Near-IR Galaxy Counts and Evolution from the Wide-Field ALHAMBRA survey
D. Cristobal-Hornillos, J. A. L. Aguerri, M. Moles, J. Perea, F. J. Castander, T. Broadhurst, E. J. Alfaro, N. Benitez, J. Cabrera, J. Cepa, M. Cervino, A. Fernandez-Soto, R. M. Gonzalez-Delgado, C. Husillos, L. Infante, I. Marquez, V. J. Martinez, J. Masegosa, A. del Olmo, F. Prada, J. M. Quintana, S. F. Sanchez
aa r X i v : . [ a s t r o - ph . C O ] F e b Near-IR Galaxy Counts and Evolution from the Wide-FieldALHAMBRA survey D. Crist´obal-Hornillos ,J. A. L. Aguerri , M. Moles , J. Perea , F. J. Castander , T.Broadhurst , E. J. Alfaro , N. Ben´ıtez , , J. Cabrera-Ca˜no , J. Cepa , , M. Cervi˜no , A.Fern´andez-Soto , R. M. Gonz´alez Delgado , C. Husillos , L. Infante , I. M´arquez , V. J.Mart´ınez , , J. Masegosa , A. del Olmo , F. Prada , J. M. Quintana , and S. F. S´anchez [email protected], [email protected], [email protected],[email protected], [email protected], [email protected], [email protected],[email protected], [email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected],[email protected] ABSTRACT
The ALHAMBRA survey aims to cover 4 square degrees using a system of20 contiguous, equal width, medium-band filters spanning the range 3500 ˚ A to9700 ˚ A plus the standard JHKs filters. Here we analyze deep near-IR numbercounts of one of our fields (ALH08) for which we have a relatively large area(0.5 square degrees) and faint photometry (J=22.4, H=21.3 and K=20.0 at the Instituto de Astrof´ısica de Andaluc´ıa, CSIC, Apdo. 3044, E-18080 Granada Instituto de Astrof´ısica de Canarias, La Laguna, Spain School of Physics and Astronomy, Tel Aviv University, Israel Departamento de F´ısica At´omica, Molecular y Nuclear, Facultad de F´ısica, Universidad de Sevilla, Spain Institut de Ci`encies de l’Espai, IEEC-CSIC, Barcelona, Spain Departamento de Astrof´ısica, Facultad de F´ısica, Universidad de la Laguna, Spain Departament d’Astronom´ıa i Astrof´ısica, Universitat de Val`encia, Val`encia, Spain Departamento de Astronom´ıa, Pontificia Universidad Cat´olica, Santiago, Chile Observatori Astron`omic de la Universitat de Val`encia, Val`encia, Spain Centro Astron´omico Hispano-Alem´an, Almer´ıa, Spain IFF(CSIC), C/Serrano 113-bis, 28005 Madrid, Spain Instituto de F´ısica de Cantabria (CSIC), 39005 Santander,Spain . , .
5] to 0.34 at [19 . , .
0] for the J band; forthe H band 0.46 at [15 . , .
0] to 0.36 at [19 . , . . , .
0] to 0.33 in the interval [18 . , . z ∼ Subject headings: cosmology: observations — galaxies: photometry — galaxies:evolution — surveys — galaxies: high-redshift — infrared: galaxies
1. Introduction
It is well understood that the stellar masses of galaxies are better examined with near-IR (NIR) observations compared to shorter wavelengths mainly because the near-IR lightis relatively less affected by recent episodes of star formation and by internal dust extinc-tion. Moreover, the K-corrections are also smaller and better constrained in the NIR andhence massive high redshift objects are relatively prominent in the NIR. Despite this rel-ative insensitivity to luminosity evolution and the effects of dust, the hope of using theNIR counts to constrain the cosmological parameters (Gardner et al. 1993; Moustakas et al.1997; Huang et al. 2001; Metcalfe et al. 2001) has not proved feasible because evolution inthe space density of galaxies was soon understood to be of comparable significance for theNIR counts as the cosmological curvature (Broadhurst et al. 1992).Disentangling the effects of cosmology from evolution is not straightforward even in theNIR, and now it has become more appropriate to turn the question around and make use ofthe impressive constraints on the cosmological parameters from WMAP (Spergel et al. 2003),and type Ia supernovae (Riess et al. 1998; Perlmutter et al. 1999), in order to measure morecarefully the rate of evolution (Martini 2001; Saracco et al. 2001; Crist´obal-Hornillos et al.2003; Eliche-Moral et al. 2006). In addition, imaging in the NIR has progressed well with Based on observations collected at the German-Spanish Astronomical Center, Calar Alto, jointly oper-ated by the Max-Planck-Institut f¨ur Astronomie Heidelberg and the Instituto de Astrof´ısica de Andaluc´ıa(CSIC). z ∼ z = 0 . ∼ z ∼ ∼ . z = 1 and z = 0 .
6. Faber et al. (2007) found adifferent evolution since z ∼ φ ∗ normalizationin the B-band even if this leads to an over-prediction of bright galaxies than is observed.Huang et al. (2001) pointed out that both the optical and NIR counts present an excessover the no-evolution models, finding passive evolution models more suitable to match thedistributions. The authors emphasize nevertheless their disappointment with the fact that inthe passive evolution models the faint number counts are dominated by early-type galaxies,whereas the real data show that spiral and Sd/Irr galaxies are the main contributors to thefaint counts even in the K-band.A characteristic feature of the NIR galaxy counts reported in several works (Gardner et al.1993; Huang et al. 2001; Crist´obal-Hornillos et al. 2003; Iovino et al. 2005) is the change ofslope at 17 ≤ Ks ≤
18. This distinctive flattening is not observed in the B-band counts.This effect has been interpreted in terms of a change in the dominant galaxy population,becoming increasingly dominated by an intrinsically bluer population (Gardner et al. 1993; 4 –Eliche-Moral et al. 2006). In the model described in Crist´obal-Hornillos et al. (2003) a delayin the formation of the bulk of the early-type galaxies to z form < z >
1, that is not present at lower redshift was found compatiblein Metcalfe et al. (1996, 2001) but that work uses a q = 0 . , Λ = 0 . φ ∗ for late-type galaxies, driven via mergers, can producesimilar results without introducing an ad hoc population that is unseen in the local LFs(Eliche-Moral et al. 2006). In any case, a low z form ∼ . ∼ × FWHM) reached in the3 NIR bands are in mean for the eight frames in ALH8: J=22.6, H=21.5 and Ks=20.1 witha 0.3 rms (Vega system), and the total area covered amounts to ∼ . = 70 km s − Mpc − , Ω M = 0 .
3, Ω Λ = 0 .
2. Observing Strategy and Data Reduction
The ALHAMBRA survey is collecting data in 23 optical-NIR filters using the CalarAlto 3.5m telescope with the cameras LAICA for the 20 optical filters, and OMEGA2000for the NIR, JHKs filters (Moles et al. 2008; Benitez et al. 2008). In this paper we discussthe galaxy number counts in the J, H and Ks bands computed in the completed ALH08pointing. Due to the OMEGA2000 and LAICA geometries, two parallel strips of ∼ × .
25 degrees are acquired in each of the eight ALHAMBRA fields. Each of these stripsis covered by four OMEGA2000 pointings. Fig. 1 shows the central part of the processedimage for one such pointing in ALH08.The OMEGA2000 camera has a focal plane array of type HAWAII-2 by Rockwell with2048 x 2048 pixels. The plate scale is 0.45 arcsec/pixel, giving a full field of view of ∼ . The JHKs images were taken using a dither pattern of 20 positions, with singleimages time exposures of 80 s in J, 60 s in H and 46 s in Ks band (obtained using respectively16, 20 and 23 software co-adds). The total exposure time was 5 ks in each of the three filters.Due to the high quantity of raw data images we have implemented a dedicated reductionpipeline to process the images. This code will be presented and discussed in a forthcomingtechnical paper. The use of the reduction pipeline guaranties the homogeneity of the process,and allows us to perform a first automatic analysis of the resulting images and to verifythe quality of the products in real time. The magnitude at the 50% of recovery efficiencyfor point-like sources in the eight final images corresponds in average to J= 22 . ± . . ± .
14 and Ks= 20 . ± .
13 in the Vega system. The galaxy number counts havebeen computed in the high signal to noise region of the final images, covering a total of ∼ , or 0.45 sq deg. Firstly, the individual images of each observing run were dark-subtracted, and flat-fielded by super-flat images constructed with the science images in each filter. In the case ofNIR imaging it is specially important to remove properly the high sky level that is changing inshort timescales. The sky structure of each image was removed with the XDIMSUM package(Stanford et al. 1995) with a sky image constructed with the median of the 6 images closestin acquisition time, which in the case of the J, H, Ks filters correspond to timescales of 480,360, 276 s respectively. During this process cosmic ray masks for each individual image werealso created.SExtractor (Bertin & Arnouts 1996) was used with the preliminary sky subtracted im-ages to compute the number of detected objects (above a given S/N and with ellipticitylower than a certain limit), and to make a robust estimate of the FWHM of each image.This information together with the sky level variation was used to automatically remove lowS/N images, lying outside the survey requirements, and also to identify exposures presentingproblems such as telescope trailing. 6 – . . h m . . . m . d m . m . Fig. 1.— Central part ( ∼ . ′ × . ′ ) of one of the pointings in the ALH08 field in the Ksband. 7 – The readout of the detector array produces ghost images coming from bright stars. Asthose spurious effects are replicated in all the readout channels (separated by 128 pixels) ofthe detector’s quadrant where the real bright source is located, it was possible to mask thembefore image combination.Linear patterns produced by moving objects were located in the images using two dif-ferent approaches: i) Objects with high ellipticity and pixel area were identified from theindividual image SExtractor catalogs. ii) Linear patterns split in multiple spots and struc-tures were located using the Hough transform. Linear patterns detected by any of the twomethods were masked.
Using XDIMSUM, the images were combined masking the cosmic rays, bad pixels andlinear patterns. Those preliminary co-added images were used to create object and brightcores masks. Object masks were used to cover the sources in the second iteration of theXDIMSUM sky subtraction procedure. Bright cores masks operate when constructing animproved version of the cosmic ray masks.At this point, the individual images have been dark current corrected, flat fielded andsky subtracted. Each individual image has an associated mask containing the bad pixels,cosmic rays, linear patterns and ghost images.To perform the final combination of the processed images we used SWARP (Bertin et al.2002), a code that combines the images, correcting at the same time the geometrical distor-tions in the individual images using the information stored in WCS headers. The astrometriccalibration of each individual image and the update of its WCS headers was done by thepipeline using an automatic module. During the SWARP combination the extinction varia-tions among the images were also corrected. More technical details on the image combinationare given in appendix A.
For the photometric calibration we used the 2MASS catalogs (Cutri et al. 2003). Afterhaving combined all the images of each pointing, the objects in common with the 2MASScatalogs were found and those with higher signal to noise ratio selected to compute a zero 8 –point offset.In Fig. 2 an example of the photometric calibration for one of the pointings in ALH08 isshown. The histogram with the rms in the photometric calibration for the ALH08 pointingsin the three NIR bands is shown in Fig. 3. The mean value for the rms is 0 . ± .
006 mags,and a mean of 36 calibration sources have been used in each frame. We have not found anyappreciable color related trend.The calibrated images were inspected for the possible presence of ring patterns thatwould have been produced by pupil ghosts. We computed for each band, and for all thesources used in the calibration process of the different final frames, the difference betweenour photometry and the 2MASS photometry as a function of the radial distance to thenominal field center.We found a significant effect, over 0.02 mags only in the J-band images, as it is shownin Fig. 4. This effect was corrected by fitting the pupil ghost, using the mscpupil task in theIRAF MSCRED package (Valdes 2002), and removing this pupil image from the flat-fieldsand individual images. The final resulting radial differences are shown for the J band inFig. 5 where it clearly appears that all the systematics was corrected well below the 1 σ level.
3. Galaxy Number Counts
The steps to compute robust counts to the 50% detection level of the images are similarto those described in Crist´obal-Hornillos et al. (2003) and in Eliche-Moral et al. (2006). Inthe next section we detail how the best set of SExtractor parameters was estimated as acompromise between optimizing the depth at the 50% completeness level while keeping lowthe number of spurious sources.
In order to compute the corrections that should be applied to the faint part of thegalaxy counts we have performed a set of Monte Carlo simulations where real sources from theimages were injected back to the same science image at different positions. The completenesscorrection to be applied depends on the surface brightness profile of the source. To accountfor this we computed a different correction function for sources in three effective radius (Re)intervals. Those Re intervals in pixels for the simulations were chosen from the histogramof the Fig. 6 (top panel): Re ≤ .
75, 1 . < Re ≤ .
25 and
Re > .
25. In Fig. 6 (bottompanel) it is shown how the Re recovered decreases as the magnitude goes fainter (see below 9 –Fig. 2.— Calibration with 2MASS stars for the one of the pointings included in the ALH08field in the H filter. Sources marked with a circle were eliminated using a 2 σ reject in thecalibration fit. Error bars correspond to the 2MASS magnitude error summed in quadraturewith the SExtractor computed error. 10 – zero point rms i m a g e s
20 40 60 i m a g e s Fig. 3.— Histogram of the photometric accuracy of the different pointings in the ALH08field. In the small panel the histogram of the number of used stars for the calibration ineach pointing is shown. 11 –Fig. 4.— Differences between 2MASS and ALHAMBRA photometry versus the distance tothe nominal pointing center in the J band. 16 pointings have been combined and a binninghave been performed in the x-axis to increase the signal. For each bin the boxplot showsthe mean ( stars ), the median, 1st and 3rd quartile ( boxes ), the minimum and maximum( circles ), values after trimming the 10% on either side of the sample in each bin. The errorbars represent the 1 σ interval. 12 –Fig. 5.— Differences between 2MASS and ALHAMBRA photometry versus the distanceto the nominal pointing center after applying the pupil ghost correction in the flat-field asexplained in the text. Symbols as in Fig. 4. Note that the scale in the y-axis has changewith respect to Fig. 4. 13 –for a description of how these values were obtained).For the simulations, bright sources were selected from the image in each Re interval.These sources were artificially dimmed to the 0.5 magnitude bin under study and injectedback on the image randomly. In each iteration 40 sources were simulated, computing therecovering fraction and the robust mean (trimming the 10% on either side of the distribution)of the SExtractor desired output parameters differences between the dimmed input sourcesand the recovered ones. Using 9 of these iterations in each magnitude bin, we estimated themean and rms of the recovered fraction, and SExtractor parameters differences over all themeaningful magnitude range. In Fig. 7 the completeness correction for the three Re rangesis shown for one of the pointings in the J band.It can be argued that with that method unrealistic pseudo-artificial sources could beproduced. Whereas this could be true, the goal of this procedure is to parameterize therecovering efficiency on the basis of the source and image characteristics without any physicalconsideration, which will be implicitly taken into account when performing the correctionson the real data. As a validation of the procedure, the same simulations have been performedusing real NICMOS F110W sources from the HDF-S Flanking Fields. The NICMOS imageswere resampled and convolved with a suitable Gaussian kernel to match the pixel scale andFWHM of the OMEGA2000 image under study. Initial sources were taken in the interval [m-1,m+1] (being m the magnitude under study), which produces a realistic mag − R e relation.As can be seen from the Fig. 7 the results in the completeness correction are the same thatusing dimmed sources from the image.In the top panel of Fig. 8 we show the depth to the 50% and 80% of recovering efficiency,computed using a linear interpolation in the magnitude vs. efficiency data. The figureindicates that a decreasing of the detection thresholds, in order to get a fainter level atthe 50% of recovery efficiency limit, will not improve by much the limit at the 80% ofcompleteness, which seems to reach a plateau. Moreover, as will be seen from the reliabilityplots, it produces a significant increase of detected spurious sources, as we explain below. To accurately compute the galaxy number counts it is important to establish the re-liability of the detections at the faint magnitude end. To find out the optimum way toevaluate that reliability we have studied the performance of three different methods. Thefirst approach was to create artificial sky images with the same rms and background distri-bution than the real ones. The ratio of spurious versus real detections was computed running 14 –Fig. 6.— (Top panel)
Histogram of Re for the sources in one of the pointings of the fieldALH08 (Bottom panel)
Differences between Re(in) and Re(out) for the dimmed injectedsources. The symbols correspond to × Re(in) ≤ .
75 pixels, (cid:3) . < Re(in) ≤ .
25 and △ Re(in) > .
25 pixels. The shaded is the range of magnitudes between the 50% and the 80%of detection efficiency. 15 –Fig. 7.— Completeness correction for the same pointing of the previous figures in the J bandusing 0.8 σ DETECT THRESH and the 2.5 pixel gaussian kernel. The vertical dotted (solid)lines are the magnitude at the 50% (80%) of detection efficiency. 16 –Fig. 8.— (Top panel)
50% vs. 80% of recovering efficiency for the same pointing as before inKs band using different SExtractor detection strategies. The size in pixels of the SExtractorGaussian convolution kernel is given in the labels. The detection thresholds are indicated atthe points. (Bottom panel)
50% of detection efficiency vs. spurious to total ratio. 17 –SExtractor over the science and the artificial sky images.We have also inspected the performance of the method used in Crist´obal-Hornillos et al.(2003). Basically half exposure time images were created from two complementary sets ofthe data. The detections were performed in the total time image and the source fluxesmeasured in the half time images using the SExtractor double image mode for the sameautomatic apertures. Those created sources showing a magnitude difference greater than 3 σ were considered spurious.The last method and the one that, at the end, produces the best results, consisted inconstructing sky images using a similar combination procedure that the used to create thescience images: combining the unregistered processed images with subtracted backgroundusing an artificial dither pattern. The major difficulty here was to remove the extendedsources that could bias the sky even when doing trimmed mean (discarding 20% of thepixels at each side). We have confirmed that SExtractor does locate these smooth deviationsover the sky rms when filtering is used. To avoid this we multiplied those sky images by -1and used them as real sky images.In the Fig. 9 we show a comparison between the spurious rate at the 50% of detectionefficiency computed over the ’real sky’ and the artificial sky. A good agreement betweenboth methods is observed, indicating that the use of artificial images to compute the ratio ofspurious to total detections is adequate. Being artificial images faster to construct we madeuse of them to estimate the detection reliability in each pointing.The bottom panel of Fig. 8 shows the magnitude reached at the 50% of detection ef-ficiency versus the spurious to total ratio at the same magnitude bin. From the figurewe can see that in order to reach a deep 50% detection limiting magnitude, maintainingat the same time the number of spurious detections below 20%, the optimum SExtractorDETECT THRESH-FILTER combinations are: DETECT THRESH=1.2 or 1.4 without fil-tering, or DETECT THRESH=0.8 using a filtering with a Gaussian kernel of size similarto the image FWHM. In the top panel of Fig. 8 it is shown that those combinations reachroughly the same magnitude at the 80% of recovery efficiency. We have decided to use thelatter filter-DETECT THRESH combination because, as can be outlined from the bottompanel in Fig. 10, the differences between the input and the recovered AUTO magnitudes inthe simulations are close to zero in all the magnitude range up to the magnitude at the 80%of recovery efficiency. Close to the magnitude at the 50% of completeness the recovered mag-nitude appears to be ∼ . − . σ ) and FILTER (F) combinations areshown. The grey area corresponds to a difference less than 0.1. 19 –following sections will be computed and corrected up to the magnitude of 80% of recoveryefficiency for point-like sources, avoiding any possible systematics due to a magnitude shiftat the 50% completeness bin.As pointed before, the photometry of the sources was obtained using MAG AUTO.Simulations indicate no significant differences between simulated and recovered magnitudes(at the 80% recovery efficiency) for the used values of the SExtractor parameters FILTERand DETECT THRESH. Using the same kind of simulations we computed the rms of therecovered MAG AUTO values in each bin to characterize the photometric error, the resultsare shown in Fig. 11. In Crist´obal-Hornillos et al. (2003) it was shown that fainter than Ks=17.0 the correc-tion due to stars is < .
06 dex. However, given the lower Galactic latitude of the ALH08field, a higher number of contaminating stars is expected. A correct star subtraction isrelevant in the intermediate magnitude range. At bright magnitudes stars can be easily sep-arated from galaxies using a compactness criteria. In contrast, at intermediate magnitudesthe star/galaxy separation is more demanding because many galaxies are barely resolvedwith small apparent sizes compared with the FWHM and pixel resolution, as can be seenfrom the diagram shown in Fig. 12.The viability of star/galaxy separation using the SExtractor neural network has alsobeen analyzed. For this purpose, using the same Monte Carlo method explained before,bright stars and galaxies from the images have been artificially dimmed to each magnitudebin and their SExtractor stellarity parameter recovered. In Fig. 13 it clearly appears how, inone final frame with FWHM=1.1, the input and recovered CLASS STAR differences are lessthan 0.1 up to Ks=18.0. But, in the next bin Ks > .
5, the CLASS STAR of the dimmedstars and galaxies could lead to some misclassification. Nevertheless, as can be seen fromthe histogram in the bottom panel of Fig. 13, a non negligible number of objects start topopulate the range from 0.4 to 0.8 in CLASS STAR at magnitudes fainter than 17 in Ks,and the selection of the CLASS STAR cut off might bias the star counts estimates.An alternative way to perform the star/galaxy separation makes use simply of color-colordiagrams. Huang et al. (1997) have established a reliable star/galaxy separation using the B-I vs I-K colors. Here we make use of the SDSS DR5 data for the ALH08 field to proceed withthis separation using the g-r vs J-Ks colors shown in Fig. 14. The star counts are correctedby the ratio of the Sloan/Alhambra completeness factors in the corresponding filter shown in 20 –Fig. 10.— Differences between the input and the SExtractor recovered AUTO magnitudesin one of the pointings of ALH08 in the J band for two SExtractor FILTER and DE-TECT THRESH combinations: no filtering and DETECT THRESH=1.2 (upper panel) , and2.5 pixel filtering and DETECT THRESH=0.8 (bottom panel) . The vertical dotted (solid)lines are the magnitude at the 50% (80%) of detection efficiency. 21 –Fig. 11.— Median photometric random errors in magnitudes per magnitude bin ( σ m ) inthe three NIR filters for the eight ALH08 pointings (crosses and dotted lines) , the threelines represent sources with Re < = 1 .
75, 1 . < Re < = 2 .
25, and
Re > .
25 pixels. Themagnitude errors are computed as the rms of the recovered sources magnitudes in each binof the simulations described in the text. Error bars represent the rms of the computed σ m among the pointings. Exponential grow fit ( σ ( m ) = σ + a exp [ b ( m − m )]) to the magnitudeerrors in each band (solid lines) . 22 –Fig. 12.— Peak/ISOPHOTAL AREA vs. Ks diagram. The red dots are object for whichthe SExtractor stellarity index is > (Top panel) CLASS STAR input-output differences as a function of input artifi-cially dimmed magnitude for a set of well defined stars (CLASS STAR(in) ∼
1) and galaxies(CLASS STAR(in) ∼ (Bottom panel) Histogram of CLASS STAR for different ranges in the Ks magni-tudes. 24 –Fig. 15. The star counts using Sloan-Alhambra colors were computed to magnitude 19.5,18.5and 18.0 respectively in the J,H and Ks band, where the Sloan/Alhambra completeness is > N ) galaxy counts is presented, showing that fainter than the magnitudes up to wherethe color-color separation could be performed the correction in the three bands is < .
4. Results
The corrected galaxy number counts have been computed for the ALH08 field in thethree standard NIR filters in a consistent way in the sense that they have been estimatedfollowing the same scheme for the three bands. The number count data, computed and cor-rected up to the magnitude of 80% of recovery efficiency for point-like sources, are presentedin the Tabs. 1, 2 and 3.The error in the number counts for each pointings are the sum in quadrature of the rmsin the estimation of the completeness corrections, with the contribution of Poisson noise andgalaxy clustering calculated for each magnitude bin following eq. 1 (Huang et al. 1997), thatincludes the angular correlation function. σ i = N i ( m ) + 5 . (cid:18) r r ⋆ (cid:19) Ω (1 − γ ) / i N i ( m ) (1)being N i the raw counts in the pointing, r = 7 . γ = 1 .
77 and 5 log( r ⋆ ) = m − M ⋆ − M ⋆ is set to -22.95,-23.69 and -23.93 for the J, H and Ks filters. The finaluncertainty in the combined counts per square degree and magnitude is given by: 25 –Fig. 14.— g-r vs J-Ks plot used to perform the star-galaxy separation. All objects in ALH08with S/N > g − r = 1 . . · ( J − Ks ) AB .The plotted symbols correspond to the Sloan classification dots for representing stars andthe crosses for galaxies. Redshift-color tracks for three galaxy models constructed using theBruzual & Charlot (2003) code are shown. The redshift values are displayed over the SingleStellar Population (SSP) track, the marks over the other 2 curves have the same redshiftspacing. The diamonds represent the mid stellar locus given in Covey et al. (2007). Twocontour lines containing the 95% and the 68% are displayed for the galaxies and stars usingthe Sloan classification. 26 –Fig. 15.— (Top panel) The ratio of sources identified in the Alhambra field for which thereis a counterpart in the Sloan SDSS DR5 catalog. (Bottom panel)
The correction subtractedfrom log(N) galaxy counts due to stars. The big open circle indicates the point up to whichthe number of stars can be estimated from the Sloan-Alhambra colors (see text), the fainterstar counts assume a flat extrapolation from this value. 27 –Fig. 16.— Star counts for the ALH08 field compared with the Robin et al. (1996) Galacticcount model. The J and Ks data have been plotted with an offset of -0.5 and 0.5 dex in they-axis. 28 – σ ( m ) = pP σ i Ω∆ m (2)In the Figs. 17, 18, and 19 the Alhambra counts in the J,H, and Ks bands are plottedtogether with the computed number counts from other surveys.Let us first point out the general aspect of those counts, leaving more detailed consider-ations for the next section. Our corrected J band galaxy counts are in overall agreement withthose computed in other works (Teplitz et al. 1999; Feulner et al. 2007), the bright end ofthe results presented by Maihara et al. (2001), and the ELAIS-N2 data from V¨ais¨anen et al.(2000). Nevertheless, our counts are lower than those given by Bershady et al. (1998) atmagnitudes J > . H >
20) of our data is significantly above the faint number count data from Yan et al.(1998) and Metcalfe et al. (2006), obtained from NICMOS observations.Regarding the Ks filter, for which there are numerous number counts studies, our galaxycounts are in good agreement with most of the published data, as can be appreciated in theFig. 19.
We have found, as in previous studies, that the slope of the galaxy number countsdisplays a clear change at Ks ∼ ∼ ∼ σ , whereas the bright slope is steeper in the Ks band.As is described in Teerikorpi (2004) the fact that the photometric error increases atfainter magnitudes, and that the differential galaxy number counts also rises towards lower 29 –Table 1. Corrected galaxy number counts in the J band. Magnitude raw counts a eff. cor. b log( N c ) c log( N m ) d area N · mag − · deg − N · mag − · deg − deg . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . a Raw counts including stars. b Effective correction, defined as (
N c + N st ) / (2 · area · raw ). c Corrected galaxy counts,errors corresponds to the Poissonian and galaxy clusteringuncertainty plus error in completeness added in quadrature. d Mean of the 8 pointings and its rms.
30 –Table 2. Corrected galaxy number counts in the H band.
Magnitude raw counts a eff. cor. b log( N c ) c log( N m ) d area N · mag − · deg − N · mag − · deg − deg . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . a Raw counts including stars. b Effective correction, defined as (
N c + N st ) / (2 · area · raw ). c Corrected galaxy counts,errors corresponds to the Poissonian and galaxy clusteringuncertainty plus error in completeness added in quadrature. d Mean of the 8 pointings and its rms.
31 –Table 3. Corrected galaxy number counts in the Ks band.
Magnitude raw counts a eff. cor. b log( N c ) c log( N m ) d area N · mag − · deg − N · mag − · deg − deg . +0 . − . . +0 . − . . +0 . − . . +0 . − . ... ... . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . a Raw counts including stars. b Effective correction, defined as (
N c + N st ) / (2 · area · raw ). c Corrected galaxy counts,errors corresponds to the Poissonian and galaxy clusteringuncertainty plus error in completeness added in quadrature. d Mean of the 8 pointings and its rms.
32 –Fig. 17.— Galaxy number counts in the J filter compared with data from other surveys.The lines correspond to the number counts models in Crist´obal-Hornillos et al. (2003) andEliche-Moral et al. (2006) described in the text. 33 –Fig. 18.— Galaxy number counts in the H filter compared with data from other surveysand the models in Crist´obal-Hornillos et al. (2003) and Eliche-Moral et al. (2006) describedin the text. 34 –Fig. 19.— Galaxy number counts in the Ks filter compared with data from the literatureand the galaxy counts models in Crist´obal-Hornillos et al. (2003) Eliche-Moral et al. (2006)described in the text. Also it is shown a model where only the passive evolution of stellarpopulations is considered (PLE). 35 –Fig. 20.— Galaxy number count bright and faint slopes found in this work. Error bars arethe Poissonian and galaxy clustering uncertainty added in quadrature with the rms in theestimation of the completeness corrections. 36 –fluxes, lead to a stepper observed slope at the faint end. This effect is related with theEddington bias (Eddington 1913). To investigate if the computed magnitude errors couldbias our slope estimates we have done the following study. First, in each filter we usethe exponential grow function fit to the magnitude errors (Fig. 11). Then we extendedour computed number counts one magnitude fainter using the corresponding slope in Tab. 4,simulating a Gaussian decay for fainter magnitudes. The parameter σ for the Gaussian is thevalue of the exponential fit to the error values for point-like sources at one magnitude fainterthat the last bin given in Tabs. 1, 2 and 3 ( σ = 0 . , .
41 and 0.44 at respectively J=23.0,H=22.0 and Ks=21.0). Using the fitted magnitude errors for point-like objects ( σ ( m )), andassuming that real distribution is close to the extended number counts ( N ( m )), we simulatethe bias produced by the photometric error on the observed counts, by convolving the N ( m )with σ ( m ) using the eq. 3. The results indicate an increase in the slope less than 0.015 inthe case of J and H filters, and 0.03 in the Ks band, meaning that the original distributionswould have a faint end slope of 0.33,0.34 and 0.30 in the J,H, and Ks filters in the rangesgiven in Tab. 4. N ( m obs ) = Z N ( m ) 1 √ πσ e ( m − mobs )22 σ m ) dm (3)The increase of the slope is not observed when we simulate this bias directly over theobserved count distribution. This is due to the fact that fainter than the 80% completenessmagnitude bin there is a fast decrease of the number of detected sources, and that in thisbin the typical photometric error ( σ m = 0 . − .
26) for the dominant point-like sources,makes that the bias do not significantly affect to the previous bins. In this case the slopesafter applying the bias are lower than the computed from the observed number counts(0 . ± .
01, 0 . ± .
02, and 0 . ± .
02 in J,H and Ks). This result would suggest that theoriginal distribution slopes at the faint end would be higher than the ones given in Tab. 4.We have used the combined results from this paragraph and the previous one to increasethe uncertainty in the slope, leaving the values computed directly from the observed numbercounts as satisfactory estimates of the real distribution slope at the faint end.Our results for the Ks band are in good agreement with other K-band surveys which alsoreport a similar change of slope in the galaxy counts in the range 17.0-18.0 (Daddi et al. 2000;Huang et al. 2001; Crist´obal-Hornillos et al. 2003; Iovino et al. 2005). At the bright partour slopes are close to the values measured in K¨ummel & Wagner (2000); Martini (2001);Crist´obal-Hornillos et al. (2003); Iovino et al. (2005) (see Tab. 5), while other referencespoint to a steeper bright slope (Gardner et al. 1993, 1996; Huang et al. 1997, 2001). Thiscould be due to the fact that the last authors could extend the power-law fit to brightermagnitudes due to their larger surveyed area, whereas our fit is closer to the magnitude 37 –where the break is found which would lead to a decrease in the slope if the break transitionis smooth. In the faint part of the Ks counts a slope of 0 .
33 found in this work is inagreement with Bershady et al. (1998); Huang et al. (2001); Imai et al. (2007). The valueof the faint slope from the ALHAMBRA data is however steeper than the value reported insome surveys covering smaller areas, where the fitted range extends to fainter magnitudes,Gardner et al. (1993); Moustakas et al. (1997); Maihara et al. (2001). Here the differencesmight be due to cosmic variance. A larger than 2 σ disagreement is found with the faintslope of Crist´obal-Hornillos et al. (2003) fitted in the range [17.5,19.5], although their valueincrease to 0.29 when the fit interval is extended to Ks=21.0. K¨ummel & Wagner (2000)give a higher value for the faint slope, however due to the brighter limiting magnitude oftheir number counts they could established a break or the beginning of a roll-over in theinterval Ks=[16.5,17.0].In the H and J bands there are fewer works reporting count-slope values. Our results,given in Tab. 4, show similar slopes for the J and H filter at the bright and faint ends. Ascan be seen in Tabs. 6 and 7 our result at the bright end are in good agreement with thebright-end slope values to H=19 given in Martini (2001) and Chen et al. (2002), and in theJ filter with the results in V¨ais¨anen et al. (2000) and Iovino et al. (2005). At the faint end,only the slope values in Maihara et al. (2001) in the J filter, estimated in an area of 4 arcsec ,and Chen et al. (2002) have a significant discrepancy.
5. Comparison with Models of Evolution
Historically, the galaxy number counts have been used to examine parameters of thecosmological model and to test different galaxy evolution scenarios. Now that the cosmo-logical parameters are fixed using other methods the consequences derived from the galaxycounts for the galaxy evolution have become more precise. The ALHAMBRA computedcounts in the three NIR bands provide a good dataset which, when combined with other op-Table 4. Measured slopes in the J,H and Ks filters
Filter Bright range Bright slope Faint range Faint slopeJ [17.0,18.5] 0.44 ± ± ± ± ± ±
38 –Table 5. Characteristics of the surveys in the K band
Reference Surveyed area limit magnitude bright range bright slope faint range faint slope filtersqarcminGardner93 5688 14.5 c [10.0,16.0] 0.67 [18.0,23.0] 0.23 K’Gardner93 582 16.75 c — — — — —Gardner93 167.7 18.75 c — — — — —Gardner93 16.5 22.5 — — — — —Glazebrook94 552 16.5 c — — — — KDjorgovski95 3 23.5 c — — [20.0,23.5] 0.32 ± c — — — — KsGardner96 35424 15.75 c < ± c — — [18.0,23.0] 0.23 ± c [12.0,16.0] 0.689 ± d — — [18.25,18-75] 0.28 K’Bershady98 1.5 24.00 b — — > c [14.5,16.5] 0.50 ± .
03 — — KsSaracco99 20 22.25 c — — [17.25,22.5] 0.38 KsV¨ais¨anen00 3492,2088 16.75,17.75 c [15.0,18.0] 0.40-0.45 — — KMartini01 180,51 17.0,18.0 c [14.0,18.0] 0.54 — — KDaddi00 701,447 18.5,19.0 c [14.0,17.5] 0.53 ± . > ± .
02 KsK¨ummel00 3348 17.25 c [10.5,17.0] 0.56 ± c — — > c — — >
19 0.28 KsHuang01 720 19.5 c < >
17 0.36 K’Cimatti02 52 19.75 c — — — — KsCristobal03 180,50 20.0,21.0 b [15.5,17.5] 0.54 [17.5,19.5] 0.25 KsIovino05 414 20.75 c [15.75,18.0] 0.47 ± ± b — — — — KsImai07 750,306 18.625,19.375 c < ± > ± c — — — — KThis work 1584,194 19.5,20.0 c [15.0,17.0] 0.53 ± ± a σ limit for point sources b
50% efficiency for point objects c the latest magnitude bin in the number counts d
80% efficiency for point objects
39 –Table 6. Characteristics of the surveys in the J band
Reference Surveyed area limit magnitude bright range bright slope faint range faint slope filtersqarcminBershady98 1.5 24.5 b — — > c — — — — JSaracco99 20 23.75 c — — [18.0,24.0] 0.36 JV¨ais¨anen00 2520,1275 18.25,19.25 c [17.0,19.5] 0.40-0.45 — — JMartini01 180,27 18.5,20.5 c [16.0,20.5] 0.54 — — JMaihara01 4 26.25 c — — [21.1,25.1] 0.23 JSaracco01 13.6 24.25 c — — >
20 0.34 JIovino05 391 22.25 c [17.25,22.25] 0.39 ± .
06 — — JFeulner07 925 22.25 c — — — — JImai07 750,306 19.625,20.375 c [17.0,19.5] 0.39 ± . > ± .
03 JThis work 1588,392 21.0,22.0 c [17.0,18.5] 0.44 ± ± a σ limit for point sources b
50% efficiency for point objects c the latest magnitude bin in the number counts Table 7. Characteristics of the surveys in the H band
Reference Surveyed area limit magnitude bright range bright slope faint range faint slope filtersqarcminTeplitz98 35.4 22.8 a — — — — F160WYan98 8.7,2.9 23.5,24.5 c — — [20,24.5] 0.315 ± b — — — — F160WMartini01 180,80 18.0,19.0 c <
19 0.47 — — HChen02 1408 20.8 d <
19 0.45 ± >
19 0.27 ± b — — — — HMetcalfe06 49 22.9 a — — — — HMetcalfe06-Nicmos 0.90 27.2 c — — — — F160WFrith06 1080 17.75 c — — — — HThis work 1598,594 20.5,21.0 c [15.5,18.0] 0.46 ± ± a σ limit for point sources b
50% efficiency for point objects c the latest magnitude bin in the number counts d S/N=5 in a 4 ′′ diameter aperture
40 –tical data and independent determinations of the local luminosity functions, allow evolutionto be examined, in particular the still uncertain question of the formation and evolutionaryhistory of early type galaxies.In this section we compare our counts with semi-analytic predictions from number-countmodels, following the recipes given in Gardner (1998), which trace back the redshift evolutionof the galaxy Spectral Energy Distribution (SED) of different galaxy classes. The SEDs havebeen computed using the codes of Bruzual & Charlot (2003). We apply dust attenuationfollowing Eliche-Moral et al. (2006), τ B = 0 . τ V = 0 . ∝ λ − power law. We apply dust extinction either directly and by the same amountto all the galaxies using Bruzual & Charlot (2003) codes, following the prescription givenin Charlot & Fall (2000), or by using the luminosity dependent extinction law proposed inWang (1991). The parameters we use to characterize four different galaxy types are givenin Tab. 8. In the LF parameterization for the different bands, M ⋆ is changed according tothe rest-frame colors of the evolved SED (from z f to z = 0), whereas α and φ ⋆ are assumedto be the same in all filters.In the first step we compare the ALHAMBRA NIR counts with the prediction ob-tained using the model proposed in Crist´obal-Hornillos et al. (2003). The extinction cor-rection was applied directly to the SEDs, as an entry parameter in the code described inBruzual & Charlot (2003) using τ V = 1 . yr , and µ = 0 . M ⋆ = − . α = − . φ ⋆ = 4 . × − calculated in Gardner et al. (1997) (Cole et al. (2001) provide the parameters for the Λ-cosmology), which were transformed to take into account the presence of different galactictypes in the local LF adopting the galaxy mixing E/S0=28%, Sab/Sbc=47%, Scd=13%.The model also adds a dwarf star-forming population, characterized by an stellar pop-ulation of age 1Gyr at all redshifts, and a steeper slope LF ( M ⋆ = − . α = − . φ ⋆ = 0 . × − ) given in Gardner (1998). The formation redshifts are z f = 2 . z f = 1 . z f = 4 . z > . φ ⋆ evolution ∝ (1 + z ) , driven via mergers, is considered for the spiral and irreg-ular galaxies. This evolution in φ ⋆ is compensated by the evolution in M ⋆ to conserve theluminosity density. Is it important to take in mind that these models calculate the galaxynumber counts tracing back the evolution of the stellar populations to z = 0, so the intrinsicbrightening with z of the stellar populations must be added to the M ⋆ evolution when iscompared with luminosity functions computed at higher redshifts. The formation redshiftfor the majority of the ellipticals and intermediate type disk galaxies in this model was setto 1.5. In the second model, the low formation redshift for the early spiral galaxies could beset to z f = 4, avoiding at the same time an unreasonable high number of late type galax-ies at high-z, using the merger parameterization φ ∗ ∝ exp [( − Q/β )((1 + z ) − β − β = 1 + (2 q ) . / q = − . Q = 1 was used as in Eliche-Moral et al. (2006). The extinction correction, whichis important in the blue bands, was set to τ B = 0 . ∼
19 in the Alhambra counts,and at H ∼
18 in data from other surveys.In order to explain the change of slope in the NIR galaxy counts, the population of redElliptical galaxies has to decrease with the redshift. Although a model taking into accountonly the stellar evolution with look back time fits the blue band counts (see Fig. 21), thismodel over-predicts the faint counts in the NIR bands as can be seen from Fig. 19. Dueto the red color of the slope change only the Elliptical population parameterized with ashort burst of star-formation can play this role. Fig. 22 shows the evolution with redshiftTable 8. Parameters for the SEDs
Galaxy type functional form τ Z/Z ⊙ IMFE/S0 Single star pop. — 1 Salpeterearly Sp Exponential 4 1 Salpeterlate Sp Exponential 7 2 / /
43 –of the J-H and J-Ks colors for an Elliptical galaxy and an early spiral formed at z=4 (withstellar populations according to the parameters in Tab. 8, and reddening in the spectraapplied directly from the Bruzual & Charlot (2003) code using τ V = 0 . µ = 0 . ∼ . ± .
03 andJ-Ks ∼ . ± .
03, providing evidence that the Elliptical population at z ∼ φ ⋆ ∝ (1 + z ) − . The formation redshifts is set to z f = 4 . z > M ⋆ , arguing that a substantial number of ellipticalsformed in spiral-spiral mergers as expected for hierarchical galaxy formation. For the earlyspiral galaxies no number-density evolution was considered, and the density evolution pa-rameterization in Eliche-Moral et al. (2006) φ ⋆ ∝ (1 + z ) was used for the two later typegalaxies. The reddening in the spectra was applied directly from the Bruzual & Charlot(2003) code using τ V = 0 . µ = 0 .
5. This model, as can be seen in the Figs. 23, 24, 25,and 26 fits the galaxy counts in the optical and NIR filters, reproducing the feature of theslope turn down in the three NIR filters.In order to avoid an unreasonable high number of late type galaxies at high-z, the simplemerger evolution φ ∗ ∝ exp [( − Q/β )((1 + z ) − β − z ∼ ∼ / φ ∗ (0). Density evolution in the early type galaxies was observed in pre-vious works studying the type-dependent LF evolution (Kauffmann et al. 1996; Fried et al.2001; Aguerri & Trujillo 2002; Wolf et al. 2003; Giallongo et al. 2005; Ilbert et al. 2006).Wolf et al. (2003) found an increase in φ ⋆ of an order of magnitude for the early type galax-ies from z ∼ . z = 0, that is over the φ ⋆ ∝ (1 + z ) − simulated here. However, theyused the spectra of a present day Sa type galaxy to separate the different galaxies, whichleads to an over-estimation of number-density evolution for the Early-type group.In Abraham et al. (2007) it is shown that evolution in the fraction of the stellar masslocked in massive early-type galaxies is produced in the interval 0 . < z < .
7. A model inwhich φ ∗ for the Elliptical galaxies is constant to z ∼ . φ ⋆ ∝ (0 . z ) − for higher redshifts also produces a good fit to the optical and NIR counts (see Figs. 23,24, 25, and 26). In this model the population of red elliptical galaxies has doubled since 44 –Fig. 22.— Color evolution with redshift of the NIR colors for an Elliptical and an earlyspiral (with the parameterizations given in Tab. 8). The two upper lines correspond to theJ-Ks color whereas the other two correspond to the J-H color. The horizontal dotted linescorrespond to the J-H ∼ ∼ a Galaxy type M ⋆AB ( r ′ ) b φ ⋆ × − M pc − α E/S0 -21.53 1.61 -0.83early Sp -21.08 3.26 -1.15late Sp -21.08 1.48 -0.71Im -20.78 0.37 -1.90 a Considering H = 70 b The characteristic galaxy luminosity given in theSloan r ′ band in AB system. Fig. 23.— Galaxy number count in B band taken from the literature. The lines correspondto the number counts predictions from the models described in the text. 46 –Fig. 24.— Galaxy number counts in the J filter compared with data from other surveys.The lines correspond to number counts models described in the text. 47 –Fig. 25.— Galaxy number counts in the H filter compared with data from other surveys andthe number count models described in the text. 48 –Fig. 26.— Galaxy number counts in the Ks filter compared with data from the literatureand the galaxy counts models described in the text. 49 – z = 1, in good agreement with the increase of a factor of ∼ φ ⋆ constant with redshift for the LF of bright galaxies. Theresults are compatible with our NIR galaxy counts and B-band counts from the literature inthe case that φ ⋆ is constant with redshift for red-ellipticals brighter than M ⋆ − . ∼ − . r ′ band in AB system), decreasing the number densities for the bulk of theellipticals as φ ⋆ ∝ (1 + z ) − .
6. Color analysis
More information about the evolution of the galaxy populations could be obtained fromcolor histograms. The separate number counts in each band at the magnitude ranges that weare sampling are less sensitive to the formation redshift (for values zf > = 4) or the e-foldingtimescale of the star formation than color histograms. Figure 28 shows the color-magnitudediagram builded with the ALHAMBRA data through the filter centered at 6130 ˚ A (F613)and Ks. The modelled evolutionary tracks for the 4 galaxy spectra considered in Tab. 8 arealso displayed. Models with no evolution (top panel) and passive evolution (bottom panel) have been considered. As can be appreciated the evolved spectra produce better matchto the data than the no evolved version, principally at the faint blue end which is betterdescribed by models considering passive evolution in the late Sp and Irr spectra.In Fig. 29 it is shown the F613-Ks color histogram for different Ks magnitude bins. Wehave used an e-folding timescale τ = 0 . φ ⋆ ∝ (1 + z ) conserving the luminosity densities. The populationof early spiral galaxies have been divided in two classes: one remain as in Tab. 8, whereasthe amount of extinction have been doubled for the other. This try to avoid the fact thatthe discretization of the actual galaxy population in four classes tend to produce sharphistograms.As can be appreciated the models reproduce the overall shape of the data for brightKs magnitudes. Nevertheless, at faint Ks magnitudes the models predict higher values in 50 –Fig. 27.— Functional form of the φ ∗ evolution parameterization. 51 –Fig. 28.— Color-magnitude diagram for the Alhambra data in the filter with effective wave-length 6130˚ A (F613) and Ks. The tracks for the galaxy classes in Tab. 8 formed at zf=4 arealso shown, for the passive evolution scenario top panel) , and the no-evolution case bottompanel) . Each galaxy track is computed for the characteristic luminosity given in Tab. 9. Thesolid tracks from top to bottom correspond to a simulated E/S0 galaxy with single stellarpopulation and e-folding timescales τ = 0 . , σ detection levels. The two dashed lines join the spectrapoints for z=0.5 and z=1.0. The median color for each Ks bin is marked with crosses. 52 –Fig. 29.— Color F613-Ks histogram (normalized for 1 square degree) for sources in differentKs bins. The histograms produced by the models have been convolved with a Gaussiankernel σ = 0 . ≤ F − Ks ≤
5. As could be inferred from Fig. 29 to obtain a bettermatch to the data the number densities of early spiral galaxies formed in a shorter time-scale has to decrease with z , such fading of the spirals will lead to an under-prediction ofthe blue-band number counts unless that the number of star-forming increases at higherredshift. In Fig. 30 the F613-Ks histograms for the Ks bins: [16.5,17.5], [17.5,18.5] show abetter concordance with the observed data. Those histograms correspond to a models wherethe number densities for the early spirals decrease with z as φ ⋆ ∝ (1 + z ) − , the late typespirals number density remain constant with redshift, and number densities of Irr galaxiesincrease ∝ (1 + z ) . The luminosity density in not conserved within any galaxy class. Similarresults could be obtained using φ ∗ ∝ exp [( − Q/β )((1 + z ) − β − ∼
5, this could be due to thefact that we only use a discrete number of galaxy parameterizations, for example is wellknow the existence of dusty starburst with the same red colors than the passive extremelyred objects (Daddi et al. 2000). Covering a wider range in galaxy internal extinction orformation timescale will tend to smear the bi-modality present in the simulated histograms.As could be seen in Fig. 31 the number counts produced by this model in B + NIR filtersalso produce good fits to the observed data points. In this models the number counts atfaint magnitudes will be dominated by the star-forming galaxies. The number count slopeat faint magnitudes will be − . α + 1) (Bershady 2003), being α the slope of the dominantluminosity function for M << M ⋆ . With this parameterization the slope of the numbercounts tend to 0 .
36 at the fainter end. 54 –
7. Summary
We have presented galaxy counts in the J,H, and Ks filters covering an area of 0.45square degrees and an average 50% detection efficiency depth of J ∼ .
4, H ∼ . ∼ . ∼ φ ⋆ ∝ (1 + z ) − with no accompanying evolution in M ⋆ , corresponding to evolution in which the majority of ellipticals formed in spiral-spiralmergers.Performing a color analysis show that also the population of early spirals has to decreaseat higher redshift in order to describe the color distribution in r-Ks. Models using theparameterization of Broadhurst et al. (1992) φ ∗ ∝ exp [( − Q/β )((1 + z ) − β − z . Agood match to the optical and NIR data is also obtained if the population of red-galaxiesin the models remain constant to z ∼ . φ ⋆ ∝ (0 . z ) − , or if the number density of red-ellipticals is constant with redshift forgalaxies brighter than M ⋆ − . ∼ − . r ′ band in AB system), decreasing as φ ⋆ ∝ (1 + z ) − for the bulk of the ellipticals.Alhambra is processing the data obtained in 20 medium-band optical and 3 NIR filtersreaching high quality photometric redshift measurements (∆ z/ (1 + z ) ≤ . z ∼
1, which willcomplement the results given in this article, disentangling what populations contribute tothe number counts at different redshift intervals. Also the study of number counts for redgalaxy populations, passive EROS or BzK (Daddi et al. 2004) galaxies will constrain theformation redshift and formation timescale for massive Elliptical galaxies. 55 –Fig. 30.— Color F613-Ks histogram for sources in different Ks bins. The histograms havebeen normalized to 1 square degree. The modelled histograms have been computed formodels in which the number densities for the early spirals decrease with redshift as φ ⋆ ∝ (1 + z ) − , the late type spirals number density remain constant with redshift, and numberdensities of Irr galaxies increase ∝ (1 + z ) . The number of E/S0 galaxies decrease with z asspecified in the labels. The histograms obtained with this models have been convolved witha Gaussian kernel σ = 0 . φ ⋆ ∝ (1 + z ) − , thelate type spirals number density remain constant with redshift, and number densities of Irrgalaxies increase ∝ (1 + z ) . 57 –The authors acknowledge support from the Spanish Ministerio de Educaci´on y Cien-cia through grants AYA2002-12685-E, AYA2003-08729-C02-01, AYA2003-0128, AYA2007-67965-C03-01, AYA2004-20014-E, AYA2004-02703, AYA2004-05395, AYA2005-06816, AYA2005-07789, AYA2006-14056, and from the Junta de Andaluc´ıa , TIC114, TIC101 and
Proyectode Excelencia
FQM-1392. NB, JALA, MC, and AFS acknowledge support from the MEC
Ram´on y Cajal
A. Individual image combination
As mentioned in the text, to combine the processed images we used SWARP (Bertin et al.2002). With this software, individual images were projected into subsections of the finalframe using the inverse mapping, in which each output pixel center was associated to a po-sition in the input image at which it is interpolated. With this schema, the code correctedat the same time the geometrical distortions in the individual images using the astrometricinformation stored in the image headers. 58 –
A.1. Estimating the relative transparency
Using a filtered version of the SExtractor catalogs computed over the sky subtractedimages, an accurate estimate of the relative transparency was computed by tracing the highS/N objects in all the images. The relative transparency values were used inside SWARPto scale the individual images to the same flux level in order to uniformize the zero pointsin the outer dither areas, this allowed to use 2MASS catalogs to calibrate the ALHAMBRANIR photometry in the final images.
A.2. Astrometry calibration
When computing the resampled version of the individual frames, SWARP uses the WCSinformation stored in the headers. In order to obtain a better matching of the individual im-ages, firstly the pipeline calculated the external astrometrical solution for a reference image.The individual images were then calibrated internally with respect to it, thus obtaining theequatorial coordinates from the reference image. In this paper the individual image with bet-ter transparency in a given pointing was used as reference. However, to get a better internalastrometry between the different filters, after completing a pointing in the 23 ALHAMBRAfilters, the images with better FWHM and transparency in a set of selected optical filters,are combined to produce a deep image that will be used afterwards as reference.We have determined that the USNO-B1.0 catalog (Monet et al. 2003) provides an ad-equate number of objects to perform a high quality external astrometric calibration. Weused our own code to match the sources with brighter apparent magnitudes in the referenceimage with those in the USNO-B1.0. Once a meaningful number of pairs was identified, theCCMAP IRAF task was used in two iterations to acquire the required astrometric solutionwith a 2nd order polynomial. A histogram of the external astrometric solution rms and thenumber of objects used for the final images of ALH08 is shown in Fig. 32. The medianexternal astrometry rms is 0 . ′′ ± .
01 in RA and 0 . ′′ ± .
01 DEC.Having calibrated a reference image, the rest of the individual images were calibratedinternally. The median internal rms in the astrometric solution for the OMEGA2000 dataused in this paper is 0 . ′′ in RA and DEC using a median of 160 objects, as shown in Fig 32. 59 –Fig. 32.— Histograms of the astrometry solution rms for the ALH08 images. (Top panel) External USNO-B1.0. (Bottom panel) internal. The small panels show the histograms ofthe number of objects that enter into the final astrometry fitting 60 –
A.3. Image co-adding
Swarp allows the user to choose among several interpolation functions for inverse map-ping. For selecting the more appropriate kernel we analyzed the resulting final image FWHMand its pixel-to-pixel correlation. Tab. 10 shows the correlation values, between adjacentpixels and for pixel pairs separated by 2 pixels, in the final images obtained using differentavailable interpolation functions. As can be seen in the table, the bilinear function producea higher correlation which translate into an underestimation of the flux errors. Using theLanczos-3 function the FWHM of the final image was improved by ∼ . ′′ compared withthe nearest neighbor interpolation, whereas the auto-correlation at 1 pixel remain acceptable ∼ .
16 (when the images are combined using the average). The Lanczos-4 function did notdecrease substantially nor the FWHM neither the correlation at 1 pixel, on the contrary itproduced large artifacts at the bad pixels and image borders, so finally we have decided totake the Lanczos-3 function. 61 –Table 10. Values for the correlation between adjacent pixels when co-adding the imagesusing different interpolation functions
Nearest Bilinear Lanczos2 Lanczos3 Lanczos4Combining with median1pix +0.017 +0.186 +0.112 +0.074 +0.0682pix -0.035 -0.013 -0.072 -0.059 -0.101Combining with average1pix +0.035 +0.274 +0.177 +0.156 +0.1302pix -0.030 -0.018 -0.069 -0.110 -0.083
62 –
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