The evolution of galaxy clustering since z = 1.5 in the ALHAMBRA Survey

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1 Mon. Not. R. Astron. Soc., 8 (2222) Printed 23 September 2 (MN LATEX style file v2.2) The evolution of galaxy clustering since z =.5 in e ALHAMBRA Survey P. Arnalte-Mur,2, V. J. Martínez,3, A. Fernández-Soto 4, A. Molino 5, A. Montero-Dorta 5, M. Stefanon, J. A. L. Aguerri 6, E. J. Alfaro 5, T. Aparicio-Villegas 5, N. Benítez 5, T. Broadhurst 7, J. Cabrera-Caño 5,8, F. J. Castander 9, J. Cepa 6,, M. Cerviño 5, D. Cristóbal-Hornillos 5,, R. M. González Delgado 5, C. Husillos 5, L. Infante 2, I. Márquez 5, J. Masegosa 5, M. Moles 5,, A. del Olmo 5, J. Perea 5, F. Prada 5, J. M. Quintana 5 Observatori Astronòmic, Universitat de València, Apartat de Correus 2285, E-467 València, Spain 2 Insitut de Física Corpuscular (CSIC-UVEG), València, Spain 3 Departament d Astronomia i Astrofísica, Universitat de Valencia, E-46 Burjassot, Spain 4 Instituto de Física de Cantabria (CSIC-UC), E-395 Santander, Spain 5 Instituto de Astrofísica de Andalucía, CSIC, Apdo. 344, E-88 Granada, Spain 6 Instituto de Astrofísica de Canarias, La Laguna, Spain 7 School of Physics and Astronomy, Tel Aviv University, Israel 8 Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Spain 9 Institut de Ciències de l Espai, IEEC-CSIC, Barcelona, Spain Departamento de Astrofísica, Facultad de Física, Universidad de la Laguna, Spain Centro de Estudios de Física del Cosmos de Aragón (CEFCA), E-44 Teruel, Spain 2 Departamento de Astronomía, Pontificia Universidad Católica, Santiago, Chile [DRAFT 3 23 September 2]Accepted 2222 December 22. Received 2222 December 2; in original form 2222 October 2 ABSTRACT The study of galaxy clustering at different redshifts or, equivalently, different cosmic times, is an important tool to obtain information about e process of grow of structures in e Universe, and about galaxy formation and evolution. We present e results of our measurements of cosmic clustering of galaxies at different redshifts ranging from z =.3 to z =.5 using data from e ALHAMBRA Survey. We find clustering properties at are compatible wi e observations in oer surveys and also at lower redshifts, but measure for e first time wi e same data e evolution of ese properties over our whole redshift range, which represents e central 5% of e history of e Universe. Key words: circumstellar matter infrared: stars. INTRODUCTION The clustering of galaxies is an important tool for e study of bo e large-scale distribution of matter, and its relation to galaxy formation and evolution. As ese phenomena evolve wi cosmic time, it is important to compare clustering measurements for local z samples to measurements at higher redshifts. The two-point correlation function ξ(r) is a simple tool pablo.arnalte@uv.es (PAM) This version is submitted to e ALHAMBRA Core Team for analysis and discussion, e auor list may be incomplete and outdated at provides very useful information about e characteristics of e galaxy clustering pattern. For samples at low redshift, ξ(r) is known to follow approximately a power-law behaviour, over a large range of scales, from hundreds of kpc to tens of Mpc (Totsuji & Kihara 969; Peebles 974; Martínez 999). However, studies wi recent larger surveys have found significant deviations from is behaviour (see, e.g., Zehavi et al. 24), which are fully consistent wi e halo model of clustering. One of e main problems (or opportunities) for e extraction of information from galaxy clustering is at galaxies are biased tracers of e matter density field [CITES?]. Galaxy bias depends on several properties of e galaxies [CITES?]. Observationally, e clearest segregation observed c 2222 RAS

2 2 P. Arnalte-Mur et al. is at due to luminosity (Hamilton 988): bright galaxies are more strongly clustered an faint ones. This can be understood in e standard hierarchical structure formation eories from e fact at bright galaxies form at more massive dark matter haloes. This effect has been clearly observed in galaxy surveys of e local universe (see, e.g. Norberg et al. 2; Tegmark et al. 24) for galaxies wi luminosities L L. This luminosity segregation, however, does not affect significantly galaxies wi L < L. Recently, ese studies of galaxy clustering and luminosity segregation have been extended to higher redshifts, using state-of-e-art pencil-beam spectroscopic surveys, such as e VIMOS-VLT Deep Survey (VVDS, Pollo et al. 26), e Deep Extragalactic Evolutionary Probe survey (DEEP2, Coil et al. 26), or e zcosmos survey (Meneux et al. 29). These works analysed e clustering in several galaxy samples extending up to z.2. Overall, e correlation function measurements were well fitted by power laws. Luminosity segregation is clearly detected, and in fact e dependence of clustering on luminosity is found to be stronger in ese cases an in local samples. In is paper, we use preliminary data from e Advanced Large, Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) Survey (Moles et al. 28) to study galaxy clustering for redshifts up to z =.5. ALHAM- BRA is a deep photometric survey, which uses a total of 23 optical and near-infrared (NIR) bands in order to obtain accurate and reliable photometric redshifts for a large number of objects, in eight fields for a total area (when finished) of 4 deg 2. It is a survey specially suited for e study of e large-scale distribution of galaxies at high redshifts, given its photometric dep, multiplicity of fields, and area covered, which improve on ose of similar spectroscopic surveys. Its main drawback is obviously e use of photometric redshifts, which may affect e clustering measurements. Our main aim is erefore to test e de-projection meod for e recovery of e real-space correlation function presented in Arnalte-Mur et al. (29). In is way, we explore e possibilities of ALHAMBRA to study e evolution of galaxy clustering and its dependence on luminosity up to high redshifts, z =.5. In Section 2, we explain in detail e characteristics of e ALHAMBRA Survey, and of e preliminary catalogue at we use here. Then, in Section 3, we select a catalogue suitable for galaxy clustering studies. This includes building e angular masks describing e selection function of e survey, eliminating possible stars in e catalogue, and selecting objects wi a reliable measure of redshift. In Section 4 we present our correlation function calculations, based on e de-projection meod of Arnalte-Mur et al. (29), for a set of samples selected in absolute magnitude, in ree redshift bins. We fit e different correlation functions by two simple models in order to extract information regarding clustering evolution and luminosity segregation. Finally, in Section 5 we discuss our results, and compare em to ose obtained for different surveys. 2 THE ALHAMBRA SURVEY The Advanced Large, Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) Survey (Moles et al. 28) is a photometric survey which will cover a total of 4 deg 2 in e sky, using 2 medium-band filters in e optical range, and ree standard broad-band filters (J, H, and K s) in e near-infrared (NIR). The aim of e survey is to study cosmic evolution in a broad sense, by providing an inventory of e contents of e Universe rough a large fraction of cosmic history. The survey was designed, erefore, to provide relatively accurate redshift estimates and spectral classification for e different objects and, at e same time, to sample a statistically significant volume at different redshifts. 2. Survey properties The survey has been carried out using e 3.5-meter telescope at e Centro Astronómico Hispano-Alemán (CAHA) in Calar Alto (Almería, Spain). The camera used for e optical observations is e Large Area Imager for Calar Alto (LAICA) 2, and Omega-2 3 is used for e NIR observations. The photometric dep of e survey is AB 25 (for a point source wi S/N = 5) for e optical filters bluer an 85 Å, wi e dep decreasing toward e red, and reaching K s 23 (all magnitudes are in e AB system). The use of a large set of medium-band filters places AL- HAMBRA half-way between e classical spectroscopic and broad-band photometric types of surveys. It reaches deeper in magnitude an previous spectroscopic surveys, even e deepest ones as VVDS or DEEP2. This means at e density of objects is higher, and it is able to sample a fainter region of e luminosity function. Regarding broad-band photometric surveys, e main advantage of ALHAMBRA is e improved accuracy for e determination of redshift and spectral type provided by e use of a large number of filters over e optical and NIR spectral range. 2.. The ALHAMBRA filter system The possibility of performing a survey using a large set of filters, in order to obtain a kind of very low resolution spectrum for each object was first discussed by Hickson et al. (994). A similar idea was implemented in e surveys Calar Alto Deep Imaging Survey (CADIS, Meisenheimer et al. 998), and Classifying Objects by Medium-Band Observations in 7 filters (COMBO-7, Wolf et al. 23). These surveys used different combinations of broad-, medium- and narrow-band filters in e optical range. The optical filter system for e ALHAMBRA survey was specifically designed to optimise e output of e survey in terms of photo-z accuracy, and number of objects wi reliable z determination, as shown in Benítez et al. (29). The chosen system consists of a set of 2 contiguous, equalwid, medium-band filters covering e full optical spectrum, between 35 and 97 Å. The wid of each of ese filters is F W HM 3 Å. The transmission curves for ese filters are shown in Fig.. This filter configuration also provides a homogeneous spectral coverage for a large

3 Evolution of clustering in e ALHAMBRA Survey 3 Figure. Response functions for e ALHAMBRA photometric system filters (colour lines). These response functions include e detector transmission, and atmospheric transmission at.2 air masses. The response functions are compared to e standard SDSS filters ugriz (broad-band filters in black lines). Figure from Aparicio Villegas et al. (2). range in waveleng. In is way, we minimise variation in e selection functions of e different objects wi redshift. Aparicio Villegas et al. (2) characterised in detail e AL- HAMBRA optical photometric system, and also provided a set of transformation equations between is system and e SDSS filter system. The survey is complemented by observations in e standard NIR filters J, H and K s. The fact of complementing e optical observations wi ese ree NIR filters is important for two reasons. On one side, to avoid e confusion between e Lyman and Balmer breaks at appears frequently when measuring photometric redshifts, creating a degeneracy between galaxies at redshifts z.5 and z 3, which affects e accuracy of e photo-z determinations (Moles et al. 28). On e oer side, e NIR observations provide valuable information about e old stellar population in galaxies, as opposed to e information about recent stellar formation an one can get from bluer wavelengs. In is way, ese observations provide information about parameters such as e mass of each galaxy Survey area and geometry The total survey area of 4 deg 2 is distributed over 8 widely separated fields in e sky. In is way, e effect of cosmic variance is minimised by measuring at independent volumes, while contiguous areas large enough to sample transverse scales up to tens of Mpc are still covered. The main criterion for e field selection was eir low extinction, and ey were chosen so at 7 out of e 8 ALHAMBRA fields have a significant overlap wi oer well-known surveys. The geometry of each of e surveyed fields is imposed by e geometry of e LAICA camera. As shown in Fig. 2, LAICA consists of four 4k 4k CCDs arranged in a 2 2 mosaic, wi e gaps between em being approximately e same size as e CCDs. In is way, a single pointing produces images for four separated patches of 5 5, Figure 2. Configuration of e four CCDs of LAICA in e focal plane. Dimensions are shown in arc minutes. Figure from LAICA s webpage ( and using four pointings a contiguous area of deg 2 can be covered. In e case of ALHAMBRA, two pointings are observed for each field, resulting in two strips of approximately deg.25 deg covered per field, adding up to e total 4 deg 2 for e full survey. The field of view of e Omega- 2 camera is equivalent to one of e LAICA CCDs, and eight of ose pointings are used to cover each of e AL- HAMBRA fields. When referring to images corresponding to a given CCD of e survey, we use e notation fa pb C, where A = (,..., 8) refers to e field (see Moles et al. 28 for details on e different fields), B = (, 2) refers to e LAICA pointing wiin is field, and C = (,..., 4) refers to e LAICA CCD wiin is pointing. In total, 64 CCDs will be observed to complete e survey. This field geometry will influence e way in which we measure galaxy clustering. In Section 3. below, we describe in detail e effective geometry of e survey taking is observing strategy into account. 2.2 The internal Data Release 3 (IDR3) In is work we have used e preliminary catalogues from e Internal Data Release 3 (IDR3), which contains data for all CCDs at had been observed in e 23 bands, and fully processed by March 2. In total, is release contains data for 39 CCDs, out of e total 64 planned for e full survey. These are distributed in ree complete fields (fields 2, 7, and 8), and four partially completed fields (fields 3, 4, 5, and 6). Thus, e nominal area covered in IDR3 is deg 2, and e total number of detected sources included in e catalogue is However, we only consider ose sources for which ere is a redshift determination (as explained below). This makes a total of 5868 objects in e catalogue. The data reduction and e preparation of e catalogues was carried out by e ALHAMBRA team and is still preliminary, but it will be very similar to at for e final ALHAMBRA catalogues. The two main points relevant for our analysis are e way in which objects are detected for inclusion in e catalogue (Husillos et al., in prep.??), and e way in which e photometric redshifts are estimated (Molino et al., in prep.??). (NOTA: Necesitamos definir estos artículos, tanto en término de autores como

4 4 P. Arnalte-Mur et al. F λ (arbitrary units) λ (Å) ES Sbc Scd SB SB2 SB3 Figure 3. SED of e six galaxy templates used for e determination of photometric redshifts for ALHAMBRA, using e BPZ software. We plot e flux per unit waveleng, wi e normalisation chosen so at all of em have e same magnitude in e I band. de contenidos incluso tener drafts lo antes posible, claro) Detection of objects The fact at e ALHAMBRA survey performs observations in 23 bands (2 medium band filters in e optical, and 3 in e NIR) makes e definition of object detection quite complex. A special strategy was defined in order to use a deep image for detection, while not biasing e detection towards any special type of objects. For each of e 39 CCDs, a deep image was constructed as e sum of a set of individual frames. These frames are ose observed rough e optical filters wi larger efficiencies (ose between A457M and A829M, included) 4, and taken under e best observational conditions, defined by an atmospheric transparency better an 5%, and a seeing better an.2 arcsec. As conditions change, is means at e deep image is a combination of different sets of frames for each CCD. However, on average, is deep image is similar to an image using e SDSS i filter, alough wi an extended wing covering a large part of e r filter. Object detection is erefore performed in is artificial deep image using e software SExtractor (Bertin & Arnouts 996), and en photometry is obtained for all objects in each of e filters using SExtractor s standard double image meod. The average dep obtained (for 3σ detections) in is catalogue is AB 24.5 for most of e optical filters, and AB 22 for e NIR filters (Moles et al. 28) Redshift determination Photometric redshifts (photo-z) for e objects in e IDR3 catalogue were obtained using an updated version of e Bayesian Photometric Redshift (BPZ) software (Benítez 2). This meod fits e observed photometry of e object to a library of template spectral energy distributions (SEDs) corresponding to different types of galaxies. In is 4 We name e ALHAMBRA filters using AλM, where λ is e effective waveleng, in nm (see Aparicio Villegas et al. 2). way, it finds e z and type at best match e observations for each object. A prior probability on e expected distribution of types and redshifts as a function of apparent magnitude is taken into account, in order to improve e accuracy of e redshift determination, and to minimise e number of catastrophic errors. In e analysis used for IDR3, e template library is an interpolation between six model SEDs corresponding to E/S, Sbc, Scd, and ree starbust types of galaxies. Hence, e best-fit spectrum for a given object can be a weighted average of two neighbouring templates. The SED of e six templates used are shown in Fig. 3. (... or someing like em... ) In order to improve e accuracy of e photo-z, e photometric zero-points in each band can be re-calibrated using e output of e photometric redshift determination (Coe et al. 26). This process is carried out independently in each of e CCDs. In e cases in which enough spectra are available ( out of e 39 CCDs), e spectroscopic redshifts z spec of ese objects are used for e re-calibration. (Definir cuantos son enough spectra ) In e rest of e cases, e re-calibration is done using purely e highquality photometric redshifts z phot obtained basically, assuming ey are exactly correct and en recalibrating e photometric zeropoints. The IDR3 catalogue contains e redshifts obtained wi e best zero-point calibration available in each case. A preliminary comparison wi e 36 spectra available in e area covered by IDR3 shows a typical error of z.2( + z) when e re-calibration is performed using z spec, and of.4( + z) when using only z phot (A. Molino, priv. comm.)(como la nota anterior, estaria bien tener una referencia real aqui, aunque sea en prep.!). The Bayesian framework used allows us to not only obtain e best-fit redshift and galaxy type for each object, but also a full redshift probability distribution function p(z). It is however not feasible to store and use e full p(z) of all galaxies in e analysis, so e catalogue contains only a set of parameters to characterise it. The first of ese parameters is e mode of e distribution, which is e best estimate for e redshift of e object, and we call simply z. The odds parameter p odds gives e probability at e redshift is contained wiin a distance ±.2( + z) from e best estimation. This parameter is erefore a reliable estimation of e quality of e redshift determination, as it gives a measure of how concentrated around e mode e obtained p(z) is. Thus, selecting objects wi values of p odds close to corresponds to selecting objects wi high-quality redshifts. Finally, e parameters z max and z min define an interval around z containing 68% of e probability. In e case in which p(z) were a Gaussian, erefore, its standard deviation would be given by σ z = zmax zmin 2. () Alough p(z) is not Gaussian in general, is can be a good approximation when we restrict e analysis to high-quality photo-z (see e.g. Fernández-Soto et al. 2; Ilbert et al. 29). Hence, we will use σ z defined above as measure to characterise e accuracy of e redshift determination in e different samples used below in our analysis.

5 Evolution of clustering in e ALHAMBRA Survey 5 SELECTION OF A CATALOGUE FOR LARGE-SCALE STRUCTURE STUDIES X (a) Weights mask Y Based on e IDR3 data, we prepared a galaxy catalogue suitable for e study of e large-scale structures (LSS). The reason for is is twofold. On one side, e original IDR3 catalogue contains all e objects which passed basic detection criteria in e deep images. This means at a large fraction of ese are spurious objects due to noise in regions wi low exposure times, or to imaging defects (e.g. fragmentation of bright saturated stars). Moreover, from e real objects of e catalogue, we should en select ose objects which are useful for e LSS analysis, i.e., galaxies wi a good photometric redshift determination, us eliminating stars and also galaxies wi low quality photo-z. On e oer side, in order to make LSS studies, such as e calculation of e two-point correlation function, we need to characterise e selection function of e survey. In e first place, we describe how we characterised e angular selection function of e survey, and eliminate e objects outside of it. We do not consider here e radial selection function of e survey, but will model it for each particular sample used in e analysis, as described in Section 4.2. We also describe how we perform e star-galaxy separation in e catalogue, and our criterion for e selection of objects wi good redshift determination. Y Angular selection function and survey masks We performed a basic characterisation of e angular selection function of e survey based on e object detection procedure. We use here a basic selection function, in e form of an angular mask which describes only which areas in e sky have been reliably observed by e survey and which have not. However, we do not study variations in completeness between different areas inside e mask. Our approach is to focus in e object detection procedure (see Section 2.2. above), and to identify areas of e images in which ere are potential problems for a correct detection of extra-galactic objects. Those identified areas are left out of e survey mask, and ose objects outside of e mask are eliminated from e catalogue. Alough most of ese objects are spurious or not very reliable detections, a fraction of em are actually good objects. Hence, a compromise is needed when choosing e actual parameters at define e mask. The actual criteria used for e definition of e mask are of two types. The first is related to e elimination of areas of e deep image wi low exposure time, and e second to e identification of defects in e image, or extended objects, which may affect e detection of near objects. We illustrate e different steps in e construction of our angular mask for a region of e CCD f2p in Fig. 4. The first criterion is based on e weight image associated to each of e deep images. This image contains a weight for each pixel which is proportional to e total exposure time at is pixel of e frames combined to build e deep image. We normalise e weights in each CCD to e maximum of e weight image. We en select only e regions of e image where is pixel weight is larger an.75. That is, we do not consider in our masks ose regions c 2222 RAS, MNRAS, X 5 (b) Bad objects mask Y X 5 (c) Negative mask Figure 4. A region of e deep image corresponding to e CCD f2p, illustrating e process to define e angular mask of e survey. It corresponds to a quarter of e CCD, covering 8 8arcmin. In each of e images, we show one of e partial masks combined to get our final mask: e mask based on e weight image (a), e mask for objects which are eier saturated or too large (b), and e mask for regions wi negative values (c). In all ree cases, e border of e mask is e blue line, and e red dots are objects in e catalogue which are excluded by e mask.

6 6 P. Arnalte-Mur et al. Pixel weight reshold.75 Object area reshold 3 pix2 = arcsec2 Object leng reshold Extra border pix = arcsec 6 pix = 3.3 arcsec 4 Y Table. Parameters used in e definition of angular masks (see e text for details). which were observed (for e deep image used for object detection) for less an e 75% of e maximum exposure time. The main effect is at, due to e diering in e observation of e different frames, we eliminate e areas around e borders of e image (see Fig. 4a). In order to apply e criteria related to particular defects or objects, we used e SExtractor software. We performed a standard object detection in each of e deep images (wi e default parameters) using SExtractor. We en selected a series of objects at may cause spurious or incorrect object detections. We masked out all objects which were flagged as saturated by SExtractor, and also ose wi an area larger an 3 pix2, or wi a major axis larger an 4 pix (see Fig. 4b). Objects wi large area may correspond to bright stars, but also to nearby galaxies. In eier case, ey would affect e detection of far extragalactic objects in e region around em. The very elongated objects would normally correspond to defects in e image (e.g. cosmic rays not corrected for), or spikes created by bright saturated stars. Finally, we also masked all objects detected in e inverted image, which correspond to regions of e image wi negative values found next to some saturated stars, or near e border of e image (see Fig. 4c). In order to eliminate e effect of ese bad objects in e neighbour regions, we also masked out an extra border of 6 pix around each of em. Table contains a summary of e parameters used when defining our survey angular mask for ALHAMBRA. This set of parameters is a conservative choice, but e gain in effective area at would be obtained by using a more relaxed choice would not be very large. Fig. 5 illustrates e final mask considered, for e same region shown in Fig. 4. Once we had defined e angular masks for each of e CCDs, we converted em to e polygon format of e mangle software (Swanson et al. 28). This software allows an easy manipulation of e masks, and also provides useful routines to perform tasks such as calculating e effective area covered by e masks, or generating random Poisson catalogues of points inside em. We combined e masks of e different CCDs into 7 masks, one for each of e fields. In e case of e ree completed fields in IDR3, e resulting mask is composed by 2 stripes of approximately 5 each, while in e rest of e fields (wi just one LAICA pointing completed), e CCDs have gaps in between em. We avoided overlaps between CCDs by simply cutting e masks where appropriate, but e overlap regions were minimal anyway. As an illustration, Fig. 6 shows e final masks used for a completed field (field 2), and a field wi only one completed pointing (field 3). The final effective area of e survey mask for IDR3 is.877 deg2, which means at we are using a 77% of X Figure 5. We show e same region of e deep image for f2p as in Fig. 4, togeer wi e final angular mask used. The border of e mask is e blue line, and e green dots are e positions of e objects inside e mask. Field No. of CCDs A (deg2 ) Nmask Nmask /Ntot % 74.6% 8.6% 79.5% 78.2% 73.% 69.3% Total % Table 2. Properties of e angular masks obtained for e different ALHAMBRA fields. For each field, we list e number of CCDs used, e effective area of our mask A, e number of objects we select inside e mask Nmask, and e fraction of ese selected objects wi respect to e total number of objects in e catalogue Ntot. e nominal area of deg2 for e 39 CCDs. We eliminated from our catalogue ose objects located outside of our mask, e 25.% of e total. This left us wi objects inside e mask. The mask area and number of objects in each of e fields is listed in Table Star-galaxy separation In order to build a catalogue for LSS studies, we need to eliminate e stars present in e original catalogue. In order to do so, we used a separation in colour, similar to e usual BzK meod (Daddi et al. 24). Adopting is meod to e ALHAMBRA photometric system, we made a cut in e (A457M J) vs. (J Ks ) diagram, shown in Fig. 7. In particular, we classified as stars objects wi (J Ks ) 6.6(A457M J).32. (2) c 2222 RAS, MNRAS, 8

7 Evolution of clustering in e ALHAMBRA Survey Stars Galaxies 4 A457M - J J - K s Figure 7. Colour-colour diagram used for our star-galaxy separation in e ALHAMBRA catalogue. For clarity, only objects wi magnitude errors smaller an. are shown. The line corresponds to e cut we use for e separation, equation (2) N Fraction (< p odds ) 5.2 Figure 6. Angular masks for e ALHAMBRA fields 2 (top) and 3 (bottom), which are illustrative of e masks obtained for fields wi two or one completed pointings, respectively. The shaded area corresponds to e regions of e survey at are included in e calculations. The red square marks e region which is shown in Figs. 4 and 5. This cut works well to separate stars from galaxies in AL- HAMBRA data (Stefanon et al., in prep). This cut selects 8674 objects from our sample as stars (23.%), hence we are left wi galaxies in our catalogue. 3.3 Redshift quality selection In order to study e LSS using photometric redshift catalogues, it is essential to select samples wi high quality redshift determination. This means bo a small average error of e redshifts, and a small number of outliers. An example of is need are e results obtained in Arnalte-Mur et al. (2) for e de-projection of e correlation function. In e case of redshifts determined by BPZ, e parameter p odds provides a reliable way to select redshifts of high quality (Siempre Benitez 2?). The distribution of is parameter in our catalogue (after e star-galaxy separation above) is shown in Fig. 8. The choice of e reshold value to make a selection should be a compromise between getting p odds Figure 8. Histogram showing e distribution of e parameter p odds in e catalogue. The wid of e bins is. units, and e histogram contains data for a total of galaxies, after e star-galaxy separation. The green continuous line gives e cumulative distribution, to be read from e right vertical axis. The red dashed line corresponds to e reshold p odds =.85 used for our selection, and to e fraction of objects at we eliminate in is way. e objects wi e best redshift quality, while retaining a large enough number of objects in our sample. However, e fact at e histogram has a pronounced peak for large values of p odds means at e result will not depend much on e exact reshold chosen. We use σ z defined as in equation () as a measure of e standard deviation of e posterior probability distribution of z, and erefore as an estimate of e error on z. We plot, in Fig. 9, e σ z obtained for each object as function of e p odds parameter. As expected, σ z decreases, on average, wi p odds. Moreover, we see at ere is a population of objects at are far from e main locus, wi values as high as σ z 2. These correspond to objects whose redshift determination is very uncertain, due to eir p(z) being very wide or having more an one peak. A large fraction of em will be outliers, in e sense at e best z estimation from

8 8 P. Arnalte-Mur et al % 68% σ z.5 N p odds z Figure 9. Distribution of e σ z obtained according to equation (), as a function of e p odds parameter. The green continuous line shows e median σ z for each value of p odds, and e shaded areas e symmetric regions containing 68% and 9% of e galaxies, as indicated. The remaining % of galaxies are plotted as blue dots. The red vertical dashed line corresponds to e reshold p odds =.85 used for our selection. BPZ will be far from eir real redshift. In order to avoid is type of objects, we select only objects wi p odds >.85. Making is selection, we have, for all objects, σ z.2, and us we minimise e possibility of having outliers in our sample. Making is selection based on e p odds parameter, we eliminate 63.% of e objects previously selected, and we are left wi 673 objects wi high redshift quality in our final LSS catalogue. Note: We may add here e σ z at is obtained wi e spectroscopic sample if exactly ese same cuts are applied, just to give more weight to e selection. I can foresee most objects from e spectroscopic sample actually passing e criteria, as ey must be bright, and having high odds, so e dispersion will be close to e nominal Characteristics of e final LSS catalogue used The final catalogue contains 673 objects after e ree selection steps explained above. The redshift distribution of e objects is shown in Fig.. The mean redshift of e catalogue is z =., and e median redshift is z m =.8. The bulk of e objects is located at z <.5, alough ere is a significant population at z [2, 3] and a small number of objects at higher z, up to e maximum z max = Note: We can comment on e fact at e distribution is bimodal. This is a natural selection effect imposed by our selection. A purely flux-limited catalogue would have one peak, but we are selecting on photometry and on photo-z quality, and it is a wellknown fact at objects at z 2.5 and higher are easy to spot based on photometric redshifts, plus ere could still be some leftover degeneration wi lower-redshift objects. As we have already made a severe selection in order to restrict e catalogue to galaxies wi high quality photometric redshifts, we can use σ z, as defined by equation (), Figure. Histogram showing e distribution of e measured redshifts for e 673 objects in our final LSS catalogue. The wid of e bins is.5 units. The mean of is distribution is z =., and e median is z m =.8. N σ z /(+z) Figure. Histogram showing e distribution of e relative redshift uncertainties calculated from equation () for e 673 objects in our final LSS catalogue. The wid of e bins is.5 units. The mean of is distribution is ( ) median value is σz +z =.. m ( σz +z ) =.2, and e σ z +z m as a measure of e redshift uncertainty for each object. We σ consider e relative uncertainty, z, and show its distribution in e catalogue in Fig.. The mean value for e +z ( ) σ final catalogue is z =.2, and e median value is +z ( ) =.. These results are in line wi e predictions for e redshift accuracy of e survey (Moles et al. 28; Benítez et al. 29), and to e preliminary results obtained in comparisons wi spectroscopic redshifts Distances, K-corrections and absolute magnitudes We added to is final catalogue two quantities at will be needed later in e sample selection and LSS studies: e distance to and absolute magnitude of each object. We calculated e co-moving distance to each object using e best-fit photometric redshift z in each case, and

9 Evolution of clustering in e ALHAMBRA Survey 9 assuming a flat fiducial cosmology wi Ω M =.27 and Ω Λ =.73, as given by e WMAP 7-year results (Komatsu et al. 2). We express all quantities in terms of h, e.g. we measure distances in units of h Mpc, so we do not need an explicit value for it. We also calculate, for each object, e corresponding absolute magnitude in e B band,. We use here e B band as it allows a more direct comparison wi results from oer surveys. Moreover, e region of e spectrum corresponding to e B band in e rest-frame is well sampled by e ALHAMBRA filter set (including e NIR filters) for redshifts as high as z 2. The same procedure used here could be used, anyway, to calculate e absolute magnitude in any given filter. We calculate in terms of e apparent magnitude m A in one of e ALHAMBRA filters as (Hogg et al. 22) = m A DM K BA, (3) where DM is e distance modulus, defined in terms of e luminosity distance d L as ( ) dl DM = 5 log, (4) pc and K BA is e K-correction term (Humason et al. 956; Oke & Sandage 968). This term accounts for e difference between e bandpass of e chosen ALHAMBRA filter in e observer s frame, and e bandpass of e B filter in e object s rest-frame. In e general case, K BA is given by K BA = 2.5 log ( ) dλλ λ L λ T +z A(λ ) dλ eλ eg λ (λ e)t B(λ e) ( + z) dλλ g λ (λ, )T A(λ ) dλ eλ el λ (λ e)t B(λ e) where L λ (λ) is e emitted-frame luminosity of e object per unit waveleng, T X(λ) is e transmission of filter X, and λ e and λ refer to wavelengs in e rest-frame and in e observer s frame, respectively. The function g λ (λ) gives e flux of e standard source defining e zero-point for e magnitude system. We use in all cases e AB magnitude system, so at g λ (λ) λ 2. One can only calculate exactly e K-correction when knowing e real emitted spectrum of e object, L λ (λ). We approximate it in our case using e best-fit spectrum determined by BPZ for each object during e photometric redshift determination (see Section 2.2.2). However, we can choose e ALHAMBRA filter m A used for e calculation in a way at minimises e dependence of K BA on e actual spectrum of e object. To is end, we choose m A A82M. This filter has an effective waveleng of λ eff = 82 nm (Aparicio Villegas et al. 2), which corresponds approximately to e effective waveleng of e B filter redshifted to e median redshift of e catalogue, z m =.8. As explained above, is best-fit spectrum is in each case a combination of two neighbouring templates in e library. We recover is spectrum in is same way in each case, for e calculation of K BA using equation (5). Fig. 2 shows e K-correction term for our choice of filters and for e six template spectra used. We see at, alough our choice of e filter A82M minimises e dependence of K AB on e selected template at z.8, ere is still (5) K BA ES Sbc Scd SB SB2 SB Figure 2. K-correction terms, as defined by equation (5), for e transformation from filter A82M in e observer s frame to filter B in e object s rest frame. They are calculated for e six BPZ template spectra shown in Fig. 3. an important dependence for different redshifts, going up to maximum differences of.5 mag in e redshift range z [.3,.5]. Therefore, using equations (3,4,5), we calculated e absolute magnitude for e objects in e catalogue. We had to exclude 448 objects from e catalogue (e.4%) which do not have a measured value of e apparent magnitude A82M. As we use all e distances in units of h Mpc, we actually calculate e quantity 5 log h. 5 We always refer to is quantity in e rest of is paper, even when we drop e second term for simplicity. Note: We can refine is a bit furer and use e normalisation of e SED instead of e filter closest to rest-frame B 4 CORRELATION FUNCTIONS FOR ALHAMBRA CATALOGUES The aim of is Section is to test e meod for e calculation of e real-space correlation function described in Arnalte-Mur et al (2) to real data from e ALHAM- BRA survey, and to use e results obtained to study e evolution and luminosity dependence of galaxy clustering. 4. Selection of samples In order to be able to study e dependence of clustering properties on bo luminosity and cosmic time, we built a series of subsamples from our catalogue, by making a selection in redshift and absolute magnitude. We selected subsamples in non-overlapping bins in redshift. The size of ese bins is limited by e requirement at ey are much larger an e distance we will integrate in e radial direction, r,max. We showed in Arnalte-Mur et al (2) at using smaller bins may introduce systematic effects in e correlation functions we want to measure. 5 For reference, 5 log h =.775 for h =.7. z

10 P. Arnalte-Mur et al. - 5 log h () = z () = -5.5 () = -6.5 () = -7.5 () = -8.5 Figure 3. Absolute B-band magnitude vs. redshift z for our LSS catalogue. The different lines show e boundaries of e samples we select for our analysis. Taking is fact into account, and e limitations in volume covered and galaxy density, we decided to use ree redshift bins. The low redshift bin (abbreviated as L in sample names) corresponds to z [.3,.6], e medium redshift one ( M ) to z [.6,.], and finally e high redshift bin ( H ) covers redshifts z [.,.5]. We note at our H redshift bin gets deeper an any previous correlation function study based on spectroscopic surveys (Coil et al. 26; Meneux et al. 29; Abbas et al. 2). From Fig., we see at it may be possible to extend our analysis to higher redshift, alough wi a much lower density. We do not explore is possibility here. On top of e redshift selection, we also apply a set of cuts in absolute magnitude. We use reshold samples, meaning at we will impose a faint luminosity reshold, but not a bright limit. In is way, we obtain approximately volume-limited samples, but also we can study e luminosity dependence of clustering, and its evolution. Following Meneux et al. (29) and Abbas et al. (2), we apply an absolute magnitude reshold depending linearly on redshift as M B (z) = M B () + Az, (6) in order to follow e evolution of samples corresponding approximately to e same galaxy population. The value of e constant A characterises e typical luminosity evolution of e galaxies in e catalogue. It can be derived from e evolution of e luminosity function (LF) parameter M. Here, we take e value A =, which is similar to e LF evolution observed in different samples at ese redshifts. However, we could refine it by measuring e LF using is same ALHAMBRA catalogue. We characterise each sample by e corresponding reshold at z =, MB (), and select e galaxies at each redshift z requiring < MB (z), as given by equation (6). We made five absolute magnitude cuts at e low redshift bin, and only kept e more luminous samples at higher redshifts. This allows us to study in detail e luminosity dependence of clustering, but we should bear in mind at ese samples (for a given redshift bin) are not independent from each oer. We show in Fig. 3 e actual cuts made in e red- Table 3: Properties of e subsamples used in e analysis. For each sample, we give e redshift bin; e absolute B magnitude reshold at z =, (), used for e luminosity cut following equation (6); e number N of galaxies in e sample; e volume V covered by e redshift bin; e mean galaxy density for is sample n; e mean redshift z; e median MB of e galaxies in e sample; e median luminosity of e galaxies in terms of e L at is redshift; e average redshift uncertainty σz calculated according to equation (); e radial distance interval r corresponding to is σz at z; and finally e maximum used for e integration along e line-of-sight in our calculation, r,max. H7.5B H8.5B H9.5B M6.5B M7.5B M8.5B M9.5B L5.5B L6.5B L7.5B L8.5B L9.5B Sample z range M B () N V (h 3 Mpc 3 ) n(h 3 Mpc 3 ) z M med B L med /L σz r( σz)(h Mpc) r,max (h Mpc)

11 Evolution of clustering in e ALHAMBRA Survey shift absolute magnitude plane to define our samples, and give details of e properties of each sample in Table 3. The name used for each sample comes from e letter L, M or H to denote e redshift bin, e absolute value of e MB () used for e cut, and a B denoting e band used for e absolute magnitudes. For each sample we give e basic properties such as number of galaxies, volume and density, but also e characteristic redshift z and B band absolute magnitude MB med of e galaxies in e sample. We compare e MB med to e characteristic absolute magnitude MB at z for each of e samples. We calculate MB(z) for is comparison using e data from Abbas et al. (2), who used e LF obtained by Ilbert et al. (25) for e VVDS. From e obtained luminosity ratios L med /L, we see at we are considering here samples wi L L. As e accuracy of e photometric redshifts depends on magnitude and redshift, it varies among our samples. We calculated e mean estimated error on e redshift determination, σ z, calculated according to equation (). We use is parameter below to determine e maximum line-ofsight distance r,max for our integration of ξ(r, r ). ρ (h 3 Mpc -3 ).5 () = () = () = () = The calculation in practice We measured bo e projected correlation function w(r ), and e de-projected real-space correlation function ξ dep (r) using e meod described in detail in our previous work (Arnalte-Mur et al. 29). In summary, we separate e distance between pairs of galaxies in two components, one along e line-of-sight (r ), and one in e transverse direction (r ), following equation XXX in at reference. We estimate e two-point correlation function ξ(r, r ) using e Landy & Szalay (993) (LS) estimator, and en integrate along e line-of-sight XXX to obtain w(r ). Finally, we use e relation XXX between e real-space correlation function ξ r(r) and w(r ) to obtain our de-projected correlation function, ξ dep (r), which should be a good estimate of ξ r(r). The actual calculation is made based on e discrete values calculated for w(r ) using equation XXX. NOTE: Rewrite ese paragraphs to quote equations from e reference article and/or write an Appendix summarising e meod. In e case of ALHAMBRA, we are dealing wi 7 fields widely separated in e sky. Correlations between different fields are erefore unimportant for our calculations. However, correlations between pairs of objects located in a different CCD or stripe but in e same field are actually important for e study of correlations at scales up to a few tens of Mpc. We erefore make e full calculation of w(r ) and ξ dep (r) for each of e fields separately, and we obtain our final result by averaging e results obtained for e different fields. When making is average, we weight each of e fields proportionally to e effective area covered in each of em (see Table 2). In order to calculate ξ(r, r ) using e LS estimator, we need an auxiliary un-clustered catalogue. This should be a realisation of an homogeneous Poisson random process, following e same selection function as e real data for e sample considered. We model e angular selection function of e survey using e mask created in Section 3., and assuming a homogeneous completeness inside it. In order to model e radial selection function, we calculate e density () = r (h - Mpc) Figure 4. Number density of e different samples used, as function of radial distance. The different samples are identified by e corresponding absolute magnitude reshold at z =, MB (). The grey lines show e original density profile, and e solid lines (red for e low-, green for e medium-, and blue for e high-redshift bin) show e actual density functions we use for our calculations after smooing wi a 3 h Mpc kernel. The limits between redshift bins are marked by vertical dot-dashed lines. along e radial direction, ρ(r), for each of e samples, averaging over e different fields. We smoo ρ(r) wi a kernel of wid 3 h Mpc, and use e resulting function as our estimate of e radial selection function. The ρ(r) obtained for each of e samples is shown in Fig. 4. Despite our selection, e samples are not exactly volume-limited, as can be seen by e global trend of ρ(r) to decrease wi r. This trend is more clear for e high-redshift bin. Moreover, we obtain a series of peaks at approximately regular intervals in ρ(r). As we are averaging over 7 separate fields, ese can not correspond to real structures in our sample, but should be e result of e data processing or redshift determination 6. Therefore, we consider ese peaks as part of e selection 6 Periodic features in e redshift distribution such as ese can be induced by e filter responses and eir reflection in e multidimensional colour space at is probed by e photo-z techniques. We are analysing ese features in more detail.

12 2 P. Arnalte-Mur et al. function. We generate e corresponding Poisson catalogues for each sample and field, containing N R = 2N D points in each case to reduce e effects of shot noise in our results. When integrating ξ(r, r ) along e line of sight to obtain w(r ) in practice, we need to set an upper limit for e integration, r,max. We showed in Arnalte-Mur et al. (29), using our simulated halo catalogues, at an optimal choice for is value is r,max 4r( z), where r( z) is e radial distance corresponding to e typical redshift uncertainty z of e sample. In e case of ALHAMBRA data, we estimate z as e mean of e σ z values (equation ) of e galaxies in e sample, and use is same choice for r,max. The actual values used for e calculations using e different samples are shown in Table 3. Regarding e upper limit r,max in e integration of w(r ) to obtain ξ dep (r), we use e values r,max = 2, 3, 4 h Mpc, respectively, for samples in e low-, medium-, and high-redshift bins. These values correspond, approximately, to e transverse co-moving distance subtended by an angle of 45 arcmin (ree times e side of a LAICA CCD) at e maximum redshift of each of e bins. In all our calculations, we use logarimic bins in bo r and r, wi a spacing of log r = Error estimation In order to estimate e error and full covariance matrix of our results, bo for w(r ) and ξ dep (r), we used e jackknife meod (see e.g. Norberg et al. 29). In is case, we used as jackknife regions e N jack = 39 CCDs in e catalogue, so e jackknife samples used were obtained omitting one of e CCDs at a time. We repeated e full calculation for each jackknife sample, taking into account e change in weighting when averaging over e fields. Our estimate for e covariance matrix between bins for w(r ) is en C ij = N jack N jack N jack (wi k w i)(wj k w j), (7) k= where wi k is e value obtained for e jackknife sample k in e r bin i, and w i is e average of e values obtained for bin i. The same meod was used to estimate e covariance matrix in ξ dep (r). The standard error estimate for a single bin is given by σ i = C ii. An alternative meod for estimating e errors would be to use directly e variance between e values observed in e 7 different fields. As e fields are separated in e sky, ey can be considered as totally independent, and us is can be a direct measure of e uncertainty in e mean value obtained. The results for σ i obtained using our jackknife meod are similar to ose obtained from e variance between fields, but e jackknife results are less noisy. This is an additional indication at our jackknife estimation is correctly taking into account not only e shot noise, but also e cosmic variance contribution to e uncertainty. Moreover, e fact of using 39 realisations instead of only 7 fields means at e results are more robust, and at we can estimate e full covariance matrix, and not just its diagonal terms. 4.3 Results Following e same procedure as in Arnalte-Mur et al. (29), wi e details explained above, we calculated bo e projected correlation function w(r ), and e deprojected real-space correlation function ξ dep (r) for our samples. Results for w(r ) are shown in Fig. 5. We see at we can reliably measure w(r ) in our different samples from scales as low as r.2 h Mpc (except for e highredshift bin), up to scales of r 3 h Mpc, depending on e sample. Deep spectroscopic surveys are typically able to measure e correlation function only for scales r. h Mpc due to e sparsity of e samples used. Using ALHAMBRA data, being a photometric survey, we can explore smaller scales due to e larger number density of galaxies in e samples. The correlation function at ese scales r. h Mpc is related to e merger rate in e galaxy population studied (Masjedi et al. 26). We ignore ese scales for e rest of is analysis, but is shows at ALHAMBRA can be a good tool to study e history of galaxy merger rates up to high redshifts (López-Sanjuan et al. 2; de Ravel et al. 2). Over e full range of scales studied, e obtained w(r ) shows qualitatively e expected behaviour. It follows approximately a power law, alough wi some deviations or changes in slope, most noticeable in e high-redshift samples. Moreover, ere is a clear segregation wi luminosity, as samples containing more luminous galaxies exhibit stronger clustering. The dependence of clustering on redshift is less evident here. We make more detailed comparisons in our analysis below. The results for e de-projected correlation functions ξ dep (r) of e different samples are shown in Fig. 6. Qualitatively, we can draw here e same conclusions as from e w(r ) results above: e correlation function is close to a power law for nearly ree decades in separation, and it shows e effect of luminosity segregation. However, e results we obtain here are noisier, and wi larger estimated errors, an ose for w(r ), as is expected for any deconvolution process. Hence, we will use only e w(r ) results for furer analysis, as it is in general possible to transform a model for ξ(r) into a model for w(r ) using equation (??) Modelling of e correlation function: dependence of clustering on luminosity and redshift In order to study e change of e clustering properties wi luminosity and redshift, we fit e obtained projected correlation function w(r ) of each sample using two models. The first of ese models is a power law in e real-space correlation function ξ(r), expressed as ( ) γ r ξ(r) =. When transforming is model, using equation (??), to a model for w(r ), we also obtain a power law which, expressed in terms of e parameters r and γ above is given by ( ) γ r Γ(/2)Γ [(γ )/2] w(r ) = r, (8) r Γ(γ/2) r