Interactions of Galaxies in the Galaxy Cluster Environment
aa r X i v : . [ a s t r o - ph ] M a y Draft version October 22, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
INTERACTIONS OF GALAXIES IN THE GALAXY CLUSTER ENVIRONMENT
Changbom Park and Ho Seong Hwang
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
Draft version October 22, 2018
ABSTRACTWe study the dependence of galaxy properties on the clustercentric radius and the environmentattributed to the nearest neighbor galaxy using the Sloan Digital Sky Survey (SDSS) galaxies as-sociated with the Abell galaxy clusters. We find that there exists a characteristic scale where theproperties of galaxies suddenly start to depend on the clustercentric radius at fixed neighbor environ-ment. The characteristic scale is 1 ∼ Subject headings: galaxies: clusters: general – galaxies: evolution – galaxies: formation – galaxies:general INTRODUCTIONIn galaxy clusters the average morphology of galax-ies changes with clustercentric radius or local density.The central region of clusters at the present epoch isdominated by early-type galaxies. This is known asthe morphology-radius or morphology-density relation(hereafter MRR and MDR, respectively). Since thelocal density is on average a monotonically decreasingfunction of clustercentric radius, they appear to con-vey us the same information (Hubble & Humason 1931;Dressler 1980; Dressler et al. 1997; Treu et al. 2003;Smith et al. 2005; Postman et al. 2005; Weinmann et al.2006). However, there is discussion about which oneplays a critical role in determining the galaxy mor-phology between the clustercentric radius and the localdensity (Whitmore et al. 1993; Dom´ınguez et al. 2001;Goto et al. 2003; Thomas & Katgert 2006). There is alsoa remaining issue what physical parameters of galax-ies (morphology, color, star formation rate, or stel-lar mass) correlate fundamentally with the environment(e.g., Christlein & Zabludoff 2005; Quintero et al. 2006;Poggianti et al. 2008; Skibba et al. 2008).A number of physical mechanisms have been pro-posed to explain this morphology-environment relation.It is suggested that tidal interactions between individ-ual galaxies can change mass profile and transform diskgalaxies into spheroidals (Byrd & Valtonen 1990). Fre-quency of galaxy-galaxy interaction depends strongly onthe clustercentric radius, and thus galaxy interactions
Electronic address: [email protected], [email protected] can result in the MRR or MDR. However, the duration oftidal interactions and thus the total tidal energy depositare expected to be too small to change galaxy propertiessignificantly for cluster galaxies that are moving at highspeeds. Due to the fast orbital motions the frequencyof galaxy mergers is also small in clusters. A seriesof frequent high-speed tidal interactions among clustergalaxies, called harassment, can produce impulsive heat-ing and cause morphology transformation (Moore et al.1996). Tidal interaction with the whole cluster potentialwell can also change the structure and activity of galaxiessignificantly (Moss & Whittle 2000; Gnedin 2003).Existence of the hot X-ray emitted by intracluster gasmakes the mechanisms relying on hydrodynamic pro-cesses appear attractive. Stripping of cold gas frominfalling late-type galaxies by a ram pressure of thehot intracluster gas, was proposed to explain the in-crease of the early-type fraction toward the cluster cen-ter (Gunn & Gott 1972). Hot gas removal from infallinggalaxies through hydrodynamic interactions with the in-tracluster medium can shut off gas supply and star for-mation activity (SFA) after the already existing cold gasis consumed. The interstellar medium of a galaxy travel-ing in the hot intracluster medium can be stripped fromthe disk due to a viscosity momentum transfer (Nulsen1982) or evaporate as the temperature of the interstellarmedium rises (Cowie & Songaila 1977). These hydro-dynamic processes have a common drawback that theycan turn spirals only to S0’s and do not produce ellipti-cals. The major effect of the hydrodynamic processes isquenching the SFA by removing or ionizing the cold gas Park & Hwangin the disk of late-type galaxies. The bulge-to-disk ratiois not expected to increase by these processes. Therefore,none of the mechanisms proposed so far is able to fullyaccount for the MRR or MDR observed in clusters.Recently, Park et al. (2008) and Park & Choi (2009)have found that galaxy properties like morphology andluminosity depend strongly on the distance and morphol-ogy of the nearest neighbor galaxy. This dependencewas found even when the large-scale background densityis fixed, and thus is completely different from the com-monly known morphology-local density relation. Mostimportantly, the effects of the nearest neighbor changeat the characteristic scale given by the virial radius ofthe neighbor galaxy. When a galaxy is located withinthe virial radius of its nearest neighbor, its morphologytends to be the same as that of the neighbor. But suchtendency disappears when the separation is larger thanthe virial radius. This fact strongly suggests that galaxiesinteract hydrodynamically when the separation to theirnearest neighbor is smaller than the virial radius of theneighbor, and that the effects of such interaction are sig-nificant enough to change their morphology and SFA.Outside the virial radius galaxy morphology still de-pends on the distance to the nearest neighbor, but issuddenly independent of neighbor’s morphology. Theprobability for a galaxy to be an early type monotoni-cally decreases as the separation increases. This stronglysupports the idea that the conformity in morphologyof galaxy pairs is not primordial but an acquired onethrough interactions since there should be no reason forthe break in morphology conformity to be at the cur-rent virial radius of the neighbor if it is initially given.Park et al. (2008) proposed that the mechanism respon-sible for this be tidal interactions causing both gravi-tational and hydrodynamic effects. Outside the virialradius the interactions are purely gravitational betweenthe galaxy plus dark halo systems, but within the virialradius hydrodynamic (and radiative) effects must be in-volved as well.A series of tidal interactions and mergers will keepthe total cold gas contents in bright galaxies decreas-ing, producing more early-type galaxies as time passes(Park et al. 2008; Park & Choi 2009; Hwang & Park2008). The speed of this process is an increasing functionof the large-scale density. Namely, even though the di-rect physical processes affecting galaxy morphology arethe gravitational and hydrodynamic interactions betweenneighboring galaxies, the large-scale background densityappears to control galaxy morphology through its sta-tistical correlation with the frequency and strength ofgalaxy-galaxy interactions. Given the knowledge thatthe MDR in most region of the universe (note that Parket al. did not resolve the cluster regions) is the resultof galaxy-galaxy interactions, one can naturally suspectthe MRR and MDR in clusters are also due to the inter-actions between individual galaxies. It is the purpose ofthis paper to explore this possibility. OBSERVATIONAL DATA SET2.1.
Sloan Digital Sky Survey Sample
We use a spectroscopic sample of galaxies in theSloan Digital Sky Survey (SDSS) Data Release 6(DR6; Adelman-McCarthy et al. 2008). The survey
Fig. 1.—
Completeness of the spectroscopic sample of clustergalaxies as a function of r -band magnitude ( upper panel ) and clus-tercentric radius ( lower panel ). Filled circles are the spectroscopiccompleteness of the data complemented by NED, while open circlesshow the completeness of the original SDSS spectroscopic sample. produced five-band ( ugriz ) photometric data for 230million objects over 8,400 deg , and optical spectro-scopic data more than one million objects of galax-ies, quasars, and stars over 6860 deg (Gunn et al.1998, 2006; Uomoto et al. 1999; Castander et al. 2001;Blanton et al. 2003; Fukugita et al. 1996; Lupton et al.2002; Hogg et al. 2001; Smith et al. 2002; Ivezi´c et al.2004; Tucker et al. 2006; Pier et al. 2003). Extensive de-scription of SDSS data products is given by York et al.(2000) and Stoughton et al. (2002).The data is supplemented by several value-addedgalaxy catalogs (VAGCs) drawn from SDSS data. Photo-metric and structure parameters of galaxies are obtainedfrom the SDSS pipeline (Stoughton et al. 2002). Com-plementary photometric parameters such as color gradi-ent, concentration index, and Petrosian radius are takenfrom the DR4plus sample of Choi et al. (2007). Thespectroscopic parameters are obtained from MPA/JHUand NYU VAGCs (Tremonti et al. 2004; Blanton et al.2005).Completeness of the spectroscopic data in SDSS is poorfor bright galaxies with m r < . ′′ on agiven plate). Therefore, it is necessary to supplementthe galaxy data to reduce the possible effects of the in-completeness problem. We search for the galaxies withinten times the virial radius of each galaxy cluster in thephotometric catalog of the SDSS galaxies, and find theirredshifts from the NASA Extragalactic Database (NED)to supplement our spectroscopic sample. Figure 1 showsthe spectroscopic completeness of our galaxy sample asa function of apparent magnitude and of clustercentricalaxy Interactions in Clusters 3distance. The open circles are the completeness of theoriginal SDSS sample, and the filled circles are that ofour sample with additional redshifts. It shows that thespectroscopic completeness of our sample is higher than85% at all magnitudes and clustercentric radii.2.2. Cluster Sample and Galaxy Membership inClusters
We used the Abell catalog of galaxy clusters(Abell et al. 1989) to identify cluster galaxies in ourgalaxy sample. Among the Abell clusters, we selectedthose that have known spectroscopic redshifts in theNED. We found 730 clusters located within the SDSSsurvey region. We adopted the position of cluster centerin the NED, but replaced it with the X-ray determinedposition if it is available in the literature.In order to determine the membership of galaxiesin a cluster, we used the “shifting gapper” method ofFadda et al. (1996) that was used for the study of kine-matics of galaxy clusters (Hwang & Lee 2007, 2008). Inthe radial velocity versus clustercentric distance space,the cluster member galaxies were selected by groupinggalaxies with connection lengths of 950 km s − in thedirection of the radial velocity and of 0.1 h − Mpc in thedirection of the clustercentric radius R . If the boundarywas not reached out to R = 3 . h − Mpc, we stopped thegrouping at R = 3 . h − Mpc. We iterated the procedureuntil the number of cluster members converges. Fromthis procedure we obtained 200 Abell clusters that havemore than or equal to 10 member galaxies.We computed a radius of r , cl (usually called thevirial radius) for each cluster where the mean overdensitydrops to 200 times the critical density of the universe ρ c ,using the formula given by Carlberg et al. (1997): r , cl = 3 / σ cl H ( z ) , (1)where σ cl is a velocity dispersion of a cluster and theHubble parameter at z is H ( z ) = H [Ω m (1 + z ) +Ω k (1 + z ) + Ω Λ ] (Peebles 1993). Ω m , Ω k , and Ω Λ arethe dimensionless density parameters. The velocity dis-persion was computed for each cluster from the redshiftdistribution of the cluster member galaxies as describedin Appendix.In addition to the sample of cluster member galaxiesobtained by the “shifting gapper” method above, we in-cluded the galaxies located at projected separations of R max < R < r , cl to investigate the variation ofgalaxy properties over a wide range of clustercentric ra-dius. R max is the largest clustercentric distance of thecluster member galaxies determined above. These ad-ditional galaxies were constrained to have velocity dif-ference relative to the cluster’s systematic velocity lessthan ∆ v = | v gal − v sys | = 1000 km s − . The final sampleconsists of galaxies smoothly distributed from the clus-ter center to R = 10 r , cl for each cluster. Figure 2shows the radial velocities of galaxies around eight clus-ters in our sample as a function of clustercentric distanceof galaxies.We rejected the clusters that appeared to be inter-acting or merging, which was decided in the galaxyvelocity versus clustercentric distance space. Dynami-cally young clusters having the brightest cluster galaxy Fig. 2.—
Radial velocity vs. clustercentric distance of galaxies.Filled circles and crosses indicate the early and late types, respec-tively, selected as galaxies associated with clusters, while open cir-cles indicate the galaxies not selected as associated members. Thehorizontal dashed lines indicate the systemic velocity of the clus-ters determined in this study. The vertical dotted lines indicatethe radius r , cl computed in this study. (BCG) at large clustercentric distance ( R BCG > . h − Mpc) were rejected too. We also eliminated the clus-ters for which survey coverages were not complete outto 10 r , cl . We finally obtained a sample of 93 relaxedAbell clusters and 34,420 associated galaxies for our anal-ysis. 2.3. Physical Parameters of Galaxies
The physical parameters of galaxies that we considerin this study are r -band absolute Petrosian magnitude( M r ), morphology, axis ratio, u − r color, equivalentwidth of Hα emission line, g − i color gradient, concen-tration index ( c in ), internal velocity dispersion ( σ ), andPetrosian radius in i -band. Here we give a brief descrip-tion of these parameters.The r -band absolute magnitude M r was computed us-ing the formula, M r = m r − r ( z )(1 + z )] − − K ( z ) − E ( z ) , (2)where r ( z ) is the comoving distance at redshift z in unitof h − Mpc, and the corresponding 5log h term in M r willbe omitted in this paper. K ( z ) is the K -correction,and E ( z ) is the luminosity evolution correction. Weadopt a flat ΛCDM cosmology with density parametersΩ Λ = 0 .
73 and Ω m = 0 .
27. The rest-frame absolutemagnitudes of individual galaxies are computed in fixedbandpasses, shifted to z = 0 .
1, using Galactic reddeningcorrection (Schlegel et al. 1998) and K -corrections as de-scribed by Blanton et al. (2003). The evolution correc-tion given by Tegmark et al. (2004), E ( z ) = 1 . z − . r -band absolute magnitudes of thecluster galaxies against their redshifts. We define the Park & Hwang Fig. 3.—
Sample definitions of our three volume-limited samplesin the absolute magnitude vs. redshift space. The bottom curvecorresponds to the apparent magnitude limit of m r = 17 . volume-limited samples of galaxies using the redshift andabsolute magnitude conditions as follows: C1 ( − . ≥ M r > − . z ≤ . − . ≥ M r > − . z ≤ . − . ≥ M r > − . z ≤ . m r =17 .
77) shown in Figure 3 is obtained using the mean K -correction relation given by equation (2) of Choi et al.(2007).Accurate morphology classification is critical in thiswork since the effects of interaction depend strongly onmorphology of the target and neighbor galaxies. Wefirst classify morphological types of galaxies included inthe DR4plus sample of Choi et al. (2007) adopting theautomated classification method given by Park & Choi(2005). Galaxies are divided into early (elliptical andlenticular) and late (spiral and irregular) morphologicaltypes based on their locations in the u − r color ver-sus g − i color gradient space and also in the i -bandconcentration index space. The resulting morphologi-cal classification has completeness and reliability reach-ing 90%. The automatic classification scheme does notperform well when an early-type galaxy starts to overlapwith another galaxy. This is because the scheme excludesgalaxies with very low concentration from the early-typeclass and blended images often erroneously give low con-centration. Since we are investigating the effects of closegalaxy-galaxy and galaxy-cluster interactions on galaxyproperties, this problem in the automatic classificationhas to be remedied. We perform an additional visualcheck of the color images of galaxies to correct misclas-sifications by the automated scheme. In this procedurewe changed the types of the blended or merging galax-ies, blue but elliptical-shaped galaxies, and dusty edge-on spirals. In addition, for the galaxies in DR6 that arenot in the DR4plus sample, we visually classified theirmorphological types using the color images.The . ( u − r ) color was computed using the extinc-tion and K -corrected model magnitude. The superscript0.1 means the rest-frame magnitude K -corrected to theredshift of 0.1, and will subsequently be dropped.We adopt the values of ( g − i ) color, concentration index ( c in ), and Petrosian radius R Pet computed forthe DR4plus sample of galaxies (Choi et al. 2007). The( g − i ) color gradient was defined by the color differencebetween the region with R < . R Pet and the annuluswith 0 . R Pet < R < R
Pet , where R Pet is the Petrosianradius estimated in i -band image. To account for theeffect of flattening or inclination of galaxies, ellipticalannuli were used to calculate the parameters. The (in-verse) concentration index is defined by R /R , where R and R are semimajor axis lengths of ellipses con-taining 50% and 90% of the Petrosian flux in the i -bandimage, respectively.The velocity dispersion value of the galaxy is adoptedfrom NYU-VAGC (Blanton et al. 2005). The value of Hα equivalent width is taken from MPA/JHU-VAGC(Tremonti et al. 2004), which is computed using thestraight integration over the fixed bandpass from thecontinuum-subtracted emission line with the model ofBruzual & Charlot (2003).In our analysis we often limit the late-type galaxysample to galaxies with i -band isophotal axis ratio b/a greater than 0.6. This is to reduce the effects of internalextinction on our results. The absolute magnitude andcolor of late-type galaxies with b/a < . Hα equivalent width, and color gradient.2.4. Nearest Neighbor Galaxy in Clusters
To account for the effects of the nearest neighborgalaxy in cluster environment, we determine the distanceand the morphology of the nearest neighbor galaxy.We define the nearest neighbor galaxy of a targetgalaxy with absolute magnitude M r as the one whichis located closest to the galaxy on the sky and is brighterthan M r + ∆ M r among those in our cluster galaxy sam-ple. We adopt ∆ M r = 0 .
5. When we adopt galaxiesfainter than the target galaxy by more than 0.5 mag asneighbors, our conclusions do not change but our statis-tics are worse since the number of target galaxies be-comes smaller (see § ρ n / ¯ ρ = γ n L n / (4 πr p ¯ ρ/ , (3)where γ n is the mass-to-light ratio of the neighbor galaxy, L n is the r -band luminosity of the neighbor, r p is the pro-jected separation of the neighbor from the target galaxy,and ¯ ρ is the mean density of the universe. We assumethat γ (early)=2 γ (late) at the same r -band luminosity,and that γ is constant with galaxy luminosity for a givenmorphological type. The value of mean density of theuniverse, ¯ ρ = (0 . ± . γL ) − ( h − Mpc) − , wasadopted, where ( γL ) − is the mass of a late-type galaxywith M r = −
20 (Park et al. 2008).Then, we define the virial radius of a neighbor galaxyas the projected radius where the mean mass density ρ n alaxy Interactions in Clusters 5 Fig. 4.—
The surface number density of early-type (upper panel)and late-type (middle panel) galaxies in the Abell cluster regions,and the corresponding early-type fraction (bottom panel) as a func-tion of the clustercentric radius normalized to the cluster virial ra-dius. The lines in the bottom panel are the best-fitting functions. within the sphere with radius of r p is 200 times the criti-cal density or 740 times the mean density of the universe,namely, r vir = (3 γL/ π/ ρ c ) / . (4)Since we adopt Ω m = 0 .
27, 200 ρ c = 200 ¯ ρ/ Ω m = 740 ¯ ρ .This is almost equal to the virialized density ρ virial =18 π / Ω m ( H t ) ¯ ρ = 766 ¯ ρ in the case of our ΛCDMuniverse (Gott & Rees 1975). This is what Park et al.(2008) used to define the virial radius. According toour formula the virial radii of galaxies with M r = − . , − . , and − . h − kpcfor early types, and 210, 240, and 280 h − kpc for latetypes, respectively. RESULTS3.1.
Morphology-Environment Relation
Figure 4 shows the surface number density of galax-ies and the fraction of early-type galaxies as a functionof projected clustercentric radius R normalized by thecluster virial radius r , cl . They are shown for threeluminosity ranges. The uncertainties of the fraction rep-resent 68% (1 σ ) confidence intervals that are determinedfrom the numerical bootstrap procedure.It shows the well-known MRR or MDR of galaxiesin clusters. In all three luminosity ranges the early-type fraction f E is almost constant at large distances,and starts to increase inwards at the critical region with R ≈ ∼ r , cl , which corresponds to the cluster in-fall region. The transition radius seems depending ongalaxy luminosity. For relatively brighter galaxies with Fig. 5.—
The characteristic clustercentric radius R cr as a func-tion of r -band absolute magnitude. R cr is the scale where the early-type fraction f E starts to rise significantly above the field value.Five luminosity subsamples are used: − ≥ M r > − , − ≥ M r > − , − ≥ M r > − . , − . ≥ M r > − . , − . ≥ M r > − .
5. The best-fit linear line is R cr /r , cl = (0 . ± . M r + (14 . ± . − . ≥ M r > − . ∼ . r , cl , but for fainter galaxies with − . ≥ M r > − . ∼ r , cl . The slope of increase is larger for less lumi-nous galaxies at small R . Since we are not distinguishingbetween ellipticals and lenticulars, we can only see theirsum is rising toward the cluster center. Fainter galaxiesseem more vulnerable to the cluster influence. This canbe considered as evidence for the direct interaction be-tween clusters and infalling galaxies, thinking that lessmassive galaxies change their morphology at farther dis-tances from clusters relative to massive ones. However, itcan be also due to the mass segregation within clustersthat massive cluster member galaxies hardly overshootbeyond the cluster virial radius while the less massiveones overshoot out to a few times the virial radius. Mas-sive galaxies outside the virial radius are likely to be theinfalling ones rather than bound cluster members.Figure 4 indicates that the early-type fraction is nearlythe same near the cluster center regardless of galaxy lu-minosity. The central value of f E = 0 . ∼ .
85 actuallymeans that the fraction is close to 1.0 at the cluster centerif the projection effect is taken into account (Ann et al.2008). At radii larger than about 4 r , cl , f E approachesthe field fraction that depends on the luminosity rangeand becomes insensitive to the large-scale environment(Park et al. 2007).To inspect this characteristic scale in more details wefit f E as a function of R/r , cl using the function f E = (0 . − f )exp( − R/R ) + f , (5)where R is a free parameter and f is an average valueof f E at R/r , cl > .
0. We define the characteristicradius R cr as the scale where f E becomes 10% largerthan its field value at fixed luminosity. Figure 5 showsan almost linear relation between the characteristic ra-dius and the absolute magnitude obtained from five lu-minosity subsets. The best-fit linear line is R cr /r , cl = Park & Hwang Fig. 6.—
Morphology-environment relation when the nearest galaxy is (left) an early-type and (right) a late-type. Absolute magnitudeof galaxies is fixed to a narrow range of − . ≥ M r > − .
0. Contours show constant early-type galaxy fraction f E . The points witherror bars above the x-axes denote the average virial radius of the BCGs. (0 . ± . M r + (14 . ± . − . ≥ M r > − . . M r ≤ − .
0. Then r vir of the nearest neighbors are calculated using theirluminosity and morphology.Dots in Figure 6 show the distribution of early-type( red points ) and late-type ( blue points ) galaxies in theprojected clustercentric radius R and projected nearestneighbor distance R n space. A spline kernel is used toobtain the smooth distributions of the median f E in eachlocation of the two panels. Contours with different col-ors mark constant early-type fractions. The left panel ofFigure 6 contains the target galaxies having early-typeneighbors. It shows that at R & r , cl all contours arenearly horizontal. This means that outside the clustervirial radius galaxy morphology is determined solely bythe nearest neighbor distance and morphology. When thenearest neighbor is an early type, f E monotonically in-creases as R n decreases. But if the neighbor is a late type,it first increases, reaches a maximum at R n ∼ r vir , n / R n decreases. The bifurcation oc-curs at R n ∼ r vir , n . This is the morphology-neighborenvironment relation that was discovered by Park et al.(2008) in the general large-scale background density en-vironment. It is interesting to see that the effects of thenearest neighbor’s distance and morphology are the dom-inant factors of galaxy morphology transformation rightdown to the cluster infall regions.The situation abruptly changes at the critical clus-tercentric radii of R cr = 1 ∼ r , cl . Within this ra-dius contours are nearly vertical when R n & . r vir , n ,but are nearly horizontal when R n . . r vir , n . When R n & . r vir , n , f E monotonically increase as R decreasesand depends almost entirely on R regardless of the mor- phological type of the nearest neighbor. Existence of thissudden transition near the cluster virial radius suggeststhat the morphology transformation of cluster galaxiesis due to the interactions between galaxies and clusters.Both gravitational and hydrodynamic processes can pro-duce the discontinuity in f E . It may be the hot clustergas confined within ∼ r , cl or gravitational tidal forceof cluster acting on galaxies trapped within the virialradius that causes the transformation. The monotonicincrease of f E at smaller R can arise by the increaseof the effects of hot cluster gas whose pressure mono-tonically increases toward the cluster center and/or byinteractions with the cluster potential for galaxies withsmaller orbital radii that have the shorter crossing time.On the other hand, Figure 6 clearly indicates thatthe clustercentric radius is not the only environmentalparameter determining the galaxy morphology but thenearest neighbor does a critical role when the neigh-bor separation is less than about 0 . r vir , n . The localgalaxy number density, to which the MDR is often at-tributed, cannot be responsible for the increase of f E inwards cluster because the density rises smoothly as R decreases and does not have a characteristic break at R cr (see Fig. 4). After all, it is the morphology-clustercentricradius-neighbor environment relation instead of the sim-ple MDR or MRR that determines the morphology ofcluster galaxies. Here neighbor environment includesboth neighbor distance and neighbor morphology.We emphasize that we are not using the nearest neigh-bor distance as a measure of local galaxy number density.It is a measure of the influence of the nearest neighborgalaxy itself irrespectively of other galaxies. However,there exists statistical correlation between R n and thelocal galaxy number density. If one uses a measure oflocal galaxy number density, one will still find some cor-relation of the measure with galaxy morphology withinthe cluster virial radius. But it is actually the galaxy-galaxy interaction that causes the correlation. This isbecause fixing R essentially fixes the local galaxy num-alaxy Interactions in Clusters 7ber density and in Figure 6 f E still changes at a fixed R .In the left panel of Figure 6 galaxies have early-typeneighbors. It is expected that both cluster and neighborgalaxy impose morphology transformation toward earlytype on galaxies through hydrodynamic or gravitationaleffects. Dominance of the role between the two dependson R and R n . At R ≈ r , cl the neighbor galaxy starts togive a major impact on galaxy morphology at the separa-tions R n < . r vir , n = 100 ∼ h − kpc (note the differ-ence of f E between the two panels). But at R ≈ . r , cl it happens at R n < . r vir , n ≈ ∼ h − kpc. Thisseems reasonable since near the cluster center the tidaleffects by the cluster potential are stronger, the clustergas has higher pressure, and thus the cluster gives moredirect impact on galaxy properties.One can note from a comparison between two panelsof Figure 6 that directions and levels of contours changecompletely depending on the morphology of the nearestneighbor galaxy at any clustercentric radius when thepair separation is small (i.e. R n . . r vir , n ). The rightpanel shows that a cluster galaxy tends to become a latetype when it has a late-type neighbor within the sepa-ration R n ≈ . r vir , n even when the pair is well withinthe cluster virial radius. For pairs with R n ≈ . r vir , n f E ≈ . R = 0 . r , cl when the neighbor is an early type. But f E is as low as0.35 for pairs with the same R n located at the same R when the neighbor is a late type. It is a clear demonstra-tion that the nearest neighbor has a dominant controlover galaxy morphology transformation in clusters whenthe distance to the neighbor is less than about one tenthof the virial radius of the neighbor galaxy.Figure 6 shows that there are not many such shortseparation pairs at a particular moment within the clus-ter virial radius and one might think that the majorityof cluster galaxies are not affected by neighbors. How-ever, it can be seen in Figure 6 that at R . . r , cl the mean separation between galaxies becomes so smallthat the virialized regions associated with galaxies areall overlapping with one another (not that the upperedge of the galaxy distribution becomes smaller than R n /r vir , n = 1 at R/r , cl . . r , cl is h v i / .If r , cl = 1 . h − Mpc and h v i / = 700 km s − ,the crossing time across r , cl is about 3 × yrs. Onthe other hand, the RMS relative velocity between tworandom cluster galaxies is √ h v i / . If the virial ra-dius of the galaxies is r vir = 300 h − kpc, their cross-ing time is 4 × yrs, an order of magnitude shorterthan the crossing time across the cluster. This means inthis figure that the cluster galaxies at R < r , cl havemigrated vertically (interaction with neighbor galaxies)many times during the time they make one travel hor-izontally (interaction with the cluster). In particular,when R < . r , cl , a galaxy starts to interact with an-other neighbor galaxy as it passes one neighbor galaxybecause the virial radii of galaxies all overlap with oneanother there. Then the nearest neighbors may haveleft significant cumulative effects on morphology of clus-ter galaxies. The amount of the cumulative effects in-creases monotonically as the clustercentric radius de-creases, which can produce the trend seen in Figure 6. It is expected that the late-type galaxy sample has ahigher fraction of interlopers in the cluster environment.The pairs involving late-type target or late-type neighborare more likely to be false pairs, and more widely sepa-rated in real space. If this effect is corrected in Figure6, the contours will be shifted upward. Furthermore, ifthe fraction of interlopers varies as a function of neigh-bor separation or clustercentric radius, the contours willbe both shifted and stretched. However, the fact thatthere are discontinuities in f E shown in Figure 6 (nearthe cluster virial radius R ≈ r , cl and the galaxy mergerscale R n ≈ . r vir , n ) and also the fact that these tran-sitions occur at physically meaningful scales, cannot beexplained if the fraction of interlopers is seriously high.This suggests that the morphology-environment relationshown by the contours in Figure 6 is not seriously affectedby the interlopers.Though we rejected the clusters that appear to be in-teracting or merging, there are some clusters ( ∼ r , cl and relative velocity is less than 1000 kms − . Therefore, the galaxies associated with these clus-ters have been counted more than once in our analysis.For example, among 3874 galaxies used in Figure 6, 874galaxies are those counted more than once. When we re-ject these galaxies, our results remain almost the same.In addition, our results do not depend sensitively on ourdefinition of the nearest neighbor. For example, when wevaried ∆ M r from 0.5 to 0.75, our results remain qualita-tively the same (see also Park et al. 2008; Park & Choi2009).The mean virial radius of the BCGs, which is typicallyabout 0 . r , cl , and its 1 σ range are shown above the x -axes of Figure 6. We do not find any characteristic fea-ture across the virial radius of the BCGs. This suggeststhat the BCGs are not directly participating in trans-forming the morphology of the cluster galaxies. Whenthe positions of BCGs are used as the centers of clus-ters, the contours in Figure 6 are basically unchanged at R & . r , cl . But the slight drop of f E at R < . r , cl seen for the E/S0 neighbor case, now disappears.3.2. Luminosity-Environment Relation
Figure 7 shows the r -band absolute magnitudes of thegalaxies in a volume-limited sample with z < . M r < − .
0. The lines with error bars are the medianvalues as a function of R . The BCGs, marked as crosses,are not used in calculating the median values. Early-typegalaxies become fainter as much as ∼ . R decreases from 10 r , cl to 0 . r , cl . The luminosity ofearly types rises again as R becomes smaller than about0 . r , cl . But the increase of luminosity near the clustercenter seems to depend on how much the BCGs are off-centered. Such a variation of the median luminosity isnot detected for late types.The dependence of luminosity on the environment canbe better understood in the two dimensional study. Con-tours in Figure 8 delineate the constant median M r lo-cations in the two-dimensional environmental parameterspace of R and R n . Four panels distinguish among fourdifferent combinations of target and neighbor morphol-ogy. At each location of the R - R n space the median valueof M r is found using the galaxies included within a splinekernel with a fixed size. The BCGs are not included in Park & Hwang Fig. 7.—
Absolute magnitude of galaxies brighter than M r = −
19 in the Abell cluster regions as a function of clustercentricradius. The upper panel shows the early types, and the lower panelshows the late types. Lines are the median magnitudes. Crossesare the BCGs, and they are not used in calculating the medianvalues. Late types with axis ratio of b/a < . r , cl . the smoothing.It can be clearly seen that galaxies with larger R n arebrighter when R is greater than about 0 . r , cl . Namely,the bright galaxies are more isolated from their influen-tial neighbors than the relatively faint galaxies are. Inthe region far outside the cluster virial radius the abso-lute magnitude of galaxies is nearly constant in R (i.e.the contours are nearly horizontal). Luminosity of galax-ies with R n & r vir , n depends very sensitively on R n . Butgalaxies with R n < r vir , n show little dependence of M r on R or R n . The same phenomenon has been found byPark et al. (2008) for galaxy pairs in the general back-ground density regions.The reason that galaxies are brighter when they arelocated outside the nearest neighbor’s virial radius wasinterpreted by Park et al. as due to luminosity trans-formation through mergers. After a galaxy merges withits closest neighbor, the second nearest neighbor will be-come the new nearest neighbor of the merger product.Since the merger product is typically located at a sepa-ration from the originally second nearest neighbor largerthan the virial radius of the neighbor, a recently mergedgalaxy will appear in general at the upper edge of thegalaxy distribution in Figure 8. As one moves towardthe cluster center, the average galaxy number densityincreases and the mean distance between galaxies de-creases. Correspondingly, the distance to the new near-est neighbor of a recently merged galaxy also decreasesstatistically for decreasing clustercentric radius, and thelocation of the recent merger products follows the upperedge of the galaxy distribution in Figure 8.The upper left panel of Figure 8, showing the early-type target galaxies having early-type neighbors (the E-e case), shows that the maximum luminosity a galaxycan attain slowly decreases as R decreases until R be-comes about 0 . r , cl . The median M r of the most sep- arated galaxies is about − . R ≈ r , cl , but de-creases to about − . R ≈ . r , cl , a more thanone magnitude drop. This can be explained if the lumi-nosity transformation process by galaxy-galaxy mergersbecomes less efficient as R decreases. This is reasonablebecause the relative velocity between neighboring galax-ies will be higher and the chance for a pair to merge willdecrease toward the cluster center.A similar R -dependent trend in luminosity is also seenfor late-type galaxies as shown in the right panels of Fig-ure 8 even though the trend is much weaker. Luminos-ity of late-type galaxies is on average lower than thatof early types. Interestingly, the late-type galaxies hav-ing an early-type neighbor (the L-e galaxies) are slightlybrighter than the early-type galaxies at R . . r , cl . Itcould be that, as R decreases, faint late types are trans-formed to early types and only relatively bright late typessurvive near the cluster center.Figure 8 also shows that galaxies located near R = r , cl and having a close neighbor are on average thefaintest. Namely, even though the most isolated galax-ies become faintest at R ≈ . r , cl , those with aclose neighbor ( R n ≈ . r vir , n ) become faintest at R ≈ . r , cl .3.3. Star Formation Activity Parameters
The left column of Figure 9 shows the u − r color ofgalaxies divided into two morphology and three magni-tude bins as a function of R . It can be seen that thegalaxy color becomes redder as R decreases for both earlyand late types. This clustercentric radius dependence ofcolor is stronger for relatively fainter galaxies (i.e. the C1sample). In the case of the galaxies in C1 the dependenceseems to occur at ∼ r , cl .Dots in Figure 10 are the intermediate luminositygalaxies with − . ≥ M r > − . R > R cr = 1 ∼ r , cl , which meansgalaxy color is independent of R and depends only on theneighbor separation R n . Inside the critical radius R cr thecolor of late-type galaxies still depends mainly on neigh-bor separation and morphology. This is evidence that hy-drodynamic interactions between individual galaxies areeffective even within the virialized region of clusters. Inthe case of the L-l galaxies there is clustercentric radiusdependence of color when R n & r vir , n /
3. It is likely thatthis is because the neighbors other than the nearest onetend to be early types as the system moves toward thecluster center. If the cluster hot gas had a direct impacton late-type galaxies’ color, both L-e and L-l galaxieswould show a similar color dependence on R .The equivalent width of the hydrogen Hα line is a mea-sure of SFA. Figure 9 shows the median W ( Hα ) as afunction of R for six different cases distinguished by mor-phology and luminosity of target galaxies. The SFA oflate-type galaxies decreases as R decreases. The depen-dence again seems to start at ∼ r , cl for the galaxiesin the C1 sample. It is important to note that both u − r color and W ( Hα ) show only mild dependence onthe clustercentric radius R , and it is actually the neigh-alaxy Interactions in Clusters 9 Fig. 8.—
Median absolute magnitude contours in the projected pair separation R n /r vir , n vs. the clustercentric distance R/r , cl forthe galaxies with z ≤ . M r ≤ − .
5. Late types with axis ratio of b/a < . Fig. 9.—
Dependence of star formation activity parameters of our target galaxies in the samples of C1, C2, and C3 on the clustercentricdistance: (left) u − r , (middle) W(H α )+1(˚ A ), and (right) ∆( g − i ). Median curves are drawn for the cases of early types (solid line) andof late types (dotted line). Late types with axis ratio of b/a < . Fig. 10.—
Dependence of u − r color, equivalent width of the Hα line, g − i color gradient of galaxies with − . ≥ M r > − . R n and the clustercentric distance R . In each column, galaxies are divided into four cases, the E-e, E-l, L-e, and L-lgalaxies. Dots are galaxies belonging to each subset. At each location of the R n /r vir , n - R/r , cl space the median value of the physicalparameter is found from those of galaxies within a certain distance from the location. Curves are the constant-parameter contours. Latetypes with axis ratio of b/a < . alaxy Interactions in Clusters 11 Fig. 11.—
Same as Fig. 9, but for (left) c in , (middle) σ (km s − ), and (right) R Pet , i ( h − kpc). Late-types with axis ratio of b/a < . boring galaxies that mainly determine the color and SFAof galaxies within clusters as we can see in Figure 10.The second column of Figure 10 shows W ( Hα ) in two-dimensional environmental parameter space. One cannotice that the constant W ( Hα ) contours look very sim-ilar to those of u − r color. Namely, the SFA of the L-egalaxies is mainly controlled by the neighbor galaxies.On the other hand, the SFA of L-l galaxies shows de-pendence on R when the nearest neighbor separation isnot too small ( R n & . r vir , n ). This is again probably be-cause the neighbors other than the nearest one tend to beearly types as R decreases. The two cases demonstratethat the SFA of the late-type cluster galaxies changesdifferently depending on the morphology of the neighborgalaxy even well inside the cluster virial radius. If thehot cluster gas could directly quench the SFA of late-typegalaxies, both L-l and L-e galaxies would show the same R -dependence of SFA regardless of the morphology of thenearest neighbor. Since this is not the case, one can con-clude that it is after all the galaxy-galaxy hydrodynamicinteraction that gives the biggest impacts on the colorand SFA of cluster galaxies and that, contrary to intu-ition, the hot cluster gas is not the main actor quenchingthe star formation in late-type cluster galaxies at leastdown to R ≈ . r , cl . We have repeated our analysesusing the fainter galaxies with − . ≥ M r > − .
0, andarrived at the same conclusion. In the case of early-typegalaxies the W ( Hα ) parameter is very small and hardlychanges.Figure 9 shows that the color gradient of galaxies de-pends only weakly on R . In all cases the central region ofgalaxies becomes slightly bluer relative to the outskirtsas R decreases. The dependence is stronger for faintergalaxies. In the right column of Figure 10 contours represent thedistribution of the median ∆( g − i ) at each location ofthe R - R n space. Unlike the u − r color and W ( Hα ), thecolor gradient ∆( g − i ) of late-type galaxies depends onboth R and R n inside r , cl as can be seen from the slantcontours. We interpret this phenomenon as a result ofgalaxy-galaxy interaction. When a late-type galaxy ap-proaches a neighbor closer than the virial radius of theneighbor, its color gradient always increases (center be-comes relatively bluer) regardless of neighbor’s morphol-ogy as shown by Park & Choi (2009, see Figs. 6 and 7).The color gradient of a late-type galaxy can increase asit moves toward the cluster center because it becomesmore likely to be affected by neighbor galaxies. Sincethere is no neighbor morphology dependence of ∆( g − i )when a late type approaches a neighbor, the ∆( g − i )contours are quite similar for L-e and L-l galaxies. It isalso possible that the center of late-type cluster galaxiesbecomes bluer at smaller R because of the tidal effectsof the cluster potential (Merritt 1984).3.4. Structure Parameters
The left column of Figure 11 shows that concentra-tion of intermediate and low luminosity late-type galax-ies increases ( c in decreases) as R decreases below R cr .But concentration of early types and high luminositylate types is nearly independent of R . As argued byPark & Choi (2009), this can be attributed to less com-pact internal structure of late types which are more vul-nerable to tidal effects than early types.The first column of Figure 12 shows the median c in contours for the intermediate luminosity galaxies with − . ≥ M r > − .
5. Again c in of early types hardlychanges as R or R n vary. On the other hand, c in of late2 Park & Hwang Fig. 12.—
Same as Fig. 10, but for (left) c in , (middle) σ (km s − ), and (right) R Pet , i ( h − kpc). Late-types with axis ratio of b/a < . types starts to decrease (galaxies become compacter) at R . R cr = 1 ∼ r , cl . It is interesting to see that thestructural parameter c in shows an abrupt change at thecharacteristic scale. A similar phenomenon can be foundalso for the central velocity dispersion.The fact that the R -dependence of c in exists only when R . R cr , gives an important clue for understanding thestructural evolution of cluster galaxies. The local galaxynumber density cannot be the reason for the discontin-uous R -dependence of c in because the local density is asmooth function of R . The discontinuity can appear dueto repeated gravitational interactions of cluster membergalaxies with cluster potential or with other galaxies asthey make trapped orbital motions within the clustervirial radius. It might also seem possible to explain thediscontinuity by the hydrodynamic effects of hot clustergas. For example, the cold gas in the outer part of late- type galaxies can evaporate or be stripped when they fallinto the hot cluster gas clump or encounter the hot halogas of their neighbor galaxies. Then their outer part willbecome redder and dimmer. This may cause the color u − r and color gradient ∆( g − i ) increase and inverseconcentration index c in decreases as R or R n decreases.However, it is difficult to explain why the central stel-lar velocity dispersion of late types should also increaseshown in the second column of Figure 12 by quenchingthe SFA in the outer part.Figure 11 (panels d, e, and f) shows that the centralvelocity dispersion of galaxies in general increases as R decreases except for low luminosity galaxies. The trend isclear for intermediate luminosity galaxies, in particular.The second column of Figure 12 shows constant σ con-tours of intermediate luminosity ( − . ≥ M r > − . σ shows a characteristic behavior that it depends only on R n at R & R cr but starts to depend only on R when R . R cr . Would the increase of σ within the clustervirial radius be due to the tidal interaction of galaxieswith other galaxies or with the cluster potential? Onecan find a clue from Figure 11 which shows that the R -dependence of c in and σ is largest for intermediateluminosity galaxies. This may be because the interme-diate luminosity galaxies have suffered from the interac-tion with cluster potential more strongly than brighteror fainter ones. Even though galaxy-galaxy encountersin general increase σ of late-type galaxies (see L-e casesat R > r , cl and Fig. 8 of Park & Choi 2009), it is nottrue at R < r , cl as can be seen in Figure 12. The verybright massive galaxies at 0 . . R/r , cl . . R cr is largerfor fainter galaxies (see Fig. 5 for example). Therefore, itis expected that the intermediate luminosity galaxies aremost susceptible to change in structure and kinematicsthrough interactions with the cluster potential.Our study of c in and σ of cluster galaxies makes itclear that late-type galaxies become more centrally con-centrated and have higher central velocity dispersion asthey approach the cluster center. Our results suggestthat late-type galaxies become earlier in SFA throughhydrodynamic interactions between galaxies and also inmorphology and kinematics through tidal interactions asthey approach the cluster center. Paucity of late-typegalaxies near cluster center is a result of combined ef-fects of gravitational and hydrodynamic interaction withthe cluster and the nearest neighbor galaxies.We use the Petrosian radius in the i -band image asa measure of galaxy size. Figure 11 (panels g, h, andi) shows that the intermediate luminosity galaxies showvery slight decrease of R Pet as R decrease. The thirdcolumn of Figure 12 shows again that there is a weakclustercentric radius dependence of R Pet at R . R cr forlate-type galaxies. The decrease of R Pet does not seem tobe due to the blending of galaxy images in high densityregions like clusters because it suddenly occurs at thephysically meaningful scale ( R cr ). The degree of blendingof galaxy images should be a smooth function of R .The size of late-type galaxies does not change signif-icantly by interactions with other galaxies as shown inFigure 8 of Park et al. (2008). Therefore, the decrease of R Pet of late types at
R < R cr shown in Figures 11 and 12should be attributed to the cluster. Late-type galaxiescan appear smaller when their outer part becomes dim-mer as they orbit within a cluster and get quenched instar formation in disks. DISCUSSIONMany mechanisms have been proposed to explain theMRR or MDR in clusters. They are divided into twocategories : mechanisms relying on gravitational and hy-drodynamic processes (see Boselli & Gavazzi 2006 for areview). The mechanisms based on gravitational inter- actions include galaxy-galaxy tidal interaction, galaxy-cluster potential tidal interaction, and interaction withthe general tidal background (harassment). Those basedon hydrodynamic interactions comprise ram pressurestripping, viscous stripping, or thermal evaporation ofcold gas of late-type galaxies by hot cluster gas, and re-moval of hot halo gas reservoir causing stopping of gassupply and quenching of star formation (strangulation).We will examine each of these mechanisms against ourfindings.1. Galaxy-galaxy tidal interactionTidal interaction between galaxies can be efficient atremoving or consuming the cold gas in galaxies, and tendto transform late types into early types (Spitzer & Baade1951; Richstone 1976; Farouki & Shapiro 1981; Icke1985; Merritt 1983). However, this mechanism is usuallyexcluded as a process responsible for the MRR or MDRbecause the orbital velocity of cluster galaxies are veryhigh and the tidal energy deposit during the short en-counters is too small to significantly affect galaxy struc-ture (Merritt 1984; Byrd & Valtonen 1990).At
R > R cr , the structural parameter of late-typegalaxies depend only on the environment determined bythe neighbor galaxies. But R < R cr they strongly de-pend on R , but only weakly or negligibly on R n (see Fig.12). This tells that the galaxy-galaxy tidal interactionsdo not instantly change the structure of cluster membergalaxies much. The parameters c in and R Pet do show aweak dependence on R n for L-e galaxies within R = R cr .But this may have also been resulted by hydrodynamicinteractions with their early-type neighbor. Even thoughwe exclude the significance of the tidal effects of galaxy-galaxy interactions on the internal structure and kine-matics of cluster galaxies, it should be emphasized thatthe hydrodynamic effects of galaxy-galaxy interactionscan give significant impacts on their SFA.2. Galaxy-cluster potential interactionIndividual galaxies can suffer from the tidal forceof the overall cluster mass (Merritt 1984; Miller 1986;Byrd & Valtonen 1990; Moss & Whittle 2000; Gnedin2003). This mechanism is usually excluded in explainingthe MRR or MDR because the time scale required formorphology transformation, being several cluster cross-ing time, is rather too long. The tidal force will bestronger toward the cluster center, and the strong de-pendence of c in and σ on R within R = R cr can eas-ily explained by this mechanism. The internal structureof the intermediate mass galaxies, in particular, seemsto have been significantly affected by this mechanism.But the tidal interaction with cluster potential may notbe sufficient for morphology transformation of the verybright or faint cluster galaxies.3. HarassmentGalaxies can be also perturbed by the tidal force back-ground from numerous distant encounters with othercluster members (Moore et al. 1996, 1998, 1999). Eventhough individual encounters are too short for the tidalforce to activate structural changes, galaxy structuremay significantly change through such numerous weakencounters. The sudden transition of the structure pa-rameters can be explained by repeated passage of mem-ber galaxies within the cluster. So both interaction withcluster potential and harassment may account for the R -dependence of morphology and structure parameters of4 Park & Hwangintermediate mass galaxies, in particular, whose clustercrossing time is reasonably short but the path length isstill long.4. Galaxy-galaxy hydrodynamic interactionThe effects of hydrodynamic interaction betweengalaxies on cluster galaxy properties have been foundimportant in this work. The galaxy-galaxy interactionturns out to be the major mechanism for quenching SFAof late-type galaxies within clusters. As can be seenin the scatter plot of galaxies in the R - R n plane, dis-tance to the neighbors monotonically decreases as R de-creases and galaxies become always located within neigh-bor galaxy’s virial radius when R . R , cl /
3. In this sit-uation galaxies are constantly undergoing hydrodynamiceffects and mass exchange with neighbors. We arguedabove that the vertical contours for c in and σ can beexplained by the gravitational tidal force from clusteritself. However, the nearly horizontal contours for the u − r and W ( Hα ) parameters can be only explained byhydrodynamic effects of neighbor galaxies. It should beemphasized that the high-speed orbital motion of clustergalaxies weakens the importance of galaxy-galaxy tidalinteractions, but can make the galaxy-galaxy hydrody-namic interaction very important.It was also found that bright galaxies are more isolatedfrom influential neighbors than relatively fainter ones inclusters, which has been interpreted as due to merger-driven luminosity transformation. The fact that early-type galaxies show such trend more strongly is consis-tent with this interpretation. Relative paucity of brightgalaxies near cluster center (except for the BCGs) seemsto indicate that the frequency of galaxy merger decreasesas the clustercentric radius decreases.5. Ram Pressure StrippingMany rich clusters like the Abell clusters we are an-alyzing, are holding hot X-ray emitting gas. A late-type galaxy falling into such a hot gas tank can stripoff its cold gas and terminate SFA (Gunn & Gott 1972;Quilis et al. 2000). The hot gas is trapped roughly withinthe virial radius of the cluster. Therefore, any mechanismrelying on hydrodynamic interaction with the hot clus-ter gas will have a characteristic scale of onset of clusterinfluence near the cluster virial radius.A major problem with the ram pressure stripping andother hydrodynamic processes in accounting for the mor-phology segregation, is that these mechanisms can onlyreduce the SFA and cannot change galaxy structure whilethe observations require the fraction of bulge-dominatedgalaxies to increase significantly as the clustercentric ra-dius decreases. Therefore, even though this mechanismcan explain the radial variation of the fraction of galaxiesthat are red and inactive, it can not explain the radialvariation of concentration or central velocity dispersion.It is also pointed out that only loosely bound thin cloudscan be swept out of the galaxy and molecular clouds aremostly unaffected by this interaction (Quilis et al. 2000).Furthermore, we have shown in Figure 10 that it is ac-tually the galaxy-galaxy interaction that mainly controlsthe color and SFA of the cluster late-type galaxies ratherthan the hot cluster gas.6. Viscous stripping / Thermal evaporationThe cold gas in a late-type galaxy moving through thehot intracluster gas can be stripped off by momentumtransfer between the cold disk gas and hot cluster gas (Nulsen 1982), or be evaporated by the thermal conduc-tion (Cowie & Songaila 1977). These mechanisms canbe activated when a galaxy fall into the hot cluster gaspool, and can give rise to a characteristic feature in theradial variation of galaxy SFA as observed in this work.However, they share the same problem the ram-pressurestripping mechanism has in that they can not modifygalaxy structure.Furthermore, the hot cluster gas cannot explain theenvironmental dependence of color and SFA of late-typegalaxies either. If the hot cluster gas predominantly con-trols the color and SFA of cluster late types, the con-tours in Figure 10 should be vertical independently of R n , which is not true.7. StrangulationAccording to the current understanding of galaxy evo-lution, spiral galaxies maintain SFA by accreting gasfrom their hot gas reservoir. It has been proposed that aspiral galaxy fell into the hot intracluster gas can loseits hot halo gas and stop supplying gas into its disk(Larson et al. 1980; Bekki et al. 2002). Then the galaxyjust consume its already existing cold gas to form stars,and the SFA halts after some time when all cold gas isconsumed. Compared to the ram pressure stripping, thismechanism will quench the SFA in late-type galaxies in adelayed action. As being a pure hydrodynamic process,it also has the problem that the structural parameters ofgalaxies can not be changed. This mechanism also pre-dicts the contours to be vertical (dominance of clusterinfluence) for the early-type fraction, color, and SFA pa-rameters in Figures 6 and 10, which is not supported byobservations.To inspect galaxy properties for their dependence onhot cluster gas in more details, we studied the early-typefraction in the R n - R space separately for X-ray bright( L x ≥ × erg s − ) and faint (0 . × ≤ L x ≤ × erg s − ) Abell clusters. Figure 13 shows thatthe magnitude of f E is not particularly higher for X-raybright clusters. This can be another evidence against theidea that the hot intracluster gas plays the main role inmorphology transformation of late-type galaxies in mas-sive clusters.To summarize, the interaction responsible for theMRR/MDR in clusters can be either galaxy-galaxy orgalaxy-cluster interactions from the point of view ofthe actor, or either gravitational (mass-mass) or hy-drodynamic (gas-gas) interactions in terms of physi-cal process. Figure 12 suggests that the galaxy-clustertidal interactions are responsible for structural and kine-matic changes of cluster late-type galaxies toward earlymorphological type. Late types seem to become morespheroidal through such interactions. Figure 10 indi-cates that the hydrodynamic interactions with early-type neighbors are responsible for reddening and SFAquenching of cluster late-type galaxies. Therefore, themorphology transformation of late-type galaxies seemsto take place in clusters through galaxy-galaxy hydro-dynamic interactions and galaxy-cluster/galaxy-galaxygravitational interactions. However, it is reasonable toaccept that all above mechanisms are contributing to theMRR/MDR in clusters to some extent and a particularprocess cannot fully account for all observational aspects. CONCLUSIONSalaxy Interactions in Clusters 15
Fig. 13.—
Same as Fig. 6, but for (a and b) X-ray bright clusters ( L X ≥ × erg s − ) and (c and d) X-ray faint clusters(0 . × ≤ L X ≤ × erg s − ). X-ray luminosities are from B¨ohringer et al. (2000, 2004). We have studied the dependence of various galaxyproperties on the clustercentric radius and the environ-ment attributed to the nearest neighbor galaxy using theSDSS galaxies associated with the Abell galaxy clusters.Our major findings are as follows.1. There exists a characteristic scale where the galaxyproperties such as morphology, color gradient, and struc-tural parameters suddenly start to depend on the clus-tercentric radius at fixed nearest neighbor environment.2. The characteristic scale depends on galaxy lumi-nosity; the faint galaxies with − . ≥ M r > − . ∼ r , cl while the scale is ∼ r , cl for thebrighter galaxies with − . ≥ M r > − . ∼ . r , cl δ for each galaxy, which indicates the local deviationsfrom the systemic velocity ( v sys ) and dispersion ( σ cl , all ) of the entire cluster (Dressler & Shectman 1988). It is definedby δ = N nn σ , all (cid:2) ( v local − v sys ) + ( σ local − σ cl , all ) (cid:3) , (1)where N nn is the number of the nearest galaxies that defines the local environment, taken to be N gal1 / in this study. N gal is the total number of member galaxies in the cluster. The nearest galaxies are those located closest to the galaxyon the sky. v local and σ local are systematic velocity and its dispersion estimated from N nn nearest galaxies, respectively.We use the galaxies with δ ≤ .0 to compute the cluster velocity dispersion.