The 0.1 < z < 1.65 evolution of the bright end of the [O ii] luminosity function

Astronomy & Astrophysics manuscript no. OII_luminosity_fct_paper c©ESO 2014August 8, 2014

The 0.1 < z < 1.65 evolution of the bright endof the [Oii] luminosity function

Johan Comparat1, 2, Johan Richard4, Jean-Paul Kneib5, Olivier Ilbert3, V. Gonzalez-Perez6, 7, Laurence Tresse3, JulienZoubian6, Stephane Arnouts3, Roland Bacon4, Joel R. Brownstein12, Carlton Baugh7, Timothee Delubac5, AnneEalet6, Stephanie Escoffier6, Jian Ge13, Eric Jullo3, Cedric Lacey7, Nicholas P. Ross8, David Schlegel9, Donald P.

Schneider14, 15, Oliver Steele10, Lidia Tasca3, Christophe Yeche11, Michael Lesser17, Zhaoji Jiang16, Yipeng Jing18,Zhou Fan16, Xiaohui Fan17, Jun Ma16, Jundan Nie16, Jiali Wang16, Zhenyu Wu16, Tianmeng Zhang16, Xu Zhou16,

Zhimin Zhou16, and Hu Zou16

(Affiliations can be found after the references)

submitted to A&A August 8, 2014

ABSTRACT

We present the [Oii] (λλ3729, 3726) luminosity function measured in the redshift range 0.1 < z < 1.65 with unprecedented depthand accuracy. Our measurements are based on medium resolution flux-calibrated spectra of emission line galaxies with the FORS2instrument at VLT and with the SDSS-III/BOSS spectrograph. The FORS2 spectra and the corresponding catalog containing redshiftsand line fluxes are released along with this paper.In this work we use a novel method to combine the aforementioned surveys with GAMA, zCOSMOS and VVDS, which have differenttarget selection, producing a consistent weighting scheme to derive the [Oii] luminosity function.The measured luminosity function is in good agreement with previous independent estimates. The comparison with two state-of-the-art semi-analytical models is very good up to z = 1.1, which is encouraging for the production of mock catalogs of [Oii] flux limitedsurveys. We observe the bright end evolution over 8.5 Gyr: we measure the decrease of log L∗ from 42.4 erg/s at redshift 1.44 to 41.2at redshift 0.165. We find the faint end slope flattening from α(z = 0.95) = −2.6 to α(z = 0.17) = −1.1.This measurement confirms the feasibility of the target selection of future baryonic acoustic oscillation surveys aiming at observing[Oii] flux limited samples.

Key words. [Oii] - cosmology - survey - galaxy evolution - star formation

1. Introduction

In the current ΛCDM paradigm the matter dominated Universeat redshift 1.6 becomes driven by dark energy at z = 0.2 (PlanckCollaboration et al. 2013). This is one of the reasons provingthe great interest in understanding the evolution of the Universeduring this time span.

The [Oii] (λλ3729, 3726) emission line doublet observed ingalaxy spectra allows an accurate redshift estimate with ground-based optical spectrographs throughout the redshift range 0 <z < 1.7. Thus, the density of [Oii] emitters as a function ofthe [Oii] luminosity is pivotal for the planning of future spec-troscopic surveys, the studies of the evolution of the geometryin the Universe and the investigation about the galaxy formationand evolution.

Future large spectroscopic surveys that aim for a precisemeasurement of the baryonic acoustic oscillations (BAO) in thepower spectrum of galaxies in the redshift range 0.7 < z < 1.6,such as DESI1 or eBOSS2, can be designed following three con-straints. First, the measured power spectrum of the tracers sur-veyed must overcome the shot noise, which requires a high den-sity of tracers. We can distinguish two regimes of selection be-low redshift z < 1.1, and above. At z = 0.7, the power spectrum

1 http://desi.lbl.gov/2 http://www.sdss.org/sdss-surveys/eboss/

of the dark matter predicted by CAMB (Lewis et al. 2000) isP(k = 0.063h Mpc−1) = 9.5 × 103h3 Mpc−3, thus a density of

3P(k) ' 3×10−4 Mpc−3 is sufficient to overcome the shot noise bya factor three (Kaiser 1986). At z = 1.1, P(k = 0.063h Mpc−1) =7. × 103h3 Mpc−3, the density required is 4.2 × 10−4 Mpc−3. Inthe redshift range 0.7 < z < 1.1, the massive M > 1011Mgalaxy population consists of a mix of star-forming and quies-cent galaxies, which number density is ∼ 2× 10−3 Mpc−3 (Ilbertet al. 2013). The galaxy densities to overcome shot noise aretherefore reachable either with the quiescent or the star-forminggalaxies. At z = 1.6, P(0.063h Mpc−1) = 5. × 103h3 Mpc−3, thedensity required is 6 × 10−4 Mpc−3. From the galaxy evolutionpoint of view, a significant change occurs in the redshift range1.1 < z < 1.6: the massive end (M > 1011M) of the mass func-tion becomes dominated by star-forming galaxies. The density ofmassive star-forming galaxies is around ∼ 10−3 Mpc−3, whereasthe density of massive quiescent galaxies drops from 6 × 10−4

Mpc−3 at z = 1.1 to 10−4 Mpc−3 at z = 1.6. Therefore above red-shift z > 1.1, the density of massive quiescent galaxies decreasestoo rapidly to overcome the shot noise in the power spectrum ofgalaxies. However, the density of massive star-forming galaxiesin the redshift range 0.7 < z < 1.6 is sufficient to sample theBAO: this tracer covers consistently this redshift range. There-fore to overcome shot noise and measure the BAO in the powerspectrum of galaxies, one must target star-forming galaxies.

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Secondly, because of the large load of required data in BAOexperiments, accurate spectroscopic redshifts must be acquiredin an effective manner. Star-forming galaxies have strong emis-sion lines in their spectrum, they are therefore good candidates:Comparat et al. (2013b) demonstrated that one can select ef-ficiently star-forming galaxies to sample the BAO to redshiftz = 1.2. The [Oii] luminosity function measurement presentedhere extends this measurement to redshift 1.65 and provides in-sight on the galaxy population considered by future BAO studiescompared to the global galaxy population.

Thirdly, there is the need to survey massive galaxies that arewell correlated to the whole matter field (luminous and dark) inorder to obtain the highest possible signal-to-noise ratio in theirpower spectrum. Comparat et al. (2013a) demonstrated that thecolor-selected galaxies for BAO have a relatively high galaxybias b ∼ 1.8, and their luminous matter - dark matter cross-correlation coefficient measured using weak-lensing is consis-tent with 1. But we are not considering this point in this article.Therefore one needs to select the most luminous galaxies of theredshift range to maximize the galaxy bias.

To detect the BAO at redshifts above z > 0.7, with opticalspectrographs, an [Oii] flux-limited sample is therefore the bestway to cover the entire redshift range with a dense enough galaxypopulation. This sample will neither be a mass-limited samplenor an SFR-limited sample.

The [Oii] luminosity function and its evolution thereforecontains the informations required to plan future spectroscopicsurveys, that will target the most luminous [Oii] galaxies untilreaching the required density in the redshift range 0.7 < z < 1.6.The [Oii] luminosity functions have been previously derived byGallego et al. (2002); Ly et al. (2007); Argence & Lamareille(2009); Zhu et al. (2009); Gilbank et al. (2010); Sobral et al.(2013); Ciardullo et al. (2013). In these analysis (spectroscopy ornarrow band photometry), the bright end of the [Oii] luminosityfunction is however not well constrained, partly due to the factthat [Oii] survey areas are small and partly due to the selectionof the galaxies using a magnitude in red optical bands (closer toa stellar mass selection than an SFR selection).

The galaxy spectra presented and released in this paper werespecifically selected using the g band to observe the strongeststar-forming and least obscured galaxies to redshift z < 1.7 andin particular to measure the bright end of the [Oii] luminosityfunction. These spectra were observed on the COSMOS field,and are highly complementary to previous redshift surveys. Thismakes the COSMOS field an ideal location to investigate theevolution of [Oii] abundance. Although this new sample is suitedfor such an analysis, we do not perform a new calibration of therelation [Oii] – SFR – dust, and leave it for future studies.

We describe the new flux-calibrated spectroscopic data ac-quired on COSMOS in the section 2 and the new emission linegalaxy spectra acquired by SDSS-III/BOSS in section 3. Thenwe derive the observed luminosity function in section 4. Finally,we compare our measurement with semi-analytical models insection 5.

Throughout the paper, we quote magnitudes in the AB sys-tem (Oke & Gunn 1982) and we provide the measurementsin Planck cosmology h = 0.673, Ωm = 0.315, ΩΛ = 0.685,wDark Energy = −1 (see Planck Collaboration et al. 2013).

2. Data from ESO/VLT on COSMOS field

We have constructed an optimized color-box using the extremelyrich ground-based photometry of the COSMOS/HST-ACS field

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(Capak et al. 2007; Scoville et al. 2007a; Ilbert et al. 2009) in or-der to target galaxies with strong emission lines that are expectedin the redshift range 0.9 < z < 1.7.

We observed 2265 targets with the VLT/FORS-2 instrumentequipped with the 600z+23 holographic grating, which is theunique multi-object spectroscopic ESO instrument that reachesout to 1µm allowing one to probe galaxies with redshift z .1.7using the [Oii] emission line. The spectral range 737 nm - 1070nm is sampled with a resolution λ/∆λ = 1390 at 900 nm. Wemade two short exposures of 309 seconds each to reach a signal-to-noise ratio of 7 in the strongest emission lines. The exposuretime calculator produces a signal-to-noise ratio of 7 at the cen-tral wavelength of an emission line at λ = 8944.8Å ([Oii] atz ∼ 1.4) with a flux 8.3 × 10−17 erg · s−1 · cm−2(three days fromnew moon; with a sky brightness of 19.9 mag arcsec−2 at an air-mass of 1.6). The targets are on the COSMOS field centered atRAJ2000 = 150 and DECJ2000 = 2.2; see Fig. 1. The field cov-ered is not perfectly continuous. Indeed, the area where slits canbe placed is smaller than the complete mask area and we de-signed the pointings without considering this effect. Thereforethere are vertical empty stripes of 36 arcseconds between eachrow of observation. The same effect applies horizontally, but issmaller < 3 arcseconds.

We perform the target selection on the COSMOS photoZ cat-alog from Ilbert et al. (2009) that contains detections over 1.73deg2 (effective area).

2.1. Selection

To fill completely the slit masks, we used six different selectionschemes using the COSMOS catalog magnitudes (we use MAGAUTO not corrected from galactic extinction):

– Class A: a griz+3.6µm selection with 20 < g < 24 and i−z >(g − i)/2 − 0.1 and r − z > (i − mag3.6µm)/3 and r − z >0.8(g− i) + 0.1; these criteria select strong [Oii] emitters thatare bright and blue. It was designed using the Cosmos MockCatalog (Jouvel et al. 2009);


Johan Comparat et al.: [Oii] LF in 0.1 < z < 1.65

Table 1. Number of spectra observed. Class is the selection schemeused. Q is the redshift quality of the spectrum observed. ’eff’ is the effi-ciency defined as the ratio (in per cent) between the number of spectrawith a quality of 3 or 4 and the total.

Q ClassA B C D E F total

0 149 43 11 39 93 168 5031 24 5 2 1 13 18 632 73 23 4 10 60 79 2493 307 62 8 15 116 262 7704 394 117 10 19 47 93 680

total 947 250 35 84 329 620 2265eff 74.0 71.6 52.9 41.5 50.3 58.1 64.7

– Class B: Herschel detected galaxies at 5σ (Lutz et al. 2011);– Class C: MIPS detected galaxies at 5σ (Le Floc’h et al.

2009);– Class D: ugr selection from Comparat et al. (2013b) (20 <

g < 23.5, −0.5 < u − g < 1, −1 < g − r < 1, −0.5 < u − r <0.5);

– Class E: gri selection from Comparat et al. (2013b) (−0.1 <g − r < 1.1, 0.8 < r − i < 1.4, 20.5 < i < 23.5);

– Class F: a photometric redshift selection 1 < zphot < 1.7 and20 < i < 24 to fill the remaining empty area of the masks.

Selection 0 is the only sample on which one can perform a stan-dalone statistical analysis. In fact, the slits placed on the otherselections were constrained by the slits placed on the ClassA targets, therefore the obtained samples are not random sub-samples of their parent selection. Table 1 describes the quan-tity of each class observed and the quality of the redshift ob-tained (see next subsection). The location of these samples inthe u − b versus MB absolute magnitude band is presented inFig. 2. It shows that the Class A and C targets are bright andblue. A comparison of this selection with DEEP 2 observations(Mostek et al. 2013) demonstrates that Class A galaxies havestellar masses between 1010M and 1011M and a star forma-tion rate S FR > 101.2M yr−1, and therefore possess strong[Oii] emission lines. The redshift efficiency for the Class A se-lection is 701/947=74.0% (692/947=73% have 0.6 < z < 1.7and 552/947=58% have 1 < z < 1.7).

2.2. Data reduction, spectroscopic redshifts

The data processing pipeline performs an extraction of the spec-trum that allows the estimation of the flux in the [Oii] emissionline. This procedure has two steps.

1. We apply the scripts and procedures from the ESO pipelinedocument3. We use fors_bias for the master bias cre-ation, fors_calib for the master calibration creation, andfors_science to apply the calibrations and subtract the sky.Figures 8.2 and 8.3 from that document show an example ofthe data reduction cascade. We use the ‘unmapped’ result ob-tained in the middle of the fors_science part of the reduction,and the matching frames containing the wavelength values.Both ‘average’ and ‘minimum’ combinations of the 2 framesare obtained on each mask.

2. Emission lines are visually identified on both average andminimum reductions. The visual inspection is more efficient

3 ftp://ftp.eso.org/pub/dfs/pipelines/fors/fors-pipeline-manual-4.4.pdf

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than an automated measurement because of the presence ofcosmic ray residuals when combining the two exposures, andthe strong variations of signal-to-noise across the 2d spec-tra (both spatially and spectrally). A quality flag Q is as-signed on each object, from 4 (secure redshift identification),3 (clear single line redshift identification), 2 (possible line,not 100% convincing), 1 (a rough estimate), 0 (strong defectpreventing redshift measurement / line identification). Weconsider Q = 3 or 4 as reliable redshifts; see Table 1. Giventhe wavelength coverage of the spectrum, there are only afew spectra with a single line that could be mis-identified. Inthose particular cases, they were attributed a quality Q = 2.

As shown in Fig. 3 the redshifts measured for the galaxies inour study fill the gap between ‘COSMOS 20k’ and ‘COSMOSDeep 4.5k’ (Scoville et al. 2007b; Lilly et al. 2009). The highestredshift in our sample is zmax = 1.73. The classes B and C mainlycontain galaxies at redshifts below z < 0.8.

There is a small overlap between the sample presented hereand previous COSMOS spectroscopic samples; this allows us tocompare the redshift of objects observed twice (the positions onthe sky match within 0.1 arc second). For the set of objects withClass A, 7 galaxies with Q = 3 and 26 with Q = 4 have acounterpart with a high quality flag. For the set of objects withClass , A, 15 galaxies with Q = 3 and 21 with Q = 4 have acounterpart with a high quality flag. Among these matches, only



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two galaxies have a spectroscopic redshift that do not agree at the10% level (dz > 0.1(1 + z)). After a second inspection of thoseredshifts we found that the redshifts we obtained are correct; seeFig. 4.

We also compare our spectroscopic redshifts to the photo-metric redshifts from Ilbert et al. (2009, 2013). We consider 1344objects with both good spectroscopic redshift and photometricredshift. A total of 97.3% (1306) of the photometric redshifts arein agreement with the spectroscopic redshift within a 15% error,and 89.9% (1207) within a 5% error (see Fig. 5). The agreementis excellent.

Finally, we fit the emission lines detected in the spectra us-ing a simple Gaussian model for every line. Given the resolu-tion of the spectrograph, one cannot detect the difference be-

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tween the fit of a single Gaussian and the fit of a doublet for the[Oii] line. From this model we determine the emission line fluxand the signal-to-noise ratio (SNR) of the detection. [Oiii] is de-tected in the redshift range 0.45 < z < 1.05 and [Oii] in the range0.9 < z < 1.75. The SNR distribution is correlated to the qual-ity flag of the redshifts; see Fig. 6. The exposure times were tooshort to measure the continuum, we therefore estimate the equiv-alent widths and the levels of the continuum using the broadbandmagnitude that contains the emission line.

Two examples of spectra are displayed on Fig. 7.

2.3. Galaxies with a flux [Oii]> 10−15 erg · s−1 · cm−2

There are three galaxies with [Oii] fluxes greater than 10−15

erg · s−1 · cm−2. Two are compact and have broad emission linesand are probably AGNs; see Figs. 8 and 9. For the luminosityfunction analysis, we removed the broad-line AGNs in order tobe able to easily compare our results with other studies. The thirdgalaxy appears disturbed and might be ongoing a merging pro-cess (Fig. 10).



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Fig. 7. Two spectra from the VLT ESO FORS2 data set at redshift 0.92 and 1.6. The one dimensional spectra is on top of the two dimensionalspectra.



Fig. 8. Id= 751767, RA= 150.26, DEC= 2.05, redshift= 0.909,quality= 4.0, photoZ= 0.91 u= 22.79, g= 22.46, r= 22.46, i= 22.1, flux[Oii] = 151.1erg · s−1 · cm−2, SN [Oii] = 184.19, L [Oii] planck= 43.43erg/s, Class = A (one pixel is ∼ 0.1 arcsec). This object is an AGN. Theslit is 1 by 6 arc seconds (red rectangle).

Fig. 9. Id= 1039412, RA= 149.99, DEC= 2.16, redshift= 1.252,quality= 4.0, photoZ= 1.227 u= 21.86, g= 21.58, r= 21.7, i= 21.56,flux [Oii] = 155.86erg · s−1 · cm−2, SN [Oii] = 95.09, L [Oii] planck=43.93 erg/s, Class = A, (one pixel is ∼ 0.1 arcsec). This object is anAGN. The slit is 1 by 6 arc seconds (red rectangle).

Fig. 10. Id= 1285943, RA= 149.86, DEC= 2.36, redshift= 1.054,quality= 3.0, photoZ= 1.466 u= 23.44, g= 23.05, r= 23.13, i= 22.92,flux [Oii] = 152.65erg · s−1 · cm−2, SN [Oii] = 407.48, L [Oii] planck=43.66 erg/s, Class = A, (one pixel is ∼ 0.1 arcsec). It object appears tobe a merger.

2.4. Two strong lensing events

After the visual inspection of all galaxies observed on the HST-COSMOS mosaic, we identified two candidates for strong lens-ing; see Fig. 11. The position of the slits and the inspection ofthe spectra indicate we obtained the redshift of the lens galaxy.The first candidate is located at RA(J2000) of 09:59:33.199and DEC(J2000) of +01:51:05.58 (left side of the figure). Thesecond candidate is located at RA(J2000) of 09:59:30.940 andDEC(J2000) of +02:34:27.76 (right side of the figure). Thesestrong lensing events were not identified in previous strong lens-ing catalogs (Faure et al. 2008; Jackson 2008).

2.5. Morphology

Using the F814W COSMOS morphology catalog from Tascaet al. (2009), we find the sample observed is dominated by disks

Fig. 11. The redshift obtained for the left candidate is z = 0.918 with an[Oii] flux of 1.085×10−17erg · s−1 · cm−2. The candidate on the right is atredshift z = 1.0754 and has an [Oii] flux of 2.11 × 10−16erg · s−1 · cm−2.

and irregular galaxies. A total 2212 galaxies match with themorphology catalog: 1131 spirals (716 with a Q ≥ 3 spectro-scopic redshift), 801 irregulars (549 with a Q ≥ 3 spectroscopicredshift), and 280 ellipticals (171 with a Q ≥ 3 spectroscopicredshift). This distribution is not surprising. The correlation be-tween the half light radius (in pixel) and the flux emitted in[Oii] is quite weak (slope of −0.08). The distribution of half lightradii of the Class A sources has its first, second and third quar-tiles at 0.73, 1.02 and 1.34 arc seconds, respectively.

2.6. Distribution of this data-set

The data collected will be of legacy value for further COSMOSstudies and is publicly available on the COSMOS informationsystem developed at the Laboratoire d’Astrophysique de Mar-seille.4 A table summarizing the observations is published onlinealong with the paper.

3. Data from SDSS-III/BOSS ELG ancillary program

Within the Sloan Digital Sky Survey III collaboration (SDSSYork et al. 2000; Eisenstein et al. 2011; Dawson et al. 2013),were observed galaxies with strong emission lines (ELG) in theredshift range 0.4 < z < 1.6 to test the target selection ofemission line galaxies on two different photometric systems forthe new SDSS-IV/eBOSS survey. These observations are part ofthe SDSS-III/BOSS ancillary program and are flagged ‘ELG’ or‘SEQUELS_ELG’. These spectra will be part of the SDSS DataRelease 12 (DR12).

3.1. CFHT-LS ugri selection

During a first observation run, a total of 2292 fibers were allo-cated over 7.1 deg2 (the area of an SDSS-III plate). The ELGwere observed during 2 hours with the spectrograph (Smee et al.2013) of the 2.5m telescope located at Apache Point Observa-tory, New Mexico, USA, Gunn et al. (2006). The targets wereselected from the Canada-France-Hawaii Telescope Legacy Sur-vey (CFHT-LS) Wide W3 field catalogue with ugri bands. Thedata and cataloguing methods are described in Ilbert et al.(2006); Coupon et al. (2009), and the T0007 release document5.

The color selection used is−0.5 < u − r < 0.7 · (g − i) + 0.1 and 20 < g < 22.8.The selection function focuses on the brightest and bluest

galaxy population; see Fig. 12. The selection provides 3784 tar-gets, we observed 2292 of them. The observations of this sam-ple were obtained on the three SDSS plates number 6931, 6932,6933.4 http://cesam.lam.fr/hstcosmos/5 http://www.cfht.hawaii.edu/Science/CFHTLS/



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Fig. 12. Observations with SDSS telescope based on the CFHTLS pho-tometry. Top row. Left. u-r vs. g-i colored according to the photometricredshift. The selection applied is the dashed box. Right. Color selectionprojected in the u-g vs MG plane which shows our selection aims forthe brightest bluest objects. Middle row. RA, DEC in degree (J2000).Left. g < 25 objects from the CFHT-LS W3 photometric redshift cata-log. Right. Targets observed spectroscopically. Bottom row. Left. Dis-tribution of the redshifts observed. It is very efficient for selecting red-shift 0.8 ELGs. Right. Spectroscopic redshift and photometric redshift.dashed lines represent the error contours at dz = 0.15(1 + z). The agree-ment is good.

The reduction and the fit of the redshift is fully automatedand performed by the version ‘v5_6_elg’ of the BOSS pipeline(Bolton et al. 2012). A total 88.7% of the spectra observed havesufficient signal to be assigned a reliable redshift; see Table 2.Of this sample 82.3% are emission line galaxies (ELGs), 5.6%are quasars (QSOs) and 0.7% are stars. A total of 11.3% of thespectra have insufficient signal to noise ratio to obtain a reli-able spectroscopic redshift. The spectroscopic redshift distribu-tion obtained is presented in Fig. 12. The photometric redshiftsfrom T0007 on CFHT-LS W3 perform well. Of the 1609 galax-ies with a photometric redshift and a good spectroscopic red-shift, 92.3% (1486) are within a 15% error and 71.9% (1157) ina 5% error. The bluer objects tend to have larger uncertaintieson the photometric redshifts. Improving CFHT-LS photometricredshifts for such population is of great interest but beyond thescope of this paper.

Table 2. Observations on the CFHT-LS Wide 3 field. The observed ob-jects are a random subsample of the selection. As three plates weresuper-imposed, the fiber collision has a negligible effect.

class N percent z success rate N deg−2

ugri selection 3784 535.3observed 2292 60.5 100% 324.5redshift measured 2032 53.7 88.7% 287.5

ELG 1888 82.3% 267.1QSO 128 5.6% 18.1stars 16 0.7% 2.3

bad data 260 11.3% 36.8

3.2. SCUSS + SDSS ugri selection

A similar target selection was applied to a combination ofSCUSS u-band survey6 (Xu Zhou et al., 2014, in preparation,Hu Zou et al., 2014, in preparation) and SDSS g, r, i photome-try on a region of the sky of 25.7 deg2 around αJ2000 ∼ 23 andδJ2000 ∼ 20. This observation run, with a total of 8099 fibers al-located, measured ELG spectra with exposure times of 1h30 andcovering 25.7 deg2.

The color selection used is similar as before but with a umagnitude limit instead of a g limit:−0.5 < u − r < 0.7 · (g − i) + 0.1 and 20 < u < 22.5.We also had a low priority ELG selection criterion (LOWP)

to fill the remaining fibers. It is the same criterion stretched inmagnitude and color to investigate the properties of the galaxiesaround the selection:

[ 20 < u < 22.7 and −0.9 < u−r ] and [ u−r < 0.7·(g−i)+0.2or u − r < 0.7 ] .

The BOSS pipeline was used to process the data and all thespectra were inspected to confirm the redshifts. The redshift dis-tribution of this sample is shifted towards lower redshifts, seeFig. 13, compared to the previous sample due to the shallowerphotometry (between 5 and 10 times shallower) from which thetargets were drawn. This sample is complementary in terms ofredshift and luminosity. Table 3 summarize the the results of theobservations.

We retain the split of the two ugri ELG samples because theparent photometry catalog are very different.

6 http://batc.bao.ac.cn/Uband/survey.html



Table 3. SCUSS – SDSS-III/BOSS ELG observed as a function of spectral types.

Selection type reliable redshift low confidence redshiftN N [deg−2] percent N N [deg−2] percent

ELG

All 4914 188.26 100Galaxies 3419 130.99 69.58 29 1.11 0.59Quasars 676 25.9 13.76 85 3.26 1.73

Stars 129 4.94 2.63 3 0.11 0.06Lousy 573 21.95 11.66

ELG LOWP

All 3185 122.02 100Galaxies 2392 91.64 75.1 33 1.26 1.04Quasars 206 7.89 6.47 22 0.84 0.69

Stars 71 2.72 2.23 0 0 0Lousy 461 17.66 14.47

1.0 0.50.0 0.5 1.0 1.5 2.0 2.5 3.0g-i

1

0

1

2

3

4

u-r

ugri ELG

ugri ELG LOWP

20<u<23 objects

20 21 22 23 24 25 26RA [deg]

18

19

20

21

22

23

DEC

[deg]

8099 ugri ELG 20<u<23 objects

0.0 0.5 1.0 1.5 2.0 2.5redshift

100

101

N [

deg−

2]

ELG

QSO

ELG LOWP

Fig. 13. Observations with SDSS telescope based on the SCUSS pho-tometry. Top row. Left panel. Color selection applied to the SDSS +SCUSS photometry. Right panel. RA, DEC in degree (J2000). All the20 < u < 23 objects (green) and the spectroscopic targets (red). Bot-tom. Observed redshift distributions per square degree per ∆z = 0.1High priority ELG (red) are at slighter higher redshift than the low pri-ority ELG (blue). This selection based on a shallower photometry thanthe CFHT-LS is not as efficient at selecting redshift 0.8 ELGs.

4. [Oii] luminosity function

We combine the data samples previously described with publiclyavailable data, to measure the observed [Oii] luminosity function(LF hereafter) in the redshift range 0.1 < z < 1.65. Given thatthe [Oii] emission lines probe the star formation history that oc-curred up to 1Gyr before its emission, we set 8 redshift bins ofwidth ∼1. Gyr.

4.1. Data selection

In addition to the previously described samples, we use:

– the public zCOSMOS 10k to enhance the completeness onthe COSMOS field (Lilly et al. 2009);

– the VVDS deep and ultra deep observation of the 2h fieldand the VVDS wide observations on the 22h field (Le Fèvreet al. 2013);

– the GAMA field near αJ2000 ∼ 217 and δJ2000 ∼ 0 (Driveret al. 2011).

We do not use the DEEP2 (Zhu et al. 2009; Newman et al. 2013)and HETDEX (Ciardullo et al. 2013) data, because the availablecatalogs do not contain all the information needed to be properlycombined with the other samples, but to remain complete withrespect to the literature, we compare their LF measurements toours.

We select reliable redshifts that have well-defined photom-etry in the two or three of the ugriz optical bands that we areusing for the weighting scheme (see next paragraph). Moreover,we request a detection of the [Oii] lines with a signal to noiseratio greater than 5. In total, we use around 20 000 spectra. Thetotal amount of spectra provided by each survey as a function ofredshift is given in Table 5.

This conjunction of surveys has a gap in redshift around red-shift 0.45. We minimized the impact of this gap by shrinking tothe minimum the redshift bin 0.4 < z < 0.5 and removed it fromthe analysis.

We tested the robustness of LF against the SNR limits be-tween 3 and 10. We distinguished two regimes: for an SNR limitdecreasing from 10 to 5, the uncertainty on the LF decreases andthe luminosity limit decreases as the sample grows in size. Fora SNR limit at 4 or 3, the number of detections increases, butthe LF is not determined with more precision. In fact, for suchlow significance detections, the weights have a large uncertainty,which impacts the LF. The optimum results are obtained usingan SNR limit of 5.

4.1.1. Measurement of the emission line flux

On BOSS spectraThe flux in the emission line derived from BOSS spec-

tra were estimated using two different pipelines, the redshiftpipeline (Bolton et al. 2012) and the Portsmouth pipeline7

(Thomas et al. 2013). These estimators produce consistent mea-surements. The BOSS spectra were observed with fiber spec-troscopy, and objects are typically larger than the area coveredby the fibers, which have a diameter of 2 arcsecond. To correct

7 http://www.sdss3.org/dr9/algorithms/galaxy_portsmouth.php#kinematics



12.5 10.8 9.4 8.6 7.3 6.4 5.5 4.7 3.9age in Gyr

46.5

47.0

47.5

48.0

48.5

49.0

49.5

50.0

50.5

log(L

[O

II])

[W

att

]

39.5

40.0

40.5

41.0

41.5

42.0

42.5

43.0

43.5

log(L

[O

II])

[erg

/s]

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6redshift

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6redshift

100

101

102

103

count

VVDS fieldsCosmos field

SDSS field

CFHT W3 field

GAMA field

all

Fig. 14. Left panel. Luminosity vs. redshift. In each redshift bin, the horizontal black lines show the 5σ completeness limit of the data presented,except in the 0.4 < z < 0.5, where we show the high completeness limit (see subsection 4.1 for details). Right panel. Redshift distribution bysurvey, on the Cosmos field (purple), on the CFHT-LS W3 field (red), and on the SCUSS - SDSS field (green).

this effect we compute the difference between the magnitude ina 2 arcsec aperture and the total model magnitude. Table 4 givesthe magnitude used as a function of the redshift of the galaxy.If the difference is within the error of the total magnitude, wedo not correct the measured [Oii] flux. If the difference is greaterthan the error, then we rescale the [Oii] flux, fmeasured, using themagnitudes m in which the [Oii] line is located. The correctionused is:

ftotal = fmeasured10|m−mfiber |/2.5 if |m − m f iber | > errm

ftotal = fmeasured if |m − m f iber | 6 errm

We cannot tell if the part of the galaxy located outside of thefiber actually emits more or less than the part measured withinthe fiber. The mean correction in flux is ∼ 2.7, i.e., the fibercaptured on average ∼40% of the total flux.

On COSMOS spectraThe zCOSMOS survey provides the correction of the aper-

ture correction for 1 arc second slits along the dispersion axis.For the newly observed galaxies on the COSMOS field describedin the first section, we use an extrapolation of the median aper-ture correction as a function of half light radius to correct thefluxes from the aperture; see Fig. 15.

With the VVDS survey We convert the measured equivalentwidth (EW) into a flux density using

f totalλ = −EWmeasured 10−(m+48.6)/2.5 c

λ2[Oii]

erg cm−2 s−1 Å−1 (1)

where m is the broad-band magnitude of the CFHTLS filter con-taining [Oii] . Table 4 gives the magnitude used as a function ofthe redshift of the galaxy. We compare this flux density with theone measured in the slit to make sure the discrepancy is of theorder of magnitude of an aperture correction and use f total in theLF.

With the GAMA survey The GAMA survey provides the in-tegrated flux measurement of emission lines, which we use toderive the LF at low redshift (Hopkins et al. 2013).

10-1 100

half light radius [arcsecond]

100

101

apert

ure

corr

ect

ion

Fig. 15. Aperture correction factor vs. half light radius on Cosmos. Thered stars represent the median correction for bins of half light radius.

4.1.2. Galactic dust correction

We correct the measured [Oii] fluxes from the extinction of ourgalaxy using the Calzetti et al. (1994) law

fcorrected(λ) = fobserved100.4 E(B−V) κ(λ) (2)

where E(B-V) is taken from the dust maps made by Schlegelet al. (1998).

4.2. Weighting scheme

The weighting scheme relates the observed galaxies to their par-ent distribution, in this subsection, we describe a novel techniqueto compute the weights that allows combining different surveys.

4.2.1. Principle

In a dust-free theory, the [Oii] emitter population can be com-pletely described by three parameters, the redshift, the contin-uum under the line (or the line equivalent width, EW) and the



Table 4. Weighting scheme as a function of redshift for the [Oii] lines.The redshift bins correspond to Megacam’s or SDSS ugriz filter setstransitions.

CFHT z range SDSS z range magnitude color0.1 - 0.461 0.1 - 0.41 g u − g

0.461 - 0.561 0.41 - 0.51 (g + r)/2 u − g0.561 - 0.811 0.51 - 0.78 r g − r0.811 - 0.911 0.78 - 0.88 (r + i)/2 g − r0.911 - 1.19 0.88 - 1.17 i r − i1.19 - 1.29 1.17 - 1.27 (i + z)/2 r − i1.29 - 1.65 1.27 - 1.65 z i − z

UV-slope that produced this emission. We denote f the functionthat connects to a point in the three dimension space (z,EW,UV-slope) to a unique [Oii] flux. Observationally, these three param-eters correspond to the emission line flux, the magnitude con-taining the emission line and the color preceding the emissionline. In reality, the dust and orientation of each galaxy inducesscatter in this parameter space introducing some scatter to thefunction f. The surroundings of each parameter of the relationshould be considered so that f can still be used to relate the ob-served distribution to the parent distribution.

To implement this weighting scheme, we use the Megacam8

and SDSS photometric broad band ugriz filters (Fukugita et al.1996; Gunn et al. 1998) systems (the SCUSS u filter is the sameas the SDSS u filter) to assign a magnitude and a color as a func-tion of the redshift of each galaxy. For example, in the Megacamsystem, a galaxy with a redshift in 0.1 < z < 0.461 will see its[Oii] line fall in the g band, we thus use the g magnitude and theu − g color to compare this galaxy to the complete population.For [Oii] redshifts in 0.461 < z < 0.561, we consider this zoneas the overlap region between the g and the r filters. The bound-aries are defined by the corresponding redshift of transition be-tween the two bands zb broadened by 0.05, thus a transition ofzb ±0.05. In this bin, we use (g + r)/2 as the magnitude and u−gas the color. Table 4 and Fig. 16 present the color and magni-tude assigned for the weighing. This process allows a consistentweighting scheme for the complete data-set that has the samephysical meaning when redshift varies.

We compute the observed density deg−2 of galaxies with asignal to noise ratio in the [Oii] emission line greater than 5 ,Nobserved with SNR[OII ]>5(zspec,m, c), as a function of spectroscopicredshift, magnitude m and color c. This value is compared tothe complete galaxy population Ntotal(zphot,m, c) to obtain a com-pleteness weight,

W(z,m, c) =Nobserved with SNR[OII ]>5(zspec,m, c)

Ntotal(zphot,m, c). (3)

To obtain the information on the complete galaxy popula-tion N_total(zphot,m, c), we use the photometric redshift catalogsfrom the CFHT-LS deep fields 1, 2, 3, 4 (WIRDS) (Ilbert et al.2006, 2013; Bielby et al. 2012) and the Stripe 82 SDSS Coaddphotometric redshift catalog (Annis et al. 2011; Reis et al. 2012)that span 3.19 deg2 and 275 deg2, respectively.

For redshifts z < 0.7, we use the number densities observedon the Stripe 82 SDSS Coadd. For redshifts above, we the CFHT-LS deep photometric redshift catalog to obtain the best possibleestimate of the parent density of galaxies (note that it is not nec-

8 http://www.cfht.hawaii.edu/Instruments/Imaging/Megacam/specsinformation.html

essary to have the parent photometry and the observed data onthe same location of the sky).

We convert all the magnitudes to the CFHT Megacam sys-tem using the calibrations of Regnault et al. (2009) to have aconsistent weighting scheme among the various surveys.

4.2.2. Implementation

To implement the weights properly and avoid edge effects dueto data binning, we adopt two 3D-tree9 (one for the data andone for the parent sample) containing the redshift, the magnitudeand the color normalized at their first and last deciles (D10 andD90), i.e., we remap the three quantities so that the informationis primarily contained in the interval 0 - 1

ztree =z − D10z

D90z − D10z, (4)

mtree =mag − D10mag

D90mag − D10mag, (5)

ctree =color − D10color

D90color − D10color. (6)

This transformation allows the estimation of distance betweentwo points in the trees without being biased by the distributionof each quantity. In this manner the distance between two pointsi, j,

∆2i, j = |zi

tree − z jtree|

2 + |mitree − m j

tree|2 + |ci

tree − c jtree|

2 (7)

represents more equally the three axes: color, magnitude and red-shift. We compute the number of galaxies around each galaxyi in the observed sample tree and in the parent sample tree:N(∆i,obs < 0.15) and N(∆i,parent < 0.15). The ratio of the twonumbers gives the individual weight for each observed galaxy.

We tested, using the jackknife method, the technique againstdifferent remapping schemes and tree distances and found thevalues mentioned above to be stable and reliable; see appendix Afor more details. This method is more reliable than constructingcolor and magnitude bins, as binning can be very sensitive to thefine tuning of each bin value, in particular at the edges of thedistributions.

We estimate the sample variance uncertainty on N(∆i,obs <0.15) and N(∆i,parent < 0.15) in two ways: the Poisson error andthe Moster et al. (2011) ‘cosmic variance’ estimator. In areasof high density of the 3D-tree, the Poisson error is negligiblecompared to the cosmic variance estimation. In regions of smalldensities, this relation is reversed. To avoid underestimating theerror, we consider the sample variance error as the maximum ofthe two estimators.

The uncertainty on the weight (wErr) is computed by vary-ing the position of the galaxy in both trees in all directions of theredshift, magnitude and color space by its error in each dimen-sion. This approach produces an upper and lower value for theweight. Note that the uncertainty in redshift is negligible com-pared to the error on the magnitude and color.

The final uncertainty on the weight is the combination of thesample variance and of the galaxy weight error. The weight errordominates on the edges of the redshift - magnitude - color space,where densities are sparse. The sample variance error dominatesin the densest zones of the redshift, magnitude, color space.

9 http://eu.wiley.com/WileyCDA/WileyTitle/productCd-EHEP001657.html



3000 4000 5000 6000 7000 8000 9000 10000wavelength Angstrom

10-2

10-1

100

transm

issi

on [

%]

0.1

0.4

61

0.5

61

0.8

11

0.9

11

1.1

9

1.2

9

1.6

5

u-g

, g

u-g

, (g

+r)

/2

g-r

, r

g-r

, (r

+i)

/2

r-i, i

r-i, (

i+z)

/2

i-z,

z

z=0.6 ELG

ugriz Megacam filters

Fig. 16. Weighting scheme. Megacam transmission filters (grey lines) and the redshift bins (purple vertical lines) used to calculate the completenessweights. A rescaled spectrum of a typical emission line galaxy at redshift 0.6 is displayed in blue.

4.3. Observed luminosity function

We define the luminosity in the [Oii] lines by

L[Oii] [erg s−1] = 4π(flux [Oii] [erg s−1cm−2]

) [ dL(z)

[cm]

]2

, (8)

where dL is the luminosity distance in cm expressed as:

dL(z) = (1 + z)c

H0

∫ u=z

u=0

du√ΩΛ + Ωm(1 + u)3

. (9)

To obtain the completeness limit, we compute the LF multi-ple times with luminosity bins varying between 0.1 dex to 0.5dex. Each time, we compute the luminosity corresponding to themaximum of the LF. The completeness limit is the median of thedistribution of the maxima’s luminosity plus the bin size used tomake sure all luminosity bins are complete.

We use the jackknife technique to estimate sample varianceon the LF. We split the sample in 10 equal-in-number sub-samples and remeasure the LF on the subsamples. The standarddeviation from the 10 estimations is our adopted sample vari-ance error. The LF measurements are shown in Fig.17. The errorbars contain the error from the weight (wErr) and the samplevariance error computed with jackknife.

Thanks to the combination of the GAMA survey and the lowredshift ELG observed in SEQUELS, we are able to estimatethe [Oii] luminosity function at low redshift (z < 0.4) and inparticular measure accurately its bright end. The combined fitwith the HETDEX measurement gives a good estimation of theparameters of the Schechter model.

In the redshift bin 0.4 < z < 0.5, the completeness fromGAMA drops and the other spectroscopic samples were selectedto be at higher redshift. Therefore it is difficult to derive a cleanLF in this bin and we exclude it from the analysis.

In the three redshift bins within 0.5 < z < 1.07, we cancompare to the DEEP2 measurements. Given that the DEEP2measurements are at a slightly higher redshift, they are brighter.In these bins, a Schechter (1976) model fits better the LF thanpower law model. In those bins, our sample is very close to sam-pling the total SFR density; see last two columns of Table 6. Inthese bins, the faint completeness limit allows us to fit well thefaint end of the LF.

In the last two redshift bins, 1.07 < z < 1.65, the LF mea-surement is in very good agreement with the previous DEEP2measurements, although our data sets are limited to the brightend that correspond to a part only of the SFR density in thesebins.

From an evolution point of view, our measurement showsclearly the evolution of the bright end of the [Oii] LF: as red-shift increases from 0.165 to 1.44, there are more luminous[Oii] emitters. The last panel of Fig. 17 show the evolution us-ing the fits.

We computed directly (without using any fit) the integratedluminosity density using the latest [Oii] SFR calibration fromMoustakas et al. (2006)

ρS FR[Oii]

M yr−1Mpc−3 =2.18 × 10−41L([Oii])

[erg s−1Mpc−3], (10)

where ρS FR[Oii] is the SFR density measured through [Oii] andL([Oii]) is the [Oii] luminosity density. Given that Moustakaset al. (2006) demonstrated that the [Oii] SFR is subject to un-certainties of ∼ 0.4 dex (a factor 2.5); the numbers in Table 6should be considered with care. This result is not corrected fromthe extinction. Also given that we integrate directly on the mea-surement and not on the fit, these values can only be consideredas lower limits to the total SFR density.

4.4. Functional form of the luminosity function

The number density of galaxies in the luminosity range L + dL,denoted Φ(L)dL, is usually fitted with a Schechter (1976) func-tion of the form

Φ(L)dL = φ∗

(LL∗

)αexp

(−

LL∗

)d

(LL∗

)(11)

where the fitted parameters are α the faint end slope, L∗ [ergs−1] the characteristic Schechter luminosity, and φ∗ [Mpc−3] thedensity of galaxies with L > L∗. The parameters fitted are usuallyhighly correlated. Gallego et al. (2002) found a faint end slope of-1.2±0.2 with a Schechter model for ELGs in the local Universe.Gilbank et al. (2010) remeasured the [Oii] luminosity function inthe local Universe, but found that a model with a double power-law and a faint end slope of −1.6 was a better representation of



40 41 42 43 44

log10(L[OII]) [erg s−1 ]

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

] Ciardullo 2013, z=0.15

Gilbank 2010, z=0

782

1273

1204

595

198

46 9

This work z=0.17

log(L ∗) =41.18, log(φ ∗) =-2.16, α=-1.1

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

] Ciardullo 2013, z=0.38

Ciardullo 2013, z=0.26

55

10 2

This work z=0.31

log(L ∗) =41.52, log(φ ∗) =-2.31, α=-1.22

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

]

871

895

627

520

323

132

42 7 1

This work z=0.6

log(L ∗) =42.31, log(φ ∗) =-3.8, α=-2.2

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

] Zhu 2009, z=0.84

326

549

746

745

570

435

260

114

23 4

This work z=0.78

log(L ∗) =42.4, log(φ ∗) =-3.82, α=-2.23

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

] Zhu 2009, z=1.0176

340

352

324

264

208

137

55 8 1

This work z=0.95

log(L ∗) =42.86, log(φ ∗) =-4.81, α=-2.62

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

] Zhu 2009, z=1.2

152

153

179

102

48

14 2

This work z=1.2

log(L ∗) =42.58, log(φ ∗) =-3.61, α=-2.16

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

] Zhu 2009, z=1.35

75

44 18 6 1

This work z=1.44

10−3.5 (10l−42.43 )−1.68

39 40 41 42 43 44


10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

]

z=0.17z=0.31z=0.6z=0.78z=0.95z=1.2z=1.44

Fig. 17. Observed luminosity function compared to previous spectroscopic surveys estimates (in their closest redshift bin). The number on top ofeach LF point gives the exact number of galaxies used. The arrows going downwards correspond to measurements with an error consistent with0. The Schechter functions are fitted with α free (magenta dashes). The power-law fit on the last bin is shown in blue dashes. The last panel showsthe evolution of the [Oii] LF from redshift 0.17 to 1.44 using the fits. The trend is that with redshift increasing there are more and more bright[Oii] emitters.

the data. Zhu et al. (2009) also found a double power law was abetter description of the [Oii] LF.

Our new LF measurement demonstrates that the Schechtermodel fits well the data except when only the bright end is mea-sured, then a power-law is sufficient to fit the data. Based on theSchechter fits or the power-law fit of the last bin, we measure theevolution over 8 Gyr of log L∗ from 42.6 at redshift 1.44 to 41.18at redshift 0.165.

The parameter α is not well constrained in the literature, now,with this measurement, we have a great insight on its value andevolution to redshift 1.1. Beyond redshift z > 1.1, the complete-ness limit is too bright to constraint α. We measure the flatteningof the LF from from α(z = 0.95) = −2.6 to α(z = 0.17) = −1.1.The results of the fits are summarized in Table 6 and are shownon the Fig. 17.


Johan Comparat et al.: [Oii] LF in 0.1 < z < 1.65Ta

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1]

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3 ]M

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2.08

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527.0

0.60

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0.1

−3.

8±

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−2.

2±

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39.3

55−

1.30

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1.28

595.0

0.77

840.7

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0.16

−3.

82±

0.12

−2.

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0.07

−1.

7±

0.5

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46−

1.31

5−

0.91

740.0



4.5. [Oii] flux limited redshift surveys

In this section, we investigate the correlations between the ob-served [Oii] fluxes and the ugriz broad-band magnitude. We settwo redshift ranges :

– 0.7 < z < 1.1 corresponding to eBOSS-ELG and where the[Oii] data is complete to a luminosity of 1041 erg s−1, whichcorresponds to a flux 2.3×10−17erg · s−1 · cm−2at redshift 0.9.

– 1.1 < z < 1.6 corresponding to DESi-ELG and where the[Oii] data is complete to a luminosity of 1042 erg s−1, whichcorresponds to a flux 8.2×10−17erg · s−1 · cm−2at redshift 1.3.

The magnitude that correlates best with the [Oii] flux is the gband in the redshift range 0.7 < z < 1.1 and the r magnitudein the range 1.1 < z < 1.6; see Fig. 18. These bands shouldthus be used to construct in the most efficient way an [Oii] fluxlimited sample. The correlation in the higher redshift bin mightbe biased because below the flux completeness limit the data isnot representative of the complete population: u or g band couldalso be used for targeting at redshift 1.1 < z < 1.6.

We project the LF densities as a function of redshift to de-rive the brightest g and r limiting magnitude that will providea sufficient density of the brightest [Oii] emitters (a flux limit of10−16 erg · s−1 · cm−2) to sample the BAO. We find that a surveywith magnitude limit of g < 22.8 and can target a tracer densitygreater than 10−4 galaxies h3Mpc−3 to z ∼ 1.2 (e.g. eBOSS). Asurvey with magnitude limit of r < 23.3 can target a tracer den-sity greater than 10−4 galaxies h3Mpc−3 to z ∼ 1.6 (e.g. DESI);see Fig. 19. Further color selection is needed to sculpt the red-shift distribution, in particular to remove lower redshift galaxies.We do not investigate color selections to separate [Oii] emittersin a given redshift range from the bulk of the galaxy populationsat unwanted redshifts here. These color selection are dependenton the photometric survey used and should rather be discussedin each survey paper.

Comparing the magnitude [Oii] fluxes correlations and thesedensities with the current observational plans of surveys suchas DESI or eBOSS broadly confirms their feasibility. Surveysaiming to observe higher galaxy densities to probe the cosmicweb in greater details will need to target fainter [Oii] emitters.

4.6. [Oii] and star formation rate

The oxygen [Oii] emission line is also an SFR indicator that ismeasurable in the optical wavelengths for galaxies with redshift0 < z < 1.7, thanks to its strength and its blue rest-frame lo-cation (Kewley et al. 2004), although the SFR-[Oii] relation isnot as direct as SFR-Hα . The oxygen emission lines are not di-rectly coupled to the ionizing continuum emitted by stars but aresensitive to metal abundance, excitation, stellar mass and dust-attenuation (e.g. Moustakas et al. 2006). The [Oii] lines are there-fore more weakly correlated to the SFR due to a number of de-generacies (Garn & Best 2010). In the past, the [Oii] luminosityfunctions have been derived and related to the SFR by Gallegoet al. (2002); Ly et al. (2007); Argence & Lamareille (2009);Zhu et al. (2009); Gilbank et al. (2010). In order to derive aclean estimation of the SFR density sampled, we would need tore-calibrated the [Oii] SFR relation in each redshift bin using asample containing the [Oii] fluxes, the FUV and IR luminosities.We leave this work for a future study.



21 22 23 24 25 26

u

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]

slope -0.32, intercept -8.55, r-value -0.737, p-value 0.0

0.7<z<1.1

21 22 23 24 25 26

u

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


1.1<z<1.65

21 22 23 24 25 26

g

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


0.7<z<1.1

21 22 23 24 25 26

g

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


1.1<z<1.65

21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0

r

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


0.7<z<1.1

21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0

r

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


1.1<z<1.65

21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0

i

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


0.7<z<1.1

21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0

i

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


1.1<z<1.65

20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5

z

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


0.7<z<1.1

21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5

z

17.5

17.0

16.5

16.0

15.5

15.0

log f

lux [

OII]

[erg

/cm

2/s

]


1.1<z<1.65

Fig. 18. Correlations between the broad band magnitudes and the[Oii] flux. The contours represent the density of galaxies predicted bythe weighted data (from dark blue to brown 10, 50, 100, 200, 500 galaxydeg−2). The g band correlates best in the redshift range 0.7 < z < 1.1.The r magnitude correlates best in the range 1.3 < z < 1.6. The fluxescorresponding to a luminosity of 1041 and 1042 erg s−1 and the meanredshift (0.9 and 1.3) are represented in dashed blue.

0.6 0.8 1.0 1.2 1.4 1.6redshift

101

102

N [

deg−

2/d

z]

3.10−4h−3 Mpc3

10−4h−3 Mpc3

g<22.8

r<23.3

flux [OII]>10−16 erg/cm2 /s

Fig. 19. Redshift distribution per square degree of galaxies with[Oii] flux greater than 10−16erg · s−1 · cm−2and magnitude g brighterthan r < 23.3 (green) and g < 22.8 (red) compared to constant den-sity of 10−3 and 3 × 10−4 h3Mpc−3 (purple).



5. Comparison to semi-analytical models

In this section we compare our observations to the predictionsfrom two semi-analytical models, galform (Cole et al. 2000)and sag (Orsi et al. 2014), which are based on a ΛCDM uni-verse with WMAP7 cosmology (Komatsu et al. 2011). In orderto make the comparison with these models, we have recomputedthe observed LF for a WMAP7 cosmology.

Semi-analytical models use simple, physically motivatedrecipes and rules to follow the fate of baryons in a universe inwhich structure grows hierarchically through gravitational insta-bility (see Baugh 2006; Benson 2010, for an overview of hierar-chical galaxy formation models).

5.1. The galform model

For the study presented here we use the Gonzalez-Perez et al.(2014) (thereafter GP14) flavour of the galform model. Thismodel uses dark matter halo trees derived from the MS-W7 N-body simulation (Lacey et al. in preparation), with a simulationbox of 500 h−1Mpc side . The GP14 model follows the physi-cal processes that shape the formation and evolution of galaxies,including:

1. the collapse and merging of dark matter haloes;2. the shock-heating and radiative cooling of gas inside dark

matter haloes, leading to the formation of galaxy discs;3. quiescent star formation in galaxy discs which takes into ac-

count both the atomic and molecular components of the gas(Lagos et al. 2011);

4. star formation bursts that can be triggered by either mergersor disk instabilities;

5. the growth of super massive black holes in galaxies;6. feedback from supernovae, from active galactic nuclei and

from photoionization of the intergalactic medium;7. chemical enrichment of the stars and gas;8. galaxy mergers driven by dynamical friction within com-

mon dark matter haloes, leading to the formation of stellarspheroids.

The end product of the calculations is a prediction for the numberand properties of galaxies that reside within dark matter haloesof different masses.

The GP14 model reproduced reasonably well the evolutionof the HαLF (Lagos et al. 2014). Hα is a recombination line andthus, its unattenuated luminosity is directly proportional to theLyman continuum, which is a direct prediction of the galformmodel. The main uncertainty for the Hα line is the dust attenu-ation (see Gonzalez-Perez et al. 2013, for a detailed descriptionof the dust treatment in the model).

In the galform model the ratio between the [Oii] and theLyman continuum is calculated using the Hii region models byStasinska (1990). The galform model uses by default eightHii region models spaning a range of metallicities but with thesame uniform density of 10 hydrogen particles per cm−3 and oneionising star in the center of the region with an effective temper-ature of 45000 K. The ionising parameter10 of these Hii regionmodels is around 10−3, with exact values depending on theirmetallicity in a non trivial way. These ionising parameters aretypical within the grid of Hii regions provided by Stasinska(1990).

10 The ionising parameter is defined here as a dimensionless quantityequal to the the ionizing photon flux per unit area per hydrogen density,normalised by the speed of light (see Stasinska 1990).

5.2. The sag model

Orsi et al. (2014) combined the SAG semi-analytical modelwith a photo-ionization code in order to predict emission linestrengths originated in Hii regions with different ionization pa-rameters. In order to do this, this model assumes an ioniza-tion parameter that depends on the cold gas metallicity of thegalaxy. This dependency introduced two new free parameters inthe model, an exponent and a normalization, that where chosenin order to reproduce the BPT diagram and the [Oii] and [Oiii] LFat different redshifts obtained by narrow band surveys.

The SAG semi-analytical model was run using an N-bodysimulation of volume (150h−1Mpc)3. This volume is too small toadequately model the properties of the brightest observed galax-ies. Tests using the galformmodel showed that a simulation boxwith side of at least 280h−1Mpc is required to study the brightend of the luminosity function.

5.3. The predicted [Oii] luminosity function

Orsi et al. (2014) obtained [Oii] luminosity functions from usingHII region models in which the ionization parameter dependson the metallicity of galaxies. Besides the marginal difference atz = 1.44, this model produces an [Oii] LF with a bright end slopethat agrees with our observations, as was expected by construc-tion. The [Oii] luminosity functions obtained in this way werefound to be bracketed by those calculated assuming a constantionization parameter with the highest and lowest available val-ues. It is possible that, if the ionization parameter has only aweek dependence on galaxy mass, when studying global proper-ties such as the LF in a given redshift range, the individual ion-ization parameters of galaxies are averaged to produce resultssimilar to assuming a single average Hii region. Besides the ion-ization parameter, there are other properties of the Hii regions,such as their ages, sizes and hydrogen densities, that might af-fect the predicted [Oii] LF.

Fig. 20 shows our observations compared to the [Oii] LF pre-dicted with the galform model at z =0.5, 0.9, 1.17, 1.38. It isimportant to stress that the galform model was not callibratedto reproduce the observed [Oii] LF. The model predictions arein reasonable agreement with the observed LF at both z ∼0.5and z ∼1, while underpredicting those at z ∼1.2 and z ∼1.4. Forthese two higher redshifts, the observations are actually closerto the predicted LF without dust attenuation, though is unlikelyfor these galaxies to be dust free. In particular if we take into ac-count that the dust extinction applied to the [Oii] line is the sameas experienced by the continuum at that wavelength; and thus theline could actually be more attenuated than predicted.

Fig. 20 shows the [Oii] LF predicted by the galform model,which is found to be dominated by central galaxies, in particularfor the bright end.

The predicted [Oii] LF by the galform model is quite sensi-tive to the assumed ionization parameter. Using extreme valuesfrom Stasinska (1990) grid of Hii regions we obtain predicted[Oii] LFs bracketing those shown in Fig. 20.

The default characteristics of the Hii region model assumedin the galform model might not be adequate at these higher red-shifts, however a detailed exploration of the source of the dis-crepancy is beyond the scope of this paper.



40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

]This work z=0.6

Galform z=0.56

- All w dust

- - All w/o dust

- r<24.56 dust

- - r<24.56 w/o dust

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

]

This work z=0.95

Galform z=0.9

- All w dust

- - All w/o dust

- i<24.51 dust

- - i<24.51 w/o dust

- Orsi+ 2014 z=0.96

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

]

This work z=1.2

Galform z=1.17

- All w dust

- - All w/o dust

- i<24.46 dust

- - i<24.46 w/o dust

- Orsi+ 2014 z=1.22

40 41 42 43 44


10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Φ [

Mpc−

3/d

log L

]This work z=1.44

Galform z=1.38

- All w dust

- - All w/o dust

- z<23.56 dust

- - z<23.56 w/o dust

- Orsi+ 2014 z=1.43

Fig. 20. LF compared to the simulation prediction. The red lines correspond to the galform prediction with a sample selected to the magnitudelimit reached by the combination of surveys. The galform predicted LF without including the effect of dust attenuation are shown by dashed lines.The green lines show the predictions from the sag model (note that there was no data available at z=0.6)

6. Conclusion

In this work we have measured the [Oii] luminosity function ev-ery gigayear in the redshift range 0.1 < z < 1.65 with un-precedented depth and accuracy. This has allowed us to wit-ness the evolution of its bright end: we measure the decreaseof log L∗ from 42.4 erg/s at redshift 1.44 to 41.2 at redshift0.165. Moreover, we perceive the faint end slope flattening fromα(z = 0.95) = −2.6 to α(z = 0.17) = −1.1. Estimating the evo-lution of the LF is of great interest to prepare the observationalstrategy of the future cosmological redshift surveys aiming at,for example, BAO measurements.

Such a measurement has been possible by combining in anovel way observations from the FORS2 instrument at VLT onthe COSMOS field (released along with the paper); the SDSS-III/BOSS spectrograph ELG ancillary programs, and with pub-lic flux calibrated spectroscopy of [Oii] emitters. Indeed, we cre-ated a new weighting scheme that combines robustly differentdata sets, for observations which provide the measurement of

the fluxes in the lines, the corresponding aperture correction andthe parent photometry.

Our measurement is independent from HETDEX andDEEP2, the two most-recent competitive [Oii] LF measurementbased on spectroscopy. There is a good agreement in the differentredshift bin between our measurement and theirs.

We have compared our observed [Oii] LF to predictionsfrom two state-of-the-art semi-analytical models, finding a goodagreement up to z = 1. Although this result is encouraging forthe viability of producing realistic mock catalogs of [Oii] fluxlimited surveys, more work is needed to understand the discrep-ancies found at higher redshifts.

Our measurement of the bright end of the LF demonstratesthe feasibility of eBOSS and DESi emission line galaxy targetselection, i.e. we have shown here that the density of galaxieswith emission lines fluxes > 10−16erg · s−1 · cm−2 is sufficient tosample the BAO to redshift 1.6.

In order to derive a more precise [Oii] LF observing about∼200 000 [Oii] emitters with log L [Oii]> 1039erg s−1 through-



out the redshift range with sky coverage larger than >100 deg2

is necessary.

Acknowledgements

JC acknowledges financial support from MINECO (Spain) underproject number AYA2012-31101.

JR acknowledges support from the ERC starting grant CAL-ENDS.

JPK and TD acknowledge support from the LIDA ERC ad-vanced grant.

Funding for SDSS-III has been provided by the Alfred P.Sloan Foundation, the Participating Institutions, the NationalScience Foundation, and the U.S. Department of Energy Officeof Science. The SDSS-III web site is http://www.sdss3.org.

SDSS-III is managed by the Astrophysical Research Con-sortium for the Participating Institutions of the SDSS-III Col-laboration including the University of Arizona, the BrazilianParticipation Group, Brookhaven National Laboratory, Univer-sity of Cambridge, Carnegie Mellon University, University ofFlorida, the French Participation Group, the German Partici-pation Group, Harvard University, the Instituto de Astrofisicade Canarias, the Michigan State/Notre Dame/JINA ParticipationGroup, Johns Hopkins University, Lawrence Berkeley NationalLaboratory, Max Planck Institute for Astrophysics, Max PlanckInstitute for Extraterrestrial Physics, New Mexico State Univer-sity, New York University, Ohio State University, PennsylvaniaState University, University of Portsmouth, Princeton University,the Spanish Participation Group, University of Tokyo, Universityof Utah, Vanderbilt University, University of Virginia, Universityof Washington, and Yale University.

The BOSS French Participation Group is supported byAgence Nationale de la Recherche under grant ANR-08-BLAN-0222.

This work used the DiRAC Data Centric system atDurham University, operated by the Institute for Computa-tional Cosmology on behalf of the STFC DiRAC HPC Facil-ity (www.dirac.ac.uk). This equipment was funded by BIS Na-tional E-infrastructure capital grant ST/K00042X/1, STFC cap-ital grant ST/H008519/1, and STFC DiRAC Operations grantST/K003267/1 and Durham University. DiRAC is part of the Na-tional E-Infrastructure. VGP acknowledges support from a Eu-ropean Research Council Starting Grant (DEGAS-259586) andthe Science and Technology Facilities Council (grant numberST/F001166/1).

Based on observations obtained with MegaPrime/Megacam,a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the Na-tional Research Council (NRC) of Canada, the Institut Nationaldes Science de l’Univers of the Centre National de la RechercheScientifique (CNRS) of France, and the University of Hawaii.

The SCUSS is funded by the Main Direction Programof Knowledge Innovation of Chinese Academy of Sciences(No. KJCX2-EW-T06). It is also an international cooperativeproject between National Astronomical Observatories, ChineseAcademy of Sciences and Steward Observatory, University ofArizona, USA. Technical supports and observational assistancesof the Bok telescope are provided by Steward Observatory. Theproject is managed by the National Astronomical Observatory ofChina and Shanghai Astronomical Observatory.

GAMA is a joint European-Australasian project basedaround a spectroscopic campaign using the Anglo-AustralianTelescope. The GAMA input catalogue is based on data taken

from the Sloan Digital Sky Survey and the UKIRT Infrared DeepSky Survey. Complementary imaging of the GAMA regions isbeing obtained by a number of independent survey programsincluding GALEX MIS, VST KiDS, VISTA VIKING, WISE,Herschel-ATLAS, GMRT and ASKAP providing UV to radiocoverage. GAMA is funded by the STFC (UK), the ARC (Aus-tralia), the AAO, and the participating institutions. The GAMAwebsite is http://www.gama-survey.org.

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1 Departamento de Fisica Teorica, Universidad Autonoma de Madrid,Spain

2 Instituto de Fisica Teorica UAM/CSIC, Spain

3 Laboratoire d’Astrophysique de Marseille - LAM, Universitéd’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388Marseille Cedex 13, France

4 CRAL, Observatoire de Lyon, Université Lyon 1, 9 Avenue Ch.André, 69561 Saint Genis Laval Cedex, France

5 Laboratoire d’astrophysique, École Polytechnique Fédérale de Lau-sanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland

6 CPPM, Université d’Aix-Marseille, CNRS/IN2P3, Marseille,France

7 Institute for Computational Cosmology, Department of Physics,University of Durham, South Road, Durham, DH1 3LE, UK

8 Department of Physics, Drexel University, 3141 Chestnut Street,Philadelphia, PA 19104, USA

9 Lawrence Berkeley National Laboratory, 1 Cyclotron Road,Berkeley, CA 94720, USA

10 Institute of Cosmology and Gravitation (ICG), Dennis SciamaBuilding, Burnaby Road, Univ. of Portsmouth, Portsmouth, PO13FX, UK

11 CEA, Centre de Saclay, IRFU, F-91191 Gif-sur-Yvette, France

12 Department of Physics and Astronomy, University of Utah, 115 S1400 E, Salt Lake City, UT 84112, USA

13 Astronomy Department, University of Florida, 211 Bryant SpaceScience Center, Gainesville, FL

14 Department of Astronomy and Astrophysics, The PennsylvaniaState University, University Park, PA 16802

15 Institute for Gravitation and the Cosmos, The Pennsylvania StateUniversity, University Park, PA 16802

16 Key laboratory of Optical Astronomy, National AstronomicalObservatories, Chinese Academy of Sciences, Beijing, 100012,China

17 Steward Observatory, University of Arizona, Tucson, AZ 85721

18 Center for Astronomy and Astrophysics, Department of Physics andAstronomy, Shangai Jiao Tong University, Shangai 200240,China

Appendix A: Weights

This appendix describes the details of the weighting scheme.The theoretical relation between the magnitude contain-

ing [Oii] , the color before this magnitude, redshift, and the[Oii] luminosity, is shown using the CMC in Fig. A.1. This repre-sentation does not take into account the dust present in the galax-ies that will induce scatter in this figure. For a constant magni-tude, the most luminous galaxies have a blue color. This simula-tion is based on Kennicutt laws, an extrapolation of the DEEP2

[Oii] LF, and ignores dust effects. Therefore this test cannot beused at face value, even less to determine the completeness limitof our sample. This analysis provides an idea on the relation be-tween the magnitude limit and the luminosity completeness limitwe can reach with a sample.

In the text, we quote as best value for the tree search a dis-tance of 0.15. This distance corresponds to a maximum dis-tance in each direction of 0.088, and constrains the search forneighbors within about ∼ ±0.5mag around the magnitude, about∼ ±0.25mag around the colors and about ∼ ±0.15 around theredshift. These values approximately correspond to the area agiven galaxy population occupies; see Fig. A.1.

We tested the LF estimation for different distance values andfound that a limit at 0.15 ± 0.01 was stable and variations in themeasurement of the LF would be smaller than the uncertaintyon the LF. Fig. A.2 displays the variation in the LF comparedto the LF estimate using the tree search distance 0.15. For treesearches that are too wide, >0.17, the weighting scheme beginsto fail i.e., the LF is inconsistent at 1σ with the fiducial LF. Fortree searches too narrow, <0.13, the weights become inaccurate,the weight error increases and the LF is less accurate.



1.0 0.5 0.0 0.5 1.0 1.5 2.0u-g

19

20

21

22

23

24

25

g

0.21<z<0.461

37.8

38.4

39.0

39.6

40.2

40.8

41.4

42.0

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

1.0 0.5 0.0 0.5 1.0 1.5 2.0u-g

19

20

21

22

23

24

25

(g+

r)/2

0.461<z<0.561

38.0

38.5

39.0

39.5

40.0

40.5

41.0

41.5

42.0

42.5

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

1.0 0.5 0.0 0.5 1.0 1.5 2.0g-r

19

20

21

22

23

24

25

r

0.561<z<0.811

38.4

39.0

39.6

40.2

40.8

41.4

42.0

42.6

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

1.0 0.5 0.0 0.5 1.0 1.5 2.0g-r

19

20

21

22

23

24

25

(r+

i)/2

0.811<z<0.911

39.0

39.6

40.2

40.8

41.4

42.0

42.6

43.2

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

1.0 0.5 0.0 0.5 1.0 1.5 2.0r-i

19

20

21

22

23

24

25

i

0.911<z<1.19

39.0

39.6

40.2

40.8

41.4

42.0

42.6

43.2

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

1.0 0.5 0.0 0.5 1.0 1.5 2.0r-i

19

20

21

22

23

24

25

(i+

z)/2

1.19<z<1.29

39.0

39.6

40.2

40.8

41.4

42.0

42.6

43.2

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

1.0 0.5 0.0 0.5 1.0 1.5 2.0i-z

19

20

21

22

23

24

25

z

1.29<z<1.6

39.5

40.0

40.5

41.0

41.5

42.0

42.5

43.0

43.5

log(L

um

inosi

ty [

OII]

erg

/cm

2/s

)

Fig. A.1. Predictions from the CMC for magnitude vs. color (in the CFHT system) and observed [Oii] luminosity for the CFHT magnitude redshiftbins described in Table 4 and Fig. 16.

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

0.1<z<0.24

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

0.24<z<0.38

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

0.38<z<0.53

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

0.53<z<0.7

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

0.7<z<0.88

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

0.88<z<1.09

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

1.09<z<1.34

40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0log10(L[Oii]) [erg/s]

10-3

10-2

10-1

100

101

% in t

he L

F w

/ tr

ee1

5

tree14

tree16

tree17

tree13

tree12

tree18

error on the LF --

1.34<z<1.65

Fig. A.2. LF(d)/LF(0.15) ratio for d=0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18 divided by the LF determined with 0.15. The vertical red line is theluminosity completeness limit. The error on the LF is shown in black dashes. The LFs with radius 0.14 and 0.16 stay well within the uncertaintyon the LF, while larger or smaller radii approach to the limit of the uncertainty of the LF.


The 0.1 < z < 1.65 evolution of the bright end of the [O ii] luminosity function

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