Abstract
Ultra-faint galaxies are hosted by small dark matter halos with shallow gravitational potential wells, hence their star formation activity is more sensitive to feedback effects. The shape of the faint end of the high-z galaxy luminosity function (LF) contains important information on star formation and its interaction with the reionization process during the Epoch of Reionization. High-z galaxies with have only recently become accessible thanks to the Frontier Fields (FFs) survey combining deep HST imaging and the gravitational lensing effect. In this paper we investigate the faint end of the LF at redshift >5 using the data of FFs clusters Abell 2744 (A2744), MACSJ0416.1-2403 (M0416), MACSJ0717.5+3745 (M0717), and MACSJ1149.5+2223 (M1149). We analyze both an empirical and a physically motivated LF model to obtain constraints on a possible turnover of LF at faint magnitudes. In the empirical model the LF drops fast when the absolute UV magnitude is much larger than a turnover absolute UV magnitude . We obtain (15.2) at the 1 (2)
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1. Introduction
During the Epoch of Reionization (EoR, 6 ≲ z ≲ 30), the intergalactic medium (IGM) was gradually ionized by energetic photons mainly emitted by the first galaxies. This in turn led to the suppression of star formation in small galaxies, because their host halos hardly collect gas from ionized environment. This feedback effect raises the following questions. How faint could the first galaxies have been? Which halos could sustain star formation activity during the EoR?
According to the hierarchical structure formation scenario, smaller dark matter halos are much more common than larger ones in the universe, resulting in an overwhelming numerical abundance of very faint galaxies (Mason et al. 2015; Liu et al. 2016; Mashian et al. 2016; Finlator et al. 2017). Thereby, faint galaxies are promising candidates as main sources of reionizing photons (e.g., Bouwens et al. 2015a; Robertson et al. 2015; Castellano et al. 2016b), with a crucial contribution possibly coming from objects far below the detection limits of even the deepest existing surveys (Choudhury & Ferrara 2007; Choudhury et al. 2008; Salvaterra et al. 2011; Dayal et al. 2013; Robertson et al. 2013; Salvaterra et al. 2013). Moreover, faint galaxies are less clustered and their environment gas is less clumped, therefore they are more effective in reionizing the IGM.
To understand the role of star-forming galaxies in the reionization process, it is thus crucial to constrain their number density and star formation efficiency by studying the UV luminosity function (LF) down to the faintest limits. The faint end of the UV LF at high redshift has been found to have a steep slope at least down to absolute UV magnitudes MUV ∼−16 (McLure et al. 2013; Bouwens et al. 2015b, B15 hereafter) in blank fields or even MUV ∼ −12 in gravitational lensing fields (Livermore et al. 2017; however, see Bouwens et al. 2017b; hereafter these are cited as L17 and B17). The high-z LFs have also been reconstructed from the number of ultra-faint dwarf galaxies—some of which are believed to be fossils of reionization galaxies—in the Local Group. For example, Weisz et al. (2014) concluded that the LF at z ∼ 5 does not have any break at least down to MUV ∼ −10. At the same time, the detection of a break or turnover would have important implications regarding the nature of the first galaxies and their contributions to reionization (e.g., Giallongo et al. 2015; Madau & Haardt 2015; Mitra et al. 2018).
Star formation in dark matter halos relies on the gas cooling process. However, both supernova explosion and ionizing radiation could prevent cooling. These feedback effects reduce the efficiency of star formation (Dayal et al. 2013; Sun & Furlanetto 2016; Xu et al. 2016) or even completely quench it, if the halo mass is too small. As a result, the number of galaxies hosted by small halos drops and we expect to see a "turnover" in the faint end of the galaxy LFs (Yue et al. 2016, Y16 hereafter). For example, in the "Cosmic Reionization on Computers" project, through galaxy formation and radiative transfer numerical simulations, it is found that the UV LF turns over at MUV ∼ −14 to ∼−12 (Gnedin 2016). And in the "FirstLight" project with radiative feedback effects, the LF has a flattening at MUV ≳ − 14 (with host halo circular velocities ∼30–40 km s−1; Ceverino et al. 2017). Modifications of the initial power spectrum as in warm dark matter (WDM) cosmologies can also have a similar effect; see, e.g., Dayal et al. (2015) and Menci et al. (2016, 2017). Observations of galaxies around the turnover would greatly increase our knowledge of the star formation physics in galaxies contributing the most to reionization, and may directly answer our questions in the first paragraph (Yue et al. 2014).
Until now, there has been no evidence that confirms or rules out the existence of such turnover in both regular surveys and in gravitational lensing surveys, probably because the turnover magnitude is still fainter than the limiting magnitudes of current measurements; see, e.g., McLure et al. (2013); B15; Atek et al. (2015b); Atek et al. (2015a; A15 hereafter); L17; Laporte et al. (2016), and Ishigaki et al. (2018; I18 hereafter).
With the help of strong magnification effects, the gravitational lensing provides an opportunity to detect galaxies below the detection limits of regular surveys. However, the cost is that the survey volume is reduced, and lensing models introduce extra uncertainties into the recovered intrinsic brightness of observed galaxies (B17).
The Frontier Fields (FFs) survey observed six massive galaxy clusters and their parallel fields in optical and near-infrared bands with the Hubble9 and Spitzer10 space telescopes (Lotz et al. 2017). These observations were also followed up by other observatories at longer and shorter wavelengths, e.g., ALMA (González-López et al. 2017a, 2017b) and Chandra (Ogrean et al. 2015, 2016; van Weeren et al. 2017). Using the clusters as lenses, these images are deep enough to unveil faint galaxy populations at the EoR.
In Y16, we derived the form of the LF faint end during and after the EoR by assuming that the star formation in halos with circular velocity below a threshold and located in ionized bubbles is quenched, where is a free parameter. In Castellano et al. (2016a; C16a hereafter), we constrained km s−1 (2
Recently, using two FFs clusters, Abell 2744 (A2744) and MACSJ0416.1-2403 (M0416), L17 found that the faint end of the LF at z ∼ 6 always has a steep slope (
B17 investigated the impact of magnification errors on the LF carefully and found that at MUV ≳ − 14 the systematic differences of magnifications from different lensing models are extremely high. They developed a new model that incorporates the magnification errors into the LF, and by analyzing four FFs clusters: A2744, M0416 plus MACSJ0717.5+3745 (M0717), and MACSJ1149.5+2223 (M1149) they obtained the constraints that the LF should not turn over at least at to −14.2 (1
In this paper, we expand the analysis presented in C16a by adding new FFs data and improved lensing models to obtain number counts in the two additional FFs clusters and update the previous two clusters. Throughout this paper we use the following cosmological parameters: , , , , (Planck Collaboration et al. 2016a); magnitudes are presented in the AB system.
2. Methods
2.1. Observations
The photometric catalogs of high-z galaxies used in the present paper are provided by the ASTRODEEP team (Castellano et al. 2016c; Merlin et al. 2016b; Di Criscienzo et al. 2017), and all the lensing models are provided by the FFs team on the project website.11
The high-z sample comprises all sources with from the ASTRODEEP catalogs of FFs clusters A2744, M0416 (Castellano et al. 2016a; Merlin et al. 2016b), M0717 and M1149 (Di Criscienzo et al. 2017)12 , where is the demagnified apparent magnitude at the HST F160W band (H band). The model described in Section 2.2 will use sample galaxies with 5.0 < z < 7.0, while the model described in Section 2.3 will use sample galaxies with 5.0 < z < 9.5; see details in the relevant sections. The original samples presented by ASTRODEEP team have redshifts up to ∼10. However, for objects z ≳ 9.5, their redshifts may be not correctly measured. Moreover, samples with z ≳ 9.5 are only detectable in one band. Considering these reasons we do not select samples with z > 9.5.
All catalogs include photometry from the available HST ACS and WFC3 bands (B435, V606, I814, Y105, J125, JH140, H160; see, e.g., Lotz et al. 2017) and from deep K-band (Brammer et al. 2016) and IRAC 3.6 and 4.5
In the top panel of Figure 1 we plot the observed H-band apparent magnitude, H160, versus redshift for our selected sample galaxies (galaxies with photometric redshifts between 5.0 and 9.5 and with demagnified H-band magnitudes larger than 27.5 in either of lensing models) in the four FFs clusters. There are 73 (87), 51 (62), 73 (76), and 34 (47) galaxies with 5.0 < z < 7.0 (5.0 < z < 9.5) in clusters A2744, M0416, M0717, and M1149, respectively. In Appendix A we list the unique ID in the ASTRODEEP catalog of all these objects, so that properties like the released SEDs can be found directly.
The magnification for each observed source is estimated on the basis of the relevant photometric redshift from shear and mass surface density values at its barycenter of the light distribution. All models made available on the STSCI website13 are used.
Compared to C16a in this paper we update the A2744 and M0416 high-z samples by exploiting the improved v3 lensing models now available, and we include in the analysis number counts from other two additional clusters, M0717 and M1149. In Table 1 we list the clusters and the corresponding lensing models used in this paper. In Figure 2 we plot the distributions of the magnification factors of our selected galaxy samples in each cluster, for our adopted lensing models. In different lensing models an identified galaxy could have different magnifications, and hence different demagnified magnitudes. Therefore, for a given cluster we can reconstruct different number counts (galaxy number per magnitude bin) when using different lensing models. The median of these number counts are our fiducial number counts. In the middle and bottom panels of Figure 1 we show the number counts of the faint () galaxies with 5.0 < z < 7.0 and 5.0 < z <9.5 in the fields of four FFs clusters (we do not use the data of the parallel blank fields), as a function of .
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Standard image High-resolution imageTable 1. The FFs Clusters and Lensing Models Used in this Paper
Cluster | Lensing model |
---|---|
Abell 2744 (A2744) | GLAFIC v3; Sharon v3; Williams v3; Zitrin-LTM-Gauss v3;Zitrin-NFW v3; CATS v3.1 |
MACSJ0416.1-2403 (M0416) | GLAFIC v3; Sharon v3; Williams v3.1; Zitrin-LTM-Gauss v3; Zitrin-LTM v3; CATS v3.1; Bradac̆ v3; Diego v3 |
MACSJ0717.5+3745 (M0717) | GLAFIC v3; Sharon v2; Williams v1; Zitrin-LTM-Gauss v1; Zitrin-LTM v1; CATS v1; Bradac̆ v1; Merten v1 |
MACSJ1149.5+2223 (M1149) | GLAFIC v3; Sharon v2.1; Williams v1; Zitrin-LTM-Gauss v1; Zitrin-LTM v1; CATS v1; Bradac̆ v1; Merten v1 |
Note. Relevant references for lensing models listed in the table: GLAFIC: Kawamata et al. (2018, 2016), Ishigaki et al. (2015), Oguri (2010). Sharon: Johnson et al. (2014), Jullo et al. (2007). Williams: Priewe et al. (2017), Sebesta et al. (2016), Grillo et al. (2015), Jauzac et al. (2014), Mohammed et al. (2014), Liesenborgs et al. (2006). Zitrin: Zitrin et al. (2013, 2009). CATS: Jauzac et al. (2015, 2014), Richard et al. (2014), Jauzac et al. (2012), Jullo & Kneib (2009). Bradac̆: Hoag et al. (2016), Bradač et al. (2009, 2005). Diego: Diego et al. (2015, 2007, 2005b, 2005a). Merten: Merten et al. (2011, 2009). All models are available on the STSCI website.
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2.2. An Empirical Description of the LF Turnover
Is there evidence of a "turnover" in the faint end of the high-z galaxy LFs from the available FFs data? To investigate this problem we adopt the following reference LF model: a standard Schechter formula modulated by a term that rapidly drops when the absolute UV magnitude MUV is much fainter than the turnover magnitude , and rapidly approaches unity when :
where erf is the error function. At the the LF drops to half the value of a standard Schechter LF. In addition to the three redshift-dependent Schechter parameters
discarding its uncertainties. We keep the
2.3. A Physically Motivated Model of the High-z Galaxy LFs
In Y16 we have developed a physically motivated analytical model that describes the faint end of the high-z galaxy LFs during the EoR. The model calibrates the "star formation efficiency" (defined as the star formation rate to halo dark matter mass ratio) - halo mass relation using the Schechter formula of observed LF at redshift ∼5, then computes the luminosity of a halo according to its mass and formation time at any redshifts (Mason et al. 2015; see also Trenti et al. 2010 and Tacchella et al. 2013). Considering the probability distribution of a halo's formation time (Giocoli et al. 2007), and the possibility of its star formation being quenched (if the circular velocity of this halo is smaller than a presumed circular velocity criterion and it is located in ionized regions), the LF is then derived from halo mass function. In this model, the LF does not necessarily decrease monotonically at its faint end but has complex shapes; see Figure 6 and Figure 7 in Y16.
The Y16 model has two free parameters, the escape fraction of ionizing photons, fesc, and the critical circular velocity, . The galaxy number counts are sensitive to but less sensitive to fesc; therefore we combine the number counts with the measured Thomson scattering optical depth to CMB photons,
2.4. Statistical Framework
Here, we summarize the procedure adopted to derive constraints on theoretical parameters from the observed galaxy number counts. A more detailed discussion can be found in C16a.
The sample galaxies of each cluster in the specified redshift range are divided into nb bins according to their demagnified magnitudes. Suppose that in the ith bin there are galaxies. For a given LF model with parameter set , we perform Monte Carlo simulations to calculate the probability of observing such a number of galaxies in this bin, . In the Monte Carlo simulations, we include the completeness as a function size and magnitude of the image. The image size of each input galaxy is derived from its luminosity using an intrinsic galaxy radius–luminosity relation given in Huang et al. (2013). This relation is comparable with the relation in Bouwens et al. (2017a, 2017b). We note that Kawamata et al. (2018) found a steeper relation slope for galaxies down to in FFs, although at this moment we do not check the influence on our results. depends on both LF models and lensing models. We use the mean probability of different lensing models (see their Equation (3)) except when comparing different lensing models.
We then build the following combined likelihood:
where L1 is the likelihood from our FFs observations, and L2 is the likelihood of additional observations that can help to improve the constraints.
For the empirical model, we build L2 from the constructed LF data points of wide blank fields at z ∼ 6,
Introducing this L2 is necessary, because although the gravitational lensing surveys are deeper, usually they have smaller effective volume, while the blank field surveys have large volume, and thereby are helpful for reducing the uncertainties.
For the physically motivated model, we build the L2 from the measured CMB scattering optical depth,
The constraints on parameter set are obtained by looking for the minimum of and its variations corresponding to different C.L. given by chi-squared distribution.
3. Results
3.1. Is a LF Turnover Observed at z ∼ 6 ?
In this subsection we investigate the constraints on parameters in the empirical model described in Section 2.2 at by analyzing galaxy samples with 5 < z < 7 in ASTRODEEP catalogs.
Using a collection of wide and deep blank field HST surveys data, including the CANDELS, HUDF09, HUDF12, ERS, and BoRG/HIPPIES fields, B15 have constructed the LFs from z ∼ 4 to z ∼ 10. We use their stepwise maximum likelihood determination of the z ∼ 6 data points to build the L2 (see Table 5 of B15). We vary
The constraints on empirical model parameters are shown in Figure 3. In the 2D -
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Standard image High-resolution imageTable 2. Constraints on and , and the Halo Mass and Absolute UV Magnitude Corresponding to Constraints
ALL | GLAFIC | CATS | Sharon | Williams | Zitrin-LTM-Gauss | ||
---|---|---|---|---|---|---|---|
1 |
≳−14.6 | ≳−12.9 | ≳−13.7 | ≳−14.3 | ≳−11.8 | ||
2 |
≳−15.2 | ≳−15.2 | ≳−14.3 | ≳−14.7 | ≳−14.9 | ≳−13.2 | |
1 |
≲48 | ≲40 | ≲45 | ≲45 | ≲34 | ||
2 |
≲59 | ≲56 | ≲49 | ≲56 | ≲54 | ≲45 | |
1 |
≲5.6 × 109 | ≲4.9 × 109 | ≲2.9 × 109 | ≲4.1 × 109 | ≲4.1 × 109 | ≲1.8 × 109 | |
2 |
≲9.2 × 109 | ≲7.9 × 109 | ≲5.3 × 109 | ≲7.9 × 109 | ≲7.0 × 109 | ≲4.1 × 109 | |
1 |
≳−14.2 | ≳−14.0 | ≳−13.2 | ≳−13.7 | ≳−13.7 | ≳−12.4 | |
2 |
≳−15.0 | ≳−14.8 | ≳−14.1 | ≳−14.8 | ≳−14.6 | ≳−13.7 | |
Mh/M⊙(z = 9.5) | 1 |
≲2.4 × 109 | ≲2.1 × 109 | ≲1.2 × 109 | ≲1.8 × 109 | ≲1.8 × 109 | ≲7.6 × 108 |
2 |
≲4.0 × 109 | ≲3.4 × 109 | ≲2.3 × 109 | ≲3.4 × 109 | ≲3.0 × 109 | ≲1.8 × 109 | |
MUV(z = 9.5) | 1 |
≳−14.0 | ≳−13.8 | ≳−13.0 | ≳−13.6 | ≳−13.6 | ≳−12.3 |
2 |
≳−14.8 | ≳−14.6 | ≳−14.0 | ≳−14.6 | ≳−14.4 | ≳−13.6 |
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We plot the LF corresponding to the constraints at z ∼ 6 in Figure 4 by curves and filled regions. As a reference and consistency check, we also plot the B15 LF data, and the LF data constructed from A2744, M0416, and M0717 and their corresponding parallel blank field in A15 at z ∼ 7, which is one of the deepest LFs, and is consistent with other LFs in the overlap magnitude range. Moreover, the L17, B17, and I18 LFs are also plotted in Figure 4.
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Standard image High-resolution imageBefore making comparisons between B17 and our results, it is necessary to clarify a dissimilarity between the definition of the "turnover magnitude" between B17 and our work. In B17, the turnover magnitude is the absolute magnitude at which the LF's derivative is zero, while in our work it is defined as the absolute magnitude where the LF decreases to half of the Schechter LF. Moreover, their LF end is modulated by a term , which could decrease gently even when MUV is higher than the turnover magnitude, depending on
The L17 constraint on LF turnover is deeper than ours, i.e., no turnover is seen until at in their work. The difference between our results and those of L17 could be due to the different methodologies adopted: (a) they built the source catalog and subtracted the ICL in a very different way than in our case. (b) They assumed different galaxy size distributions. (c) In our case, we first construct the number count for each lensing model independently, then take the median of the number counts reconstructed from different lensing models; while in L17, for the image of each galaxy they take the flux-weighted magnification of different lensing models, then construct the LF.
We now investigate the systematic differences between the various lensing models. In Figure 5 we show the
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Standard image High-resolution imageIndeed, the discrepancies between lensing models are rather evident, especially for the boundaries. This is because these lensing models use different mass distribution and observations as constraint inputs; as a result, although the number counts (the middle panels of Figure 5) are basically consistent with each other at , at the faintest end they are rather different from. Detailed investigations about the systematics among lensing models could be found in Acebron et al. (2017), Meneghetti et al. (2017), Priewe et al. (2017), and the references of each lensing model listed below in Table 1. In all the cases, the upper boundaries are open, implying that no turnover is apparent.
In the bottom panels of Figure 5 we also plot the absolute magnitudes of the faintest galaxies in each lensing model with vertical lines. Usually, the constraints are shallower than these faintest magnitudes. We check the influence of the faintest galaxies on the constraints. We find that in Figure 5, the fainest galaxy (referring to the demagnified magnitude) for the Williams lensing model is in the M0717 field, while for other lensing models it is in the M0416 field.
For the GLAFIC and CATS lensing models, the faintest galaxy is the same one whose observed apparent magnitude , and demagnified magnitudes and 32.9 in these two lensing models, respectively. For the Sharon, Williams, and Zitrin-LTM-Gauss lensing models, the faintest galaxies have H160 = 28.0, 28.6, and 26.7, and , 32.5 and 34.6 respectively. An investigation of the influence of the photometric errors is featured in Appendix B.
Although we have checked all the galaxies one-by-one visually and do not find any reason to consider the above faint galaxies past our checkup spurious objects, we still check their influences. When including (removing) them in (from) samples, we obtain the 2
3.2. Constraints on
We then investigate the constraints we can put on the physically motivated model. Since in this model both fesc and are redshift-independent parameters, we use all the data in . In the top panel of Figure 6 we show the constraints on fesc and , using the combination of galaxy number counts in the FFs fields and the latest Planck2016 Thomson scattering optical depth to CMB photons:
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Standard image High-resolution imageWe also find that different clusters do not contribute equally to the final constraint. If we respectively remove A2744, M0416, M0717, and M1149 each time, we obtain 65, 61, 62, and 58 km s−1 (all at the 2
We also investigate the discrepancies between different lensing models in this case. When using one lensing model at a time, as mentioned in the last subsection, we obtain the 2
4. Conclusions
We investigated the LF of galaxies in the reionization epoch at low luminosities under the explicit assumption that any deviation from a pure Schechter LF at faint magnitudes is imprinted by feedback effects during reionization itself. We considered two LF models, and obtained constraints on their parameters from the observed high-z ultra-faint galaxy number counts in four FFs gravitational lensing cluster fields. We first test an empirical model where the standard Schechter formula is modulated by the suppressing term . The LF is unchanged when , and drops rapidly when . Second, we consider the physically motivated model proposed by Y16 and analyzed in C16a. In this model the star formation is quenched in halos with circular velocity smaller than , during and after the EoR, as long as they are located in ionized regions. As a result, the LF has complex behavior at low luminosities.
We used the photometric catalogs and redshifts of the four FFs clusters A2744, M0416, M0717, and M1149 provided by the ASTRODEEP collaboration. The first two clusters have already been analyzed in a previous work, C16a, therefore in this paper we only considered the lensing models with versions later than 3.0, which were not adopted in C16a. For the other two clusters, we used all available lensing models, and where multiple versions were available we adopted the latest ones.
For the empirical model, at 1
For the physically motivated model we obtained km s−1 at 2
All the numerical results of both the empirical model and the physically motivated model are listed in Table 2, and in the physically motivated model we have translated the constraints into the MUV constraints at z = 5 and z = 9.5. Although the constraints on can be translated into constraints on through the luminosity–halo mass relations, we note that in the empirical model the constraints are purely from the galaxy surveys, while in the physically motivated model the constraints are from both the galaxy surveys and the CMB scattering optical depth. In spite of this, the results of these models are considered consistent in the fiducial case (see the ALL model in Table 2): e.g., versus .
Thanks to the combined power of gravitational lensing and deep HST multi-band imaging we are just starting to observe the faintest galaxy populations that are likely responsible for reionization. The present analysis and similar ones in the past have not yet found significant evidence of the presence of feedback effects suppressing the formation of galaxies at faint UV magnitudes. This is likely due to the uncertainties and systematics involved in lensing models and in the selection and characterization of distant, faint sources. In this respect, the completion of the FFs survey, and improvements in lensing model accuracy, as well as high-redshift sample selection that will be enabled by future JWST photometric and spectroscopic observations, will be crucial for improving our understanding of reionization.
We thank the anonymous referee for the useful suggestions helpful for improving the paper. This work utilizes gravitational lensing models produced by PIs Bradac̆ Natarajan & Kneib (CATS), Merten & Zitrin, Sharon, and Williams, and the GLAFIC and Diego groups. This lens modeling was partially funded by 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). B.Y. acknowledges the support of the CAS Pioneer Hundred Talents (Young Talents) program, the NSFC grant 11653003, the NSFC-CAS joint fund for space scientific satellites No. U1738125, and the NSFC-ISF joint research program No. 11761141012. R.A. acknowledges support from the ERC Advanced Grant 695671 QUENCH. M.J.M. acknowledges the support of the National Science Centre, Poland through the POLONEZ grant 2015/19/P/ST9/04010. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 665778.
Appendix A: List of Our Selected Galaxy Samples
We provide the IDs, the apparent magnitudes, and photometric redshifts of our selected samples in Table 3. The SEDs, cutouts, and all ancillary Information could be found on the ASTRODEEP CDS Interface at http://astrodeep.u-strasbg.fr/ff/.
Table 3. Our Selected Galaxies in ASTRODEEP Catalogs
A2744 | M0416 | M0717 | M1149 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
ID | H160 | z | ID | H160 | z | ID | H160 | z | ID | H160 | z | |
54 | 27.81 ± 0.15 | 5.10 ± 0.11 | 73 | 28.03 ± 0.15 | 6.07 ± 0.07 | 69 | 27.09 ± 0.12 | 5.18 ± 0.09 | 354 | 28.03 ± 0.15 | 5.66 ± 0.14 | |
62 | 25.18 ± 0.05 | 6.13 ± 0.03 | 132 | 28.11 ± 0.26 | 5.03 ± 0.08 | 75 | 28.56 ± 0.22 | 5.19 ± 0.47 | 362 | 27.14 ± 0.09 | 5.61 ± 0.17 | |
67 | 27.17 ± 0.12 | 5.54 ± 0.07 | 141a | 27.77 ± 0.13 | 6.68 ± 0.99 | 82 | 26.77 ± 0.08 | 6.05 ± 0.05 | 396 | 28.35 ± 0.18 | 6.92 ± 1.01 | |
73 | 26.50 ± 0.05 | 6.85 ± 0.04 | 143a | 26.97 ± 0.08 | 6.55 ± 1.00 | 96 | 27.44 ± 0.19 | 7.90 ± 0.04 | 402 | 28.17 ± 0.19 | 6.38 ± 0.08 | |
145 | 27.08 ± 0.13 | 5.87 ± 0.30 | 158 | 28.00 ± 0.24 | 8.27 ± 0.10 | 151 | 27.65 ± 0.18 | 5.43 ± 0.05 | 433 | 27.75 ± 0.13 | 6.16 ± 0.02 | |
189 | 28.01 ± 0.14 | 5.68 ± 0.15 | 201a | 28.70 ± 0.21 | 5.70 ± 2.45 | 165 | 27.52 ± 0.17 | 5.49 ± 3.24 | 448 | 28.66 ± 0.26 | 5.05 ± 0.19 | |
203 | 28.59 ± 0.19 | 5.53 ± 0.03 | 220 | 27.74 ± 0.15 | 5.82 ± 0.06 | 222a | 27.53 ± 0.26 | 5.05 ± 0.85 | 531 | 27.92 ± 0.14 | 6.56 ± 0.13 | |
222 | 27.23 ± 0.11 | 5.02 ± 0.03 | 246 | 28.81 ± 0.40 | 6.41 ± 0.02 | 248a | 27.73 ± 0.16 | 5.42 ± 0.53 | 546 | 28.22 ± 0.26 | 5.01 ± 0.03 | |
263 | 27.08 ± 0.12 | 5.25 ± 0.09 | 247a | 27.22 ± 0.10 | 7.13 ± 0.11 | 272 | 28.29 ± 0.20 | 5.66 ± 0.12 | 574 | 28.01 ± 0.20 | 5.21 ± 2.12 | |
292a | 27.59 ± 0.10 | 5.38 ± 0.03 | 265 | 27.58 ± 0.21 | 5.24 ± 2.00 | 336 | 27.10 ± 0.10 | 6.10 ± 0.05 | 708 | 28.10 ± 0.19 | 5.14 ± 0.11 | |
321 | 28.83 ± 0.19 | 5.71 ± 0.03 | 286a | 28.20 ± 0.17 | 8.14 ± 0.18 | 356 | 28.45 ± 0.23 | 6.16 ± 0.12 | 905 | 25.93 ± 0.03 | 5.05 ± 0.10 | |
345a | 28.46 ± 0.17 | 5.35 ± 0.13 | 354 | 28.41 ± 0.23 | 5.24 ± 0.05 | 361 | 26.17 ± 0.10 | 6.45 ± 0.03 | 942a | 26.90 ± 0.09 | 6.25 ± 3.93 | |
379 | 28.15 ± 0.16 | 6.61 ± 0.21 | 355 | 27.87 ± 0.17 | 6.24 ± 0.03 | 374a | 27.37 ± 0.17 | 6.25 ± 0.08 | 945 | 27.92 ± 0.13 | 6.68 ± 0.09 | |
389 | 27.44 ± 0.10 | 5.36 ± 0.08 | 465 | 27.40 ± 0.11 | 5.33 ± 0.09 | 392a | 27.54 ± 0.24 | 6.03 ± 0.20 | 1144 | 27.96 ± 0.14 | 5.41 ± 0.19 | |
394 | 28.40 ± 0.17 | 6.60 ± 0.06 | 513a | 28.12 ± 0.21 | 6.79 ± 2.58 | 471 | 26.68 ± 0.08 | 6.53 ± 0.03 | 1180 | 27.31 ± 0.14 | 7.17 ± 0.14 | |
397 | 27.17 ± 0.10 | 6.31 ± 0.11 | 524 | 28.11 ± 0.15 | 5.20 ± 0.07 | 510 | 26.87 ± 0.08 | 6.46 ± 0.03 | 1226 | 28.35 ± 0.17 | 9.14 ± 3.51 | |
409 | 28.32 ± 0.19 | 7.66 ± 0.01 | 637a | 27.69 ± 0.13 | 6.41 ± 0.20 | 511 | 27.36 ± 0.11 | 5.20 ± 0.06 | 1243 | 27.44 ± 0.11 | 5.92 ± 0.07 | |
411 | 28.01 ± 0.17 | 7.44 ± 0.05 | 678 | 28.48 ± 0.19 | 5.37 ± 0.03 | 630a | 27.31 ± 0.10 | 5.44 ± 0.04 | 1268 | 28.37 ± 0.17 | 5.20 ± 0.08 | |
422 | 28.35 ± 0.24 | 5.55 ± 0.03 | 726 | 26.76 ± 0.06 | 8.32 ± 0.07 | 636 | 28.19 ± 0.23 | 5.34 ± 0.18 | 1388 | 27.58 ± 0.17 | 7.29 ± 0.25 | |
425 | 26.76 ± 0.07 | 5.24 ± 0.07 | 915 | 27.56 ± 0.23 | 5.31 ± 1.93 | 640 | 26.87 ± 0.09 | 6.02 ± 0.02 | 1428 | 28.34 ± 0.17 | 6.89 ± 0.07 | |
437 | 28.67 ± 0.22 | 5.87 ± 0.09 | 1024 | 28.06 ± 0.16 | 7.49 ± 0.07 | 653 | 24.65 ± 0.01 | 5.42 ± 0.07 | 1434 | 28.40 ± 0.21 | 6.39 ± 0.15 | |
446 | 27.60 ± 0.13 | 6.02 ± 0.02 | 1074 | 26.68 ± 0.10 | 5.78 ± 2.23 | 774 | 28.07 ± 0.16 | 5.93 ± 0.09 | 1494 | 26.11 ± 0.05 | 5.76 ± 0.09 | |
466 | 27.12 ± 0.14 | 5.75 ± 0.02 | 1105 | 27.90 ± 0.17 | 5.29 ± 2.01 | 790 | 25.52 ± 0.02 | 5.78 ± 0.11 | 1513 | 28.75 ± 0.32 | 8.54 ± 0.01 | |
475 | 27.82 ± 0.19 | 5.10 ± 0.10 | 1164 | 28.55 ± 0.24 | 5.96 ± 0.09 | 797 | 25.31 ± 0.04 | 5.97 ± 2.29 | 1529 | 27.38 ± 0.10 | 5.08 ± 0.06 | |
491 | 28.58 ± 0.25 | 5.16 ± 0.05 | 1260 | 28.59 ± 0.21 | 5.24 ± 0.01 | 813 | 28.20 ± 0.18 | 5.90 ± 0.09 | 1733 | 26.82 ± 0.20 | 8.76 ± 0.85 | |
535 | 28.09 ± 0.25 | 5.12 ± 0.49 | 1333 | 26.68 ± 0.06 | 5.16 ± 0.09 | 880 | 27.04 ± 0.12 | 5.19 ± 0.59 | 1751 | 28.12 ± 0.41 | 8.32 ± 0.04 | |
548a | 28.42 ± 0.20 | 8.56 ± 0.02 | 1405 | 26.33 ± 0.06 | 5.16 ± 0.04 | 922 | 26.86 ± 0.10 | 5.49 ± 0.03 | 1758 | 26.65 ± 0.18 | 8.96 ± 4.24 | |
560 | 29.03 ± 0.22 | 5.18 ± 0.11 | 1457 | 28.64 ± 0.28 | 6.07 ± 0.24 | 955 | 24.52 ± 0.03 | 5.54 ± 0.26 | 1970 | 28.08 ± 0.30 | 5.41 ± 2.38 | |
561 | 26.78 ± 0.10 | 6.37 ± 0.02 | 1494 | 27.57 ± 0.21 | 7.08 ± 0.03 | 1028 | 27.67 ± 0.12 | 5.65 ± 0.08 | 2014 | 27.80 ± 0.24 | 6.61 ± 0.05 | |
626 | 27.48 ± 0.09 | 5.55 ± 0.01 | 1589 | 27.12 ± 0.16 | 7.50 ± 0.12 | 1095 | 26.52 ± 0.11 | 5.73 ± 0.07 | 2316 | 28.81 ± 0.27 | 7.93 ± 0.04 | |
657 | 28.55 ± 0.29 | 9.33 ± 0.07 | 1608 | 27.24 ± 0.23 | 5.03 ± 0.21 | 1178 | 26.82 ± 0.06 | 6.00 ± 0.05 | 2364 | 28.81 ± 0.23 | 5.71 ± 0.06 | |
707 | 29.01 ± 0.23 | 6.59 ± 0.04 | 1614 | 27.15 ± 0.18 | 6.29 ± 0.21 | 1286 | 27.41 ± 0.19 | 5.05 ± 0.26 | 2368 | 26.60 ± 0.07 | 5.94 ± 0.06 | |
709 | 28.27 ± 0.27 | 6.31 ± 0.02 | 1632 | 28.17 ± 0.36 | 6.08 ± 2.29 | 1333 | 28.15 ± 0.27 | 5.22 ± 0.33 | 2410 | 27.10 ± 0.10 | 6.00 ± 0.03 | |
742 | 27.24 ± 0.08 | 6.55 ± 0.26 | 1635 | 27.24 ± 0.20 | 5.61 ± 2.31 | 1363a | 26.50 ± 0.09 | 5.16 ± 0.74 | 2535 | 26.91 ± 0.07 | 5.54 ± 0.09 | |
808 | 26.60 ± 0.07 | 5.36 ± 0.01 | 1660 | 26.83 ± 0.12 | 5.51 ± 0.44 | 1398 | 26.48 ± 0.11 | 5.17 ± 0.07 | 2619 | 27.09 ± 0.07 | 5.79 ± 0.11 | |
809 | 27.55 ± 0.11 | 5.42 ± 0.04 | 1706 | 26.91 ± 0.11 | 5.42 ± 0.12 | 1481 | 26.92 ± 0.10 | 5.15 ± 2.19 | 2747 | 28.15 ± 0.23 | 6.17 ± 0.04 | |
834 | 26.40 ± 0.10 | 5.58 ± 0.07 | 1815 | 27.19 ± 0.16 | 7.22 ± 2.78 | 1563 | 28.31 ± 0.20 | 6.86 ± 0.03 | 2764 | 27.18 ± 0.10 | 5.67 ± 0.07 | |
835 | 27.69 ± 0.18 | 6.15 ± 0.09 | 1827 | 27.31 ± 0.14 | 5.91 ± 0.02 | 1584 | 28.28 ± 0.19 | 6.22 ± 0.04 | 2792 | 28.14 ± 0.16 | 7.18 ± 0.11 | |
855 | 27.60 ± 0.13 | 6.02 ± 0.03 | 1829 | 28.65 ± 0.20 | 5.96 ± 0.01 | 1622 | 27.60 ± 0.12 | 6.25 ± 0.03 | 2833 | 27.70 ± 0.12 | 7.26 ± 0.09 | |
863 | 27.01 ± 0.07 | 5.87 ± 0.06 | 1900 | 29.14 ± 0.91 | 5.17 ± 0.30 | 1737 | 26.89 ± 0.13 | 6.04 ± 0.07 | 2950a | 28.19 ± 0.21 | 8.62 ± 3.19 | |
902 | 29.02 ± 0.53 | 5.21 ± 0.06 | 1909 | 27.86 ± 0.21 | 5.43 ± 2.28 | 1772 | 24.55 ± 0.03 | 5.14 ± 0.10 | 2966 | 27.51 ± 0.11 | 6.40 ± 0.03 | |
921 | 28.74 ± 0.49 | 5.28 ± 0.09 | 1956 | 28.16 ± 0.16 | 7.81 ± 0.04 | 1802 | 25.87 ± 0.05 | 5.53 ± 0.04 | 3027 | 28.03 ± 0.16 | 5.83 ± 0.01 | |
943 | 28.18 ± 0.22 | 6.97 ± 0.07 | 1997 | 27.56 ± 0.17 | 8.10 ± 0.05 | 1841 | 27.81 ± 0.13 | 5.74 ± 0.05 | 3073 | 28.13 ± 0.18 | 5.10 ± 0.10 | |
945 | 28.61 ± 0.29 | 5.62 ± 0.19 | 2018a | 28.26 ± 0.15 | 5.31 ± 0.84 | 1868 | 25.49 ± 0.02 | 5.64 ± 2.39 | 3162 | 27.67 ± 0.14 | 6.07 ± 0.15 | |
1012 | 28.31 ± 0.13 | 5.24 ± 0.41 | 2067 | 28.19 ± 0.23 | 5.07 ± 0.20 | 1874a | 27.27 ± 0.11 | 5.48 ± 0.08 | 3195a | 28.71 ± 0.48 | 6.14 ± 3.67 | |
1020 | 29.06 ± 0.62 | 5.70 ± 0.07 | 2157 | 28.34 ± 0.17 | 5.36 ± 0.09 | 2156 | 25.26 ± 0.05 | 5.50 ± 2.31 | 3236a | 27.12 ± 0.23 | 9.11 ± 1.04 | |
1028a | 27.62 ± 0.20 | 7.08 ± 0.14 | 2169 | 28.09 ± 0.15 | 5.97 ± 0.03 | 2191 | 27.31 ± 0.13 | 5.46 ± 0.26 | 3374 | 26.95 ± 0.12 | 7.43 ± 0.09 | |
1032 | 28.21 ± 0.14 | 7.09 ± 0.08 | 2179 | 26.69 ± 0.07 | 6.25 ± 0.03 | 2204 | 27.19 ± 0.07 | 5.38 ± 2.16 | ||||
1051 | 27.11 ± 0.21 | 6.56 ± 0.07 | 2190 | 28.25 ± 0.18 | 5.40 ± 2.19 | 2302 | 27.01 ± 0.14 | 5.37 ± 0.10 | ||||
1273 | 27.31 ± 0.11 | 6.61 ± 0.02 | 2196 | 28.56 ± 0.29 | 5.91 ± 0.06 | 2312 | 26.45 ± 0.05 | 6.12 ± 0.04 | ||||
1333 | 27.23 ± 0.09 | 5.64 ± 0.03 | 2204 | 26.99 ± 0.13 | 6.30 ± 0.03 | 2321 | 27.76 ± 0.23 | 5.10 ± 0.14 | ||||
1387a | 27.29 ± 0.11 | 6.72 ± 0.23 | 2236 | 27.67 ± 0.13 | 5.97 ± 0.03 | 2368a | 26.54 ± 0.16 | 5.75 ± 0.08 | ||||
1399 | 26.94 ± 0.08 | 5.11 ± 0.01 | 2240 | 27.96 ± 0.07 | 5.75 ± 0.07 | 2429 | 28.15 ± 0.21 | 5.05 ± 0.10 | ||||
1450 | 28.30 ± 0.26 | 5.48 ± 0.25 | 2315a | 27.46 ± 0.15 | 5.13 ± 0.06 | 2442 | 26.66 ± 0.08 | 5.21 ± 0.11 | ||||
1516 | 28.15 ± 0.15 | 5.14 ± 0.06 | 2323 | 28.40 ± 0.18 | 5.18 ± 0.03 | 2520a | 27.20 ± 0.17 | 9.14 ± 1.04 | ||||
1622 | 28.94 ± 0.39 | 5.87 ± 0.06 | 2324 | 28.15 ± 0.25 | 6.29 ± 0.02 | 2575 | 28.24 ± 0.26 | 6.17 ± 0.23 | ||||
1686 | 28.06 ± 0.16 | 5.02 ± 0.06 | 2337 | 27.30 ± 0.16 | 6.16 ± 0.03 | 2584 | 28.61 ± 0.30 | 5.17 ± 1.83 | ||||
1718 | 24.03 ± 0.01 | 6.21 ± 0.09 | 2385 | 28.09 ± 0.16 | 8.83 ± 0.03 | 2585 | 27.63 ± 0.21 | 5.69 ± 0.12 | ||||
1747a | 27.69 ± 0.10 | 5.20 ± 2.53 | 2411 | 28.65 ± 0.20 | 5.91 ± 0.05 | 2625 | 27.41 ± 0.21 | 5.70 ± 0.15 | ||||
1762 | 28.65 ± 0.18 | 5.25 ± 0.01 | 2462 | 28.39 ± 0.18 | 5.69 ± 0.03 | 2656 | 28.90 ± 0.61 | 5.59 ± 2.50 | ||||
1968a | 27.38 ± 0.09 | 5.19 ± 0.08 | 2554 | 27.81 ± 0.21 | 5.90 ± 0.03 | 2667a | 26.83 ± 0.09 | 5.27 ± 0.37 | ||||
1990 | 27.99 ± 0.21 | 7.07 ± 0.13 | 2555 | 27.52 ± 0.20 | 6.00 ± 0.02 | 2730 | 26.90 ± 0.12 | 5.36 ± 0.19 | ||||
2002 | 28.25 ± 0.16 | 6.46 ± 0.02 | 2745 | 26.83 ± 0.12 | 5.06 ± 0.24 | |||||||
2007 | 28.70 ± 0.29 | 5.82 ± 0.07 | 2782 | 27.38 ± 0.23 | 5.27 ± 2.23 | |||||||
2036 | 26.95 ± 0.07 | 8.32 ± 0.03 | 2799 | 28.40 ± 0.26 | 5.22 ± 0.03 | |||||||
2037 | 28.22 ± 0.15 | 5.08 ± 0.07 | 2840 | 28.04 ± 0.21 | 5.18 ± 0.20 | |||||||
2066a | 27.82 ± 0.16 | 5.95 ± 2.34 | 2843 | 26.01 ± 0.06 | 5.47 ± 2.23 | |||||||
2112 | 28.45 ± 0.17 | 5.07 ± 0.07 | 2852 | 27.67 ± 0.14 | 5.08 ± 0.22 | |||||||
2181 | 28.01 ± 0.21 | 5.17 ± 0.14 | 2860 | 28.02 ± 0.25 | 5.37 ± 0.06 | |||||||
2202 | 27.69 ± 0.11 | 5.86 ± 0.01 | 2883 | 25.91 ± 0.06 | 6.37 ± 0.04 | |||||||
2241 | 28.33 ± 0.16 | 6.84 ± 0.04 | 2902 | 27.71 ± 0.23 | 6.25 ± 0.04 | |||||||
2257 | 28.62 ± 0.18 | 7.53 ± 0.43 | 3015 | 28.53 ± 0.25 | 5.76 ± 0.42 | |||||||
2261 | 27.29 ± 0.10 | 7.97 ± 0.10 | 3017 | 27.66 ± 0.18 | 5.04 ± 0.69 | |||||||
2287 | 27.97 ± 0.16 | 8.50 ± 0.94 | 3066 | 28.62 ± 0.25 | 6.24 ± 0.01 | |||||||
2316 | 27.98 ± 0.19 | 7.66 ± 0.02 | 3067 | 27.21 ± 0.15 | 5.97 ± 0.12 | |||||||
2325 | 28.54 ± 0.18 | 5.36 ± 0.03 | 3076a | 27.36 ± 0.14 | 9.19 ± 1.04 | |||||||
2338 | 28.86 ± 0.22 | 6.87 ± 0.04 | ||||||||||
2346 | 26.78 ± 0.06 | 7.79 ± 0.04 | ||||||||||
2380 | 27.71 ± 0.22 | 7.93 ± 0.14 | ||||||||||
2388 | 27.57 ± 0.21 | 5.17 ± 0.09 | ||||||||||
2434 | 28.40 ± 0.16 | 5.82 ± 0.07 | ||||||||||
2446 | 28.05 ± 0.15 | 5.73 ± 0.08 | ||||||||||
2452 | 27.00 ± 0.09 | 5.74 ± 0.07 | ||||||||||
2471 | 28.72 ± 0.18 | 5.66 ± 0.07 | ||||||||||
2544 | 27.03 ± 0.11 | 5.26 ± 0.08 | ||||||||||
2567a | 28.98 ± 0.27 | 5.10 ± 0.15 | ||||||||||
2595 | 27.14 ± 0.10 | 6.33 ± 0.05 |
Note.
aSome objects with possibly problematic SEDs are marked with "*". They are mostly objects showing some flux below the Lyman break, plus some sources detected only in one band. However, we verified that there are no solid reasons to remove them and the photometric redshift solutions appear to be reliable. In particular, the cases of detected flux below the break are mostly due to some contamination from nearby sources or to noise or background fluctuations.Appendix B: The Influence of Photometric Errors
In this section we investigate the influence of the photometric errors on the final constraints on the turnover magnitude. For each galaxy with 5.0 < z < 7.0, according to its H160 and photometric error, we randomly assign a new H160 from the Gaussian probability distribution. We then get the corresponding new demagnified magnitude and build new number counts. For each galaxy we make 10,000 random realizations and finally we have 10,000 number count realizations. Based on these realizations we get the corresponding 1
Download figure:
Standard image High-resolution imageWe then obtain the new constraints on the turnover magnitude using the 1
Footnotes
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Download at http://www.astrodeep.eu/frontier-fields-download/. The catalog interface can be found at http://astrodeep.u-strasbg.fr/ff/index.html.
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