New Determinations of the UV Luminosity Functions from z~9 to z~2 show a remarkable consistency with halo growth and a constant star formation efficiency
R.J. Bouwens, P.A. Oesch, M. Stefanon, G. Illingworth, I. Labbe, N. Reddy, H. Atek, M. Montes, R. Naidu, T. Nanayakkara, E. Nelson, S. Wilkins
aa r X i v : . [ a s t r o - ph . GA ] F e b Draft version February 17, 2021
Preprint typeset using L A TEX style emulateapj v. 12/16/11
NEW DETERMINATIONS OF THE UV LUMINOSITY FUNCTIONS FROM Z ∼ Z ∼ R.J. Bouwens , P.A. Oesch , M. Stefanon , G. Illingworth , I. Labb´e , N. Reddy , H. Atek , M. Montes , R.Naidu , T. Nanayakkara , E. Nelson , S. Wilkins Draft version February 17, 2021
ABSTRACTHere we provide the most comprehensive determinations of the rest-frame
U V
LF available to datewith
HST at z ∼
2, 3, 4, 5, 6, 7, 8, and 9. Essentially all of the non-cluster extragalactic legacyfields are utilized, including the Hubble Ultra Deep Field (HUDF), the Hubble Frontier Field parallelfields, and all five CANDELS fields, for a total survey area of 1136 arcmin . Our determinationsinclude galaxies at z ∼ ∼
150 arcmin area in the GOODS North and GOODS South regions. All together, ourcollective samples include > > . × larger than previous selections with HST . 5766,6332, 7240, 3449, 1066, 601, 246, and 33 sources are identified at z ∼
2, 3, 4, 5, 6, 7, 8, and 9,respectively. Combining our results with an earlier z ∼
10 LF determination by Oesch et al. (2018a),we quantify the evolution of the
U V
LF. Our results indicate that there is (1) a smooth flatteningof the faint-end slope α from α ∼ − . z ∼
10 to − . z ∼
2, (2) minimal evolution in thecharacteristic luminosity M ∗ at z ≥ .
5, and (3) a monotonic increase in the normalization log φ ∗ from z ∼
10 to z ∼
2, which can be well described by a simple second-order polynomial, consistentwith an “accelerated” evolution scenario. We find that each of these trends (from z ∼
10 to z ∼ . INTRODUCTION
Quantifying the build-up of galaxies in the early uni-verse remains one of a principal area of interest in ex-tragalactic astronomy involves (e.g., Madau & Dickinson2014; Davidzon et al. 2017). Studies of galaxy build-up have become increasingly mature, with ever more de-tailed efforts to measure the star formation rates and stel-lar masses of galaxies (e.g., Salmon et al. 2015; Leja et al.2019; Stefanon et al. 2021, in prep). Determinations ofthe volume density in the context of star formation rateand stellar mass measurements allow for connections tothe underlying dark matter halos (e.g., Behroozi et al.2013; Harikane et al. 2016, 2018; Stefanon et al. 2017a). Leiden Observatory, Leiden University, NL-2300 RA Leiden,Netherlands Department of Astronomy, University of Geneva, CheminPegasi 51, 1290 Versoix, Switzerland Cosmic Dawn Center (DAWN), Niels Bohr Institute, Uni-versity of Copenhagen, Jagtvej 128, København N, DK-2200,Denmark UCO/Lick Observatory, University of California, SantaCruz, CA 95064 Centre for Astrophysics & Supercomputing, Swinburne Uni-versity of Technology, PO Box 218, Hawthorn, VIC 3112, Aus-tralia University of California, Riverside, CA 92521, USA Institut d’Astrophysics de Paris, 98bis Boulevard Arago,75014 Paris, France Space Telescope Science Institute, 3700 San Martin Drive,Baltimore, MD 21218 Center for Astrophsics, 60 Garden St, Cambridge, MA02138, United States Astrophysical & Planetary Sciences, 391 UCB, 2000 Col-orado Ave, Boulder, CO 80309, Duane Physics Building, Rm.E226 Department of Physics & Astronomy, University of Sussex,Falmer, Brighton, BN1 9QH, United Kingdom
One prominent, long-standing gauge of galaxy build-up is the luminosity function of galaxies in the rest-frame
U V , which represents the volume density of galaxies asa function of the
U V luminosity. As the time-averagedstar formation rate of galaxies is proportional to the un-obscured luminosities of galaxies in the rest-frame
U V ,the
U V luminosity function provides us with a measureof how quickly galaxies grow with cosmic time.There is already significant work on the
U V
LF acrossa wide range in redshifts, from local studies to studiesin the early universe. Broadly, the normalization φ ∗ and faint-end slope α of the U V
LF have been foundto increase and to flatten, respectively, with cosmic time(Bouwens et al. 2015, 2017; Finkelstein et al. 2015;Bowler et al. 2015; Parsa et al. 2016; Ishigaki et al.2018), while the characteristic luminosity remains fixedwith cosmic time (Bouwens et al. 2015, 2017; Finkelsteinet al. 2015; Bowler et al. 2015; Parsa et al. 2016) or be-comes fainter (Arnouts et al. 2005). Motivated by manytheoretical models, Bouwens et al. (2015) showed thatthe evolution of the faint-end slope from z ∼ z ∼ U V
LF with redshift, galaxy evolutionstudies are entering an era where precision measurementsbecome increasingly key. To date, there has been no sys-tematic, self-consistent determination of the evolution ofthe rest-frame
U V
LF from z ∼ z ∼ Fig. 1.—
The layout of the search fields we utilize with WFC3/UVIS UV U ∼ µ m data to identify z ∼ ∼
93 arcmin HDUV fields (Oesch et al. 2018b), the ∼ UVUDF field (Teplitz et al. 2013), and the ∼
50 arcmin ERS(Windhorst et al. 2011) data set. The cyan footprint shown over the GOODS-North shows the WFC3/UVIS imaging data available fromthe CANDELS program in the F275W (Grogin et al. 2011) and has an exposure time equivalent to ∼ ∼
150 arcmin search area to identify > z ∼ tions from the WFC3/IR Early Release Science (ERS)and UVUDF programs (Windhorst et al. 2011; Teplitzet al. 2013) allow us to extend the Bouwens et al. (2015)study of the U V
LF down to z ∼
2, while adding valuablestatistics and leverage at the bright and faint ends.In addition, through inclusion of observations from theHubble Frontier Fields program (Lotz et al. 2017), we canfurther refine our earlier determinations of the
U V
LFat z ∼ ∼ U V
LF, we ex-pressly focus on blank field search results for z ∼ U V
LF determinationsare only impacted by systematic errors specific to blankfield studies (Bouwens et al. 2017a, Bouwens et al. 2017b;Atek et al. 2018). In a follow-up paper (Bouwens et al.2021, in prep), we will provide separate determinations ofthe
U V
LF using observations over the Hubble FrontierFields clusters, and then we will compare the LF resultsfrom the lensing fields with the blank fields and test forconsistency.We now present a plan for this paper. § §
3, we summarize ourprocedure for deriving LF results, while also presentingour new UV LF results. In §
4, we discuss the new trendswe find and compare our new LF results with previous results in the literature. Finally, § L ∗ z =3 derived at z ∼ HST
F225W,F275W, F336W, F435W, F606W, F600LP, F775W,F814W, F850LP, F098M, F105W, F125W, F140W, andF160W bands as
U V , U V , U , B , V , V , i , I , z , Y , Y , J , JH , and H , re-spectively, for simplicity. The standard concordance cos-mology Ω = 0 .
3, Ω Λ = 0 .
7, and H = 70 km/s/Mpc isassumed for consistency with previous LF studies. Allmagnitudes are in the AB system (Oke & Gunn 1983). DATA SETS AND CATALOGUES
HDUV + ERS
The primary data for our z = 2-3 LF results arethe sensitive near-UV observations obtained over a ∼ area within the GOODS-South and GOODS-North fields using the HDUV program (Oesch et al.2018b). For a description of the characteristics and re-duction of those data, we refer the interested readerto Oesch et al. (2018b). Optical and near-IR observa-tions over this field were obtained by making use of thev1.0 Hubble Legacy Field (HLF: Illingworth et al. 2016;Whitaker et al. 2019; G.D. Illingworth et al. 2021, inprep) reductions. The HLF reductions constitute a com-prehensive reduction of all the archival optical/ACS +near-IR/WFC3/IR observations over the GOODS-Southand GOODS-North fields.For our z = 2-3 selections and LF results, we also Fig. 2.—
Surface densities of the candidate z ∼ z ∼ blue points ), HDUV ( black points ), and the UVUDF ( red points ). Surface densities are presented as a function of the V and I bandmagnitudes that provide the best measure of the rest-frame UV flux of galaxies at 1600˚ A for our z ∼ z ∼ z ∼ i band magnitudes are presented here instead (due to the significantly greater depth of the i -banddata). A slight horizontal offset of the points relative to each other has been applied for clarity. The onset of incompleteness in our differentsamples is clearly seen in the observed decrease in surface density of sources near the magnitude limit. We do not make use of the faintestsources in each search field, i.e., V /i /I magnitudes fainter than 26.5, 28.0, and 29.0 for the ERS, HDUV, and UVUDF fields,respectively, given the large uncertainties in the completeness (and contamination) corrections. make use of the WFC3/UVIS U V
U V U observa-tions that were part of the WFC3 ERS program overthe GOODS South field. These data cover ∼
50 arcmin .The ERS observations, together with the HDUV obser-vations, cover an area of 143 arcmin in total. First se-lections of z ∼ U V
LF results were obtained by Hathi et al.(2010) and Oesch et al. (2010). As in the case of theHDUV data, we make use of the reduction of optical andnear-IR observations over the ERS area from the HLFprogram.Figure 1 shows the layout of the WFC3/UVIS observa-tions from the HDUV and ERS fields over the GOODS-South and GOODS-North fields.
UVUDF/XDF
We also made use of near-UV, optical, and near-IRobservations over the HUDF from the UVUDF program(Teplitz et al. 2013), optical ACS HUDF program (Beck-with et al. 2016), HUDF09/HUDF12 programs (Bouwenset al. 2011; Ellis et al. 2013), and any other
HST ob-servations that have been taken over the HUDF/XDF.Illingworth et al. (2013) combined all existing optical andnear-IR observations over the HUDF (including manyarchival observations) into an especially deep reductioncalled the eXtreme Deep field (XDF). The XDF opticalreductions include all ACS and WFC3/IR data on theHUDF through 2013 and are ∼ Observations for epoch 3 of the UVUDFprogram were divided equally across the F225W, F275W,and F336W bands, with 15 orbits of time allocated toeach band. The 5 σ depths we measure for the epoch-3UVUDF data in 0 . ′′ -diameter apertures are 27.1, 27.2,and 27.8 mag, respectively. No use was made of thefirst 45 orbits of data from the UVUDF program, giventhe impact of CTE degration on those data which wereacquired without post-flash (see Teplitz et al. 2013). Parallel Fields to the Hubble Ultra Deep Field
Another valuable data set we use for our z ∼ HST . A total of 8, 12, and 13 orbits in the Y , J , and H bands, respectively, were obtainedover HUDF09-1 parallel field, while 11, 18, and 19 orbitsin the Y , J , H bands, respectively, were obtainedover HUDF09-2 parallel field. Very deep ( >
100 orbits)optical data in the V i I z bands also exist overthese two fields from the HUDF05, HUDF09, HUDF12,and other programs (Oesch et al. 2007; Bouwens et al.2011; Ellis et al. 2013). Hubble Frontier Fields Parallels
In addition to the data already utilized in Bouwens etal. (2015) and Bouwens et al. (2016) for blank-field LFresults at z = 4, 5, 6, 7, 8, and 9, we also add the sensitive https://archive.stsci.edu/prepds/uvudf/ TABLE 1Total number of sources in the z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , and z ∼ samples from this paper andOesch et al. 2018a Area z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ ) § § § § optical and near-IR observations obtained over six deepparallel fields from the HFF program (Coe et al. 2015;Lotz et al. 2017). These deep parallel fields supplementthe deep optical and near-IR observations obtained bythe HFF program over the centers of six different clus-ters (Abell 2744, MACS0416, MACS0717, MACS1149,Abell 370, and Abell S1063) and are separated from thecluster centers by ∼ HST ob-servations, we also made use of the ∼ Spitzer /IRAC observations over the parallel fields to theHFF clusters to allow for the selection of galaxies to z ∼
9. The available observations were drizzled togetherto construct sensitive mosaics of each cluster at ∼ Source Detection and Photometry
Our procedures for pursuing source detection and pho-tometry are very similar to most of our previous work(e.g., Bouwens et al. 2011, 2015). We use the SExtrac-tor software (Bertin & Arnouts 1996) to handle sourcedetection and photometry. We run the SExtractor soft-ware in dual-image mode, with the detection image takento equal the square root of χ image (Szalay et al.1999: similar to a coadded image) constructed fromthe V i I z images for our z ∼ Y J JH H images for our z ∼ J JH H images for our z ∼ JH and H images for our z ∼ z band (if the color measure-ment only includes the optical bands) or the H band(if the color measurement includes a near-infrared band).Measurements of the total magnitude are made by cor-recting the smaller-scalable aperture flux measurementsto account for the excess flux measured in the larger-scalable apertures relative to the smaller-scalable aper-tures and also for the light on the wings on the PSF(typically a ∼ z ∼ HST JH and H TABLE 2A complete list of the sources included in the z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , and z ∼ samples fromthe present selection and that of Oesch et al. 2018a * ID R.A. Dec m AB a Sample b Data Set c z phot d,e XDFB-2384848214 03:32:38.49 − − − − − − − − − − * Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regardingits form and content. a Apparent magnitude in V , I , and H band for galaxies in the z ∼ z ∼
3, and z ∼ i band for z ∼ b The mean redshift of the sample in which the source was included for the purposes of deriving LFs. c The data set from which the source was selected: 1 = HUDF/XDF, 2 = HUDF09-1, 3 = HUDF09-2, 4 = ERS, 5 = CANDELS-GS, 6= CANDELS-GN, 7 = CANDELS-UDS, 8 = CANDELS-COSMOS, 9 = CANDELS-EGS, 10 = BoRG/HIPPIES or other pure-parallelprograms, 11 = Abell2744-Par, 12 = MACS0416-Par, 13 = MACS0717-Par, 14 = MACS1149-Par, 15 = Abell S1063, and 16 = Abell 370 d Most likely redshift in the range z = 2 . § e “*” indicates that for a flat redshift prior, the EAZY photometric redshift code (Brammer et al. 2008) estimates that this source showsat least a 68% probability for having a redshift significantly lower than the nominal low-redshift limit for a sample, i.e., z < . z < . z < . z < . z < . z < . z < .
3, and z < z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
8, and z ∼
10 galaxies,respectively. probe the spectral slope of galaxies redward of theLyman-break providing us with very limited leverageto distinguish bona-fide star-forming galaxies at z ∼ z ∼ ∼ µ m and 4.5 µ m using the mophongo software(Labb´e et al. 2006, 2010a, 2010b, 2013, 2015). Deriv-ing fluxes for sources in the 3 . µ m and 4 . µ m bands ischallenging due to the broad PSF of the Spitzer /IRACdata, which causes light from neighboring sources toblend together on the images. To overcome these issues, mophongo uses the high spatial resolution
HST data tocreate template images of each source in the lower spatialresolution
Spitzer /IRAC data and then the fluxes of thesource and its neighbors is varied to obtain the best fit.The model profiles of the neighboring sources is then sub-tracted from the image, and then the flux of the sourceis measured in 1 . ′′ -diameter apertures. These fluxes arethen extrapolated to total based on the model profile ofthe source convolved with the PSF.In selecting candidate z = 2-9 galaxies, we required thecandidate galaxies in our z ∼ z ∼ z ∼
8, and z ∼ χ images used to detect sources.Sources which correspond to diffraction spikes, are theclear result of an elevated background around a brightsource (e.g., for a bright elliptical galaxy), or correspondto other artifacts in the data are removed by visual in-spection.We clean the sample by removing all bright ( H ,AB <
27) sources with SExtractor stellarity parameters in ex-cess of 0.9, i.e., star-like. SExtractor stellarity parame-ters of 0 and 1 correspond to extended and point sources,respectively. We also removed all sources with whoseSExtractor stellarity parameter is in excess of 0.6 andwhose
HST photometry is much better fit with an SEDof a low-mass star (∆ χ >
2) from the SpeX library (Burgasser et al. 2004) than with a linear combination ofgalaxy templates from EAZY (Brammer et al. 2008).
Selection of z = 2 -3 Galaxies As in our own previous searches for z ∼ z ∼ z ∼ z ∼ U V − B > ∧ (( V − z < . ∨ (( U V − B > V − z )) ∧ ( V − z < . U V − V > ∧ (( V − z < . ∨ (( U V − V > V − z )) ∧ ( V − z < . ∧ (SN( U V ) < ∧ , ∨ , and SN represents the logical AND op-eration, the logical OR operation, and signal to noisecomputed in small scalable apertures, respectively. Thefluxes of sources not detected are set to the 1 σ upperlimits on the flux in the undetected band.We then make use of the photometric redshift soft-ware EAZY (Brammer et al. 2008) to determine the red- Fig. 3.—
Shown is the approximate redshift distribution expected for sources in our selections of z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
8, and z ∼ z ∼ z ∼ z ∼
10 selection from the companion study of Oesch et al. (2018a). Theprecise redshift distribution exhibits a modest dependence on the available
HST passbands for a data set, as illustrated e.g. in Figure 4 ofBouwens et al. (2015). shift likelihood distribution for each source. Consider-ation was made of the photometry we derived in theWFC3/UVIS (UV , U ), ACS ( B , V , i , I , z ), and WFC3/IR ( Y , Y , J , JH , and H )bands. The SED templates we used were the EAZY v1.0set supplemented by SED templates from the GalaxyEvolutionary Synthesis Models (GALEV: Kotulla et al.2009). Nebular continuum and emission lines were addedto the later templates using the Anders & Fritze-v. Al-vensleben (2003) prescription, a 0 . Z ⊙ metallicity, anda rest-frame EW for H α of 1300˚A. To allow for possiblesystematics in our photometry and differences betweenthe observed and model SEDs, we assume an additional7% uncertainty in our flux measurements when derivingphotometric redshifts with EAZY.For selection, we additionally required that >
65% ofthe integrated probability in the photometric redshiftlikelihood distribution lie at > χ be less than 25 (equivalent to χ reduced . .
5) to in-clude sources where we can obtain a reasonable SED fitto the photometry. Sources where the best-fit photomet-ric redshift lie in the range z = 1 . z = 2 . z ∼ z ∼ Selection of z = 4 -8 Galaxies As in previous work (Bouwens et al. 2015), we se-lect z = 4-9 galaxies from the HFF parallel fields usingLyman-break color criteria. Sources in our z ∼ B − V > . ∧ ( I − J < . ∧ ( B − V > . . I − J ) ∧ [not in z ∼ z ∼ V − I > . ∧ ( V − I > .
32 + 1 . Y − H )) ∧ ( Y − H < . ∧ (SN( B ) < ∧ [not in z ∼ − z ∼ z ∼ I − Y > . ∧ ( Y − H < . ∧ ( I − Y > . Y − H )) ∧ ( Y − H < .
52 + 0 . J − H ) ∧ SN( B < ∧ (( χ opt ( B , V ) < ∨ ( V − Y > . ∧ [not in z ∼ χ opt is calculated as follows χ opt =Σ i SGN( f i )( f i /σ i ) where f i is the flux in band i in a consistent aperture, σ i is the uncertainty in thisflux, and SGN( f i ) is equal to 1 if f i > − f i < z ∼ Y − J > . ∧ ( Y − J > .
525 + 0 . J − H ) ∧ ( J − H < . ∧ ( χ opt, . ′′ < ∧ ( χ opt,Kron < ∧ ( χ opt, . ′′ < ∧ [not in z ∼ z ∼ χ statistic lessthan 4 (i.e., < σ detection) combining the B , V ,and I -band flux measurements in both small scalableapertures and fixed 0.35 ′′ -diameter apertures.We divide the z ∼ z ∼ z ∼ z < . z ∼ z < . < z > . z ∼ z ∼ χ statistic less Fig. 4.— ( upper ) Histogram of the HST selections considered here. ( lower ) Redshift vs. apparentmagnitudes ( blue filled circles ) for all sources in the present
HST samples (and those of Oesch et al. 2018a). The source at z ∼ . H ,AB magnitude of 25.9 mag is GN-z11 (Bouwens et al. 2010; Oesch et al. 2014, 2016). than 4 (i.e., < σ detection) combining the B and V flux measurements in small scalable apertures and fixed0.35 ′′ -diameter apertures. Selection of z ∼ Galaxies
In selecting candidate z ∼ JH observations, we make use fo the following colorcriteria to identify candidate z & Y − H ) + 2( J − JH ) > . ∧ (( Y − H ) + 2( J − JH ) > . . JH − H )) ∧ (( Y − H ) + ( Y − JH ) > ∧ ( JH − H < . ∧ ( χ opt, . ′′ < ∧ ( χ opt,Kron < ∧ ( χ opt, . ′′ < χ opt, . ′′ , χ opt,Kron , and χ opt, . ′′ , respectively,represent the “ χ ” statistic computed from the opticalfluxes in 0.35 ′′ -diameter apertures, small-scalable Kronapertures, and small 0.2 ′′ -diameter apertures (before PSF-matching the optical data to the lower resolutionnear-IR data).For the two deep parallel fields to the HUDF, HUDF09-1 and HUDF09-2, deep JH -band data are not avail-able, and so we utilize the following color criteria:(( Y − H ) + 2( J − H ) > . ∧ ( J − H < . ∧ ( χ opt, . ′′ < ∧ ( χ opt,Kron < ∧ ( χ opt, . ′′ < σ upper limits for the purposes of deriving mea-sured colors to apply the above criteria.Our z ∼ Y and J bands and the “average” flux information inthe JH and H bands to measure the size of the ap-parent break in the spectrum of candidate z ∼ χ statistic for sources in our z ∼ Y .To maximize the robustness of the sources in our se-lection, we also made use of the Spitzer /IRAC observa-tions of the z ∼ Spitzer /IRAC flux measurements in the pres-ence of source crowding, we only excluded sources if theyshowed at least a 3 σ detection both from our own pho-tometry and that from Shipley et al. (2018) and if thesource showed a H − [3 .
6] color redder than 0.7 mag.Finally, sources are required to have a best-fit photo-metric redshift calculated with EAZY between z = 8 . z = 9 . >
70% of the redshift likelihooddistribution above z ∼
7. We used the same SED tem-plate set to compute this redshift likelihood distributionas we used in § z ∼ area. While we have already provided an extensive de-scription of this selection in Bouwens et al. (2019), someadditional Y and JH imaging has become avail-able on z ∼ Y and Y -band obser-vations from those program further confirm the natureof COS910-1, EGS910-9, and EGS910-10, with estimated P ( z >
8) probabilities of 0.97, 0.75, and 1.0, respectively,and strengthen the case that EGS910-15 is at z >
8, with P ( z >
8) being 0.56.Our previous z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ Derived Samples of z ∼ -9 Galaxies Applying our selection criteria to the WFC3/UVIS +optical ACS + WFC3/IR observations over the GOODSSouth and GOODS North fields, we identify a total of5766 z ∼ z ∼ z ∼ V band is shown inFigure 2, while the surface densities of our z ∼ I , i , and i band magnitudes, respectively.These bands probe close to 1600˚A in the rest frame.For comparison, Hathi et al. (2010) identified 66 z ∼ . U V dropouts, 151 z ∼ . U V dropouts, and 256 z ∼ . U dropouts over the ∼
50 arcmin WFC3/IRERS field. Meanwhile, Oesch et al. (2010) find 60
U V ,99
U V , and 403 U dropouts over the same ERSfield. Combining the individual subsamples, Hathi et al.(2010) and Oesch et al. (2010) find 473 z ∼ z ∼ z ∼ z ∼ TABLE 3Magnification Factors Adopted for Each of the HFFParallel Fields
Field Typical Magnification Factor µ a Abell 2744-Par 1.16MACS0416-Par 1.05MACS0717-Par 1.16MACS1149-Par 1.04Abell S1063-Par 1.05Abell 370-Par 1.10 a Estimated from the version 1 lensing models of Merten (2016). (2010) and Oesch et al. (2010) cut off approximately ∼ z ∼ z ∼ ∼ ∼
26 mag,we find 876 z ∼ ∼ UVUDF data set, Mehta et al.(2017) identify 852 z ∼ z ∼ z ∼ − , is also comparable, but 29% larger, thanthe 93 galaxy arcmin − surface density we find over theHDUV fields. It is because of the combination of depthand area of the current UVUDF+UVUDF data sets, i.e., ∼ × larger areathan UVUDF+HDUV data sets relative to previousERSand UVUDF data sets alone that the present z ∼ > × larger than the previous z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
8, and z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ HST samples at z = 2-11 is 24741, 12643 of which are inthe redshift range z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
8, and z ∼ z ∼
10 selection from Oesch et al.(2018).The top panel of Figure 4 shows the total number ofthe sources per unit ∆ z ∼ .
25, while the lower panelshows the full distribution of magnitudes and redshiftsthat sources in our samples occupy. LUMINOSITY FUNCTION RESULTS
The purpose of the present section is to summarize ourprocedures for deriving the
U V
LFs at z ∼
2, 3, 4, 5, 6, 7,8, and 9. The present determinations leverage a varietyof new data sets to improve on the results obtained inOesch et al. (2010), Bouwens et al. (2015), and Bouwenset al. (2016).Given that the present analysis aims to improve on ear-lier LF analyses from Oesch et al. (2010), Bouwens et al.(2015), and Bouwens et al. (2016), our new determina-tions still incorporate constraints from earlier data sets,such as the HUDF, the two HUDF parallel fields, theWFC3/IR ERS field, the five CANDELS fields, and 220arcmin in search area from BoRG+HIPPIES utilized inBouwens et al. (2015) and Bouwens et al. (2016). Wealso include z ∼ z ∼ z ∼ z ∼ z ) − . and using the same U V color dis-tribution as Bouwens et al. (2009) and Bouwens et al.(2014). Selection volumes for our UVUDF selections arecreated in a similar way, but computing photometric red-shifts for the sources detected in the simulations andapplying our selection criteria to determine if a simu-lated source is selected or not. Since these simulationsuse similar-luminosity z ∼ z ∼ z ∼ z ∼ HST observations. Bona-fidehigh-redshift sources and low redshift contaminants werefirst identified in those data. Noise was then added tothe observations to emulate the properties of the shal-lower observations, and sources were selected from theseshallower data. The contamination rate was determinedby determining which fraction of selected sources in theshallower data were clearly at lower redshift in the deeperdata. The typical contamination fractions are estimatedto be .
5% but reach contamination fractions as high as ∼
10% in the faintest magnitude bin.In deriving constraints on the
U V
LF from a compre-hensive set of search fields, we rely on the same sam-ple of sources that Bouwens et al. (2015) utilize overall fields, while also including constraints from the newdata sets. Combining the new samples with the z ∼ Fig. 5.—
The stepwise LF constraints ( solid circles )) we deriveon the UV LFs at z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
8, and z ∼ HST ( shown in grey, blue, magenta, green, cyan, black, red,orange, and dark purple, respectively ). The recent stepwise LFconstraints at z ∼
10 from Oesch et al. (2018a) are shown withthe dark purple circles. The best-fit Schechter LFs are shown withthe grey, blue, magenta, green, cyan, black, red, orange, and darkpurple lines, respectively. z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
8, and z ∼ L of matching the binned number counts in all of our fields L = Π field Π i p ( m i ) (1)where i runs over all magnitude intervals in each of oursearch fields. For our z ∼ p ( m i ) to be p ( m i ) = (cid:18) n expected,i Σ j n expected,j (cid:19) n observed,i (2)for all sources in our z = 2-8 samples, where n expected,i and n expected,j the expected number of sources in mag-nitude intervals i and j and n observed,i is the observednumber of sources in magnitude interval i . As such, our z = 2-8 LFs are computed using the standard stepwisemaximum likelihood procedure (Efstathiou et al. 1988)to take advantage of the modest number of sources foundin each search field and overcome large-scale structureuncertainties.Given the much smaller number of sources that areavailable per search field to determine the shape of the U V
LF for our z ∼ p ( m i ) = Π j e − n expected,j ( n expected,j ) n observed,j ( n observed,j )! (3)For our stepwise LFs, we generally adopt a width of 0.5-mag for our z = 2-8 and 0.8-mag for our LFs at z = 9-10.We compute the expected number of sources in a given0 TABLE 4Stepwise Determination of the rest-frame UV LF at z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , and z ∼ using the SWML method fromthe HUDF, HFF parallel fields, and a comprehensive set of blank search fields. a M ,AB φ k (Mpc − mag − ) M ,AB φ k (Mpc − mag − ) M ,AB φ k (Mpc − mag − ) z ∼ z ∼ z ∼ − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± z ∼ − ± − ± − ± − ± − ± − ± − ± − ± z ∼ − ± − ± z ∼ − ± − ± − ± − ± − ± − ± − ± z ∼
10 galaxies − ± − ± − < − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± z ∼ z ∼ − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± a These binned stepwise LF parameters represent updates to those derived in Bouwens et al. (2015).
Fig. 6.—
68% and 95% confidence intervals on various pairs of parameters in a Schechter representation of the UV LF at z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
9, and z ∼
10. Given our relatively poor constraints on the bright end form of the z ∼ z ∼ M ∗ , no confidence intervals are presented in the left and center panels for the LF results at z ∼ z ∼
10. The z ∼ φ ∗ of the UV LF and the faint-end slope α smoothly increaseand flatten from z ∼ z ∼
2, while the characteristic luminosity M ∗ shows no substantial evolution from z ∼ z ∼ TABLE 5Determinations of the Schechter Parameters for therest-frame UV LFs at z ∼ , z ∼ , z ∼ , z ∼ , z ∼ , and z ∼ from the HUDF, HFF parallels, and a comprehensiveset of other blank search fields a Dropout φ ∗ (10 − Sample < z > M ∗ UV Mpc − ) αU − ± +0 . − . − ± U − ± +0 . − . − ± B − ± +0 . − . − ± V − ± +0 . − . − ± i − ± +0 . − . − ± z − ± +0 . − . − ± Y − ± +0 . − . − ± J − +0 . − . − ± J − +0 . − . − ± a These Schechter parameters represent updates to those derivedin Bouwens et al. (2015) and incorporate all the new search resultsindicated in Table 1. magnitude interval n expected,i as n expected,i = Σ j φ j V i,j (4)where V i,j is the effective volume over which a source ofabsolute magnitude j might be expected to be found inthe observed magnitude interval i . The effective volume V i,j is computed from extensive Monte-Carlo simulationswhere we add artificial sources of absolute magnitude j to the real observations and then quantify the fraction ofthese sources that will be both selected as part of a givenhigh-redshift samples and measured to have an apparentmagnitude i .In deriving n observed,i from our large z ∼
2, 3, 4, 5, 6, 7,8, and 9 selections, we use the measured total magnitudeof sources in the V , I , i , z , Y , J , H ,and H , respectively, since those magnitudes lie closestto rest-frame 1600˚A. For some search fields and redshiftsamples, flux measurements are not available in thesebands. For our HFF selections, magnitude measurementsin the I , Y , and Y bands, respectively, are usedfor our z ∼ z ∼
5, and z ∼ J bandare used for our z ∼ z ∼
6, and z ∼ z ∼ i band are used.In making use of the search constraints to derive LFresults, we only consider results to specific limiting mag-nitudes to avoid having the results be significantly im-pacted by uncertain completeness corrections or contam-ination rates. We adopt the same limiting magnitudes asBouwens et al. (2015), except in the cases of the new sam-ples considered here, including our z ∼ z ∼ z ∼ z ∼ U V
LF at z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼ z ∼
10 results from Oesch et al. (2018a) designed to com-plement this study.
U V
LF results are similarly derivedusing a Schechter parameterization by first fitting for theshape of the LF as in the SWML approach as in Sandageet al. (1979) and then determining the normalization φ ∗ .The best-fit Schechter results are provided in Table 5,together with the z ∼
10 results of Oesch et al. (2018a).For our z ∼ M ∗ to the value implied by the fittingformula derived in § − z ∼
10 LF constraints, we similarly fixed M ∗ to be − .
19 mag, while fitting for constraints on φ ∗ and α .Included in our best-fit LFs are the quoted stepwiseconstraints from a large variety of different ground-basedprobes including Stefanon et al. (2019), Bowler et al.(2015), and the brightest two magnitude bins in Bowleret al. (2015) where their selection of bright z ∼ z ∼ z ∼ −
23 mag from Ono et al. (2018)are included in our fits. If constraints brighter than − U V
LF fits, we find that theLF constraints are not well represented by a Schechterfunction-type form and the characteristic luminosity isdriven towards higher values.Figure 6 shows the 68% and 95% confidence intervalswe compute for various two-dimentional projections ofthe Schechter parameters. We discuss evolution in theSchechter parameters in § DISCUSSION
Comparison with Previous LF Results
There is now a quite substantial body of work on the
U V
LF at high redshift, from z ∼ z ∼ z ∼ U V
LFs against many previous determinations toquantify possible differences in the results. Given thatthe present results utilize blank-field surveys to arrive atthe LFs results, we focus on comparisons with previousblank-field determinations to keep the comparisons mostdirect.Accordingly, in Figures 7 and 8, we provide a com-prehensive set of comparisons of our new z = 2-9 LFresults from the HFFs with a variety of noteworthy pre-vious work, including Steidel et al. (1999), Bouwens et2 Fig. 7.—
Comparison of the new z = 2-5 UV LFs we derived updating and extending the redshift baseline of the Bouwens et al. (2015)and Bouwens et al. (2016: solid red circles ) results against previous blank-field LF results in the literature including those from Reddy &Steidel (2009: open blue circles ), Oesch et al. (2010: open red circles ), Mehta et al. (2017: magenta solid squares ), Parsa et al. (2016: blackopen circles ), Moutard et al. (2020: solid green squares ), Finkelstein et al. (2015: open gray circles ), van den Bosch et al. (2010: black solidsquares ), Steidel et al. (1999: blue solid squares ), Ono et al. (2018: solid green circles ), Adams et al. (2018: solid violet circles ), Stevanset al. (2018: open violet circles ), and Bouwens et al. (2007: solid blue circles ). The present determinations are in broad agreement withprevious work. No results from lensing cluster studies are included here to keep the discussion simple, but will be included in a forthcomingcompanion paper focusing on the HFF clusters. al. (2007), Reddy & Steidel (2009), Oesch et al. (2010),van der Berg et al. (2010), Bradley et al. (2012), Oesch etal. (2012), McLure et al. (2013), Bouwens et al. (2015),Bowler et al. (2015), Finkelstein et al. (2015), Bouwenset al. (2016), Parsa et al. (2016), Bouwens et al. (2016),McLeod et al. (2016), Ono et al. (2018), and Stefanon etal. (2019).We consider the redshift intervals in turn, below: z ∼ U V luminosities of ∼ L ∗ ( −
20 magto −
17 mag), most existing LF results at z ∼ z ∼ −
20, where essentially all recent studies(this study; Reddy & Steidel 2009; Oesch et al. 2010;Parsa et al. 2016; Mehta et al. 2017; Moutard et al. 2020)show approximately (modulo < z ∼ z ∼ ∼ z ∼ Fig. 8.—
Similar to Figure 7 but for our newly derived LFs at z = 6-9. Included in these comparisons are the results of Bouwens etal. (2007: solid blue circles ), Bouwens et al. (2015: solid black circles ), Ono et al. (2018: solid green circles ), Bowler et al. (2015: solidmagenta circles ), Finkelstein et al. (2015: open gray circles ), McLure et al. (2013: solid light red circles ), Bowler et al. (2017: solid magentacircles ), Oesch et al. (2012: solid gray circles ), Bradley et al. (2012: solid magenta circles ), Bridge et al. (2019: open green circle ), Bowleret al. (2020: green solid circles ), Rojas-Ruiz et al. (2020: open magenta circles ), Bouwens et al. (2019: solid black squares ), Stefanon et al.(2019: solid red squares ), Bouwens et al. (2016: open red circles ), Oesch et al. (2013: open red squares ), McLeod et al. (2016: open bluesquares ), Calvi et al. (2016: solid light red squares ), Morishita et al. (2018: open red triangle ), and Livermore et al. (2018: light red upperlimits ). results of Oesch et al. (2010), which appear to be afactor of ∼ z ∼ z ∼ . U -dropout criteriaas given in Oesch et al. (2010) and compared it to thepresent selection of z ∼ B band. Our z ∼ ∼ × more sources, i.e., 245, to the same magnitudelimit as Oesch et al. (2010) use. If the estimate of theselection volume at z ∼ z ∼ U and U bands, which in turn is sensitive to the sourcesize and surface brightness. Additionally, a differencein the mean redshift of the Oesch et al. (2010) z ∼ . z ∼ . z ∼ . z ∼ z ∼ z ∼ z ∼ z ∼ −
17 to −
16 mag, our z ∼ /V max estimator to derivethe Schechter function parameters. LF determinationsusing the 1 /V max estimator can be impacted if thesearch fields probing a particular luminosity range showa significant overdensity or underdensity of sources.In the case of the HUDF/XDF, our best-fit z ∼ ±
7% more z ∼ ∼ α ∼ − . α , consistent with theobserved differences. z ∼ z ∼ U V
LFs at z ∼ −
19 mag,where the results would be sensitive to the faintestsources in the CANDELS selections and the estimatedselection volumes, the Finkelstein et al. (2015) z ∼ z ∼ ∼ selected populationof z ∼ from CANDELS (which would tendto include only the highest surface brightness sources)for the completeness estimates, this could explain thedifferences at ∼−
19 mag. In any case, at z ∼ −
19 mag regardless of whether we rely on thesignificantly deeper HFF or CANDELS data. z ∼ z ∼ z ∼ ∼ )searches are consistent with what we derive, but extendto higher luminosities. While the Calvi et al. (2016) re-sults from the BoRG/HIPPIES pure-parallel fields are somewhat in excess of our own, this is without inclusionof the Spitzer /IRAC observations into the analysis to ex-clude lower-redshift interlopers and AGN. The Morishitaet al. (2018) analyses of the BoRG/HIPPIES fields are inmuch better agreement with our results, supporting thisconclusion. The z ∼ −
23 mag is clearly higher than the other LF deter-minations that probe this regime (Stefanon et al. 2019;Bowler et al. 2020), but is based on only a single sourceand therefore the uncertainties are large. At fainter lumi-nosities, the faint-end results from McLure et al. (2018)and McLeod et al. (2016) are also encouragingly consis-tent with the new LF results we have obtained includingall six parallel fields in the HFF program.
Evolution in α , M ∗ , and φ ∗ As in our previous comprehensive analyses of the
U V
LF at z ∼ U V
LF to examine evolution in theSchechter parameters.While the evolution in these quantities is already clearbased on previous work (e.g., Bouwens et al. 2015; Bowleret al. 2015; Finkelstein et al. 2015), the new observationsallow us to improve our previous determinations evenfurther to map out the evolutionary trends. While rec-ognizing the value of
U V
LF results that rely on lensingmagnification by galaxy clusters, we intentionally do notinclude them in the present determinations to avoid anysystematics that might result from managing uncertain-ties in the lensing models or uncertainties in the sizes ofthe lowest luminosity sources.While our primary interest here is in looking at thefaint-end slope trend, we will also look at how the othertwo Schechter parameters evolve. Based on the plottedcontours in Figure 6, the normalization φ ∗ shows a sim-ilarly smooth increase with cosmic time, while the faint-end slope α shows a smooth evolution from very steepvalues to shallower values at later points in cosmic time.As in our previous work, e.g., Bouwens et al. (2008), weassume that the evolution is linear in α and M ∗ , but willtake the evolution in log φ ∗ to be quadratic in form.To account for impact of quenching on the high star for-mation end of the main sequence (e.g., Ilbert et al. 2013;Muzzin et al. 2013), we allow for a break in the linearevolution of the U V
LF at z . .
5, fitting separately forthe transition redshift z t and linear trend at z . .
5. Infitting for the trend in the characteristic luminosity, wemake use of the Wyder et al. (2005) UV LF results at z ∼ . z ∼ . z ∼ . z ∼ M ∗ UV = ( − . ± . z < z t ( − . ± . z − z t ) , ( − . ± . z > z t ( − . ± . z − ,φ ∗ = (0 . ± . − Mpc − )10 ( − . ± . z − − . ± . z − α = ( − . ± .
03) + ( − . ± . z − Fig. 9.—
Determinations of the faint-end slope α , character-istic luminosity M ∗ , and normalization φ ∗ to the UV LF de-rived at z = 2-10 in this work and Oesch et al. (2018a: O18a)from blank-field observations alone ( solid red circles ). The plot-ted z ∼ z ∼ z ∼ .
055 is shown, an average of the z ∼ . z = 0 . z = 0 . z = 0 . z = 1 . α , M ∗ , and log φ ∗ inferred from a fit to the present LFresults. The plotted z < M ∗ from Wyder et al.(2005), Arnouts et al. (2005), and Moutard et al. (2020) are usedin deriving the best-fit relations. The present fits represent anupdate to the determinations in Parsa et al. (2016) who look atthe evolution of the LF parameters over a similar redshift baseline(see also Moutard et al. 2020, Bowler et al. 2020, and Finkelstein2016). Interestingly, the observed evolution can be remarkably wellexplained by the predicted evolution in the halo mass function anda fixed star-formation efficiency model (see § where z t = 2 . ± .
11. A comparison of the best-fittrends with the derived Schechter parameters for the
U V
LF from z ∼ z ∼
10 is presented in Figure 9.As in previous work, the faint-end slope α of the U V
LF is well described by a linear flattening in α from α ∼− . z ∼ α ∼ − .
5, at z ∼
2. Moreover, an extrapolation of ourresults to z ∼ z ∼ . z ∼ .
3, and Moutard et al. (2020) over the redshiftrange z ∼ . α with redshift we find, i.e., dα/dz = − . ± .
01 is very similar with predicted flat-tening based on the evolution in the halo mass func-tion. Bouwens et al. (2015) find that dα/dz = − . α appears tomaintain a roughly linear relationship with redshift downto z ∼
0. At first glance, this might seem surprising giventhe increasing importance of other physical processes likeAGN feedback (e.g., Scannapieco & Oh 2004; Croton etal. 2006) and the potential impact of this feedback on starformation in lower mass halos. The trends we find hereare very similar to what we reported in our earlier LFstudy (Bouwens et al. 2015), i.e., dα/dz = − . ± . dα/dz ∼ − .
11 trend Parsa etal. (2016) and Finkelstein (2016) find fitting the then-available LF constraints in the literature.The characteristic luminosity M ∗ maintains a rela-tively fixed value of − .
02 mag over the redshift range z ∼ z ∼
3. The best-fit dependence of M ∗ on red-shift is − . ± .
02 and nominally significant at 2 σ . Ashas been argued by Bouwens et al. (2009) and Reddy etal. (2010), the observed exponential cut-off at the brightend of the U V
LF likely occurs due to the impact of dustextinction in sources with the highest masses and SFRs.Galaxies with masses and SFRs higher than some criti-cal value (e.g., Spitler et al. 2014; Stefanon et al. 2017b)tend to suffer sufficient attenuation that these sourcesactually become fainter in the rest-
U V than lower mass,lower SFR sources. The critical
U V luminosity wherethe UV luminosity vs. SFR relationship transitions frombeing positively correlated to negative correlatively ap-pears to set the value of the characteristic luminosity(e.g., Bouwens et al. 2009; Reddy et al. 2010). The rela-tively minimal evolution in the characteristic luminosity M ∗ with redshift suggests that this critical SFR doesnot evolve dramatically with redshift, as Bouwens et al.(2015) illustrate with the conditional luminosity functionmodel they present in their § φ ∗ of the U V
LF increases mono-tonically with cosmic time from z ∼
10 to z ∼
2, witha steeper dependence on redshift from z ∼
10 to z ∼ z ∼ z ∼
2. We found that the depen-dence of log φ ∗ with redshift could be well describedby a second-order polynomial. The amplitude of thesecond-order term, i.e., − . ± . σ . The change in the dependence of log φ ∗ with red-shift has been previous framed as “accelerated” evolutionby Oesch et al. (2012). Analyses of subsequent observa-tions in Oesch et al. (2014), Oesch et al. (2018a), andIshigaki et al. (2018: but see also McLeod et al. 2016)provide further evidence for this result.6 Fig. 10.—
Comparison of the observational constraints presentedin Figure 9 with the predictions ( red lines ) of the simple constantstar formation efficiency model presented in Appendix I of Bouwenset al. (2015), while keeping the characteristic luminosity M ∗ fixedto the − . − . z −
6) mag parameterization derived from ourempirical fits ( § The observed evolution can fairly naturally be ex-plained, using a constant star formation efficiency model,by the evolution of the halo mass function (e.g., Bouwenset al. 2008; Tacchella et al. 2013; Bouwens et al. 2015;Mason et al. 2015; Oesch et al. 2018; Harikane et al. 2018;Tacchella et al. 2018). Oesch et al. (2018), for example,showed with such a model that one could reproduce theobserved evolution in the dust-corrected UV luminosityfrom z ∼
10 to z ∼
4. Adopting the conditional LFmodel from Bouwens et al. (2015: their Appendix I), fix- ing the characteristic luminosity M ∗ to ∼ − .
03 magpreferred from our empirical fitting formula, and fittingfor φ ∗ and α , we find a best-fit parameterization for φ ∗ of (0.00036 Mpc − ) 10 − . z − − . z − , remarkablysimilar to the coefficients we recovered in deriving theLF fitting formula from the observations. In derivingSchechter parameters from the model LF results fromBouwens et al. (2015), we minimized the square loga-rithmic difference between the condition LF predictionsand the Schechter function fits over the range −
22 to − M ∗ instead to thatfound in our fitting formula, i.e., − . − . z −
6) mag,we find a best-fit parameterization for φ ∗ of (0.00036Mpc − ) 10 − . z − − . z − . This confirms that con-stant star formation efficiency models do clearly predicta second-order dependence in the Schechter parameters,i.e., “acceleration,” vs. redshift. In Figure 10, we com-pare the predictions of this simple model with the obser-vational results, and it is striking how well the evolution-ary trends of such a model agrees with the observations.This strongly suggests that much of the evolution of the U V
LF can be explained by largely explained by the evo-lution of the halo mass function and an unevolved starformation efficiency.Given our reliance on what is currently the largest
HST sample of z = 2-10 galaxy candidates to date, our derivedevolutionary trends arguably represent the most accuratedeterminations obtained to date. SUMMARY
In this paper, we make use of a suite of new data setsto significantly expand current
HST samples of z ∼ U V
LF based on
HST data.For our z ∼ ∼
94 arcmin area at ∼ µ mand 0.34 µ m. By combining this data set with the ∼ WFC3/UVIS ERS (Windhorst et al. 2011) and ∼ UVUDF (Teplitz et al. 2013) data, we use atotal search area of ∼
150 arcmin to construct samplesof z ∼ z ∼ > × larger than thesamples of z ∼ HST in earlier determinations of the
U V
LF at z ∼ z ∼ HST optical and near-IR observations ob-tained over the six parallel fields from the Hubble Fron-tier Fields program (Lotz et al. 2017). Those observa-tions probe galaxies to
U V luminosities of ∼ L ∗ z =3 and are only exceeded by the HUDF in terms of theirsensitivity. From the six parallel fields to the HFF clus-ters, we identify 1381 z ∼
4, 448 z ∼
5, 209 z ∼
6, 122 z ∼
7, 34 z ∼
8, and 13 z ∼ > HST -basedfield samples.7All together and including the z ∼ z = 2-11 galaxiesfrom HST fields include 24741 galaxies. This is morethan twice the number of sources as the largest previoussamples of galaxies over this redshift range.We leverage the present, even larger samples of z = 2-9galaxies to construct new and improved determinationsof the U V
LFs at z ∼ z ∼
10 LF resultfrom Oesch et al. (2018a), we are in position to reassessthe evolution derived in a self-consistent way, particularlyin terms of known Schechter function parameters like thefaint-end slope α and the normalization φ ∗ of the LF.As in previous studies, we find that the faint-end slope α steepens towards high redshift at approximately a fixedrate vs. redshift (e.g., Bouwens et al. 2015; Parsa etal. 2016; Finkelstein 2016). The observed evolution ap-pears to be almost identical to what would expect, i.e., dα/dz ∼ − .
12 based on changes to the slope of the halomass function across the observed redshift range (e.g.,Bouwens et al. 2015).We find that the characteristic luminosity M ∗ remainsrelatively fixed at ∼ − .
02 mag over the redshift range z ∼ z ∼ z . . U V
LF at z & U V lumi-nosities where the increased dust extinction in galaxiesmore than offsets increases in the SFRs in galaxies. Theabsence of strong evolution in M ∗ suggests a similar lackof evolution in this transition SFR or U V luminosity.Finally, we find a systematic decrease in the normaliza- tion φ ∗ of the U V
LF towards high redshift (e.g., McLureet al. 2010; Bouwens et al. 2015). log φ ∗ can be welldescribed by quadratic relationship in redshift, with asignificantly flatter relationship at z < z >
7, consistent with the conclusions from studies fa-voring “accelerated” evolution at z > φ ∗ re-markably well (as shown in Figure 10). Similar to ourdiscussion in Bouwens et al. (2015), consistency of the U V
LF results with fixed star formation efficiency modelshas also been argued in Oesch et al. (2018) and Tacchellaet al. (2018). Again, this demonstrates that much of theevolution in the
U V
LF (from z ∼
10 to z ∼ . U V
LF at z ∼ REFERENCESAdams, N. J., Bowler, R. A. A., Jarvis, M. J., et al. 2020,MNRAS, 494, 1771Aihara, H., Arimoto, N., Armstrong, R., et al. 2018a, PASJ, 70,S4Aihara, H., Armstrong, R., Bickerton, S., et al. 2018b, PASJ, 70,S8Alavi, A., Siana, B., Richard, J., et al. 2016, ApJ, 832, 56Anderson, J., & Bedin, L. R. 2010, PASP, 122, 1035Arnouts, S., Schiminovich, D., Ilbert, O., et al. 2005, ApJ, 619,L43Atek, H., Richard, J., Kneib, J.-P., & Schaerer, D. 2018, MNRAS,479, 5184Beckwith, S. V. W., Stiavelli, M., Koekemoer, A. M., et al. 2006,AJ, 132, 1729Behroozi, P. S., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57Bertin, E. and Arnouts, S. 1996, A&AS, 117, 39Bouwens, R., Broadhurst, T. and Silk, J. 1998, ApJ, 506, 557Bouwens, R., Broadhurst, T., & Illingworth, G. 2003a, ApJ, 593,640Bouwens, R. J., Illingworth, G. D., Franx, M., et al. 2007, ApJ,670, 928Bouwens, R. J., Illingworth, G. D., Franx, M., & Ford, H. 2008,ApJ, 686, 230Bouwens, R. J., Illingworth, G. D., Franx, M., et al. 2009, ApJ,705, 936 Bouwens, R. J., Illingworth, G. D., Gonz´alez, V., et al. 2010,ApJ, 725, 1587Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2011, ApJ,737, 90Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2015, ApJ,803, 34Bouwens, R. 2015, HST Proposal, 14459Bouwens, R. J., Aravena, M., Decarli, R., et al. 2016a, ApJ, 833,72Bouwens, R. J., Oesch, P. A., Labb´e, I., et al. 2016b, ApJ, 830, 67Bouwens, R. J., Oesch, P. A., Illingworth, G. D., et al. 2017b,ApJ, 843, 129Bouwens, R. J., Stefanon, M., Oesch, P. A., et al. 2019, ApJ, 880,25Bowler, R. A. A., Dunlop, J. S., McLure, R. J., et al. 2015,MNRAS, 452, 1817Bowler, R. A. A., Jarvis, M. J., Dunlop, J. S., et al. 2020,MNRAS, 493, 2059Bradley, L. D., Trenti, M., Oesch, P. A., et al. 2012, ApJ, 760, 108Brammer, G. B., van Dokkum, P. G., & Coppi, P. 2008, ApJ,686, 1503Bridge, J. S., Holwerda, B. W., Stefanon, M., et al. 2019, ApJ,882, 42Capak, P., Aussel, H., Ajiki, M., et al. 2007, ApJS, 172, 998