent galaxies in the FENIKS survey use the P(z) and physical properties derived using the $K$-split filters (as outlined in Section 4.4).

To determine which of our sample are quiescent we looked at both a sSFR selection and a UVJ selection³³3It is noted here that the rest-frame J band beyond $z\sim 4$ are based on the best-fit EAzY template from limited photometric sampling. using rest-frame colors determined with EAzY. The UVJ selection is a rest-frame color selection which allows separation of quiescent galaxies from dust-reddened star-forming galaxies (Patel et al., 2011). While UVJ selection has been demonstrated to be successful in identifying high-redshift quiescent galaxies, it has also been shown to exclude recently quenched galaxies with younger ages and bluer UV colors (as in Schreiber et al., 2018). sSFR selection can therefore be a useful comparison with the caveat that the SFR can be sensitive to the chosen SFH model (see Merlin et al., 2018; Carnall et al., 2019). In our analysis, we test this sensitivity by deriving SFRs based on the rest-frame UV flux of the EAzY best-fit SED. As the EAzY templates are based on empirically derived SEDs, both UVJ colors and rest-frame UV derived SFR are independent of SFH model assumptions. Additionally rest-frame UV SFR are more sensitive to recent SF events of order 10-30 Myr as opposed to parametric SFH models which are implicitly assessed over larger timescales $\gtrsim$ 100 Myr. For UV SFRs, it is important to ensure the best-fit SED represents the observed photometry. This is generally not an issue due to the flexible nature of EAzY fitting which uses linear combinations of many templates to determine best-fit SEDs.

The result of the quiescent search for our galaxy sample is that we identify four galaxies that are UVJ quiescent selected and three galaxies that have sSFR$<0.05$ Gyr^-1, two of which are not selected by the UVJ cut. Fig. 10 shows the UVJ plot for our galaxy sample. The two low sSFR galaxies that do not make the UVJ selection have bluer rest-frame U-V colors (0.6-0.9), young ages (0.1-0.2 Gyr) and are likely recently quenched galaxies similar to those identified in Schreiber et al. (2018), and also seen in Marsan et al. (2015). Inspecting their SEDs show these galaxies exhibit substantial star-formation. To further investigate their SFR, we calculate the rest-frame 1500 Å flux using EAzY (with errors based on 16th and 84th percentiles the rest-frame flux) and the scaling relation for SFR_UV from Madau & Dickinson (2014). It is noted that these SFRs are not corrected for dust extinction and so represent lower limits. Rest-frame SFR_UV indicate that the recently quenched galaxies exhibit more substantial star-formation that would exclude them for the sSFR$<0.05$ Gyr^-1 selection and are therefore not considered as quiescent. The quiescent sample reported here is therefore the UVJ selected sample, which represents 33$\%$ of the total massive galaxy sample.

Inspecting the SEDs of the UVJ selected quiescent galaxies show that all of them have some indication of residual star-formation (albeit at lower levels compared to the sSFR selected galaxies). Again calculating their rest-frame UV SFR, the galaxies indicate low SFR with an average of 5$\pm$1 M_⊙yr^-1. UV slopes, $\beta$, are fitted using the $F_{\lambda}\propto\lambda^{\beta}$ using a similar approach with rest-frame filters sampling 1500 Å-2500 Å wavelength range. The average UV slope for the UVJ selected galaxies is $\beta$=$-1\pm$0.3, consistent with moderate far-UV attenuation ($A_{1500}$ $\sim$ 2.5 or a factor 10) based on the A${}_{FUV}-\beta$ relation (Noll & Pierini, 2005), corresponding to A_V = 1.0 for a Calzetti (2001) attenuation law. Therefore the ongoing SFRs could be an order of magnitude higher.

The combination of the physical properties of these galaxies, i.e. high stellar masses, log($M*/M_{\odot}$) $=11.2$, and old stellar populations of 1 Gyr, low dust attenuation and relatively low SFR indicate these galaxies are moving off the star-formation main sequence. Taken at face value, the very low $<$sSFR$>$ $\simeq$ 0.03-0.3 Gyr^-1 values are well below ($5-50\times$) the star-forming main sequence at $z=4$ of sSFR = 1.5 Gyr ^-1 (see Schreiber et al., 2018), consistent with being a post starburst galaxy. It is possible that significant star-formation could be dust obscured. Sub-millimeter data, such as those from ALMA are capable of making direct constraints on the dust obscured SFRs (e.g., Schreiber et al., 2018; Santini et al., 2019), however an archival search for our quiescent galaxy sample showed no coverage was available. Further study of them could potentially provide clues to the causes for quiescence in massive galaxies and will be addressed in an upcoming paper (Esdaile in prep).

Finally, the number of massive quiescent galaxies encountered in our pilot survey are consistent with the range of GSMFs shown in Fig 8, including a no redshift evolution of the $3<z<4$ passive GSMF in Muzzin et al. (2013) and the Caputi et al. (2015) and Grazian et al. (2015) GSMF assuming a 15$\%$ quiescent fraction. The significance of these agreements however are low considering small number statistics, field-to-field variation, and the potential dust obscured star-formation present in the UVJ selected galaxies.

The F2 medium $K$-split filters also have the ability to select emission line galaxies at $z>2$ (H$\alpha$ and [NII] emission $2<z<2.8$ and [OIII] at $3<z<4$). The $K$-split filters are spaced such that they are able to measure the boosted flux of emission lines in one filter but not the other. A $|K_{\mathrm{blue}}$-$K_{\mathrm{red}}|$ = 0.5 mag corresponds to very strong line equivalent widths of 350-400 Å (Marmol-Queralto et al., 2015). We made a selection of $|K_{\mathrm{blue}}$-$K_{\mathrm{red}}|>0.3$ mag and identified potential emission line galaxies, a sample of which are shown in Fig. 11. These galaxies include examples of [OII] and H$\alpha$ and [NII] emission lines boosting either $K_{\mathrm{blue}}$ or $K_{\mathrm{red}}$. The bottom left panel of Fig. 11 shows a galaxy with the $K_{\mathrm{blue}}$ filter 1 magnitude above the best-fit SED continuum flux, which corresponds to an H$\alpha$ equivalent width (EW) of $\sim$ 1000 Å (or 600 $M_{\odot}$ yr^-1). Based on the H$\alpha$ flux, this galaxy has six times the star formation rate compared to the star formation main-sequence at this epoch and stellar mass (similar galaxies were also identified by Santini et al., 2017; Tran et al., 2020).

To see the impact of the $K$-split filters on spectroscopically confirmed galaxies, we use spectroscopic redshifts from the existing legacy catalogues and supplement with more recent spectroscopic surveys from VANDELS (McLure et al., 2018) and 3D-HST (Momcheva et al., 2016; Brammer et al., 2012). While there is no overlap with our COSMOS fields, there is good coverage in our CDFS field with over 100, $z>2$ spectroscopic redshifts (using only the highest quality flags). The agreement of spectroscopic redshift and photometric redshift is good with an NMAD scatter in $|z_{\mathrm{spec}}-z_{\mathrm{phot}}|$ / $(1+z_{\mathrm{spec}})$ of $\sigma_{\textsubscript{NMAD}}$ = 0.022 at $z>2$, consistent with the ZFOURGE results. There are also a handful of strong $K_{\mathrm{blue}}$ - $K_{\mathrm{red}}$ color signatures that are consistent with spectroscopic redshifts as in the upper right panel of Fig. 11, which suggests the H$\alpha$ boosted $K_{\mathrm{blue}}$ is physical and not just from measurement scatter. While the photometric redshift is generally consistent with the legacy catalogues, strong color signatures can have decisive impacts on the photometric redshift precision. For example, there is boosting of both $K_{\mathrm{blue}}$ and $K_{s}$ but not $K_{\mathrm{red}}$, in the SED shown in the lower left panel of Fig. 11. There are also instances where the $K_{\mathrm{blue}}$ - $K_{\mathrm{red}}$ color signature highlights one of the only distinct spectral features, such as in the lower right panel of Fig. 11. This galaxy in particular has a dust extinction of A_V = 2.0 mag and therefore rest-frame UV features are significantly suppressed, making photometric redshifts difficult to determine. The $K$-split filters have an impact in this case increasing the photometric redshift precision $\sigma_{\textsubscript{NMAD}}$ from 0.08 to 0.05 (similar improvement to what was seen in the simulations shown in section 3.1).