Kinematic unrest of low mass galaxy groups
G. Gozaliasl, A. Finoguenov, H. G. Khosroshahi, C. Laigle, C. C. Kirkpatrick, K. Kiiveri, J. Devriendt, Y. Dubois, J. Ahoranta
AAstronomy & Astrophysics manuscript no. aanda c (cid:13)
ESO 2020January 22, 2020
Kinematic unrest of low mass galaxy groups
G. Gozaliasl , , , (cid:63) , A. Finoguenov , H. G. Khosroshahi , C. Laigle , C. C. Kirkpatrick , K. Kiiveri , ,J. Devriendt , Y. Dubois , and J. Ahoranta Finnish centre for Astronomy with ESO (FINCA), Quantum, Vesilinnantie 5, University of Turku, FI-20014 Turku,Finland Department of Physics, University of Helsinki, P. O. Box 64, FI-00014 , Helsinki, Finland Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014, Helsinki, Finland School of Astronomy, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran CNRS, UMR 7095 & UPMC, Institut ďAstrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France Sub-department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RHReceived ; accepted
ABSTRACT
In an effort to better understand the formation of galaxy groups, we examine the kinematics of a large sample ofspectroscopically confirmed X-ray galaxy groups in the Cosmic Evolution Survey (COSMOS) with a high sampling ofgalaxy group members up to z = 1 . We compare our results with predictions from the cosmological hydrodynamicalsimulation of Horizon-AGN . Using a phase-space analysis of dynamics of groups with halo masses of M ∼ . − . M (cid:12) , we show that the brightest group galaxies (BGG) in low mass galaxy groups ( M < × M (cid:12) ) havelarger proper motions relative to the group velocity dispersion than high mass groups. The dispersion in the ratio ofthe BGG proper velocity to the velocity dispersion of the group, σ BGG /σ group , is on average . ± . for low massgroups and . ± . for high mass groups. A comparative analysis of the Horizon-AGN simulation reveals a similarincrease in the spread of peculiar velocities of BGGs with decreasing group mass, though consistency in the amplitude,shape, and mode of the BGG peculiar velocity distribution is only achieved for high mass groups. The groups hostinga BGG with a large peculiar velocity are more likely to be offset from the L x − σ v relation; this is probably becausethe peculiar motion of the BGG is influenced by the accretion of new members. Key words.
Galaxy groups–galaxies–Galaxy Cluster
1. Introduction
Galaxy groups represent a transitional environment be-tween rich clusters and Milky Way-like halos. Understand-ing the dynamics of these structures is pivotal both forcosmology and galaxy evolution. Unlike in galaxy clus-ters, scaling relations involving total gravitational mass, X-ray temperature, X-ray luminosity, group velocity disper-sion, and other observable properties exhibit a large scat-ter (Khosroshahi et al. 2007; McCarthy et al. 2010; Wojtak2013), which needs to be understood in order for galaxygroups to be considered as cosmological probes to the samelevel as clusters are.On the other hand, galaxy evolution depends on the as-sembly history of their host group. Indeed, the dynamicalage of galaxy group halos has also been shown to be corre-lated with galaxy properties. For instance, Khosroshahi etal. (2017) demonstrate that active galactic nuclei (AGN)radio flux, at a given stellar mass, is significantly lowerfor BGGs in dynamically relaxed groups compared to thebrightest group galaxies (BGGs) of the same mass in dy-namically evolving groups. This suggests that the AGN ac-tivity of BGGs, as probed by the radio emission, dependsnot only on the host mass but also on the dynamical stateof the group (e.g. the degree of virialisation of the halo and (cid:63) ghassem.gozaliasl@helsinki.fi the presence or absence of a second bright galaxy, as quan-tified from the luminosity gap).A phase-space analysis of the group members shouldhelp to trace the assembly history of the groups and clus-ters of galaxies back. Seen in phase-space (the line-of-sightvelocity versus the distance from cluster centre), galaxieswhich were accreted at early epochs do indeed tend to oc-cupy the central virialised region with a low spread of rela-tive velocities, while infalling or recently accreted galaxieshave a higher relative velocity spread and are usually spa-tially offset from the centre of the virialised region (Nobleet al. 2016). The analysis of numerical simulations by Rheeet al. (2017) shows that simulated galaxies tend to followa typical path in phase-space as they settle into the clusterpotential, and different regions of phase-space can be linkedwith different times since the first infall onto the cluster.From this analysis, they demonstrate that the location ofcluster galaxies is connected to the tidal mass loss, hencequantifying how much galaxy evolution is impacted by thecluster environment.In this work, we aim at applying similar techniques to asample of X-ray selected galaxy groups in the Cosmic Evo-lution Survey (COSMOS) (Gozaliasl et al. 2019) to shedlight on their assembly history as a function of mass. COS-MOS covers a two square-degree equatorial region of skyand was designed to probe the formation and evolution ofgalaxies as a function of the local galaxy environment and
Article number, page 1 of 9 a r X i v : . [ a s t r o - ph . GA ] J a n &A proofs: manuscript no. aanda z )12.513.013.514.014.515.0 l o g ( M c / M ) S-II S-III S-IV S-I groups with N 5 spec-z membersCOSMOS X-ray groups
Fig. 1.
Distribution of the COSMOS X-ray groups in the halo mass versus redshift plane (open black circles). The filled magentacircles show the 95 groups with N ≥ spectroscopic members which are used in this study. To inspect the redshift and halomass evolution of the dynamics of BGGs and their satellites, we divide the hosting groups’ sample (magenta circles) into foursub-samples, marked with four dashed blue boxes and labelled S-I, S-II, S-III, and S-IV. the cosmic time (Scoville et al. 2007). The COSMOS fieldhas been observed at all accessible wavelengths from the X-ray to the radio by several major space- and ground-basedtelescopes and offers a unique combination of deep (e.g. AB ∼ − in the optical bands) multi-wavelength data.The COSMOS field has also been frequently targeted byseveral large spectroscopic programs, such as zCOSMOS,VIMOS Ultra Deep Survey (VUDS), FMOS-COSMOS, andKeck-DEIMOS (see e.g. Lilly et al. 2007; Kartaltepe et al.2010; Comparat et al. 2015; Hasinger et al. 2018). We there-fore rely on this wealth of spectroscopic follow up to confirmthe membership of our group members and study the dy-namics of the brightest group galaxies (BGGs) and theirsatellite galaxies since z=1.0 to the present day.This paper is organised as follows: section 2 describesthe data, sample selection and the measurement of line-of-sight velocity and velocity dispersion. In section 3, wepresent the phase-space analysis and distribution of therelative peculiar velocity for satellites and BGGs, and thescaling relation between the X-ray luminosity and the ob-served velocity dispersion of groups (hereafter, L x − σ v, obs ).We summarise the results together with our final remarksin section 4. We assume a standard Λ CDM cosmologythroughout the paper, with H = 70 . km s − M pc − , Ω M = 0 . , Ω Λ = 0 . .
2. Data and sample selection
The COSMOS benefits from X-ray coverage by both the
Chandra X-ray Observatory and
XMM-Newton . Severalspectroscopic follow up campaigns have been carried out inthe COSMOS field (e.g. Lilly et al. 2007; Kartaltepe et al.2010; Comparat et al. 2015). More recently, Hasinger et al. For information on the COSMOS multi-wavelengths observa-tions, the list of broad-, intermediate- and narrow-band filtersand filter transmissions, we refer readers to the COSMOS homeweb-page ( http://cosmos.astro.caltech.edu/ ). (2018) presented a new catalogue of spectroscopic redshiftsfor 10,718 objects in COSMOS observed in the − nm wavelength range using the Deep Imaging Multi-ObjectSpectrograph (DEIMOS) on the Keck II telescope.The catalogue of X-ray galaxy groups used in this studyhas been presented in Gozaliasl et al. (2019). Once theredshift and group membership are estimated, a mass-dependent radial cut is chosen to sample analogous areasof each group. If the total mass of a group is known, theradial cut is determined using the following relation: M ∆ = 4 π × ρ crit × r , (1)where ρ crit is the critical density of the universe and r ∆ is the radius delimiting an interior density of ∆ times thecritical density of the universe at the group redshift. Inprevious studies, ∆ ranged usually between 180 and 500times the mean or critical density in the Universe (Diaferioet al. 2001; Kravtsov et al. 2004). In this study we assume ∆ = 200 and apply r c in our analysis.The halo mass of our groups are calculated from anempirical mass-luminosity relation described in Leauthaudet al. (2010) and applied to the COSMOS groups (see alsoConnelly et al. 2012; Kettula et al. 2015): log ( M ,c ) = p − log E ( z ) + log ( M )+ p [log ( L x /E ( z )) − log ( L )] , (2)where M c is the mass within r c , in units of M (cid:12) . p and p are the fitting parameters, log M and log L are thecalibration parameters and E ( z ) is the correction for theredshift evolution of scaling relations. An extra error of . dex which corresponds to log-normal scatter in the L x − M c relation is also included in our mass measurementas detailed in Allevato et al. (2012). While we describe thesample using this convention, we also reexamine the relationof L x to the halo mass as traced by galaxy dynamics in §3.4.Fig. 1 shows the halo mass log ( M / M (cid:12) ) as a func-tion of redshift for the entire sample of X-ray galaxy groups(open circles) in the COSMOS field. Halo masses ( M ) Article number, page 2 of 9. Gozaliasl et al.: Kinematic unrest of low mass galaxy groups range between . to . M (cid:12) over . < z < . . Wehighlight in magenta the 95 groups with N ≥ spectro-scopic members (excluding the BGGs). In order to studymass and redshift evolution, we define the following foursub-samples (labelled as S-I, S-II, S-III, and S-IV in Fig. 1): . < z < . & . < log ( M /M (cid:12) ) < . (S-I) . < z < . & . < log ( M /M (cid:12) ) < . (S-II) . < z < . & . < log ( M /M (cid:12) ) < . (S-III) . < z < . & . < log ( M /M (cid:12) ) < . (S-IV).Throughout this paper, we use the position of the X-rayemission peak obtained by high spatial resolution Chandraimaging as a proxy for the group centre. This study also re-lies on our previous identification and selection of the BGGs(Gozaliasl et al. 2014; Gozaliasl et al. 2019). In brief, theCOSMOS2015 photometric redshift catalogue (Laigle et al.2016) is used to rank galaxies as a function of mass, and ineach group, a BGG is selected as the most massive galaxy.Groups for which a putative BGG does not have a spectro-scopic redshift are not considered in this study.In order to compute the observed velocity dispersion(hereafter, σ v, obs ), we first select member galaxies for eachcluster and group. Thanks to the wealth of COSMOS data,the redshift of each halo can be robustly estimated. Theproper velocity of each galaxy within r is first esti-mated from v prop = c ( z g − z h ) / (1+ z h ) (Danese et al. 1980),where z g and z h are the redshifts of the galaxy and its as-sociated group halo, respectively. The velocity dispersionis then computed and galaxies deviating by more than 3-sigma are removed from the sample. The groups are thenvisually inspected to remove additional outliers and sub-structure along the line of sight following the proceduresdescribed in Clerc et al. (2016).We compute the mean redshift of the halo using the bi-weight average of the spectroscopic members (Beers et al.1990), excluding the BGG. The proper velocity, v prop , isrecomputed for every galaxy using this redshift. When alarge number of members is available, the velocity disper-sion, σ v , obs , is calculated as the square root of the biweightvariance of the member galaxies’ proper velocity. When thegroups have less than 15 spectroscopic members, which oc-curs frequently in our sample, we use the gapper method(still excluding the BGG), known to give more robust re-sults with a low number of members (Beers et al. 1990).Following Carlberg et al. (1997), the velocity dispersionof a group is estimated from the virial theorem (VT) as σ v, VT = 10 r × H ( z ) √ , (3)where H ( z ) is the Hubble constant at redshift z and r is the projected and empirically determined radius of thegroup, the radius at which the mean interior overdensity is200 times the critical density. In the simulation, we simplytake the halo virial radius and convert it to r c (see e.g.White 2001). In order to compare our observational results with theoret-ical predictions, we extracted a group catalogue from thehydrodynamical simulation light-cone of
Horizon-AGN (Dubois et al. 2014). The
Horizon-AGN is a cosmolog-ical hydrodynamical simulation (100 Mpc /h a side) runwith the adaptive mesh refinement (AMR) code RAM-SES (Teyssier 2002), using a cosmology compatible with WMAP-7 (Komatsu et al. 2011). The volume contains dark matter (DM) particles (which corresponds toa DM mass resolution of M DM , res = 8 × M (cid:12) ). The evo-lution of the gas is followed on the AMR grid down to ascale of 1 kpc, and includes gas heating by a uniform UVbackground (Haardt & Madau 1996) and cooling via H, Heand metals (Sutherland & Dopita 1993). Star formation ismodelled via a Schmidt law with a constant star formationefficiency per free-fall time of 2 percent (Kennicutt 1998).Feedback from stellar winds and supernovae (both type Iaand II) is accounted for with mass, energy, and metal re-leases in the ambient inter-stellar medium. Feedback fromblack holes is accounted for in either quasar or radio modesdepending on the accretion rate. More details on the physicsimplemented in the simulation can be found in Dubois et al.(2014). The simulation reproduces the overall evolution ofgalaxy populations throughout cosmic time (see e.g. Duboiset al. 2016; Kaviraj et al. 2017).The light-cone in the Horizon-AGN box subtends 1degree by 2.5 degrees out to redshift one. The evolution ofthe lightcone is sampled 22,000 times out to z=8.The
AdaptaHOP halo finder (Aubert et al. 2004)has been run on both the stellar and DM particle distri-butions in order to identify galaxies and halos respectively(see Laigle et al. 2019, for more details). For galaxies, lo-cal stellar particle density is determined from the 20 near-est neighbours, and structures are selected with a densitythreshold equal to 178 times the average matter density atthat redshift. Only galaxies with more than 50 stellar parti-cles (i.e., with log M ∗ > M (cid:12) ) are kept in the catalogue.For halos the methodology is the same but with a densitythreshold of 80 times the average matter density. Halos withmore than 100 DM particles are kept in the catalogue. As inDarragh Ford et al. (2019), each galaxy is associated withits closest main halo. To match the observational definition,the BGG is identified as the most massive galaxy within thevirial radius of the main halo. Using Eq. 3 introduced above,we obtain the velocity dispersion of the simulated groupsusing the virial mass of the hosting DM halo. As in obser-vations, we refer to this estimation as σ v, VT . To match theobservational limitation, the velocity dispersion of galaxygroups from the simulation is computed along one axis. Werefer hereafter to the velocity dispersion of galaxies fromthe Horizon-AGN simulation as σ v, D1 . The choice of theaxis for the projection does not impact our results.
3. Results
Fig. 2 compares the velocity dispersion of groups inferredfrom the virial theorem to the observed velocity dispersionmeasured from spectroscopy in COSMOS ( upper panel ) andin the
Horizon-AGN simulation ( lower panel ). Red datapoints correspond to groups within S-I and blue points togroups in S-II, S-III, and S-IV.Although an overall correlation is recovered, both inCOSMOS and in
Horizon-AGN , the observed σ v, obs isfound to scatter significantly at a given σ v, VT , especially forlow mass groups (S-I). This scatter might be driven eitherby complex substructures within the groups (or more gen-erally by the anisotropy of galaxy spatial distribution) or byinfalling galaxies in non-virialised orbits. At higher masses, Article number, page 3 of 9 &A proofs: manuscript no. aanda v , VT [ km s ]10 v , o b s [ k m s ] S-I & S-II to S-IV N N N v , VT [ km s ]10 v , D [ k m s ] S-I & S-II to S-IV N N Fig. 2.
Observed velocity dispersion ( σ v, obs ) of groups deter-mined using their spec-z members within r versus the veloc-ity dispersion predicted by the virial theorem (Eq 3, σ v, VT ), inCOSMOS based on L x - halo mass scaling relation in observa-tions ( upper panel ) and using the virial mass in the Horizon-AGN simulation ( lower panel ). Groups with N ≥ are plottedwith filled blue circles and red squares. Groups with N ≥ spectroscopic members are shown with open green circles. Thesolid and dashed black lines show the 1:1 relation and ± in-tervals. The filled red squares and blue circles represent groupsin S-I and S-II to S-IV respectively. the measured line-of-sight velocity also deviates from the1-to-1 relation in both COSMOS and the Horizon-AGN simulation.
In order to better understand the assembly history ofgroups and the reason for the scatter observed in Fig. 2,we construct phase-space diagrams using the line-of-sightvelocity of the member galaxies and the groupcentric ra- dius. The phase-space diagram is used as an indicator ofthe accretion history of cluster and group member galaxies:galaxies which were recently accreted onto a cluster/grouptend to have high relative velocities and large groupcen-tric radius offsets from the bottom of the potential well (asestimated from the centre of clusters and groups).Fig. 3 presents the location of group member galaxiesin the phase-space diagram for the S-I ( upper panels ), thecombined S-II and S-III ( middle panels ), and the S-IV sub-samples ( lower panels ). The proper velocity is normalisedeither to σ v, VT ( left panels ) or to σ v, obs ( right panels ).The BGGs and satellite galaxies (hereafter, SGs) are shownwith filled blue circles and filled grey triangles respectively.Solid black lines and shaded areas represent the densitycontours of respectively the BGG and SGs distributions inthis plane, estimated using the Kernel Density Estimation(KDE) method.Using simulations, Rhee et al. (2017) measured forgalaxies in this plane the time spent since they crossedthe virial radius of the cluster for the first time ( t inf ) andshowed that different locations of galaxies in phase-spacecorrelate with different times since infall ( t inf ). They subse-quently define four different regions in phase-space allowingto classify galaxies as follows: (i)‘the first infallers’ whichhave not yet definitively fallen into clusters; (ii)‘Recentinfallers’ whose t inf ranges as < t inf / Gyr < . ;(iii) ‘intermediate infallers’ with . < t inf / Gyr < . ;and (iv)‘ancient infallers’, those galaxies having . BGGsSGsAncient infallerIntermediate infallerrecent Infaller0 . . . . . . . groupcentric radius ( r proj /r c ) . . . . . . . v p r o p / σ v , V T S-IV . . . . . . . . . . . . . . v p r o p / σ v , V T S-II & S-III . . . . . . . . . . . . . . v p r o p / σ v , o b s S-I BGGsSGsAncient infallerIntermediate infallerrecent Infaller0 . . . . . . . groupcentric radius ( r proj /r c ) . . . . . . . v p r o p / σ v , o b s S-IV . . . . . . . . . . . . . . v p r o p / σ v , o b s S-II & S-III Fig. 3. Phase-space diagrams showing the relative line-of-sight velocity of group galaxies as a function of distance from the groupX-ray centre for S-I, S-II & S-III, and S-IV. The orbital velocities of galaxies are normalised either to the velocity dispersion derivedusing the virial theorem ( left panels ) or to the observed velocity dispersion ( right panels ). The blue and grey data points show theBGGs and all satellite galaxies (SGs) respectively. Solid black lines and shaded area represent the density contours of respectivelythe BGG and SGs distributions in this plane, estimated using the KDE method. The dash-dotted red, dashed orange, and solidlime isocontours are taken from Fig. 8 in Rhee et al. (2017) and represent the regions where galaxies in these areas are ‘ancientinfallers’, ‘intermediate infallers’, and ‘recent infallers’ with probabilities of 40%, 25%, and 40%. The majority of the BGGs arefound in the ancient infallers area. It should be noted however that we probe a lower mass range than described in Rhee et al.(2017). Article number, page 5 of 9 &A proofs: manuscript no. aanda v prop / v , VT P r o b a b ili t y d e n s i t y Obs: BGGs [S-II:S-IV]Obs: BGGs [S-I]HZ-AGN: BGGs [S-II:S-IV]HZ-AGN: BGGs [S-I] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 v prop / v , VT P r o b a b ili t y d e n s i t y Obs: SGs [S-II:S-IV]Obs: SGs [S-I]HZ-AGN: SGs [S-II:S-IV]HZ-AGN: SGs [S-I] Fig. 4. Distributions of the ratio of the line-of-sight velocity to the group velocity dispersion for BGG ( left ) and satellite ( right )( v prop /σ v, VT ), for the S-I (dotted lines) and combined S-II to S-IV samples (solid lines) in COSMOS (black) and Horizon-AGN (orange). We find no significant redshift evolution of the distribution in both observations and simulation, thus the sub-samplesS-II to S-IV are combined here. The distribution for BGGs in low mass groups at z < . suggest they are in relatively dynamicallyunrelaxed systems. Table 1. The dispersion of the ratio of the BGGs and SGs line-of-sight velocity to the group velocity dispersion of in bothobservations (COSMOS) and Horizon-AGN (HZ-AGN). Column 1 presents the sub-sample IDs. Column 2 reports the dispersionof the observed v prop /σ v , obs of BGGs referred as σ BGG , obs . Column 3 presents the dispersion of the v prop /σ v , VT of BGGs referredas σ BGG , VT . As in columns 2 and 3, columns 4 and 5 present the results for SGs. This estimation is performed using the gapperestimator. The Jackknife technique is used to estimate the error. sub-sample ID σ BGG , obs σ BGG , VT σ SGs , obs σ SGs , VT COSMOS (S-I) 1.729 ± . ± . 128 1 . ± . 051 0 . ± . COSMOS (S-II) . ± . 137 1 . ± . 147 1 . ± . 035 0 . ± . COSMOS (S-III) . ± . 151 0 . ± . 123 0 . ± . 047 0 . ± . COSMOS (S-IV) . ± . 188 1 . ± . 219 1 . ± . 039 0 . ± . HZ-AGN (S-I) . ± . 289 1 . ± . 167 1 . ± . 052 1 . ± . HZ-AGN (S-II) . ± . 237 0 . ± . 270 1 . ± . 048 1 . ± . HZ-AGN (S-III) . ± . 106 0 . ± . 175 1 . ± . 028 1 . ± . HZ-AGN (S-IV) . ± . 155 1 . ± . 193 1 . ± . 036 1 . ± . within low mass groups tend not to have any preferred ve-locity direction. In the case of higher mass halos, the peakof the BGG distribution lies below v prop ∼ . × σ v, VT and at r proj /r ∼ . . Here again (and as expected), theBGGs mostly occupy the ancient infaller region. In sum-mary, we find that the BGGs within low mass groups at . ≤ z < . are kinematically distinct from the bulkof the population of other member galaxies (either satellitegalaxies or BGG in higher mass groups). The left panel of Fig 4 shows the KDE distribution of theratio of the BGG line-of-sight velocity to σ v, VT for S-IIto S-IV (solid black line) and S-I (dotted black line) andcompares them to predictions from Horizon-AGN . The right panel similarly illustrates the v prop /σ v , VT distribu- tions for the SGs in observations and the predicted distri-butions from Horizon-AGN .In agreement with predictions from Horizon-AGN simulation, the distribution of v prop /σ v , VT for BGGs withinmassive groups (S-II to S-IV) peaks at ∼ . , indicatingthat BGGs in massive halos are well settled at the bottomof the potential well, which is an indication for the group tobe relaxed. BGGs peculiar velocities in low mass groups (S-I) are distributed over a larger dynamical range than in highmass groups. A similar trend is seen in the Horizon-AGN simulation, although the observed and predicted distribu-tions have different amplitudes, modes and shapes.For SGs, the distributions of v prop /σ v , VT in the S-I andS-II to S-IV sub-samples, in both observations and the sim-ulation, peak below v prop /σ v , VT ∼ . . This indicates thatthere is no preferred direction for the velocity of satellitegalaxies, so it is likely that satellite galaxies are isotropi-cally distributed. Article number, page 6 of 9. Gozaliasl et al.: Kinematic unrest of low mass galaxy groups Using the gapper estimator (Beers et al. 1990), we mea-sured the velocity dispersion of the BGG and SG popula-tions associated with each sub-sample (S-I to S-II). Sinceall groups within each sub-sample do not have the samevelocity dispersion, we measured the dispersion of the nor-malised and dimensionless line-of-sight velocities expressedas v prop /σ v , obs and v prop /σ v , VT for BGGs within each sub-sample. In Table 1 we refer to these unitless dispersionsas σ BGG , obs and σ BGG , VT , and similarly as σ SGs , obs and σ SGs , VT for SGs and we report these values for both obser-vations and the Horizon-AGN simulation.For BGGs in low mass groups (S-I), we measure σ BGG , obs = 1 . ± . and σ BGG , VT = 1 . ± . )in COSMOS, while we have σ BGG , D1 = 1 . ± . and σ BGG , VT = 1 . ± . in Horizon-AGN .For the S-II to S-IV combined samples, we measure a σ BGG , obs = 1 . ± . and σ BGG , VT = 1 . ± . inobservations and σ BGG , D1 = 0 . ± . and σ BGG , VT =0 . ± . in Horizon-AGN . The X-ray luminosity-velocity dispersion ( L X − σ v,obs ) re-lation of galaxy clusters and groups is critical to under-standing the dynamical states of clusters and groups andtheir impact on the scaling relations, as well as the X-rayselection (e.g. Wu et al. 1999; Plionis, & Tovmassian 2004;Zhang et al. 2011). Within the context of this work, we aimto quantify how much the offset from the L X − σ v,obs rela-tion is a consequence of kinematic unrest of the group, asquantified from the proper velocity of the BGG. We startby determining the correlation between the X-ray luminos-ity, log( L x ) , and velocity dispersion, log ( σ v , obs ) . Usingthe data shown in Fig. 5, we find a positive Pearson corre-lation coefficient of r = 0 . . In fitting the scaling relation,we normalise the velocity dispersion and X-ray luminos-ity of groups and convert them to dimensionless parame-ters using their median values: σ v, pivot = 315 km s − and L x, pivot = 3 . × erg s − . The relation between σ v, obs and L x in the natural logarithmic scale can be approxi-mated by a power-law as follows: ln (cid:18) σ v, obs σ v, pivot (cid:19) = ln (cid:20) b × (cid:18) L x L x, pivot (cid:19) m (cid:21) , (4)where m is the slope of the relation and b is the interceptof the relation. We fitted Eq. 4 to the data, taking into ac-count the observed uncertainties and an expected intrinsicscatter ( σ intrln σ v, obs | ln L x ) in the likelihood function being fit.The maximum of likelihood function and the errors on pa-rameters are determined following the procedure presentedby Hogget al. (2010).The upper panel of Fig. 5 presents the scaling re-lation between the observed ln ( σ v, obs / km s − ) , and ln ( L x / erg s − ) for the sample of X-ray groups galaxiesin COSMOS (blue circles). We added axes showing the 10-base logarithmic scale too. The dashed white line illustratesthe best-fit scaling relation. The orange area represents ± σ errors estimated using the Markov Chain Monte Carlo(MCMC) method (see Hogget al. 2010). The black lines cor-respond to 50 different realisations of the scaling relation,drawn from the multivariate Gaussian distribution of three parameters (slope, intercept and intrinsic scatter). The lower panel represents the one- and two-dimensional projec-tions of the marginalised posterior probability distributionsof parameters in our model (Eq. 4) from our re-sampling.The slope and intercept of the mean scaling relation (Eq.4) are found as: m = 0 . +0 . − . , ln b = 0 . ± . , and σ intrln σ v, obs | ln L x = 0 . ± . . We note that the error onthe estimated parameters corresponds to ± σ uncertainty.We then try to understand the scatter in this relationby measuring the correlation between the offset from thefitted L x − σ v, obs relation (hereafter ∆ σ ) and v prop /σ v, obs ,which quantifies to some extent the kinematic unrest of thegroups. We use S-I and the combined S-II to S-IV sub-samples, referring to these as low and high mass groups,respectively. Then the linear correlation between this pa-rameter and the BGG proper velocity is estimated usingthe Pearson correlation coefficient. In the simulation, ∆ σ is given as the difference between the one dimensional ve-locity dispersion and the velocity dispersion measured fromthe virial theorem ( ∆ σ = σ v , VT − σ v , ). We assume σ v , VT as the true velocity dispersion of groups. The correlationcoefficient between ∆ σ and v prop /σ v, obs of BGGs withinlow mass groups in the observations and the Horizon-AGN simulation are found to be equal to . ± . and . ± . in comparison with those for the BGGs in highmass groups, which are . ± . and − . ± . , re-spectively. We used the Jackknife method to estimate theerror on the correlation coefficients.The correlation in simulation is found to be less thanthat in observation. While the influence of gravitationalinteraction on the velocity of the member galaxies is a re-sult of n-body interaction, the qualitative effect can be esti-mated using the tidal approximation of Spitzer (1958). Theextra energy acquired by the perturbed object scales with M × < r > (averaging matter density with r weight), soin case the total matter profile of the group is either steeperor flatter than r − density profile, it acquires differences invelocities, which manifest themselves in the sloshing of thecore. The larger velocity difference observed could there-fore be interpreted as evidence for stronger departures, forinstance a larger concentration and a larger scatter in thetotal matter profiles, compared to that in a simulation. Inaddition, we cannot rule out the possibility that X-ray se-lection leads to preferential selection of more concentratedhalos, which enhances the effect. 4. Summary and conclusions We construct a phase-space diagram for X-ray galaxygroups in the COSMOS survey using the determinationsof group centres based on Chandra imaging and demon-strate that the brightest group galaxies in low mass halos( < × M (cid:12) ) are distributed over a wide range of orbitalvelocities, in contrast to BGGs in more massive groups atsimilar ( z < . ) or higher redshifts. The BGGs in massivegroups are more likely to be located at the bottom of thepotential well.We determine the correlation coefficient between the rel-ative proper velocity of the BGGs ( v prop /σ v, obs ) and theoffset from the fitted L x − σ v, obs scaling relation. We find apositive correlation coefficient of 0.63 for the low mass sub-sample of groups (S-I) in comparison with the lower corre-lation coefficient of 0.37 for the high mass groups (S-II to S- Article number, page 7 of 9 &A proofs: manuscript no. aanda 95 96 97 98 99 100 101 ln ( L x / erg s − ) . . . . . . . l n ( σ v , o b s / k m s − ) mean relation ± σ 50 random relationsdata . . . . . . l og ( σ v , o b s / k m s − ) . . . . . . log ( L x / erg s − ) m = 0 . +0 . − . − . . . . l n b ln b = 0 . ± . − . 06 0 . 00 0 . 06 0 . m . . . . σ i n tr l n σ v , o b s | l n L x − . 06 0 . 00 0 . 06 0 . ln b . 30 0 . 35 0 . 40 0 . σ intrln σ v , obs | ln L x σ intrln σ v , obs | ln L x = 0 . ± . Fig. 5. ( Upper panel: ) The scaling relation between the natural logarithm of the observed velocity dispersion of groups( ln ( σ v, obs /km s − ) ) determined using their spec-z members within r and the natural logarithm of the X-ray luminosityof groups ( ln ( L x /erg s − ) ) at z < . in COSMOS (blue points with associated errors). We also added axes showing the 10-base logarithmic scale. The highlighted orange area shows ± σ uncertainties around the mean scaling relation (white dashedline). The black lines are a set of 50 different realisations, drawn from the multivariate Gaussian distribution of the parameters( (cid:104) m (cid:105) = 0 . , (cid:104) ln b (cid:105) = 0 . , (cid:68) σ intrln σ v, obs | ln L x (cid:69) = 0 . ) and the scatter covariance matrix is estimated from the MCMC chain.( Lower panel: ) The one- and two dimensional marginalised posterior distributions of parameters of the scaling relation (Eq. 4),shown as 68% and 95% credible regions.Article number, page 8 of 9. Gozaliasl et al.: Kinematic unrest of low mass galaxy groups IV), while the Horizon-AGN simulations are characterisedby the values of 0.4 and 0.2, correspondingly. The uncer-tainty of the correlation coefficients measurements is foundto be 0.12, using a Jackknife resampling method. These re-sults argue in favour of the dominant role of group dynamicsin the scatter in the L x − σ v, obs scaling relation. Comparedto expectations from numerical simulations based on devi-ations from the halo mass, a stronger correlation betweenthe relative line-of-sight velocity of BGG and the offset fromthe L x − σ v, obs in the observations might be due to an ad-ditional (negative) covariant scatter in L x with the mergerstate of clusters and groups, as has been studied in detailin Mulroy et al. (2017, 2019). 5. Acknowledgements We acknowledge M. Salvato and G. Hasinger and entirezCOSMOS, DEIMOS, VUDS, MOSFIRE, FORS2, FMOS,MOIRCS, LEGA-C, and the COSMOS teams for their ef-fort in the COSMOS spectroscopic observations and theirwillingness to share the spectroscopic redshift catalogues.We wish to thank Kenneth P. K. Quek for his use-ful comments. The author acknowledges the usage of thefollowing python packages, in alphabetical order: astropy (Astropy Collaboration et al. 2013, 2018), chainConsumer (Hinton 2019), emcee (Foreman-Mackey et al. 2019), matplotlib (Hunter 2007), numpy (Oliphant T. E., 2006;van der Walt S. et al. 2011), and scipy (Virtanen et al.2019). References