X-ray Analysis

All the blank fields considered in our analysis are observed extensively in the X-ray with Chandra andXM M−N ewton. Firstly, we remove point sources in both of theChandra andXM M−N ewtonimages following the procedure explained in Finoguenov et al. (2009).

Then the residual images were coadded, taking into account the different sensitivity of each instrument. The ”residual” image, free of point sources, is then used to identify extended emission. Groups and clusters are selected as extended emission with at least 4σ significance with respect to the background (see Finoguenov et al. (2009) for further details regarding the precise definition of background and detection significance level). A redshift to each systems on the basis of spectroscopic redshifts, when available, or otherwise

photometric redshift is assigned. The X-ray luminosity LX is estimated within r5001 after taking into account the possible missed flux through the use of the beta-model. The total masses M200, within r200, are estimated based on the measured LX and its errors, using the scaling relation from weak lensing calibration of Leauthaud et al. (2010). The intrinsic scatter for mass in this relation is 20% (Leauthaud et al., 2010; Allevato et al., 2012) which is larger than a formal statistical error associated with the measurement of LX.

The X-ray group catalogs derived with this approach comprise 52 detections in AEGIS (Erfanianfar et al. 2013), 277 detections in the COSMOS field (George et al. 2011), 50 detections in the ECDFS (Finoguenov et al. in prep.) and 27 detection in CDFN. We present the full CDFN X-ray group catalog in the Appendix. In the following section we describe how we select a subsample of “secure” groups and how we associate them to the respective galaxy population.

Group Identification

To associate the respective galaxy population to any X-ray extended emission and to define properly the group redshift we follow the same procedure described in Erfanianfar et al.

(2013) and performed on the AEGIS X-ray dataset. We extend here this procedure to all the other fields described in the previous section. In brief, we estimate the galaxy over-density along the line of sight in the region of each X-ray extended emission following the red sequence technique (Finn et al. 2010). Additionally we screen for the existence of an over-density of red galaxies in the 3rd dimension using the spectroscopic redshift distribution of the X-ray extended source.

As described in Erfanianfar et al. (2013), we assigned to each X-ray extended source a flag that describes the quality of the identification. We define the following flags:

- flag=1 indicates a confident redshift assignment, significant X-ray emission, and a well-determined center of red galaxies with respect to X-ray emission center

- flag=2 indicates that the centering has a large uncertainty (∼15^′′) - flag=3 indicates no secure spectroscopic confirmation but good centering

- flag=4 or more depending on the survey indicates that we have uncertain redshifts due to the lack of spectroscopic objects and red galaxies, and also a large uncertainty in centering or unreliable cases for which we could not identify any redshift.

For the purpose of this work we consider only X-ray extended emission with a secure redshift definition with flag 1 or 2. Out of the initial 406 X-ray group candidates in the four considered fields, we identify 244 secure groups. The secure redshift estimate is used to refine the initial X-ray luminosity of the groups and, thus, the mass M200 with the scaling relation of Leauthaud et al. (2010) as described in the previous paragraph. The final step

1r∆(where ∆ = 500,200) is the radius at which the density of a cluster is equal to ∆ times the critical density of the universe (ρc) and M∆is defined as M∆= (4π/3)∆ρcr³∆.

3.2 The dataset 61

of the analysis is the identification of the group galaxy members via dynamical analysis as described below.

Group Membership

In order to properly define the galaxy membership of each group, we identify among our 244 secure groups those which are relatively isolated. Indeed, the presence of a close companion may bias the estimate of the velocity dispersion of the group and, thus, also the galaxy membership definition which relies on this quantity. This procedure leads to a subsample of 211 clean isolated groups. We follow the procedure described in Erfanianfar et al.

(2013) to estimate the group velocity dispersion and the galaxy membership definition.

The procedure is iterative and it needs a first guess of the velocity dispersion to define the redshift interval around the group redshift to determine the initial galaxy membership. We derive the first guess of the velocity dispersion from the group’s X-ray luminosity LX by using the relation of Leauthaud et al. 2010. This velocity dispersion provides the intrinsic velocity dispersion (σ(v)_intr-which can be achieved by subtracting the errors of the redshift measurements in quadrature from the rest frame velocity dispersion) of the group. We estimate, then, the observed velocity dispersion by considering the redshift of the group (z_group) and the errors of the redshift in our spectroscopic samples, h∆(v)i² according to these relations:

σ(v)²_rest =σ(v)²_intr +h∆(v)i² (3.1)

σ(v)obs =σ(v)rest×(1 +zgroup) (3.2)

We consider as initial group members all galaxies within |z−z_group| < δ(z)_max where δ(z)_max = 2^σ(v)_c^obs and within virial radii (r₂₀₀) from the X-ray center. We recompute the observed velocity dispersion of the groups, σ(v)obs using the “gapper” estimator method which gives more accurate measurements of velocity dispersion for small size groups (Beers, Flynn & Gebhardt 1990; Wilman et al. 2005) in comparison to the usual formula for standard deviation (see Erfanianfar et al. 2013 for more details). The observed velocity dispersion is estimated according to:

σ(v)obs = 1.135c×

√π N(N−1)

n−1

X

i=1

ωigi (3.3)

where wi =i(N −i) , gi =zi+1−zi and N is the total number of spectroscopic members.

In this way we measure the velocity dispersion using the line-of-sight velocity gaps where the velocities have been sorted into ascending order. The factor 1.135 corrects for the 2σ clipping of the Gaussian velocity distribution. We iterate the entire process until we obtain a stable membership solution. We then calculate errors for our velocity dispersions using the Jackknife technique (Efron 1982). The procedure can be considered reliable for groups with at least 10 galaxy members. The 10 galaxy members threshold is reached for

10⁴² 10⁴³ 10⁴⁴

100 1000

L0.1-2.4keVEz-1 (erg s-1 )

σ(km s^-1)

Figure 3.1: L_X −σ relation for X-ray groups. The dashed blue line show our expectation for LX−σ relation from scaling relations (Leauthaud et al. 2010) and the solid red line is our bisector fit to data.

36 groups out of 211. For the groups with less than 10 members but still more than 5 members within r₂₀₀, we base the velocity dispersion estimate on M₂₀₀ and the relation between σ and r200 as in Carlberg, Yee & Ellingson (1997). This leads to a sample of 111 groups out of 211. Figure 3.1 shows the Lx−σ relation for X-ray groups with more than 10 spectroscopic members, whereσ is estimated via dynamical analysis. The solid red line shows the power-law fit to the relation. The bisector procedure is used for this fit (Akritas

& Bershady 1996). We also plot the Lx −σ relation (dashed blue line) expected from scaling relations obtained for a sample of groups with similar luminosities in the 0< z <1 redshift range in COSMOS (Leauthaud et al. 2010). The consistency between two relations ensures that the estimate of the velocity dispersion derived from the X-ray luminosity and the one calculated via dynamical analysis are in good agreement.

Once we have the estimate of the velocity dispersion of each group, we define as group members all galaxies within 2×r200 in the angular direction and ±3×(σ/c)×(1 +zgroup) in the line of sight direction in order to consider also the infalling regions of the groups.

When a member galaxy is associated to more than one group, we consider it as a member of the group for which the distance to the galaxy is lowest in units of virial radii.