The bright end of the z ~ 7 UV Luminosity Function from a wide and deep HAWK-I survey
M. Castellano, A. Fontana, D. Paris, A. Grazian, L. Pentericci, K. Boutsia, P. Santini, V. Testa, M. Dickinson, M. Giavalisco, R. Bouwens, J.-G. Cuby, F. Mannucci, B. Clément, S. Cristiani, F. Fiore, S. Gallozzi, E. Giallongo, R. Maiolino, N. Menci, A. Moorwood, M. Nonino, A. Renzini, P. Rosati, S. Salimbeni, E. Vanzella
aa r X i v : . [ a s t r o - ph . C O ] J u l Astronomy&Astrophysicsmanuscript no. HawkI˙PAPER2 © ESO 2018October 15, 2018
The bright end of the z ∼ M. Castellano , A. Fontana , D. Paris , A. Grazian , L. Pentericci , K. Boutsia , P. Santini , V. Testa , M. Dickinson ,M. Giavalisco , R. Bouwens , J.-G. Cuby , F. Mannucci , B. Cl´ement , S. Cristiani , F. Fiore , S. Gallozzi , E.Giallongo , R. Maiolino , N. Menci , A. Moorwood , M. Nonino , A. Renzini , P. Rosati , S. Salimbeni , and E.Vanzella INAF - Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monteporzio (RM), Italy NOAO, 950 N. Cherry Avenue, Tucson, AZ 85719, USA Department of Astronomy, University of Massachusetts, 710 North Pleasant Street, Amherst, MA 01003 Lick Observatory, University of California, Santa Cruz, CA 95064, USA, Laboratoire d’Astrophysique de Marseille, OAMP, Universit´e Aix-Marseille & CNRS, 38 rue Fr´ed´eric Joliot Curie, 13388 Marseillecedex 13, France INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy INAF - Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, 34131 Trieste, Italy European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, ItalyReceived .... ; accepted ....
ABSTRACT
Aims.
We perform a deep search for galaxies in the redshift range 6 . ≤ z ≤ .
5, to measure the evolution of the number density ofluminous galaxies in this redshift range and derive useful constraints on the evolution of their luminosity function.
Methods.
We present here the second half of an ESO Large Programme, which exploits the unique combination of area and sensitivityprovided in the near–IR by the camera Hawk-I at the VLT. We have obtained ∼
30 observing hours with Hawk-I in the Y -band of twohigh galactic latitude fields. We combined the Y -band data with deep J and K Hawk-I observations, and with FORS1 / FORS2 U , B , V , R , I , and Z observations to select z -drop galaxies having Z − Y >
1, no optical detection and flat Y − J and Y − K colour terms. Results.
We detect 8 high-quality candidates in the magnitude range Y = . − . z -drop candidates selectedin two Hawk-I pointings over the GOODS-South field. We use this full sample of 15 objects found in ∼ arcmin of our surveyto constrain the average physical properties and the evolution of the number density of z ∼ z = . + . − . and an E ( B − V ) = . + . − . . We compute a binned estimate of the z ∼ ff ects of photometric scatter and model uncertainties on the statistical constraints. After accounting for the expectedincompleteness through MonteCarlo simulations, we strengthen our previous finding that a Schechter luminosity function constantfrom z = = &
99% confidence level, even including the e ff ects of cosmic variance. For galaxies brighter than M = − .
0, we derive a luminosity density ρ UV = . + . − . × erg s − Hz − M pc − , implying a decrease by a factor 3.5 from z = z ≃ .
8. We find that, under standard assumptions, the emission rate of ionizing photons coming from UV bright galaxies islower by at least a factor of two than the value required for reionization. Finally, we exploit deep Hawk-I J and K band observationsto derive an upper limit on the number density of M . − . z ∼ Y -dropouts). Key words.
Galaxies: distances and redshift - Galaxies: evolution - Galaxies: high redshift - Galaxies: luminosity function
1. Introduction
The search and study of galaxy populations at very high redshiftis one of the most promising research areas of today astrophysicsand cosmology. It derives its importance on two di ff erent andinterrelated aspects: 1) The estimate of the UV photon budgetprovided by star-forming galaxies and its role on the reioniza-tion of the universe at z >
6; 2) The study of the formation andthe physical properties of the first bulding blocks of present-daygalaxies.There is observational evidence that the Universe is highlyionized at z ∼ Send o ff print requests to : M. Castellano, e-mail: [email protected] ties remains on the homogeneity (e.g. Mesinger & Furlanetto2009) and on the exact timeline of the reionization process(e.g. Gallerani et al. 2006). Whether the UV light emitted bystar-forming galaxies is capable of reionizing the Universe bythese epochs remains an open question that should be answeredthrough the analysis of large samples of high redshift objects.The search for high-redshift star forming galaxies has beencarried out so far mainly with renditions of the Lyman Break,or “drop-out” technique that has been proved to be extremelye ffi cient at redshift from 2 to 6 (e.g. Steidel et al. 1995, 1999;Adelberger et al. 2004; Dickinson et al. 2004; Giavalisco et al.2004; Ouchi et al. 2004; Bouwens et al. 2007; McLure et al.2009), or through narrow-band studies targeting the Ly α emis-sion (e.g. Iye et al. 2006; Kashikawa et al. 2006; Ouchi et al.2009b). The application of the Lyman Break technique at z > M. Castellano et al.: The bright end of the z ∼ J + H NICMOS data (e.g. Bouwens et al. 2004), and it hasrecently acquired momentum thanks to the installation of theWFC3 camera onboard of the Hubble Space Telescope yield-ing to a sample of tens of faint Lyman Break galaxies (LBGs)(Bouwens et al. 2010c; Oesch et al. 2010; McLure et al. 2010;Bunker et al. 2009; Yan et al. 2009; Wilkins et al. 2010a,b).In the meantime, ground based surveys (Ouchi et al. 2009a;Capak et al. 2009; Hickey et al. 2010; Castellano et al. 2010,C10 hereafter), along with refined analysis of archival NICMOSobservations (Bouwens et al. 2010a) have expanded the numberof bright LBGs known.The basic feature of the high redshift galaxy popula-tion that can be analysed through the present datasets isits UV luminosity function (LF). The current picture of theevolution of the UV LF points to a factor of 6-11 de-crease in the number density of UV bright galaxies from z ∼ z ∼ M ∗ and / or a decrease ofthe normalization factor φ (Bouwens et al. 2008; McLure et al.2010; Ouchi et al. 2009a; Yan et al. 2009; Castellano et al. 2010;Bouwens et al. 2010a). The recent WFC3-based analysis byOesch et al. (2010) also found evidence for a steep faint-end( α ∼ − . z ∼
7, the lat-est analysis of the WFC3 data have also provided a first estimateof the evolution at z ∼ − ff erent works, both at z ∼ − z ∼ − ff ect of cosmicvariance (e.g. Trenti & Stiavelli 2008; Robertson 2010), but alsoto the di ffi culties in avoiding systematic e ff ects in the di ff erentestimates of completeness level, contamination from lower red-shift interlopers, volume elements, and redshift distributions inthe various samples (Stanway et al. 2008), all worsened by theknown degeneracy among the parameters adopted to fit the LF.The strong decrease observed in the UV emission comingfrom relatively bright sources seems to imply that reionizationcannot be explained on the basis of UV bright galaxies only. Anincreased number of low luminosity galaxies indicated by thesteep faint end of the Schechter LF might play a decisive rolein the reionization process. Large and reliable samples of high-zgalaxies both at the bright and at the faint end of the LF are thusnecessary to shed light on this issue, and, possibly to highlightthe need to search for even more intriguing sources of the reion-izing radiation with future facilities (see e.g. Venkatesan et al.2003; Madau et al. 2004).Latest surveys have also given the opportunity of analysingthe physical properties of high redshift galaxies, whose knowl-edge is also a decisive factor to understand the very role ofthese sources in the reionization process. Recent studies havegiven the first estimates of masses, ages and SFRs for sin- Fig. 1.
Colour-composite image of the BDF (left) and NTTDF(right) fields, created using the weighted mean of Hawk-I Y , J and K images as red, the FORS2 Z as green, and the weightedmean of FORS1 / FORS2 optical images as blue.gle z & . Y band over four independent point-ings, aimed at the detection of relatively bright LBGs at 6 . < z < .
5. Thanks to the extreme e ffi ciency and large field ofview (7.5 × Y ∼ . > σ (roughly corresponding to M = − . z = ∼
99 % c.l.) decrease, withrespect to z ∼
6, of the number density of UV-bright galaxies.In this paper we present the z ∼ ff ect-ing the selection are discussed; in Section 4 we present our fi-nal sample of candidate z -drop LBGs. In Section 5 we discussa stacking analysis of all the z -drop galaxies found in the fourHawk-I pointings, that are used to constrain the z > z ∼ Λ -CDM concor-dance model ( H = km / s / M pc , Ω M = .
3, and Ω Λ = .
2. Data
This work is based on deep Y –band images obtained with the IRcamera Hawk-I at the VLT, and on deep optical FORS2 obser- . Castellano et al.: The bright end of the z ∼ Table 1.
BDF - Observations
Filter Instr. Exp. Time (s) Seeing (arcsec) Mag. Limit a V-High FORS2 13800 0.75 29.1R-Special FORS2 11600 0.63 29.3I-Bessel FORS2 4800 0.70 27.8Z-Gunn FORS2 64800 0.59 28.6Y-Open HAWK-I 56940 0.52 28.3 b J-Open HAWK-I 18720 0.54 26.5Ks-Open HAWK-I 30060 0.44 26.0a - S / N =
1b - Y = / N = Table 2.
NTTDF - Observations
Filter Instr. Exp. Time (s) Seeing (arcsec) Mag. Limit a U-Bessel FORS1 32876 0.84 27.8B-Bessel FORS1 16064 0.56 28.9V-Bessel FORS1 10500 0.47 29.0R-Special FORS2 14000 0.79 28.4I-Bessel FORS2 7830 0.61 28.0Z-Gunn FORS2 46386 0.60 28.4Y-Open HAWK-I 54180 0.49 28.3 b J-Open HAWK-I 14400 0.47 26.7Ks-Open HAWK-I 24720 0.39 26.3a - S / N =
1b - Y = / N = vations. We use data collected through a dedicated ESO LargeProgramme in 2008 and 2009. The first set of data, coveringtwo adjacent regions of the GOODS-S field has been presentedin C10. Here we present the analysis of two other pointings(Fig. 1), chosen for the wealth of deep, public observations pre-viously exploited by other authors to search for z ∼ − = = -35.17°(Lehnert & Bremer2003), and the New Technology Telescope Deep Field (NTTDF)at Ra = = -7.72°(Arnouts et al. 1999; Fontana et al.2000, 2003). The total exposure time is 15h49m for BDF and15h03m for the NTTDF in the Y band.The Y band images were reduced using standard techniquesfor IR data - flat fielding, sky subtraction among consecutiveframes, and final coaddition. The reduction procedure, which isdescribed in detail in our first paper C10, has been specificallydesigned to enhance the reliability of the images at the faintestfluxes, and to get rid of persistence e ff ects and cross-talk reso-nances.We determine an FWHM of 0.52 ± .
01 arcsec ( ≃ ± .
01 arcsec ( ≃ σ magnitude in one arcsec is in the range26.7-26.8 over more than 60% of the whole image, and > . Y band pixel-sizeand astrometric solution.Along with the main Y –band pointings, we also acquireddeep J and K s
Hawk-I observations of both fields. We alsoobtained ∼ Z band coverage for eachfield, that we coadded with the already existing FORS2 images(Fontana et al. 2003) to reach the required depth. We also re-reduced the archive U , B , V , R , I FORS2 and FORS1 observa-tions of the NTTDF, and the FORS2 R and I images of the BDF.Finally, we obtained ∼ V -FORS2 observations on theBDF. The full dataset is presented in Tab. 1 and Tab. 2. We obtained the photometric catalogue using the SExtractorcode V2.5 (Bertin & Arnouts 1996) and the Y band as detec-tion image with the r.m.s. map derived as described above. Sincehigh redshift galaxies are almost unresolved in ground-based im-ages, and SExtractor’s MAG_BEST are known to underestimatethe total flux of faint objects ( Y >
24 in our case), we choseto use aperture-corrected total magnitudes. We computed aper-ture magnitudes in a 2 FWHM diameter and corrected them tototal magnitudes adopting aperture corrections from bright non-saturated stars in each field. While this choice might give slightlyunderestimated fluxes for the more extended high redshift can-didates, we can easily take into account this systematic throughthe simulations that we use to estimate the LF (Sect. 6.1) thatare based on the observed profile of LBGs with known spec-troscopic redshifts 5 . < z < . M. Castellano et al.: The bright end of the z ∼ the ratio between ’negative’ and ’positive’ detections at the faintend of the number counts. As expected, we find that the bestparameters for faint objects detection on BDF and NTTDF Y -band images are the same adopted for the similar set of imagesover GOODS-South: we require 10 contiguous pixels each at S / N > . . σ detection, and we re-strict the analysis to the regions where the r.m.s is less than ∼ Y < .
2, anda fraction of negative detections less than 5% of the real onesat fainter magnitudes. However, a posteriori , the latter valueoverestimates the actual rate of spurious detections. Indeed, allspurious sources should appear as “drop-out” candidates with asingle-band detection. On the contrary, all the Y > . z -drop sample are confirmed by detections in other IRbands. Indeed, as we discuss also in C10, the test on the negativeimage is probably influenced by non-trivial issues concerningthe subtraction of the background or a potential asymmetry inthe noise distribution. A multiwavelength catalogue containing self-consistent magni-tudes in all available bands was built running SExtractor in dualmode using the Y -band Hawk-I image as the detection imagewith the detection parameters indicated above. Aperture fluxeswere computed within a 2FWHM aperture and converted to to-tal applying appropriate aperture corrections in each band.The typical 1 σ limiting magnitudes in a 2FWHM apertureare in the range 27 . − . J ∼ . − . K s ∼ . − .
3. The corresponding 1 σ limiting magnitudein the Z band, which is used to define the ’dropout’ selection, is ∼ . ∼ . ffi ciently homogeneous. The candidates found in thisarea will be used for the evaluation of the LF. We used Y -banddetected objects only in the regions selected on the basis of thenegative image test explained above. In addition, we also maskedborders, CCD defects and noisiest regions in the other images ofour data-set. The areas selected in this way correspond to ∼ Y -band coverage in the BDF, and ∼
56% in the NTTDF(due to strong vignetting in the Z -band image). As a result, thetotal area used for z -drop detection amounts to 71 . .We will subtract to this value the fraction of area covered bylower redshift objects ( ∼ ff ective volumes inSect. 6 and Sect. 7.
3. The selection of z > . galaxies We select candidate z > . Z ⊙ ; age from 0.01 Gyr to the maximal age of theUniverse at a given z ; E(B-V) = α rest-frame equivalent width in the range 0-200 Å. Intergalacticabsorption following Madau (1995). The same range of model Fig. 2.
Left : Z − Y colour of star forming galaxies as a function ofredshift. In the upper part, the e ffi ciency curve of the two filtersis shown, computed at observed wavelength of a Lyman- α emis-sion at the corresponding redshift. Right : Z − Y vs. Y − J colourdiagram showing the expected colours of LBGs (same as in leftpanel, black points), passively evolving galaxies (red squares)and reddened starbursts (green circles) at 1 . < z < z > . Z − Y colour which is due to the sampling withinthese two filters of the sharp drop shortward of the Lyman- α ,where most of the photons are absorbed by the intervening HIin the intergalactic medium. The drop in the flux observed short-ward of the Y band is analogous to the one used to select starforming galaxies at lower redshifts, like i -drops at z ∼ V -dropsat z ∼ ff erence with respect to the standardLyman break technique being that the Y band does not samplethe continuum around 1500 Å but a region shortward of it, con-taminated by both the larger IGM absorption at z > α emission line. These e ff ects can only be accuratelyaccounted for by realistic imaging simulations, as we discuss indetail in C10 and in section 6.1 of this paper. Following thistest, we choose Z − Y > z > . Z -band observations, aswell as the optical ones, used in the present paper are slightlyshallower than the GOODS-ACS ones, we limit our selection at Y < . Y < . z -drop galaxies cannot be solely based onthe Z − Y colour, since other classes of objects can display a red Z − Y colour similar to that of z > . z ∼ We tailored our IR colour selection to exclude any possible con-tamination in our z -drop sample from known classes of lowerredshift objects:i) We modelled passively evolving galaxies and dusty star-burst galaxies at z > . . Castellano et al.: The bright end of the z ∼ shift galaxies to predict the colours of such objects at 1 . < z <
4, using a combination of short star formation exponentialtimescales (0 . − > . < E ( B − V ) < . > (Y-K); (Z-Y) > + < < T e f f < CH and H O absorption bands and by H reso-nant absorption (e.g. Chabrier et al. 2005; Burgasser et al. 2006)that produce a sharp break in their IR colours. We used themost up-to-date estimate of the T-dwarfs number density (as ob-served in the J band) of Burgasser et al 2007 to compute theexpected number of faint, cool dwarfs in our fields. Adoptingan average Y − J colour of 0.8 mags estimated from the cata-logue of observed dwarfs compiled by Leggett et al. (2010), andconsidering the dependence on galactic latitude as in Burgasser(2004), we estimated that ∼ Y < . z -dropouts in the Y − J colour, and the Y − J criterion weadopt allows us to exclude these objects from our selection win-dow. We note that the brown dwarf discovered in the NTTDF byCuby et al. (1999), having Z − Y ∼ Y − J colour.iii) Finally, we cross-checked each object selected accordingto the above criteria against variability, by analysing images ac-quired at di ff erent epochs. The BDF observations have been splitin two separated epochs with a 3 months gap (September andDecember 2009), while the NTTDF have been observed duringfour runs in January, February, April and May 2009. We veri-fied that all the objects in our sample are clearly detected, andthat they have a consistent total flux (within 2 σ ), in the di ff erentepochs. In the NTTDF case, we checked that a detection > σ ofthe faintest candidate ( Y ∼ .
5) was possible in the two epochswith larger integration time.We summarise here the full set of colour selection criteria: Y < . Z − Y ) > . Z − Y ) > ( Y − K )( Z − Y ) > . + . Y − J )( Y − J ) < . Y − K ) < . In our analysis of the GOODS-South field we exploited the ACSV2.0 B , V , I , Z observations (M. Giavalisco and the GOODS Team, in preparation) to select z -drop galaxies and to excludelower redshift interlopers showing significant detection in theoptical bands. The main concern we have to consider to pro-vide a z -drop selection as clean as the one in the GOODS fieldregards the di ff erence in resolution between FORS2 optical ob-servations of BDF and NTTDF and their corresponding ACS-GOODS images we used to remove interlopers from the colour-selected sample.Indeed, in C10 we found that a sample of galaxies selectedwith IR criteria only is populated also by faint contaminantsshowing significant detection in filters covering wavelengthsshorter than the redshifted Lyman limit at z > U , B , V , R , I )where high redshift LBGs are not expected to present any flux.These objects are, in most cases, clearly extended, but their spec-tral energy distributions cannot be reproduced by a straightfor-ward application of the CB07 models. While determining theirnature is beyond the scope of the present analysis, we note thatthey might be faint galaxies with a very blue continuum whoseSED is altered by strong emission lines such as in unobscuredAGNs, or in star-forming galaxies like the blue compact dwarfgalaxies (Izotov et al. 2004, 2007) or the ultra strong emissionline galaxies (USELs, Hu et al. 2009). Potential contaminationof z ∼ < σ ) has also been suggested by Capak et al.(2009). Their objects are brighter than those found in our fieldsbut display similar colours. Given the unknown nature of thiscontaminants, at present, the only feasible approach is to adoptmore stringent criteria on the optical non-detections. Follow-up spectroscopy of z ∼ / N ratios in small apertures (0.6”)exploiting the high resolution of ACS images.In order to obtain optical selection criteria as e ff ective asthe ones used with the GOODS dataset, we performed testscomputing S / N ratios and photometry on the GOODS-ACS im-ages degraded and smoothed to the depth / seeing of the BDFand NTTDF corresponding ones. We then re-selected GOODSdropouts on “mock” BDF / GOODS and NTTDF / GOODS cat-alogues built in the same way as the real BDF and NTTDFcatalogues. We verified that the criteria already adopted in theGOODS fields are e ff ective in the NTTDF case: S / N < σ S / N in all the optical bands and < σ S / N in at least four of them.In the BDF, given the absence of U and B images and theslightly shallower I imaging, we adopted the conservative cri-terion S / N < σ S / N in all the optical bands. We verified thatthis criterion allows us to safely remove all those objects, upto Y = σ S / N indicated above is the r.m.s. of the S / Ndistribution estimated, as in C10, dropping random apertures inportions of the images free of detected objects. This procedureallows us to take into account the sky noise distribution andthe presence of faint, undetected foreground objects at the sametime.
4. Detected z > . galaxies Adopting the selection criteria outlined above we find a total ofeight candidates, three in the BDF and five in the NTTDF field,whose coordinates, Y magnitudes and Z − Y colours are listed M. Castellano et al.: The bright end of the z ∼ Fig. 3.
Thumbnails showing the images of the 8 selected high-redshift candidates in the di ff erent observed bands.in Tab 3. Thumbnails of the candidates are presented in Fig. 3.We note that two of them are clearly detected, and two othersare marginally detected (S / N ∼ Z band. Three of thefive candidates present in the NTTDF are also detected at S / N ∼ − J and K bands, thanks to the slightly deeper imagesavailable for this field (see Tab 2). We also verified that eachcandidate is undetected in the image obtained as the weightedsum of its V , R and I observations.As a final check we performed a stacking of all the objectsin the available images. This test allows us to confirm the non-detection in the optical images, and to obtain a clear detections in the J (S / N ∼
5) and K band (S / N ∼
4) stacked images. Thestacked object shows an average colour Z − Y ≃ . z -drop candidates found in the BDF and NTTDF pointings withthe sample discussed in C10, obtained from the two point-ings over the GOODS-South field, to find their average prop-erties through a stacking analysis, and to constrain their LF. TheGOODS z -drop sample includes seven candidates in the range Y ∼ . − .
7, selected through colour selection criteria analo-gous to the ones outlined above, whose reliability has also beenchecked on the available IRAC and NICMOS observations. . Castellano et al.: The bright end of the z ∼ Fig. 5.
Best-fit SED to the stacked photometry, with relevant photometric redshift at z = . Fig. 4.
Thumbnails showing the stacked images of the 15 high-redshift candidates selected in the GOODS1, GOODS2, BDFand NTTDF fields. The observed bands are shown in the legends.
Table 3.
Candidates in the BDF and NTTDF fields
ID R.A. (deg) DEC. (deg) Y Z-Y S / N (Y)BDF 521 336.9444 -35.1188 25.86 2.13 10.2BDF 3299 337.0511 -35.1665 26.15 > >
5. Mean properties of Hawk-I z ∼ galaxies We perform a weighted mean of the images in the available fil-ters from the U to the K band for all the 15 objects detectedin the Hawk-I fields. We did not attempt a similar stacking ofthe IRAC images, since most of our GOODS candidates are par-tially or extremely blended with other foreground sources, andthe candidates in the other fields are either not covered by IRACobservations, or they are present in shallower exposures with re-spect to GOODS. We matched the ACS images to the Hawk-IPSF and masked all the foreground objects surrounding the can- didates in each image. The stacked object shows an S / N & Z , J and K bands and a non-detection in all theoptical bands, corresponding to an ( optical − Y ) colour of > χ minimisation procedure to find the best-fitting spectral template to the observed colours among the fullCB07 library. While the ACS optical filters used in the GOODSfield have di ff erent passbands with respect to the FORS2 onesused in BDF and NTTDF fields, this is not a significant con-cern since they all span a wavelength range where no flux isexpected for z > ff erence be-tween FORS2 and ACS Z -band filters does not provide signif-icant variations in the redshift selection window defined by the Z − Y colour which is the main constraint to the photometricredshift. The resulting SED provides a unique photometric red-shift solution at z = . + . − . . Relevant thumbnails and SEDare shown in Figure 4 and 5. Given the absence of IRAC,most physical parameters are largely unconstrained, apart fromthe E(B-V) parameter whose estimate is mostly based on the Y − J and Y − K colours. We find that our stacked SED is fit-ted by an E ( B − V ) = . + . − . at a 68% confidence level. Thisvalue is consistent with the E(B-V) distribution obtained fromthe analysis of z ∼ − z ∼ A V values found by Gonz´alez et al. (2010) and by Labb´e et al.(2010) for the mean SED of their z -drop samples, and with theblue UV continuum slope measured by Bouwens et al. (2010d).
6. The evolution of the LF
When small galaxy samples are used to constrain the high-redshift LF, it is necessary to exploit detailed imaging simula-tions to appropriately treat the systematic e ff ects arising fromfaint object detection, and from the application of colour selec-tion criteria. To this aim we use the CB07 synthetic libraries de-scribed in Sect. 3 to produce, for each field, a set of ∼ × simulated LBGs with redshift in the range 5 . < z < . M. Castellano et al.: The bright end of the z ∼ Table 4.
Stepwise determination of the UV LF
Mag. Range φ (10 − M pc − mag − ) − . < M < − . . ± . − . < M < − . . ± . observed magnitudes computed in the same filter set used forthe observations. These galaxies are placed at random positionsof the Y -band images, and catalogs are extracted exactly as inthe original frames. To avoid an excessive crowding in the simu-lated images, we include only 200 objects each time, after mask-ing the regions of the images where real objects are present. Asin C10, we randomly assign to each of our simulated galaxiesthe light profile of one of the four most distant spectroscopicallyconfirmed LBGs observed with ACS in GOODS ( z = . − . The magnitude range covered by our survey, Y ≃ . − . M . M ∗ . For this reason, we first perform a binned estimateof the number density of the Hawk-I z -drop galaxies throughthe stepwise method (see, e.g. Bouwens et al. 2008). The step-wise estimate is a non-parametric method based on the assump-tion that the rest-frame LF of galaxies can be approximated by abinned distribution, where the number density φ i in each bin is afree parameter. To evalute also the potential systematics and thee ff ects of observational uncertainties in this kind of estimates,we use two di ff erent procedures to compute the stepwise LF.The first one is the procedure commonly adopted in the litera-ture based on the average relation between the observed Y andthe UV continuum magnitude at 1500Å ( M ), and on an es-timate of the completeness in the di ff erent UV magnitude bins.The second, more conservative, procedure takes in considerationthe uncertainties in the Y - M conversion due to photometricscatter, to the redshift distribution and to the intrinsic proper-ties of di ff erent galaxy models. In a separate work we will com-bine this stepwise analysis with similar estimates at fainter andbrighter magnitudes to determine the Schechter parameters at z ∼ Through a linear regression we compute the average Y − M relation at the median redshift of our sample (z = z -drop galaxies. We then divide our sample intwo bins centered at M = − . M = − .
4, anduse the imaging simulations to estimate the completeness of ourselection. Finally, we convert the redshift dependent complete-ness distribution into e ff ective volumes of our survey at thesemagnitudes. The values of the stepwise LF estimated in this wayare reported in Tab. 4 and plotted as filled squares in Fig 6, withvertical error bars given by Poisson uncertainties in the numbercounts. The horizontal error bars indicate the relevant magnituderange of each bin. Fig. 6.
Number densities in two rest-frame magnitude intervalsestimated for our Hawk-I data set in a stepwise form with a stan-dard Y -UV conversion of the observed number counts as dis-cussed in the text (black filled squares), or with a χ methodconsidering also photometric and model uncertainties (blackempty circles). Other points are from Bouwens et al. (2010a)(NICMOS, red empty squares), Ouchi et al. (2009a) (SUBARU,blue empty squares and upper limits) and Oesch et al. (2010)(WFC3-UDF, magenta empty circles). For a comparison weshow the recent determinations of the LF at z ∼ A more conservative estimate can be computed assuming astepwise LF made of three bins in the wider magnitude range − . < M < − .
0. This interval takes into account thephotometric scatter and the variation of the Y − M relationwith redshift and galaxy models (see Fig.7). We assume a fixed,constant, reference density φ re f , and we exploit the set of simu-lations described in Sect. 6.1 to compute for each field the dis-tribution of observed magnitudes originating in each rest-framebin for LBGs in the redshift range sampled by our colour selec-tion. The simulated number counts are then scaled to the rele-vant observed areas and summed together. Finally, we find thecombination of binned densities φ i = w i · φ re f , that best repro-duces the total number counts of our survey, where w i are mul-tiplicative factors to the reference density that we determine bycomparing observed and simulated distributions through a sim-ple χ test. We plot as black empty circles in Fig 6 the two bins at M < − .
8. The third, faintest, bin at M > − . ff ect of Malmquist bias. Vertical error bars indicate the sta-tistical uncertainties given by the χ test. . Castellano et al.: The bright end of the z ∼ Fig. 7.
The normalized distribution of UV continuum magni-tudes (estimated from the average Y − M relation) for the15 Hawk-I candidates divided in two bins (dashed histograms).The solid curves show the expected distributions of UV magni-tudes for objects in the same observed ranges when photometricuncertainties are taken into account through MonteCarlo simu-lations.The two methods give consistent results, and they are in per-fect agreement with other stepwise estimates in the same mag-nitude range (see Fig. 6). However, the error bars and the rele-vant magnitude range are much larger when using the χ mini-mization procedure. While an average conversion from observedto rest-frame magnitudes, along with an estimate of e ff ectivevolumes, can provide a first order-of-magnitude estimate of thebinned number density of LBGs, we emphasize that significantstatistical uncertainties can arise due to photometric scatter, andto the di ff erent relation between Y and UV continuum magni-tudes for di ff erent galaxy models and redshifts. We estimate how significant is the evolution of the LF at z > ff erent evolving Schechter LFs (Schechter 1976) after ac-counting for the expected systematics in the detection process(e.g. Bouwens et al. 2007; Mannucci et al. 2007; McLure et al.2009). As in C10, we assume that the LF can be described bya Schechter function with parameters φ and M ∗ evolving fromtheir value at z = . log ( φ ( z )) = log ( φ ( z )) + dlog ( φ ) / dz · ( z − z ) M ∗ ( z ) = M ∗ ( z ) + M ′∗ · ( z − z )Since our faint limit is close to the expected value of the char-acteristic luminosity M ∗ , we fix the faint end slope to the value α = − .
71 of the z ∼ ff erences are found when fixing α to di ff erent values ( α = − . , − . M ′∗ and dlog ( φ ) / dz (see Fig. 8) we sim- Fig. 8. χ contour levels for the dlog ( φ ) / dz , M ′∗ parameters de-rived for the Schechter–like LF considering all the four Hawk-Ifields. The lower and left axis refer to the evolutionary terms M ′∗ and dlog ( φ ) / dz with respect to the best-fit z = M ∗ and φ values at the median red-shift estimated for our sample (z = z ∼ z and UV mag-nitude M for a population of 3 × galaxies. These objectsare randomly extracted from the larger database of simulatedgalaxies described in Sect. 6.1, which encompasses a broadrange of the physical parameters determining the rest frame pho-tometry, like E(B-V), metallicity, Ly α EW etc.The distributions of Y magnitudes and Z − Y colours for eachsimulated population are scaled to the observed area in each ofthe fields and compared to the observed ones with a maximumlikelihood test, under the assumption of simple Poissonian statis-tics. For each of the two distributions, and for each field, we buildthe likelihood function L : L = Y i e − N exp , i ( N exp , i ) N obs , i ( N obs , i )! (1)where N obs , i is the observed number of sources in the magnitude(colour) interval i , N exp , i is the expected number of sources in thesame magnitude (colour) interval, and Π i is the product symbol.For each field, we associate to every model a likelihood com-puted as the product of those obtained for the magnitude andcolour distributions separately. We then compute a final likeli-hood as the product of the GOODS, BDF and NTTDF likeli-hoods.The colour plot in Fig. 8 shows the 68%, 95%, and 99%likelihood intervals on the evolutionary terms M ′∗ and dlog ( φ ) / dz (left and bottom axes) and for the resulting Schechter parameters ∼ at the median redshift z = χ distribution obtained underthe usual assumption χ = − . · ln ( L ) (e.g. Cash 1979). Wereject at &
99% confidence level the hypothesis that the LF re-mains constant in both parameters above z = ( φ ) / dz = and M ′∗ = dM ∗ / dz = , black point in Fig. 8) . In Fig. 8 itis also shown the 99% c.l. region on the Schechter evolutionaryterms estimated on the basis of the two GOODS-South pointingsonly (C10). Although the degeneracy between M ∗ and φ is stillpresent, the analysis of the BDF and NTTDF fields considerablyreduces the allowed parameter space.The region of allowed values for the LF parameters in ourfinal likelihood map points to a pronounced decrease of φ alongwith a brightening of M ∗ with redshift. However, the best-fit val-ues for M ∗ and φ at z ∼ M ∗ , still fall within the 2 σ region constrained by our maximum likelihood (grey points inFig. 8), and they are consistent with our estimate once the un-certainties are considered. We argue that cosmic variance (seeSect. 6.4) and the limited sample of very bright objects availablemay explain the discrepancies among di ff erent results: in ourcase, an inspection of the likelihood maps obtained separatelyon each field shows that the NTTDF, having two bright objects( Y ∼ . − .
7, approximately M . − . z = . ff ect in skewing the global likelihood towards brightervalues of M ∗ . We also note that some theoretical models (e.g.Trenti et al. 2010; Finlator et al. 2010) predict a dimming of M ∗ with redshift. However, several model parameters are largely un-constrained by the observations, while a large dust extinctionmight be required to match observed and predicted LFs at thebright end (Lacey et al. 2010). The e ff ects of cosmic variance are reduced in our case, sinceour data come from three independent areas, albeit of di ff er-ent sizes (the GOODS-South field being covered by two ofthe four Hawk-I pointings). We evaluate the possible impact ofcosmic variance using the mock catalogues of the MillenniumSimulation (Kitzbichler & White 2007) in the same way as dis-cussed in C10. For each of the three Hawk-I areas (GOODS-South, BDF, NTTDF), we extract 200 fields of the same sizefrom independent Millennium light-cones, and we apply a cor-responding photometric selection criteria on galaxies at 6 . < z < . ∼
21% a ff ects the total numbercounts of z -drop LBGs in our survey. We find that the evolutionis still confirmed at a &
99% confidence level by our maximumlikelihood approach even allowing a ∼
21% variation in the to-tal number density. Indeed, after accounting for all the observa-tional e ff ects, we estimate that we would have observed ∼ z -drops in our survey in the case of a non-evolving LF: a factorof two higher than the observed number. However, while cosmicvariance has not a significant e ff ect on our conclusion that theLF strongly evolves from z ∼ z ∼
6, it can have a great ef-fect in determining the form of this evolution. Cosmic varianceis strongly luminosity dependent, and it is as high as 41% forgalaxies brighter than Y = . ff ecting thedetermination of the M ∗ parameter. Table 5.
Properties of the z ∼ a ρ UV . + . − . erg s − Hz − M pc − SFRD 3 . + . − . − M ⊙ yr − M pc − log ( ˙ N ion ) 49 . + . − . M pc − a - LFs in the 95% c.l. region ( M < − . While the M ∗ and φ parameters are highly degenerate, the num-ber density of bright galaxies, i.e. the integral of the bright endof the LF is much better constrained, and so are derived inte-gral quantities such as the UV luminosity density ( ρ UV ) and starformation rate density (SFRD).We conservatively consider the model LFs within the 95%c.l. region of our likelihood analysis to derive the ρ UV by inte-grating L · Φ ( L ) up to the luminosity corresponding to M = − .
0. We convert these values in a SFRD following the stan-dard formula by Madau et al. (1998) and applying the extinc-tion correction of Meurer et al. (1999) (considering an averageUV slope β = − . ρ UV to evaluate the emis-sion rate ˙ N ion of hydrogen ionizing photons per M pc follow-ing Bolton & Haehnelt (2007). We consider an escape fraction f esc = .
2, a spectral index α s = . ǫ g = ρ UV / . ρ UV , SFRD and log ( ˙ N ion ). These values are perfectly consistent with the anal-ogous ones presented in C10 and derived from the LFs in the68% c.l. region of the GOODS likelihood. Considering the sameintegral of the z = ρ UV implies a drop of a factor ∼ . =
6. The lower limit for the ionization raterequired to balance recombination at z =
7, computed accord-ing to Madau et al. (1999) and assuming an HII clumping factorequal to one, is log ( ˙ N rec ) = .
1, which is a factor of two higherthan the highest value allowed by our analysis. This demon-strates that, under usual assumptions, bright UV galaxies alonecannot keep the universe reionized at z ∼
7. By varying the es-cape fraction, we obtain that values larger than f esc = . z ∼ ff erent physical propertieswith respect to lower redshift LBGs, or, most probably, a crucialcontribution to the reionization process comes from galaxies atthe faint end of the LFs or from other kind of sources. Once dif-ferent integration limits are taken into account, our estimates arein agreement with the results obtained by Bouwens et al. (2008);Ouchi et al. (2009a); Gonz´alez et al. (2010).
7. Constraints on the LBG number density at z ∼ We exploited deep Hawk-I J - and K -band observations to put anupper limit on the number density z & . Y -drop galaxies in oursurvey. We used the observations of the BDF and NTTDF fieldspresented in Sect. 2, and deep observations of the two GOODS-South pointings obtained both in our program as well as througha similar ESO observing program (Cl´ement et al. in preparation).We obtained a multicolour catalogue with the J -band as detec-tion image using SExtractor in dual mode over the full imag-ing set presented in this paper and in C10. We used the samedetection parameters and 2FWHM apertures adopted for the Y -detected catalogue, computing aperture corrected total magni- . Castellano et al.: The bright end of the z ∼ Table 6.
LBG number density at z ∼ Mag. Range φ (10 − M pc − ) M < − . < . tudes through appropriate corrections in each band. We chosethe colour selection criteria in order to isolate galaxies havingthe Lyman-break sampled by the Y − J colour, and to excludecontamination from lower redshift galaxies on the basis of theexpected colours for passive and dusty-starburst galaxies mod-elled as described in Sect. 3.2:( Y − J ) > . Y − J ) > . + . · ( J − K )We also required no detection in the optical bands adoptingthe same S / N criteria outlined for the selection of z -drop galax-ies. We limited our selection to J = z -drop galaxies in order toavoid the noisiest regions in any image.With these criteria we found no candidate Y -drop galaxy inour survey. Considered the average J − M relation at the me-dian redshift of our colour selection (z = M < M ∗ region of the LF at M ∼ − .
5. We report in Tab. 6an upper limit on the number density of very bright Y -drop LBGsestimated as the inverse of the volume sampled by our survey inthe redshift interval 7 . < z < .
8. Summary and conclusions
We presented in this work the results of a Y –band survey of thetwo high galactic latitude BDF and NTTDF fields aimed at de-tecting galaxies at z & . Y , J , K bandobservations performed with Hawk-I, the new near-IR camerainstalled at the VLT, and of FORS2 Z -band observations. Wematched and combined these data with deep archive FORS1 andFORS2 observations in the U , B , V , R , I filters to detect highredshift LBGs under the main criterion Z − Y >
1, requiring nooptical detection and flat Y − J and Y − K colours. The colourselection criteria have been tailored in order to exclude lowerredshift passive galaxies and dusty starbursts, Galactic T-dwarfsand galaxies exhibiting large Z − Y colours as well as signifi-cant emission in the optical bands, possibly intermediate redshiftsources with bright emission lines.As a result, we isolated 8 highly reliable z -drop candidatesin the magnitude range Y ≃ . − . arcmin . We combined this z -drop sample with the similarone extracted from two pointings over the GOODS-South fieldcomprising seven galaxies at Y < . M ∼ M ∗ galaxies at z & . z = . + . − . in perfect agreement with the estimated selection window of oursurvey. The stacked SED is fitted by an E ( B − V ) = . + . − . ata 68% confidence level, indicating a low dust content in agree-ment with previous analysis of z ∼ − / N measure due to overlapping unresolved sources,or other e ff ects. We first computed a binned estimate of thegalaxy number density at z ∼ ff erent proce-dures. The first one, which is based on an average Y - M rela-tion and on an estimate of the redshift dependent completenessof our selection, is the procedure commonly adopted in the lit-erature. The second method is more conservative, and exploitsa χ minimization to compare the observed number counts tothose predicted on the basis of MonteCarlo simulations for dif-ferent combinations of galaxy densities. This second procedureintrinsically considers the uncertainties in the Y - M conver-sion due to photometric scatter, to the redshift distribution and tothe intrinsic properties of di ff erent galaxy models. We find thatthe two procedures are consistent and they are in agreement withsimilar analysis from the literature. However, the more conser-vative procedure highlights that sources of statistical uncertaintyare usually underestimated.To assess the degree of evolution of the UV LF at z > . ff erent UVSchechter functions with linearly evolving parameters log ( φ )and M ∗ . For each of the four Hawk-I pointings we comparedthe resulting distributions of simulated magnitudes and colourswith the observed ones following a maximum likelihood ap-proach. We find strong evidence of evolution of the LF abovez =
6: our analysis rules out at a >
99% confidence level that theLF remains constant in both φ and M ∗ above z =
6. Our likeli-hood maps for the Schechter parameters indicate a strong evo-lution in φ and a brightening of M ∗ with redshift. However, thedetection of two bright objects ( Y ∼ . − .
7, correspond-ing to M . − .
2) in the NTTDF pointing have a majorrole in skewing the evolution of M ∗ towards bright values. Thetwo Schechter parameters are, however, highly degenerate andour findings are also consistent within the uncertainties with amilder evolution of φ and a constant or slightly dimming M ∗ as indicated by other authors (Bouwens et al. 2008; Ouchi et al.2009a). We estimate that the possible e ff ect of cosmic varianceis not capable of reconciling the observed number density of z -drop galaxies with the one predicted for a non-evolving LF.However, the strong dependence on luminosity of the cosmicvariance, and the relatively small magnitude range probed by oursurvey at M . M ∗ , can influence the determination of the formof the evolving LF and provide an explanation for the di ff erencebetween the evolution we determine and other estimates in theliterature.The uncertainty and the degeneracy in the M ∗ and φ best-fitvalues are not reflected in a comparable uncertainty in the num-ber density of bright galaxies. We conservatively consider themodel LFs within the 95% c.l. region of our likelihood analysisto derive for galaxies at M < − . ρ UV = . + . − . erg s − Hz − M pc − , a star formation ratedensity S FRD = . + . − . − M ⊙ yr − M pc − and an emissionrate of hydrogen ionizing photons log ( ˙ N ion ) = . + . − . M pc − .The UV luminosity density is lower than the corresponding oneat z ∼ ∼ .
5, while ˙ N ion is lower by at least afactor of ∼ f esc = . ff erent from those of lower redshift ∼ LBGs (e.g. f esc > .
5, harder UV spectrum etc.). Most probably,the crucial contribution to reionization comes from galaxies atthe faint end of the LF or from other kind of sources. Finally, weexploit the Hawk-I J and K band observations of our survey toderive an upper limit of 2 · − M pc − for the number densityof M ∼ − . z ∼ Y -dropgalaxies up to J ∼ Acknowledgements.
Observations were carried out using the Very LargeTelescope at the ESO Paranal Observatory under Programme IDs LP181.A-0717, LP168.A-0485, ID 170.A-0788, ID 181.A-0485, ID 283.A-5052 and theESO Science Archive under Programme IDs 67.A-0249, 71.A-0584, 73.A-0564,68.A-0563, 69.A-0539, 70.A-0048, 64.O-0643, 66.A-0572, 68.A-0544, 164.O-0561, 163.N-0210, and 60.A-9120. We acknowledge support from AgenziaSpaziale Italiana.
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