arXiv:2105.02248v1 [astro-ph.GA] 5 May 2021 [email protected] orsodn uhr ogogShi Dongdong author: Corresponding es tutrsi h al nvre h intersec- The ( “protoclusters” universe. over- host filaments early such sheet-like of the tions or in filamentary structures dense large-scale oc- along preferentially formation for- curs galaxy structure that of predict theories mation (ΛCDM), constant mological yee sn L using 2021 Typeset 7, May version Draft nacl akmte nvredmntdb cos- a by dominated universe matter dark cold a In pcrsoi ofimto ftoEteeyMsieProtoc Massive Extremely two of Confirmation Spectroscopic ogDn Shi Dong Dong M a tal. et Cai ulyeov noteCm-yeglx lseso vnlre.Tog larger. even or clusters galaxy substructure Coma-type the dense into the evolve that tually suggest results Our respectively. OS52fiaet epciey hyaetems vres ga overdense most the are They respectively. filament, BOSS1542 h cl f1 Mcae22 are cMpc 15 of scale the z esitsae ieymrigt omalre ytm ncontrast In 247 of system. dispersion velocity larger BOSS124 low a of a form region with to structure SW filamentary merging the likely that space, find redshift we Interestingly, respectively. rdt aeat date to ered ietcnraino ag-cl omcwbi h al Universe early the in web cosmic large-scale a of confirmation direct a Keywords: extremely the trace to BO used in be pair can quasar pairs Universe. one quasar BOSS1441, these in formation in pairs the detected quasar in two stages are assembly there different more, in are they that indicating OS24adBS14,tae ygop fChrnl Strong Coherently of groups by traced BOSS1542, and BOSS1244 I SS I)adietfida vreste fnarrowband-sele of overdensities fr quasars as of identified number and a of III) spectra (SDSS absorption III the in imprinted tems ot-et(W opnn at component (SW) South-West a M/MR n B/UIna-nrrd(I)setocp,w spectroscopy, ( (NIR) BOSS1244 near-infrared the LBT/LUCI and MMT/MMIRS 1 upeMuti bevtr,CieeAaeyo Sciences, of Academy Chinese Observatory, Mountain Purple 2 = epeetsetocpccnraino w e asv aayp galaxy massive new two of confirmation spectroscopic present We SW 2 4 colo srnm n pc cecs nvriyo Scien of University Sciences, Space and Astronomy of School eateto srnm n snhaCne o Astrophysi for Center Tsinghua and Astronomy of Department . (1 = 246 A 3 T 1. twr bevtr,Uiest fAioa 3 ot Cher North 933 Arizona, of University Observatory, Steward E ± ( . X 59 2017a e:hg-esit—glxe:eouin—Lresaesrcueof structure Large-scale — evolution galaxies: galaxies: — — BOSS1542) high-redshift and ies: (BOSS1244 individual clusters: galaxies: , ,2 3 2, 1, INTRODUCTION 0 twocolumn ± . 0 ihteln-fsgtvlct iprin f405 of dispersions velocity line-of-sight the with 001 0 > z ∼ . hn Cai, Zheng ,teeeteeymsieoedniisat overdensities massive extremely these ), 20) 5arcmin 55 .Teessesaeepce obcm iilzdat virialized become to expected are systems These 2. × 10 tl nAASTeX63 in style 15 . M 9 4 2 ± ⊙ n OS52( BOSS1542 and ) iou Fan, Xiaohui 4 , . M ,10 9, NE a Albada van z . (0 = 9 2 = ± 2 . . 83 . ,ad20 and 5, 3 230 ABSTRACT inZogZheng, Zhong Xian ± 0 z ± ∼ . 11) 2 = 0 1arcmin 61 . 0 n nte ot-at(E opnn at component (NE) North-East another and 002 . × . 5 24 ± 10 1961 n hi rwhi h al nvrei ceeae in accelerated is universe early the (SFRs), in Rates growth Formation their Star and mas- specific more lower be with to universe. sive, appear early environments the dense in in evolution Galaxies and formation dependence galaxy environment of the and environments properties dense galaxy in study to laboratories ideal provide ters 2000 vleit iaie asv aaycutr tthe at clusters galaxy (e.g., massive epoch present viralized into evolve 0Ya u od ajn,Jagu202,China 210023, Jiangsu Nanjing, Road, Hua Yuan 10 3 eadTcnlg fCia ee 306 China 230026, Hefei China, of Technology and ce 15 . o h OS24S,BS14 E and NE, BOSS1244 SW, BOSS1244 the for 9 s snhaUiest,Biig108,China 100084, Beijing University, Tsinghua cs, M ± ; ; 2 ebe 1970 Peebles ude ta.2015 al. et Muldrew ⊙ z 2k s km 32 ed,rsetvl.BS14 displays BOSS1244 respectively. fields, ) fBS14 n OS52wl even- will BOSS1542 and BOSS1244 of s yAeu,Tco,A 52,USA 85721, AZ Tucson, Avenue, ry 2 = and ,2 1, utr OS24adBS14 at BOSS1542 and BOSS1244 lusters asv ag-cl tutrso the of structures large-scale massive aypoolses( protoclusters laxy − M ± tdH cted u-snHuang, Yun-Hsin te ihBS14 ecie in described BOSS1441 with ether OS52ehbt nextended an exhibits BOSS1542 , − mteSonDgtlSySurvey Sky Digital Sloan the om feryglx lses Further- clusters. galaxy early of xii ieetmorphologies, different exhibit 3 filament 1 0 ms km 202 S24adBS14,CoSLAs BOSS1542, and SS1244 otistosbtutrsin substructures two contains 4 h aayoverdensities galaxy The . Ly oolsesat rotoclusters ofim4 n 6HE in HAEs 36 and 46 confirm e at α ; z α uye edvc 1972 Zeldovich & Sunyaev z 2 = bopin(oL)sys- (CoSLA) Absorption ode l 1996 al. et Bond (1 = mtes(As.Using (HAEs). emitters ∼ − h universe the 1 . ihattlms of mass total a with 0 241 ; n 377 and . 42 omto galax- — formation vrir2016 Overzier ± ± 3 δ 0 z 0 g n icunXu Jiachuan and . . 0,providing 001, 18) 2 = > ± 0 discov- 20) × . 9k s km 99 24 ; 10 e Ostriker & Cen ± 15 .Protoclus- ). δ 0 M g . − 02, on ⊙ 1 , , ,which ), 3 2 Shi et al. the sense that protocluster galaxies formed most of their Cai et al. (2016) demonstrated that the extremely stars earlier than field galaxies (Hatch et al. 2011). massive overdensities at z =2 3 traced by groups of Co- − Present-day massive galaxy clusters are dominated herently Strong intergalactic Lyα absorption (CoSLA). by spheroidal galaxies with low star formation activ- This approach utilizes the largest library of quasar spec- ities while those in the general fields are mostly still tra, such as those from the SDSS-III Baryon Oscilla- actively forming stars (Skibba et al. 2009; Collins et al. tions Spectroscopic Survey (BOSS), to locate extremely 2009; Santos et al. 2014, 2015). These galaxy clus- rare, strong H I absorption from the IGM and select ters are key to tracing the formation of the most mas- candidates for the most massive protoclusters (e.g., sive dark matter halos, galaxies and supermassive black Liang et al. 2021). Cai et al. (2016) used cosmological holes (SMBHs) (Springel et al. 2005). Cluster galaxies simulations to show that the correlation between IGM show a tight “red sequence” and obey the “morphology- Lyα optical depth and matter overdensities peaks on density” relation, indicating the impact of dense en- the scale of 10 30 h−1 comoving Mpc (cMpc), finding − vironments on the star formation activities of the in- that the strongest IGM Lyα absorption systems trace habitants (Visvanathan & Sandage 1977; Dressler 1980; 4σ extreme tail of mass overdensities on 15 h−1 cMpc Bower et al. 1992; Goto et al. 2003). To understand the (Lee et al. 2018; Mukae et al. 2020). This technique physical processes that drive both the mass build-up in is referred as MApping the Most Massive Overden- galaxies and the quenching of star formation, we need sity Through Hydrogen (MAMMOTH). Using MAM- to investigate galaxies and their surrounding gas within MOTH technique, the massive BOSS1441 overdensity and around the precursors of present-day massive galaxy at z =2.32 0.02 is selected from the early data release ± clusters protoclusters at z > 2. The transition period of SDSS-III BOSS. The LAE overdensity in BOSS1441 − before protocluster member galaxies began to quench is 10.8 2.6 on a 15 cMpc scale, which could collapse ± 15 and evolved to the massive clusters currently observed is to a massive cluster with 10 M⊙ at the present ≥ a crucial phase to study their physical properties and the day (Cai et al. 2017a). Furthermore, an ultra-luminous mechanisms driving their evolution (Kartaltepe et al. Enormous Lyα nebulae (also known as MAMMOTH-1) 2019). with a size of 442kpc at z = 2.32 is discovered at ∼ In the last decades, protoclusters at z > 2 have the density peak of BOSS1441 (Cai et al. 2017b), which been successfully discovered and several techniques is used to trace the densest and most active regions for tracing the overdense regions have been de- of galaxy and cluster formation (e.g., Cantalupo et al. veloped. These include performing “blind” deep 2014; Arrigoni Battaia et al. 2015; Borisova et al. 2016; surveys (of Hα emitters (HAEs), Lyα emitters Cai et al. 2018, 2019). (LAEs), Lyman break galaxies (LBGs) and photo- Two more CoSLA candidates selected using the z selected galaxies) (Steidel et al. 1998, 2000, 2003; MAMMOTH technique, BOSS1244 and BOSS1542, Shimasaku et al. 2003; Steidel et al. 2005; Ouchi et al. have been confirmed to be extremely massive overdensi- 2005; Toshikawa et al. 2012; Chiang et al. 2014; ties within 20 h−1 cMpc at z =2.24 0.02 using the Hα ± Le F`evre et al. 2015; Planck Collaboration et al. 2015; Emitter (HAE) candidates identified from near-infrared Toshikawa et al. 2016; Jiang et al. 2018; Lemaux et al. (NIR) narrow-band imaging (Zheng et al. 2021). Cur- 2018; Shi et al. 2020) and targeting rare massive rently, only a few protoclusters at z 2 are identi- ≥ halo tracers, e.g., quasars, radio galaxies, Lyα fied by NIR spectroscopy of HAEs. For example, the blobs (LABs) and submilimeter galaxies (SMGs; well-studied PKS 1138 at z = 2.16 and USS 1558 at Pascarelle et al. 1996; Pentericci et al. 2000; Kurk et al. z =2.53 protoclusters associated with radio galaxy en- 2000, 2004a; Venemans et al. 2002, 2004, 2005, 2007; vironments will evolve into the massive galaxy clusters 15 Daddi et al. 2009; Kuiper et al. 2011; Hatch et al. 2011, with masses of 10 M⊙ at z 0 (Kurk et al. 2004a; ∼ ∼ 2014; Hayashi et al. 2012; Cooke et al. 2014, 2016; Hayashi et al. 2012; Shimakawa et al. 2014, 2018a,b). Husband et al. 2016; Casasola et al. 2018). The for- Tanaka et al. (2011) reported a protocluster associated mer is limited by their relatively small survey volumes, with the radio galaxy 4C 23.56 at z =2.48 had 5 6 ∼ − while the latter may suffer from the strong selection times excess of HAEs from the general field, which biases and small duty cycles (Cai et al. 2016, 2017a). might evolve into a galaxy cluster with the present-day 14 A promising selection technique for protoclusters is mass of > 10 M⊙. Darvish et al. (2020) confirmed through the group of gas absorption systems along a protocluster CC2.2 at z = 2.23 with a present-day 14 multiple sightlights to background quasars or galax- mass of 9.2 10 M⊙ through the NIR spectroscopy × ies (Lee et al. 2014a; Stark et al. 2015; Cai et al. 2016; of HAEs. Recently, Koyama et al. (2021) presented a Miller et al. 2019). Planck-selected protocluster at z =2.16 associated with Discoveries of two protoclusters at z =2.24 3
Figure 1. Slitmask regions of MMT/MMIRS (red boxes: 4′ × 6.′9) and LBT/LUCI (red dot-dashed boxes: 4.′0 × 2.′8) in BOSS1244 (left) and BOSS1542 (right). BOSS1244-mask1 and BOSS1244-mask2 are located in the SW and NE regions, respectively. The dashed blue box in the right panel refers to BOSS1542-mask1, which was not observed due to the bad weather conditions. These structures are traced by groups of Lyα absorption systems (green diamonds) and BOSS quasars (blue stars) at the redshift of z = 2.24±0.02. The black circles are the selected HAE candidates and the filled circles show the spectroscopically confirmed HAEs through MMT/MMIRS and LBT/LUCI NIR spectroscopy. The solid and dashed lines represent contours of the density map of HAEs. A galaxy number density of 0.2 per arcmin2 is adopted as the contour interval and the inner density peak reaches ∼ 2 arcmin−2.
−1 −1 an overdensity of HAEs, six HAEs at z =2.150 2.164 and H0 = 70kms Mpc and magnitudes are pre- − were identified through spectroscopy. Although they do sented in the AB system unless otherwise specified. At not calculate the present-day mass, we estimate that z = 2.24, 1′ corresponds to 0.495physical Mpc (pMpc) the fate of the protocluster may be a Virgo-type galaxy and 1.602 comoving Mpc (cMpc), respectively. 14 cluster ( 10 M⊙) at present day based on the volume ∼ 2. OBSERVATIONS AND DATA REDUCTIONS they gave. In this paper, we present NIR spectroscopic followup Zheng et al. (2021) carried out deep NIR imaging observations with Canada France Hawaii Telescope observations of these HAE candidates, quantitatively − − showing that BOSS1244 and BOSS1542 are indeed ex- (CFHT) through the narrowband (NB) H2S1 and tremely overdense, and will collapse to two extremely broadband (BB) Ks filters to identify emission-line ob- massive clusters (like Coma cluster or even larger) at jects. The NB technique selects objects with an excess z 0. We also use these identified HAEs to analyze dy- of emission at λ = 2.13 µm. The emission-line may be ∼ [O III] from emitters at z 3.25, [O II] at z 4.71 or namical properties (e.g., velocity dispersion, dynamical ≃ ≃ Paα/Paβ at z 0.14/0.66 and [S III] at z 1.23/1.35 mass) and evolutionary stages of two overdensities. Fur- ≃ ≃ thermore, we estimate the total mass of the two overden- (e.g., Geach et al. 2008; Sobral et al. 2012). In to- sities to the present-day based on the galaxy overden- tal, 244/223 line emitters are selected with rest-frame sities. The physical properties of HAEs in BOSS1244 EW>45 A˚ and H2S1<22.5 mag over the effective area 2 and BOSS1542 will be presented in future work (Shi, of 417/399 arcmin in BOSS1244/BOSS1542. As shown D.D. et al. in preparation). The spectroscopic obser- in Zheng et al. (2021), about 80% of these emitters are HAEs at z = 2.24 0.02, and the Hα luminosity func- vations and data reduction are descried in Section 2. ± In Section 3, we present the main analyses and results, tions (LF) can be derived in a statistical manner. Their and discuss the implications for the extremely over- results show that the shape of the Hα LF of BOSS1244 dense regions in Section 4. Our conclusions are sum- agrees well with that of the general fields, while in marized in Section 5. Throughout this paper, we adopt BOSS1542, the LF exhibits a prominent excess at the the cosmological parameters of ΩM = 0.3, ΩΛ = 0.7 high end, likely caused by the enhanced star formation or AGN activity. We perform NIR spectroscopic obser- 4 Shi et al. vations to confirm the extremely overdense nature of two #slit-2 z=2.234 regions and better quantify their overdensities. #slit-3 z=2.235 #slit-4 z=2.221 2.1. MMT/MMIRS Spectroscopy #slit-5 z=2.235 #slit-13 z=2.229 Spectroscopic observations of the HAE candidates in #slit-14 z=2.230 the density peak regions of BOSS1244 and BOSS1542 #slit-15 z=2.226 #slit-17 z=2.247 are carried out using the Multiple Mirror Telescope #slit-18 z=2.227 (MMT) and Magellan Infrared Spectrograph (MMIRS; #slit-19 z=2.235 #slit-20 z=2.225 McLeod et al. 2012), mounted on the MMT telescope #slit-21 z=2.220 (PI: Zheng, X.Z.) in 2017. MMIRS is a near infrared #slit-23 z=2.250 (NIR) imager with an imaging Field of View (FOV) #slit-22 z=2.213 ′ ′ #slit-26 z=2.253 6.9 6.9 and multi-object spectrograph (MOS) over #slit-27 z=2.242 ′ × ′ 1 2 4 6.9. We use the “xfitmask” program to design #slit-29 z=2.255 × #slit-30 z=2.244 our slit masks. There are two masks designed in each #slit-31 z=2.245 field. The red rectangles in Figure 1 are the observed slit mask regions of two fields and the dashed blue rect- angle in BOSS1542 is the unobserved slit mask region Figure 2. 2D spectra of 19 HAEs in BOSS1244 observed via ′′ due to the bad weather. A slit width of 1. 0 and a slit MMT/MMIRS slit mask1. Skyline residuals are marked as length of 7′′. 0 are adopted for observing our science tar- vertical lines with a higher noise level. The slit and spectrum gets, and the low noise gain (0.95) is used. The tar- number are labeled. Almost all spectra (excluding slit-23 and slit-30) have only one emission line, and their continua are gets are prioritized based on their Ks magnitudes with 0′′. 7 aperture: we rank the highest, medium and lowest barely detected. The spectrum of slit-13 is consistent with a quasar with a broad Hα emission line. priorities to objects with Ks magnitudes in the range of 18.9 22.8, 22.8 24.3, 24.3 25.0 mag, respectively. − − − The K3000 grism and Kspec filter are used to take tracted from the original frames without resampling af- spectra over the wavelength coverage of 1.90 2.45 µm − ter tracing and distortion mapping, and we set per-slit (Chilingarian et al. 2015). With these configurations, normalization for flat-fielding due to the imperfect il- the resolution of 1′′. 0 slit width in the K3000 grism and lumination of the detector plane. We use airglow OH Kspec filter corresponds to R = 1200. We dither along lines for wavelength calibration given our faint targets the slit between individual 300 s exposures. Three out and long exposure time (300s), but internal arc frames of four masks were successfully observed under the av- will be used if the OH based computation fails. The erage seeing conditions of 0′′. 83 1′′. 16 with the total − sky subtraction is done using a technique modified from integration time of 8.69 hrs in Semester 2017A. Four the original one given in Kelson (2003). For telluric cor- to five alignment stars with 13.5 Table 1. MMT/MMIRS and LBT/LUCI NIR spectroscopic observations for the BOSS1244 and BOSS1542 fields. Field/SlitMask Nobj R.A. Decl. P.A. Grism+Filter Exp.time ObsDate Seeing (J2000.0) (J2000.0) (deg) (second) Average (′′) (1) (2) (3) (4) (5) (6) (7) (8) (9) h m s BOSS1244/mask1 19/28 12 43 31.28 +35◦55′44′′. 38 180 K3000 + Kspec 12,024 2017/06/14,18 1.16 h m s BOSS1244/mask2 18/18 12 44 21.26 +36◦04′44′′. 62 −104 K3000 + Kspec 12,024 2017/06/11,12,17 1.05 h m s BOSS1542/mask1 0/26 15 42 53.20 +38◦52′06′′. 50 −11 K3000 + Kspec ...... h m s BOSS1542/mask2 14/23 15 42 41.78 +39◦01′07′′. 62 −13 K3000 + Kspec 7,236 2017/05/14 0.83 h m s BOSS1244/mask 8/18 12 43 34.76 +35◦55′07′′. 33 90 HKspec+HKspec 5,256 2017/04/13 ≤ 1.2 h m s BOSS1542/mask1 8/14 15 42 51.80 +38◦49′49′′. 37 30 HKspec+HKspec 7,668 2017/04/12 ≤ 1.2 h m s BOSS1542/mask2 7/9 15 42 48.18 +38◦53′35′′. 39 0 HKspec+HKspec 6,480 2017/04/13 ≤ 1.2 BOSS1542/mask3 7/13 15h42m37.66s +38◦57′59′′. 07 −25 HKspec+HKspec 5,508 2017/04/13 ≤ 1.2 Note— Above double lines are the MMT/MMIRS observations, below the double lines are the observations in LBT/LUCI. The number to the left of slash in column (2) is the number of successfully confirmed galaxies, and the number to the right of slash in column (2) is total number of HAE candidates in the slitmask. No observations in MMT/MMIRS BOSS1542/mask1 due to bad weather. calibration, and the scaling factors are 5 10−22 in In total 46 HAE targets in BOSS1244 (two masks) ∼ × the H2S1 and Ks bands, which is 1 3 times larger than and 23 HAE targets in BOSS1542 (one mask) are cov- − the aforementioned method. This may be mainly due to ered in the MMT/MMIRS observations. We use a single the large slit width (4′′) of alignment stars so that more Gaussian function to fit the emission line and measure light is collected. Therefore, we use NB excess flux to the observed wavelength through Hα line (the rest frame take the absolute flux calibration for our final calibrated Hα emission line is 6564.61A˚4 in vacuum) to derive the spectra. redshift of HAEs. If multiple components are detected, we will use multiple Gaussians in multiple regions to fit them. The equation z = λobs/λrest 1 is used to com- − pute the redshift, where λrest is the rest-frame wave- #slit-1 z=2.243 length and λobs is the observe-frame wavelength. #slit-2 z=2.244 #slit-3 z=2.240 2.2. LBT/LUCI Spectroscopy #slit-4 z=2.239 #slit-5 z=2.229 To increase the sample size of spectroscopically- #slit-6 z=2.253 confirmed HAEs, three masks (36 targets) in BOSS1542 #slit-7 z=2.251 #slit-8 z=2.245 and one mask (18 targets) in BOSS1244 were observed #slit-9 z=2.247 using the LBT Utility Camera in the Infrared (LUCI) #slit-10 z=2.244 mounted on the Large Binocular Telescope (LBT) in #slit-11 z=2.253 #slit-12 z=2.242 semester 2017A (PI: Fan, X.). The relatively small dot- #slit-13 z=2.248 dashed red boxes in Figure 1 are the observed slit mask #slit-16 z=2.244 regions of two fields. LUCI5 is able to provide imag- #slit-17 z=2.250 #slit-20 z=2.248 ing, longslit spectroscopy, and MOS spectroscopy over a #slit-21 z=2.248 FOV of four square arcminutes. We choose MOS spec- #slit-22 z=2.244 troscopy and the slit masks are designed through the LMS6 software. Six alignment stars are used to cor- rect telescope pointing and instrument rotation angle. Figure 3. 2D spectra of 18 HAEs in BOSS1244 observed via MMT/MMIRS slit mask2. Skyline residuals are marked as vertical lines with a higher noise level. The slit and spectrum 4 http://classic.sdss.org/dr7/algorithms/linestable.html number are labeled. The spectra of slit 9, 20 and 21 show 5 https://www.lsw.uni-heidelberg.de/users/jheidt/LBT links/ multiple lines. The rest exhibit only a single emission line. LUCI UserMan.pdf Continuum is barely visible in all spectra. 6 https://sites.google.com/a/lbto.org/luci/preparing-to-observe/ mask-preparation 6 Shi et al. 3. RESULTS AND ANALYSIS 3.1. Spectroscopic Confirmation of HAE Candidates #slit-25 z=2.216 #slit-27 z=3.302 We detect emission lines in 37 of 46 HAE candidates in #slit-21 z=2.213 BOSS1244 with spectra obtained from MMT/MMIRS. #slit-24 z=2.253 All of them are confirmed to be HAEs in redshift range #slit-23 z=2.215 #slit-17 z=2.211 of 2.213 Figure 5. MMT/MMIRS 1D spectra of 12 HAEs obtained from the BOSS1244 slitmasks, including one BOSS quasar. The blue line in every plot is the sky line and the vertical blue dashed line is the Hα emission. The vertical cyan dashed line is the [NII] emission. z < 2.253 are confirmed through MMT/MMIRS spec- in BOSS1244 and in BOSS1542, respectively. As dis- troscopic observations. The detection rate is 14/23 cussed below, our spectroscopic observations confirm (61%), lower than that of the previous two masks in BOSS1244 and BOSS1542 as extreme galaxy overden- BOSS1244. We note that the mask in BOSS1542 has sities, indicating that HAEs are an effective tracer of a shorter integration time although it was observed the overdense region of large-scale structures. We will under a better condition. In addition, we identify present the physical properties of HAEs in the extremely slit-27 as an [O III] emitter at z = 3.302, because overdense environments in a subsequent paper (Shi, [O III]λλ4960, 5008A˚ lines are resolved. Excluding the D.D. et al. in preparation). slit-27 target, the detection rate of HAEs is 13/23 (57%). This low detection rate in BOSS1542 is mainly due to 3.2. Redshift distributions of HAEs the shorter exposure time (shown in Table 1). Simi- Figure 9 shows the redshift distributions of HAEs larly, we identify 22 of 36 targets at 2.215 Figure 6. MMT/MMIRS 1D spectra of eight HAEs in BOSS1542. The bottom-right panel shows the spectrum of an [O III] emitter at z=3.302. The blue curves represent the sky emission. The vertical dashed lines mark the emission lines Hα or [O III]λλ4960, 5008A˚ emission. at z = 2.24). The two components are covered by our arcmin−2. Sobral et al. (2013) performed a large Hα MMT/MMIRS observations. Further, we find that the survey at z = 2.23, 1.47, 0.84 and 0.4 in the Cosmo- SW region also shows the double peak in redshift dis- logical Evolution Survey (COSMOS) and Ultra Deep tribution. One is at z = 2.230 0.002 and another Survey (UDS) fields. Using the same criteria of HAE ± is at z = 2.245 0.001, which is the consistent with candidates, the average surface densities in COSMOS ± the redshift of NE region. Moreover, from the pro- and UDS are estimated to be (8.25 0.36) 10−2 and ± × jected sky space, the two substructures of SW region (7.01 0.53) 10−2 HAE arcmin−2, respectively. Note ± × may be merging and forming a larger structure. Alto- that there is an overdense region in COSMOS so that the gether, BOSS1244 has two distinct components both in surface density is higher than that in ECDFS and UDS, sky and redshift space. In contrast, BOSS1542 shows which is reported in Geach et al. (2012). If the over- a very extended filamentary structure over the scale of dense region is masked, the surface density in COSMOS 14.′6, or 23.4cMpc from South to North region and is (7.42 0.35) 10−2 HAE arcmin−2. In addition, 11 ∼ ± × may be forming a cosmic filament, and the redshift spike HAE candidates at z =2.19 0.02 over 70 arcmin2 are ± ∼ is z =2.241 0.001. reported in the Great Observatories Origins Deep Sur- ± vey North (GOODS-N) field (Tadaki et al. 2011), the 3.3. Overdensity and Present-day Masses Estimate surface density is 0.157 0.047HAE arcmin−2, which is ± Galaxy overdensity δg is estimated from the galaxy about twice as high as other general fields (like ECDFS, Σgroup surface density, where δg is defined as δg = 1, COSMOS and UDS). This is mainly due to the limited Σfield 2 − Σgroup is the HAE number per arcmin within the over- NB survey area (Tadaki et al. 2011). For a comparison, we expect 31 6 HAEs in our areas, based on integrating density, and Σfield is the surface density of HAEs in ± the random fields. Our NIR spectroscopically-confirmed the Hα luminosity function (Sobral et al. 2013) and the HAEs indicate that BOSS1244 and BOSS1542 are in- completeness function of HAEs. The surface density in random fields is (7.43 1.44) 10−2 HAE arcmin−2. The deed extremely overdense. The surface densities of HAE ± × candidates at z =2.24 in the BOSS1244 and BOSS1542 method is described in Lee et al. (2014b). Here we adopt −2 fields are 0.585 0.037 and 0.559 0.037HAE arcmin−2, as the average surface density (7.25 0.51) 10 HAE ± ± −2 ± × respectively. The surface density Σfield of HAEs is cal- arcmin of HAE candidates in the ECDFS, COSMOS culated through some popular general fields with large and UDS fields for estimating HAE overdensities of the HAE surveys. An et al. (2014) detected 28 5 HAE can- BOSS1244 and BOSS1542 fields. ± didates at z = 2.24 with the same narrowband, detec- We do not map out all the HAE candidates in our tion depth and selection criteria over 383 arcmin2 area in NIR spectroscopic observations. However, consider- ECDFS and the surface density (7.31 1.38) 10−2 HAE ing the fore- and back-ground emitter contaminations, ± × Discoveries of two protoclusters at z =2.24 9 Figure 7. LBT/LUCI 1D and 2D spectra of four HAEs in BOSS1244. The blue line in each panel is the sky line and the vertical blue dashed line is the Hα emission. we assume that 80% of our sample are true HAEs at 56.9 cMpc, we measure the overdensity in a circular area z = 2.24 0.02 based on the detect rate from our 8.7 cMpc in diameter, which corresponds to the volume ± NIR spectroscopic analyses, and the galaxy overdensi- of (15cMpc)3. In BOSS1244, two density peaks re- ties δg in BOSS1244 and BOSS1542 are computed to be gions (NE and SW area) are separated in space and 5.5 0.7 and 5.2 0.6, respectively. The results are con- redshift obviously. The number of HAEs within a di- ± ± sistent with Zheng et al. (2021). These two overdensi- ameter of 8.7cMpc (5.4arcmin) centered on the po- ties are the most overdense fields currently known over sition [α, δ] = [190.892, 35.909] in the SW dense re- the volumes of (40)3 cMpc3, and thus provide ideal gion is 40 6, corresponding to a surface density of ∼ ± laboratories to study galaxy properties in dense envi- 1.73 0.26, and δg = 22.9 4.0. The number of HAEs ± ± ronments and the environmental dependence of galaxy within a diameter of 8.7 cMpc centered on the position mass assembly at the cosmic noon. [α, δ] = [191.074, 36.079] in the NE dense region is 20 4, ± The characteristic size of a protocluster is 15cMpc corresponding to surface density of 0.87 0.17, and δg is ∼ ± (10.5 h−1 cMpc), and the protocluster mass is typi- 10.9 2.5, which is lower than that in the SW region. ± cally calculated in a volume of (15 cMpc)3 (Steidel et al. In BOSS1542, it shows a giant filament structure with 1998, 2005; Chiang et al. 2013; Stark et al. 2015; 14.′6 ( 23.4 cMpc) along the South to North region. ∼ ∼ Muldrew et al. 2015). To compare with our two over- We further calculate that the δg through an elliptical densities (protoclusters), we measure δg in BOSS1244 area with an axial ratio of 1/3 centered on the posi- and BOSS1542 over the typical protocluster scale (vol- tion [α, δ] = [235.682, 38.954]. The estimated δg in the ume). Since the line-of-sight depth of our survey is (15 cMpc)3 volume is 20.5 3.9. The uncertainties are ± 10 Shi et al. Figure 8. LBT/LUCI 1D and 2D spectra of six HAEs in BOSS1542. The blue line in each panel is the sky line and the vertical blue dashed line is the Hα emission. Discoveries of two protoclusters at z =2.24 11 Figure 9. The redshift distributions of the confirmed HAEs in BOSS1244 (left) and BOSS1542 (right). The inner panel of left figure is the redshift distribution of HAEs in the BOSS1244 SW and NE regions. The black solid line is the transmission curve of the NB filter. estimated in the galaxy number counts within an over- to the galaxy overdensity by 1 + bδm = C(1 + δg), where +0.1 dense region by including poisson shot noise and cosmic b is the HAE bias factor. We take bHAE =2.4−0.2 from variance (clustering effect) (Lee et al. 2014b; Cai et al. Geach et al. (2012) to be the HAE bias at z =2.24. C is 2017a). the correction factor which is an estimation of the effects Galaxy formation models predict that galaxies inside of redshift-space distortions caused by peculiar veloci- large-scale overdensities should be older than those out- ties (Steidel et al. 1998), which is a function of matter side, because matter fluctuations inside overdensities are overdensity δm and redshift z. In the case of spheri- sitting on a large-scale pedestal and easier to collapse cal collapse, the correction factor C can be estimated 1 by crossing the threshold of δc = 1.69. We estimate using the expression of C =1+ f f(1 δm) 3 , where 4/7 − − the total masses at z 0 in our two overdensities us- f =Ωm(z) , which we take to be f =0.96 at z =2.24. ∼ ing the galaxy overdensity factor and the appropriate We obtain the correction factor C = 0.62 0.03 and ± volume based on the approach outlined by Steidel et al. matter overdensity δm =1.69 0.15 in BOSS1244, while ± (1998, 2005), although there are some uncertainties such C =0.64 0.03 and matter overdensity δm =1.62 0.14 ± ± as systematic and random errors from the assumption in BOSS1542. According to the theory of density per- of spherical collapse model (Chiang et al. 2013; Overzier turbation, we use the approximation for spherical col- 2016). The equation is given by: lapse from the equation 18 in Mo & White (1996) to the linear matter density δL. The linear overdensity δL in BOSS1244 and BOSS1542 is 0.74 and 0.73. If Mz=0 =ρV ¯ true(1 + δm) (1) it evolves to the redshift of z = 0, the linear overdensi- whereρ ¯ is the the mean comoving matter density ties δL in BOSS1244 and BOSS1542 are 2.17 and 2.14, 2 3H0 respectively, which is exceeding the collapse threshold of the universe, which is equal to 8πG Ωm = 4.1 10 −3 × 10 M⊙ cMpc , and Vtrue is the volume in real space of δc =1.69. We thus expect the entire BOSS1244 and that encloses the observed galaxy overdensity after cor- BOSS1542 overdensities to be virialized by z = 0. Using recting the effects of redshift-space distortions. So Equa- the Equation 1, the total masses at z = 0 in the over- 10 all BOSS1244 and BOSS1542 fields are (0.89 0.07) tion 1 is equivalent to Mz=0 = [4.1 10 M⊙](1 + 16 16 ± × 3 × 10 M⊙ and (0.82 0.06) 10 M⊙, respectively. We δm)[Vtrue/ cMpc ], and Vtrue = Vapparent/C. Vapparent ± × is the observed comoving volume. The observed vol- find that the same volume without an overdensity δm re- 3 3 15 ume Vapparent is 60,964 cMpc and 58,332cMpc in sults in a mass of (3.70 0.18) 10 M⊙ in BOSS1244 15± × BOSS1244 and BOSS1542, respectively. Namely, and (3.48 0.16) 10 M⊙ in BOSS1542. Kurk et al. ∼ ± × 20.′4 20.′4 region in BOSS1244 and 20.′0 20.′0 region (2004b) explained that the masses may be mostly in- × × in BOSS1542 are covered on the plane of sky between tergalactic gas which will disappear out of the cluster z = 2.223 2.267 (the sight of comoving distance is with the Hubble flow, and eventually evolve into the − about 56.9 cMpc). The matter overdensity δm is related mass of the bound system, although they gave an error 12 Shi et al. Table 2. Galaxy overdensities and present-day masses in BOSS1244 and BOSS1542. Cluster Redshift Scale δg Present-day Mass 15 name (1) (2) (3) (4) (5) BOSS1244a 2.24 39.4 7.1±0.8 10.70±0.80 BOSS1244b 2.24 39.4 5.5±0.7 8.90±0.70 BOSS1244 NE 2.246±0.001 15 10.9±2.5 0.83±0.11 BOSS1244 SW 2.230±0.002 15 22.9±4.9 1.59±0.20 BOSS1542c 2.24 38.8 6.7±0.7 9.80±0.70 BOSS1542d 2.24 38.8 5.2±0.6 8.20±0.60 BOSS1542 Filament 2.241±0.001 15 20.5±3.9 1.42±0.18 aThe emission line galaxy overdensity in BOSS1244. bThe HAE overdensity in BOSS1244 assuming 80% sample are true HAEs. cThe emission line galaxy over- density in BOSS1542. dThe HAE overdensity in BOSS1542 assuming 80% sample are true HAEs. in computing the value ofρV ¯ true, being pointed out in total mass, we estimate the descendant cluster masses 15 Steidel et al. (2005). Mz=0 are > 2 10 M⊙ in BOSS1244 SW region and × 15 The progenitors of galaxy clusters at z 0 have a in (1.24 0.24) 10 M⊙ NE region, and Mz=0 in ∼ ± × 15 characteristic size of 15 cMpc, we thus estimate the to- BOSS1542 is > 2 10 M⊙. By comparison of the × tal present-day masses of the density peak structures in method of Steidel et al. (1998), we find that mass esti- the volume of (15 cMpc)3. The density peak regions in mation presented by Chiang et al. (2013) is about twice BOSS1244 and BOSS1542 are expected to be virialized as high as the method in Steidel et al. (1998), but both at z 0. As described in Section 3.2, BOSS1244 has two mass estimates suggest that BOSS1244 and BOSS1542 ∼ different components: the NE region with δg = 10.9 2.5 protoclusters over the 15 cMpc scale will evolve into ± 15 and SW region with δg = 22.9 4.0 over the 15 cMpc Coma-type ( 10 M⊙) clusters in the present epoch. ± ≥ scale. Using the Equation 1, the total masses at z = 0 in 15 3.4. Velocity Dispersions of Two Overdensities NE and SW are expected to be (0.83 0.11) 10 M⊙ 15 ± × and (1.59 0.20) 10 M⊙, respectively. The mass in As described in 3.2, BOSS1244 shows two distinct ± × SW is about twice the mass in NE, which is related to spikes at z = 2.230 in the SW region and z = 2.246 the HAE overdensity. In contrast, BOSS1542 displays a in the NE region, and the SW region appears to be much denser than that the NE region. The line-of-sight huge filamentary structure and δg is 20.5 3.9 over the ± 15cMpc scale at z =2.241, and the present-day mass is depth between z = 2.230 and z = 2.246 is 21cMpc. In 15 both regions, we estimate the line-of-sight velocity dis- (1.42 0.18) 10 M⊙. We summarize δg and present- ± × day masses of the BOSS1244 and BOSS1542 fields in persion from our measured spectroscopic redshifts us- Table 2. ing two Gaussian functions. The velocity dispersion in the SW region is 405 202kms−1, similar to the ve- Furthermore, we estimate the total enclosed mass ± locity dispersion in the NE region (377 99kms−1). from the scaling relation based on cosmological simu- ± lation. Chiang et al. (2013) presented the correlation SW region in BOSS1244 also presents two substruc- tures in redshift distribution (the left inner panel of between mass overdensity δm at different redshifts and the descendant cluster mass M in the (13.1 cMpc)3 Figure 9) and the velocity dispersions of these two z=0 − 3 substructures are 484 181kms 1 at z = 2.230 and and (24.1 cMpc) tophat box windows. We thus esti- ± 152 58kms−1 at z = 2.245. The lower velocity dis- mate Mz=0 based on our calculated matter overdensity ± in the same volume. Using b = 2.4 as above, in the persion infers that the structure might perpendicular 3 to the line-of-sight (Venemans et al. 2007), or might be volume of (13.1 cMpc) , the matter overdensity δm in BOSS1244 SW and NE regions is 12.6 2.5and 5.6 1.6, due to the smaller number HAEs that we estimate the ± ± velocity dispersion. For BOSS1542, our NIR spectro- respectively, and δm in BOSS1542 is 9.3 2.1. According ± to the correlation between overdensity and present-day scopic observations present an extended and narrow fil- amentary structure on the scale of 23.4 cMpc (the right Discoveries of two protoclusters at z =2.24 13 Table 3. Dynamical properties in this work and other protoclusters at z = 2 − 3. Cluster Redshift σlos r200 M200 Reference −1 13 name z [km s ] [Mpc] [10 M⊙] (1) (2) (3) (4) (5) (6) SSA 22 Blue 3.069 350±53 0.19 ± 0.03 1.6 ± 0.7 Topping et al. (2016) SSA 22 Red 3.095 540±40 0.29 ± 0.02 5.9 ± 1.3 Topping et al. (2016) MRC 0943–242 2.92 715±105 0.41 ± 0.06 15 ± 6 Venemans et al. (2007) MRC 0052–241 2.86 980 ±120 0.57 ± 0.07 38 ± 14 Venemans et al. (2007) USS 1558-003 C1 2.53 284 0.19 1.00 Shimakawa et al. (2014) USS 1558-003 C2 2.53 574 0.38 8.70 Shimakawa et al. (2014) CL J1001 2.506 530±120 0.36±0.08 7.94±3.80 Wang et al. (2016) PCL1002 2.47 426 0.29 3.7 Casey et al. (2015) PKS 1138-262 2.16 683 0.53 17.10 Shimakawa et al. (2014) +70 BOSS1441 2.32 943±500 0.7±0.4 40.0−39 Cai et al. (2017a) CC2.2 2.23 645±69 0.49±0.05 14.0±5.0 Darvish et al. (2020) BOSS1244 NE 2.246 377±99 0.28±0.07 2.80±2.20 This work BOSS1244 SW 2.230 405±202 0.30±0.15 3.00±5.00 This work BOSS1542 Filament 2.241 247±32 0.19±0.02 0.79±0.31 This work panel of Figure 9). The estimated velocity dispersion is system (Lemaux et al. 2014; Dey et al. 2016; Overzier 247 32kms−1 at z =2.241, which is much lower than 2016). We apply the method for virialized systems to ± that in BOSS1244. The lower velocity dispersion may our protoclusters to draw an upper limit of dynamical indicate that BOSS1542 is a dynamically young proto- mass and examine their dynamical state. cluster (Dey et al. 2016). We first assume that BOSS1244 and BOSS1542 pro- We also use the bi-weight method to check the line- toclusters at z = 2.24 are virialized and the halos of-sight velocity dispersion from the measured spectro- of the two protoclusters are spherical region within scopic redshifts considering that this method is shown which the average density is 200 ρc(z). The virial mass 4π 3 to be robust against a few outliers and for non-Gaussian M200 = 3 r200200ρc(z), where r200 is the virial ra- 2 underlying distributions (Beers et al. 1990). The veloc- dius and ρc(z) = 3H (z)/(8πG) is the critical den- ity dispersions of NE and SW regions are 320 60kms−1 sity of the universe at redshift of z. Using a spheri- ± at z = 2.247 and 431 99kms−1 at z = 2.231, respec- cal symmetry combined with the virial theorem and the ± tively. The velocity dispersions of two components in line-of-sight velocity dispersion σlos, the virial radius −1 2 the SW region are 304 99kms at z = 2.246 and is r200 = GM200/(3σ ), where G is the gravitational ± los 430 119kms−1 at z = 2.230. The velocity dispersion constant. Using above three formulae, we can derive ± −1 in the BOSS1542 filament within 2σ is 255 48kms r200 and M200 as a function of σlos and H(z): M200 = ± 3 at z = 2.241. All these estimates are consistent with (√3σlos) /(10GH(z)) and r200 = √3σlos/(10H(z)). For the results obtained with the Gaussian methods. We BOSS1542 protocluster, we estimate virial radius r200 = adopt the measured results using the Gaussian method 0.19 0.02 Mpc and virial mass M200 = (0.79 0.31) 13 ± ± × hereafter. 10 M⊙. For BOSS1244 protocluster, we estimate r200 = 0.28 0.07 Mpc and M200 = (2.80 2.20) 13 ± ± × 3.5. Dynamical Mass 10 M⊙ in the NE region, and r200 = 0.30 0.15Mpc 13 ± Protocluster systems are not virialized, and the veloc- and M200 = (3.00 5.00) 10 M⊙ are computed in ± × ity dispersion of member galaxies traces the dynamical the SW region. The large errors in mass are due to the state of system rather than the halo mass (Wang et al. relatively large velocity dispersion errors. 2016; Darvish et al. 2020). Still, dynamical mass esti- We also use the scaling relation between velocity dis- mates provide upper limits for the actual masses, given persion and total mass presented in Evrard et al. (2008) that the galaxies most likely populate multiple halos within the protocluster system rather than one virialized 14 Shi et al. to estimate the dynamical total masses. measure the Lyα absorption. These background quasars 2 30 cMpc away from the center of two fields in sky h(z)M α − 200 projection, with the effective optical depths of IGM ab- σDM(M,z)= σDM,15 15 (2) 10 M⊙ sorption of 3 5 the average optical depth ( 0.25) at − × ∼ 15 z = 2.24. We find that no CoSLAs are in the dense where σDM,15 is normalization at mass 10 M⊙ and region in BOSS1244, and all of them are distributed in α is the logarithmic slope. Using σDM 15 = 1082.9 , ± 4.0kms−1 and α = 0.3361 0.0026, we can derive the the periphery of the BOSS1244 field. In contrast, two ± halo masses in our protoclusters (see also Munari et al. CoSLAs are located in the BOSS1542 filamentary struc- ture and others are in the outskirts of the BOSS1542 2013). The virial masses M200 in the BOSS1244 NE re- gion, BOSS1244 SW region and BOSS1542 filament are field. 13 13 (1.90 1.50) 10 M⊙, (2.30 3.50) 10 M⊙ and In BOSS1244, we note that the background quasar ± × 12 ± × marked “1” is located between SW and NE regions and (5.30 2.10) 10 M⊙, respectively. The derived M200 ± × is 6.85 cMpc away from the field center. The line- using the scaling relation is consistent with our estimate ∼ based on the virial theorem. of-sight distance between SW and NE region and the We find that the dynamical masses of two substruc- CoSLAs at z = 2.24 detected by background quasar tures in BOSS1244 are 2 3 times that of BOSS1542, is 7.8cMpc and 13.0 cMpc, respectively. From the up- ∼ − indicating that they may be in different dynamic evo- per left of the figure 1 of Zheng et al. (2021), we find lution states. Wang et al. (2016) discovered an X- that this CoSLA shows a double peak in the line-of- sight distance with > 3 the average optical depth, ray detected galaxy cluster with a halo of M200 × 13.7±0.2 ∼ corresponding to the comoving distance of 0 10 cMpc 10 M⊙ based on the velocity dispersion of 530 − −1 ± and 10 20 cMpc. It confirms that BOSS1244 should 120kms at z = 2.506. Shimakawa et al. (2014) pre- − sented two protoclusters PKS 1138-262 at z =2.16 and consists of two separated components along the line- USS 1558-003 at z = 2.53, and the dynamical mass of of-sight direction, which is consistent with our spectro- 14 scopic observations. The background quasar marked “2” the core is estimated to be M200 =1.71 10 M⊙with −1 × is around the SW region with the line-of-sight distance the velocity dispersion of 683 km s and M200 =0.87 14 −1 × of 10 20cMpc, the background quasars marked “3” and 10 M⊙ with the velocity dispersion of 574 km s , re- − spectively. Recently, Darvish et al. (2020) showed a new “4” are around the NE region with the line-of-sight dis- tance of 0 10 cMpc. Similarly, BOSS1542 also shows protocluster CC2.2 in COSMOS at z = 2.23. The red- − shift and selection technique of HAEs are the same as the consistent results from the effective optical depth ours used for BOSS1244 and BOSS1542. The dynamical profile described in the figure 2 of Zheng et al. (2021). In 14 short, these reflect the importance of NIR spectroscopic mass of CC2.2 is M200 = (1.40 0.5) 10 M⊙ and the ± × velocity dispersion is 645 69kms−1. They are summa- observations and indicate that the redshift we measured ± rized in Table 3. These protocluster systems will evolve is reliable. into fully collapsed and virialized Coma-type structures Furthermore, there are five BOSS quasars at z = 15 2.23 2.26 in BOSS1244 and three BOSS quasars at with a total mass of M200 10 M⊙ at z = 0, so they − ∼ z = 2.23 2.25 in BOSS1542, as shown in Table 4. are likely to be in transition phase between protoclusters − and mature clusters. However, the dynamical masses in We find that the measured redshifts of the HAEs are the BOSS1244 and BOSS1542 protoclusters are 1 2 consistent with the redshifts of these quasars around ∼ − order-of-magnitude lower than that in above mentioned them, and most of these BOSS quasars are in the protoclusters, suggesting that BOSS1244 and BOSS1542 overdense regions of BOSS1244 and BOSS1542, indi- protoclusters are pre-virialized, younger systems. This cating that these quasars are likely to be associated provides evidence on earlier phase during which the clus- with the two overdensities. In BOSS1244, we find that QSO2/QSO5 with projected separation 1.2 pMpc ters and their members are actually forming. ∼ and velocity offset 1570km s−1 meets the defini- ∼ 4. DISCUSSIONS tion of quasar pairs with a projected separation < −1 −1 4.1. CoSLAs and Quasar Pairs in the Two 2(= 1.4h ) pMpc and velocity offset < 2300kms Overdensities (Onoue et al. 2018). In BOSS1542, QSO2/QSO3 with projected separation 1.9 pMpc and velocity offset Protoclusters are not only traced by overdensities of − ∼ 740km s 1 is a quasar pair. Interestingly, the quasar galaxies, but also by intergalactic hydrogen gas that ∼ pairs QSO2/QSO5 in BOSS1244 and QSO2/QSO3 in can produce Lyα absorption in the spectra of back- BOSS1542 are located in the overdense region, suggest- ground quasars. Four out of five background quasars ing that the overdensities of galaxy are associated with at 2.3 Table 4. BOSS QSOs (including background QSOs) in the the three-dimensional spatial distribution of HAEs in BOSS1244 and BOSS1542 fields. BOSS1244 and BOSS1542, the color-coded filled points are the confirmed HAEs with NIR spectroscopy. In Field ID R.A. Decl. Redshift terms of the large-scale geometry, the BOSS1244 and (J2000.0) (J2000.0) z BOSS1542 protoclusters are very different, suggesting BG QSO1 191.11745 36.122048 3.212 that they are in different stages of evolution. BG QSO2 190.70921 35.966921 3.143 BG QSO3 190.81858 36.145731 2.888 4.2.1. BOSS1244 with multiple components BG QSO4 191.08365 36.151788 2.863 BOSS1244 shows two distinct components (NE and BOSS1244 BG QSO5 190.90702 36.031874 2.437 SW) both in space and in redshift distribution, and two QSO1 (HAE) 191.10603 36.132581 2.260 substructures in the SW region. The redshift difference QSO2 (HAE) 190.91308 35.901003 2.245 between SW and NE regions is ∆z =0.016 (the line-of- QSO3 (HAE) 191.01176 35.935079 2.235 sight depth is 20.8 cMpc), and the projected separation QSO4 (HAE) 191.11257 36.152239 2.233 between them is 13.′5 ( 21.6 cMpc). The right panel in ∼ QSO5 (HAE) 190.90429 35.941498 2.228 Figure 10 is the spectroscopic confirmed HAEs, we find BG QSO1 235.47301 38.774797 2.781 that serveral substructures are in the SW and NE re- BG QSO2 235.43314 39.149935 2.717 gions. In the SW region, there are about five subgroups with 3 5 galaxies at 2.213 Redshift 2.22 2.23 2.24 2.25 Figure 10. Three-dimensional distribution of the protocluster galaxies in the BOSS1244 field. Sky coordinates are listed relative to the centre of the BOSS1244 field. The color-coded points and stars are the confirmed HAEs and quasars at z = 2.213 − 2.260. Left: HAEs plotted as Decl. vs. R.A. The black circles are the HAE candidates in BOSS1244. Right: Confirmed HAEs plotted Decl. vs. z. There is a separation in the distributions of galaxies both in Decl. and z. density of 10.5 2.8. They estimated the dynamical Recently, Darvish et al. (2020) reported a protocluster ± 14 mass of 3 10 M⊙, and expected a halo mass (CC2.2) in the COSMOS field at z = 2.23 traced by ∼ × 15 of (3.67 8.69) 10 M⊙ for the z = 0 cluster. the spectroscopic confirmation of HAEs. The galaxy ∼ − × Cucciati et al. (2018) presented a proto-supercluster at overdensity is 6.6 over the volume of 5500cMpc3, ∼ ∼ 14 z =2.45 by identifying seven galaxy groups within a vol- corresponding to the halo mass of 9.20 10 M⊙ at 3 ∼ × 14 ume of 60 60 150 cMpc . The total mass in each z = 0. The dynamical mass is (1 2) 10 M⊙, ∼ × × 12 14 ∼ − × galaxy group at z = 0 is about 9.2 10 2.6 10 M⊙, suggesting the CC2.2 protocluster is not fully virialized × − × and the estimated present-day mass in the effective vol- at z = 2.23. Similarly, our protoclusters are also iden- 4 3 15 ume of 9.5 10 cMpc is 4.8 10 M⊙. The effective tified by the NIR spectroscopy of HAEs at the same × ∼ × volume of the proto-supercluster is slightly larger than redshift, suggesting that our protocluster system are dy- that in our protoclusters (6.2 104 cMpc3), but esti- namically younger and in the process of galaxy accretion × mated present-day mass is 2 3 times less than ours. and merging, which are far from virialization, especially − The main reason is that the estimation of mass depends for the BOSS1542 protocluster. The NE protocluster not only on volume, but also on the galaxy overden- in BOSS1244 is similar to the CC2.2 protocluster given sity. Topping et al. (2018) investigated the nature of their consistent galaxy overdensities and expected halo large-scale structure in the SSA22 protocluster region at masses at z = 0. z =3.09 with a galaxy overdensity of 7.6 1.4. The ex- Cai et al. (2017a) reported the first MAMMOTH ± 15 pected total halo mass at z = 0 is (3.19 0.40) 10 M⊙ protocluster BOSS1441 at z = 2.32. This proto- ± × over a volume of 12 14 43 cMpc3. They re- cluster contains a dominant dark matter halo that ∼ × × vealed two separated overdensities at z = 3.065 and would likely collapse into a virialized cluster with mass 15 z =3.095, corresponding to the present-day masses are Mz=0 = 10 M⊙. For BOSS1441, BOSS1244 and 15 15 (0.76 0.17) 10 M⊙ and (2.15 0.32) 10 M⊙, BOSS1542, the three overdensities selected from the ± × ± × respectively. Our findings of the large-scale structures same technique display dramatically different in mor- in BOSS1244 seem to exhibit a consistent size and phology, representing different stages of galaxy cluster number of components with similar present-day masses. assembly. We suspect BOSS1441 is a nearly-virialized 18 Shi et al. Redshift 2.21 2.22 2.23 2.24 2.25 2.26 Figure 11. Three-dimensional distribution of the protocluster galaxies in the BOSS1542 field. Sky coordinates are listed relative to the centre of the BOSS1542 field. The color-coded points and stars are the confirmed HAEs and quasars at z = 2.206 − 2.269. Left: HAEs plotted as Decl. vs. R.A. The black circles are the HAE candidates in BOSS1244. Right: Confirmed HAEs plotted Decl. vs. z. There is no significant difference in the distributions of galaxies in Decl. protocluster, BOSS1244 is forming one or two pro- ter (CC2.2) at z = 2.23 in the COSMOS field over the toclusters, and BOSS1542 is forming a filamentary volume of 5.48 105 cMpc−3 and the corresponding ∼ × structure. These processes are also expected in the volume density is 1.8 10−6 cMpc−3, which is higher × cosmological simulations (Shandarin & Zeldovich 1989; than our result. This reason is due to their limited ef- van de Weygaert & Bond 2008; Shandarin & Sunyaev fective volume. According to simulations, Topping et al. 2009; Libeskind et al. 2018). Namely, considering a non- (2018) found that the presence of two massive halos sep- spherical collapse of an ellipsoildal overdensity for the arated by 2000kms−1 around the SSA22 protocluster is real perturbations, the expansion turns into collapse 7.4 Gpc−3 at z 3. The BOSS1244 with two massive ∼ along shortest axis first to form a “pancake” sheet struc- protoclusters separated by 1500kms−1 is similar to the ture, then along the intermediate axis to form filaments, SSA22 protocluster, and their occurrence rate of such a and only at the end to fully collapse along the longest structure is consistent. axis to form clusters (e.g., Libeskind et al. 2018). For the rarity of these two structures, Cai et al. 4.3. Velocity Structure (2017a) found 11 fields at z = 2 3 that contain BOSS1244 and BOSS1542 are the most massive struc- − groups of strong IGM Lyα absorption over the vol- tures consisting of multiple components. BOSS1244 ume of 108 cMpc3, but 30% of the 11 absorptions has two distinct protoclusters in the SW and NE re- 15 − have > 10 M⊙, where BOSS1441, BOSS1244 and gions, the velocity dispersions are 405 202kms 1 and ± BOSS1542 are included and identified. Namely, the 377 99kms−1, respectively. Furthermore, the SW pro- 15 ± volume density of high-mass of > 10 M⊙ is 3 tocluster in BOSS1244 appears to be two components − − ∼ × 10 8 cMpc 3. However, BOSS1244 and BOSS1542 have with the velocity dispersions of 484 181kms−1 and ± currently the highest galaxy overdensities over the vol- 152 58kms−1. In contrast, the estimated velocity dis- 3 ± ume of (39 cMpc) , corresponding to the present-day persion in BOSS1542 filament is 247 32kms−1. Note ∼ 16 ± total masses of 10 M⊙, so the occurrence rate of that we do not map all the HAEs in BOSS1244 and ∼ − − such structures is expected to be 2 10 8 cMpc 3 at BOSS1542 due to the limited NIR spectroscopic obser- × z = 2.2. Darvish et al. (2020) detected one protoclus- vations. Discoveries of two protoclusters at z =2.24 19 Figure 12. Left panel: velocity dispersion of protoclusters as a function of redshift and the histogram of the velocity dispersion of protoclusters. The red squares are the SW and NE protoclusters in BOSS1244, the blue square is the protocluster in BOSS1542, and other black symbols are the other protoclusters from the literature (Chiang et al. 2013; Lemaux et al. 2014; Dey et al. 2016; Wang et al. 2016; Franck & McGaugh 2016; Topping et al. 2016; Cai et al. 2017a; Cucciati et al. 2014, 2018; Oteo et al. 2018; Toshikawa et al. 2020; Darvish et al. 2020; Hill et al. 2020). The dashed lines show the redshift evolution of dark 14 14 matter velocity dispersion of 1 × 10 M⊙ and 5 × 10 M⊙ halos at z = 0, which is from Toshikawa et al. (2020). Right panel: virial mass Mvir derived from velocity dispersion, vs. the present-day total mass Mtot estimated from galaxy overdensity. The red squares are the SW and NE protoclusters in BOSS1244 and the blue square is the protocluster in BOSS1542. The rightmost red square is our estimated velocity dispersion of the entire BOSS1244 system. Other symbols are the other protoclusters from the literature (Cucciati et al. 2014; Lemaux et al. 2014; Franck & McGaugh 2016; Cai et al. 2017a; Topping et al. 2016, 2018; Cucciati et al. 2018; Darvish et al. 2020). The dot-dashed line shows the 1:1 relation between Mvir and Mtot. The line-of-sight velocity dispersions of density peaks It indicates that all these protoclusters may be in dif- in BOSS1244 and BOSS1542 are relatively small com- ferent dynamical state. The velocity dispersions of pared with those of studied protoclusters in the litera- other known protocluster candidates at z > 2 have ture. For example, The velocity dispersions of the proto- been compiled (Kuiper et al. 2011; Cucciati et al. 2014; supercluster with seven density peaks at z = 2.45 are Toshikawa et al. 2014; Wang et al. 2016; Lemaux et al. 320 737kms−1 (Cucciati et al. 2018). Venemans et al. 2014, 2018; Miller et al. 2018; Chanchaiworawit et al. − (2007) discovered six protoclusters around eight radio 2019) in Figure 12. The left panel of Figure 12 presents galaxies at z = 2.0 5.2, the velocity dispersions for a relationship between velocity dispersion and redshift − these clusters were measured to be ranging from of protoclusters. No significant correlation is seen be- ∼ 250kms−1 to 1000kms−1. In that sample, MRC 1138- tween velocity dispersion and redshift, although the ve- 262 (PKS 1138-262) at z = 2.16 and MRC 0052-241 locity dispersion is expected to increase with protoclus- at z = 2.86 protoclusters showed bimodal redshift dis- ter growth. Most protoclusters have velocity dispersions tributions: MRC 1138-262 had double peaks with ve- of < 600kms−1, but some protoclusters show higher locity dispersions of 280 km s−1 and 520kms−1, and velocity dispersions, even > 1000kms−1. We estimate MRC 0052-241 had double peaks with velocity disper- the velocity dispersion for the whole BOSS1244 field is sions of 185kms−1 and 230kms−1. The best-studied 1670 963kms−1 using the Gaussian fitting. We also ± system SSA22 protocluster (similar to the BOSS1244 apply the biweight method and estimate the velocity protocluster) at z = 3.09 showed two substructures dispersion to be 1058 142kms−1, consistent with pre- ± with velocity dispersions of 350 km s−1 and 540kms−1 vious mentioned. Previous works explain that the pro- (Topping et al. 2016). Using NIR spectroscopy of HAE toclusters with higher velocity dispersions are in merg- sample, Darvish et al. (2020) estimated that the veloc- ing processes and forming more massive structures, and ity dispersion of protocluster CC2.2 at z = 2.23 is their dynamical state may be far from virialization (e.g., 645kms−1, which is higher than the velocity disper- Dey et al. 2016; Toshikawa et al. 2020). sions of our protoclusters. We calculate the velocity The right panel of Figure 12 presents dynamical dispersion of BOSS1441 protocluster at z = 2.32 from masses based on the estimation of velocity dispersion 18 Lyα spectroscopy is 943kms−1 (Cai et al. 2017a). as a function of present-day masses based on the Equa- 20 Shi et al. tion 1. The dot-dashed line lies on the 1:1 relation. 2011). The protocluster USS 1558 at z = 2.5 is sug- Cucciati et al. (2018) presented a “Hyperion” proto- gested to be a growing protocluster (Shimakawa et al. supercluster with seven density peaks, the estimated two 2018a,b). In the maturing stage, the members of pro- sets of masses are surprisingly consistent with the agree- toclusters may be undergoing a rapid transition from ment of < 2σ. Moreover, one of the seven peaks (orange dusty starbursts to quenching populations, red sequence square in Figure 12) has already been identified as a viri- and high AGN fraction can be seen (Williams et al. alized structure (Wang et al. 2016), but they suggested 2009; Whitaker et al. 2011). The protocluster PKS 1138 Mtotal may be underestimated given the most distant at z = 2.2 is considering to be a maturing proto- in reconstruction from the 1:1 relation between Mtotal cluster (Shimakawa et al. 2018a). Due to the insuffi- and Mvir. The evolution of a density fluctuation from cient gas accretion, cluster members in the hot inter- the beginning of collapse to virialization can take a few cluster medium enriched by superheated plasma would gigayears. Furthermore, galaxies outside the peaks’ vol- no longer maintain their star formation in the declin- umes may be included in the velocity distribution along ing phase (e.g., Kereˇset al. 2005; Hughes et al. 2013; the line-of-sight. Thus, the estimated dynamical masses Hayashi et al. 2017), including environmental quenching based on the velocity dispersion of protoclusters have (e.g., Bamford et al. 2009; Peng et al. 2010; Gobat et al. relatively small changes, while Mtotal varies by chang- 2015; Ji et al. 2018). Based on the cold flows and shock- ing the overdensity threshold to define the density peaks heated medium as a function of total mass and redshift (Cucciati et al. 2018). described in Dekel & Birnboim (2006) and the afore- We may infer the level of virialization of a density mentioned scenario, we predict that BOSS1542 is in the peak based on the comparison between Mtotal and Mvir, cold in the evolutionary stage of cool gas filament, may although there are some uncertainties. We have com- still be in the growing phase like USS 1558, BOSS1441 piled some known protoclusters in the literature, as may be similar to PKS 1138, it is probably a maturing shown in the right panel of Figure 12. We find that protocluster, and BOSS1244 could be the transitional some protoclusters locate on the relation between Mtotal stage between BOSS1542 and BOSS1441. The discov- and Mvir, while some protoclusters show that Mvir is ery of these three MAMMOTH protoclusters provides 2 3 orders of magnitude lower than Mtotal. We ar- us with new insights into the formation and evolution of − gue that some protoclusters are near-virialized (e.g., galaxy cluster at the present epoch. Wang et al. 2016; Cai et al. 2017a; Cucciati et al. 2018; Darvish et al. 2020), representing an important tran- 5. SUMMARY sition phase between protoclusters and mature clus- BOSS1244 and BOSS1542 are two extreme overden- ters, and some protocluster systems are far from viri- sities traced by Lyα absorbers within 20cMpc at ∼ alization (e.g., Cucciati et al. 2014; Lemaux et al. 2014; z = 2.24 0.02. They have been confirmed with ± Topping et al. 2016), providing direct evidence on the HAEs identified using the NIR NB imaging technique. earlier formation phase. BOSS1441 protocluster might Using the NIR MMT/MMIRS and LBT/LUCI instru- be a near-virialized structure, while the protoclus- ments, 46 and 36 HAEs are spectroscopically identified ters in BOSS1244 and BOSS1542 show much smaller in BOSS1244 and BOSS1542, respectively. We analyze Mtotal/Mvir ratios, indicating that these structures are the properties of the two overdensities taking advantage far from virialization, they may be collapsing and form- of NIR spectroscopy. The results are summarized as ing much more massive large-scale structures. There- follows. fore, we conclude that the protoclusters in BOSS1441, BOSS1244 and BOSS1542 are likely to be at differ- (1) We identify 46/36 HAEs at z 2.24 in the ∼ ent stages of their evolution, and will become virialized BOSS1244/BOSS1542 field through NIR spec- structures later. troscopic observations. The detection rate in Recently, Shimakawa et al. (2018a) proposed a spec- BOSS1244 is 80%, while the success rate is 57% ulation of formation and evolution histories of galaxy in BOSS1542. This is due to the shorter exposure clusters. They divided the formation of galaxy clusters time in the slit-masks in BOSS1542, and 4% ∼ into three stages: growing phase at z 3, maturing contaminations in HAE sample given an [O III] ≥ phase at z = 2 3 and declining phase at z 2. In emitter galaxy at z = 3.302 is detected. These − ≤ the growing stage, cold gas stream in the hot gas is able confirmed HAEs suggest that the BOSS1244 and to support the active star formation in massive galax- BOSS1542 fields are indeed extremely overdense. ies (e.g., Kereˇset al. 2005; Dekel & Birnboim 2006; (2) In BOSS1244, there are two distinct peaks in Ocvirk et al. 2008; Kereˇset al. 2009; van de Voort et al. the SW and NE regions at z = 2.230 and z = Discoveries of two protoclusters at z =2.24 21 2.246 segregated on the sky and redshift distri- structures. We caveat that it may be not very ac- ′ bution, the projected separation is about 13.5 curate to use log(Mtotal/Mvir) to judge whether a (21.6 cMpc). The estimated line-of-sight veloc- system is virialized beacuse the estimated veloc- ity dispersions are 405 202kms−1 and 377 ity dispersions include the galaxies outside peaks’ −1 ± ± 99kms , respectively. Moreover, two substruc- volume and Mtotal varies by changing the overden- tures in the SW region of the BOSS1244 are found. sity threshold to define the density peaks, but it Comparatively, BOSS1542 presents an enormous is very helpful to understand the protocluster sys- filamentary structure at z = 2.241 with a very tems quantitatively. small velocity dispersion of 247 32kms−1, sug- ± gesting that it might be a dynamically younger (6) We stress that BOSS1441, BOSS1244 and system and providing a direct detection of cosmic BOSS1542 protoclusters display dramatically dif- web in the early universe. ferent morphologies, representing different stages of galaxy cluster assembly. Namely, BOSS1441 (3) We recompute the HAE overdensities δg in may be a near-virialized protocluster, BOSS1244 BOSS1244 and BOSS1542. Assuming 80% HAE is forming one or two protoclusters, and BOSS1542 candidates are true HAEs at z = 2.24, δg in is forming a filament. Besides, two quasar pairs the BOSS1244 and BOSS1542 fields are 5.5 0.7 in BOSS1441, one quasar pair in BOSS1244 and ± and 5.2 0.6, respectively. For the protoclus- BOSS1542, these quasar pairs may work with ± ter scale of 15 cMpc, δg in the BOSS1244 SW, CoSLAs to trace the most massive large-scale NE regions and BOSS1542 filament are 22.9 4.9 structures of universe. ± and 10.9 2.5,20.5 3.9, respectively. Therefore, ± ± Taken together, our results imply that BOSS1244 and BOSS1244 and BOSS1542 are the most overdense BOSS1542 are dynamically young and pre-virialization. galaxy protoclusters (δg > 20.0) discovered to date Using the obtained high-quality data, we will investigate at z > 2. the properties of galaxies in the overdense environemnts at z =2 3, including SFR, gas-phase metallicity, mor- (4) The BOSS1244 and BOSS1542 overdensities are − expected to be virialized at z 0, so we can cal- phology and AGN fraction relative to galaxies in the ∼ general fields in forthcoming works. Moreover, much culate their present-day total masses Mtotal based more follow-up spectroscopy are needed to further ex- on the galaxy overdensity δg. BOSS1244 and BOSS1542 are expected to evolve into a cluster plore BOSS1244 and BOSS1542. 16 with halo masses of (0.89 0.07) 10 M⊙ and 16 ± × (0.82 0.06) 10 M⊙. On the scale of 15 cMpc, ± × the present-day masses in BOSS1244 SW and NE ACKNOWLEDGMENTS 15 density peaks are (1.59 0.20) 10 M⊙ and We thank anonymous referee for the valuable and 15 ± × (0.83 0.11) 10 M⊙, and the expected total helpful comments. We thank Mengtao Tang, Jinyi ± × mass in the BOSS1542 filament is (1.42 0.18) Yang, Chun Ly, Igor Chilingarian, Yongming Liang and 15 ± × 10 M⊙. The masses without galaxy overden- FangXia An for their useful discussions on this work. sities in BOSS1244 and BOSS1542 are (3.70 This work is supported by the National Science Foun- 15 15 ± 0.18) 10 M⊙ and (3.48 0.16) 10 M⊙ in dation of China (11773076, 12073078 and 12073014), × ± × BOSS1542. For the density peaks in BOSS1244 the National Key R&D Program of China (grant No. and BOSS1542, they will evolve into Coma-type 2017YFA0402703 and No. 2018YFA0404503), the Ma- galaxy clusters at z = 0. jor Science and Technology Project of Qinghai Province (2019-ZJ-A10), and the Chinese Academy of Sciences (5) The dynamical masses Mvir in BOSS1244 and (CAS) through a China-Chile Joint Research Fund BOSS1542 are estimated using the line-of-sight (CCJRF #1809) administered by the CAS South Amer- velocity dispersion assuming that these systems ica Centre for Astronomy (CASSACA). DDS gratefully are virialized. The dynamical masses for the acknowledges the supports from the China Scholarship BOSS1244 SW, NE region, and BOSS1542 fila- Council (201806340059) in 2018 2020. 13 − ment are (2.30 3.50) 10 M⊙ , (1.90 1.50) 13 ± × ± 12 × 10 M⊙, and Mvir = (5.30 2.10) 10 M⊙ ± × , respectively. The log(Mtotal/Mvir) ratios are Facilities: MMT (MMIRS), LBT (LUCI) 1.64 2.43, indicating that our protoclusters are − far from virialization, especially for the BOSS1542 22 Shi et al. APPENDIX We show all the 2D spectra of HAEs in BOSS1244 and BOSS1542 based on the LBT/ LUCI observations, as shown in Figure 13. Figure 13. 2D spectra of HAEs in BOSS1244 and BOSS1542 observed via LBT/LUCI slit masks. Skyline residuals are visible as vertical lines with a higher noise level. The slit and spectrum ID in each mask are indicated. The upper left panel is the mask in the BOSS1244 field. The rest are the three masks in the BOSS1542 field. Table A1 and Table A2 list the catalog of spectroscopically-confirmed HAEs and an [O III] emitter in BOSS1244 and BOSS1542. Discoveries of two protoclusters at z =2.24 23 Table A1. The sky positions, redshifts and total magnitudes at Ks-band for the spectroscopically-confirmed HAEs in BOSS1244. SlitMask ID R.A. Decl. Redshift Ks (J2000.0) (J2000.0) z (mag) slit-2 12:43:24.01 +35:58:47.98 2.234 23.30±0.14 slit-3 12:43:24.95 +35:58:38.59 2.235 22.79±0.08 slit-4 12:43:27.98 +35:58:16.75 2.221 20.56±0.01 slit-5 12:43:26.88 +35:58:06.74 2.235 22.45±0.08 slit-13a 12:43:37.03 +35:56:29.58 2.229 20.39±0.01 slit-14 12:43:36.69 +35:56:21.21 2.230 21.71±0.04 slit-15 12:43:38.80 +35:56:11.17 2.226 21.80±0.05 slit-17 12:43:29.71 +35:55:50.79 2.247 23.09±0.11 slit-18 12:43:39.68 +35:55:40.21 2.227 22.08±0.04 MMIRS-mask1 slit-19 12:43:23.35 +35:55:31.22 2.235 20.56±0.01 slit-20 12:43:38.43 +35:55:21.58 2.225 21.69±0.04 slit-21 12:43:33.30 +35:55:10.79 2.220 22.52±0.07 slit-22b 12:43:28.42 +35:54:59.30 2.213 21.54±0.04 slit-23b 12:43:32.44 +35:54:46.00 2.250 21.77±0.03 slit-26b 12:43:27.69 +35:53:57.44 2.253 22.08±0.06 slit-27 12:43:29.22 +35:53:44.75 2.242 22.55±0.07 slit-29 12:43:35.15 +35:53:16.44 2.255 21.74±0.04 slit-30 12:43:29.54 +35:53:08.90 2.244 22.21±0.04 slit-31 12:43:33.17 +35:52:50.99 2.245 22.18±0.05 slit-1 12:44:13.61 +36:02:58.60 2.243 22.72±0.08 slit-2 12:44:34.29 +36:06:55.98 2.244 22.42±0.09 slit-3 12:44:33.60 +36:06:35.31 2.240 22.96±0.13 slit-4 12:44:35.55 +36:04:20.98 2.239 22.41±0.07 slit-5 12:44:33.48 +36:05:20.73 2.229 22.66±0.06 slit-6 12:44:32.00 +36:05:04.60 2.253 21.95±0.05 slit-7 12:44:30.59 +36:05:21.79 2.251 21.71±0.03 slit-8 12:44:28.04 +36:03:52.50 2.245 21.54±0.03 MMIRS-mask2 slit-9 12:44:25.62 +36:03:59.77 2.247 21.87±0.04 slit-10 12:44:23.73 +36:03:54.10 2.244 23.27±0.09 slit-11 12:44:22.41 +36:03:24.96 2.253 22.58±0.09 slit-12 12:44:17.83 +36:05:39.97 2.242 23.06±0.10 slit-13 12:44:17.54 +36:05:15.89 2.248 22.67±0.10 slit-16 12:44:15.86 +36:03:54.11 2.244 22.91±0.07 slit-17 12:44:13.61 +36:02:58.60 2.250 22.44±0.08 slit-20 12:44:08.17 +36:04:02.92 2.248 22.27±0.09 slit-21 12:44:07.75 +36:03:13.92 2.248 21.14±0.04 slit-22 12:44:05.18 +36:04:44.78 2.244 23.26±0.10 slit-10 12:43:43.41 +35:54:49.69 2.231 22.06±0.06 slit-11 12:43:42.66 +35:54:53.55 2.228 23.12±0.09 slit-12 12:43:40.61 +35:54:08.32 2.217 20.50±0.02 LUCI-mask slit-14 12:43:39.09 +35:54:03.71 2.246 20.54±0.01 slit-21c 12:43:32.43 +35:54:46.07 2.249 21.77±0.03 slit-23 12:43:29.86 +35:55:57.53 2.246 22.27±0.04 slit-25c 12:43:28.44 +35:54:59.41 2.214 21.54±0.04 slit-26c 12:43:27.68 +35:53:57.40 2.253 22.08±0.06 Note—aslit-13 in MMIRS-mask1 is the QSO5 listed in Table 4. bslit-22, slit-23 and slit-26 in MMIRS-mask1 are the same with cslit-25, slit-21 and slit-26 in LUCI-mask. Their measured redshifts are consistent. 24 Shi et al. Table A2. The sky positions, redshifts and total magnitudes at Ks-band for the spectroscopically-confirmed HAEs in BOSS1542. SlitMask ID R.A. Decl. Redshift Ks (J2000.0) (J2000.0) z (mag) slit-1 15:42:50.52 +38:58:18.48 2.244 22.59±0.10 slit-4 15:42:36.90 +38:58:17.55 2.239 22.54±0.06 slit-6a 15:42:34.96 +38:59:09.63 2.243 22.37±0.09 slit-7 15:42:46.90 +38:59:49.53 2.229 22.33±0.07 slit-8 15:42:41.55 +38:59:59.62 2.227 23.31±0.14 slit-10 15:42:41.04 +39:00:19.09 2.251 22.09±0.05 slit-11 15:42:36.31 +39:00:18.43 2.240 22.69±0.10 MMIRS-mask2 slit-15 15:42:42.66 +39:01:40.51 2.206 22.17±0.06 slit-17 15:42:47.98 +39:02:22.66 2.211 22.05±0.06 slit-21 15:42:48.39 +39:03:35.89 2.213 23.48±0.17 slit-23 15:42:47.58 +39:03:49.58 2.215 22.82±0.11 slit-24 15:42:39.88 +39:03:39.26 2.253 23.71 ±0.22 slit-25 15:42:40.60 +39:03:51.47 2.216 22.78±0.10 slit-27b 15:42:29.55 +39:03:47.10 3.302 22.72±0.07 slit-11 15:42:49.44 +38:51:58.53 2.256 22.10±0.06 slit-14 15:42:52.83 +38:50:31.18 2.237 22.44±0.07 slit-15 15:42:51.55 +38:50:29.29 2.241 21.63±0.06 LUCI-mask1 slit-16 15:42:57.86 +38:49:40.00 2.269 18.94 ±0.02 slit-17 15:42:56.87 +38:49:28.27 2.238 22.62±0.11 slit-19 15:42:50.72 +38:49:41.08 2.241 22.27±0.08 slit-20 15:42:52.78 +38:48:28.48 2.246 22.77±0.11 slit-21 15:42:45.24 +38:48:30.69 2.238 22.06±0.05 slit-10 15:42:45.35 +38:54:52.78 2.215 23.06±0.15 slit-11 15:42:48.24 +38:54:18.03 2.238 22.12±0.08 slit-12c 15:42:47.01 +38:53:42.34 2.241 19.42±0.01 LUCI-mask2 slit-13 15:42:49.56 +38:53:20.48 2.243 20.77±0.07 slit-14 15:42:50.51 +38:52:14.80 2.242 22.78±0.07 slit-15 15:42:49.44 +38:51:58.44 2.258 22.10±0.06 slit-17 15:42:49.77 +38:52:50.46 2.241 22.94±0.11 slit-12 15:42:32.86 +38:59:27.41 2.242 22.12±0.05 slit-13d 15:42:34.97 +38:59:09.56 2.244 22.37±0.09 slit-14 15:42:29.92 +38:58:33.08 2.242 22.88±0.12 LUCI-mask3 slit-17 15:42:42.12 +38:58:20.20 2.237 21.64±0.06 slit-18 15:42:40.69 +38:58:03.00 2.242 20.24 ±0.05 slit-21 15:42:41.55 +38:56:50.88 2.240 21.75±0.05 slit-22 15:42:43.27 +38:56:31.21 2.238 21.64±0.05 Note—aslit-6 in MMIRS-mask2 is the same with dslit-13 in LUCI-mask3, and the measured redshift is consistent. bslit-27 in MMIRS-mask2 is an [O III] emitter. cslit-12 in LUCI-mask2 is the QSO3 listed in Table 4. Discoveries of two protoclusters at z =2.24 25 REFERENCES An, F. X., Zheng, X. Z., Wang, W.-H., et al. 2014, ApJ, Collins, C. A., Stott, J. P., Hilton, M., et al. 2009, Nature, 784, 152, doi: 10.1088/0004-637X/784/2/152 458, 603, doi: 10.1038/nature07865 Arrigoni Battaia, F., Hennawi, J. F., Prochaska, J. X., & Cooke, E. A., Hatch, N. A., Muldrew, S. I., Rigby, E. E., & Cantalupo, S. 2015, ApJ, 809, 163, Kurk, J. D. 2014, MNRAS, 440, 3262, doi: 10.1088/0004-637X/809/2/163 doi: 10.1093/mnras/stu522 Bagchi, J., Sankhyayan, S., Sarkar, P., et al. 2017, ApJ, Cooke, E. A., Hatch, N. A., Stern, D., et al. 2016, ApJ, 844, 25, doi: 10.3847/1538-4357/aa7949 816, 83, doi: 10.3847/0004-637X/816/2/83 Bamford, S. P., Nichol, R. C., Baldry, I. K., et al. 2009, Cucciati, O., Zamorani, G., Lemaux, B. C., et al. 2014, MNRAS, 393, 1324, A&A, 570, A16, doi: 10.1051/0004-6361/201423811 doi: 10.1111/j.1365-2966.2008.14252.x Cucciati, O., Lemaux, B. C., Zamorani, G., et al. 2018, Beers, T. C., Flynn, K., & Gebhardt, K. 1990, AJ, 100, 32, A&A, 619, A49, doi: 10.1051/0004-6361/201833655 doi: 10.1086/115487 Daddi, E., Cimatti, A., Renzini, A., et al. 2004, ApJ, 617, Belli, S., Contursi, A., & Davies, R. I. 2018, MNRAS, 478, 746, doi: 10.1086/425569 2097, doi: 10.1093/mnras/sty1236 Daddi, E., Dannerbauer, H., Stern, D., et al. 2009, ApJ, Bond, J. R., Kofman, L., & Pogosyan, D. 1996, Nature, 694, 1517, doi: 10.1088/0004-637X/694/2/1517 380, 603, doi: 10.1038/380603a0 Darvish, B., Scoville, N. Z., Martin, C., et al. 2020, ApJ, Borisova, E., Cantalupo, S., Lilly, S. J., et al. 2016, ApJ, 892, 8, doi: 10.3847/1538-4357/ab75c3 831, 39, doi: 10.3847/0004-637X/831/1/39 Dekel, A., & Birnboim, Y. 2006, MNRAS, 368, 2, Bower, R. G., Lucey, J. R., & Ellis, R. S. 1992, MNRAS, doi: 10.1111/j.1365-2966.2006.10145.x 254, 601, doi: 10.1093/mnras/254.4.601 Dey, A., Lee, K.-S., Reddy, N., et al. 2016, ApJ, 823, 11, Cai, Z., Fan, X., Peirani, S., et al. 2016, ApJ, 833, 135, doi: 10.3847/0004-637X/823/1/11 doi: 10.3847/1538-4357/833/2/135 Dressler, A. 1980, ApJ, 236, 351, doi: 10.1086/157753 Cai, Z., Fan, X., Bian, F., et al. 2017a, ApJ, 839, 131, Evrard, A. E., Bialek, J., Busha, M., et al. 2008, ApJ, 672, doi: 10.3847/1538-4357/aa6a1a 122, doi: 10.1086/521616 Cai, Z., Fan, X., Yang, Y., et al. 2017b, ApJ, 837, 71, Farina, E. P., Falomo, R., & Treves, A. 2011, MNRAS, 415, doi: 10.3847/1538-4357/aa5d14 3163, doi: 10.1111/j.1365-2966.2011.18931.x Cai, Z., Hamden, E., Matuszewski, M., et al. 2018, ApJL, Franck, J. R., & McGaugh, S. S. 2016, ApJ, 833, 15, 861, L3, doi: 10.3847/2041-8213/aacce6 doi: 10.3847/0004-637X/833/1/15 Cai, Z., Cantalupo, S., Prochaska, J. X., et al. 2019, ApJS, Fukugita, M., Nakamura, O., Schneider, D. P., Doi, M., & 245, 23, doi: 10.3847/1538-4365/ab4796 Kashikawa, N. 2004, ApJL, 603, L65, doi: 10.1086/383222 Cantalupo, S., Arrigoni-Battaia, F., Prochaska, J. X., Geach, J. E., , D., Hickox, R. C., et al. 2012, MNRAS, 426, Hennawi, J. F., & Madau, P. 2014, Nature, 506, 63, 679, doi: 10.1111/j.1365-2966.2012.21725.x doi: 10.1038/nature12898 Geach, J. E., Smail, I., Best, P. N., et al. 2008, MNRAS, Casasola, V., Magrini, L., Combes, F., et al. 2018, A&A, 388, 1473, doi: 10.1111/j.1365-2966.2008.13481.x 618, A128, doi: 10.1051/0004-6361/201833052 Gobat, R., Daddi, E., B´ethermin, M., et al. 2015, A&A, Casey, C. M., Cooray, A., Capak, P., et al. 2015, ApJL, 581, A56, doi: 10.1051/0004-6361/201526274 808, L33, doi: 10.1088/2041-8205/808/2/L33 Goto, T., Yamauchi, C., Fujita, Y., et al. 2003, MNRAS, Cen, R., & Ostriker, J. P. 2000, ApJ, 538, 83, 346, 601, doi: 10.1046/j.1365-2966.2003.07114.x doi: 10.1086/309090 Green, P. J., Myers, A. D., Barkhouse, W. A., et al. 2011, Chanchaiworawit, K., Guzm´an, R., Salvador-Sol´e, E., et al. ApJ, 743, 81, doi: 10.1088/0004-637X/743/1/81 2019, ApJ, 877, 51, doi: 10.3847/1538-4357/ab1a34 Hatch, N. A., De Breuck, C., Galametz, A., et al. 2011, Chiang, Y.-K., Overzier, R., & Gebhardt, K. 2013, ApJ, MNRAS, 410, 1537, 779, 127, doi: 10.1088/0004-637X/779/2/127 doi: 10.1111/j.1365-2966.2010.17538.x —. 2014, ApJL, 782, L3, doi: 10.1088/2041-8205/782/1/L3 Hatch, N. A., Wylezalek, D., Kurk, J. D., et al. 2014, Chilingarian, I., Beletsky, Y., Moran, S., et al. 2015, PASP, MNRAS, 445, 280, doi: 10.1093/mnras/stu1725 127, 406, doi: 10.1086/680598 Hayashi, M., Kodama, T., Tadaki, K.-i., Koyama, Y., & Codis, S., Pichon, C., Devriendt, J., et al. 2012, MNRAS, Tanaka, I. 2012, ApJ, 757, 15, 427, 3320, doi: 10.1111/j.1365-2966.2012.21636.x doi: 10.1088/0004-637X/757/1/15 26 Shi et al. Hayashi, M., Kodama, T., Kohno, K., et al. 2017, ApJL, Kurk, J. D., R¨ottgering, H. J. A., Pentericci, L., et al. 2000, 841, L21, doi: 10.3847/2041-8213/aa71ad A&A, 358, L1. https://arxiv.org/abs/astro-ph/0005058 Hennawi, J. F., Prochaska, J. X., Cantalupo, S., & Laigle, C., Pichon, C., Codis, S., et al. 2015, MNRAS, 446, Arrigoni-Battaia, F. 2015, Science, 348, 779, 2744, doi: 10.1093/mnras/stu2289 doi: 10.1126/science.aaa5397 Le F`evre, O., Tasca, L. A. M., Cassata, P., et al. 2015, Hill, R., Chapman, S., Scott, D., et al. 2020, MNRAS, A&A, 576, A79, doi: 10.1051/0004-6361/201423829 doi: 10.1093/mnras/staa1275 Lee, K.-G., Hennawi, J. F., White, M., Croft, R. A. C., & Hughes, T. M., Cortese, L., Boselli, A., Gavazzi, G., & Ozbek, M. 2014a, ApJ, 788, 49, Davies, J. I. 2013, A&A, 550, A115, doi: 10.1088/0004-637X/788/1/49 doi: 10.1051/0004-6361/201218822 Lee, K.-G., Hennawi, J. F., White, M., et al. 2016, ApJ, Husband, K., Bremer, M. N., Stott, J. P., & Murphy, 817, 160, doi: 10.3847/0004-637X/817/2/160 D. N. A. 2016, MNRAS, 462, 421, Lee, K.-G., Krolewski, A., White, M., et al. 2018, ApJS, doi: 10.1093/mnras/stw1520 237, 31, doi: 10.3847/1538-4365/aace58 Ji, Z., Giavalisco, M., Williams, C. C., et al. 2018, ApJ, Lee, K.-S., Dey, A., Hong, S., et al. 2014b, ApJ, 796, 126, 862, 135, doi: 10.3847/1538-4357/aacc2c doi: 10.1088/0004-637X/796/2/126 Jiang, L., Wu, J., Bian, F., et al. 2018, Nature Astronomy, Lemaux, B. C., Gal, R. R., Lubin, L. M., et al. 2012, ApJ, 2, 962, doi: 10.1038/s41550-018-0587-9 745, 106, doi: 10.1088/0004-637X/745/2/106 Lemaux, B. C., Cucciati, O., Tasca, L. A. M., et al. 2014, Kartaltepe, J., Casey, C., Dickinson, M., et al. 2019, A&A, 572, A41, doi: 10.1051/0004-6361/201423828 BAAS, 51, 395. https://arxiv.org/abs/1903.05026 Lemaux, B. C., Le F`evre, O., Cucciati, O., et al. 2018, Kauffmann, G., Colberg, J. M., Diaferio, A., & White, S. A&A, 615, A77, doi: 10.1051/0004-6361/201730870 D. M. 1999, MNRAS, 303, 188, Liang, Y., Kashikawa, N., Cai, Z., et al. 2021, ApJ, 907, 3, doi: 10.1046/j.1365-8711.1999.02202.x doi: 10.3847/1538-4357/abcd93 Kauffmann, G., & White, S. D. M. 1993, MNRAS, 261, Libeskind, N. I., van de Weygaert, R., Cautun, M., et al. 921, doi: 10.1093/mnras/261.4.921 2018, MNRAS, 473, 1195, doi: 10.1093/mnras/stx1976 Kelson, D. D. 2003, PASP, 115, 688, doi: 10.1086/375502 Lubin, L. M., Brunner, R., Metzger, M. R., Postman, M., & Kereˇs, D., Katz, N., Fardal, M., Dav´e, R., & Weinberg, Oke, J. B. 2000, ApJL, 531, L5, doi: 10.1086/312518 D. H. 2009, MNRAS, 395, 160, Martin, D. C., Chang, D., Matuszewski, M., et al. 2014, doi: 10.1111/j.1365-2966.2009.14541.x ApJ, 786, 107, doi: 10.1088/0004-637X/786/2/107 Kereˇs, D., Katz, N., Weinberg, D. H., & Dav´e, R. 2005, Martizzi, D., Vogelsberger, M., Artale, M. C., et al. 2019, MNRAS, 363, 2, doi: 10.1111/j.1365-2966.2005.09451.x MNRAS, 486, 3766, doi: 10.1093/mnras/stz1106 Kikuta, S., Matsuda, Y., Cen, R., et al. 2019, PASJ, 71, L2, McLeod, B., Fabricant, D., Nystrom, G., et al. 2012, PASP, doi: 10.1093/pasj/psz055 124, 1318, doi: 10.1086/669044 Kim, J.-W., Im, M., Lee, S.-K., et al. 2016, ApJL, 821, L10, Miller, J. S. A., Bolton, J. S., & Hatch, N. 2019, MNRAS, doi: 10.3847/2041-8205/821/1/L10 489, 5381, doi: 10.1093/mnras/stz2504 Koyama, Y., Polletta, M. d. C., Tanaka, I., et al. 2021, Miller, T. B., Chapman, S. C., Aravena, M., et al. 2018, MNRAS, 503, L1, doi: 10.1093/mnrasl/slab013 Nature, 556, 469, doi: 10.1038/s41586-018-0025-2 Kraljic, K., Arnouts, S., Pichon, C., et al. 2018, MNRAS, Mo, H. J., & White, S. D. M. 1996, MNRAS, 282, 347, 474, 547, doi: 10.1093/mnras/stx2638 doi: 10.1093/mnras/282.2.347 Kuchner, U., Arag´on-Salamanca, A., Pearce, F. R., et al. Mukae, S., Ouchi, M., Hill, G. J., et al. 2020, ApJ, 903, 24, 2020, MNRAS, doi: 10.1093/mnras/staa1083 doi: 10.3847/1538-4357/abb81b Kuiper, E., Hatch, N. A., Venemans, B. P., et al. 2011, Muldrew, S. I., Hatch, N. A., & Cooke, E. A. 2015, MNRAS, 417, 1088, MNRAS, 452, 2528, doi: 10.1093/mnras/stv1449 doi: 10.1111/j.1365-2966.2011.19324.x Munari, E., Biviano, A., Borgani, S., Murante, G., & Kurk, J. D., Pentericci, L., Overzier, R. A., R¨ottgering, Fabjan, D. 2013, MNRAS, 430, 2638, H. J. A., & Miley, G. K. 2004a, A&A, 428, 817, doi: 10.1093/mnras/stt049 doi: 10.1051/0004-6361:20041819 Ocvirk, P., Pichon, C., & Teyssier, R. 2008, MNRAS, 390, Kurk, J. D., Pentericci, L., R¨ottgering, H. J. A., & Miley, 1326, doi: 10.1111/j.1365-2966.2008.13763.x G. K. 2004b, A&A, 428, 793, Onoue, M., Kashikawa, N., Uchiyama, H., et al. 2018, doi: 10.1051/0004-6361:20040075 PASJ, 70, S31, doi: 10.1093/pasj/psx092 Discoveries of two protoclusters at z =2.24 27 Oteo, I., Ivison, R. J., Dunne, L., et al. 2018, ApJ, 856, 72, Springel, V., White, S. D. M., Jenkins, A., et al. 2005, doi: 10.3847/1538-4357/aaa1f1 Nature, 435, 629, doi: 10.1038/nature03597 Ouchi, M., Shimasaku, K., Akiyama, M., et al. 2005, ApJL, Stark, C. W., White, M., Lee, K.-G., & Hennawi, J. F. 620, L1, doi: 10.1086/428499 2015, MNRAS, 453, 311, doi: 10.1093/mnras/stv1620 Overzier, R. A. 2016, A&A Rv, 24, 14, Steidel, C. C., Adelberger, K. L., Dickinson, M., et al. 1998, doi: 10.1007/s00159-016-0100-3 ApJ, 492, 428, doi: 10.1086/305073 Pascarelle, S. M., Windhorst, R. A., Keel, W. C., & Steidel, C. C., Adelberger, K. L., Shapley, A. E., et al. Odewahn, S. C. 1996, Nature, 383, 45, 2005, ApJ, 626, 44, doi: 10.1086/429989 doi: 10.1038/383045a0 —. 2000, ApJ, 532, 170, doi: 10.1086/308568 Peebles, P. J. E. 1970, AJ, 75, 13, doi: 10.1086/110933 —. 2003, ApJ, 592, 728, doi: 10.1086/375772 Peng, Y.-j., Lilly, S. J., Kovaˇc, K., et al. 2010, ApJ, 721, Sunyaev, R. A., & Zeldovich, Y. B. 1972, A&A, 20, 189 193, doi: 10.1088/0004-637X/721/1/193 Swinbank, A. M., Edge, A. C., Smail, I., et al. 2007, Pentericci, L., Kurk, J. D., R¨ottgering, H. J. A., et al. 2000, MNRAS, 379, 1343, A&A, 361, L25. https://arxiv.org/abs/astro-ph/0008143 doi: 10.1111/j.1365-2966.2007.12037.x Planck Collaboration, Aghanim, N., Altieri, B., et al. 2015, Tadaki, K.-I., Kodama, T., Koyama, Y., et al. 2011, PASJ, A&A, 582, A30, doi: 10.1051/0004-6361/201424790 63, 437, doi: 10.1093/pasj/63.sp2.S437 Rosati, P., Stanford, S. A., Eisenhardt, P. R., et al. 1999, Tanaka, I., De Breuck, C., Kurk, J. D., et al. 2011, PASJ, 63, 415, doi: 10.1093/pasj/63.sp2.S415 AJ, 118, 76, doi: 10.1086/300934 Tempel, E., Stoica, R. S., Mart´ınez, V. J., et al. 2014, Sandrinelli, A., Falomo, R., Treves, A., Farina, E. P., & MNRAS, 438, 3465, doi: 10.1093/mnras/stt2454 Uslenghi, M. 2014, MNRAS, 444, 1835, Topping, M. W., Shapley, A. E., & Steidel, C. C. 2016, doi: 10.1093/mnras/stu1526 ApJL, 824, L11, doi: 10.3847/2041-8205/824/1/L11 Sandrinelli, A., Falomo, R., Treves, A., Scarpa, R., & Topping, M. W., Shapley, A. E., Steidel, C. C., Naoz, S., & Uslenghi, M. 2018, MNRAS, 474, 4925, Primack, J. R. 2018, ApJ, 852, 134, doi: 10.1093/mnras/stx2822 doi: 10.3847/1538-4357/aa9f0f Santos, J. S., Altieri, B., Tanaka, M., et al. 2014, MNRAS, Toshikawa, J., Malkan, M. A., Kashikawa, N., et al. 2020, 438, 2565, doi: 10.1093/mnras/stt2376 ApJ, 888, 89, doi: 10.3847/1538-4357/ab5e85 Santos, J. S., Altieri, B., Valtchanov, I., et al. 2015, Toshikawa, J., Kashikawa, N., Ota, K., et al. 2012, ApJ, MNRAS, 447, L65, doi: 10.1093/mnrasl/slu180 750, 137, doi: 10.1088/0004-637X/750/2/137 Shandarin, S. F., & Sunyaev, R. A. 2009, A&A, 500, 19, Toshikawa, J., Kashikawa, N., Overzier, R., et al. 2014, doi: 10.1051/0004-6361/200912144 ApJ, 792, 15, doi: 10.1088/0004-637X/792/1/15 Shandarin, S. F., & Zeldovich, Y. B. 1989, Reviews of —. 2016, ApJ, 826, 114, doi: 10.3847/0004-637X/826/2/114 Modern Physics, 61, 185, Umehata, H., Fumagalli, M., Smail, I., et al. 2019, Science, doi: 10.1103/RevModPhys.61.185 366, 97, doi: 10.1126/science.aaw5949 Shi, K., Toshikawa, J., Cai, Z., Lee, K.-S., & Fang, T. 2020, van Albada, G. B. 1961, AJ, 66, 590, doi: 10.1086/108469 ApJ, 899, 79, doi: 10.3847/1538-4357/aba626 van de Voort, F., Schaye, J., Booth, C. M., Haas, M. R., & Shimakawa, R., Kodama, T., Tadaki, K. I., et al. 2014, Dalla Vecchia, C. 2011, MNRAS, 414, 2458, MNRAS, 441, L1, doi: 10.1093/mnrasl/slu029 doi: 10.1111/j.1365-2966.2011.18565.x Shimakawa, R., Koyama, Y., R¨ottgering, H. J. A., et al. van de Weygaert, R., & Bond, J. R. 2008, Clusters and the 2018a, MNRAS, 481, 5630, doi: 10.1093/mnras/sty2618 Theory of the Cosmic Web, ed. M. Plionis, Shimakawa, R., Kodama, T., Hayashi, M., et al. 2018b, O. L´opez-Cruz, & D. Hughes, Vol. 740, 335, MNRAS, 473, 1977, doi: 10.1093/mnras/stx2494 doi: 10.1007/978-1-4020-6941-3 10 Shimasaku, K., Ouchi, M., Okamura, S., et al. 2003, ApJL, Venemans, B. P., Kurk, J. D., Miley, G. K., et al. 2002, 586, L111, doi: 10.1086/374880 ApJL, 569, L11, doi: 10.1086/340563 Skibba, R. A., Bamford, S. P., Nichol, R. C., et al. 2009, Venemans, B. P., R¨ottgering, H. J. A., Overzier, R. A., MNRAS, 399, 966, doi: 10.1111/j.1365-2966.2009.15334.x et al. 2004, A&A, 424, L17, Sobral, D., Best, P. N., Matsuda, Y., et al. 2012, MNRAS, doi: 10.1051/0004-6361:200400041 420, 1926, doi: 10.1111/j.1365-2966.2011.19977.x Venemans, B. P., R¨ottgering, H. J. A., Miley, G. K., et al. Sobral, D., Smail, I., Best, P. N., et al. 2013, MNRAS, 428, 2005, A&A, 431, 793, doi: 10.1051/0004-6361:20042038 1128, doi: 10.1093/mnras/sts096 —. 2007, A&A, 461, 823, doi: 10.1051/0004-6361:20053941 28 Shi et al. Visvanathan, N., & Sandage, A. 1977, ApJ, 216, 214, Whitaker, K. E., Labb´e, I., van Dokkum, P. G., et al. 2011, ApJ, 735, 86, doi: 10.1088/0004-637X/735/2/86 doi: 10.1086/155464 Williams, R. J., Quadri, R. F., Franx, M., van Dokkum, P., & Labb´e, I. 2009, ApJ, 691, 1879, Wang, T., Elbaz, D., Daddi, E., et al. 2016, ApJ, 828, 56, doi: 10.1088/0004-637X/691/2/1879 Zheng, X. Z., Cai, Z., An, F. X., Fan, X., & Shi, D. D. doi: 10.3847/0004-637X/828/1/56 2021, MNRAS, 500, 4354, doi: 10.1093/mnras/staa2882