GOLDRUSH - II. Clustering of galaxies at z ∼ 4–6 revealed with the half-million dropouts over the 100 deg2 area corresponding to 1 Gpc3

We present clustering properties from 579,492 Lyman break galaxies (LBGs) at z~4-6 over the 100 deg^2 sky (corresponding to a 1.4 Gpc^3 volume) identified in early data of the Hyper Suprime-Cam (HSC) Subaru strategic program survey. We derive angular correlation functions (ACFs) of the HSC LBGs with unprecedentedly high statistical accuracies at z~4-6, and compare them with the halo occupation distribution (HOD) models. We clearly identify significant ACF excesses in 10"<$\theta$<90", the transition scale between 1- and 2-halo terms, suggestive of the existence of the non-linear halo bias effect. Combining the HOD models and previous clustering measurements of faint LBGs at z~4-7, we investigate dark-matter halo mass (Mh) of the z~4-7 LBGs and its correlation with various physical properties including the star-formation rate (SFR), the stellar-to-halo mass ratio (SHMR), and the dark matter accretion rate (dotMh) over a wide-mass range of Mh/M$_\odot$=4x10^10-4x10^12. We find that the SHMR increases from z~4 to 7 by a factor of ~4 at Mh~1x10^11 M$_\odot$, while the SHMR shows no strong evolution in the similar redshift range at Mh~1x10^12 M$_\odot$. Interestingly, we identify a tight relation of SFR/dotMh-Mh showing no significant evolution beyond 0.15 dex in this wide-mass range over z~4-7. This weak evolution suggests that the SFR/dotMh-Mh relation is a fundamental relation in high-redshift galaxy formation whose star formation activities are regulated by the dark matter mass assembly. Assuming this fundamental relation, we calculate the cosmic SFR densities (SFRDs) over z=0-10 (a.k.a. Madau-Lilly plot). The cosmic SFRD evolution based on the fundamental relation agrees with the one obtained by observations, suggesting that the cosmic SFRD increase from z~10 to 4-2 (decrease from z~4-2 to 0) is mainly driven by the increase of the halo abundance (the decrease of the accretion rate).

[1]  S. White,et al.  A Universal Density Profile from Hierarchical Clustering , 1996, astro-ph/9611107.

[2]  C. Baugh,et al.  The clustering of dark matter haloes: scale-dependent bias on quasi-linear scales , 2015, 1509.06715.

[3]  O. Fèvre,et al.  Probing the galaxy–halo connection in UltraVISTA to z ∼ 2 , 2014, 1411.4983.

[4]  A. Szalay,et al.  Bias and variance of angular correlation functions , 1993 .

[5]  C. Steidel,et al.  SPECTROSCOPIC MEASUREMENTS OF THE FAR-ULTRAVIOLET DUST ATTENUATION CURVE AT z ∼ 3 , 2016, 1606.00434.

[6]  Masayuki Tanaka,et al.  PHOTOMETRIC REDSHIFT WITH BAYESIAN PRIORS ON PHYSICAL PROPERTIES OF GALAXIES , 2015, 1501.02047.

[7]  M. Brodwin,et al.  The Spitzer South Pole Telescope Deep-Field Survey: Linking galaxies and haloes at z = 1.5 , 2014, 1404.2930.

[8]  Princeton University.,et al.  A COMPREHENSIVE ANALYSIS OF UNCERTAINTIES AFFECTING THE STELLAR MASS–HALO MASS RELATION FOR 0 < z < 4 , 2010, 1001.0015.

[9]  H. Rix,et al.  THE LARGE APEX BOLOMETER CAMERA SURVEY OF THE EXTENDED CHANDRA DEEP FIELD SOUTH , 2009, 0910.2821.

[10]  R. Bouwens,et al.  UV-CONTINUUM SLOPES OF >4000 z ∼ 4–8 GALAXIES FROM THE HUDF/XDF, HUDF09, ERS, CANDELS-SOUTH, AND CANDELS-NORTH FIELDS , 2013, 1306.2950.

[11]  G. Chabrier.  Galactic Stellar and Substellar Initial Mass Function , 2003, astro-ph/0304382.

[12]  Timothy M. Heckman,et al.  Dust Absorption and the Ultraviolet Luminosity Density at z ≈ 3 as Calibrated by Local Starburst Galaxies , 1999, astro-ph/9903054.

[13]  Mauro Giavalisco,et al.  Lyman-Break Galaxies , 2002 .

[14]  R. Davé,et al.  THE LBT BOÖTES FIELD SURVEY. I. THE REST-FRAME ULTRAVIOLET AND NEAR-INFRARED LUMINOSITY FUNCTIONS AND CLUSTERING OF BRIGHT LYMAN BREAK GALAXIES AT Z ∼ 3 , 2013, 1307.4835.

[15]  Satoshi Miyazaki,et al.  The on-site quality-assurance system for Hyper Suprime-Cam: OSQAH , 2018 .

[16]  Yen-Ting Lin,et al.  GOLDRUSH. III. A systematic search for protoclusters at z ∼ 4 based on the >100 deg2 area , 2017, 1708.09421.

[17]  M. Pettini,et al.  The Spatial Clustering of Star-forming Galaxies at Redshifts 1.4 ≲ z ≲ 3.5 , 2004, astro-ph/0410165.

[18]  T. Nagao,et al.  Systematic Identification of LAEs for Visible Exploration and Reionization Research Using Subaru HSC (SILVERRUSH). I. Program strategy and clustering properties of ∼2000 Lyα emitters at z = 6–7 over the 0.3–0.5 Gpc2 survey area , 2017, 1704.07455.

[19]  AMAZE - I. The evolution of the mass–metallicity relation at z $>$ 3 , 2008, 0806.2410.

[20]  V. Springel,et al.  Introducing the Illustris Project: the evolution of galaxy populations across cosmic time , 2014, 1405.3749.

[21]  Philip J. Tait,et al.  Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs). II. Discovery of 32 quasars and luminous galaxies at 5.7 < z ≤ 6.8 , 2017, 1704.05854.

[22]  C. Steidel,et al.  A STEEP FAINT-END SLOPE OF THE UV LUMINOSITY FUNCTION AT z ∼ 2–3: IMPLICATIONS FOR THE GLOBAL STELLAR MASS DENSITY AND STAR FORMATION IN LOW-MASS HALOS , 2008, 0810.2788.

[23]  D. L. Clements,et al.  The Canada-United Kingdom Deep Submillimeter Survey. V. The submillimeter properties of Lyman break galaxies , 2002 .

[24]  E. Salpeter.  The Luminosity function and stellar evolution , 1955 .

[25]  J. Gunn,et al.  THE PROPAGATION OF UNCERTAINTIES IN STELLAR POPULATION SYNTHESIS MODELING. II. THE CHALLENGE OF COMPARING GALAXY EVOLUTION MODELS TO OBSERVATIONS , 2009, 0904.0002.

[26]  V. Springel,et al.  Introducing the Illustris Project: simulating the coevolution of dark and visible matter in the Universe , 2014, 1405.2921.

[27]  K. Nagamine,et al.  MOLECULAR HYDROGEN REGULATED STAR FORMATION IN COSMOLOGICAL SMOOTHED PARTICLE HYDRODYNAMICS SIMULATIONS , 2013, 1301.0063.

[28]  Satoshi Miyazaki,et al.  Characterization and Photometric Performance of the Hyper Suprime-Cam Software Pipeline , 2017, 1705.01599.

[29]  B. Garilli,et al.  The VIMOS Ultra Deep Survey. Luminosity and stellar mass dependence of galaxy clustering at z 3 , 2017, 1703.02049.

[30]  J. Falcón-Barroso,et al.  Secular Evolution of Galaxies , 2013 .

[31]  P. Schneider,et al.  Why your model parameter confidences might be too optimistic - unbiased estimation of the inverse covariance matrix , 2006, astro-ph/0608064.

[32]  A. Benson,et al.  THE DWARFS BEYOND: THE STELLAR-TO-HALO MASS RELATION FOR A NEW SAMPLE OF INTERMEDIATE REDSHIFT LOW-MASS GALAXIES , 2013, 1310.1079.

[33]  H. Umemura.  Ultraviolet‐background‐induced bifurcation of galactic morphology , 2000, astro-ph/0006007.

[34]  Masayuki Tanaka,et al.  SILVERRUSH. III. Deep Optical and Near-Infrared Spectroscopy for Lya and UV-Nebular Lines of Bright Lya Emitters at z=6-7 , 2017, 1705.00733.

[35]  Yu Feng,et al.  The clustering of z > 7 galaxies: predictions from the BLUETIDES simulation , 2017, 1707.02312.

[36]  M. Jarvis,et al.  The environment and host haloes of the brightest z~6 Lyman-break galaxies , 2017, 1702.03309.

[37]  M.Vaccari,et al.  The galaxy–halo connection in the VIDEO survey at 0.5 < z < 1.7 , 2015, 1511.05476.

[38]  N. Kashikawa,et al.  The very wide-field gzK Galaxy Survey – II. The relationship between star-forming galaxies at z ∼ 2 and their host haloes based upon HOD modelling , 2016, 1602.01845.

[39]  S. Furlanetto,et al.  Constraints on the star formation efficiency of galaxies during the epoch of reionization , 2015, 1512.06219.

[40]  H. Trac,et al.  SCORCH. I. THE GALAXY–HALO CONNECTION IN THE FIRST BILLION YEARS , 2015, 1507.02685.

[41]  S. White,et al.  Galactic star formation and accretion histories from matching galaxies to dark matter haloes , 2012, 1205.5807.

[42]  L. Waerbeke,et al.  CARS: the CFHTLS-Archive-Research Survey - II. Weighing dark matter halos of Lyman-break galaxies at z = 3–5 , 2009, 0903.3951.

[43]  M. Dickinson,et al.  Cosmic Star-Formation History , 1996, 1403.0007.

[44]  T. Okamoto,et al.  Reproducing cosmic evolution of galaxy population from z = 4 to 0 , 2014, 1404.7579.

[45]  Michael S. Warren,et al.  Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality , 2008, 0803.2706.

[46]  Yen-Ting Lin,et al.  Second data release of the Hyper Suprime-Cam Subaru Strategic Program , 2019, Publications of the Astronomical Society of Japan.

[47]  A. Fontana,et al.  THE EVOLUTION OF THE GALAXY STELLAR MASS FUNCTION AT z = 4–8: A STEEPENING LOW-MASS-END SLOPE WITH INCREASING REDSHIFT , 2015, 1507.05636.

[48]  S. White,et al.  The Structure of cold dark matter halos , 1995, astro-ph/9508025.

[49]  G. Bruzual,et al.  Stellar population synthesis at the resolution of 2003 , 2003, astro-ph/0309134.

[50]  Eduardo Serrano,et al.  LSST: From Science Drivers to Reference Design and Anticipated Data Products , 2008, The Astrophysical Journal.

[51]  STAR FORMATION IN GALAXIES ALONG THE HUBBLE SEQUENCE , 1998, astro-ph/9807187.

[52]  J. Gunn,et al.  THE PROPAGATION OF UNCERTAINTIES IN STELLAR POPULATION SYNTHESIS MODELING. III. MODEL CALIBRATION, COMPARISON, AND EVALUATION , 2009, 0911.3151.

[53]  Masami Ouchi,et al.  MORPHOLOGIES OF ∼190,000 GALAXIES AT z = 0–10 REVEALED WITH HST LEGACY DATA. II. EVOLUTION OF CLUMPY GALAXIES , 2015, 1511.07054.

[54]  Philip J. Tait,et al.  SUBARU HIGH-z EXPLORATION OF LOW-LUMINOSITY QUASARS (SHELLQs). I. DISCOVERY OF 15 QUASARS AND BRIGHT GALAXIES AT 5.7 < z < 6.9 , 2016, 1603.02281.

[55]  A. Kinney,et al.  The Dust Content and Opacity of Actively Star-forming Galaxies , 1999, astro-ph/9911459.

[56]  R. Davé,et al.  Galaxies in a simulated ΛCDM universe – II. Observable properties and constraints on feedback , 2009, 0901.1880.

[57]  R. Somerville,et al.  Star formation in semi-analytic galaxy formation models with multiphase gas , 2015, 1503.00755.

[58]  R. Wechsler,et al.  THE RELATION BETWEEN STAR FORMATION RATE AND STELLAR MASS FOR GALAXIES AT 3.5 ⩽ z ⩽ 6.5 IN CANDELS , 2014, 1407.6012.

[59]  S. Faber,et al.  Constraining the galaxy–halo connection over the last 13.3 Gyr: star formation histories, galaxy mergers and structural properties , 2017, 1703.04542.

[60]  Song Huang,et al.  The Hyper Suprime-Cam Software Pipeline , 2017, 1705.06766.

[61]  H. Ferguson,et al.  The Large-Scale and Small-Scale Clustering of Lyman Break Galaxies at 3.5 ⩽ z ⩽ 5.5 from the GOODS Survey , 2005, astro-ph/0508090.

[62]  M. Franx,et al.  UV LUMINOSITY FUNCTIONS AT REDSHIFTS z ∼ 4 TO z ∼ 10: 10,000 GALAXIES FROM HST LEGACY FIELDS , 2014, 1403.4295.

[63]  T. Budavari,et al.  The GALEX-VVDS Measurement of the Evolution of the Far-Ultraviolet Luminosity Density and the Cosmic Star Formation Rate , 2004, astro-ph/0411424.

[64]  B. Reid,et al.  CONSTRAINING THE LUMINOUS RED GALAXY HALO OCCUPATION DISTRIBUTION USING COUNTS-IN-CYLINDERS , 2008, 0809.4505.

[65]  J. Silk,et al.  Galaxy formation and Hubble sequence , 1993 .

[66]  Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies , 2004, astro-ph/0408564.

[67]  D. Schlegel,et al.  Maps of Dust IR Emission for Use in Estimation of Reddening and CMBR Foregrounds , 1997, astro-ph/9710327.

[68]  Properties of host haloes of Lyman-break galaxies and Lyman α emitters from their number densities and angular clustering , 2003, astro-ph/0307207.

[69]  B. Guiderdoni,et al.  The UV, Lyman α, and dark matter halo properties of high-redshift galaxies , 2015, 1503.06635.

[70]  M. Pettini,et al.  Rest-Frame Ultraviolet Spectra of z ∼ 3 Lyman Break Galaxies , 2003, astro-ph/0301230.

[71]  Supercomputing,et al.  Dark-ages reionization and galaxy formation simulation–XI. Clustering and halo masses of high redshift galaxies , 2017, 1703.05419.

[72]  J. B. Oke,et al.  Secondary standard stars for absolute spectrophotometry , 1983 .

[73]  B. Lundgren,et al.  GALAXY CLUSTERING IN THE NEWFIRM MEDIUM BAND SURVEY: THE RELATIONSHIP BETWEEN STELLAR MASS AND DARK MATTER HALO MASS AT 1 < z < 2 , 2010, 1012.1317.

[74]  Masami Ouchi,et al.  MORPHOLOGIES OF ∼190,000 GALAXIES AT z = 0–10 REVEALED WITH HST LEGACY DATA. I. SIZE EVOLUTION , 2015, 1503.07481.

[75]  Satoshi Miyazaki,et al.  The bright-star masks for the HSC-SSP survey , 2017, 1705.00622.

[76]  Walter A. Siegmund,et al.  The Second Data Release of the Sloan Digital Sky Survey , 2004 .

[77]  D. Schlegel,et al.  Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds , 1998 .

[78]  J. Dunlop,et al.  The galaxy UV luminosity function at z≃ 2–4; new results on faint-end slope and the evolution of luminosity density , 2015, 1507.05629.

[79]  M. Boylan-Kolchin,et al.  The merger rates and mass assembly histories of dark matter haloes in the two Millennium simulations , 2010, 1001.2304.

[80]  M. Dickinson,et al.  Spectroscopic Confirmation of a Population of Normal Star-forming Galaxies at Redshifts z > 3* , 1996 .

[81]  H. Ferguson,et al.  AN INCREASING STELLAR BARYON FRACTION IN BRIGHT GALAXIES AT HIGH REDSHIFT , 2015, 1504.00005.

[82]  E. Bertin,et al.  SExtractor: Software for source extraction , 1996 .

[83]  S. M. Fall,et al.  The Morphological Diversities among Star-forming Galaxies at High Redshifts in the Great Observatories Origins Deep Survey , 2006, astro-ph/0606696.

[84]  R. Teyssier,et al.  Cold streams in early massive hot haloes as the main mode of galaxy formation , 2008, Nature.

[85]  S. More,et al.  EVOLUTION OF STELLAR-TO-HALO MASS RATIO AT z = 0–7 IDENTIFIED BY CLUSTERING ANALYSIS WITH THE HUBBLE LEGACY IMAGING AND EARLY SUBARU/HYPER SUPRIME-CAM SURVEY DATA , 2015, 1511.07873.

[86]  J. Brownstein,et al.  The Correlation between Halo Mass and Stellar Mass for the Most Massive Galaxies in the Universe , 2016, 1607.04678.

[87]  Lihwai Lin,et al.  Evolution of Galactic Outflows at Revealed with SDSS, DEEP2, and Keck Spectra , 2017, 1703.01885.

[88]  R. Wechsler,et al.  Modeling Luminosity-dependent Galaxy Clustering through Cosmic Time , 2005, astro-ph/0512234.

[89]  D. Erb,et al.  GALACTIC OUTFLOWS IN ABSORPTION AND EMISSION: NEAR-ULTRAVIOLET SPECTROSCOPY OF GALAXIES AT 1 < z < 2 , 2012, 1209.4903.

[90]  P. W. Wang,et al.  The VIMOS Ultra-Deep Survey: ~10 000 galaxies with spectroscopic redshifts to study galaxy assembly at early epochs 2 < z ≃ 6 , 2014, 1403.3938.

[91]  Rotation curve decomposition for size–mass relations of bulge, disk, and dark halo components in spiral galaxies , 2015, 1510.05752.

[92]  Phillip James Edwin Peebles,et al.  Statistical analysis of catalogs of extragalactic objects. VII. Two- and three-point correlation functions for the high-resolution Shane-Wirtanen catalog of galaxies , 1977 .

[93]  To Appear in the Astrophysical Journal Letters Preprint typeset using L ATEX style emulateapj v. 6/22/04 DEFINITIVE IDENTIFICATION OF THE TRANSITION BETWEEN SMALL- TO LARGE-SCALE CLUSTERING FOR LYMAN BREAK GALAXIES 1 , 2005 .

[94]  C. Conselice,et al.  The SCUBA-2 Cosmology Legacy Survey: Multi-wavelength Properties of ALMA-identified Submillimeter Galaxies in UKIDSS UDS , 2016, 1611.03084.

[95]  E. Quataert,et al.  On the Maximum Luminosity of Galaxies and Their Central Black Holes: Feedback from Momentum-driven Winds , 2004, astro-ph/0406070.

[96]  B. Garilli,et al.  The galaxy-halo connection from a joint lensing, clustering and abundance analysis in the CFHTLenS/VIPERS field , 2015, 1502.02867.

[97]  P. Peebles,et al.  The Large-Scale Structure of the Universe , 1980 .

[98]  Case Western Reserve University,et al.  Galaxy evolution from halo occupation distribution modeling of deep2 and sdss galaxy clustering , 2007, astro-ph/0703457.

[99]  Risa H. Wechsler,et al.  ON THE LACK OF EVOLUTION IN GALAXY STAR FORMATION EFFICIENCY , 2012, 1209.3013.

[100]  M. Giavalisco,et al.  The Rest-Frame Optical Properties of z ≃ 3 Galaxies , 2001, astro-ph/0107324.

[101]  K. Subramanian,et al.  Spatial Clustering of High Redshift Lyman Break Galaxies , 2012, 1208.2097.

[102]  H. F. Erguson,et al.  THE MORPHOLOGICAL DIVERSITIES AMONG STAR-FORMING GALAXIES AT HIGH REDSHIFTS IN THE GREAT OBSERVATORIES ORIGINS DEEP SURVEY , 2008 .

[103]  C. Steidel,et al.  Accepted for publication in ApJ Preprint typeset using L ATEX style emulateapj v. 12/14/05 Hα OBSERVATIONS OF A LARGE SAMPLE OF GALAXIES AT z ∼ 2: IMPLICATIONS FOR STAR FORMATION IN HIGH REDSHIFT GALAXIES 1 , 2006 .

[104]  Tristan L. Smith,et al.  NEW CONSTRAINTS ON THE EVOLUTION OF THE STELLAR-TO-DARK MATTER CONNECTION: A COMBINED ANALYSIS OF GALAXY–GALAXY LENSING, CLUSTERING, AND STELLAR MASS FUNCTIONS FROM z = 0.2 to z = 1 , 2011, 1104.0928.

[105]  S. More,et al.  Satellite kinematics – III. Halo masses of central galaxies in SDSS , 2010, 1003.3203.

[106]  A. K. Inoue,et al.  The Hyper Suprime-Cam SSP Survey: Overview and Survey Design , 2017, 1704.05858.

[107]  C. Steidel,et al.  THE HALO MASSES AND GALAXY ENVIRONMENTS OF HYPERLUMINOUS QSOs AT z ≃ 2.7 IN THE KECK BARYONIC STRUCTURE SURVEY , 2012, 1204.3636.

[108]  S. Kay,et al.  Dark matter halo concentrations in the Wilkinson Microwave Anisotropy Probe year 5 cosmology , 2008, 0804.2486.

[109]  M. Rees,et al.  Cooling, dynamics and fragmentation of massive gas clouds: clues to the masses and radii of galaxies and clusters , 1977 .

[110]  P. A. Price,et al.  THE PAN-STARRS 1 PHOTOMETRIC REFERENCE LADDER, RELEASE 12.01 , 2013, 1303.3634.

[111]  T. Grav,et al.  PHOTOMETRIC CALIBRATION OF THE FIRST 1.5 YEARS OF THE PAN-STARRS1 SURVEY , 2012, 1201.2208.

[112]  R. J. Wainscoat,et al.  THE Pan-STARRS1 PHOTOMETRIC SYSTEM , 2012, 1203.0297.

[113]  Michael S. Warren,et al.  THE LARGE-SCALE BIAS OF DARK MATTER HALOS: NUMERICAL CALIBRATION AND MODEL TESTS , 2010, 1001.3162.

[114]  Shannon G. Patel,et al.  3D-HST WFC3-SELECTED PHOTOMETRIC CATALOGS IN THE FIVE CANDELS/3D-HST FIELDS: PHOTOMETRY, PHOTOMETRIC REDSHIFTS, AND STELLAR MASSES , 2014, 1403.3689.

[115]  R. Bouwens,et al.  MEASUREMENT OF GALAXY CLUSTERING AT z ∼ 7.2 AND THE EVOLUTION OF GALAXY BIAS FROM 3.8 < z < 8 IN THE XDF, GOODS-S, AND GOODS-N , 2014, 1407.7316.

[116]  J. Tinker,et al.  THE CONNECTION BETWEEN GALAXIES AND DARK MATTER STRUCTURES IN THE LOCAL UNIVERSE , 2012, 1207.2160.

[117]  T. Treu,et al.  THE GALAXY UV LUMINOSITY FUNCTION BEFORE THE EPOCH OF REIONIZATION , 2015, Proceedings of the International Astronomical Union.

[118]  O. Fèvre,et al.  THE COSMOS2015 CATALOG: EXPLORING THE 1 < z < 6 UNIVERSE WITH HALF A MILLION GALAXIES , 2016, 1604.02350.

[119]  R. Bouwens,et al.  The Rest-frame Optical (900 nm) Galaxy Luminosity Function at z ∼ 4–7: Abundance Matching Points to Limited Evolution in the MSTAR/MHALO Ratio at z ≥ 4 , 2016, 1611.09354.

[120]  C. A. Oxborrow,et al.  Planck2015 results , 2015, Astronomy &amp; Astrophysics.

[121]  Y. Mellier,et al.  Galaxy clustering in the CFHTLS-Wide: the changing relationship between galaxies and haloes since z ~ 1.2 , 2011, 1107.0616.

[122]  Masayuki Tanaka,et al.  SILVERRUSH. II. First Catalogs and Properties of ~2,000 Lya Emitters and Blobs at z~6-7 Identified over the 14-21 deg2 Sky , 2017, 1704.08140.

[123]  Yukiko Kamata,et al.  Hyper Suprime-Cam: Camera dewar design , 2018 .

[124]  J. Anthony Tyson,et al.  Toward Precision LSST Weak-Lensing Measurement. I. Impacts of Atmospheric Turbulence and Optical Aberration , 2010, 1011.1913.

[125]  Potsdam,et al.  The Dark Side of the Halo Occupation Distribution , 2003, astro-ph/0308519.

[126]  J. Peacock,et al.  Stable clustering, the halo model and non-linear cosmological power spectra , 2002, astro-ph/0207664.

[127]  C. Baugh,et al.  The clustering and halo occupation distribution of Lyman-break galaxies at z ˜ 4. , 2015, 1511.01983.

[128]  C. Frenk,et al.  The clustering of the first galaxy haloes , 2008, 0804.0004.

[129]  Masayuki Tanaka,et al.  The Galaxy–Halo Connection in High-redshift Universe: Details and Evolution of Stellar-to-halo Mass Ratios of Lyman Break Galaxies on CFHTLS Deep Fields , 2016, 1612.06869.

[130]  L. Infante,et al.  The VLT LBG Redshift Survey - III. The clustering and dynamics of Lyman-break galaxies at z ~ 3 , 2012, 1204.3635.

[131]  Craig Loomis,et al.  Hyper Suprime-Cam , 2012, Other Conferences.

[132]  R. Wechsler,et al.  THE AVERAGE STAR FORMATION HISTORIES OF GALAXIES IN DARK MATTER HALOS FROM z = 0–8 , 2012, 1207.6105.

[133]  Piero Madau,et al.  Radiative transfer in a clumpy universe: The colors of high-redshift galaxies , 1995 .

[134]  Mohammad Akhlaghi,et al.  Great Optically Luminous Dropout Research Using Subaru HSC (GOLDRUSH). I. UV Luminosity Functions at $z \sim 4-7$ Derived with the Half-Million Dropouts on the 100 deg$^2$ Sky , 2017, 1704.06004.

[135]  T. Nagao,et al.  SILVERRUSH. IV. Lyα luminosity functions at z = 5.7 and 6.6 studied with ∼1300 Lyα emitters on the 14–21 deg2 sky , 2017, 1705.01222.

[136]  O. Fèvre,et al.  The FMOS-COSMOS Survey of Star-forming Galaxies at Z ∼ 1.6. V: Properties of Dark Matter Halos Containing Hα Emitting Galaxies , 2017, 1703.08326.

[137]  M. Dopita,et al.  Cooling functions for low-density astrophysical plasmas , 1993 .

[138]  C. Baugh,et al.  Understanding the non-linear clustering of high-redshift galaxies. , 2017, 1702.00853.

[139]  Yu Feng,et al.  Forecasts for the WFIRST High Latitude Survey using the BlueTides simulation , 2016, 1605.05670.

[140]  Andrew P. Hearin,et al.  Connecting massive galaxies to dark matter haloes in BOSS - I. Is galaxy colour a stochastic process in high-mass haloes? , 2015, 1509.00482.

[141]  Masayuki Umemura,et al.  Formation of Dwarf Galaxies during the Cosmic Reionization , 2003 .