次毫米波星系的環境研究

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(1)Environments of submillimeter galaxies Kuan-Chou Hou Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan.

(2) 摘要次毫米波星系是一種位於高紅移的星系，它的大質量和非常高的恆星形成率，一般相信是由星系合併所產生的結果。本篇論文主要研究次毫米波星系的性質以及它們在大尺度結構中所扮演的角色。研究方法是計算次毫米波星系周圍的可見光星系密度，以及藉由關聯性方程式這種統計方法來分析次毫米波星系與萊曼α發射星系的關係。主要研究的範圍是 COSMOS 和 ECDF-S 天區。在 ECDF-S 天區中，LABOCA 和 AzTEC 儀器所觀測到的次毫米波星系有紅位移的估計，可以有效減少天空中投影的效應。我們取半徑為 1-2 個百萬秒差距計算次毫米波星系周圍的星系密度，結果顯示在紅移 2.5 和 3.5 的地方有些微的訊號，不過還是需要注意紅移的誤差造成的不確定性。我們更進一步使用 B、z 、K 三個濾鏡選取出 BzK 星系，它們可以區分出星系是否還有恆星生成。我們發現在一個百萬秒差距內，低恆星生成率的 BzK 星系與次毫米星系有較高的關聯性。另一方面，使用關聯性方程式分析次毫米波星系與萊曼α發射星系，結果沒有顯示任何訊號，亦即兩種星係可能沒有空間上的關連性。最後我們討論了次毫米波星系所在的大尺度結構的性質以及次毫米波星系與其他高紅移星系之間的交互關係。關鍵字：高紅移星系、次毫米波星系 .

(3) –2– ABSTRACT. To study the environment of high-redshift star-forming galaxy — submillimeter galaxies (SMGs) — and their role during large-scale structure formation, we have estimated the galaxy number density fluctuations around SMGs, and analyzed their cross correlation functions with lyman alpha emitters (LAEs), and optically-selected galaxies with photometric redshift in the COSMOS and ECDFS fields. We first measured the galaxy density around SMGs based on SMGs with photometric redshift zSMG compiled from data obtained by LABOCA and AzTEC in the ECDFS field. The number density of surrounding galaxies within projected radius of 1–2 Mpc and zSMG ± 0.1 suggests a marginal signal of excess galaxy count at z ∼ 2.5 and ∼ 3.5, although the uncertainty of redshift estimate is still large. We have further investigated the density of passive and starforming BzK galaxies at similar redshift around SMGs and find that BzKs have overdensity around LABOCA-SMGs at radius smaller than 1 Mpc, especially passive BzKs. On the other hand, our second task, the cross correlation functions between SMGs and LAEs, detects no correlation signal between the two populations, even after the exclusion of the SMGs with redshift significantly far from that of LAEs. Finally we discuss the property of the large scale structure where SMGs are located and the interconnection between SMGs and other high-redshift galaxy populations. Subject headings: Galaxies: high-redshift — submillimetre: galaxies.

(4) –3– Contents. Contents. 3. 1 Introduction. 5. 2 Data. 12. 2.1. SMGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13. 2.1.1. photometric redshift . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13. Galaxy samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16. 2.2.1. BzKs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16. 2.2.2. LAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. 2.2. 3 Galaxy density 3.1. 3.2. 20. Optical galaxy density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21. 3.1.1. Monte Carlo test . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23. BzKs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26. 3.2.1. 29. Random positions test . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Correlation function analysis. 31. 4.1. LAE-SMG cross-correlation function . . . . . . . . . . . . . . . . . . . . . .. 33. 4.2. Background and foreground contamination . . . . . . . . . . . . . . . . . . .. 36. 4.2.1. 37. Monte Carlo test of CCF . . . . . . . . . . . . . . . . . . . . . . . . ..

(5) –4– 4.3. Correlation length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38. 5 Discussion. 39. 6 Summary. 42. References. 43. 7 Appendix. 48. 7.1. Galaxy density around SMGs without redshift . . . . . . . . . . . . . . . . .. 48. 7.2. LAE rest frame UV color . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50. 7.2.1. Red/blue LAEs? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50. 7.2.2. Identification of LAE optical counterparts . . . . . . . . . . . . . . .. 50. 7.2.3. CCF of SMGs and red/blue LAEs . . . . . . . . . . . . . . . . . . . .. 50. 7.2.4. Bright/Faint LAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51. SMGs flux ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55. 7.3.

(6) –5– 1.. Introduction. Millimeter and submillimeter observations are a powerful tool to study the distant universe. Strong far-infrared continuum from dusty star-forming galaxies due to cosmological redshift can be observed at (sub)millimeter wavelength (submillimeter galaxies, SMGs). Because the cosmological dimming of the submillimeter flux is counterbalanced by the redshifting of its spectral energy distribution (negative K-correction), the same IR luminosity can be detected over a broad redshift range (Blain & Longair 1993) (Fig. 1 left). SMGs are massive, gas-rich and dust-obscured starburst galaxies with star formation rate (SFR) of up to few hundreds to thousand MJ yr−1 . Their rest-frame infrared luminosity (8 - 1000 µm) is up to LIR ∼ 1012 − 1013 LJ (Smail et al. 1997; Hughes et al. 1998; Barger et al. 1998), so they are usually considered as distant ultra luminous infrared galaxies (ULIRGs). Because of the low angular resolution (>15 arcsec) of submillimeter facilities and the faintness of counterparts in UV and optical bands, it is not easy to derive their redshifts. Nevertheless, a strong correlation exists between the far-infrared (FIR) and radio flux densities of SMG host galaxies (Condon 1992; Gear et al. 2000). Using deep VLA radio maps at 1.4 GHz, Chapman et al. (2005) had identified optical counterparts of subsamples of SMGs and derived their spectroscopic redshift distribution. More recently, spectral energy distribution fitting from multi-wavelength data is another way to estimate the photometric redshift of SMGs (Wardlow et al. 2011; Yun et al. 2012). Both spectroscopic and photometric analyses suggest that SMG is a high redshift population lying at z > 1 with a peak at z ∼ 2.2 or beyond (Fig. 1 right). Resulting of clustering analysis, SMGs could be the progenitors of massive elliptical galaxies in the local universe (Scott et al. 2002; Blain et al. 2004). And their high SFR could be produced by major merger (Tacconi et al. 2008). So SMGs are expected to.

(7) –6–. Fig. 4. The predicted flux density of a dusty galaxy as a function of redshift in various submm atmospheric windows, and at shorter wavelengths that will be probed by forthcoming space missions. Note the powerful K correction in the mm and submm wavebands at wavelengths longer than about 250 µm, which yields a flux density that is almost independent of redshift. The template spectrum is chosen to reproduce the typical properties of distant submm-selected galaxies (Fig. 2). Subtle effects due to the additional heating of dust by the CMB, and fine details of the radio SED of galaxies are not included; these effects are illustrated in Fig. 8.. Fig. 1.— Left: The predicted flux density of a dusty galaxy as a function of redshift at various submillimeter wavelengths (Blain et al. 2002). Right: Histogram is redshift distribution of. theexpected SMGto produce samples. linethan is their predicted model ies are greaterSolid flux densities more proximate counterparts.. redshift distributions for SMGs with S850. 5 the mJy et al. 2005).relations decline Noteµm that > both radio(Chapman and optical flux-density–redshift steeply with increasing redshift, and so high-redshift galaxies are not selected preferentially in those wavebands. The advantage that faint radio and optical galaxy surveys have over submm surveys comes from the complementary probe be located in high-density regions such as clusters of astrophysical signatures, and the combination of greater fields of view and finer angular resolution.. or proto-clusters. Daddi et al. (2009). and Tamura et al. (2009) have shown evidences that SMGs are associated with galaxy. A submm telescope that is sufficiently sensitive to detect a certain class of galaxy at redshift z ≃ 0.5, can detect any similar galaxies out to a redshift structures atthat high redshift. That z ∼proto-clusters 10 (Blain and Longair,or 1993a). Note, however, surveys to exploit this unusual K correction are not immune to selection effects. The K correction. is consistent with the hierarchical model. of galaxy formation: massive galaxies grow via merging and accreting, and the peak of mass 19. assembly of galaxies is at redshifts between 2 and 3. However, recent works found that not all the SMGs trace the most dense region and are highly clustering (Chapman et al. 2009; Wardlow et al. 2011) and properties of SMGs are not well constrained yet (Magnelli et al. 2012). So to study how SMGs are connected with other high redshift galaxy populations and environments can therefore provide insightful information of formation and evolution of SMGs. For this study we chose the Cosmic Evolution Surveys (COSMOS) field and Extended.

(8) –7– Chandra Deep Field South (ECDF-S) field. Both fields are multi-wavelength deep surveys and there are good quality photometric redshift estimate (Ilbert et al. 2009; Cardamone et al. 2010) available to investigate the association between SMGs and galaxies in different epochs. A popular technique to identify high redshift galaxy populations is to select them according to their color. The BzK galaxies (hereafter BzKs) are selected by B − z and z − K colors that were proposed for selecting galaxies whose stellar mess (∼ 1011 MJ ) and redshift range (1.4 6 z 6 2.5) are comparable to that of SMGs. They can be further classified as star-forming and passive galaxies (Daddi et al. 2004, 2005).. Fig. 2.— Daddi et al. (2004) proposed a color-color criterion to define BzK galaxies. A different technique to select high redshift galaxy populations is using narrowband observe high redshift emission line. Partridge & Peebles (1967) predicted young star-forming galaxies can emit significant Lyman α emission by recombination of ionized hydrogen in the interstellar medium. Cowie & Hu (1998) used narrowband filter to discover Lyman alpha.

(9) –8– emitters (LAEs) for the first time. Several surveys have detected LAEs between 2 < z < 7 in recent years (Steidel et al. 2000; Gronwall et al. 2007; Ouchi et al. 2008; Nilsson et al. 2009; Guaita et al. 2010; Ouchi et al. 2010). LAEs are selected based on their strong Lyman α line emission produced by UV light and usually have been found to be extremely faint at longer wavelengths (Fig. 3 left). LAEs appear to be young, less massive and dust free galaxies (Gawiser et al. 2007). Because their detection is based on narrowband observations of the Lyman α emission line, we can obtain relatively precise redshift of LAEs and help tracing high-z large-scale structure (Ouchi et al. 2003; Hayashino et al. 2004; Matsuda et al. 2005) (Fig. 3 right). To investigate the SMG and LAE connection, we adopt the correlation function analysis that is a powerful statistic tool to study the galaxy spatial distribution (Peebles 1980)..

(10) –9–. Fig. 3.— Left:Gronwall et al. (2007) show the transmission curve of the NB5000 narrow-band filter, B and V broadband filters. The narrowband filter isolates the emission line of Lyα sources around z = 3.1 in the ECDF-S field. They also show a typical Lyα galaxy template. Right: Sky distribution of Lyα emitters (black points, the sizes represents flux) in SSA22 field. The green dashed lines indicate the high-density region of the emitters (Hayashino et al. 2004)..

(11) – 10 – This thesis is organized as follows. The data sets for our study are described in chapter 2, followed by an analysis of the SMG environments from the density analysis in chapter 3. Chapter 4 presents the correlation function analysis and results. Implications of our results are discussed in chapter 5 and a summary and conclusions of this thesis are given in the in the final chapter. Throughout this study, we assume a cosmology with H0 = 70 km s−1 Mpc−1 , ΩΛ = 0.7, and ΩM = 0.3..

(12) – 11 –. Table 1: Abbreviations Abbreviation. Full name. ACF. Auto correlation function. ASTE. Atacama Submillimeter Telescope Experiment. APEX. Atacama Pathfinder EXperiment. AzTEC. Astronomical Thermal Emission Camera. CCF. Cross correlation function. COSMOS. Cosmic Evolution survey. ECDF-S. Extended Chandra deep field south. FWHM. Full width at half-maximum. GOODS-S. The great observatories origins deep survey south. GOODS-N. The great observatories origins deep survey nouth. LAEs. Lyman alpha emitters. LABOCA. Large APEX Bolometer Camera. SMGs. Submillimeter galaxies. SDF. Subaru deep field. SXDS. Subaru and XMM newton deep survey. ULIRG. Ultra luminous infrared galaxiy.

(13) – 12 – 2.. Data. There are many submillimeter surveys in the past few years conducted with AzTEC and LABOCA, including: AKARI deep field south, COSMOS, ECDF-S, GOODS-S, GOODS-N, Lockman hole, SSA22 and SXDS fields (for full names, see Table 1) (Perera et al. 2008; Scott et al. 2008; Chapin et al. 2009; Hatsukade et al. 2009; Weiß et al. 2009; Austermann et al. 2010; Aretxaga et al. 2011; Downes et al. 2012). On the other hand, there also are many narrow-band surveys targeting LAEs from z = 2 − 7 in different fields such as: COSMOS, ECDF-S, GOODS-S, GOODS-N, SDF, SSA22, SXDS and others (Steidel et al. 2000; Gronwall et al. 2007; Murayama et al. 2007; Nilsson et al. 2007; Ouchi et al. 2008; Nilsson et al. 2009; Ouchi et al. 2009; Shioya et al. 2009; Guaita et al. 2010). One of the purpose of this study is to investigate correlation between SMGs and LAEs, so we chose the COSMOS and ECDF-S fields, and these two fields have both submillimeter and narrow-band surveys with publicly available catalogs. Galaxy data in these two fields also include precise photometric redshift estimate extending to high redshift, making them suitable for studying the connection of high redshift galaxies. The data are summarized in Table 2 and the details are given below..

(14) – 13 – 2.1.. SMGs. A 1260 arcmin2 region that covers the ECDF-S has been imaged at 870 µm with the Large APEX Bolometer Camera (LABOCA) (Siringo et al. 2009) on the Atacama Pathfinder EXperiment (APEX) (G¨ usten et al. 2006). The survey depth is 1σ ' 1.2mJy beam−1 at 870 µm. 126 sources are listed with signal to noise ratio (S/N) ≥ 3.7 (Weiß et al. 2009) (hereafter LABOCA-SMGs). There is another survey at 1.1 mm with AzTEC mm-wavelength camera (Wilson et al. 2008) on the 10-m Atacama Submillimeter Telescope Experiment (ASTE). They imaged a 270 arcmin2 field (GOODS-S field, included in ECDF-S) to a 1σ depth of 0.48 - 0.73 mJy beam−1 with 48 sources are listed in the catalog with S/N ≥ 3.5 detection (Scott et al. 2010) (hereafter AzTEC-SMGs). LABOCA ECDF-S Submillimeter Survey includes the entire region mapped by AzTEC at 1.1mm. For the other field, COSMOS, Aretxaga et al. (2011) presented a 0.72 deg2 contiguous 1.1-mm survey carried out to a 1σ ' 1.26 mJy beam−1 depth with the AzTEC camera. There are 189 candidate sources at a S/N ≥ 3.5, out of which, 129 with S/N ≥ 4.. 2.1.1.. photometric redshift. Wardlow et al. (2011) combined VLA, MIPS 24-µm and IRAC observations to identify the optical and NIR counterparts of LABOCA-SMGs. Then, they derived the photometric redshifts from the optical to mid-infrared photometry of 78 counterparts to 72 LABOCA-SMGs. The redshift peak is at z = 2.2. Yun et al. (2012) presented photometric redshift of AzTEC detected SMGs in the smaller field, GOODS-S. One or more counterpart candidates are found for 41 AzTEC sources. In addition to optical to NIR photometric redshift, they also derived.

(15) – 14 – an independent estimate of photometric redshift, IR luminosity and dust-obscured SFR (SFRIR ) by analysing the observed IR/mm/radio part of the SED. Both redshift distributions are in good agreement with each other and previous works (Chapin et al. 2009), and can be described as a lognormal distribution with zmean = 2.6. But the uncertainties of redshift of SMGs are very large especially for some of LABOCA-SMGs, we excluded sources with zerror greater than 2 (Fig. 5).. Fig. 4.— Redshift distribution of SMGs from Wardlow et al. (2011) and Yun et al. (2012).

(16) – 15 –. Fig. 5.— Cumulative fraction of SMGs (the right/left panel for LABOCA-SMGs/AzTECSMGs detected, respectively) with 1 sigma photo z greater than or equal to zerror shown on the abscissa..

(17) – 16 – 2.2.. Galaxy samples. The galaxy catalogs we used are the 30-band COSMOS photometric redshifts catalog and Multi-wavelength Survey by Yale-Chile (MUSYC) public 32-band photometric data for ECDF-S (Ilbert et al. 2009; Cardamone et al. 2010); ∆z/(1 + z) of the galaxy photo-z are 0.06 at 1.5 < z < 3 and 0.019 at 1.2 < z < 3.7 for COSMOS and ECDF-S samples respectively, where ∆z is zspec − zphoto .. 2.2.1.. BzKs. We used the criteria proposed by Daddi et al. (2004) (z − K)AB − (B − z)AB ≥ −0.2 for star forming BzK; (z − K)AB − (B − z)AB ≤ −0.2 and (z − K)AB > 2 for passive BzK. After applying the filter corrections and flux limit used in Cardamone et al. (2010), that is -0.04 mag in (z − K) , 0.56 mag in (B − z) and KAB 6 21.84, we have identified 112 passive and 776 star-forming BzKs in ECDF-S field and Fig. 6 shows their photometric redshift distribution. The median of redshift is 1.5 and 1.8 for passive and star-forming BzKs in the ECDF-S field respectively. In COSMOS field, we identified 720 passive and ∼26000 star-forming BzKs. We note that our passive BzKs number is much less than that obtained in McCracken et al. (2010) (nearly 4000). What cause this difference is unclear, so the discussion we will focus on the EDCF-S field (including the GOODS-S field)..

(18) – 17 –. Fig. 6.— Photometric redshift distribution of BzKs in the ECDF-S field. The left penal is star-forming BzKs; the right penal is passive BzKs..

(19) – 18 – 2.2.2.. LAEs. We collected the data of narrowband observed galaxy. There are 160 LAEs at z ' 3.1 in the ECDF-S field detected by a λ5000 filter on CTIO Blanco 4m telescope (Gronwall et al. 2007). The full width at half-maximum (FWHM) of the λ5000 filter is 50 ˚ A, corresponding redshift range is 3.09 < z < 3.13. In the COSMOS field, 187 LAE candidates were detected by the Wide-Field Imager on the MPG/ESO 2.2 m telescope on La Silla. The observation used a narrow-band filter, the central wavelength is 3963 ˚ A and FWHM is 129 ˚ A, and corresponding redshift range is 2.2 < z < 2.3. (Nilsson et al. 2009)..

(20) – 19 –. Table 2: Summary of data in this work COSMOS. GOODS-S. ECDF-S. References. AzTEC. AzTEC. LABOCA. a,b,c,d,e. Numbers. 189. 48(421 ). 126(721 ). Area (arcmin2 ). 2592. 270. 1260. 4.4. 1.8. 4.6(2.32 ). Instrument SMG. Flux limit (mJy). LAE. BzK. Redshift. z ∼ 2.25. z ∼ 3.1. Numbers. 187. 160. Area (arcmin2 ). 1190. 993. Flux limit (AB mag). 25.1. 25.2. ∼26000. 720. this work. 720. 112. this work. Star-forming Passive. f,g. 1:Number of SMGs with redshift estimate. 2:1.1 mm flux limit, assuming 870 µm to 1.1 mm flux ratio is 2.0 (Scott et al. 2010) a: Aretxaga et al. (2011) b: Scott et al. (2010) c: Yun et al. (2012) d: Weiß et al. (2009) e: Wardlow et al. (2011) f: Nilsson et al. (2011) g: Gawiser et al. (2007).

(21) – 20 – 3.. Galaxy density. In this chapter is to study the environment in which SMGs are located in. We have measured the environment overdensity δ, which is defined as δ=. naperture − nf ield , nf ield. (1). which is a measure of galaxy density fluctuation for the regions around SMGs with fixed apertures from 1 to 2 Mpc, and nf ield is the galaxy density of the whole field. These aperture sizes are of the scale of galaxy cluster, even though size of (proto)cluster at high redshift may be different. For calculating density, we have to consider the boundary of surveys. In the ECDF-S field, submillimeter survey area is a little larger than optical survey area. There is a bias when we count δ for the SMGs whose positions are close to the boundary. So we reduced the selected region with increasing radius of apertures to ensure an unbiased estimate, but it also means the SMG number will decrease with increasing aperture size. There is no the same problem for the COSMOS and GOODS-S fields, because the optical survey areas are much larger than submillimeter survey area. To avoid the holes produced by bright stars, we simply use the optical galaxy catalog and split image into small grids, the length of each grid is ∼10 arcsec. Then we count the galaxy number for grids, if the galaxy number in a grid is much lower than the mean galaxy number of all grids, we consider it is in a bright star hole. Finally we got a mask of bright stars..

(22) – 21 – 3.1.. Optical galaxy density. Before there are redshift estimate for SMGs, we try to find SMGs tend to be at which redshift by calculating galaxy δ at every redshift bin. But, it does not work, we put that result in the Appendix Ch. 7.1. Now, there are redshift estimate for SMGs, we could investigate the environment of SMGs at different epoch. We calculated the δ for SMGs and averaged the δ every 0.2 redshift interval between 1 < z < 4. We used only SMG samples with photometric redshift estimate (Wardlow et al. 2011; Yun et al. 2012), that could help us eliminate the foreground and background contaminations. We counted galaxies within a zSM G ± ∆zgalaxy range, where ∆zgalaxy is photometric redshift error of optical galaxies, ∆zgalaxy /(1 + zgalaxy ) is 0.019 for galaxies in the ECDF-S field. The errors are Poisson error. After considering the boundary which mentioned in the previous section, number of LABOCA-SMGs is 63, 52 and 42 in the analysis of 1, 1.5 and 2 Mpc aperture sizes. Number of AzTEC-SMGs is 42 for three radii. The flux limit is 26.4 in BVR band in AB magnitude (the detail of BVR band, please see Cardamone et al. (2010)) and the luminosity we cut at -11 absolute magnitude in BVR band. For LABOCA-SMGs, there is a 2-σ signal at z ∼ 2.5 and the signals shows nearly 0 at other redshifts (Fig. 7 right). And AzTEC-SMGs are located at over-density region at z = 3.3 and 3.7 with greater than 3-σ signals (Fig. 7 left). Although we reducing the contaminations of higher and lower redshift of galaxies, the ∆zgalaxy we used is still much larger than a real structure size, so we only could conclude that most SMGs are not located at the very dense environments, otherwise we should find more and clear signals. Only subsamples of SMGs seem to be associated with structure at certain redshift like: LABOCA-SMGs at z ∼ 2.5 and AzTEC-SMGs at z = 3.3 and 3.7. To examine these results, we did the two following tests..

(23) – 22 –. Fig. 7.— Environment index of SMGs as a function of z. The left panels are for AzTECSMGs; the right panels are for LABOCA-SMGs. Panels from top to bottom show results obtained with different aperture radii: 1Mpc, 1.5 Mpc and 2 Mpc..

(24) – 23 – 3.1.1.. Monte Carlo test. To check the effect due to SMGs redshift uncertainty and how robust our results are (Fig. 7), we varied SMGs redshift within a Gaussian function with given zSM G and σ (Wardlow et al. 2011; Yun et al. 2012). Then we did the same procedure as in Ch.3.1 1000 times and calculated the δ dispersion of each redshift bin (Fig. 8). For AzTEC-SMGs, only the signals at z = 3.3 and 3.7 are above 1 sigma at 1.5 and 2 Mpc apertures. All the LABOCA-SMGs signals are embedded in the 1 σ uncertainty interval, only the signal at z = 2.5 is close to 1 σ level. The data quality is not good enough to count δ at 1 Mpc aperture size, all the signals are overwhelmed by the large uncertainty..

(25) – 24 –. Fig. 8.— Test of varied redshift of SMGs. Data points are the same as shown in Fig 7. Gray area is 1 σ scatter from 1000 times simulation. Other informations are the same as Fig. 7..

(26) – 25 – For another uncertainty examination, we randomly generated positions for SMGs within the boundary of the observed field, then recalculated the δ as described in Ch. 3 1000 times and found their dispersion for every redshift bin. The overdensity signals at z = 3.3 and 3.7 for AzTEC-SMGs are in 1 - 2 σ at three radii; and LABOCA-SMGs at z ∼ 2.5 is above 2σ at 1.5 and 2 Mpc apertures (Fig. 12). We found 1 Mpc aperture size is too small for LABOCA-SMGs. Based on the results of two tests, we need more galaxy to reduce the errors and uncertainties.. Fig. 9.— Random position test. Gary area is the 1 σ dispersion of 1000 times simulation. Other informations are the same as in Fig. 8..

(27) – 26 – 3.2.. BzKs. According to the previous BzKs studies (see Ch. 1), these galaxies are massive and highly clustered, and furthermore some evidences indicate that they are embedded in dense regions at high redshift (Kong et al. 2006; McCracken et al. 2010; Lin et al. 2011), so SMGs may highly associate with BzK galaxies. And BzKs can further distinguish into passive and star-forming BzKs, that could help us to study the environments of SMGs more detail. We calculated BzKs δ around all SMGs with fixed apertures from 0.5 to 2 Mpc (assuming z = 1.8 and 1.5 for star-forming and passive BzKs respectively) in three datasets (AzTEC-SMGs, LABOCA-SMGs and SMGs in COSMOS field). The definition of δ is the same as in Ch. 3.1. Although we know the photometric redshift of BzKs, the number of BzKs is not enough to divide BzKs into different redshift bins, we just calculated the projected BzKs δ around SMGs (Fig. 10). The result of BzK δ (Fig. 10) shows passive BzKs have higher density around LABOCA-SMGs than star-forming BzKs in the ECDF-S field. The same phenomenon also appears in the COSMOS field at radius smaller than 1 Mpc. But the number of passive BzKs in the COSMOS field is much smaller than McCracken et al. (2010), they found, so this result need to do a further examination. For AzTEC-SMGs, they are not associated with both star-forming and passive BzKs..

(28) – 27 –. Fig. 10.— BzKs δ around SMGs from 0.5 to 2 Mpc. Cross and square symbols represent passive and star-forming BzK counts around SMGs respectively..

(29) – 28 – To further improve our analysis, we counted the SMG samples only with redshift estimate and excluded the sources with redshift greater than 3 or smaller than 1, because they are almost impossible to be associated with BzKs. However, there is no redshift estimate for the SMGs in COSMOS field to do for the same analysis. After excluding the background and foreground SMGs, the signals are increasing at radii smaller than 1 Mpc, except one signal of AzTEC-SMGs at 0.5 Mpc aperture. Fig. 11 shows the same phenomenon as previous one, LABOCA-SMGs are more strongly associated with passive BzKs than star-forming BzKs but it is still not shown for AzTEC-SMGs.. Fig. 11.— BzKs δ around the SMGs with 1 < z < 3. Symbols are the same as Fig. 10..

(30) – 29 – 3.2.1.. Random positions test. To examine the above result (Fig. 11), we gave random positions for SMGs and BzKs within the survey region. Then we recalculated δ 1000 times and got the dispersions (Fig. 12). The data points are the same as in Fig. 11 and yellow area shows the 1 σ dispersion of the simulation. The signals of LABOCA-SMGs are above 3-σ at separation smaller than 1 Mpc. For AzTEC-SMGs whose star-forming BzKs δ are above only 1-σ and the data points of passive BzKs δ all embedded in the simulation. Based on the result, the GOODS-S field is too small to do this analysis, the ECDF-S field size (30 × 30 arcmin2 ) is needed..

(31) – 30 –. Fig. 12.— BzK δ around SMGs with 1 < z < 3. The left panels are star-forming BzK δ and the right panels are passive BzK δ. Yellow area is 1σ uncertainty from random the position test. Data points are the same as Fig. 11. (See e-copy for color version).

(32) – 31 – 4.. Correlation function analysis. To study the association between SMGs and LAEs, we adopt the correlation function technique which is a statistical tool to study galaxies distribution and clustering. The two point correlation function ω(θ) is a spatial correlation function on the sky and is defined as the excess of δP of finding galaxies at a radius in a surface in comparison with the case of random distribution δP = n2 [1 + ω(θ)]δθ1 δθ2 ,. (2). where δθ1 and δθ2 are elements of solid angle and n is mean surface density of galaxy samples (Peebles 1980). The correlation function measures the pair counts of galaxies between θ − δθ/2 and θ + δθ/2. We adopted the Landy & Szalay (1993) estimator for auto-correlation, DD(θ) − 2DR(θ) + RR(θ) , RR(θ). (3). DD(θ) − DR(θ) − RD(θ) + RR(θ) , RR(θ). (4). ω(θ) = and for cross-correlation, ω(θ) =. where DD, DR and RR terms are data-data, data-random and random-random pair counts at a separation θ. And for each separation bin there is a Poisson error, s 1 + ω(θ) σ(θ) = . DD(θ). (5). Based on previous observations, the ACF of galaxy distribution is well represented by a power-law of slope γ, ω(θ) = Aω θ−β . But due to the limited survey region, the correlation function is underestimated by a constant called integral constraint: Z Z ΣRR(θ)ω(θ) 1 ω(θ)dΩ2 dΩ1 = . C= 2 Ω 1 2 ΣRR(θ). (6). To determine Aω , we fit the following equation with assuming typical value β = 0.8: ωobs (θ) = Aω θ−β − C = Aω (θ−β −. C ) Aω. (7).

(33) – 32 – C/Aω is a function of θ. Then we can easily transform amplitude Aω to the correlation length r0 via the relativistic Limber equation (Peebles 1980; Magliocchetti & Maddox 1999). The spatial correlation function is then given by ξ(r) =. r r0. −γ ,. where γ is 1 + β. And we simply assumed the top-hat function for N (z).. (8).

(34) – 33 – 4.1.. LAE-SMG cross-correlation function. We calculated the cross-correlation function for three datasets, namely LAEs at z ∼ 2.25 and SMGs in the COSMOS field, z ∼ 3.1 LAEs and LABOCA-SMGs/AzTEC-SMGs in ECDF-S/GOODS-S field respectively. The numbers of LAEs and SMGs used in this analysis are summarized in Table 3. The results show no correlation or clear signals between these two populations in any dataset (Fig. 13, square points). In Fig. 14, we also compared the LAEs-SMGs cross correlation function to LAE auto-correlation function singular. The ACF results show that clustering of LAEs in each dataset is not as strong as the case of SSA22 (see Fig. 18), there is probably no a proto-cluster scale structure (as traced by LAEs) is possibly not in these fields. Table 3: Numbers of LAEs and SMGs in CCF COSMOS. GOODS-S. ECDFS. LAEs. 84. 85. 160. SMGs. 187. 48. 110.

(35) – 34 –. Fig. 13.— Cross correlation functions between LAEs and SMGs. Star symbols are LAEs at z ∼ 2.25 and SMGs in the COSMOS fild; diamond symbols are LAEs z ∼ 3.1 and LABOCA-SMGs in the ECDF-S field; square symbols are LAEs z ∼ 3.1 and AzTEC-SMGs in the GOODS-S field. (See e-copy for color version).

(36) – 35 –. Fig. 14.— LAEs-SMGs CCF compared to LAEs ACF in three fields. Stars are ACF and squares are CCF..

(37) – 36 – 4.2.. Background and foreground contamination. To reduce the contamination from background and foreground SMGs, we recalculated the cross-correlation function for SMGs with redshift close enough to the LAEs epoch based on zSM G calculated by Wardlow et al. (2011) and Yun et al. (2012). For the AzTEC-SMGs/LABOCA-SMGs, we chose the redshift range 3.1 ± 0.3 and 8/6 SMG sources were selected in each field. Even after excluding the samples which are not within the redshift range, the correlation function results did not show stronger signals (Fig. 15), so signals are diluted by background and foreground SMGs is not supported by this result. But we need to be careful about the bias that we only use the samples which have redshift and the number of SMGs with redshift between 3.1 ± 0.3 is small; and ± 0.3 redshift range is a very large volume.. Fig. 15.— Cross correlation functions between LAEs and the SMGs whose redshift are constrained to be between 3.1 ± 0.3 in the ECDF-S and GOODS-S fields..

(38) – 37 – 4.2.1.. Monte Carlo test of CCF. As in Ch. 3.1.1, we checked the uncertainty of galaxy δ which come from SMGs redshift estimate. To examine the LAEs-SMGs cross correlation function results (Fig. 15), we generated new redshift for SMGs within a Gaussian function with given zSM G and σ. And we selected the mock SMGs within a redshift range 3.1 ± 0.3, then we calculated the CCF 1000 times and got their scatter distributions (Fig. 16). Data points are the same as in Fig. 15, most of them embedded in the 1 σ dispersion of simulation.. Fig. 16.— Simulation LAE-SMG CCF (squares, the same result as shown in Fig. 15) in comparison with the scatter of 1000 CCF of LAEs and pseudo-SMGs with redshift perturbed by observation error..

(39) – 38 – 4.3.. Correlation length. To know SMGs at which redshift have most association with galaxies, we divided the optically selected galaxies into subsets by photometric redshift with 0.2 intervals. Then we calculated cross correlation function (CCF) between SMGs and the galaxies at different redshift bins. Final we fitted a power-law function to the CCF for every redshift bin and computed the cross correlation length. Detail of the method is described in Ch. 4. In Fig. 17, we also plotted galaxies auto correlation lengths for comparison. For display purpose, if there are no positive correlation signals, we forced the value r0 = 0. There are almost no clear relation between SMGs and galaxies in each redshift range, except that AzTEC-SMGs have a marginal correlation with galaxies at z ∼ 2.6 and 3.6.. Fig. 17.— Correlation lengths in the COSMOS and ECDF-S fields. The left panel: star symbols are SMGs detected by AzTEC in the COSMOS cross correlated with galaxies. The right panel: triangle and star symbols are cross correlation lengths between galaxies and LABOCA-SMGs and AzTEC-SMGs in the ECDF-S field. (See e-copy for color version).

(40) – 39 – 5.. Discussion. Based on galaxy δ results (Ch. 3.1), we found SMGs at most redshifts did not show the overdens signals. It seems against the expectation of hierarchical model. However, even there are photometric redshift estimates for SMGs and galaxies, the accuracy is still a problem. Most of signals may be diluted by many unrelated sources. For LABOCA-SMGs at z ∼ 2.5 and AzTEC-SMGs at z = 3.3 and 3.7, they seem to be associated with structures, although the signals are about 1-2 σ. We examined the individual sources, they are not caused by one or two SMGs located at very dense region at that redshift. If the signals are real, does it mean different wavelength selected SMGs tend to be associated galaxies at different epoch, or that is caused by cosmic variance. To identify whether it is true or just a coincident, we need spectroscopic redshift data or to consider the probability distribution function of redshift for SMGs and galaxies to derive more reliable results. Our results of BzK δ show LABOCA-SMGs are more associated with passive BzKs than star-forming BzKs (Fig. 10 and Fig. 11). Passive BzK is a good tracer of dense region, so this result can support the environments of SMGs are dense. For the difference of AzTEC-SMG result, there are two possible explanations. One is that there is a difference of redshift distribution between LABOCA-SMGs and AzTEC-SMGs (see Fig. 4). The redshift distribution of AzTEC-SMGs (mean redshift is 2.6) is a little far from the redshift peaks of star-forming and passive BzKs at z ∼ 1.8 and z ∼ 1.5. Another explanation is the small field (GOODS-S) caused the large cosmic variance, this can be supported by our MC simulation (Fig. 12) that shows the large uncertainty of BzKs δ of AzTEC-SMGs. But we also could not rule out that LAOBCA-SMGs have higher passive BzKs density than AzTEC-SMGs is caused by cosmic variance. The selection bias of submillimeter wavelengths is one of explanations for our results,.

(41) – 40 – so we did an independent analysis of SMGs of 870µm and 1.1 mm flux ratio. But the result shows no evidence of 2 SMG populations in terms of spectrum (see Appendix Ch. 7.3). In this work, we find no detectable SMG-LAE cross-correlation signal in our selected fields, unlike the result (Fig. 18) from previous study of SSA22 field (Tamura et al. 2009), which shows a spatial correlation between the two populations. Another high-z proto-cluster, the Francis field, at z = 2.38, was found by Francis et al. (1996, 1997), and Palunas et al. (2004) and Francis et al. (2004) had observed 37 Lyα-emitting objects. Beelen et al. (2008) had observed 32 submillimeter sources at an overdense region of the proto-cluster using LABOCA. From their analysis they concluded that several of SMGs could be associated with a z = 2.38 large scale structure. While a close LAE-SMG spatial correlation may have been revealed in the case of the SSA22 and Francis fields which are both toward to high-z structures, our study demonstrates a more spatially detached relationship between these 2 populations based on data outside the structure. We further excluded most SMGs whose redshift far from the redshift of LAEs and found no significant signal appear in the results either, so the background and foreground contaminations may only play a minor role. Combining previous results and our results, we infer that these two populations are not necessary to have correlation outside clusters or structure at high redshift. To date, the properties of LAEs have not been well constrained. Lai et al. (2008) in their work found 30 percent of LAEs have IRAC 3.6 µm detection, and they are different in stellar mass and age from others. We had divided LAEs into two populations by rest frame UV colors, but the results did not show different LAE populations (Appendix Ch. 7.2). Furthermore, although there are studies showing evidence that part of LAEs appeared to be ULIRGs. But the ULIRGs fraction is quite low at z ∼ 3 and may not change much of our results (Nilsson & Møller 2009; Ono et al. 2010; Nilsson & Møller 2011)..

(42) 0. 22 h 17 min 1.0. 0.8. 0.4. 0.2. 22 h 17 min. nsion (J2000). Galaxies per arcmin2. 0.6. physical connection between the galaxies and the foreground structure. Some authors20,21 have reported correlations between bright – 41 – selected low-redshift galaxies (sub)millimetre sources and optically (mostly at z , 1) in other regions of the sky. In general, SMGs are often found at high redshift (median, z 5 2.2; ref. 22), and the maximal gravitational lensing magnification for a background galaxy at z > 2 occurs when the foreground lensing structure is at z < 0.5. Therefore, they concluded that the correlation signal is most probably the result of amplification of background SMGs due to gravitational weak lensing by the foreground low-redshift galaxies. By contrast, the origin of the correlation signals in SSA 22 is most likely intrinsic to the large-scale structure in which both populations, SMGs and Lya emitters, are embedded. Because the redshift estimates for the SMGs place them at distances coeval with the Lya emitters, it is unlikely that the correlation seen in SSA 22 is due to amplification of a much higher-redshift (z ? 3.1) SMG population lensed by the structure traced by the Lya emitters, which are all located at z 5 3.1 (not z < 0.5). 1.0 Angular cross-correlation function. Signal-to-noise ratio. 5. accuracy of the catalogue is ,10 arcsec. * Observed flux density before flux bias correction, plus the 1s error. { Deboosted flux density (flux density corrected for the flux bias due to confusion noise using the method described elsewhere28), plus the 68% confidence interval.. 0.8 0.6 0.4 0.2. sources and Lya emitters towards the olour scale shows the map of signal-to0 ws 30 sources with signal-to-noise SSA 22 (field centre at –0.2 0099 (J2000)) were obtained using the m, mounted on the ASTE 10-m 0 2 4 6 8 10 12 14 16 uly–September 2007 observing season. Angular distance (arcmin) ntegration time on source under Figure 2 | Angular cross-correlation between submillimetre galaxies and eric opacity at 220 GHz, n a root-mean-square noise level of Lya emitters. The two-point angular cross-correlation function shown here min2. The point spread is computed for the 166 Lya emitters the LAEs 15 brightest Fig.function 18.—ofSpatial correlation between SMGsand and in SSA22 field. Blue squares are alf-maximum of 28 6 1 arcsec. b, The (S1,100 mm $ 2.7 mJy) submillimetre galaxies (orange circles). For reference, galaxies with S1,100 ACF we alsocircles show the two-point angular autocorrelation the SSAis22a clear association mm $ 2.7 ofmJy LAEs, yellow are CCF between SMGs andfunction LAEs.forThere tters at z 5 3.1 (white dots). The sizes Ly-a emitters (blue squares). Small-number statistics prevent us from to their 1,100 mm fluxes. The number constraining the auto-correlation function well for the submillimetre at angular separation smaller than 5 arcmin. (Tamura et al. 2009) galaxies. The correlation functions are computed using the estimator of ref. wn in the colour scale, highlighting the 29. The error bars are estimated from the root mean square of 1,000 ters, which is thought to trace out the bootstrap samples. See Supplementary Information for details. 5 3.1. ©2009 Macmillan Publishers Limited. All rights reserved.

(43) – 42 – 6.. Summary. In this work, we have investigated the environments of SMGs at different redshifts based on multiwavelength data from the COSMOS and ECDF-S (including the GOODS-S) fields. Our first approach is to count the number density of galaxies with photometric redshift and BzKs centered at each SMG. We then did a cross-correlation analysis of SMGs and a young, small and dust free galaxy population, LAEs. Our main results are the following. (i) Based on the result of galaxy number density, SMGs are not necessarily in the most dense regions, at least in the epochs included in this study. LABOCA-SMGs and AzTEC-SMGs only have marginal signal at z ∼ 2.5 and z ∼ 3.5 (Fig. 7). (ii) There are overdensities of BzKs around SMGs at separation smaller than 1 Mpc and passive BzKs have higher signal than star forming BzKs (Fig. 10). (iii) There is no detectable correlation between SMGs and LAEs, suggesting outside galaxy structures (compared with previous results in SSA22 field), SMGs and LAEs seem not associated (Fig. 13). Although SMGs tend to be located in relatively dense regions, they may not be a population only with very massive galaxy that can always trace the most dense environments such as the center of (proto)clusters..

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(49) – 48 – 7. 7.1.. Appendix. Galaxy density around SMGs without redshift. Before there are redshift estimates for SMGs, to know which redshift most of SMGs locate at, we did this analysis. If SMGs are highly associated with galaxies, galaxy δ at the redshift SMGs are at should be higher than other redshifts. So starting from z = 1 to 4, we divided galaxies into redshift bins with 0.2 δz interval. In each redshift bin, we computed the mean δ for all SMGs (without considering the redshift of SMGs). All three fields (Fig. 19) show that SMGs tend to be located at relatively dense regions at z > 2.3. Based on our results of galaxy overdensity (Fig. 19), we find that SMGs tend to be found in relatively dense regions at redshift > 2, which is consistent with the expected merger scenario of SMG origins (see Ch. 1). The result on the contrary suggests that SMGs are not necessarily embedded in overdense regions at 1.5 < z < 2..

(50) – 49 –. Fig. 19.— Average environment δ in a region of radius from r = 0.5 to 2 Mpc centered at SMGs (see text for details)..

(51) – 50 – 7.2.. LAE rest frame UV color 7.2.1.. Red/blue LAEs?. In recent years, several studies have proposed that Lyα emitters may have a wide range of properties (Lai et al. 2008; Finkelstein et al. 2009; Ono et al. 2010). Lai et al. (2008) investigated the LAEs with IRAC detection and found that the best fitting model of stellar population has age = 1.6 Gyr and mass = 9 × 109 M

(52) , which numbers are much greater than what previous studies have found, 10 − 100 Myr and 106 − 109 M

(53) (Gawiser et al. 2007; Nilsson et al. 2007; Pirzkal et al. 2007). Nilsson et al. (2009) used (V − i) color to separate LAEs into red and blue samples and, based on stacking SED of red and blue samples, suggested LAEs are not a single population. We follow this suggestion to investigate if only subsample of LAEs are associated with SMGs.. 7.2.2.. Identification of LAE optical counterparts. We looked for the LAE counterparts from the MUSYC and COSMOS catalogs with 1.4 arcsec radii criterion, 93 of 160 and 107 of 187 LAEs had been found at z ∼ 3.1 and 2.25 in the ECDFS and COSMOS fields. The LAE sources without counterpart are called faint LAEs and those detected in broad band detected samples are bright LAEs.. 7.2.3.. CCF of SMGs and red/blue LAEs. Guaita et al. (2010) used B − R = 1 to divide z ∼ 2.3 LAEs into blue and red samples; here we use similar rest-frame wavelength B − r = 1 and R − z = 1 as the criteria to separate z ∼ 2.25 and 3.1 LAEs to blue and red sample (hereafter called blue LAEs and red LAEs). B − r and R − z diagrams (Fig. 20) did not suggest the existence of different.

(54) – 51 – populations. Fig. 21 to Fig. 23 show the CCF between SMGs and blue/red LAEs and there are no different phenomena between blue/red samples results.. 7.2.4.. Bright/Faint LAEs. In addition to the LAE subpopulations difined by color, we also investigated whether the associations between SMGs and faint/bright LAEs are different. We test bright/faint LAEs by their ACF and CCF with SMGs (Fig. 24 and Fig. 25). The faint samples, a subset of z ∼ 3.1 LAEs, seem to have higher auto correlation and there is an anti-correlation between faint samples and LABOCA-SMGs at angular separation smaller than 4 arcmin (∼ 2 Mpc) (Fig. 24 right). In COSMOS field (Fig. 26), faint and bright z ∼ 2.25 LAEs have opposite ACF result compared to that of z ∼ 3.1 LAEs. CCF between SMGs and bright/faint z ∼ 2.25 LAEs are not much different. The diverse results of the bright/faint LAE analysis are puzzling but yet interesting, we need more samples and cases for further comparison before any conclusion can be made.. Fig. 20.— Distribution of UV color of LAEs.

(55) – 52 –. Fig. 21.— Red and blue z ∼ 3.1 LAEs CCF with LABOCA-SMGs in the ECDF-S field. (See e-copy for color version). Fig. 22.— Red and blue z ∼ 3.1 LAEs CCF with LABOCA-SMGs in the GOODS-S field. (See e-copy for color version).

(56) – 53 –. Fig. 23.— Red and blue z ∼ 2.25 LAEs CCF with SMGs in the COSMOS field. (See e-copy for color version). Fig. 24.— Bright and faint z ∼ 3.1 LAEs CCF LABOCA-SMGs in the ECDF-S field..

(57) – 54 –. Fig. 25.— Bright and faint z ∼ 3.1 LAEs CCF with AzTEC-SMGs in the GOODS-S field.. Fig. 26.— Bright and faint z ∼ 2.25 LAEs CCF with SMGs in the COSMOS field..

(58) – 55 – 7.3.. SMGs flux ratio. Are there different SMG populations? To study this question, we have calculated the flux ratio for the SMGs both detected by LABOCA and AzTEC within GOODS-S field. The flux ratio shows a wide distribution (Fig. 27 left), and lower limit of only LABOCA detected sources seem interesting and very different from others. But submillimeter flux measurements are not reliable. There is a region both observed by AzTEC/JCMT and AzTEC/ASTE in COSMOS field (Scott et al. 2008; Aretxaga et al. 2011). Although observed at the same wavelength, not all SMGs are detected by both facilities. And the same source has different submillimeter flux measurement between two observations (Fig. 27 right). Because of the level of incompleteness at low S/N at submillimter wavelength, not all sources are expected to be found in both facilities. And the same instrument on different telescope, their beam size also influenced detections. So the accuracy of submillimeter flux seems not good enough and we did not further study the wide flux ratio distribution of 870 µm and 1100 µm..

(59) – 56 –. GOODS!S 15 AzTEC + LABOCA AzTEC only LABOCA only. SMG Counts. 10. 5. 0 0. 1. 2 3 Flux ratio (s870/s1100). 4. 5. Fig. 27.— The left panel: The SMGs 870/1100 µm flux ratio. Data come from Weiß et al. (2009) and Scott et al. (2010) (Detail see Ch. 2.1). The red line and purple line is upper and lower limit of the SMGs detected by AzTEC and LABOCA, black solid line is the SMGs detected by both instruments. The right penal: Aretxaga et al. (2011) showed the flux of the same SMGs detected by AzTEC on different telescopes..

(60)