使用UKIDSS深遠巡天觀測探索星系群的性質到z=2

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(1)國立台灣師範大學理學院地球科學研究所. Department of Earth Sciences College of Science National Taiwan Normal University. 使用 UKIDSS 深遠巡天觀測探索星系群的性質到 z=2 Properties of galaxies in groups up to z=2 from the UKIDSS Ultra-Deep Survey. 蕭赫 Hsiao, Ho. 指導教授 : 傅谷石教授(Prof. Sébastien Foucaud). 中華民國一百零二年八月 August 2013.

(2) 摘要星系傾向在密度高的群體的環境下，因此群體在星系演化下扮演很重要的角色。星系合併與一些環境造成的過程是造成星系演化的原因。觀測星系群在高紅移是個困難的挑戰，特別在紅色(被動)的星系系統。其他近期的觀測方式是用可見光的波段，針對紅色(被動)的成對星系或星系群，但這個方試容易低估部分的星系演化。我們使用最好的世界發佈資料，使用來自 UKIDSS-UDS-DR8 的近紅外波段，結合 Subaru 以及 CFHT 的可見光部分，我們採用 photo-z 的技術,並使用 pfof 的方法重建星系群到 z=2。我們以 Millennuim 模擬和 X 射線源探測資料作為重建星系群的基準，雖然 Millennuim 模擬的資料分布情形並不能代表我們真實的 K-band 資料。且 spec-z 需要大量的時間，X-ray source 的成員星系數量也並不齊全。導致我們使用 PFOF 重建出的星系群體會有"不完備性"以及"碎裂性"在第一個方法上，而第二個方法由於 spec-z 的數量不足造成有許多錯誤的星系群被偵測出來。. 關鍵字: 環境、合併、紅移、probabilistic Friends-of-Friends、Millennium 模擬、photometric redshift.

(3) –2– ABSTRACT. Galaxies live preferentially in groups environment, therefore groups play a very important role in galaxy evolution. Merging activity is fostered in groups and some environmental processes could eventually take place in groups and have an impact on galaxy evolution. Observing and detecting groups at high redshift is extremely challenging, especially for the redder systems, involving passive galaxies. The current generation of optically-selected surveys are biased against the passive population in pairs and groups, leading to an underestimation of their role in the galaxy evolution. Making the best use of the worldwide release of the near-infrared data UKIDSS-UDS DR8, combined with Subaru and CFHT data in the optical waveband, we coupled photometric redshift with a probabilistic Friends-of-Friends algorithm to build a groups catalog up to redshift z = 2. As we only have a limited access to spectroscopic redshifts, our overdensity (cluster/group) finder algorithm has to rely heavily on photometric redhifts, so we are using a probablistic Friend-of-Friend method. Here we discuss the work we conducted to select groups up to z = 2, which relied heavily on how the probabilistic Friends-of-Friends algorithm is trained. We used both Mock catalogs (from the Millennium simulation) and X-ray detections (from XMM-Newton observation). We demonstrate that first the Mock catalog does not reproduce our K-band selected sample, which spread doubts on the reliability of the training and that secondly that the incomplete memberships to the X-ray groups (limited by the availability of spectroscopic data) prevent us to rely as well on X-ray training. Training our algorithm lead to a low completeness and fragmentation of our group sample in the first case, and many false detection in the second case. Subject headings: environment, merging, redshift, probabilistic Friends-of-Friends,.

(4) –3– Millennium simulation, photometric redshift.

(5) –4– Contents. 1 Introduction. 6. 1.1. Current paradigm of Galaxy evolution . . . . . . . . . . . . . . . . . . . . .. 6. 1.2. Influence of local environment on galaxy evolution . . . . . . . . . . . . . . .. 8. 2 Datasets. 14. 2.1. The UKIDSS-Ultra Deep Survey and Subaru-XMM Deep Survey . . . . . . .. 14. 2.2. The XMM-Newton group catalog . . . . . . . . . . . . . . . . . . . . . . . .. 17. 2.3. Photometric Redshifts, absolute magnitudes and rest-frame colours . . . . .. 18. 2.4. Mock Galaxy Sample from Millennium Run . . . . . . . . . . . . . . . . . .. 20. 3 Tracing overdense systems 3.1. 29. Detecting overdensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29. 3.1.1. Detecting groups and clusters in X-ray . . . . . . . . . . . . . . . . .. 29. 3.1.2. Detecting groups and clusters with optical/near-infrared galaxy catalogs 30. 3.2. Probabilistic Friend-of-Friend algorithm . . . . . . . . . . . . . . . . . . . . .. 33. 3.3. Purity and Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35. 4 Building up a galaxy group catalog to z=2 4.1. Training the parameters for pFoF . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. 37 38. How to train your dragon: optimisation of richness and pFoF parameters 38.

(6) –5–. 4.2. 4.1.2. Millenium Mock trained catalog . . . . . . . . . . . . . . . . . . . . .. 40. 4.1.3. X-ray trained catalog . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43. UKIDSS-DR8 Group and Cluster catalogs . . . . . . . . . . . . . . . . . . .. 46. 5 Conclusions. 53.

(7) –6– 1. 1.1.. Introduction. Current paradigm of Galaxy evolution. The way galaxies were formed to how there are today, is still an open question which puzzles the astronomical community. However the current paradigm of galaxy evolution is widely accepted although many details still required to be sorted. The main accepted framework of galaxy evolution is the Lambda Cold Dark Matter scenario (or ΛCDM) which states that growth under the combined influence of gravity and cosmological expansion of the original small disturbance in matter distribution led to the large scale structure structures observed today. The Cold Dark Matter (CDM), which cannot be directly observed by radiation, dominates the budget of matter in the Universe and is composed by slow moving (non-relativistic) particles. In the ΛCDM theory, the CDM imprints the behaviour of all matter. The original perturbation produces localized gas overdensities which triggered formation of stars and in the higher density peaks of density form the first galaxies. Thus the birth of galaxies and the early universe physics are closely related (e.g. Blumenthal et al. 1984). While the evolution of matter at large scale is globally understood, the detailed processes and mechanisms in action in galaxy formation are still not completely clear.(Ryden Barbara et al. 2006) . For instance it is observationally well established that the Star-Formation Rate increase from high redshift to peak at redshift z = 2 − 3 and decrease dramatically since z = 1 to the value of today (which is around 20 times lower) (Kentaro Nagamine et al. 2006). But the exact mechanisms responsible for this massive global quenching in galaxies are still not well constrained. There is an agreement amongst the community that some feedback processes generated by Supernovae and/or Supermassive black holes are probable playing a very important role, but their relative effects are still poorly constrained(Cooper et al. 2007) ..

(8) –7– Actually these feedback effects are also visible in the properties of galaxies today directly. Indeed, galaxies in the local universe broadly fall into two main categories: blue star-forming disks typically found in lower density environments, and red and ”dead” ellipticals found in galaxy clusters. Galaxy formation proposed that original clouds of gas collapsed under gravity to form rotating discs of star formation (Eggen et al. 1962), but some mechanisms like merging and ram pressure would transform spirals into ellipticals through dynamical processes (Toomre & Toomre 1972; Balogh et al. 2000). Such effects, which will quench star formation, could also contribute to the color transformation from blue and star-forming to red and dead observed since z = 1.8, also they may not be the main players(Roberto G. Abraham et al. 2005) . Given the correlation between morphology and color, such mechanism must also lead to morphological transformation of disk-dominated galaxies into bulge-dominated ones, either through disruption or disk fading and bulge growth. Whatever mechanisms are responsible for such quenching they seems to be dependent of one of the most fundamental properties of galaxies, their stellar mass. Indeed many observations lead to describe a phenomenon called ”Galactic downsizing”, in which massive galaxies complete faster their activities than low mass galaxy (here activities mean galactic merging, environment effect, etc.)(C. Firmani et al. 2010) . Indeed, in the local universe, most part of star-forming galaxies are low mass galaxy(Cooper et al. 2006) . This phenomenon can be explained by the fact that massive galaxies, which have stronger gravitational potential, were formed first and were interacting with massive objects first. Such galaxies would also encounter a quenching of their Star Formation earlier, this is why we witness a decrease since high redshift(Cowie, L. L et al. 1996)..

(9) –8– 1.2.. Influence of local environment on galaxy evolution. Because galaxies are formed in the highest peak of matter density, they are naturally clustered, and form in local over density naturally. Indeed observations indicate that galaxies live preferentially in groups environment, and therefore groups must play a very important role in galaxy evolution (Cooper et.al 2006, Cucciati et. al 2005). To explain the way galaxies are shaped into their current appearances, and explain the observed relation between morphology and local density (Poggianti et al. 2008), we need to effectively separate two (combined) kind processes involved in galaxy evolution, we characterise as ”nature” and ”nurture”. Natural, also called ”secular”, processes are related to the evolution of galaxies themselves, without any external trigger, such as Active Galactic Nuclei, star-formation bursts or bars in spiral galaxies. Such processes may quench star-formation and act on the morphological evolution passively, for instance reducing the size of the disc when star formation has stopped (e. g. Kovac et al. 2010). Nurtural, also called ”peer”, processes are resulting from an external phenomenon, due to the interaction of the galaxy with other galaxies or its local environment. Major mergers (between galaxies of similar masses) for instance will directly affect the stellar kinematics and galactic structure, triggering a burst of star-formation and eventually nuclear activity (e. g. Kovac et al. 2010). Major mergers are more common in groups than in clusters, as the velocity dispersion of galaxies in clusters is to high to favourite direct interactions (Cavaliere et al. 1992). On the other hand, ram pressure is a pressure exerted on a body which is moving through a fluid medium (see figure 1), which is favorised by cluster environments (Gunn & Gott 1972). It causes a strong drag force to be exerted on the body, this pressure will strip cold gas when a galaxy infall a hot gas environment. Harassment is phenomenon in cluster that pulls and drags between galaxy and galaxy, although they do not merge, but it lead to the gas of star formation that will be destroy.

(10) –9– (Dressler et al. 1980). The red fraction is defined as the ration between the number of red galaxies and total number of galaxies in a given structure (field, group or clusters). It is know since long time (e. g. Butcher & Oemler 1978) that red passive galaxies are more frequent in denser environments, hence that the red fraction is higher in more dense environment. However it is also known that more massive galaxies are typical redder in the local Universe (Bell E. F. et al., 2004) and that the most massive galaxies are located in denser environment (Davis & Geller et al. 1976) . There is therefore a degeneracy between nurtural and natural effects. Then what is really need is to investigate the red fraction for similar stellar masses (as measured from long-wavelength Infrared photometry) and determine how this varies with redshifts. By comparing the same group mass at different redshift, a higher red fraction is observed in the local universe (Cooper et al. (2007)). However red galaxies present a strong clustering at z > 1.5 (Daddi et al. 2003; Quadri et al. 2007; Hartley et al. 2008; Hartley et al. 2010) which suggests that a colour-density relation may also exist at these higher redshifts. All these observations are in agreement with a ”Cosmic Downsizing” scenario, in which more massive galaxies are evolving more early than less massive galaxies and therefore present a higher red fraction. Figure 2, extracted from Kovac et al. (2010), illustrates well this mixed evolution between secular evolution and environment effect. Within the same panel, galaxies in group have higher red fraction, i.e. are more subject to transformation linked to quenching, than field and isolated galaxies. When comparing different panels with different luminosity bins, hence mass bins, massive group galaxies obviously present an earlier evolution than the galaxies of low mass. As demonstrated by figure 3, our current understanding is that environment is acting on galaxy evolution as a catalyser, accelerating the evolution processes which will happen.

(11) – 10 – anyway (Balogh et al. 2009)..

(12) – 11 –. Fig. 1.— From Steinhauser et al. (2012): This simulation presents the evolution with time of the Surface density of the Inter-stellar Medium (green) and of the newly formed stars (isolines) for a ram-pressure stripping scenario of model galaxy in an Intra-Cluster Medium with a density of 1027g.cm−3 . Note the colorbars for both distributions. Four different time steps are shown. New stars in the wake are formed in the dense gas knots. After 200 Myr many stars are present also in front of the disc. The stars formed in the wake are gravitationally attracted by the disc and due to the collisionless dynamics, these stars from the wake are falling through the disc. Furthermore, with the initial onset of ram pressure, the gas disc is pushed back from the stellar disc, as can be seen in the timestep after 50 Myr of evolution in the ICM..

(13) – 12 –. Fig. 2.— From Kovac et al. (2010): The redshift/look-back time evolution of the fraction of early type galaxies in different environments. The red and yellow symbols represent the group galaxies, black circles represent the field galaxies and the green triangles represent the isolated galaxies in the indicated MB -bins of galaxies..

(14) – 13 –. Fig. 3.— From Balogh et al. (2009): Galaxies show a halo-mass dependence: Red fractions of groups intermediate between cluster and field environments..

(15) – 14 – 2. 2.1.. Datasets. The UKIDSS-Ultra Deep Survey and Subaru-XMM Deep Survey. The Ultra Deep Survey (UDS)1 is the deepest component of the UKIRT Infrared Deep Sky Survey (UKIDSS - Lawrence et al. 2007) and is the deepest near-infrared survey ever conducted over such a large area (0.8 sq. degrees - see figure 4). The aim of this survey is to understand how and when galaxies are formed and trace their evolution over the last 12 billion years. Using the WFCAM camera (Casali et al. 2007) on the UKIRT 4m telescope, the survey began in 2005 and continued until end of 2012. The Data Release 8 (DR8) used in this work is public worldwide since April 2012, and the latest release DR10 is public to ESO member since January 2013 and will be released worldwide in June 2014. The final release incorporating all data taken during the 7 years of the survey will be release at the end of 2013 to ESO. The DR8 data reach depths of JAB = 24.9, HAB = 24.2 and KAB = 24.6, and comprises over two hundred thousand detected galaxies. The UDS is centred on the Subaru/XMM-Newton Deep Survey (SXDS), in order to take advantage of the broad wealth of data available on this field. Indeed the SXDS is a major multi-wavelength survey of a 1.3 sq. degree region of sky observed using the SuprimeCam on the Subaru 8.2m telescope (Masanori et al. 2004). The SXDS optical imagery represents an unprecedented combination of depth and area coverage, and will be combined with suitably deep images at other wavelengths to provide an accurate census of the contents of the Universe without suffering from the biasing effects of large-scale structure. A total area of 1.22 sq. deg. is covered in five contiguous sub-fields, each of which corresponds to a single Suprime-Cam field of view (340 × 270 ), in five broad-band filters B, V , Rc, i0 and z 0 , to the depths of B = 28.4, V = 27.8, Rc = 27.7, i0 = 27.7 and z 0 = 26.6 (AB, 3σ, 2” aperture). The data are reduced and compiled into five multi-waveband photometric 1. http://www.nottingham.ac.uk/astronomy/UDS.

(16) – 15 – catalogs, separately for each Suprime-Cam pointing. The i’-band catalogs contain about 900,000 objects, making the SXDS catalogs one of the largest multi-waveband catalogs in corresponding depth and area coverage. The SXDS catalogs can be used for an extensive range of astronomical applications such as the number density of the Galactic halo stars to the large scale structures at the distant universe (Furusawa et al. 2008). We also use the u∗-band data from the CFHT-Megacam, with a magnitude limit of u∗ = 27 (AB, 3σ, 2” aperture). MegaCam is the wide-field optical imaging facility at CFHT, covering a full 1 × 1 sq. degree field-of-view with a resolution of 0.187 arcsecond per pixel, which is very efficient in the blue throughput (Boulade et al. 1998). The data were acquired in 2007-2008, during two programs lead by O. Almaini and S. Foucaud. In addition archival data were also added to these two campaigns. The average seeing of the image is < 0.9”. Finally, the UDS Spitzer Legacy Program (SpUDS, PI:Dunlop) provides deep data in Mid-Infrared waveband with the channels 1 and 2 of IRAC, as well as Multiband Imaging Photometer for Spitzer (MIPS) 24µm data, all of which are used during our analysis. SpUDS data reach 5σ depths of 24.2 and 24.0 (AB) at 3.6µm and 4.5µm respectively, while the public 24µm catalogue used here is limited to 300µJy (15σ). The co-incident area of all these different data sets after masking of bad regions and bright stars is 0.62 sq. degrees. In addition to our deep photometry, the UDS field was also the target of a unique spectroscopic survey: the UDSz (Almaini et al., in preparation). The UDSz is based on an European Southern Observatory Large Programme targeting a large sample of galaxies (∼ 3500) at zphot > 1 with KAB < 23.0, plus a low-redshift control sample. The survey comprised eight pointings of VIsible MultiObject Spectrograph (VIMOS) in LR-Blue and LR-Red and 20 FORS2 masks with the GRS 300I grating. This survey has produced.

(17) – 16 – ∼ 1500 secure redshifts to date which are used along with archival redshift (of ∼ 4000 objects), details of which can be found in Simpson et al. (2012) and references therein.. Fig. 4.— The UKIDSS-UDS field, The UKIDSS-UDS field. This is a composite image of 3 bands (BzK). Zooming into a small section of the UDS field from K-band image. Light from many of the faint red galaxies has travelled over 12 billion light years to reach our telescopes. The right two fields, represent for the upper one the GOODS-South field, covered with VLT/ISAAC near-infrared imaging on areas of 172.5, 159.6 and 173.1 arcmin2 in J, H, and Ks bands, respectively; and for the lower one the FIRES field, which depths reach approximately 26.3, 25.8, 25.5 in J, H, and Ks, for a total coverage of about 23.6 arcmin2 ..

(18) – 17 –. Fig. 5.— This figure show the spatial distribution of galaxies on UKIDSS-UDS field, this field included in the Subaru/XMM-Newton Deep Survey field, which lies at the centre of one of the DXS fields, the XMM-LSS field. Its total coverage is 0.8 square degrees, and we select KAB < 24.6.. 2.2.. The XMM-Newton group catalog. XMM-Newton’s main strengths is the simultaneous operation of six science instruments, providing high X-ray throughput, important redundancy, and unprecedented spectroscopic capabilities. Three independent Wolter I telescopes consisting of 58 nested mirror shells each offer an unparalleled effective area of 2000 cm2 (at 1 keV) in conjunction with the three European Photon Imaging Cameras (EPIC). The EPIC cameras provide a wide (half-degree) field of view, with a point-spread function diameter of about 5 (FWHM) and low resolution spectroscopy. In addition XMM-Newton’s two reflection grating.

(19) – 18 – spectrometers (RGS) offer high-resolution X-ray spectroscopy with by far the highest effective area so far available for X-ray grating spectroscopy below 1 keV (Jansen et al. 2001). The Subaru-XMM Deep Field Survey (SXDS) incorporates a deep, large-area X-ray mosaic with XMM-Newton, consisting of seven overlapping pointings covering a ∼ 1.3 sq. degree region of the high Galactic latitude sky with an exposure time of 100 ks in the central field (in separate exposures) and 50 ks in the flanking fields (for details see Geach et al. 2007). Four of the pointings were carried out in 2000 August, and the remaining three were made in 2002 August and 2003 January, using the European Photon Imaging Cameras (EPIC): the pn-CCD camera (St¨ uder et al. 2001) and the MOS-CCD cameras (Turner et al. 2001). All EPIC-pn observations have been performed using the Thin filter, while both EPIC-MOS cameras used the Medium filter. The images reach a depth for a total cluster flux in the 0.5 − 2 keV band of 2 × 10−15 erg.cm2 .s−1 over the full ∼ 1.3 sq. degree. Finoguenov et al. (2010) used this dataset to identify 57 galaxy groups and clusters in the SXDS/UDS field. In addition they have worked out memberships to confirm the redshift of the clusters. They have associated galaxies to the clusters using spectroscopy (132 galaxies for 57 groups). However the member sample is highly incomplete: they don’t have the memberships of all the galaxies in the clusters. Only few galaxies are associated with few clusters, and it is probably very biased (usually galaxies confirmed spectroscopically as members of clusters are red galaxies). Figure 6 shows the spatial distribution of these spectroscopically confirmed galaxy groups and clusters.. 2.3.. Photometric Redshifts, absolute magnitudes and rest-frame colours. The photometric redshifts (photo-z) technique consists on estimating galaxy distances based on their observed colors (e. g. EAZY; Brammer et al. 2008). This method is.

(20) – 19 – extremely efficient for assembling large redshift samples for faint galaxies. This technique is based on the spectral energy distributions of galaxies can also infer physical properties such as age, stellar mass, dust reddening, metallicity, redshift, and star formation rate. The photometric redshifts used in this work were computed by Hartley et al. (2013) with EAZY, including an apparent K-band magnitude prior, after correcting the observed fluxes for Galactic extinction (Schlegel, Finkbeiner & Davis 1998). We used 7 templates (6 default EAZY templates plus a template constructed from the EAZY’s bluer template with a slight SMC-like extinction), to fit our 11 photometric bands (u∗, B, V , Rc, i, z, J, H, K, 3.6µm and 4.5µm). We also used an iterative method correct the photometric zero-points making advantage of our UDSz spectra and following the method by Ilbert et al. (2006). The final photometric redshifts of the subset with spectra are compared with their spectroscopic redshifts in figure 7. The dispersion of zphot − zspec for these redshifts after excluding outliers (objects with z/(1 + z) > 0.15, i. e. η < 4% of objects) is σz = z/(1 + z) ' 0.031. Because we are not entirely sure that such estimation of redshift error is completely reliable, especially at higher redshift, we adopt a more conservative value of σz = 0.05 in the following work. Figures 8 & 9 show the redshift distributions of our galaxy sample (red representing the photometric redshifts and blue the spectroscopic redshifts). Our redshift distribution is wide with a long tail at high redshift, thanks to our K-band elected sample! Some more or less broad features are present, potentially showing structures in our field (for the narrowest ones) as confirmed by the spectroscopic redshift distributions. However some wider features may be due to the prior method used to compute the photometric redshift, which have tendency to ”mimic” too much the spectroscopic sample. The fact that our spectroscopic sample is not flux limited but rather from a very complicated selection window (a large fraction of our spectroscopic redshifts coming from a photometric redshift.

(21) – 20 – based selection at z > 1, the remaining being an heterogeneous sample from the literature), may be at the origin of such artificial broad features. We are exploring an alternative way to compute our redshift based on a more simple method (without priors).. 2.4.. Mock Galaxy Sample from Millennium Run. The work we are presenting here make use of simulations to train our algorithm (pFoF see section 3). We need to use a mock catalog which reproduces the observational features of our selected sample. We used a mock galaxy catalog based on the Millennium Run simulation (Springel et al. 2005), one of the largest N-body simulation project in cosmology, operated by Max-Plank Institute for Astrophysics (MPA). The Millennium simulation is designed for a 500h−1 Mpc comoving cubic box in side, containing 21603 pure dark matter particles, each of mass of M = 8.6 × 108 M

(22) . This simulation reproduces very well the observed behaviour at large scale and is one of the most commonly used N-body simulation. On the top of the behaviour of the dark matter haloes, once need to plug the complex physical processes in action to reproduce galaxy formation and evolution. The method used is called Semi-Analytical Model (SAM) and implies to empirically reproduce the cooling of the gas, star-formation, Supernovae and AGN feedback, and all processes in action during galaxy evolution. We are using here the SAM produced by Henriques et al. (2012) and available through the Millennium database2 . The resultant galaxies that occupy the Dark Matter haloes can then be converted to observable luminosities through stellar-population synthesis models (e.g. Bruzual & Charlot 2003.) Given enough adjustment of the free-parameter values and 2. http://www.mpa-garching.mpg.de/millennium.

(23) – 21 – phenomenological ingredients to represent time dependant feedback effects, any one quantity such as the empirically determined Luminosity Function (Cole et al. 2001), can be approximated arbitrarily well in principle. A major test of a model’s veracity therefore rests in its capacity to reproduce observables that were not involved in it’s original calibration. One such test is to determine how well a SAM agrees with observed merger rates (or fractions). Several studies have compared the evolution of the galaxy merger rate obtained by the close-pairs technique to that of SAMs implemented in the Millennium Run (Darg et al. 2011). The simulation provides galaxy magnitudes in both BVRIK (Vega) and ugriz (SDSS) filters for each object. The physical properties of our mock galaxy sample sources provided 23 parameters in this catalogue and the magnitudes we adopted are the (AB) standard SDSS filters (e.g. Fukugita et al. 1996). Figure 10 show the galaxies of the semi-analytic model overlayed on a gray-scale image of the dark matter density. The volume of the sphere representing each galaxy is proportional to its stellar mass, and the chosen colours encode the restframe stellar B V colour index. The mock catalog is a good way to train the pFoF parameters. The advantage is that with a mock you have access to all the necessary information on all galaxies! You know to which Dark-Matter Halo they are associated to, so you know the group and cluster memberships. The mock catalog is complete and unbiased. We have therefore constructed a mock catalog on a similar area of our survey with similar magnitude selections (the distribution of mock galaxies are displayed on figure 12). Unfortunately as shown in figure 12, the mock catalog does not reproduce something as fundamental as our K-band number counts. In fact at the same magnitude limit the mock catalog predict ∼ 2.8 more objects than detected in our observations. There is a fundamental problem here linked to maybe the number of satellite dark-matter haloes produced by the N-body simulation and/or the star-formation and.

(24) – 22 – feedback processes which allows the creation of many faint red galaxies..

(25) – 23 –. Fig. 6.— Spatial distribution of X-ray detected groups and clusters in the SXDS/UDS (Finoguenov et al. 2010). Black points are spectroscopically confirmed cluster/group members. Each cluster/group is represented by a circle centred on the position of the peak of X-ray emission, with sizes scaled with the R200 of the cluster/group, and colours corresponding to different redshift ranges: red, orange, green, blue and dark-blue corresponding to 0 < z < 0.4, 0.4 < z < 0.8, 0.8 < z < 1.2, 1.2 < z < 1.6 and 1.6 < z < 2.0, respectively..

(26) – 24 –. Fig. 7.— Comparison of our photometric redshifts (zphot) with spectroscopic redshifts (zspec). The computation of zphot by SED fitting is from the public EAZY code, the σz = ∆z/(1 + z) = is 0.031. But as a conservative, the σz = ∆z/(1 + z) would be taken to be 0.05..

(27) – 25 –. 7000. Count. 6000 5000 4000 3000 2000 1000 0 0.0. 0.5. 1.0. 1.5. 2 .0. 2 .5. 3.0. 3 .5. 4 .0. photoz. Fig. 8.— Photometric redshift distribution of our galaxy sample with KAB < 24.6. The total number of galaxies is 89763. The distribution extend broadly to z = 4 thanks to our K-band based selection. Some peaks in the distribution are visible which are potentially real structures for the narrowest ones but probably fake for the broadest (see text for details).. 5. 0. 1 e0 3. Count. 5. 0. 1 e0 2 5. 0. 1 e0 1 5. 0. 0.0. 0.5. 1.0. 1 .5. 2 .0. 2 .5. 3 .0. 3 .5. 4.0. z. Fig. 9.— Photometric redshift distribution of our galaxy sample in red and spectroscopic redshift distribution in blue. This figure confirms that the peaks in the photometric redshift distribution follow the same peak from the spectroscopic redshift distribution..

(28) – 26 –. Fig. 10.— From Springel et al. 2005: This figure shows the galaxy distribution in the Millennium simulation for a rich cluster of galaxies where one can see them individually. This cluster locate at z=0, the volume of the sphere representing each galaxy is proportional to its stellar mass, and the chosen colours encode the restframe stellar B-V colour index..

(29) – 27 –. Fig. 11.— Spatial distribution of our mock galaxies from the Millennium simulation (Henriques et al. 2012) on the same area that our data (∼ 0.8deg2 ). In order to balance the number of galaxies, we restrict the mock catalog to KsAB < 23.3, instead of the KAB < 24.6 limit used for our data (see figure 12)..

(30) – 28 –. x10. 4. 3.5 3.0. Count. 2.5 2.0 1.5 1.0 0.5 0.0 18. 19. 20. 21. 22. 23. 24. 25. MAG_BEST_K. Fig. 12.— K-band galaxy number counts of our UDS-DR8 data down to KAB < 24.6 in red, and number counts for our Millennium mock catalog to KAB < 24.6 in blue and to KsAB < 23.3 in green. If the more stringent magnitude cut is not applied, then the number of K-band selected galaxies in the mock catalog is 2.8 times higher than in the real data..

(31) – 29 – 3.. Tracing overdense systems. 3.1.. Detecting overdensities. Observing and detecting groups at high redshift (z > 1) is extremely challenging. Detecting ove densities can be done directly from the distribution of galaxies or indirectly by looking for other tracers of dense regions such as the hot gas emission in the X-ray bands (or by strong gravitational lensing).. 3.1.1.. Detecting groups and clusters in X-ray. Due to the deep gravitational potential of groups and clusters, gas in the intergalactic medium is heated up by its higher kinetic energy, and emits abundantly X-ray photons. We can identify this extended intracluster hot gas easily in X-ray observations(Michael Loewenstein et al. 2003) . X-ray allows to identify directly secure massive groups and clusters, but the limits of sensitivity of X-ray observation result in difficulties to identify small loose groups. Also the X-ray luminosity decrease rapidly with redshifts, limiting the detections at z > 1, especially as the number density of high-mass dark-matter-halo at high redshift is small(O. Ilbert et al. 2009) . At high-redshift, not only the poor sensitivity restricts the observation, but also the poor spatial resolution present a huge challenge, implying we need to compare others group’s finding methods to secure our sources selection. Furthermore detecting an over density in X-ray does not provide information on the redshift and on the members associated to this extended X-ray emission. Therefore an alternative technique is necessary once the over density detected to associate galaxies to it..

(32) – 30 – 3.1.2.. Detecting groups and clusters with optical/near-infrared galaxy catalogs. Even if the position of the group or cluster is indicated by indirect method (X-ray or strong gravitational arc) we have to rely on the position of galaxies to associate members to the overdense region. Alternatively we can use directly this method to detect the cluster or group. Galaxies bounded in an overdense system, like a group or a cluster, present a statistical dispersion of velocities, linked to the potential energy of the system, we call ”Velocity dispersion”. Velocity dispersions of galaxies range from ∼ 50 km.s−1 (in the local group it is about 61 km.s−1 - e.g. Van den Bergh et al. 1999) to ∼ 1000 km.s−1 (for instance in the Coma cluster - Struble et al. 1999). Therefore it is essential to identify an over density to be able to characterise velocities dispersion on the direction of the line-of-sight with a sufficient resolution. Spectroscopic redshifts provide such a precise position, as with an error of i∆z ∼ 0.001 at z = 1, they allow to resolve velocity dispersions at ∼ 100 km.s−1 . It is therefore possible to identify structures on the line-of-sight with spectroscopic redshifts (Percival, Will J. et al. 2009) The most efficient algorithms to trace overdensities from galaxies catalogs are based on redshift space distribution. For instance the friend-of-friend (FoF) is a typical method to associate objects by physical quantities, such as position. Galaxies in the same galaxy group must be spatially associated and therefore must be able to be identified by FoF. The Friend-of-Friend algorithm typically work the following way. We first select randomly a source and look for the closets object B bellow a defined distance of this object (call linking length). We then process to the next closest object C (which is not A), until there is no more objects closer than this linking length. Then all these objects are bounded together as a reconstructed group we found. Figure 13 schematises the FoF algorithm. These methods are very efficient when used on very complete spectroscopic survey, where a.

(33) – 31 –. D C. C. B. B A. Fig. 13.— Schema of the FoF algorithm (for simplification it is shown in 2D, without considering the redshift-dimension). All the filled circles are galaxies, the dashed circle is the linking-length region. In this situation, galaxies A-B-C-D are friends, and belong to the same group.. very large fraction of objects have spectroscopic redshifts. However such surveys are very telescope time consuming and are limited in the flux limits reachable, especially at high redshifts (Bolzonella, M. et al. 2000). Alternatively, for faint galaxies or when the completeness of the spectroscopic survey is low, once need to use photometric information to identify the clusters or groups on the direction of the line of sight. For instance our spectroscopic data are very limited on the UKIDSS-UDS (anyway very few flux limited samples allow to reach z = 2), so we need to rely on photometric redshifts. As we have described in section 2.3, the error given by comparing our UKIDSS-UDS spectroscopic and.

(34) – 32 – photometric redshifts is σz = 0.031. So at z=1, this error of ∆z ' 0.1, corresponds to a resolution of ∼ 10, 000 km.s−1 way larger than the velocity dispersion even in clusters! The Red sequence method has proven to be a very efficient way of selecting clusters. Dense environment tends to quench star-formation in galaxies, therefore the budget of stars in such galaxy are dominated by red old stars, hence the fraction of red galaxies is higher in overdense regions. So identifying overdensities in red galaxy distribution can be used to select over dense regions. This is usually done by combining an automatic identification of the red sequence in a color-magnitude diagram and a projected overdensity detection algorithm, such as Voronoi tessellation (2D) (Marinoni et al. (2002)) or FoF (Huchra & Geller 1982) . In fact once identified the red sequence is also a very good indicator of the redshift of the cluster. This method is usually used in conjunction with other methods as a sanity check. However this method by definition does not help selecting loose groups as well, as in such environments the red fraction may be lower than in massive groups and clusters. In addition at high redshift (z > 1) it is not entirely clear if the quenching has been efficient enough to generate such red sequence in all groups and clusters, and this method would eventually miss ”blue groups and clusters” at high redshifts(Bell, Eric F. et al. 2004) . Another way is to rely directly on photometric redshifts. Indeed the FoF method on projected space (and other 2D overdensity selection methods) can be combined with the photometric redshifts and can potentially detect small groups even at high redshifts without relying on red sequence. However the poor accuracy of the photometric redshifts (corresponding at best to a resolution on velocity dispersion of several 1000km/s in average), does not allow to identify the structure on the line-of-sight directly(Baum, W. A. et al. 1962) . For this we need to use a careful approach which is the Probabilistic Friend-of-Friend algorithm..

(35) – 33 – 3.2.. Probabilistic Friend-of-Friend algorithm. The algorithm we are using here is called ”probabilistic Friend-of-Friend” and has been developed in Liu et al. (2008), and further used in Jian et al. (2013). We refer to these papers for more detailed descriptions, and here we just summarise briefly the main components. To overcome the disadvantages of the FoF algorithms , three major considerations are part of the construction of our new algorithm: 1. At any stage of the group-finding process, each galaxy retains its redshift uncertainty. 2. The galaxy redshift uncertainties are dealt with in the linking criteria by a statistical method. The redshift uncertainty of each galaxy can be modelled independently. But the group-finding algorithm should have unified criteria, which naturally accommodate data with various uncertainties. 3. In the ideal case where all galaxies have no redshift uncertainty, the performance of this algorithm converges to the original FoF. The algorithm work by constraining at the same time the projected overdense region (2D) and discriminate objects that are not bounded on the direction of the line-of-sight. First, we need to restrict the linking length in 2D. We define the linking distance (Lxy ) as the the comoving length maximal for two galaxies of distance (d12 ) to be bounded: d12 < Lxy .. (1). Second, we restrict the linking length in line-of-sight direction, i.e. redshift direction. We then introduce the probability of two galaxies, with photometric redshift probability distribution functions G1 and G2 respectively, to be bounded by the linking length in redshift (Lz ), following: Z P (|z2 − z1 | ≤ Lz ) ≡. ∞. Z. z+lz. dzG1 (z) 0. 0. 0. G2 (z )dz . z−lz. (2).

(36) – 34 – This probability is represented schematically in figure 14. The we define a probability threshold (Pth ) for which the two galaxies are bounded as: P (|z2 − z1 | ≤ lz ) ≥ Pth .. (3). If two galaxies are satisfying criteria 1 and 3 they are called ”Friends”, in the same way than in the FoF method.. G1. P ability (z) Proba. G2 G2(z’). G2(z (z’)). z’ > z ‐ z’ > z lz. z’ < z+ l ’ lz G1(z). Redshift (z) Fig. 14.— From Jian et al. (2013): G1 and G2 are Gaussian distribution of two galaxies, the G1 σz is smaller than G2 σz . The probability for this two galaxies to be separated by a linking length Lz , is shown by the dashed area.. The pFoF algorithm required to be trained on a known sample in order to be able to identify real groups. Parameters such as the linking distance Lxy , linking length Lz and.

(37) – 35 – probability threshold Pth , need to be adapted for our own sample. One caveat of such method, is that it can lead to a lot of false positive detections.. 3.3.. Purity and Completeness. To evaluate the performance on pFoF we need to compare the results with a catalog of ”real” groups and clusters (either from previous observational studies or simulations). We are here introducing some parameters to assess our results between the real groups and the reconstructed groups: purity and completeness. There are different definitions for purity and completeness, and we are following the definition from Gerke et al. (2005). We define a pure group a reconstructed group for which more than 50% of galaxy members are members of the real group. Then a complete group is a real group for which more than 50% of the galaxy members are members of the reconstructed group. Therefore purity and completeness of the sample are computed following:. Npure , NpFoF. (4). Ncomplete , Nreal. (5). p1 =. c1 =. where Npure and Ncomplete are the number of pure groups and complete groups, Npfof and Nreal are the number of reconstructed groups and real groups. Moreover, if a reconstructed group is a pure group but the corresponding real group is not a complete group, or a the real group is a complete group but the corresponding reconstructed group is not a pure group, we call it one-way-match. So two-way-match need to satisfy reconstructed group is pure group, and real group is complete group (see figure 15). Then we introduce another purity and completeness for our samples:.

(38) – 36 –. p2 =. N2 , NpFoF. (6). c2 =. N2 , Nreal. (7). where N2 is the number of pure and complete groups.. Fig. 15.— From Knobel et al. (2009): the left big circle is real group catalogue, and the right big circle is reconstructed group catalogue, the single arrow and double arrow represent oneway-match and two-way-match individually. Each point displays a galaxy and the encircled points inside the big circles constitute groups.. In fact purity and completeness are in competition when training our algorithm (usually to get a better purity one needs to relax the constrains on completeness and vice-versa), which leads to two phenomena, overmerging and fragmentation . Figure 15 of comparing a real group catalog to a reconstructed group catalog as obtained.

(39) – 37 – from DM simulation. Here we just want to discuss some encounter situation. For example, if a real group corresponds to be made up by many reconstructed groups, we call that Fragmentation. On the contrary, if a reconstructed group corresponds to be build up by some real groups, we call Overmerging. In order to find the best parameter set to train pFoF, we need to define other parameters, such as g1 , g2 , and ge1 which are normalized between 0 and 1. g1 is a parameter that can balance between purity and completeness, and if there are no overmerging and no fragmentation, it is close to 0. r g1 =. (1 − p1 )2 + (1 − c1 )2 . 2. (8). However the parameter g1 express only a one-way match, between real and reconstructed group catalogs. So to take into account the two-way matching we introduce two supplementary parameters: g2 is a parameter to balance between overmerging and fragmentation, close to 1 in the best case scenario. g2 =. c2 p 2 . c1 p 1. (9). The last parameter is ge1 , which is similar to g1 , but for two-way-match. If there are no overmerging and no fragmentation, it is close to 0. r (1 − p2 )2 + (1 − c2 )2 ge1 = . 2. (10). The optimum sets of parameter can be determine by satisfying the above conditions.. 4.. Building up a galaxy group catalog to z=2. The current generation of optically-selected surveys are biased against redder galaxies, implying that there are not efficient to select high redshift galaxies (z > 1) but also dusty.

(40) – 38 – star-forming and passive galaxies. Therefore the current generation of group and cluster catalogs are limited to z < 1 and are biased against the passive population in pairs and groups, leading to an underestimation of their role in the galaxy evolution. Making the best use of the worldwide release of the near-infrared data UKIDSS-UDS DR8, combined with Subaru and CFHT data in the optical waveband, and Spitzer-IRAC mid-infrared data, our goal in this work is to couple accurate photometric redshifts with the probabilistic Friends-of-Friends algorithm to build a groups catalog up to redshift z=2.. 4.1.. Training the parameters for pFoF. As described in section 3.2 the pFoF algorithm requires its parameters (Lxy , Lz and Pth ) to be determined in order to extract efficiently the group catalog (as probed by the parameters g1 , g2 , and ge1 ). To train these parameters we are using two sets of data: the Millennium Mock-based catalog and the X-ray-based catalog.. 4.1.1.. How to train your dragon: optimisation of richness and pFoF parameters. The Richness is defined as the number of objects included in the group. To train the pFoF parameters, we need to select a minimum richness above which we consider the structure as a group. In order to define the best richness for our sample we use the mock catalog. In fact what we want to investigate is given our dispersion on the redshift, what are the chances to identify a fake group of a given richness randomly. If groups of this given richness are more likely to be fake, then we should probably not try to identify them. For this we can create a random catalog with similar characteristics than our mock catalog, and run pFoF on both the mock and our random catalog to determine how many groups of given richness are detected. However this is a vicious circle as we need then to choose some pFoF parameters to extract the groups. Therefore we define first the richness of groups to.

(41) – 39 – be > 4, and we will check the validity of this parameter later. Then we need to determine the other pFoF parameters. First we set the probability threshold (Pth ) arbitrarily as there is a relation between Lz and Pth . According to the rule of thumb (cf Jian et al. 2013), we find that when the σz =0.05, the best value for the threshold is Pth = 0.001. Then we fine-tune the values of Lxy and Lz which minize the parameter ge1 closer to 0. Then we can compare between reconstructive group and the original (mock or X-ray) group and determine the purity p1 and completeness c1 , and estimate how big the overmerging or fragmentation problem. Once we have the pFoF parameters trained we can run the algorithm on our mock and random catalogs and verify that the value chosen for Richness is valid or not. For example using the parameters extracted from the Millennium Mock catalog (see section 4.1.2), we computed the number of groups constructed at a given Richness, for two cases: first using the ”spectroscopic” redshifts provided by the simulation (figure 16 and table 1), and by randomly modifying the redshift of each galaxy within σz = 0.05 to reproduce the effect of our ”photometric redshifts” (figure 17 and table 2). Richness. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Groups (mock). 66585. 2946. 568. 245. 105. 50. 43. 33. 16. 14. Groups (random). 76669. 551. 8. 1. 0. 0. 0. 0. 0. 0. Table 1: Number of groups of given richness for mock catalog and a random catalog. The pFoF parameters used here were trained on the mock catalog assuming ”spectroscopic” redshifts (i.e. σz = ∆z/(1 + z) = 0).. In any cases we see that the number of groups with richness R > 4 selected from the random catalog is negligeable compared to the number of groups from the mock catalog..

(42) – 40 –. 5 .0. 1e0 4 5 .0. 1e0 3 N. 5 .0. 1e0 2 5 .0. 1e0 1 5 .0. 1. 2. 3. 4. 5 6 Richness. 7. 8. 9. 10. Fig. 16.— Number of groups as a function of richness for the mock catalogs in red and the random catalog in blue. The pFoF parameters used here for the reconstructed groups were trained on the mock catalog assuming ”spectroscopic” redshifts. It is clear that at richness R > 4, the probability to find a group by luck is far lower than the group to be real.. 4.1.2.. Millenium Mock trained catalog. The Mock catalog build out from the Millennium simulation (see section 2.4) would be ideal to train our pFoF parameters as it provides all required information on Dark matter haloes and galaxies. Unfortunately as we explained, the Mock catalog does not reproduce the basic characteristics of our K-band selected catalog. Nevertheless, as all other SAM-based mock catalog available present similar issues (Somerville, Rachel S. 1999) , this is the best simulated catalog we can use, so we decided to train our pFoF parameters with it. Figures 5 & 11 shows the two data sets, the distribution of UKIDSS-UDS DR8 and Millennium simulation. They both detect under about 92000 data. To match the number of galaxies in our UKIDSS-UDS catalog at KAB < 24.6, we cut the MN-mock catalog from.

(43) – 41 –. Richness. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Groups (mock). 66585. 2946. 568. 245. 105. 50. 43. 33. 16. 14. Groups (random). 68651. 3983. 361. 26. 2. 2. 0. 0. 0. 0. Table 2: Number of groups of given richness for mock catalog and a random catalog. The pFoF parameters used here were trained on the mock catalog assuming ”photometric” redshifts (i.e. σz = ∆z/(1 + z) = 0.05). Henriques et al. (2012) at Ks < 23.3, because the member counts are always higher in Mock catalog than in real data. Once again we need to insist on the fact that the mock catalogs are therefore not really suitable to train our pFoF parameters, as they are a very poor representation of our data. But as there is no better mock catalog available, we are using the Henriques et al.’s catalog. As shown in figure 7, the dispersion between the photometric and spectroscopic redshifts from our UKIDSS-UDS catalog is σz = ∆z/(1 + z) = 0.05. We selected galaxy a sample with K < 24.6 in the redshift range between 0 to 2. In order to use the Mock catalog for determining the parameters of our sample, we applied the same redshift dispersion than for our data (σz = 0.05) and the same redshift and richness cuts. As the completeness of our data is changing with redshifts due to the Malmquist bias, hence that we have more faint objects at low redshifts implying a higher density, we need to use different linking lengths at different redshifts, to avoid missing a large amount of group members at high redshifts.To solve this problem, we actually used luminosity distances to definite the different linking length at different redshift. We determined the best pFoF parameters using the millennium simulation catalog, and we identified 654 reconstructed groups (with richness greater than 4) for 736 dark-matter haloes initially in the mock (real groups)..

(44) – 42 –. 5 .0. 1e0 4 5 .0. N. 1e0 3 5 .0. 1e0 2 5 .0. 1e0 1 5 .0. 1. 2. 3. 4. 5 6 Richness. 7. 8. 9. 10. Fig. 17.— Number of groups as a function of richness for the mock catalogs in red and the random catalog in blue. The pFoF parameters used here for the reconstructed groups were trained on the mock catalog assuming ”photometric” redshifts. Still in this case, at richness R > 4, the probability to find a group by luck is far lower than the group to be real.. Figure 18 shows the spatial distribution in degrees of dark matter Haloes on Millennium simulation. Assuming each individual halo can be identified as a group, the number of groups from the mock catalog is 736. Figure 19 shows the spatial distribution for our 654 reconstructed groups using MN-best-parameters (the position of the group centre is determined as the mean positions of the galaxies member of the group). The optimal set of parameters identified for our Millennium mock catalog, involve a purity and completeness of p1 = 0.653 , c1 = 0.461, as well as other parameters p2 = 0.509, c2 = 0.452, g1 = 0.454, g2 = 0.766, and ge1 = 0.520. The perfect match between real and reconstructed groups would infer a purity and a completeness of 1. As shown in Figure 15, as our completeness is low, we are exactly in a.

(45) – 43 – case of fragmentation, where the real (mock) group is corresponding to several reconstructed groups. This lead with an underestimation of the size of the groups, and even large structures such as clusters, are separated in several smaller structures. 0. 4 0. 3 0. 2. Dec.. 0. 1 -0.0 -0.1 -0.2 -0.3 -0.4 -0.4. -0.3. -0.2. -0.1. -0.0. 0.1. 0.2. 0 .3. 0.4. R.A.. f. Fig. 18.— Spatial distribution of mock Dark Matter Haloes from Millennium simulation, the red points are the overdensity systems, which total numbers are 736.. 4.1.3.. X-ray trained catalog. As seen in the previous section, the selection we made by training our algorithm based on our Millennium mock catalog, is not ideal as we do not trust the mock catalog. We alternatively decided to train pFoF using the X-ray based group catalog, despite the fact that less massive groups are very faint in X-ray and so they should not be detected. Furthermore X-ray does not provide a direct information of membership of galaxies associated to these clusters and groups, and one need to exploit information in optical or infrared waveband to assign members to their respective clusters. We used the X-ray detected group and cluster catalog from Finoguenov et al. (2010) to.

(46) – 44 – 0. 4 0. 3 0. 2. Dec.. 0. 1 -0.0 -0.1 -0.2 -0.3 -0.4 -0.4. -0.3. -0.2. -0.1. -0.0. 0 .1. 0.2. 0 .3. 0. 4. R.A.. Fig. 19.— Spatial distribution of reconstructed group using MN-best-parameter, the red points are the reconstructed groups, which total numbers are 645.. train as well our pFoF parameter set. As described in section 2.2, Finoguenov et al. (2010) has used the combination of XMM-Newton X-ray data on the Subaru-XMM Deep Field, with the Subaru and UKIDSS-UDS data, to construct a catalog of galaxy groups and clusters, as well as listing their associated potential members (based on combination of photometric and spectroscopic redshifts). So here we can use this catalog of galaxies and their association with X-ray detected clusters to train the pFoF parameters. We still need to be careful as the memberships are very much incomplete This catalog consists of 132 spectroscopically confirmed galaxies for 57 groups, and 57 sources on X-ray detection. Amongst these 57 groups, only 17 include more than two spectroscopically confirmed galaxies, so we use only these 17 groups to train our pFoF parameters. Figure 20 shows the spatial distribution in degrees of these 17 groups. With our optimised set of parameters, we were able to reconstruct 16 of these 17 R ≥ 2 groups. Figure 21 shows the spatial distribution of our 16 reconstructed groups using X-ray-best-parameters..

(47) – 45 –. -4.5 -4.6 -4.7 -4.8. Dec.. -4.9 -5.0 -5.1 -5.2 -5.3 -5.4 -5.5. 34.1. 34.2. 34.3. 34.4. 34.5 R.A.. 34.6. 34.7. 34.8. 34.9. Fig. 20.— Spatial distribution of galaxy groups identified by X-ray confirmed spectroscopically with richness R ≥2 (to ease comparison with reconstructed groups). Their total numbers of groups are 17.. With the optimal set of parameters identified for our X-ray catalog, we are deriving a purity and completeness of p1 = 1.000, c1 = 0.941, and other parameters such as p2 = 1.000, c2 = 0.941 g1 = 0.042, g2 = 1.000, and ge1 = 0.042. Although the X-ray trained the optimal parameter are apparently very good as allowing very high purity and completeness, they are not necessary the best parameters for our UKIDSS-UDS data. First X-ray groups are generally at low redshift, given how fast the X-ray luminosity drop as a function of redshift, and furthermore X-ray does not provide membership for galaxies directly and requires spectroscopic follow-up, which is generally limited. As we will see in section 4.2, this set of pFoF parameter lease to far too many fake detections..

(48) – 46 –. -4.5 -4.6 -4.7 -4.8. Dec.. -4.9 -5.0 -5.1 -5.2 -5.3 -5.4 -5.5. 34.1. 34.2. 34.3. 34.4. 34.5 R.A.. 34.6. 34.7. 34.8. 34.9. Fig. 21.— Spatial distribution of reconstructed groups built using pFoF trained X-ray parameters, with richness R ≥2 (to ease comparison with reconstructed groups). Their total numbers of groups are 16.. 4.2.. UKIDSS-DR8 Group and Cluster catalogs. As described in sections 2.1 & 2.3, we selected 89763 galaxies with KAB < 24.6 and redshift z < 2 from our UKIDSS-UDS survey, and we applied the two sets of pFoF parameters (from Millennium mock and X-ray, c.f. section 4.1.2 and section 4.1.3 respectively) to build two group catalogs up to z < 2. We divided our catalogs in five different redshift bins: (a) 0 < z < 0.4, (b) 0.4 < z < 0.8, (c) 0.8 < z < 1.2, (d) 1.2 < z < 1.6, and (e) 1.6 < z < 2.0. We first used the MN-mock trained pFoF parameters to extract UDS groups, and identified 390 groups with richness R ≥ 4. Figure 22 shows the spatial distribution in degrees of these group candidates. This number of groups is in agreement with the expected 736 Dark-matter haloes predicted by our mock catalog. As a sanity check we matched these reconstructed groups with the Finoguenov et al. (2010) X-ray detected catalog, using the R200 radius of the X-ray clusters provided. Each.

(49) – 47 – reconstructed groups with its centre within the R200 radius of the X-ray cluster and with a redshift within σz = ∆a/(1 + z) = 0.05 is identified as a match; 16 of our reconstructed groups are matched with a X-ray cluster, as shown in figure 23. However by comparing figure 22 and figure 23, it is clear that the matching is not very good, as the size of the matched clusters do not really relate(See figure 24). . Furthermore, by taking a random spatial distribution of points following the same redshift distribution of our 390 reconstructed groups and matching, using the same method, this random catalog with the Finoguenov et al. (2010) catalog, we find a similar number of matches. Therefore, as in fact expected, although the catalog of reconstructed groups appears to be reliable, it is not representing the reality of our group distribution in the field. To have a reliable reconstructed group catalog, we need to have a set of parameters trained on a mock catalog that is representative of our dataset. Here are some groups overlapping together (See figure 22) , perhaps they are some X-ray overlapping on the line-of-sigh. However, according to our completeness of parameter, we believe that here is hiding the problem of fragmentation, We dont consider this parameter is optimal for our UDS-DR8 date (See Figure 12), we have mentioned previously, its not unfair that using the same linking length on different redshift, because we use the real data, we would miss too many faint member of galaxies in high redshift, but mock is not. So we require a better simulation which reproduces better our observations. We then used the X-ray trained pFoF parameters to extract UDS reconstructed groups. Figure 25 show the spatial distribution in degrees of our 3822 group candidates with richness R ≥ 4 in different redshift bins. The number of groups extracted using this parameters is just not realistic at all, with one order of magnitude more objects than the number of Dark Matter halos predicted by the Millennium simulation. We believe the incomplete baseline information, it would lead the optimal linking length.

(50) – 48 – disordering. For our example, our standard spectroscopic members of galaxy are 132, when we found the optimal linking length on X-ray standard, we would miss the real member between members we dont have. That mean we need longer linking length to link each other, so if we use this longer linking length to train our UDS-DR8, we would link too many members for each other, this longer linking length trend to find friends around. The poor constraint due to the very limited number of spectroscopically confirmed members of the X-ray detected groups is a the origin of such discrepancy. To be able to reconstruct a reliable group catalog, we need to have access to a highly complete spectroscopic sample..

(51) – 49 –. Fig. 22.— Spatial distribution of UDS-DR8 groups built using pFoF with MN-mock-basedparameters. The total number of groups with richness R ≥ 4 is 390. The increasing sizes correspond to increasing richness, and colours relate to different redshift ranges: red, orange, green, blue and dark-blue corresponding to 0 < z < 0.4, 0.4 < z < 0.8, 0.8 < z < 1.2, 1.2 < z < 1.6 and 1.6 < z < 2.0, respectively..

(52) – 50 –. Fig. 23.— Distribution of groups matched between our MN-trained reconstructed catalog and the X-ray catalog from Finoguenov et al. (2010). The total number of matched groups with R ≥ 4 is 16. Each cluster/group is represented by a circle centred on the position of the peak of X-ray emission, with sizes scaled with the R200 of the cluster/group, and colours corresponding to different redshift ranges: red, orange, green, blue and dark-blue corresponding to 0 < z < 0.4, 0.4 < z < 0.8, 0.8 < z < 1.2, 1.2 < z < 1.6 and 1.6 < z < 2.0, respectively..

(53) – 51 –. 3 .4 3 .2 3 .0 2 .8. R200. 2 .6 2 .4 2 .2 2 .0 1 .8 1 .6 1 .4 1 .2 1 .0 4 .0. 4. 5. 5 .0. 5.5. 6 .0. 6 .5. 7.0. Richness. Fig. 24.— This figure shows the matching source of distribution between richness of groups and R2 00 of X-ray source, the unit of the R2 00 is arcmin, the total numbers of group are 16..

(54) – 52 –. Fig. 25.— Spatial distribution of UDS-DR8 groups built using pFoF with X-ray-basedparameters. The total number of groups with richness R ≥ 4 is 3822. The increasing sizes correspond to increasing richness, and colours relate to different redshift ranges: red, orange, green, blue and dark-blue corresponding to 0 < z < 0.4, 0.4 < z < 0.8, 0.8 < z < 1.2, 1.2 < z < 1.6 and 1.6 < z < 2.0, respectively..

(55) – 53 – 5.. Conclusions. We used the SXDS/UDS DR8 to construct a group catalog up to z = 2 using photometric redshifts and a probabilistic Friend-of-friend algorithm (pFoF). Our photometric redshifts are evaluated to present a dispersion σz = ∆z/(1 + z) = 0.05 up to KAB = 24.6 compare to a sample of spectroscopic redshifts. In order to train the parameters required for pFoF to construct a group catalo, we used (1) a mock galaxy sample from the output of the Millennium Run simulation from Henriques et al. (2012) and (2) a X-ray detected group catalog (57 sources) along with some spectroscopically confirmed galaxy members from Finoguenov et al. (2010). Our study lead to the following conclusions: • By comparing our UKIDSS-UDS-DR8 with the mock catalog, we realised that the the mock catalog does not reproduce the basic properties of our catalog (for instance it overestimate the number of objects by a factor ∼ 3). We nonetheless used this catalog to train the pFoF parameters and extracted the best parameters with purity p1 = 0.653 and completeness c2 = 0.454, low values leading to fragmentation of the reconstructed groups. • The X-ray detected group catalog would be a good way to train the pFoF parameters, but the number of galaxy members confirmed spectroscopically is very small. We nonetheless used this catalog to train the pFoF parameters and extracted the best parameters with purity p1 = 1.000 and completeness c2 = 0.942. Such high values in fact hide the fact that the incompleteness of the galaxy sample prevent to extract realistic parameters (132 members of group with spectroscopic redshift for 57 X-ray source). • We the used the two sets of best trained pFoF-parameters on our UDS-DR8 data. 1. Based on the optimal parameter from Millennium simulation, we reconstructed 390 groups with richness R ≥ 4, a quantity in agreement with the number of Dark matter haloes predicted by the simulation. However, when matching with the 57 X-ray detected.

(56) – 54 – groups, only ∼ 30% of the groups are recovered, which is not better than a random match. We conclude that this set of parameters is not consistent with the reality of our sample. A more realistic mock catalog is required to train accurately our parameters. 2. Based on the optimal parameter from X-ray of member galaxies, we reconstructed 3822 groups with richness R ≥ 4, 10 times more groups than the Dark matter haloes predicted by the Millennium simulation. Here again we need a more complete sample of galaxy members to extract reliable pFoF parameters. • Overmerging and Fragmentation coexist in our reconstructed group, with fragmentation being more serious. We are investigating ways to recombine these fragmented groups and rebuild a reasonable group catalog..

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