The galaxy population in the Hubble Frontier Fields and CLASH surveys: The LF and further evidence for a smooth decline in UV luminosity density at
We present the results of a search for galaxies within the first 8 pointings of the Hubble Frontier Fields (HFF) survey (4 clusters plus 4 parallel fields) and 20 cluster fields from the CLASH survey. Combined with our previous analysis of the Hubble Ultra-Deep field (HUDF), we have now completed a search for galaxies over arcmin, spread across 29 HST WFC3/IR pointings. As in our recent study of the first two HFF fields, we confine our primary search for high-redshift candidates in the HFF imaging to the uniformly deep (i.e. AB mag in 0.5-arcsec diameter apertures), relatively low magnification regions. In the CLASH fields our search was confined to uniformly deep regions where AB mag. Our spectral energy distribution fitting analysis unveils a sample of 33 galaxy candidates at , five of which have primary photometric redshift solutions in the range . By calculating a de-lensed effective volume for each candidate, the improved statistics and reduced cosmic variance provided by our new sample allows a more accurate determination of the UV-selected galaxy luminosity function (LF) at . Our new results strengthen our previous conclusion that the LF appears to evolve smoothly from to , an evolution which can be equally well modelled by a factor of drop in density, or a dimming of mag in . Moreover, based on our new sample, we are able to place initial constraints on the LF, finding that the number density at is , a factor of lower than at . Finally, we use our new results to re-visit the issue of the decline in UV luminosity density () at . We conclude that the data continue to support a smooth decline in over the redshift interval , in agreement with simple models of early galaxy evolution driven by the growth in the underlying dark matter halo mass function.
keywords:galaxies: high-redshift - galaxies: evolution - galaxies: formation
Our understanding of cosmic history within the first billion years after the Big Bang has improved dramatically in recent times, largely thanks to the near-infrared capabilities of the Hubble Space Telescope (HST) as realised through Wide Field Camera 3 (WFC3/IR). It has now become relatively routine to assemble catalogues of galaxies out to , either via colour-colour selection or spectral energy distribution (SED) fitting (e.g. McLure et al. 2010, 2011; Bouwens et al. 2011; review by Dunlop 2013), with the current frontier of observations now at (e.g. McLure et al. 2013; Oesch et al. 2014; McLeod et al. 2015; Bouwens et al. 2015).
An important measure of the evolution of the high-redshift galaxy population is the UV-selected galaxy luminosity function (LF). To determine the form and evolution of the UV galaxy LF, it is crucial to establish a wide baseline in UV luminosity, and this can now be achieved by combining the ultra-deep imaging provided by the Hubble Ultra Deep Field (HUDF) with the shallower, wider data of the CANDELS fields, and the still wider, shallower ground-based imaging obtained in the UKIDSS Ultra Deep Survey (UDS) and UltraVista/COSMOS fields (McCracken et al. 2012; Bowler et al. 2012, 2014, 2015). Other surveys, such as the pure-parallel HST BoRG survey (Trenti et al. 2011) also provide the opportunity to study the bright end of the LF at high redshift via multiple, shallow, pencil-beam pointings. The LF at redshift has been the subject of numerous studies in the recent literature, and is now largely well-understood at magnitudes fainter than (see McLure et al. 2013; Finkelstein et al. 2014; Bowler et al. 2014, 2015; Bouwens et al. 2015).
By integrating the luminosity-weighted LF, one arrives at the UV luminosity density (), which can then be converted into a star-formation rate density (; see Kennicutt & Evans 2012). As expected, given the agreement in the form of the faint end of the LF, the determinations of are in general concordance out to . Due to observational constraints, the determination of these quantities at even earlier epochs is challenging, and different studies have reached different conclusions.
The first meaningful study of the galaxy population was undertaken by Ellis et al. (2013) and McLure et al. (2013), based on the small sample of galaxies uncovered within the HUDF12 dataset (which featured the key ultra-deep imaging necessary to identify robust galaxy candidates; Koekemoer et al. 2013). Based on this sample, Ellis et al. (2013) concluded that the decline in beyond continued relatively smoothly beyond , indicative of a gentle decline of star-formation rate density back to earlier epochs, as naturally required to consistently explain cosmic reionization and recent constraints on Thomson scattering optical depth delivered by WMAP and Planck (e.g. Robertson et al. 2013, 2015). However, in contrast, Oesch et al. (2014) conclude that marks the onset of a dramatic fall-off in , at which the decline of luminosity density switches suddenly from , to a much more rapid .
To resolve this disagreement, what is required is more deep near-infrared imaging, including the crucial WFC3/IR filter, and ideally involving many different sightlines to minimize the uncertainty introduced by cosmic variance. Such imaging is now being delivered by the Hubble Frontier Fields (HFF) programme, from which the HST WFC3/IR imaging has now been released for four clusters and their corresponding parallel fields. The HFF programme has already proven to be instrumental in furthering our knowledge of galaxies in the young Universe, with a number of studies already published on high-redshift galaxy populations (e.g. Zheng et al. 2014; Zitrin et al. 2014; Atek et al. 2015; Ishigaki et al. 2015). One of the primary aims of the HFF survey is to exploit the gravitational lensing provided by the cluster fields to aid the discovery and study of faint galaxies at high redshift. However, as discussed in McLeod et al. (2015) and further below, the parallel pointings are arguably more powerful than the cluster pointings for advancing our knowledge of the galaxy UV LF at extreme redshifts.
In McLeod et al. (2015) we analysed the imaging from the first two HFF cluster+parallel pointings to derive improved constraints on the LF and revisit the issue of the decline in at . We uncovered twelve galaxies in the redshift range from within the area covered by these four WFC3/IR pointings, enabling us to place the best constraints to date on the evolution of the LF from to . Our main finding was that the decline in beyond was smooth and relatively modest, with falling off much less steeply than as claimed by Oesch et al. (2014). Indeed we found that the decline of from to could be well described by a simple linear function of redshift, extrapolation of which to agreed with the (albeit highly uncertain) determination of Oesch et al. (2014).
However, we are still in the regime of small number statistics at , and more data are still required to resolve this important issue. We thus here present a new study of galaxy evolution beyond which improves on that presented in McLeod et al. (2015) in several respects. Firstly, the available HFF dataset has now been doubled by the release of the imaging of the third and fourth cluster and parallel fields (i.e. of MACS0717 and MACS1149), and we have now extended our search for galaxies to include these new WFC3/IR pointings. Secondly, while our most robust results transpire to be driven primarily by the homogeneous survey area provided by the HFF parallel fields, we have also undertaken a thorough analysis of more strongly lensed regions of the imaging, and in particular have utilised this approach to search for galaxies in twenty fields from the CLASH survey. Finally, we have now also searched both the HFF and CLASH datasets for galaxies at .
As important as lensed fields are for searching for the earliest galaxies, especially intrinsically faint objects, extracting robust quantitative information on high-redshift galaxy evolution from gravitationally lensed fields is challenging and often problematic. A number of groups have provided lensing maps for each of the HFF clusters, and similarly Zitrin et al. (2013) have provided two alternative lensing maps for all of the CLASH fields. Unfortunately, the magnifications predicted by the different models are often significantly different, and these discrepancies are often particularly severe in the high magnification regions around the critical lines. This does not just affect the individual candidates in a sample, but also the effective selection volume that one derives for a particular lensed field. Due to these effects, a determination of the LF from a strongly lensed field can be drastically wrong unless the lensing uncertainties can be controlled. Finally, the intracluster light often significantly reduces the effective photometric depth for much of the on-cluster image unless it can be reliably removed.
Due to these issues, in McLeod et al. (2015) we decided to focus our attention on the clean, homogeneously deep regions of the imaging in the Abell2744 and MACS0416 fields. While this approach reduced the available search area somewhat, it crucially allowed us to derive well-defined samples from robust cosmological volumes determined from regions of the imaging with negligible or low/well-constrained magnification factors (). In the new study presented here, we have retained this deliberately conservative approach to derive our most robust new determination of the LF, now based on applying this method to all eight available HFF pointings.
However, in an attempt to exploit all the available deep imaging, in this study we have supplemented the eight HFF pointings with a search for galaxies in the CLASH survey (Postman et al. 2012). Although the WFC3/IR imaging of the CLASH clusters is significantly shallower than the HFF imaging, the effective depth of much of the lensed CLASH imaging is comparable to the depth of the unlensed imaging in the HFF parallel fields. Notwithstanding the aforementioned concerns about uncertain lensing magnifications, an attraction of incorporating the CLASH imaging is that it provides a large number of widely separated pointings on the sky, potentially reducing the impact of cosmic variance (see Trenti & Stiavelli 2008).
This paper is structured as follows. In Section 2 we discuss the HFF and CLASH imaging data, and provide a brief description of the selection of our high-redshift galaxy candidates. This includes a discussion of how we have used deconfused longer-wavelength photometry from Spitzer IRAC imaging to aid in cleaning our sample of potential low-redshift contaminants. In Section 3, we present and discuss our final sample of galaxies and summarise their basic properties. In Section 4 we present our new, updated determination of the LF from the blank-field method, (i.e. constraining galaxy selection to the cleanest, homogeneous regions of the imaging). In Section 5 we extend our analysis to derive the lensed-field LF determination at , and to provide new constraints on the LF at . Finally, in Section 6 we present our new and improved measurement of the early rise of , and compare our results to a range of theoretical predictions. Our conclusions are summarised in Section 7.
Throughout the paper we will refer to the following HST ACS+WFC3/IR filters: F435W, F475W, F555W, F606W, F625W, F775W, F814W, F850LP, F105W, F110W, F125W, F140W & F160W as , , , , , , , , , , , & respectively. All magnitudes are quoted in the AB system (Oke 1974; Oke & Gunn 1983). For cosmological calculations, we adopt and kmsMpc.
2 Data and Candidate Selection
2.1.1 Hubble Frontier Fields
In this section we review the optical, near-IR and mid-IR data used in this study. From the HFF survey we utilised the first four clusters and their corresponding parallel fields. For each of these, HST imaging was carried out in three ACS wavebands (, , ) and four WFC3/IR wavebands (, , , ). Global depths for each of the images were calculated from apertures corrected to enclose 85% of the total flux, assuming a point source. In the parallel fields, the median depths in this format were =28.8, =28.8, =28.9, =28.9, =28.4, =28.3 and =28.2. Note that the MACS0717 parallel field was typically magnitudes shallower than these values, due to a higher background level. The HFF cluster fields were also typically shallower than these depths due to source crowding and intracluster light. In the ‘clean’ regions of the cluster imaging the depths are similar to those of the parallel fields.
For the first two cluster/parallel fields, Abell2744 and MACS0416, HAWK-I data at m (PI Brammer, ESO Programme ID 092.A-0472) was available. For a 1 diameter aperture, enclosing 75% of total flux, the depth in was typically 25.6 mag. All eight HFF fields had Spitzer Space Telescope Infrared Array Camera (IRAC) imaging (PI Soifer111Program IDs: 90257, 90258, 90259 and 90260.) available in channel 1 (m) and channel 2 (m). This data typically reaches a depth of 24.5 mag (at 85% of total), although this is specific to the cleaner parallel regions and is subject to the ability to perform effective deconfusion (see Section 2.4).
From the CLASH survey we analysed 23 of the 25 available fields, omitting those which did not have any archival IRAC imaging (Abell1423 and CLJ1226) to avoid having any candidates for which there was no available long-wavelength photometry to check for low-redshift contamination. No public -band imaging was available for the CLASH fields. Three of the CLASH fields are also HFF fields, and so our final sample only exploits the superior HFF data for these clusters. The CLASH imaging of these clusters was however still analysed in the same manner, and used in order to check for consistency. Our final analysis of the CLASH candidates is therefore confined to the twenty fields unique to the CLASH survey and with IRAC imaging.
The CLASH imaging used in this study consisted primarily of the optical bands , , , , , and near-infrared wavebands , , , and , although some CLASH fields have also been imaged in and . The median 5 global depths (at 85% of total assuming a point source) across the CLASH fields were found to be =26.8, =27.1, =27.5, =27.4, =26.8, =26.6, =27.1, =26.2, =26.8, =26.9, =26.7, =26.7 and =26.5, although in practice there are again significant variations in depth due to varying levels of source crowding and intracluster light. The IRAC imaging222Program IDs: 90009, 80168, 40652, 60034, 545 and 50393. used was in the m and m filters, with a 5 median depth for both channels of 23.9 mag (at 85% point-source flux). However, the range of depths varied between 22.5 and 24.2 mag. The CLASH survey also features WFC3/UVIS imaging in the F225W, F275W, F336W and F390W bands. This data was not included in our SED fitting analysis because the UVIS imaging is significantly shallower than the ACS data. Nevertheless, in compiling the final candidate list, the UVIS imaging was inspected as an extra check against possible contamination by low-redshift interlopers in the sample.
In total, the raw search area provided by the eight HFF pointings, the HUDF and the twenty CLASH pointings totals 130 arcmin.
2.2 Photometric catalogues
For each of the survey fields, initial photometric catalogues were constructed by running SExtractor 2.8.6 (Bertin & Arnouts 1996) in dual-image mode, using each of the WFC3/IR images longward of the Lyman break at as detection images. Additionally, stacks of the relevant near-IR imaging (, & ) were also used as detection images, in order to boost the sensitivity to objects.
Every object detected at in each catalogue was retained, and a master catalogue was produced containing every unique object from all of the detection catalogues. For each object, the highest signal-to-noise detection was propagated to the final catalogue. Given the position of the redshifted Lyman break, it is expected that no candidate would be detected in the optical bands, and so candidates were required to be undetected at the level in every filter shortward of . Various stacks of the optical photometry were also produced in order to further ensure that candidates were robustly undetected shortward of .
The photometry was measured in 0.4 diameter apertures in the ACS and filters and in 0.44, 0.44, 0.47 and 0.5 apertures for the , , and imaging respectively. This ensures 70% of point-source flux is included in the near-IR bands and 80-85% of point-source flux in the ACS bands. All fluxes were then corrected to a uniform 85% of total point-source flux for the purposes of SED fitting.
2.3 Local depth analysis
Accurate photometric errors are crucial for obtaining a robust sample of high-redshift galaxies. Firstly, they are used in the optical flux cuts to remove possible low-redshift contaminants, and in the detection band magnitude cut to remove objects that are too faint. Secondly, the SED fitting requires robust photometric errors in order to produce accurate photometric redshifts. Every lensed field in this study is subject to significant variations in the background and depth across the image, which is exacerbated by source crowding and intracluster light. Although less of an issue in the parallel fields, even here there are still slight variations in the depth. Following McLeod et al. (2015), local aperture-to-aperture rms depths were calculated for every object in the photometric catalogues, based on large grids of apertures placed on blank sky regions. Based on the rms of the closest 150–200 apertures it was possible to calculate a robust local depth for every object, in every filter. These aperture-to-aperture rms measurements are more accurate in capturing the various systematics than the drizzled rms maps supplied with the data.
By calculating the estimated local depth across the fields, detailed depth maps were produced for each HFF and CLASH field. The depth maps for the new MACS0717 and MACS1149 images and their respective parallel fields are shown in Fig. 1, and illustrate the reduced depth in the central regions of the galaxy clusters. It is notable how severe this is for the MACS0717 cluster field, for which the WFC3/IR imaging is positioned such that the field-of-view is almost completely filled by the cluster. Due to the presence of a bright star and multiple large bright foreground galaxies, the MACS0717 parallel image also suffers a significant loss of useful survey area compared to the other HFF parallel images.
2.4 Longer wavelength photometry
In this study we include, where available, VLT HAWK-I and Spitzer IRAC m and m data. This is primarily to guard against low-redshift interlopers contaminating our galaxy sample. As discussed in McLeod et al. (2015), secondary photometric redshift solutions typically correspond to significantly reddened galaxies, or galaxies at with quiescent stellar populations. With the added longer-wavelength photometry, these alternative redshift solutions can usually be robustly excluded or confirmed. Even though the available imaging is significantly shallower than the shorter-wavelength HST imaging, non-detections can be vital in this process.
Obtaining accurate photometry in the IRAC bands is notoriously difficult given the (relatively) low spatial resolution and the resulting heavy blending of objects in deep imaging. In this study we therefore employed the deconfusion code tphot (Merlin et al. 2015) in order to extract IRAC and band photometry. In brief, this code utilizes the positional and surface-brightness information of galaxies detected in a high spatial resolution image (HRI) to produce a model of the corresponding low spatial resolution image (LRI). Two dimensional galaxy templates are extracted from the HRI and convolved with a transfer kernel to match the resolution of the LRI. These low-resolution templates are then used to produce a best-fitting model of the LRI image, in which the flux of each template is fit simultaneously. In this study we used the ++ stack as the HRI prior image because it provides the highest signal-to-noise ratio templates for objects. Full details of the tphot algorithm can be found in Merlin et al. (2015).
2.5 Photometric redshifts
Once the catalogue was culled of potential low-redshift objects with 2 optical detections, a photometric redshift analysis was performed. For this the SED template fitting code LePhare333www.cfht.hawaii.edu/ arnouts/LEPHARE/lephare.html (Arnouts & Ilbert 2011) was used. The SED template library was based on the models of Bruzual & Charlot 2003 (BC03), utilising IGM absorption according to the prescription by Madau (1995) and a Calzetti (2000) dust extinction law (allowing reddening to range up to ). This conservative set of parameters allows highly-reddened low-redshift solutions to be considered in addition to any potential high-redshift solution (Dunlop et al. 2007).
Photometric redshift determinations were performed with and without the and IRAC photometry. Objects that had a high-redshift () primary solution in both runs were retained. Such objects were then visually inspected in all images to check that they were real, and that they were not marginally detected in any optical image or optical image stack. Although the inclusion of -band and IRAC fluxes helped distinguish between low and high-redshift solutions, in practice the primary photometric redshift of the high-redshift candidates was generally unaffected by the exclusion or inclusion of the long-wavelength data. This is as expected, given that the derived value of at high-redshift is primarily driven by the position of the Lyman break.
3 High-redshift Galaxy candidates
In this section we list all of the robust galaxy candidates that were found in our search of the CLASH and HFF datasets. The basic measured and derived properties of the galaxies in the final sample are provided in Tables 1 & 2. First we discuss the HFF candidates, including those from the two new data releases. We then discuss the candidates found in the twenty CLASH fields analysed in this study. For a more detailed comparison with previous searches in the first two HFF datasets, the reader is referred to McLeod et al. (2015).
3.1 HFF: Abell 2744 and MACS0416.1-2403 cluster and parallel fields
In McLeod et al. (2015) we found twelve galaxies in the redshift range in the cluster and parallel fields of Abell2744 and MACS0416. However, the IRAC photometry was not included in the SED fitting performed in McLeod et al. (2015). A re-analysis of these fields using both and IRAC data recovers all of these galaxies in the redshift range of interest. Notably, one extra candidate is included from the MACS0416 parallel field. HFF2P-9-5 was found in the McLeod et al. (2015) study, but was deemed too insecure to be included in the final sample. However, thanks to the inclusion of the longer wavelength IRAC photometry, this candidate now has a secure primary redshift solution of =.
3.2 HFF: MACS J0717.5+3745 cluster and parallel fields
The imaging of the MACS J0717.5+3745 field constituted the third data release from the HFF programme. A study of the cluster field by Kawamata et al. (2015) produced no galaxy candidates. Most recently, a study of the cluster and parallel field by Laporte et al. (2016) also revealed no candidates. Our new, independent, analysis also reveals no credible galaxy candidates in either the cluster or the parallel field. As noted previously, the effective area of the MACS0717 cluster field is much lower than that of the other HFF fields, due to severe source crowding which reduces the depth over much of the image.
3.3 HFF: MACS J1149+2223 cluster and parallel fields
The MACS J1149+2223 cluster field was previously studied as part of the CLASH programme and yielded one robust galaxy candidate, which was identified in the analysis of both Zheng et al. (2012) and Bouwens et al. (2014). In their more recent analysis of the much deeper HFF imaging of the MACS1149 cluster field, Kawamata et al. (2015) identified four candidates, one of which was the original object identified from the CLASH dataset.
Our analysis of the MACS1149 cluster field has identified two galaxy candidates. The first (HFF4C-9-1, ) is the original CLASH candidate and the second (HFF4C-9-2, ) is a candidate which also identified by Kawamata et al. (2015). Consequently, there are two candidates identified by Kawamata et al. (2015) in the MACS1149 cluster field which do not feature in our final sample. The first of these (HFF4C-Y2 in Kawamata et al.) is included in our original catalogues, but is located in a region of the HFF imaging which is too shallow to be included in our blank-field search area. Our primary photometric redshift solution for this object is . However, the very flat distribution means that we cannot rule-out the possibility that this object is at high redshift. We cannot rule-out the possibility that the second object (HFF4C-YJ4) is at high redshift either. This object does not feature in our final high signal-to-noise catalogues, simply because it lies close to the cluster core in a region of shallow depth and large (but uncertain) magnification.
Our analysis of the HFF imaging of the MACS1149 parallel field identifies two new candidates; HFF4P-9-1 at and HFF4P-10-1 at . To date, there are no other analyses of the HFF imaging of the MACS1149 parallel field in the literature.
3.4 The CLASH survey
In their study of the CLASH dataset, Bouwens et al. (2014) found a single candidate in each of MACS1115 and MACS1720 clusters. Our new analysis of the CLASH dataset has produced a final sample of 15 galaxy candidates in the redshift range , including the two candidates previously identified by Bouwens et al. (2014).
Of the thirteen candidates in our final sample which were not identified by Bouwens et al. (2014), four have been selected from CLASH clusters which were not analysed by Bouwens et al. (2014). The remaining nine objects either have colours which just fail to satisfy the Bouwens et al. selection criteria, or have photometric redshifts outside the range where the Bouwens et al. colour-colour selection is designed to operate.
We note that our final CLASH sample features one object at (M0647-11-1). This object was first discovered by Coe et al. (2013) as JD1. In that study, Coe et al. identified two possible counter images of this object; JD2 and JD3. Based on our photometry, we could not confirm the high-redshift solution for JD2, and so it is not included here. Our SED fitting analysis of JD3 produces a primary high-redshift solution at and this object is listed in Table 2 as M0647-10-1.
|HFF1C-9-1||00:14:24.93||30:22:56.15||8.4||26.75||1.5||27.2||19.9||4, 5, 6, 7|
|HFF4C-9-1||11:49:33.59||22:24:45.76||9.3||25.58||8.7||27.9||19.4||1, 3, 8|
4 The Luminosity Function at z=9: Blank Field Method
4.1 Effective search area
By analysing the local depth maps, object selection and effective survey area can be usefully confined to only the cleanest and deepest regions of the HST imaging. As in McLeod et al. (2015), we refer to this as the “blank field” method for determining the LF. For the HFF the depth cut was chosen to be 28.0 mag in (at 85% of total assuming point-source), as in McLeod et al. (2015), again meaning that we focus on regions where mag (or deeper) in a 0.5 diameter aperture. For the CLASH fields the cut-off was at 85% of total.
In addition to imaging depth, one also has to consider the reduction in effective area produced by factoring in the magnification maps. For the HFF fields analysed here, we have employed the CATS (Richard et al. 2014) and Zitrin LTM (Zitrin et al. 2013) lensing maps. For the CLASH fields, two lensing maps have been publicly released, the NFW and LTM-gauss (LTMG) models by Zitrin et al. (2013), and so the analysis was done using those. In Fig. 4, we plot the effective de-lensed area of our combined CLASH imaging as a function of the survey depth for the lensing models adopted.
The lensing maps were also used to calculate the magnification of each candidate. For each map, the magnification was based on the average model magnification within a 0.5 diameter aperture around each object. For this blank-field method, the magnification factor was taken as the average of the different model values, with the extremes as the error bounds.
Using the aforementioned magnitude cuts, the delensed areas found were 20.4 arcmin (NFW) and 14.5 arcmin (LTMG) for CLASH, with 18.6 arcmin for HFF. For the latter, the area is completely dominated by the parallel fields, which together contribute around 16.5 arcmin of effective survey area. The area adopted for the HFF clusters was the average area from the two lensing maps used.
Completeness was calculated following the prescription described in McLure et al. (2013). Simulations in which sources were injected into the imaging and recovered were performed in order to find the completeness as a function of magnitude. The interested reader is referred to McLeod et al. (2015) for more details.
4.2 The luminosity function
Using the blank-field sample, we are now in a position to better constrain the UV LF at this epoch. We find that none of the CLASH objects contribute to any LF determination in the blank field approach. This is is because they either lie in regions of the imaging that are shallower than the adopted cut-off limit or, when de-magnified, they are intrinsically too faint to be detected if the field is assumed to be a blank one. Incompleteness prevents us from including the fainter, , galaxies uncovered in the HFF pointings, but we can extend our study to fainter magnitudes by combining our new HFF results with the HUDF12 results at derived by McLure et al. (2013). This results in four luminosity bins at , spanning the absolute magnitude range . Finally, we did not find any galaxies brighter than in our search of CLASH and the HFF datasets, and therefore derive an upper limit at at this magnitude (corresponding to a single object in the CLASH+HFF+HUDF volume searched).
These new results are presented in Fig. 5, which shows the UV LF as determined by restricting our analysis to the clean regions of the HFF and HUDF imaging, covering an area of 22 arcmin. The fainter two bins come from an area of 4 arcmin provided by the HUDF alone. The upper limit at the bright end is derived from the unsuccessful search for candidates brighter than within a total area of arcmin from the CLASH, HFF and HUDF imaging which reached 5 depths greater than 26.8 mag.
As also shown in Fig. 5, we have fitted a Schechter function (Schechter 1976) to the data. Because the data at still do not provide enough accuracy and/or dynamic range to allow a robust measurement of the faint-end slope, during the fitting this was held fixed at the value of , as determined by McLure et al. (2013). We also cannot yet distinguish whether density or luminosity evolution better describes the evolution of the LF from to , finding that the LF can be well described either by a drop in density by a factor to (for a fixed ), or by a dimming of the characteristic magnitude by magnitudes to (for a fixed ). These two alternative Schechter function fits at are both shown in Fig. 5, and are essentially indistinguishable from the LF fits derived and presented by McLeod et al. (2015).
As previously mentioned, these results are derived by adopting the average magnifications of the two alternative lensing models available for the new HFF fields. However, it can be seen from Fig. 4 that there is very little difference in the derived effective survey area between the different HFF lensing models for objects at our adopted blank-field magnitude limit.
5 The Luminosity Function at : Lensed Field Method
5.1 Lensed areas
By adopting the blank field method, none of our high-redshift candidates from the CLASH fields feature in the LF determination. To be as inclusive of our CLASH candidates as possible, we attempted to derive a luminosity function using the full available area of the CLASH survey, including the more highly-lensed regions. This comes with the risk of introducing biases in any derived number densities, due to uncertainties in the magnifications. As the majority of the CLASH candidates have come from a stacked image, the analysis was carried out on a stacked image for all fields. For each object, the delensed flux is compared to the delensed depth map of every cluster field. Any pixels that are of sufficient depth that the object would be detectable at 5 in the stack contributed to the total available cosmological volume. Subject to a completeness correction, we are then left with the effective volume contribution of each candidate in the sample. The magnification models were treated entirely separately when calculating magnification values and effective volumes. The delensed area-magnitude plots shown in Fig. 6 illustrate how this modifies the effective area calculations.
5.2 Lensed LF calculation
In Fig. 7 we present our alternative estimate of the LF based on the lensed CLASH galaxies. We plot two alternative LFs, corresponding to the two alternative lensing models. Comparing with the blank field LF determination derived earlier, it can be seen that the two methods are generally consistent. Although for the lensed case both models yield higher number densities in the fainter () bin, the results can all be comfortably reconciled through the large Poissonian uncertainties associated with such small number statistics. Due to the uncertainties between the models, we treat this alternative LF calculation simply as a consistency check. As the blank field LF determination is less systematically biased, we adopt this as the best estimate of the LF.
5.3 Extension to
As the vast majority of our candidates come from the CLASH fields (see Tables 1 and 2), the blank-field approach cannot yet be used to determine a meaningful estimate of galaxy number densities at . Adopting the full-area lensed approach, depending on the assumed lensing model, we have either five candidates (NFW model) or three candidates (LTMG model) that can be placed in an absolute magnitude bin centred at at . One of the candidates comes from the HFF (HFF4P-10-1), with the rest coming from the CLASH survey. The overall search area contribution from the HFF, and the number density contribution from the sole HFF candidate, were found to be very similar whatever magnification model was adopted, in part due to the dominance of the parallel fields. In the following we have adopted the CATS magnification model for the HFF data, but the result is very similar if we substitute this for the Zitrin et al. LTM model.
We present our resulting alternative estimates of galaxy comoving number density at in a single luminosity bin in Fig. 8. This figure also shows our results, as well as other recent comoving number densities derived at by Oesch et al. (2014). We have fitted a Schechter function through the average of our datapoints, again fixing at and assuming either pure or pure evolution (fixing the other parameter as appropriate). For density evolution, we find that evolves in a similar manner between and as between and , with a further inferred decrease of a factor to =3.90. For luminosity evolution, we find that the dims by 0.25 mag from to , to . Although it is clearly difficult to draw detailed conclusions from a single data point, the LF at appears to reflect a smooth extrapolation of the evolution found between and .
6 Evolution of luminosity density at
Given our improved measurement of the galaxy UV LF at , and our new estimate of the likely evolution to , we now revisit the evolution of UV luminosity density () at these early epochs. As discussed in the introduction, this is currently the subject of some debate and controversy, given the conclusion reached by several recent studies (e.g. Oesch et al. 2014; Bouwens et al. 2015), that there is a dramatic fall-off in at .
To facilitate comparison with these recent results, we perform the luminosity-weighted integration of the best-fitting Schechter functions shown in Fig. 8 (adopting the luminosity-evolved fits indicated by the dashed lines) down to a faint-end magnitude limit of . When performing this calculation we do not dust correct the data, meaning that we are deliberately calculating the observed UV luminosity density. However, it should be noted that at , dust correcting using standard techniques (i.e. based on the average UV slopes) has a negligible impact on the derived values of . As can be seen in Fig. 9, we find at , and at . We convert this into a comoving star-formation rate density, , by assuming the conversion of Madau, Pozetti and Dickinson (1998) and a Salpeter IMF, which yields at and at (as also shown in Fig. 9, reading from the right-hand axis).
It is clear from Fig. 9 that our new determinations lie between the two extreme alternative extrapolations of the evolution of beyond discussed by Oesch et al. (2014). Instead, our new results provide further support for the smooth decline of to high redshifts as deduced by McLeod et al. (2015), which can be reasonably described via a linear relation between and . With our new expanded dataset, the best fitting linear relation at is given by , and this is plotted as the red line in Fig. 9. Alternatively, if one wants to adopt a power-law relation in , then we find that also provides a good description of the decline in beyond .
Finally, it is interesting to compare our new observational estimate of the high-redshift evolution of with the predictions of recently-published models of galaxy evolution.
Our data-points are plotted against the predictions of seven such models in Fig. 10. It is important to acknowledge that some of these predictions are at least partly based on hydrodynamic simulations, while others are semi-analytic models, some of which have been effectively tuned to reproduce the UV LF at moderately high redshift (e.g. ). Thus, in a sense, this comparison is not completely fair, and cannot be simply regarded as specifically favouring one form of model over another. Nevertheless, some important general trends can be deduced. In particular, the Illustris (Genel et al. 2014) and Munich (Henriques et al. 2015) models, while clearly capable of reproducing many (often quite complex) aspects of galaxy evolution, both clearly under-predict at redshifts higher than . We stress that this discrepancy is already clear by (where the measured value of is well established) and is simply confirmed and strengthened by our new results at and . The challenge, then, for such models is to be able to produce star-formation activity which extends to higher redshifts than currently predicted. Indeed, the only model shown here that systematically over-predicts is that of Behroozi & Silk (2015). We note that the over-prediction of raw observed at redshifts by the Illustris and Khochfar et al. simulations is not really a fundamental problem, as both of these models do not include the impact of dust obscuration.
Although the Khochfar et al. simulation produces more star-formation rate density at higher redshift than either the Illustris or Munich models, the best predictions are produced by the fairly simple analytic models of Dayal et al. (2015), Cai et al. (2014) and Mason et al. (2015). This might be regarded as unsurprising given that, as mentioned above, these models are to some extent based on mappings between the dark matter halo mass function and the UV luminosity function that have been ‘calibrated’ at high redshift. Nevertheless, the fact that such models do such a good job in reproducing the rate of decline in from to is surely not a coincidence, and implies that galaxy evolution at these early times is indeed fairly simple, and driven primarily by the growth in the underlying dark matter.
As final evidence in support of this basic result, in Fig. 11 we compare our results with the generic analytic prediction of the high-redshift evolution of deduced by Hernquist & Springel (2003). As a result of an effort to understand the physical processes driving the cosmic star formation rate, Hernquist & Springel (2003) predicted that at high redshift, beyond its peak, should decline smoothly in a manner very well approximated by the simple relation . In other words, in the absence of significant dust obscuration, they predicted a linear descent of with , and predicted the slope of this relation based on the assumption that the evolution is driven simply by the growth of the underlying dark matter. In Fig. 11 we show our derived evolution of integrated down to (as previously plotted in Figs 9 and 10), but also show the results of integrating down by approximately another order-of-magnitude in luminosity, to . Interestingly, while the results based on the shallower integration can, as already shown in Fig. 9, be described by a linear relation between and , the slope of this relation is clearly steeper than predicted by Hernquist & Springel (2003). However, by simply integrating down to , to provide a more complete measurement of (especially at high redshift), it can be seen that the observed and predicted rate of decline of shift into excellent agreement.
In this study we have assembled the largest sample of galaxy candidates to date, identifying a total of 33 candidates in the redshift range from the HFF and CLASH datasets. When combined with four candidates identified from our previous analysis of the HUDF, our final sample consists of 37 galaxy candidates at selected from 29 independent WFC3/IR pointings (total area arcmin). Based on this sample we have produced an improved measurement of the UV-selected galaxy LF at and placed initial constraints on the LF at . In addition, we have revisited the issue of the decline in UV luminosity density at . Our main conclusions can be summarised as follows:
Employing an analysis restricted to the uniformly deep, and low magnification, regions of the HFF+HUDF datasets, we have derived an improved measurement of the UV-selected galaxy LF at . Based on this “blank field” method, our new results strengthen the evidence that the LF continues to evolve smoothly between and . Specifically, within this redshift interval, we find that the evolution of the LF can be equally well described by a 0.5 magnitude dimming in (pure luminosity evolution) or a factor of drop in (pure density evolution).
As a consistency check, we have also used the full lensed area of our CLASH survey dataset to derive an independent estimate of the LF. The determinations of the LF based on the blank-field and lensed samples are found to be fully consistent.
Using the combined CLASH+HFF+HUDF datasets we have derived initial constraints on the UV-selected galaxy LF at . We find that the number density of galaxies at is , a factor of lower than at .
Based on our new results we have revisited the issue of the decline in UV luminosity density at . We conclude that the data continue to support a smooth decline in over the interval , in agreement with simple models of galaxy evolution driven by the growth in the underlying dark matter halo mass function.
DJM and RJM acknowledge the support of the European Research Council via the award of a
Consolidator Grant (PI McLure). JSD acknowledges the support of the European Research Council via the award of an Advanced Grant,
and the contribution of the EC FP7 SPACE project ASTRODEEP (Ref. No.: 312725).
This work is based in part on observations made with the NASA/ESA Hubble Space Telescope, which is operated by the Association
of Universities for Research in Astronomy, Inc, under NASA contract NAS5-26555.
This work is also based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory,
California Institute of Technology under NASA contract 1407.
This work utilizes gravitational lensing models produced by PIs Bradač, Natarajan & Kneib (CATS), Merten & Zitrin, Sharon, and Williams funded as part of the HST Frontier Fields program conducted by STScI. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. The lens models were obtained from the Mikulski Archive for Space Telescopes (MAST). For CLASH we also used mass models constructed by A. Zitrin et al. (2013, 2015), obtained through the Hubble Space Telescope Archive, as a high-end science product.
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