The H α Luminosity Function and Star Formation Rate at z≈0.24 in the Cosmos 2 Square-Degree Field
Y. Shioya, Y. Taniguchi, S. S. Sasaki, T. Nagao, T. Murayama, M. I. Takahashi, M. Ajiki, Y. Ideue, S. Mihara, A. Nakajima, N. Z. Scoville, B. Mobasher, H. Aussel, M. Giavalisco, L. Guzzo, G. Hasinger, C. Impey, O. LeFevre, S. Lilly, A. Renzini, M. Rich, D. B. Sanders, E. Schinnerer, P. Shopbell, A. Leauthaud, J.-P. Kneib, J. Rhodes, R. Massey
aa r X i v : . [ a s t r o - ph ] S e p Draft version October 28, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
THE H α LUMINOSITY FUNCTION AND STAR FORMATION RATE AT Z ≈ .
24 IN THE COSMOS 2SQUARE-DEGREE FIELD Y. Shioya , Y. Taniguchi , S. S. Sasaki
2, 3, 5 , T. Nagao , T. Murayama , M. I. Takahashi , M. Ajiki , Y. Ideue , S. Mihara , A. Nakajima , N. Z. Scoville
5, 6 , B. Mobasher , H. Aussel , M. Giavalisco , L. Guzzo , G.Hasinger , C. Impey , O. LeFevre , S. Lilly , A. Renzini , M. Rich , D. B. Sanders , E. Schinnerer ,P. Shopbell , A. Leauthaud , J.-P. Kneib , J. Rhodes , and R. Massey Draft version October 28, 2018
ABSTRACTTo derive a new H α luminosity function and to understand the clustering properties of star-forminggalaxies at z ≈ .
24, we have made a narrow-band imaging survey for H α emitting galaxies in theHST COSMOS 2 square degree field. We used the narrow-band filter NB816 ( λ c = 8150 ˚A, ∆ λ = 120˚A) and sampled H α emitters with EW obs (H α + [N ii ]) >
12 ˚A in a redshift range between z = 0 . z = 0 .
251 corresponding to a depth of 70 Mpc. We obtained 980 H α emitting galaxies in a skyarea of 5540 arcmin , corresponding to a survey volume of 3 . × Mpc . We derive a H α luminosityfunction with a best-fit Schechter function parameter set of α = − . +0 . − . , log φ ∗ = − . +0 . − . ,and log L ∗ (erg s − ) = 41 . +0 . − . . The H α luminosity density is 2 . +0 . − . × ergs s − Mpc − . Aftersubtracting the AGN contribution (15 %) to the H α luminosity density, the star formation rate densityis evaluated as 1 . +0 . − . × − M ⊙ yr − Mpc − . The angular two-point correlation function of H α emitting galaxies of log L (H α ) > . w ( θ ) = 0 . +0 . − . θ − . ± . ,corresponding to the correlation function of ξ ( r ) = ( r/ . − . . We also find that the H α emitterswith higher H α luminosity are more strongly clustered than those with lower luminosity. Subject headings: galaxies: distances and redshifts — galaxies: evolution — galaxies: luminosityfunction, mass function INTRODUCTION
It is important to understand when and where intensestar formation occurred during the course of galaxy evo-lution. Although the star formation history in individualgalaxies is interesting, a general trend of star formation Based on data collected at Subaru Telescope, which is operatedby the National Astronomical Observatory of Japan. Graduate School of Science and Engineering, Ehime Univer-sity, Bunkyo-cho, Matsuyama 790-8577, Japan Astronomical Institute, Graduate School of Science, TohokuUniversity, Aramaki, Aoba, Sendai 980-8578, Japan National Astronomical Observatory of Japan, Mitaka, Tokyo181-8588, Japan Department of Astronomy, MS 105-24, California Institute ofTechnology, Pasadena, CA 91125 Institute for Astronomy, University of Hawaii, 2680 WoodlawnDrive, HI 96822 Space Telescope Science Institute, 3700 San Martin Drive, Bal-timore, MD 21218 CEA Saclay, DSM/DAPNIA/SAp, 91191 Gif-sur-YvetteCedex, France Osservatorio Astronomico di Brera, via Brera, Milan, Italy Max Planck Institut fuer Extraterrestrische Physik, D-85478Garching, Germany Steward Observatory, University of Arizona, 933 NorthCherry Avenue, Tucson, AZ 85721 Laboratoire d’Astrophysique de Marseille, BP 8, Traverse duSiphon, 13376 Marseille Cedex 12, France Department of Physics, Swiss Federal Institute of Technology(ETH-Zurich), CH-8093 Zurich, Switzerland European Southern Observatory, Karl-Schwarzschild-Str. 2,D-85748 Garching, Germany Department of Physics and Astronomy, University of Califor-nia, Los Angeles, CA 90095 Max Planck Institut f¨ur Astronomie, K¨onigstuhl 17, Heidel-berg, D-69117, Germany Jet Propulsion Laboratory, Pasadena, CA 91109 in galaxies as a function of time (or redshift) also providesimportant insights on the global star formation historyas well as on the metal enrichment history in the uni-verse. Therefore, the star formation rate density (SFRD)is one of the important observables for our understand-ing of galaxy formation and evolution. In the last decade,many works have followed the pioneer work of Madau etal. (1996) which compiled the evolution of SFRD, ρ SFR ,as a function of redshift for the first time. The evolutionof ρ SFR is now widely accepted as follows: ρ SFR steeplyincreases from z ≃ z ∼
1, and seems to be con-stant between z ∼ z ∼ z ∼ Galaxy Evolution Explorer (GALEX) and the
Spitzer Space Telescope have con-firmed that ρ SFR increases from z ∼ z ∼ z ) while the UV luminosity densityevolves as (1 + z ) . . This may imply that extinction bydust and reradiation from dust becomes to play a moreimportant role at higher redshift. One of the remainingproblems in this field is a relation between star-formationactivity and large-scale structure formation. To studythis issue, wide-field deep surveys are important.There are several star formation rate (SFR) estima-tors, e.g., UV continuum, H α emission, [O ii ] emission,far-infrared (FIR) emission (Kennicutt 1998), and radiocontinuum (Condon 1992). Each estimator has both ad-vantage and disadvantage to estimate SFR. UV contin- Shioya et al.uum and nebular emission lines are considered to be di-rect tracers of hot massive young stars. However, theyare often affected by dust obscuration. On the otherhand, FIR and radio continuum are insensitive to dustobscuration. FIR emission is due to the dust heated bythe general interstellar radiation field. If most of thebolometric luminosity of a galaxy absorbed by dust isradiated from young stars, as in the case of dusty star-bursts, the FIR luminosity is a good SFR estimator. Forearly-type galaxies, much of the FIR emission is consid-ered to be related to the old stars and the FIR emissionis not a good SFR estimator (Sauvage & Thuan 1992;Kennicutt 1998). For star-forming galaxies, there is atight radio-FIR correlation (Condon 1992). This rela-tion suggests that the radio continuum also provides agood SFR estimator. The radio continuum is consideredto be dominated by synchrotron radiation from relativis-tic electrons which are accelerated in supernova remnants(SNRs) (Lequeux 1971; Kennicutt 1983a; Gavazzi, Coc-ito, & Vettolani 1986). We note that the radio continuumemission of some galaxies is dominated by the AGN com-ponent, although such galaxies are distinguished fromstar-forming galaxies by using the tight radio-FIR cor-relation (Sopp & Alexander 1991; Condon 1992). Thenearly linear radio-FIR correlation also suggests that ra-dio continuum is affected by the efficiency of cosmic-rayconfinement, since the degree of dust attenuation be-comes larger for more luminous galaxies (Bell 2003). Al-though SFRs evaluated from different SFR estimatorsare consistent with each other within a factor of 3 if theappropriate correction is applied for each case (e.g., Hop-kins et al. 2003; Charlot & Longhetti 2001; Charlot etal. 2002), samples selected with a different method mayhave different biases. For example, samples selected byan objective-prism imaging survey are biased toward thesystem with large equivalent width (e.g., Gallego et al.1995), while those selected by UV radiation are biasedagainst heavily dusty galaxies (Meurer et al. 2006). Toevaluate the true SFRD, it is important to correct the ob-tained SFR appropriately and to know probable biasesfor the sample selection.In this work, we use the H α luminosity as a SFR es-timator. The H α luminosity is directly connected tothe ionizing photon production rate. There are two ap-proaches to measure H α luminosities of galaxies. Oneis a spectroscopic survey and the other is a narrow-bandimaging survey. Although spectroscopic observations tellus details of emission line properties, e.g., Balmer decre-ment, metallicity, and so on, it is difficult to obtain spec-tra of a large sample of faint galaxies. On the otherhand, narrow-band imaging observations make it possibleto measure an emission-line flux of galaxies over a widefield of view. Another advantage of narrow-band imag-ing is that aperture corrections dose not need to eval-uate the total flux of H α emission. However, there aresome shortcomings in this method: e.g., narrow-band fil-ter cannot separate H α emission from [N ii ] λλ , α emitters. If this is the case, brighter (i.e., rarer) H α emitters could be missed in such an imaging survey.In order to study the H α luminosity function unambigu-ously, we need a large sample of H α emitters covering awide range of H α luminosity. On the other hand, thisrestriction allows us to investigate large-scale structuresof emission-line galaxies (mostly, star-forming galaxies)at a concerned redshift slice.Motivated by this in part, we have carried out anarrow-band imaging survey of the HST COSMOSfield centered at α (J2000)= 10 h m . s and δ (J2000)=+02 ◦ ′ . ′′ ; the Cosmic Evolution Survey (Scoville etal. 2007). Since this field covers 2 square degree, it issuitable for our purpose. Our optical narrow-band imag-ing observations of the HST COSMOS field have beenmade with the Suprime-Cam (Miyazaki et al. 2002) onthe Subaru Telescope (Kaifu et al. 2000; Iye et al. 2004).Since the Suprime-Cam consists of ten 2k ×
4k CCD chipsand provides a very wide field of view (34 ′ × ′ ), this issuitable for any wide-field optical imaging surveys. In ourobservations, we used the narrow-passband filter, NB λ = 120 ˚A.Our NB816 imaging data are also used to search both forLy α emitters at z ≈ . ii ] emitters at z ≈ . α emitters at z ≈ . matter = 0 . Λ = 0 .
7, and H = 70 km s − Mpc − . PHOTOMETRIC CATALOG
In this analysis, we use the COSMOS official photo-metric redshift catalog which includes objects whose to-tal i magnitudes ( i ′ or i ∗ ) are brighter than 25. Thecatalog presents 3 ′′ diameter aperture magnitude ofSubaru/Suprime-Cam B , V , r ′ , i ′ , z ′ , and N B .Details of the Suprime-Cam observations are given inTaniguchi et al. (2007). Details of the COSMOS officialphotometric redshift catalog is also described in Capaket al. (2007) and Mobasher et al. (2007). Since theaccuracy of standard star calibration ( ± .
05 magnitude)is too large to obtain an accurate photometric redshift,Capak et al. (2007) re-calibrated the photometric zero-points for photometric redshift using the SEDs of galax-ies with spectroscopic redshift. Following the recommen-dation of Capak et al. (2007), we apply the zero-pointcorrection to the photometric data in the official cata-log. The offset values are 0.189, 0.04, − . − . − .
072 for B , V , r ′ , i ′ , z ′ , and N B B = 27 . V = 26 . r ′ = 26 . i ′ = 26 . z ′ = 25 . N B
816 = 25 . σ detection on a 3 ′′ diameteraperture. The catalog also includes 3 ′′ diameter aperturemagnitude of CFHT i ∗ . We use the CFHT i ∗ magni-tude for bright galaxies with i ′ <
21 because such brightgalaxies appear to be slightly affected by the saturationeffect in i ′ obtained with Suprime-Cam. We also applythe Galactic extinction correction adopting the medianvalue E ( B − V ) = 0 . Our SDSS broad-band filters are designated as g + , r + , i + ,and z + in Capak et al. (2007) to distinguish from the originalSDSS filters. Also, our B and V filters are designated as B J and V J in Capak et al. (2007) where J means Johnson and Cousinsfilter system used in Landolt (1992). α luminosity function at z ≈ .
24 3objects. A photometric correction for each band is asfollows (see Table 8 of Capak et al. 2007): A B = 0 . A V = 0 . A r ′ = 0 . A i ′ = 0 . A z ′ = 0 . A NB = 0 . A i ∗ = 0 . RESULTS
Selection of NB816-Excess Objects
We select H α emitter candidates using 3 ′′ diameteraperture magnitude in the official catalog. In order toselect NB i ′ (394.9 THz) and z ′ (333.6 THz)filters, we newly make a frequency-matched continuum,“ iz continuum”, using the following linear combination; f iz = 0 . f i ′ + 0 . f z ′ where f i ′ and f z ′ are the i ′ and z ′ flux densities, respectively. Its 3 σ limiting magnitudeis iz ≃ .
03 in a 3 ′′ diameter aperture. For the brightgalaxies with i ′ <
21, “ iz continuum” is calculated as f iz = 0 . f i ∗ + 0 . f z ′ , where f i ∗ is the i ∗ flux density,since i ′ magnitude is incorrect because of the saturationeffect.Since we use the ACS catalog prepared for studyingweak lensing (Leauthaud et al. 2007) to separate galax-ies from stars, our survey area is restricted to the areamapped in I band with Advanced Camera for Sur-veys (ACS) on HST. After subtracting the masked outarea, the effective survey area is 5540 arcmin . Sincethe covered redshift range is between 0.233 and 0.251(∆ z = 0 . . × Mpc .We selected NB iz − N B > . , (1)and iz − N B > σ ( iz − N B , (2)where3 σ ( iz − N B − . − p ( f σ NB ) + ( f σ iz ) /f NB ) . (3)In the calculation of 3 σ ( iz − N B i ′ - and z ′ -band. The former criterion corresponds EW obs >
12 ˚A. This criterion is exactly same as thatof Fujita et al. (2003) and similar to that of Tresse &Maddox (1998) [ EW (H α + [NII]) rest >
10 ˚A]. Taking ac-count of the scatter of iz − N B
816 color, we added thelatter criterion. These two criteria are shown by the solidand dashed lines, respectively, in Figure 1. As we will de-scribe in the next section, we use the broad-band colors ofgalaxies to separate H α emitters from other emission-linegalaxies. To avoid the ambiguity of broad-band colors,we select galaxies detected above 3 σ in all bands. Finally,we find 6176 galaxies that satisfy the above criteria. Selection of NB816-Excess Objects at z ≈ . α emitters at z = 0 .
24 but also possibly[O iii ] emitters at z = 0 .
63, or H β emitters at z = 0 . ii ] emitters at z = 1 .
19 (Tresse et al. 1999; Ken-nicutt 1992b). We also note here that the narrowband filter passband is too wide to separate [N ii ] λλ , α .In order to distinguish H α emitters at z ≈ .
24 fromemission-line objects at other redshifts, we investigatetheir broad-band color properties comparing observedcolors of our 6176 emitters with model ones that are es-timated by using the model spectral energy distributionderived by Coleman, Wu, & Weedman (1980). In Fig-ures 2 & 3, we show the B − V vs. V − r ′ and B − r ′ vs. i ′ − z ′ color-color diagram of the 6176 sources andthe loci of model galaxies. Then we find that H α emit-ters at z ≈ .
24 can be selected by adopting the fol-lowing three criteria; (1) B − V > V − r ′ ) − .
2, (2) B − r ′ > i ′ − z ′ ) − .
3, and (3) B − r ′ > . i ′ − z ′ )+0 . α emitters from [O iii ] or H β emitters using the first criterion. We can also distin-guish H α emitters from [O ii ] emitters using the secondand third criteria. We have checked the validity of ourphotometric selection criteria using both the photomet-ric data and spectroscopic redshifts of galaxies in theGOODS-N region (Cowie et al. 2004). Galaxies withredshifts corresponding to our H α , [O iii ], H β , and [O ii ]emitters are separately plotted in Figs. 2 & 3. It isshown that our criteria can separate well H α emittersfrom [O iii ], H β , and [O ii ] emitters. These criteria giveus a sample of 981 H α emitting galaxy candidates. Theproperties of GOODS-N galaxies presented in Figs. 2and 3 suggest that there is few contamination in our H α emitter sample. H α Luminosity
As we mentioned in section 1, one of the advantages ofnarrow-band imaging is to measure the total flux of H α emission directly without any aperture correction. Toderive the total H α flux, we have used the total flux of i ′ (or i ∗ ), z ′ , and N B
816 using public images. Our pro-cedure is the same as that given in Capak et al. (2007);MAG AUTO in SExtractor (Bertin & Arnouts 1996).Because of the contamination of the foreground galax-ies, one galaxy has a negative value of iz − N B
816 basedon the total magnitudes. We do not use this object infurther analysis. Therefore, our final sample contains 980H α emitters.Adopting the same method as that used by Pascual etal. (2001), we express the flux density in each filter bandas the sum of the line flux, F L , and the continuum fluxdensity, f C : f NB = f C + F L ∆ N B , (4) f i ′ = f C + F L ∆ i ′ , (5)and f z ′ = f C , (6)where ∆ N B and ∆ i ′ are the effective bandwidths of NB816 and i ′ , respectively. The iz continuum, f iz , isexpressed as f iz = 0 . f i ′ + 0 . f z ′ = f C + 0 . F L ∆ i ′ . (7) http://irsa.ipac.caltech.edu/data/COSMOS/ Shioya et al.Using equation 4 and 7, the line flux F L is calculated by F L = ∆ N B f NB − f iz − . N B/ ∆ i ′ ) . (8)The line flux evaluated above includes both H α and[N ii ] λλ , α emission line is also affected by the internal extinc-tion. Therefore, we have to correct the contaminationof [N ii ] λλ , A H α . Although several correction methods have beenproposed (e.g., Kennicutt 1992a; Gallego et al. 1997;Tresse et al. 1994; Helmboldt et al. 2004 for [N ii ] con-tamination: Kennicutt 1983b; Niklas et al. 1997; Ken-nicutt 1998; Hopkins et al. 2001; Afonso et al. 2003for A H α ), there is few study which gives both correctionsbased on a single sample of galaxies. Helmboldt et al.(2004) have derived the relation between [N ii ]/H α and M R and that between A H α and M R based on the dataof the Nearby Field Galaxy Survey (Jansen et al. 2000a,2000b). We therefore adopt their relations to correct the[N ii ] contamination and A H α . After correcting to theAB magnitude system (Meurer et al. 2006), the relationbetween [N ii ]/H α and M R islog w = − . M R − . , (9)where w ≡ F [NII]6583 ˚ A F H α (10)and that between A H α and M R islog A H α = − . M R − . . (11)To derive M R used in equations (9) & (11) for eachgalaxy, we assume that the redshift of the galaxy is z = 0 . k -correction using theaverage SED of Coleman et al. (1980)’s Sbc and Irr. Tak-ing account of the luminosity distance and k -correction(average value of Scd and Irr), M R is calculated from r ′ -band total magnitude, r ′ , as M R = r ′ − . α flux is given by: F cor (H α ) = F L × f (H α ) f (H α ) + f ([N ii ]) × . A H α × . . (12)Finally the H α luminosity is estimated by L (H α ) =4 πd F cor (H α ). In this procedure, we assume that allthe H α emitters are located at z = 0 .
242 that is theredshift corresponding to the central wavelength of our NB
816 filter. Therefore, the luminosity distance is set tobe d L = 1213 Mpc.We summarize the total magnitude of i ′ , z ′ , NB816 ,and iz and the color excess of iz − N B
816 for our H α emission-line galaxy candidates in Table 1. Table 1 alsoincludes log F L , log F cor (H α ), and log L (H α ). DISCUSSION
Luminosity function of H α emitters Figure 4 shows the H α luminosity function (LF) at z ≈ .
24 for our H α emitter sample. The H α LF isconstructed by the relationΦ(log L i ) = 1∆ log L X j V j (13)with | log L j − log L i | <
12 ∆ log L, (14)where V j is the volume of the narrow band slice in therange of redshift covered by the filter. We have used∆ log L (H α ) = 0 .
2. If the shape of the filter responseis square, our survey volume is 3 . × Mpc . How-ever, effective survey volume is affected by the shape offilter transmission curve. For example, since the trans-mission at 8092 ˚A is a half of the peak value, the colorexcess, iz − N B α emitter at z = 0 .
233 with EW (H α + [N ii ]) = 12˚A is observed as 0.05 which doesnot satisfy our selection criterion, iz − N B > . α emitters with L (H α ) > . ergs s − ; α = − . +0 . − . , log φ ∗ = − . +0 . − . , andlog L ∗ (erg s − ) = 41 . +0 . − . (black solid line).Together with our H α LF, Figure 4 shows H α LFs ofprevious studies in which H α emitters at z < . α = − . φ ∗ = 10 − . Mpc − , and L ∗ = 10 . ergs s − ; note that these parameters wereconverted by Hopkins (2004) to those of our adopted cos-mology], Fujita et al. (2003), Hippelein et al. (2003) andLy et al. (2007). Fujita et al. (2003), Ly et al. (2007),and this work are based on the NB816 imaging obtainedwith the Subaru Telescope. Tresse & Maddox (1998)is based on the Canada-France Redshift Survey (CFRS)and Hippelein et al. (2003) is based on the Calar AltoDeep Imaging Survey (CADIS).First, we compare our H α LF with that derived by Lyet al. (2007). Their best-fit Schechter function parame-ters ( α = − .
71, log φ ∗ = − .
7, log L ∗ = 42 .
2) are quitedifferent from those of our H α LF. However we note thatthe data points between log L (H α ) ∼ . ∼ . α LF of Ly et al. (2007) itself is basically con-sistent with ours except the brightest point. The differ-ence of Schechter parameters between ours and Ly et al’smay arise from the data points of the brightest and thefaintest ones, especially the brightest one. Since the fieldof view of the COSMOS is about an order wider thanthat of the SDF, we consider that our H α LF is moreaccurate by determined than that of Ly et al. (2007) atthe bright end.Second, we compare our H α LF with the other H α LFs. Although our H α LF is similar to those of Tresse &Maddox (1998) and Hippelein et al. (2003), the H α LF ofFujita et al. (2003) shows a steeper faint-end slope and α luminosity function at z ≈ .
24 5a higher number density for the same luminosity thanours. These differences may be attributed to the follow-ing different source selection procedures: (1) Fujita etal. (2003) used their
NB816 -selected galaxies while weused i ′ -selected galaxies, Tresse & Maddox (1998) used I -selected Canada-France Redshift Survey (CFRS) galax-ies, and Hippelein et al. (2003) used Fabry-Perot imagesfor pre-selection of emission-line galaxies. As Fujita et al.(2003) demonstrated, samples based on a broad-band se-lected catalog are biased against galaxies with faint con-tinuum. (2) Fujita et al. (2003) used their B − R C vs. R C − I C color - color diagram to isolate H α emitters fromother low- z emitters at different redshifts. However, wefind that there are possible contaminations of [O iii ] emit-ters if one uses the B − R C vs. R C − I C diagram, becauseof the small difference between H α and [O iii ] emitters onthat color - color diagram. On the other hand, we used B − V vs. V − r ′ to isolate H α emitters from [O iii ] emit-ters. Due to the large separation between H α emittersand [O iii ] emitters on the B − V vs. V − r ′ diagram,we can reduce the contamination of [O iii ] emitters. (3)Fujita et al. (2003) used population synthesis model GIS-SEL96 (Bruzual & Charlot 1993) to determine the cri-teria for selecting H α emitters. To check the validityof the criterion, we compare colors of GOODS-N galax-ies at z ∼ .
24, 0.63, 0.68 & 1.19 with model colors atcorresponding redshifts based on GISSEL96 (Figure 5).Unfortunately, the predicted colors are slightly differentfrom those of observed galaxies. We therefore redeter-mined the selection criteria using the SED of Coleman,Wu, & Weedman (1980) as( B − R C ) > . R C − I C ) + 0 . . If we adopt this revised criterion, the number of H α emit-ters in the Fujita et al. (2003) is reduced by about 20 %(Figure 5). This is one reason why the number density ofH α emitters in Fujita et al. (2003) is higher than othersurveys. Recently, Ly et al. (2007) pointed out that thefraction of [O iii ] emitters in the H α emitter sample ofFujita et al. (2003) may be about 50 % using the HawaiiHDF-N sources with redshifts observed as N B α LF of Fujita et al. (2003) reduced by50 % appears to be quite similar to our H α LF.
Luminosity density and star formation rate density
By integrating the luminosity function, i.e., L (H α ) = Z ∞ Φ( L ) LdL = Γ( α + 2) φ ∗ L ∗ , (15)we obtain a total H α luminosity density of 2 . +0 . − . × ergs s − Mpc − at z ≈ .
24 from our best fit LF. The starformation rate is estimated from the H α luminosity usingthe relation SF R = 7 . × − L (H α ) M ⊙ yr − , where L (H α ) is in units of ergs s − (Kennicutt 1998). Usingthis relation, the H α luminosity density can be translatedinto the SFR density of ρ SFR ≃ . +1 . − . × − M ⊙ yr − Mpc − .However, not all the H α luminosity is produced by starformation, because active galactic nuclei (AGNs) can alsocontribute to the H α luminosity. For example, previ-ous studies obtained the following estimates; 8-17% ofthe galaxies in the CFRS low- z sample (Tresse et al. 1996), 8% in the Universidad Complutense de Madrid(UCM) survey of local H α emission line galaxies (Gal-lego et al. 1995), and 17-28% in the 15R survey (Carteret al. 2001). Recently, Hao et al. (2005) obtained anH α luminosity function of active galactic nuclei based onthe sample of the Sloan Digital Sky Survey within a red-shift range of 0 < z < .
15. The H α luminosity densitycalculated from Schechter function parameters which areshown in the paper is 1 . × erg s − Mpc − (with noreddening correction). Taking account of the reddeningcorrection and the H α luminosity density radiated fromstar-forming galaxies (Gallego et al. 1995), the fractionof AGN contribution to the total H α luminosity densityis about 15 % in the local universe. If we assume thatthe 15 % of the H α luminosity density is radiated fromAGNs, the corrected SFRD is 1 . +0 . − . × − M ⊙ yr − Mpc − .We note here that the error to ρ SFR (and L (H α )) isprobably underestimated, since it does not include theeffect of different correction methods and selection bi-ases. For example, adopting the different relation forcorrecting A H α may cause a different value of SFRD.We compare our result with the previous investigationscompiled by Hopkins (2004) in Figure 6. We also showthe evolution of SFRD derived from the observation ofGALEX with mean attenuation of A measUV = 1 .
8, evalu-ated from the FUV slope β ( f λ ∝ λ β ) and the relationof A FUV = 4 .
43 + 1 . β . If we adopt the more represen-tative value A minUV = 1 (Schiminovich et al. 2005) deter-mined by using the F dust /F UV ratio (Buat et al. 2005),their SFRD becomes smaller by a factor of 2, being sim-ilar to our SFRD.The left panel of Figure 6 shows the evolution of theSFRD as a function of redshift from z = 0 to z = 2.The right panel of Figure 6 shows that as a function ofthe look-back time. It clearly shows that SFRD mono-tonically decreasing for 10 Gyr with increasing cosmictime. We note that the error of SFRD of our evaluationincludes only random error, since we adopt the same as-sumptions as those in Hopkins (2004).Our SFRD evaluated above seems roughly consis-tent with but slightly smaller than the previous eval-uations, e.g., Tresse & Maddox (1998) and Fujita etal. (2003). Since we select emission-line galaxies with EW (H α + [N ii ]) obs >
12 ˚A, our sample is considered tobe biased against star-forming galaxies with small spe-cific SFR which is defined as the ratio of SFR to stellarmass of galaxy. Since our criterion is similar to that ofTresse & Maddox (1998) and the same as that of Fujitaet al. (2003), we consider that the difference between oursurvey and theirs is not caused by the different criteria of EW (H α + [N ii ]) obs . As we mentioned in section 4.1, theSFRD of Fujita et al. (2003) was overestimated becauseof the contamination of [O iii ] emitters. On the otherhand, the difference between Tresse & Maddox (19989and our work seems to be real; e.g., the cosmic variance.We discuss further the effect of the selection criterion of EW (H α + [N ii ]) obs >
12 ˚A on the evaluation of SFRD.Being different from the previous H α emission-line galaxysurveys using the objective-prism, the fraction of galaxieshaving EW (H α ) >
50 ˚A is 12 % in our sample, which issimilar to or less than the value of the local universe (15-20 %: Heckman 1998) and SINGG SR1 (14.5 %: Han- Shioya et al.ish et al. 2006). On the other hand, the fractions ofthe galaxies with EW (H α ) >
50 ˚A are 42 % and 35 %in the KPNO International Spectroscopic Survey (KISS)(Gronwall et al. 2004) and UCM objective-prism sur-veys, respectively. Our sample seems to be not stronglybiased toward galaxies with high equivalent width. Han-ish et al. (2006) showed that 4.5 % of the H α luminositydensity comes from galaxies with EW (H α ) <
10 ˚A inlocal universe. If the fraction (4.5 %) is valid for thestar-forming galaxies at z ≈ .
24, our estimate of SFRDwould be about 5 % smaller than the true SFRD.
Spatial Distribution and Angular Two-PointCorrelation Function
Figure 7 shows the spatial distribution of our 980 H α emitter candidates. There are some clustering regionsover the field. To discuss the clustering properties morequantitatively, we derive the angular two-point correla-tion function (ACF), w ( θ ), using the estimator definedby Landy & Szalay (1993), w ( θ ) = DD ( θ ) − DR ( θ ) + RR ( θ ) RR ( θ ) , (16)where DD ( θ ), DR ( θ ), and RR ( θ ) are normalizednumbers of galaxy-galaxy, galaxy-random, random-random pairs, respectively. The random sample con-sists of 100,000 sources with the same geometrical con-straints as the galaxy sample. Figure 4 demonstratesthat our H α emitter sample is quite incomplete forlog L (H α )(erg s − ) < .
8. We therefore show the ACFfor 693 H α emitter candidates with log L (H α )(erg s − ) > . w ( θ ) = 0 . +0 . − . θ − . ± . . Recently, the departurefrom a power-law of the correlation function is reported(Zehavi et al. 2004; Ouchi et al. 2005). Such departuremay be interpreted as the transition from a large-scaleregime, where the pair of galaxies reside in separate ha-los, to a small-scale regime, where the pair of galaxiesreside within the same halo. We find no evidence forsuch departure in our result. We however consider thatthe number of our sample is too small to discuss thisproblem.For Lyman break galaxies, brighter galaxies (witha larger star formation rate) tend to show moreclustered structures than faint ones (with a smallerstar formation rate) (e.g., Ouchi et al. 2004;Kashikawa et al. 2006). We also show theACF of H α emitters with larger H α luminosity[log L (H α )(erg s − ) > .
94 = log(0 . L ∗ )] and thatwith lower H α luminosity (39 . < log L (H α )(erg s − ) ≤ .
94) in Figure 8. Both ACFs are well fit witha power law form: w ( θ ) = 0 . +0 . − . θ − . ± . for objects with log L (H α )(erg s − ) > .
94, while w ( θ ) = 0 . +0 . − . θ − . ± . for objects with 39 . < log L (H α )(erg s − ) ≤ .
94, respectively. We concludethat galaxies with a higher star formation rate are morestrongly clustered than ones with a lower star formationrate. This fact is interpreted as that galaxies with ahigher star formation rate reside in more massive darkmatter halos, which are more clustered in the hierarchicalstructure formation scenario. It is useful to evaluate the correlation length r of thetwo-point correlation function ξ ( r ) = ( r/r ) − γ . A cor-relation length is derived from the ACF through Lim-ber’s equation (e.g., Peebles 1980). Assuming that theredshift distribution of H α emitters is a top hat shapeof z = 0 . ± . r = 1 . α emitters is written as ξ ( r ) =( r/ . − . . The correlation length of H α emitterswith log L (H α )(erg s − ) > .
94 is 2.9 Mpc, while thatof H α emitters with 39 . < log L (H α )(erg s − ) ≤ . L ∗ galaxies ( ∼ z ∼ ∼ z ∼ L (H α )and R C -band absolute magnitude M R for our sample.Our sample includes many faint ( M R > −
18) galax-ies. However, the correlation length for galaxies with − < M r < −
17 (3.8 Mpc: Zehavi et al. 2005) is stilllarger than that of our sample. This discrepancy mayimply a weak clustering of emission-line galaxies. SUMMARY
We have performed the H α emitter survey in the HSTCOSMOS 2 square degree field using the COSMOS of-ficial photometric catalog. Our results and conclusionsare summarized as follows.1. We found 980 H α emission-line galaxy candi-dates using the narrow-band imaging method. TheH α luminosity function is well fit by Schechter func-tion with α = − . +0 . − . , log φ ∗ = − . +0 . − . , andlog L ∗ (erg s − ) = 41 . +0 . − . . Using the parameter setof Schechter function, the H α luminosity density is eval-uated as 2 . +0 . − . × erg s − Mpc − . If we adoptthe AGN contribution to the H α luminosity densityis 15 %, we obtain the star formation rate density of1 . +0 . − . × − M ⊙ yr − Mpc − . This error includes onlyrandom error. Our result supports the strong increase inthe SFRD from z = 0 to z = 1.2. We studied the clustering properties of H α emittersat z ∼ .
24. The two-point correlation function is well fitby power law, w ( θ ) = 0 . +0 . − . θ − . ± . , which leadsto the correlation function of ( r/ . − . . We can-not find the departure from a power law, which is recentlyfound in both low- and high- z galaxies. Although thepower of − .
88 is consistent with the power for nearbygalaxies, the derived correlation length of r = 1 . α luminosity function at z ≈ .
24 7COSMOS science meeting in May 2005 was supportedby in part by the NSF through grant OISE-0456439.We would also like to thank the Subaru Telescope staff for their invaluable help. This work was financiallysupported in part by the JSPS (Nos. 15340059 and17253001). SSS and TN are JSPS fellows.
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Shioya et al.
TABLE 1A list of H α emitter candidates. i ′ z ′ NB iz iz − NB
816 log F L log F cor log L (H α ) EW obs (deg) (deg) (mag) (mag) (mag) (mag) (mag) (erg s − cm − ) (erg s − cm − ) (erg s − ) (˚A)1 58612 150.72533 1.611834 20.99 20.92 20.86 20.96 0.10 -16.11 -15.81 40.44 122 62649 150.67970 1.594458 20.89 20.64 20.64 20.78 0.13 -15.88 -15.57 40.67 173 101151 150.46013 1.600051 21.05 21.05 20.93 21.05 0.12 -16.05 -15.76 40.49 144 135016 150.33841 1.622284 22.98 22.58 22.70 22.79 0.09 -16.87 -16.67 39.58 115 137365 150.32673 1.605641 23.01 22.91 22.84 22.96 0.13 -16.78 -16.58 39.67 16 The complete version of the this table is in the electric edition of the Journal. The printed edition contains only a sample. α luminosity function at z ≈ .
24 9
Fig. 1.—
Diagram of iz − NB
816 vs. NB
816 for all objects classified as galaxies in the ACS catalog. The horizontal solid line correspondsto iz − NB
816 = 0 .
1. The dashed lines show the distribution of 3 σ error. the dot-dashed line shows the limiting magnitude of iz . Since thetotal i ′ -magnitudes of galaxies in the official photometric redshift catalog are brighter than 25, iz magnitudes of most of them are brighterthan the limiting magnitude. Fig. 2.—
Diagrams between B − V vs. V − r ′ . Top : Colors of model galaxies (CWW) from z = 0 to z = 3 are shown with dottedlines: red, orange, green, and blue lines show the loci of E, Sbc, Scd, and Irr galaxies, respectively. Colors of z = 0 .
24, 0 .
64, 0 .
68, and 1 . α , [O iii ], H β , and [O ii ] emitters, respectively) are shown with red, green, light blue, and blue lines, respectively. Orange asterisksshow Gunn and Stryker (1983)’s star. Bottom : Plot of B − V vs. V − r ′ for the 6176 sources found with emitter selection criteria. In thisdiagram, H α emitters are located above the black line, that is adopted by us as one of the criteria for the selection of H α emitters. The980 H α emitters are shown as black dots and other emission-line galaxy candidates are shown by gray dots. Galaxies in GOODS-N (Cowieet al. 2004) with redshifts corresponding to H α emitters, [O iii ] emitters, H β emitters and [O ii ] emitters are shown as red, green, light blueand blue open squares, respectively. α luminosity function at z ≈ .
24 11
Fig. 3.—
Diagrams between B − r ′ vs. i ′ − z ′ . Top : Colors of model galaxies (CWW) from z = 0 to z = 3 are shown with dotted lines:red, orange, green, and blue lines show the loci of E, Sbc, Scd, and Irr galaxies, respectively. Colors of z = 0 .
24, 0 .
64, 0 .
68, and 1 .
18 (forH α , [O iii ], H β , and [O ii ] emitters, respectively) are shown with red, green, light blue, and blue lines, respectively. Orange asterisks showGunn and Stryker (1983)’s star. Bottom : Plot of B − r ′ vs. i ′ − z ′ for the 6176 sources found with emitter selection criteria (black dots).In this diagram, H α emitters are located above the both of black lines, that is adopted by us as one of the criteria for the selection of H α emitters. The 980 H α emitters are shown as black dots and other emission-line galaxy candidates are shown by gray dots. Galaxies inGOODS-N (Cowie et al. 2004) with redshifts corresponding to H α emitters, [O iii ] emitters, H β emitters and [O ii ] emitters are shown asred, green, light blue and blue open squares, respectively. Fig. 4.—
Our H α luminosity function (filled squares and thick solid line) and H α luminosity functions in previous works. The Tresse &Maddox (1998)’s H α luminosity function at z ≤ . α luminosity functions derived by Fujita et al.(2003), Hippelein et al. (2003), and Ly et al. (2007) are shown with the dotted line, the dot-dashed line, and dashed and double-dottedline, respectively. Data points of Ly et al. (2007)’s H α LF are shown as gray crosses.
Fig. 5.— B − R C vs. R C − I C color - color diagram of model galaxies. Colors of z = 0 .
24, 0 .
64, 0 .
68, and 1 .
18 (for H α , [O iii ], H β ,and [O ii ] emitters, respectively) are shown with red, green, light blue, and blue lines, respectively. The loci calculated by using GISSEL96(Bruzual & Charlot 1993) are shown by solid lines and those calculated by using CWW are shown by dashed lines. Galaxies in GOODS-N(Cowie et al. 2004) with redshifts corresponding to H α emitters, [O iii ] emitters, H β emitters and [O ii ] emitters are shown as red, green,light blue and blue open squares, respectively. Fujita et al. (2003) selected galaxies above the black solid line as H α emitter candidates. Ifwe reselect H α emitter candidates as sources above the black dashed line, some of the H α emitter candidates (black dots) do not satisfythe new criterion. α luminosity function at z ≈ .
24 13
Fig. 6.—
Star formation rate density (SFRD) at z ≈ .
24 derived from this study (large red filled circle) shown together with theprevious investigations compiled by Hopkins (2004). SFRDs estimated from H α , [O ii ], and UV continuum are shown as orange open circles(P´erez-Gonz´alez et al. 2003; Tresse et al. 2002; Moorwood et al. 2000; Hopkins et al. 2000; Glazebrook et al. 1999; Yan et al. 1999; Tresse& Maddox 1998; Gallego et al. 1995), green open diamonds (Teplitz et al. 2003; Gallego et al. 2002; Hogg et al. 1998; Hammer et al.1997), and blue squares (Wilson et al. 2002; Massarotti et al. 2001; Sullivan et al. 2000; Cowie et al. 1999; Treyer et al. 1998; Connolly etal. 1997; Lilly et al. 1996). The light blue open squares show SFRDs based on the UV luminosity density by Schiminovich et al. (2005),assuming A FUV = 1 .
8. An orange open square and an orange open diamond show SFRDs at z ≈ .
24 derived by Fujita et al. (2003) andLy et al. (2007), respectively. In the left panel, we show the evolution of SFRD as a function of redshift, and in the right panel, we showit as a function of lookback time.
Fig. 7.—
Spatial distributions of our H α emitter candidates (black filled circles and black dots). Gray open squares in the both panelsshow our survey area. The shadowed regions in the right panel show the areas masked out for the detection. We show the luminous H α emitters [log L (H α )(erg s − ) > .
94] as large filled circles and the faint H α emitters [39 . < log L (H α )(erg s − ) ≤ .
94] as small filledcircles. H α emitters with log L (H α )(erg s − ) ≤ . Fig. 8.—
Angular two-point correlation function of all H α emitter candidates (filled circles), bright H α emitter candidates(log L (H α )(erg s − ) > .
94: open squares), and faint H α emitter candidates (39 . < log L (H α )(erg s − ) ≤ .
94: open triangles).Solid line shows the relation of w ( θ ) = 0 . θ − . . Dashed line shows the best-fitting power law for bright ones, w ( θ ) = 0 . θ − . , anddotted line shows that for faint ones, w ( θ ) = 0 . θ − . . Fig. 9.—
Relation between H α luminosities and R -band absolute magnitudes for our H αα