High redshift galaxies in the ALHAMBRA survey: I. selection method and number counts based on redshift PDFs
K. Viironen, A. Marín-Franch, C. López-Sanjuan, J. Varela, J. Chaves-Montero, D. Cristóbal-Hornillos, A. Molino, A. Fernández-Soto, G. Vilella-Rojo, B. Ascaso, A. J. Cenarro, M. Cerviño, J. Cepa, A. Ederoclite, I. Márquez, J. Masegosa, M. Moles, I. Oteo, M. Pović, J. A. L. Aguerri, E. Alfaro, T. Aparicio-Villegas, N. Benítez, T. Broadhurst, J. Cabrera-Caño, J. F. Castander, A. Del Olmo, R. M. González Delgado, C. Husillos, L. Infante, V. J. Martínez, J. Perea, F. Prada, J. M. Quintana
aa r X i v : . [ a s t r o - ph . GA ] F e b Astronomy&Astrophysicsmanuscript no. viironen˙feb15 c (cid:13)
ESO 2018September 26, 2018
High redshift galaxies in the ALHAMBRA survey
I. selection method and number counts based on redshift PDFs ⋆ K. Viironen , A. Mar´ın-Franch , C. L ´opez-Sanjuan , J. Varela , J. Chaves-Montero , D. Crist´obal-Hornillos , A.Molino , , A. Fern´andez-Soto , , G. Vilella-Rojo , B. Ascaso , , A. J. Cenarro , M. Cervi˜no , , , J. Cepa , , A.Ederoclite , I. M´arquez , J. Masegosa , M. Moles , , I. Oteo , , M. Povi´c , J. A. L. Aguerri , , E. Alfaro , T.Aparicio-Villegas , , N. Ben´ıtez , T. Broadhurst , J. Cabrera-Ca˜no , J. F. Castander , A. Del Olmo , R. M.Gonz´alez Delgado , C. Husillos , L. Infante , V. J. Mart´ınez , , J. Perea , F. Prada , and J. M. Quintana Centro de Estudios de F´ısica del Cosmos de Arag´on, Plaza San Juan 1, planta 2, 44001 Teruel, Spaine-mail: [email protected] Instituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, Universidade de S˜ao Paulo, S˜ao Paulo, Brazil Instituto de Astrof´ısica de Andaluc´ıa (IAA-CSIC), Glorieta de la astronom´ıa s / n, 18008 Granada, Spain Instituto de F´ısica de Cantabria, Avenida de los Castros s / n, 39005 Santander, Spain Unidad Asociada Observatori Astronomic (IFCA-UV), C / Catedr´atico Jos´e Beltr´an 2, 46980 Paterna, Spain GEPI, Paris Observatory, 77 av. Denfert Rochereau, 75014 Paris, France Instituto de Astrof´ısica de Canarias, V´ıa L´actea s / n, La Laguna, 38200 Tenerife, Spain Departamento de Astrof´ısica, Facultad de F´ısica, Universidad de la Laguna, 38200 La Laguna, Spain Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Observat´orio Nacional, COAA, Rua General Jos´e Cristino 77, 20921-400 Rio de Janeiro, Brazil Department of Theoretical Physics, University of the Basque Country UPV / EHU, Bilbao, Spain Departamento de F´ısica At´omica, Molecular y Nuclear, Facultad de F´ısica, Universidad de Sevilla, Spain Institut de Ci`encies de l’Espai (ICE-CSIC), Facultat de Ci`encies, Campus UAB, 08193 Bellaterra, Spain Departamento de Astronom´ıa, Ponticia Universidad Cat´olica. Santiago, Chile Departament d’Astronomia i Astrof´ısica, Universitat de Val`encia, 46100 Burjassot, Spain
ABSTRACT
Context.
Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using theso-called dropout technique or Ly- α selection. However, the availability of multifilter data now allows the dropout selections to be re-placed by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the populationof high redshift galaxies in the ALHAMBRA survey data. Aims.
Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies inALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing to the studyof the brightest, least frequent, high redshift galaxies.
Methods.
The methodology is based on redshift probability distribution functions (zPDFs). It is shown how a clean galaxy samplecan be obtained by selecting the galaxies with high integrated probability of being within a given redshift interval. However, reachingboth a complete and clean sample with this method is challenging. Hence, a method to derive statistical properties by summing thezPDFs of all the galaxies in the redshift bin of interest is introduced.
Results.
Using this methodology we derive the galaxy rest frame UV number counts in five redshift bins centred at z = . , . , . , .
0, and 4.5, being complete up to the limiting magnitude at m UV (AB) =
24, where m UV refers to the first ALHAMBRAfilter redwards of the Ly- α line. With the wide field ALHAMBRA data we especially contribute to the study of the brightest ends ofthese counts, accurately sampling the surface densities down to m UV (AB) = Conclusions.
We show that using the zPDFs it is easy to select a very clean sample of high redshift galaxies. We also show thatit is better to do statistical analysis of the properties of galaxies using a probabilistic approach, which takes into account both theincompleteness and contamination issues in a natural way.
Key words.
Galaxies: evolution – Galaxies: distances and redshifts – Galaxies: high-redshift – Galaxies: statistics
1. Introduction
Identifying and studying high redshift galaxies is crucial forour understanding of the early epochs of galaxy evolution. At ⋆ Based on observations collected at the German-SpanishAstronomical Center, Calar Alto, jointly operated by the Max-Planck-Institut f¨ur Astronomie (MPIA) at Heidelberg and the Institutode Astrof´ısica de Andaluc´ıa (CSIC) the beginning of the nineties, the implementation of the so-called dropout technique opened the era for detections of co-pious numbers of these early galaxies (e.g. Guhathakurta et al.1990; Steidel & Hamilton 1992, 1993; Steidel et al. 1996a,b).These galaxies are discovered based on their broadband colours,i.e. by measuring the drop in brightness due to the Lyman breakat rest frame 912 Å and / or the Lyman forest between 912 Å and1216 Å. For high redshift galaxies ( z ≥
2) these features are
1. Viironen et al.: High redshift galaxies in the ALHAMBRA survey detected at optical or infrared wavelengths and permit the detec-tion of these so-called Lyman-break galaxies (LBGs) from theground. The dropout technique is sensitive to galaxies that areyoung enough to produce copious amounts of ultraviolet light,and are su ffi ciently dust free for a fair amount of this light toescape the galaxy.Detections of high redshift galaxies opened the possibil-ity for observational studies of some fundamental questions ofgalaxy evolution and cosmology at early epochs. One of themost widely studied properties are the LBG rest frame ultraviolet(UV) luminosity functions. The UV luminosities of the galaxies(once corrected for dust extinction) are directly proportional totheir star formation rates. Hence, the study of the UV luminositydensity, derived by integrating the luminosity function at di ff er-ent redshifts, gives information about the star formation historyin the Universe.Lyman-break galaxies can also act as tracers of dark mat-ter at high redshift through the study of their clustering proper-ties. The formation history of galaxies is basically understoodthrough two fundamental evolutionary processes, i.e. the pro-duction of stars and the accumulation of dark matter. While thebaryonic matter, i.e. stars, gas, and dust, can be studied throughthe light they emit, the dark matter cannot be directly detectedusing electromagnetic waves. However, the clustering propertiesof galaxies are closely related to the distribution and amount ofthe underlying dark matter (see Ouchi et al. 2004b, and refer-ences therein).Most of these studies, up to the very recent ones,have applied the dropout technique for candidate selection(e.g. Ouchi et al. 2004b,a; Shim et al. 2007; Reddy et al. 2008;Ly et al. 2011; Bouwens et al. 2014, and many more). While thistechnique is e ffi cient at selecting high redshift galaxies, it is alsoa ff ected by significant incompleteness and contamination, los-ing some fraction of the population at the selected redshift, orallowing galaxies at other redshifts to enter the sample. Whilethe latter can be dealt with by obtaining spectroscopic redshifts(see e.g. Steidel et al. 1996a,b; Reddy et al. 2006), the former re-mains a serious di ffi culty. We are not yet at the point of spectro-scopic blind surveys, hence, a step forward towards less biasedcandidate selection is o ff ered by multifilter surveys. They com-bine the e ffi ciency and unbiased nature of photometric surveyswith very low resolution spectral information, permitting us toderive more information on the surveyed objects such as theiraccurate photometric redshifts.Many authors (e.g. Shim et al. 2007; Ly et al. 2011) havecombined the data of their colour selected LBG samples with in-formation at other passbands in order to carry out spectral energydistribution (SED) fitting and to derive more information on theobjects in question, like their photometric redshifts. However,basing the actual candidate selection on photometric redshiftsas, for example, McLure et al. (2006) have done, has only re-cently started to become a common practice. As discussed byMcLure et al. (2011), when multifilter data are available this ap-proach has several advantages over the traditional colour selec-tion. It makes the best use of the available information in mul-tiple filters, it should be less biased as any colour preselectionis not required, and it directly o ff ers the photometric redshiftsfor the galaxies of interest and allows the competing photomet-ric redshift solutions at low redshift to be investigated. Recently,Le Fevre et al. (2014) have used photometric redshifts to selectan unbiased target sample of high redshift galaxies for the VUDSsurvey. Photometric redshift selection is also used in the frame-work of the CLASH survey (e.g. Bradley et al. 2014) and in the recent works of Finkelstein et al. (2014) and Bowler et al.(2014).In this paper we introduce a method for studying high red-shift ( z ∼ −
5) galaxies based on their photometric redshifts.Our study makes use of the complete redshift probability dis-tribution functions (zPDFs), rather than the best redshift (i.e.the median derived from the zPDF or the highest peak of thezPDF). We show how a very clean candidate selection can bemade based on the zPDFs and discuss how this technique alsosu ff ers from contamination issues if completeness is tried to bereached. Finally, we discuss why for many statistical purposescandidate selection is not needed. Instead, these studies can bebased directly on the redshift (and the corresponding luminos-ity, mass, star formation rate, etc.) probability distributions. Asan example we present probabilistic number counts for severalhigh redshift bins. These counts should be free from contami-nation and incompleteness issues, if the used zPDFs correctlyreflect the uncertainties in the redshift estimations.The method is developed and tested with the data from theAdvanced Large, Homogeneous Area Medium Band RedshiftAstronomical (ALHAMBRA, Moles et al. 2008) Survey. Thetotal area used for our study is 2.38 deg , covered with 20medium band optical filters, plus J , H , and K s in the near in-frared (NIR). In addition to the novel methodology, an advantageof our ALHAMBRA high redshift galaxy study as compared tothe previous LBG studies is the large area the survey covers, splitinto eight independent fields, reducing biases due to the cosmicvariance and allowing the study of the rarest, brightest, high red-shift galaxies. Galaxies at z ∼ z > Ω m = Ω Λ = =
70 km s − Mpc − . Magnitudes are givenin the AB system (Oke & Gunn 1983).
2. Data
ALHAMBRA (Moles et al. 2008) has mapped a total of 4 deg of the northern sky in eight separate fields during a seven yearperiod (2005 − havebeen completed with all the filters (2.38 deg after masking,as will be detailed in Sect. 4). ALHAMBRA uses a speciallydesigned filter system (Aparicio Villegas et al. 2010) that cov-ers the optical range from 3500 Å to 9700 Å with 20 con-tiguous, equal width ( ∼
300 Å FWHM), medium band filters,
2. Viironen et al.: High redshift galaxies in the ALHAMBRA survey λ [Å] F ν / T ( λ ) [ a r b i t r a r y un i t s ] z =2.2 z =3.0 z =4.0 z =5.0 Fig. 1.
The z ∼ z = . , . , . , and 5.0 considering thevariation of the intergalactic opacity with redshift (blue lines). For clarity, the spectra are shifted vertically and plotted only up to1460Å (restframe). The ALHAMBRA optical filter transmission curves are overplotted as shaded grey areas, and the dashed redline corresponds to the synthetic F W filter. The first filter redwards of the Ly- α line in each redshift is marked in darker grey. [ Acolour version of this figure is available in the online edition. ]plus the three standard broadbands, J , H , and K s , in the NIR.The photometric system has been specifically designed to op-timise photometric redshift depth and accuracy (Ben´ıtez et al.2009). The observations were carried out with the Calar Alto3.5m telescope using two wide field cameras: LAICA in the op-tical, and OMEGA-2000 in the NIR. The 5 σ limiting magni-tude reaches &
24 for all filters below 8000 Å and increasessteeply towards redder medium-band filters, up to m(AB) ∼ . ∼ J , ∼ . H , and ∼
22 for K s . For details about theNIR data reduction see Crist´obal-Hornillos et al. (2009), whilethe optical reduction is described in Crist´obal-Hornillos et al.(in prep). The ALHAMBRA object catalogues and the asso-ciated Bayesian photometric redshifts (BPZs) are described inMolino et al. (2014) and are available through the ALHAMBRAweb page . At the moment only the best BPZs are public; thefull zPDFs will be published in the future. In Fig. 1 we show thetransmission curves of the optical ALHAMBRA filters togetherwith the z ∼ ff erent redshifts.
3. Photometric redshifts
The work in this paper relies on the photometric redshifts pro-vided for all the objects in the ALHAMBRA catalogue as de-tailed by Molino et al. (2014). These photometric redshifts wereestimated using BPZ2.0 (Ben´ıtez et al., in prep), an updated ver-sion of the Bayesian Photometric Redshift (BPZ) code (Ben´ıtez2000). This code uses Bayesian inference where a maximumlikelihood, resulting from a χ minimisation between the ob-served and predicted colours for a galaxy among a range ofredshifts and templates, is weighted by a prior probability. Themaximum likelihood (ML) method may su ff er from colour–redshift degeneracies (like 4000Å break vs. Lyman break) and http: // alhambrasurvey.com the inclusion of a suitable prior information can help to breakthese degeneracies. However, both maximum likelihood andBayesian redshift probability distributions are available for allthe ALHAMBRA sources.The BPZ2.0 SED library (see Molino et al. 2014) consistsof 11 SEDs: five templates for elliptical galaxies, two for spi-ral galaxies, and four for starburst galaxies along with emis-sion lines and dust extinction. The opacity of the intergalacticmedium has been applied as described in Madau (1995). Theprior used gives the probability of a galaxy with apparent mag-nitude m having a certain redshift z and spectral type T . Theprior has been empirically derived for each spectral type andmagnitude by fitting luminosity functions provided by GOODS-MUSIC (Santini et al. 2009), COSMOS (Scoville et al. 2007),and UDF (Coe et al. 2006).For each catalogued ALHAMBRA object both the maxi-mum likelihood and Bayesian redshift probability distributionfunctions (zPDFs) are given separately for each template used inthe χ -fitting. We are not interested in limiting ourselves to anygalaxy type, hence, we use the redshift PDFs integrated over alltemplates, and normalised to one: Z PDF ( z )d z = Z Z
PDF ( z , T )d z d T = . (1)These zPDFs give the probability along the redshift axis of agalaxy in question to be at that redshift. Hence, the probability, p , that a galaxy is within the redshift bin z < z < z is p = Z z z PDF ( z )d z . (2) − z galaxies The first questions to solve before blindly using the photomet-ric redshift information for analysing high redshift galaxies are:Can we really trust these redshifts for high-z galaxies? Is it more
3. Viironen et al.: High redshift galaxies in the ALHAMBRA survey reliable to use the maximum likelihood (ML) or the Bayesian,full probability (FP), redshift probability distributions?The idea of the prior information is to reduce the redshiftestimation uncertainties. However, the prior information shouldbe used only if it really can be trusted. The complete censusof high redshift galaxies is still poorly known and the knowncensus is most probably biased (see e.g. Le Fevre et al. 2014).Hence, using any prior information based on such a census couldintroduce undesired biases or uncertainties. For this reason, ouranswer to the second question above would a priori be to baseour study on the ML redshift information. This will be furtherstudied in the following.While the accuracy of the ALHAMBRA BPZs is well testedand demonstrated (Molino et al. 2014) for galaxies up to z ∼ . ∼ ∼ z = . m =
24 in the first filter redwards of the Ly- α line. A litera-ture search reveales that five of these are classified as quasars,and as the BPZ template library does not include quasar spec-tra, we do not expect to be able to accurately recover theirredshifts. Hence, we are left with seven spectroscopically con-firmed bright normal high redshift galaxies. In Fig. 2 we showthe ALHAMBRA ML and FP zPDFs for these seven galaxiestogether with their ALHAMBRA coordinates and spectroscopicredshift (from Barger et al. 2008). We see that for five of them(Nos. 1, 3, 4, 6, 7), the redshift is reasonably well recovered, ∆ z . .
3, where ∆ z is the di ff erence between the first peak ofthe zPDF and the spectroscopic redshift. For galaxy 4, whoseshift between the spectroscopic and photomnetric redshift is thelargest of the five, the shift corresponds almost exactly to a widthof one filter, i.e. it seems BPZ has mistaken the location of theLy- α break by one filter. Of the remaining two, for galaxy 2, thefirst peaks of both ML and FP zPDFs are located at low redshift,but the peaks at high redshift enclose most of the probability.Galaxy 5 shows a secondary peak at high redshift (higher thanthe spectroscopic redshift), but most of the probability residesat low redshift. The spectra of these objects are not public mak-ing it hard to further study the reason for these discrepanciesbetween the spectroscopic and photometric redshifts. Howeverfrom the ALHAMBRA SEDs we infer that, most probably, thesediscrepancies derive from the common confusion between the4000Å break and Lyman break.To have a better control on the expected redshifts, and awider range of magnitudes to be tested, we carried out a sim-ulation. For this purpose we used the z = ff erent redshifts: z = . , . , . , .
0. The lowest redshift wasselected such that the Lyman forest would be sampled at least byone ALHAMBRA filter, while considering the previous work onLBG number counts (e.g. Yoshida et al. 2006), we do not expectto discover many galaxies above z = ff erent redshifts, the original spectrum wasfirst moved to redshift z = ff ect of cosmic opac-ity using the equations of Madau (1995), then the same equa-tions were used to simulate the spectra at di ff erent redshifts. Theoriginal spectrum cover the wavelength range from 920 Å to 2000 Å. To cover the whole ALHAMBRA optical wavelengthrange in the simulated redshifts, we artificially extended it as-suming a flat behaviour of the UV continuum ( F ν = constant, i.e. F λ ∝ λ − ) from 2000 Å redwards up to the Balmer break at 4000Å, and from 920 Å bluewards, down to 912 Å where the flux isassumed to drop abruptly adopting a cosmic opacity τ e f f = λ <
912 Å.The resulting spectra were convolved with the ALHAMBRAfilters. The convolved spectra were scaled to the desired magni-tudes (at the first filter redwards from the Ly- α ) to sample themagnitude range m = . − .
0. The lower magnitude wasdefined so that we really could expect to have galaxies of thismagnitude at our lowest redshift bin (see Ly et al. 2011), whilethe upper limit was set to reach the ALHAMBRA sensitivitylimit.We also considered realistic errors for each magnitudeat each filter. To obtain these, we selected one arbitraryALHAMBRA field and studied how the magnitude error variedwith magnitude for each filter. Using all the objects in the field,we created mag vs. mag err curves for each filter and found thebest fitting solutions of the form mag err = a + b ∗ e c ∗ mag . Theexpected errors at each magnitude and filter were then obtainedfrom these equations and assigned to the simulated LBG spectra.Finally, a Monte Carlo simulation was carried out. EachLBG spectrum was perturbed inside its error bars 100 times.When the simulated magnitude was below the 1 σ detection limit(adapted again from one arbitrary ALHAMBRA field), it wasreplaced by this 1 σ limiting magnitude, as required by BPZ fornon-detections. The BPZ code was run for each of the simulatedspectra to obtain both their FP and ML redshift probability dis-tributions. We studied the recovered distributions with two ques-tions in mind: 1) How well can we recover LBGs as high redshiftgalaxies? For this, we used equation (2) and tested how often thegalaxies would be recovered to have a probability p > . . < z < .
3. The redshift bin was selectedto be wider than the range of the input redshifts so that smallerrors in redshift would not place the borderline objects outsidethe tested range; and 2) How accurately is the redshift of thesesimulated galaxies recovered?The recovery rate of LBGs as high-redshift galaxies is sum-marised in Table 1, where the percentage of simulated LBGshaving a probability greater than 90% to be within the desiredredshift range for each input redshift and magnitude are listedfor both the FP and ML redshift distributions. We see that, ingeneral, the recovered fraction is worse for the z = . α breakand it is seen with fewer filters. We also see that while the MLmethod recovers the high redshift nature of the simulated galax-ies very well, the Bayesian approach gives worse results. It sys-tematically fails for the brightest magnitudes, reducing the prob-ability of the LBGs to be at high redshift below our 90% limit,and also starts failing for the fainter magnitudes earlier than theML approach.We note that according to earlier studies (see Yoshida et al.2006) for galaxies at redshift z ≥
4. Viironen et al.: High redshift galaxies in the ALHAMBRA survey
1: (189.2605,62.3393) 2: (189.4096, 62.2935)3: (189.3466, 62.2901) 4: (189.3478, 62.289)5: (189.2636, 62.2765) z
6: (189.3726, 62.2613) z
7: (189.3672, 62.2445) z s = 2.216 z s = 3.19z s = 2.225 z s = 2.223z s = 3.239 z s = 2.408z s = 2.551 Fig. 2.
The maximum likelihood (solid blue line) and Bayesian (dashed green line) zPDFs for eight galaxies with spectroscopicredshifts. The spectroscopic redshifts ( z s ) are given in each panel and are also marked as dashed black vertical lines. See the text formore details. [ A colour version of this figure is available in the online edition. ] Table 1.
The percentage fraction of simulated LBGs of di ff erentredshifts and magnitudes fulfilling our selection criterion. Maximum likelihood Bayesian ❛❛ z Mag 2.2 3.0 4.0 5.0 2.2 3.0 4.0 5.020.2 100 100 100 100 0 0 0 021. 99 100 100 100 0 0 0 022. 95 100 100 100 70 14 9 123. 73 100 100 100 61 99 100 024. 55 95 99 97 38 68 77 35 the high redshift galaxy population is still very incomplete andmost probably biased. Hence, basing any study on prior knowl-edge of such a population might be dangerous and could lead tofurther biases as our simulation also indicates. We do not wantto take the risk of losing the especially interesting bright objects.For these reasons, we decided to base our study on the ML red-shift probability distributions, i.e. to assume a flat prior.To test the accuracy of the recovered redshifts, we summedthe ML zPDFs of the simulated LBGs in order to see how wellthe input redshifts were recovered. In Fig. 3 we show these
Table 2.
The recovered redshifts for 100 simulated LBGs at dif-ferent magnitudes and redshifts. Presented are the average valueand its standard deviation derived from Gaussian approxima-tions of the summed zPDFs in Fig. 3.
Mag z in = z in = z in = z in = ± .
02 2.92 ± .
02 3.909 ± .
007 4.975 ± . ± .
04 3.2 ± . ± .
01 4.975 ± . ± . ± . ± .
01 4.97 ± . ± . ± . ± .
03 4.97 ± . ± . ± . ± .
07 4.98 ± . summed zPDFs at three di ff erent magnitudes. In Table 2 we listthe input redshifts and the recovered average redshifts and theirsigma, derived from Gaussian approximations of the summedzPDFs. The recovered redshifts generally show a bias towardssmaller or higher z than the input redshift, the bias becomingsmaller with increasing z . It is not surprising that the redshift isworse recovered at the lower simulated z , as at lower z the Lymanforest is sampled by fewer ALHAMBRA filters (see Fig. 1), andthe Ly- α break is less pronounced at lower redshifts. However,it is intriguing to see that even though the recovered redshift
5. Viironen et al.: High redshift galaxies in the ALHAMBRA survey z (cid:0) P D F ( z ) m=20.2 z (cid:1) P D F ( z ) m=22 z (cid:2) P D F ( z ) m=24 Fig. 3.
Recovered summed redshift distributions, normalised toone at the integrated probability, for 100 simulated LBGs atz = = = = ff erent rest frame UV magnitudes.The solid lines correspond to the simulation with the originalcomposite LBG spectrum, and the dashed and dotted lines tothe simulations with the same spectrum, but the Ly- α line re-moved and doubled, respectively. [ A colour version of this figureis available in the online edition. ]becomes more and more peaked towards higher z , a system-atic bias towards smaller redshift remains. Bayesian PhotometricRedshift templates do not include the Ly- α emission line, whilethis line is present in the composite spectrum used for the simu-lations. The presence of the line could dilute the Ly- α break and cause the bias in the redshift estimation towards lower z . To testthis hypothesis, we manually removed the Ly- α line from thecomposite spectrum, and repeated the simulation. We also re-peated the simulation doubling the Ly- α line strength. We haveplotted the resulting summed zPDFs in Fig. 3 together with theoriginal results. In the two largest simulated redshifts the ten-dency of increasing Ly- α line strength to increasingly underesti-mate the redshift is obvious. At the two lower redshifts this is notenough to explain the involved uncertainties. However, in all thesimulated redshifts the average sizes of the biases are ∆ z ≤ .
4. A sample selection approach
In this section we present one way of selecting a clean sample ofhigh redshift galaxy candidates, using the zPDFs, and check itagainst traditional dropout selections. Our sample selection con-sists of two steps: cleaning the catalogue from non-desired de-tections, and applying a redshift selection. While the first step isalways needed, we will discuss later that, while sometimes use-ful, for many purposes a redshift selection is actually not needed.
We start our candidate selection by cleaning the ALHAMBRAcatalogues of any possible spurious or false detections, du-plicated detections, and stars. For this purpose we used themasks defined in Arnalte-Mur et al. (2014) describing the skyarea which has been reliably observed, and the stellar flag pro-vided in the ALHAMBRA catalogues (see Molino et al. 2014),setting ”Stellar Flag” < .
51 in order to remove stars. Thisshould remove the stars up to m < . F814W . Above this magnitude the stellar flag is not defined,and slight contamination by faint stars may remain. However,for fainter magnitudes, the fraction of stars compared to galax-ies declines rapidly, with a contribution of ∼
10% for magni-tudes m ( F W ) = .
5, declining to ∼
1% for magnitudes m ( F W ) = . . There is no one single correct way of applying zPDFs forcandidate selection. The best redshift (e.g. the first peak) canbe derived from the zPDF and assigned to each galaxy (e.g.Le Fevre et al. 2014) or the zPDF can be integrated and usedin one way or another to select a list of candidates (e.g.McLure et al. 2011; Duncan et al. 2014). Here we use the secondapproach in a very simplified way in order to select a clean sam-ple of high redshift ALHAMBRA galaxies. With this approachone is not obliged to be limited to any specific redshift range.However, we limit our study to the redshift range 2 . < z ≤ . α line, with at least one fil-ter. Because of the depth of ALHAMBRA we do not expect tofind many galaxies at the upper limit of z > .
0. In addition, theALHAMBRA sensitivity limit worsens rapidly for wavelengthsabove ∼ α break in at leasttwo filters bluer than 8000Å.When all of the information on the redshift probability distri-bution is used, one can select as candidates all the galaxies that
6. Viironen et al.: High redshift galaxies in the ALHAMBRA survey z P D F ( z ) z P D F ( z ) Fig. 4. zPDFs for two galaxies with very di ff erent ML Odds (black lines),
Top:
ML Odds = Bottom:
ML Odds = A colour version of this fig-ure is available in the online edition. ]have a probability greater than a given threshold of being at thedesired redshift interval. This threshold can then be selected toobtain the desired balance between completeness and contami-nation. To introduce this technique, we decided to opt for a cleanselection and select as candidates the objects fulfilling the crite-rion Z . . PDF ( z ) d z ≥ . , (3)i.e. all the galaxies with a probability of 90% or higher of beingat the redshift range that we are interested in. This leads to asample of a total of 9203 high redshift galaxies.We note that methodologically this selection could easily befurther refined, if needed. One way would be to study the con-centration of the probability distribution around its peak value,e.g. by calculating the ML analogy for the Odds parameter of-fered by the BPZ (Ben´ıtez 2000). The
Odds quality parameteris a proxy for the photometric redshift reliability of the sources.The
Odds parameter is defined as the redshift probability en-closed on a ± K (1 + z ) region around the main peak in the zPDFof the source, where the constant K is specific for each photo-metric survey. Molino et al. (2014) find that K = Odds ∈ [0 ,
1] and (cid:3) (z) N Fig. 5.
The redshift error distribution for a Gaussian approxima-tion for our sample of galaxies at high redshift.it is related to the confidence of the photometric redshifts, mak-ing it possible to derive high quality samples with better accu-racy and a lower rate of catastrophic outliers. As an example, inFig. 4 we show two zPDFs satisfying criterion (3), but with verydi ff erent ML Odds parameters. We also show the Gaussian ap-proximations of the corresponding redshift distributions. Whileit is obvious that a selection in
Odds can refine the redshift se-lection, we do not make any further selection of this kind. Wedo not need such a high precision in redshift in order to rejectthe objects like the one in the bottom panel of Fig. 4. Instead,for all of the galaxies that pass our selection criterion, we calcu-lated the σ of their redshift distribution for the Gaussian approx-imation. The σ distribution for the sample galaxies is shown inFig. 5. The average and median of this distribution are 0.13 and0.11, respectively. We consider this precision to be high enough.Alternatively, in the probabilistic approach (Sect. 5), the wholeredshift distribution is taken into account in a natural way; how-ever, we will come back to the question of Odds in Sect. 5. Wenote that in addition to the random errors, we can expect to havesystematic errors in the derived redshifts, as was discussed inSect. 3.1 and shown in Fig. 3 and Table 2. However, consider-ing the expected size of these biases, when working with coarseredshift bins, this should not be a problem.
We estimate here the expected level of contamination and in-completeness of our sample within the limiting magnitude ofALHAMBRA and assuming that the zPDFs correctly reflect theuncertainties in the redshift estimations.
Presuming the assumption of a flat prior is true, the upper limitfor the contamination is directly set by our selection criterion:as we select the objects with a ≥
90% probability of being atdesired redshift, we automatically allow a contamination of ≤
10% by galaxies at other redshifts. To get a more exact value ofthe expected contamination, we summed the probabilities of theobjects selected by criterion (3) within the redshift interval 2 . ≤ z ≤ .
0. The resultant average probability is ∼
7. Viironen et al.: High redshift galaxies in the ALHAMBRA survey selection criterion (3) is rather strict; there may be galaxies with,e.g., a >
50% probability of being within our redshift bin butwhich are not selected by our criterion. This naturally leads to alow level of completeness in our sample as will be discussed inthe next section.We expect that the most significant source of contaminationof our high redshift galaxy sample are the faint red galaxies atlow redshifts because of the confusion between the 4000 Å andLyman breaks. In addition, some faint cold stars may be in-cluded, as the preselection against stars is statistical and not de-fined for magnitudes fainter than m ∼ . The completeness at a given redshift bin is defined as the ratioof galaxies at the corresponding redshift that are detected andthat also pass the selection criteria to all the rest frame UV-brightgalaxies at the given redshift bin actually present in the Universe.It has been shown in Molino et al. (2014) that the ALHAMBRAcatalogues are ∼ m =
24 in the F W de-tection filter. For the high redshift galaxies that we are interestedin, this filter traces the UV continuum redwards of the Ly- α , theLy- α break only slightly entering the F W passband at z = F ν = constant), we can also expect a completedetection up to m =
24 in the first filter towards the Ly- α line forthe galaxies that we are interested in.If the flat prior assumption is correct, the expected com-pleteness due to our candidate selection can be derived by sum-ming the probability distributions within the redshift interval thatwe are interested in for all the objects in our cleaned cataloguewhich do not fulfil our selection criterion, i.e. N = X i Z . . PDF i ( z )d z (4)for all the objects i fulfilling the criterion Z . . PDF i ( z )d z < . . (5)This sum gives the expected total number of galaxies that arelocated in the redshift range that we are interested in, but not se-lected as such by our criterion. The total number is 40166.8, i.e. ∼ . Quasar spectra are not included in the BPZ spectral templates.Hence, our selection can contain quasars, but we do not ex-pect a complete selection of quasars. We tested if the knownquasars observed by ALHAMBRA would fulfil our redshift se-lection criterion (3). In total we found 205 ALHAMBRA objects that had counterparts identified as quasars with spectroscopicredshift in other surveys. They consist of 170 sources fromMatute et al. (2012) (see also references therein), one quasar at z = .
41 from Matute et al. (2013), 15 sources from the SDSSquasar catalogue DR10 (Pˆaris et al. 2014), and 19 X-ray sourcesfrom CHANDRA that have an associated optical and infraredcounterpart (Civano et al. 2012). For the CHANDRA sourceswe also demanded that they were classified as point sourcesand their variability parameter was greater than 0.25, in agree-ment with Salvato et al. (2009). Of these 205 quasars, 48 havea spectroscopic redshift in the range that we are interested in(2 . ≤ z ≤ .
0) and 2 are at higher redshifts ( z = .
07 and z = . z = .
07 is placed at z = . ± .
03, i.e. also enters our redshiftselection, and the quasar at z = .
41 is placed at z = . ± . i − bandnumber counts of quasars at the redshift range z = . − . z ≃ − i − band number counts of quasars at z = . − . − quasarswith m i < =
24 is derived. Hence, in the ALHAMBRA area wewould expect to have 2 .
38 deg ×
263 deg − =
626 quasars brighterthan m i =
24. The total number of galaxies brighter than m = k -correction be-tween the i − band and our ALHAMBRA bands. If 10% of thequasars at the ALHAMBRA area enter our selection, as we in-fer from the spectroscopic sample, the total (maximum) rate ofcontamination of our clean sample by high-redshift quasars is0 . × / = . < z < . . < z < .
2, giving 99.6 deg − quasars with m i < =
24. Doubling this to account for (i.e. overestimate for the muchsmaller volume) the quasars at the redshift range 0 . < z < . × . − × .
38 deg × . = m i =
24 at 0 . < z < . m =
24 in our clean sample(2296 galaxies), an additional maximum contamination rate of0.3% is obtained.
8. Viironen et al.: High redshift galaxies in the ALHAMBRA survey −0.5 0.0 0.5 1.0 1.5
G−R U n − G −0.4−0.2 0.0 0.2 0.4 0.6 0.8 R−i (cid:2) B − R −0.2 0.0 0.2 0.4 0.6 0.8 1.0 i (cid:2) −z (cid:2) V − i (cid:2) −0.2 0.0 0.2 0.4 0.6 0.8 1.0 i (cid:2) −z (cid:2) R − i (cid:2) z =2.96 ′0.29 z =2.20 ′0.32 z =4.0 ′0.3z =4.7 ′0.3 z =4.9 ′0.2 Fig. 6.
Locations of our clean sample candidates in four colour–colour diagrams used for traditional dropout selections. The selectionboxes in each diagram are shown with dashed lines and the redshift ranges they target are indicated in each panel. We only plotthe candidates in the redshift range within 1 σ of the one targeted by these diagrams (blue crosses). In the top left diagram the bluecrosses refer to the BX selection while the magenta dots to the LBG selection. See the text for more details. [ A colour version ofthis figure is available in the online edition. ] To see if the candidates in our clean sample would have been se-lected by traditional dropout methods, we tested how they wouldbe located in some traditional colour–colour diagrams. In partic-ular, we opted for testing the BX selection ( h z i = . ± . h z i = . ± . BRi ′ ( h z i = . ± . Vi ′ z ′ ( h z i = . ± . Ri ′ z ′ ( h z i = . ± .
2) LBG selectionsof Yoshida et al. (2006).First, we carried out SED fitting on our sample galaxiesin order to find a spectrum which we could then convolvewith the broadband filters used in the above dropout selections.To assure a good SED-fitting, we considered only the galax-ies with good quality photometry in all of the filters by set-ting ”irms OPT Flag” = =
0. This re-quirement reduced our sample to 8023 galaxies. For the SEDfitting we used the single stellar population (SSP) models ofBruzual & Charlot (2003) of all the available metallicities (sixmetallicity values in the range Z = . − .
05) and of 40 agesroughly logarithmically spaced from 10 Myr to the age of theUniverse. We added the extinction law of Leitherer et al. (2002)at the wavelength range 970 Å-1200 Å, and that of Calzetti et al.(2000) for longer wavelengths. At wavelengths below 970 Å,where neither of the two laws is defined, we adopted a constantextinction with a value equal to that at 970 Å. The colour excess, E ( B − V ), was varied in a range of realistic values: from 0.0 to0.5 (Shapley et al. 2003) in steps of ∆ E ( B − V ) = . ∆ z = .
025 tosample the redshift range that we are interested in, so that at eachredshift only the SSPs up to the age of the Universe at that timewere considered. The Lyman forest was modelled following the prescriptions of Madau (1995), considering the H α , H β , H γ , andH δ line blanketing. Below 912 Å the opacity was assumed to in-crease abruptly, leading to practically zero flux bluewards of theLyman break.These template spectra were convolved with theALHAMBRA filter passbands. Each galaxy in our samplewas fitted by this template library using the χ -method so thatonly the templates with redshifts z template = h z i ± σ z wereconsidered, i.e. those templates whose redshift is inside 1 σ fromthe median redshift of the fitted galaxy as derived from its zPDF.The template spectrum whose fit produced the lowest value of χ was then assigned as the best fit template for each galaxy inour sample. Finally, only the galaxies brighter than m =
24 inthe first filter redwards from the Ly- α line and with the reduced χ r < χ r = χ / (1 − N ), where N is the number of filters usedin the fit) were accepted for the analysis. These steps reducedour sample to 1844 and 1327 galaxies, respectively.The original spectra of these best fit templates were thenconvolved with the filter passbands of the broadband filters ofinterest and the objects were placed in the colour–colour dia-grams used in the dropout selections (Fig. 6). To simulate the G , R , and U n passband data used in the selections of Steidel et al.(2003) and Steidel et al. (2004), we downloaded the correspond-ing transmission curves from KPNO website . To simulate theselection of Yoshida et al. (2006), the B , R , V , i ′ , and z ′ transmis-sion curves were downloaded from NAOJ website .In each diagram in Fig. 6 we plotted only those candidates ofour sample whose (ALHAMBRA median) redshifts are within1 σ from the one targeted by the corresponding dropout selec- https: // / kpno / mosaic / filters / filters.html http: // / Observing / Instruments / SCam / sensitivity.html9. Viironen et al.: High redshift galaxies in the ALHAMBRA survey z P D F ( z ) Fig. 7.
Redshift probability distribution of a galaxy with a sig-nificant probability at both high and low redshift (black line).Overplotted is the corresponding Gaussian approximation of thedistribution (dashed red line). [
A colour version of this figure isavailable in the online edition. ]tions. We see that basically all of our candidates would also beselected by these traditional colour–colour diagrams. The per-centages of the candidates inside the selection boxes are 99%,99%, 97%, and 94%, for the LBG,
BRi ′ , Vi ′ z ′ , and Ri ′ z ′ selec-tions, respectively. The BX diagram shows the largest scatteroutside the selection box, the fraction of candidates inside thebox being 83%. The galaxy clearly outside the selection boxesin the bottom right corners of the bottom diagrams is the sameone in both diagrams. It is a very faint object, and even thoughit is brighter than m =
24 in the first filter redwards of the Ly- α (the magnitude being m = . σ limiting magnitude for the corresponding filter.
5. Probabilistic approach
The selection of the clean sample above is an example of theuse of zPDFs when one needs a candidate selection and wantsto be certain that the selected galaxies really are at desired red-shift. However, selecting both a clean and complete sample ischallenging. If one would like to have a more complete sample,one could relax selection criterion (3). However, relaxing it, forexample, to allow all the galaxies with a probability ≥
50% to beat high redshift to enter the sample would automatically lead to acontamination rate of ≤
50% (assuming the flat prior assumptionis correct). Hence, for any statistical study one should carefullytake care of the incompleteness and contamination corrections.For many purposes the candidate selection is not needed,but the galaxies and their properties can instead be consid-ered as continua described by their zPDFs. For each cataloguedALHAMBRA object, a zPDF is provided. For some galaxies, asfor many objects in our clean sample, this distribution is narrowand could be approximated by a Gaussian distribution withoutlosing much information. However, in other cases the distribu-tion is much more spread out and / or is double peaked. This issuewas recently discussed in detail by L´opez-Sanjuan et al. (2014).In Fig. 7 we show an example of a two-peaked and a spreadout distribution. Now, if we claimed the galaxy of Fig. 7 to beat any certain redshift bin z − z we would certainly fail (un-less this bin were wide enough to cover the whole range wherethe PDF(z) > p of equation (2) as fractions. A similar approach was adopted by McLure et al. (2009) when derivingLBG luminosity functions. In Fig. 8 we show the distribution of the whole set ofALHAMBRA galaxies as density contours in the same colour–colour diagrams as in Fig. 6. To obtain these contours, the cat-alogue was cleaned as explained in Sect. 4.1. In addition, goodquality photometry was required in all the filters. All the objectswere fitted by Bruzual & Charlot (2003) SSP models and con-volved with the broadband filter passbands to find their broad-band colours as in Sect. 4.4. Finally, only the galaxies brighterthan m UV =
24 in the first filter redwards from the Ly- α , andof good quality SED-fitting ( χ r < BRi ′ , Vi ′ z ′ , and Ri ′ z ′ selections, respectively, 35%, 39%, 46%, 37%,and 39%, i.e. more than one third of the restframe UV brightgalaxies would be missed by these selections. The existence ofgalaxies outside the selection boxes supports the known fact thatthe dropout selections are not complete. A recent spectroscopicstudy of high redshift galaxies in VUDS survey (Le Fevre et al.2014) also demonstrates the existence of high redshift galax-ies outside the UGR -selection box, albeit finding a smaller per-centage than we did (20%) of galaxies in the redshift range2 . < z < . . ≤ z ≤ . UGR -selection box, while 17%of those with a ‘very reliable’ flag are located outside the box.Of these two surveys, our selection function resembles more thatof the VVDS survey (pure magnitude selection) than that of theVUDS where a photometric redshift selection was also carriedout.
In order to obtain the number N of objects in a redshift bin z < z < z and magnitude bin m < m < m , we carried outa summation over all the objects i in the cleaned ALHAMBRAcatalogue of the form N = X m < m i < m Z z z PDF i ( z )d z . (6)For each redshift bin the apparent magnitude refers to the mag-nitude at the UV continuum as measured by the first filter red-wards from the Ly- α (and not containing the possible Ly- α line)at the corresponding redshift. The summation was carried out infive redshift bins. The redshift bins were selected inside the red-shift range we consider reliable in our ALHAMBRA data (seeSect. 3.1), i.e. 2 . < z < .
0, and we opted for a bin width of ∆ z = . z = . , . , . , . , and 4.5 in a total area of 8572.5 arcmin areshown in Fig. 9. These counts are also listed in Table 3.
10. Viironen et al.: High redshift galaxies in the ALHAMBRA survey −0.5 0.0 0.5 1.0 1.5
G−R U n − G −0.4−0.2 0.0 0.2 0.4 0.6 0.8 R−i (cid:2) B − R −0.2 0.0 0.2 0.4 0.6 0.8 1.0 i (cid:2) −z (cid:2) V − i (cid:2) −0.2 0.0 0.2 0.4 0.6 0.8 1.0 i (cid:2) −z (cid:2) R − i (cid:2) z =2.96 ′0.29 z =2.20 ′0.32 z =4.0 ′0.3z =4.7 ′0.3 z =4.9 ′0.2 Fig. 8.
Density of the ALHAMBRA high redshift galaxies in four colour–colour diagrams used for traditional dropout selections.The densities are derived using our probabilistic approach. The selection boxes in each diagram are shown with dashed lines, andthe redshift ranges they target are indicated in each panel. The contours enclosing 20%, 40%, 60%, 80%, and 90% of the objects aremarked as solid lines (dashed lines for the BX selection). See the text for more details. [
A colour version of this figure is availablein the online edition. ]This method implicitly takes into account both the incom-pleteness and contamination issues. However, this method alsosu ff ers from quasar contamination as these objects are not con-sidered by the BPZ. We estimated the maximum quasar contam-ination rate in the same way as in Sect. 4.3.3 above. We car-ried out the summation (6) over all the magnitudes and from z = . z = . z > . . / = . ≃
17% ofthe high-redshift quasars contaminate our counts. A similar ex-ercise for all non-stellar ALHAMBRA quasars with spectro-scopic redshift z < . m =
24 in the redshift range 2 . < z < . . × / . = . < m =
24 in the redshiftrange 2 . < z < . × . − × .
38 deg × . / . = . < . BRi ′ and Vi ′ z ′ dropout selected LBG candidates ofYoshida et al. (2006, Y06). According to R08, their samples arecentred at redshifts z ∼ . ± .
32 (BX) and z ∼ . ± . z ∼ . ± . BRi ′ ) and z ∼ . ± . Vi ′ z ′ ). We have also overplottedin Fig. 9 the z ∼ z ∼ z = . ± .
3) we have plotted both the BX and LBG candidatesof Reddy et al. (2008) as our redshift bin is actually in betweenthe redshift ranges targeted by these two selections.Bouwens et al. (2014) lists the surface densities and their er-rors in a table (Table 6 in B14) and we have plotted them inFig. 9. The plotted errors for the Y06 and R08 samples reflectthe Poisson errors, and we have corrected the Y06 and R08counts for incompleteness and contamination according to theinformation given in the corresponding articles: Y06 have stud-ied the completeness and contamination of their sample by sim-ulations. They list the expected number of interlopers for eachredshift selection and magnitude bin in tables while the com-pleteness vs. redshift is given in graphic form for each magni-tude bin. For each magnitude bin we opted to adopt the maxi-mum completeness from the distribution for the correspondingmagnitude bin. The spectroscopic sample of R08 gives the ex-pected contamination rate for each magnitude and redshift bin,while R08 studied the completeness of their sample (limited to M AB (1700Å) < − .
33) by simulations and found that ∼
58% ofthe restframe UV-bright galaxies in the redshift bin 1 . ≤ z ≤ . ∼
47% of the sim-ilar galaxies in the redshift bin 2 . ≤ z ≤ . ∼
42% and ∼
53% of these galaxies outside the BX andLBG selection boxes, respectively, quite higher fractions thanour estimate in Sect. 5.1 above.Detailed comparison of our counts with the counts derivedfrom dropout selections is not straightforward. The dropout se-lections target a certain redshift range, but a fraction of galaxiesfrom a much wider range of redshift can enter the selections.For example, the BX selection of R08 targets the redshift range
11. Viironen et al.: High redshift galaxies in the ALHAMBRA survey
18 19 20 21 22 23 24 25 26 mag [4890 (cid:4) A] -4 -3 -2 -1 N / m a g / a r c m i n Our countsz (cid:5) (cid:6) z=2.5 (cid:7)
18 19 20 21 22 23 24 25 26 mag [5510 (cid:8) A] -4 -3 -2 -1 N / m a g / a r c m i n Our countsz (cid:9) z=3.0 (cid:10)
18 19 20 21 22 23 24 25 26 mag [6130 (cid:11) A] -4 -3 -2 -1 N / m a g / a r c m i n Our counts z=3.5 (cid:12)
18 19 20 21 22 23 24 25 26 mag [6750 (cid:13) A] -4 -3 -2 -1 N / m a g / a r c m i n Our countsz (cid:14) (cid:15) z (cid:16) (cid:17)
18 19 20 21 22 23 24 25 26 mag [7370 (cid:18) A] -4 -3 -2 -1 N / m a g / a r c m i n Our countsz (cid:19) (cid:20) (cid:21) z (cid:22) (cid:23) Fig. 9.
Observed number counts for high redshift ALHAMBRA galaxies ( crosses ). The error bars reflect Poisson errors. For com-parison, we show the BX (z ∼ . ± . filled triangles ) and LBG (z ∼ . ± . filled squares ) number counts of Reddy etal. (2008; R08), the BRi ′ (z ∼ . ± . open circles ) and Vi ′ z ′ (z ∼ . ± . filled circles ) LBG number counts of Yoshida et al.(2006; Y06), and the ∼ open triangles ) and ∼ open inverted triangles ) LBG number counts of Bouwens et al. (2014; B14).The ALHAMBRA limiting magnitude is marked at m =
24 with a blue dashed line. See the text for more details. [
A colour versionof this figure is available in the online edition. ] z ∼ . ± .
32, but the spectroscopic redshift distribution ofthe galaxies entering the sample, and not considered as contam-inants, varies from z ∼ . z ∼ .
4. Our methodology sim-ply targets the adopted redshift range. The dropout selectionsrely on contamination and incompleteness corrections, while ourmethodology takes these into account implicitly. Despite thesedi ff erences, the general trends of our counts and the counts from literature coincide. However, in the two lowest redshift bins(centred at z = . z = .
0) there is a clear di ff erence be-tween the brightest end of our counts and the brightest bin ofR08 counts. The last bin of R08 is wide (from m =
19 to m = ff erence be-
12. Viironen et al.: High redshift galaxies in the ALHAMBRA survey
18 19 20 21 22 23 24 25 26 mag [4890 (cid:24) A] -4 -3 -2 -1 N / m a g / a r c m i n ML countsFP countsOdds counts z=2.5 (cid:25)
18 19 20 21 22 23 24 25 26 mag [5510 (cid:26) A] -4 -3 -2 -1 N / m a g / a r c m i n ML countsFP countsOdds counts z=3.0 (cid:27)
18 19 20 21 22 23 24 25 26 mag [6130 (cid:28) A] -4 -3 -2 -1 N / m a g / a r c m i n ML countsFP countsOdds counts z=3.5 (cid:29)
18 19 20 21 22 23 24 25 26 mag [6750 (cid:30) A] -4 -3 -2 -1 N / m a g / a r c m i n ML countsFP countsOdds counts z (cid:31)
18 19 20 21 22 23 24 25 26 mag [7370 ! A] -4 -3 -2 -1 N / m a g / a r c m i n ML countsFP countsOdds counts z " Fig. 10.
Observed probabilistic number counts for high redshift ALHAMBRA galaxies. The ML counts are shown as crosses, theFP counts as open squares, and the counts derived from an ”
Odds ” selected sample are shown as open circles. The error bars reflectPoisson errors. The ALHAMBRA limiting magnitude is marked at m =
24 with a blue dashed line. See the text for more details. [
Acolour version of this figure is available in the online edition. ]tween our counts and their counts. However, this is not enoughto explain the di ff erence. We do not know where this di ff erencecomes from, but we note that our sampling at the brightest endis clearly better which inclines us to consider our counts morereliable.Finally, we want to note that in all the redshift bins our countso ff er a good sampling of the bright end of the surface densities,down to the magnitudes m = −
22. It is also remarkable thataccording to our counts the total number of ALHAMBRA galax- ies brighter than m UV =
24 and at redshifts as high as ∼ . ∼ . The use of flat (i.e. no prior at all) or very permissive priors inhigh redshift studies is a common practice (e.g. McLure et al.2009; Bradley et al. 2014; Le Fevre et al. 2014; Duncan et al.2014) due to the uncertainties of the prior at high redshift. This
13. Viironen et al.: High redshift galaxies in the ALHAMBRA survey
Table 3.
Probabilistic number counts per magnitude bin at each redshift bin. The total area considered here is 8572.5 arcsec . Magnitude range N ( z = . ± .
3) N ( z = . ± .
3) N ( z = . ± .
3) N ( z = . ± .
3) N ( z = . ± .
17 18 19 20 21 22 23 24 mag [F814W] O S R Fig. 11.
The fraction of galaxies with
Odds > . F W magnitude for di ff erent redshift bins: 0 . < z < z = . ± . z = . ± . z = . ± . z = . ± . z = . ± . A colour version of this figure is availablein the online edition. ]means that variation in the density of galaxies as a function ofredshift was not considered when deriving the zPDFs. This, inturn, could lead to net contribution of objects from the denserredshift bins to the less dense ones caused by the galaxies withbadly defined, flat zPDFs. To test the possible e ff ect of this onour number counts, we carried out two tests.First, we derived the counts using a slightly di ff erent ap-proach. For each object in the cleaned ALHAMBRA cataloguewe calculated its ML Odds (see Sect. 4) integrating the ML zPDFwithin the range z ml ± . + z ml ), where z ml refers to the red-shift of the highest peak of the distribution. Then we eliminatedthe galaxies with a low ML Odds value in order to discard the ob-jects with flat zPDFs. To do this, we opted to set
ML Odds > . Odds derived counts tend to be lower than the ML (andFP) counts for the two lowest redshift bins (centred at z = . z = . z = . z = .
0) all counts coincide in all magnitudes (up to the limit-ing magnitude), and in the last bin (centred at z = .
5) the
Odds derived counts tend to be higher in the faintest magnitudes thanthe ML / FP counts. This could mean that at the lower redshiftbins and fainter magnitudes a net contribution from low redshiftgalaxies with flat zPDFs a ff ects our counts and tends to overes-timate them, while at the brightest magnitude bins the e ff ect isthe opposite. However, considering that the ML and FP countsdo agree in these magnitude bins, we do not believe this is thecase. The same e ff ect can be obtained if a smaller number ofhigh redshift galaxies have good Odds values at the first redshiftbins than the lower redshift galaxies, and the opposite would betrue for the last redshift bin.To study this in greater detail, we derived the Odds samplingrate (OSR) as introduced in L´opez-Sanjuan et al. (2014). Thisgives the fraction of galaxies with good
Odds values (in this case
Odds > .
3) to the total number of galaxies as a function ofmagnitude in the detection filter, F W . In Fig. 11 we show
14. Viironen et al.: High redshift galaxies in the ALHAMBRA survey the OSR vs. magnitude derived for 0 . < z < z = . ± . , . ± . , . ± . , . ± .
3, and 4 . ± .
3. We see that, at magnitudesfainter than ∼
20, the OSR indeed depends on redshift, beinglowest for our lowest redshift bin and systematically increasingwith redshift, the OSR of our highest redshift bin being higherthan that of the reference curve. Actually, this behaviour is alsovisible in the recovered summed zPDFs of our simulated highredshift galaxies in Sect. 3.1. In Fig. 3 we see how the recoveredsummed zPDF becomes narrower with increasing redshift.To summarise, deriving the galaxy redshift distribution froman
Odds selected sample should be considered with caution asat high redshift OSR strongly depends on redshift. Luckily, wedo not need to rely on such an approach as, despite our worriesabout the use of a prior in our high redshift study (Sect. 3.1), theprior does not seem to influence our counts significantly; bothML and FP zPDFs give similar results. As the prior takes intoaccount the varying galaxy density with redshift, and the FP andML counts coincide, there clearly is no significant net contribu-tion of objects with spread out zPDFs from the denser redshiftbins to the less dense ones. The study of the very brightest andnoisy end of our counts (from m ∼
19 to m ∼ −
22) needs towait for data from larger area surveys, like J-PLUS and J-PAS.From the number counts derived in this section, we estimate thatthese surveys will detect tens of thousands of high redshift galax-ies brighter than m = .
6. Summary
So far, most of the studies of the high redshift UV bright galaxypopulation have been based on dropout selections. Spectroscopicfollow-up of dropout selected samples (e.g. Reddy et al. 2008)have shown that the dropout selection su ff ers from severe con-tamination. Simulations (e.g. Yoshida et al. 2006; Reddy et al.2008) and a spectroscopic study of high redshift galaxies se-lected from a purely flux-selected sample (Le F`evre et al. 2005)have shown that the dropout selection is also highly incom-plete. This is further supported by a wide spectroscopic sampleby Le Fevre et al. (2014), where the candidates are selected us-ing photometric redshifts. We expect an alternative probabilisticmethod, like the one presented here, would help to remove thiskind of biases.We have studied the high redshift UV bright galaxy popu-lation in ALHAMBRA data adopting a novel approach basedon redshift probability distribution functions (zPDFs). We haveshown how a clean sample of high redshift galaxies can be de-rived from the ALHAMBRA catalogue, integrating the zPDFsand selecting only those galaxies with very high probability tobe at high redshift. We studied whether this clean sample wouldbe selected by the traditional dropout techniques, and basicallyall of the galaxies in our sample actually would also be selectedby these methods at 83 −
99% levels. However, the benefit ofour selection compared to the traditional dropout selections isthe expected very low percentage of interlopers.We have also shown that our clean sample su ff ers from se-vere incompleteness and is not able to derive any reliable sta-tistical properties about the high redshift galaxy population. Wehave introduced a probabilistic method which takes into accountboth incompleteness and contamination in a natural way. In thisapproach, the galaxies are not treated as unities but rather as frac-tions in each redshift, where the size of this fraction is derivedby integrating the corresponding zPDF of each galaxy at the red-shift range of interest. Using this approach, we have studied the distribution of the ALHAMBRA high redshift galaxies in the tra-ditional colour–colour diagrams and discovered that a significantpercentage of them ( > z = . z = .
5. The strengthof our counts is the good sampling of the bright end, down to m UV (AB) = ∼ ) J-PLUS and J-PAS multifilter surveys are avail-able. From the number counts derived in this work, we estimatethat we could detect tens of thousands of high redshift galaxiesbrighter than m UV (AB) = ML Odds > .
3) and scaling these to the total num-ber of objects in each magnitude bin. In the faintest magnitudebins we find di ff erences between these and the direct ML counts.Considering that the FP and ML counts roughly coincide in allmagnitude bins, we inferred that the di ff erences seen with thecounts derived from the Odds selected sample are due to varia-tions in the fractional amount of galaxies with good
Odds val-ues with redshift. We studied the evolution of this fraction as afunction of magnitude and redshift, and found out that at faintmagnitudes this fraction indeed varies with redshift.Even though we have discussed here only the application ofthe probabilistic method of deriving the galaxy number counts, asimilar approach could be used to study any redshift dependentgalaxy property. McLure et al. (2009) used a similar approach toderive LBG luminosity functions and, recently, Lopez-Sanjuanet al. (2014) discussed a similar approach to study the galaxymerger fraction. We will further study the ALHAMBRA highredshift galaxies using this methodology in the forthcoming pa-pers.Theoretically, our probabilistic method is totally free of bi-ases due to incompleteness and contamination. However, this isnot totally true, as our photo-z estimations are limited to whatis already known about the galaxy population because empiri-cal templates are used. The way to improve this aspect of themethod is to create unbiased lists of candidates, spectroscop-ically confirm them, and consequently refine the high redshifttemplates. For the unbiased candidate selection, zPDFs o ff er aunique opportunity. A wide spectroscopic campaign on candi-dates selected using zPDFs is already in progress (Le Fevre et al.2014). Once the spectra of objects derived from unbiased sam-ples are available, these can be used to improve the photo-z esti-mations at high redshift, and subsequently improve the accuracyof the statistical methods like the one presented here. Acknowledgements.
We acknowledge the anonymous referee for the usefulcomments. K. Viironen acknowledges the Juan de la Cierva fellowship ofthe Spanish government. We acknowledge funding from the FITE (Fondos deInversiones de Teruel) and support from the Spanish Ministry for Economy andCompetitiveness and FEDER funds through grants AYA2012-30789, AYA2006-
15. Viironen et al.: High redshift galaxies in the ALHAMBRA survey /
064 and PROMETEOII / / cosmicism . A. J. Cenarro acknowledges the Ram´on y Cajalfellowship of the Spanish government. M. Povi´c acknowledges financial supportfrom JAE-Doc program of the Spanish National Research Council (CSIC), co-funded by the European Social Fund. This research made use of Matplotlib, a2D graphics package used for Python for publication-quality image generationacross user interfaces and operating systems (Hunter 2007). References