Ram pressure stripping of HI-rich galaxies infalling into massive clusters
Jing Wang, Weiwei Xu, Bumhyun Lee, Min Du, Roderik Overzier, Li Shao
DDraft version September 18, 2020
Typeset using L A TEX twocolumn style in AASTeX62
Ram pressure stripping of HI-rich galaxies infalling into massive clusters
Jing Wang, Weiwei Xu, Bumhyun Lee, Min Du, Roderik Overzier, and Li Shao Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China Observat´orio Nacional/MCTIC, Rua General Jos´e Cristino, 77, S˜ao Crist´ov˜ao, Rio de Janeiro, RJ 20921-400, Brazil National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China
ABSTRACTWe estimate the strength of ram pressure stripping (RPS) for H i -rich galaxies in X-ray detectedclusters. We find that galaxies under stronger RPS tend to show more significantly reduced total H i mass and enhanced central SFR, compared to control galaxies in the field which have similar stellarmass, stellar surface density and integral star formation rate. Galaxies under strong or weak RPSaccount for ∼
40% of the H i -rich population at R , and even beyond R in the most massiveclusters. Our results imply the important role of RPS as a channel of environmental processing farbefore the galaxies reach the core region of clusters. Keywords:
Galaxy evolution (594), Interstellar atomic gas (833) INTRODUCTIONAll galaxies including the Milky Way suffer from grav-itational and hydro-dynamic effects of the external en-vironment. Strong environmental effects remove the hotand cold gases as well as stellar outer disks, leadingto the cessation of star formation and aging of stellarpopulation. With little input of the dynamically cold,young stars, disks suffering from the continuous heatingfrom the external perturbations, undergo morphologi-cal transformation. Galaxy evolution is hence acceler-ated by these effects. Massive clusters provide an ideallaboratory to study a variety of environmental effects,particularly the ram pressure stripping (RPS) which ismuch weaker in smaller groups.Gunn & Gott (1972) provided the first analyticalmodel of RPS, in which the interstellar gas of a galaxygets stripped if the ram pressure is higher than the an-chor force. In this model, the ram pressure depends onthe density of the intra-cluster medium (ICM) and thevelocity of the galaxy, and the anchor force depends thesurface density of the ISM and the internal gravity onit in the direction perpendicular to the disk. Later hy-drodynamic simulations found that RPS is stronger forface-on infalling galaxies than for edge-on ones (J´achymet al. 2009; Roediger & Br¨uggen 2006), and the orbitsof infall affect the cumulative effect of RPS (Tonnesen2019). Pressures from the hot gas halo help constrainthe interstellar gas against the ram pressure (Cora et al.2018; Stevens & Brown 2017), though a significant frac-tion of the galaxies should have lost the hot gas halo and start strangulation (Larson et al. 1980) during an earlystage of the infall (Bah´e et al. 2013; Bekki 2009). Someof the interstellar gases stripped off the disk plane maybe accreted later if they do not reach the escape veloc-ity (Vollmer et al. 2001). Despite these uncertainties,the model of Gunn & Gott (1972) is a good approxima-tion to quantify the strength of ram pressure stripping.It is widely applied in semi-analytical models (SAM) ofgalaxy evolution with RPS (Lotz et al. 2019; Cora et al.2018; Stevens & Brown 2017; Luo et al. 2016; Henriqueset al. 2015; Gonzalez-Perez et al. 2014) and used to inter-pret observational trends. Based on the Gunn & Gott(1972) model, we expect RPS to be most effective inthe core region of massive clusters and on the low-massgalaxies.Observations confirmed RPS as one effective mecha-nism in the evolution of both individual galaxies andthe general star-forming population near the cores ofclusters. Galaxies under RPS were identified in nearbyclusters, with a truncated edge on the leading side and atail on the trailing side of infalling gas disks (e.g. Gavazziet al. 2018; Boselli et al. 2016; Yagi et al. 2017; Abram-son et al. 2011; Chung et al. 2009). These galaxies typ-ically show high H i deficiency, indicative of a recent gasremoval and future quenching of star formation (Boselliet al. 2016; Chung et al. 2009; Bravo-Alfaro et al. 2000a;Cayatte et al. 1994). They represent a subset of thegalaxies under strong RPS, as the observability of tailscan depend on both the observing angle and the ther-mal pressure of the ICM (Tonnesen & Bryan 2010). Theaveraged behavior of galaxies in clusters also supports a r X i v : . [ a s t r o - ph . GA ] S e p the importance of RPS. Both the gas mass and SFRof galaxies at a given stellar mass decrease on averagetoward the cluster centers (Brown et al. 2017; Odekonet al. 2016; Hess & Wilcots 2013; Woo et al. 2013).These trends are more prominent for low-mass galaxiesthan for high-mass galaxies (Cortese et al. 2011; Zhanget al. 2013), in more massive halos than in less massivehalos (Brown et al. 2017; Odekon et al. 2016). The in-terstellar medium and SFR show an averaged behaviorof outside-in shrinking within galaxies near the core ofclusters: when compared to the field galaxies, the mostextended component H i shows the strongest deficiency,the less extended dust, molecular gas and integral SFRare also reduced but to a less extent, and the inner mostcentral SFR is the least affected (Boselli et al. 2020;Mok et al. 2017; Boselli et al. 2014a; Cortese et al. 2010;Boselli et al. 2006a; Crowl et al. 2005). These trendsare qualitatively consistent with the way that RPS ispredicted to work, and indicate the dominating role ofRPS near the core of clusters.The relative importance of RPS among many other en-vironmental effects is less clear in the outer region (i.e.near and beyond the virial radius) of clusters (Koop-mann & Kenney 2004a). Galactic tidal stripping andmergers are expected and observed to be relatively fre-quent there (Chung et al. 2009), as the galaxy densitiesare higher than in the field but the relative velocitiesof galaxies are not as high as those near the clustercores (Boselli et al. 2006a). Strangulation due to re-moval of the hot gas halo is also expected to happenat much larger cluster-centric distance than RPS of thecold gas (Bah´e et al. 2013; McCarthy et al. 2008; Lar-son et al. 1980). There is still not consensus on how thestar formation activity of galaxies is reduced through theclusters. A slow+fast declining mode is derived by sev-eral authors (Wijesinghe et al. 2012; Wetzel et al. 2012,2013; Muzzin et al. 2012); others rather indicate a slowdecline (von der Linden et al. 2010; Wolf et al. 2009;McGee et al. 2009; Paccagnella et al. 2016), while oth-ers suggest a rapid quenching (Boselli et al. 2016; Oman& Hudson 2016). These debates, while may be partlyattributed to biases in sample selection or analysis meth-ods, suggest a complexity in environmental effects. Thegalaxies with a fast declining SFR are usually associatedwith strong RPS, which theoretically can remove 70% ofthe cold gas in a few hundreds Myrs (Yun et al. 2019);while those with a slowly declining SFR may be undera mixture of effects including weak RPS. Some insightsabout the relative role of RPS could be gained from cos-mological simulations, but due to the complex natureof galaxies, properly modeling the H i and SFR of cen-tral and satellite galaxies in clusters has been difficult (Stevens et al. 2019; Lotz et al. 2019; Cora et al. 2018;Stevens & Brown 2017; Luo et al. 2016; Henriques et al.2015; Gonzalez-Perez et al. 2014). More observationalinputs may help constrain the simulations.One way of better separating the effect of RPS inobservations, is to derive model motivated parameters.The ram pressure and the anchor force in the Gunn& Gott (1972) model can be roughly estimated fromobservations in X-ray, optical, and H i or ionized gas.Studies based on the IFU survey of Jellyfish galaxies,GASP (Poggianti et al. 2017), found that the observedsignificance of RPS tails in the ionized gas are consis-tent with the levels of ram pressures in comparison toanchor forces (Jaff´e et al. 2018). Another useful toolis the projected phase-space diagram (PSD), a plot ofthe radial velocities as a function of the projected clus-ter centric distances, which effectively traces the infallstage of galaxies (Mahajan et al. 2011; Oman et al. 2013;Oman & Hudson 2016; Rhee et al. 2017). By requiringthe ram pressure to be larger than the anchor force at allgalactic radii, a “stripping region” of H i , where galaxiesare undetected in shallow H i surveys, was successfullypredicted on the projected PSD for several massive clus-ters (Jaff´e et al. 2015, 2016; Yoon et al. 2017). Stud-ies based on high-resolution H i images show H i richnessconsistent with infall stages indicated by the projectedPSD positions, but the galaxies displaying RPS tails aretypically found beyond the stripping regions (Yoon et al.2017), which is reasonable as the RPS timescale in thestripping region is short (a few tens of Myr, Abadi et al.1999).H i is an excellent tracer of the relatively early stageof environmental processing on star-forming galaxies. Itis the reservoir for forming stars, and sensitive to per-turbations when it is more extended than the stellardisks. Thus, its richness is associated with both thestrength of environmental effects and the progress ofstar formation cessation (Boselli et al. 2006a; Boselli &Gavazzi 2014). High-resolution interferometric imagesfor selected galaxies in nearby clusters, particularly inVirgo, have revealed the morphological and kinematicfeatures of H i in galaxies in response to RPS and otherenvironmental processes (Chung et al. 2009; Yoon et al.2017). They provide valuable constraints to zoom-insimulations modeling physical details of the RPS pro-cess (e.g. Tonnesen & Bryan 2009). On the hand, low-resolution (usually single-dish) but blind and contiguousH i surveys provide opportunities to completely map acluster out to several times the virial radius, and coverstatistically significant number of clusters and galaxies(Haynes et al. 2018; Jaff´e et al. 2016, 2015). Studiesbased on this type of data characterize the statisticalbehavior of galaxies when they are potentially affectedby RPS (Odekon et al. 2016; Yoon & Rosenberg 2015;Hess & Wilcots 2013). These statistical observationalresults help constrain simulations under a cosmologi-cal context, focusing on the role that RPS plays amongmany other processes in the general evolution of galaxies(e.g. Stevens et al. 2019; Yun et al. 2019).A major limitation of the blind H i surveys is the lowresolution, while RPS is predicted to be dependent onthe H i surface density at a given radius in the galaxies(Gunn & Gott 1972). Hence, predicting the H i radialdistribution based on rules extracted from the interfer-ometry data of nearby galaxies will provide some in-sights when one attempts to link the observed total H i mass to the RPS process. Such an analysis has beenoften used in statistical studies with low-resolution H i data on the topic of RPS (Boselli et al. 2018; Jaff´e et al.2016, 2015; Boselli et al. 2014b) . Exploring methodsto enhance the science value of low-resolution H i datais also in line with a preparation for SKA pathfinder H i surveys, for the number of new H i detections will ex-plode but the majority of them will be unresolved inthese surveys (Staveley-Smith & Oosterloo 2015).Recent advances in observations enable us to pre-dict H i radial profiles with higher accuracy than before.Based on H i images for over 500 nearby galaxies, Wanget al. (2016) found that all these galaxies lie tightly ona relation between the H i mass and a characteristic ra-dius of the H i disks ( R HI ); the relation is partly becausethe outer region of H i disks have similar radial profileswhen the radius is normalized by R HI (also see Wanget al. 2014). The similarities seem to be a result fromthe sophisticated balance between different physical pro-cesses, including the accretion, radial flow, and depletionof the H i (Bah´e et al. 2016; Wang et al. 2014). Usingthe median H i radial profile (normalized by R HI ) fromWang et al. (2016), Wang et al. (2020) showed that theH i mass beyond and within the optical radius of galaxiescan be predicted to a high accuracy. Because the ma-jority of the galaxies from the Virgo cluster lie on thesame H i size-mass relation, and exhibit a similar medianH i radial profile as the field galaxies (Wang et al. 2016),we may also use these characteristics to predict the H i radial profile of galaxies in clusters for statistical studiesof RPS.In this paper, we combine the Gunn & Gott (1972)model with the projected PSD, and conduct a statisti-cal analysis of RPS effects on H i -detected galaxies be- The gas is assumed to be distributed exponentially in themulti-zone chemo spectrophotometric model of Boselli et al. (2018,2014b). yond the stripping regions of X-ray detected, massiveclusters. We modify the classical way of estimatingthe anchor forces, by better predicting the H i distribu-tion in individual galaxies. Compared to many earlierstudies which characterized the relatively strong type ofRPS with galaxies showing significant H i deficiencies,we more focus on a relatively early stage of RPS whichis weak and has not strongly depleted the H i or sup-pressed the SFR of galaxies yet. We attempt to evaluatethe statistical significance of weak RPS among the HI-rich population falling into clusters, particularly in thecluster outer regions where many environmental effectsco-exist. We ask out to what cluster centric radius doesRPS occur in the selected clusters? What is the frac-tion of H i -rich galaxies affected by RPS at each clustercentric distance? How different are the galaxies underrelatively weak RPS from the field galaxies with sim-ilar integral SFR? We present the sample selection inSec. 2.1, and the estimate of RPS strengths in Sec 3.We present the results in Sec. 4, discuss in Sec. 5 , andconclude in Sec. 6. Throughout this paper, we assumea Chabrier initial mass function (Chabrier 2003), and aΛCDM cosmology with Ω m = 0 .
3, Ω λ = 0 . h = 0 . i properties, unless specified. DATA2.1.
X-ray detected clusters
The HIFLUGCS and RXGC samples
We use two X-ray samples of nearby clusters, theHIghest X-ray FLUx Galaxy Cluster Sample (HI-FLUGCS, Reiprich & B¨ohringer 2002) and RASS-basedextended X-ray Galaxy Cluster Catalog (RXGCC, Xuet al. in prep).HIFLUGCS selected from the ROSAT All-Sky Survey(RASS) the 63 brightest clusters, with Galactic latitude | b II | > ◦ , and outside the LMC, SMC and Virgo re-gions. Reiprich & B¨ohringer (2002) fit beta models tothe X-ray surface brightness profiles of the high-massclusters S ( r ) = S (0)(1 + r /r c ) − β +1 / , (1)where S ( r ) is the surface brightness at radius r . As-suming the ICM to be in hydrostatic equilibrium andisothermal, they derived R based on the best-fit X-ray surface brightness models, where R is the radiuswithin which the averaged mass density is 200 times thecritical cosmic matter density at the redshift. Their as-sumption of ICM status ignored the local dynamics, butprovides reasonable description for large-scale propertieslike R . The HIFLUGCS clusters have been exten-sively studied in the literature, including their detailedICM distributions (Eckert et al. 2011).RXGCC used a state-of-art algorithm, which includesthe wavelet filtering, source extraction and maximumlikelihood fitting, to extract from X-ray images the lowsurface density groups or clusters, and built a sampleof 764 clusters and groups from RASS (Xu et al. 2018,Xu et al. in prep). In Xu et al. 2018, the R isobtained from the appearance of galaxy clusters and thesignificance radius, which is derived from the growth-curve analysis. They further derived R ≈ . R assuming NFW profiles with a concentration index of4. The RXGCC optimized the measurements for thefaint clusters and groups, and is complementary to theHIFLUGCS sample.We select clusters with redshift z < .
05 to match theALFALFA redshift range, and are left with 45 and 207clusters in HIFLUGCS and RXGCC. The M distri-bution of HIFLUGCS after the redshift selection has 20,50 and 80 percentiles of 1.63, 4.52 and 6.73 × M (cid:12) ,and for RXGCC the percentiles are 0.42, 0.89 and 1.84 × M (cid:12) . We select clusters with M > × M (cid:12) and < × M (cid:12) from HIFLUGCS and RXGCC re-spectively, and are left with 37 and 170 clusters in eachsample. We call the subsamples out of HIFLUCGS andRXGCC the high-mass and low-mass cluster samples re-spectively in the following analysis. Despite the relativedifference in mass, both types of clusters are massiveclusters compared to optically selected groups, as sug-gested by the detection in the X-ray.2.1.2. Parameters that define the cluster region
In the next section, we select member galaxies of theclusters based on the distribution of galaxies on the pro-jected PSD of radial velocity difference as a function ofprojected cluster centric distance.We firstly derive the relation of the escape velocity( v esc, ) as a function cluster centric distance ( d ), assum-ing an Navarro-Frenk & White (NFW, Navarro et al.1997) profile for the dark matter distribution. We as-sume for the NFW profiles a concentration index of 4.Because of projection effects, we replace d with the av-eraged, projected cluster centric distance d proj ∼ π/ d ,and because only radial velocities are observable, wereplace v esc with the averaged, radial escape velocity v esc ∼ v esc, / √
3. The v esc - d proj relation has beenproven to be effective in identifying infalling and settledgalaxies of clusters (Oman et al. 2013).In this paper, a galaxy is identified as a (settled or in-falling) member of a cluster if d proj < R , and the ra-dial velocity difference | ∆ v rad | is smaller than the valueof v esc expected at d proj . 2.2. HI detected galaxies
Selection from ALFALFA, MPA / JHU catalog, andGSWLC-2
ALFALFA (Haynes et al. 2018) mapped 7000 deg inthe southern sky with a typical rms of 1.6 mJy at a chan-nel width of 18 km / s (after smoothing). The angularresolution (beam size) is 3.5 arcmin in full-width half-maximum. ALFALFA provided each detected galaxythe integral H i mass, M HI . We estimate the charac-teristic radius R HI , based on the H i size-mass relation(Wang et al. 2016), where R HI is the semi-major axisof the 1 M (cid:12) pc − isophote of H i disks. The ALFALFAcatalog has assigned each H i detection an optical coun-terpart from SDSS or DSS, based on the projected dis-tance, redshift, color, morphology, and additional scien-tific judgement from its authors (Haynes et al. 2011).We will use the optical coordinates of the ALFALFAdetected galaxies in cross-matching with other galaxycatalogs.The MPA / JHU catalog (Kauffmann et al. 2003) pro-vides spectroscopic measurements of galaxies from DataRelease 7 of SDSS (Abazajian et al. 2009). We will usethe spectral indices D , and equivalent width of theH α emission ( EW ( Hα ), positive values for emissionshere) to indicate the star forming status in the galacticcenter. D is produced mainly because spectrum tothe blue side of 4000 ˚ A is strongly absorbed by metalsin the atmosphere of old stars. So low values of D suggest existence of a significant amount of young stellarpopulation. Hα emission is produced by ionizing radia-tion from O stars with a typical life time of 10 Myr. Wealso use the photometric measurements of g -band R (semi-major axis of the 25 mag arcsec − isophote), i -band R (half-light radius), and r -band R (90%-lightradius), R and R d (the scale-length). We calculate µ ∗ , the averaged stellar surface density within the i -band R , and the concentration index R /R in the r -band.The GALEX-SDSS-WISE Legacy Catalog 2 (GSWLC-2, Salim et al. 2016) selected galaxies overlapping inGALEX (Martin et al. 2005), SDSS and WISE (Wrightet al. 2010). It estimated the integral star formationrate (SFR) and stellar mass ( M ∗ ) of galaxies by fittingstellar synthesis models to the broad-band spectral en-ergy distribution ranging from the mid-infrared to thefar-ultraviolet. The SFRs are mainly indicated by theattenuation corrected ultraviolet light, with sensitivityon a timescale of ∼
100 Myr.We firstly search for member galaxies of each clusterfrom the ALFALFA catalog, using the criterial based on R and v esc . We match the optical coordinates of theAFALFA detected galaxies to the MPA / JHU catalog,and then to GSWLC-2, by requiring the projected dis-tance to be less than 3 arcsec, and the radial velocity dif-ference less than 200 km/s. These cross-matching resultin 158 and 144 galaxies in high- and low-mass clusters.We note that the sample size is much smaller a few pre-vious studies on ALFALFA and SDSS detected galax-ies in X-ray clusters (e.g. Odekon et al. 2016), mostlybecause of our selection by v esc instead of using groupcatalogs built with friend-of-friend member finders (e.g.Yang et al. 2007).Motivated by the previous results that environmentaleffects on gas content and SFRs are most significant inlow-mass galaxies (Woo et al. 2017; Boselli et al. 2014b;Boselli & Gavazzi 2014; Catinella et al. 2013; Wetzelet al. 2013; Gavazzi et al. 2010), we select the galaxieswith log M ∗ /M (cid:12) <
11. In order to focus on the H i -richgalaxies under active environmental processing insteadof already being fully processed, we further limit thesample to galaxies with R HI > R . By this selection, wefocus on RPS of the H i gas and may miss galaxies whichhave little H i but the ionized gas still being stripped bythe ram pressure (e.g. NGC 4569 in the Virgo cluster,Chung et al. 2009; Boselli et al. 2018).These selection criteria reduce the sample to 142 and128 galaxies in the high and low-mass clusters, which werefer to as the cluster sample.2.2.2. The control sample and final main sample
We first built a pool of all galaxies with redshift be-low 0.05 and detected simultaneously in the ALFALFA,MPA/JHU and GWSLC-2 catalogs. It includes 13273galaxies. For each galaxy in the cluster sample, we ran-domly select 8 control galaxies with replacement fromthe galaxy pool, with M ∗ , SF R , µ ∗ and z differing byless than 0.15 dex, 0.2 dex, 0.25 dex and 0.002 respec-tively. We require each galaxy from the cluster sampleto have at least 5 unique control galaxies, which reducesthe sample to 134 and 109 galaxies for the high- andlow-mass clusters. This is our final, main sample ofgalaxies.
We show their distributions in the diagrams ofSFR, M HI , and µ ∗ versus M ∗ (Fig. 1). They are by se-lection strongly biased toward the H i -rich, star-forming,low surface density population, and do not representthe general galaxy population in clusters which are onaverage older and gas poorer than the field galaxies.These galaxies are useful when searching for signaturesof the relatively early and weak environmental process-ing prevalent in the relatively outer region of clusters,which may just start to deviate galaxies from the pa-rameter space of unperturbed galaxies. They are on theother hand, highly incomplete when studying the rela-tively strong environment effects (including strong RPS) which can quick move galaxies below the detection limitof ALFALFA.These galaxies are from 7 high-mass clusters and 19low-mass clusters. We list properties of these clusters,including the number of selected galaxies from each clus-ter, in Table 1. Among the galaxies from high-mass clus-ters, 43% of them come from the Coma cluster, another49% come from A1367, A2147 and MKW8, and the restfrom the remaining 3 clusters. For low-mass clusters,the galaxies are more evenly contributed by each clus-ter, with a median number of 5 per cluster. ANALYSIS3.1.
ICM density and ram pressure
The ram pressure stripping (RPS) strength of the ICMis calculated as ρ (∆ v ) , where ρ is the mass density ofthe ICM and ∆ v is the relative velocity between theICM and the galaxy.The density distribution of an isothermal ICM is re-lated to the beta model of the X-ray surface brightnessaccording to ρ ( r ) = ρ (0)(1 + r /r c ) − β/ . (2) r c and β are the same as the model of the X-ray surfacebrightness, and ρ (0) can be derived by integrating theprofile out to R , and comparing the result with thegas mass ( M gas, ) expected from scaling relations. Wecan use the scaling relation from Ettori (2015) to esti-mate M gas, from M , the mass within R . So thekey parameters needed are R and the parameters ofthe beta model ( β and r c ), which are derived in differentways for the high-mass and low-mass clusters.Because nearly one third of the X-ray luminous, high-mass clusters have cool cores, deviating from the hy-drostatic equilibrium and isothermal state, Eckert et al.(2011) use a scaling relation to estimate R from thevirial temperature of the clusters (Hudson et al. 2010).The median ratio of R from Reiprich & B¨ohringer(2002) over R from Eckert et al. (2011) is 1.44 ± R /R = 1 .
50 expected from an NFWprofile, assuming a halo mass of 3 × M (cid:12) and a con-centration of 4. Eckert et al. (2011) combined XMM-Newton and Chandra data to derive the X-ray surfacebrightness profiles for the high-mass clusters. Because asingle-beta model does not describe the shape of the ra-dial profile in cool core clusters well, Eckert et al. (2011)fit a double-beta model for cool core clusters, and a sin-gle beta model for No-cool core clusters. We use the(double-) beta models from Eckert et al. (2011) to de-rive ICM densities.Following Xu et al. (2018), we assume a single betamodel for the low-mass clusters, fixing β = 2 / r c = logM * ( M )3210123 l o gS F R ( M / y r ) xGASSH- M L- M logM * ( M )8.08.59.09.510.010.5 l o g M H I ( M ) logM * ( M )78910 l o g * ( M / k p c ) Figure 1.
Scaling relations of selected cluster galaxies. From left to right, we plot the relations of SFR, M HI and µ ∗ as afunction of M ∗ for galaxies in low-mass (cyan) and high-mass (orange) clusters. The xGASS (Catinella et al. 2018) sample of M ∗ and z selected galaxies are plotted in grey as a reference. The upper limits of M HI in the xGASS sample are plotted asvertical bars. R /
7, where R has been obtained from the curve-of-growth fitting. Then we estimate M gas and ρ (0) in asimilar way as for high-mass clusters.We approximate the ram pressure as P = ρ ( d proj ) ∆ v rad .Such approximation has a few uncertainties, including • Projection effects. ρ ( d proj ) can only be viewed asan upper limit of ρ ( d ). Similarly, ∆ v rad can onlybe viewed as a lower limit of ∆ v . Despite these ob-vious offsets, we find that ram pressure estimatedin this way still leads to useful analysis. We willfurther discuss the influence of the projection ef-fects on our main results in Sec. 5. • Extrapolation effects. The ROSAT data typicallydoes not detect ICM out to 2 R . For high-massclusters, the typical maximum radius to detect X-ray flux in a cluster is ∼ . R (Reiprich &B¨ohringer 2002), and for low-mass clusters, it is ∼ . R (Xu in prep.). So when d proj is largerthan the maximum detectable radius, ρ ( d proj ) hasuncertainties due to extrapolation. • Sub-structures in the ρ distribution. These struc-tures are typically associated with infalling groupsor galactic mergers which induce shocks in theICM (Ruggiero et al. 2019; Roediger et al. 2014;Tonnesen & Bryan 2008; Markevitch & Vikhlinin2007), and sometimes significantly raise the locallevel of ram pressure (Kenney et al. 2004). Thistype of shocks were found in some of our selectedclusters (e.g. A 1367, Ge et al. 2019). As most ofthe cluster merger associated shocks found so farare distant ( > <
3, Markevitch et al.2005; Markevitch & Vikhlinin 2007; Ogrean et al.2014; Itahana et al. 2015; Dasadia et al. 2016), we assume that the filling factor of strong shock frontsto be small in a typical cluster at low redshift, anddo not significantly affect statistical analysis. • Isothermal assumption. Because the temperaturedrops in the core region of high-mass, cool-coreclusters, ρ in the same region are likely under-estimated. But because the temperature varia-tions are typically less than twice in the core regionof clusters in the high-mass cluster sample (Hud-son et al. 2010), and the X-ray power emissivityscales with ρ T . (so for the same X-ray surfacedensity, ρ ∼ T − . ), the under-estimation of ρ should be small ( < . HI density profile and anchor force
The anchor force to hold the interstellar medium gasat a radius r in the galactic disc plane can be calculatedas F r = 2 πG (Σ ∗ ,r + Σ HI ,r )Σ HI ,r , (3)where Σ ∗ ,r and Σ HI ,r are the stellar and H i surface den-sity at r . This is a modified form of the Gunn & Gott(1972) formalism, to take into account the self-gravity ofthe H i gas, which cannot be ignored in the outer disks.Similar modifications can be found in Stevens & Brown(2017); Fujita (2004); Abadi et al. (1999).We estimate the anchor forces F R and F RHI at twocharacteristic radii, R and R HI . We use the methodoutlined in Wang et al. (2020) to estimate Σ HI ,R foreach galaxy. The method makes use of the H i size-massrelation, and the homogeneous shape of H i radial pro-files in the galactic outer region. The method works bestwhen the given radius is within the exponential droppingpart of the H i surface density profile, and R is a goodoption of such radius. Following the previous work ofJaff´e et al. (2018) and others, we assume an exponential Name N ga RA DEC Redshift M R R σ C β N H (0) N H, (0) r c r c, (deg) (deg) (10 M (cid:12) ) (Mpc) (Mpc) ( km/s ) ( cm − ) ( cm − ) (kpc) (kpc)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)High-mass clustersA1367 26 176.1903 19.7030 0.022 3.95 1.49 0.95 633.9 0.62 0.0011 - 290 -A2052 6 229.1846 7.0211 0.035 2.15 1.22 0.87 516.8 0.75 0.0016 0.0250 159 32A2063 5 230.7734 8.6112 0.035 3.15 1.38 0.97 587.5 0.73 0.0018 0.0064 194 54A2147 24 240.5628 15.9586 0.035 3.36 1.41 1.00 600.3 0.37 0.0022 - 61 -COMA 58 194.9468 27.9388 0.023 13.46 2.24 1.51, 956.9 0.65 0.0034 - 249 -MKW3 1 230.4643 7.7059 0.045 3.36 1.41 0.98 600.3 0.63 0.0048 0.0172 86 27MKW8 15 220.1596 3.4717 0.027 2.31 1.24 0.82 529.4 0.50 0.0026 - 94 -Low-mass clustersRXG306 6 129.4660 25.1040 0.028 1.06 1.02 0.67 451.8 0.66 0.0031 - 96 -RXG325 1 138.9910 17.5620 0.029 0.80 0.93 0.61 410.6 0.66 0.0029 - 87 -RXG327 4 139.9350 33.7620 0.023 0.43 0.75 0.49 333.9 0.66 0.0027 - 70 -RXG367 1 155.4160 23.8950 0.040 1.22 1.09 0.72 474.1 0.66 0.0030 - 102 -RXG389 2 162.5900 0.2790 0.041 0.95 1.01 0.66 434.9 0.66 0.0028 - 94 -RXG395 6 164.6220 1.6030 0.039 0.91 0.99 0.65 429.8 0.66 0.0028 - 93 -RXG401 11 167.6670 28.7090 0.032 0.99 1.01 0.66 441.7 0.66 0.0030 - 94 -RXG411 1 169.0880 29.3040 0.047 1.43 1.16 0.76 499.6 0.66 0.0029 - 109 -RXG457 7 181.0140 20.2900 0.023 0.38 0.72 0.47 320.9 0.66 0.0026 - 68 -RXG515 7 200.0590 33.1510 0.037 0.89 0.98 0.64 426.6 0.66 0.0029 - 92 -RXG527 7 202.4190 11.7790 0.023 0.49 0.78 0.51 348.4 0.66 0.0028 - 73 -RXG538 9 203.6270 34.7030 0.025 0.39 0.73 0.48 323.0 0.66 0.0026 - 68 -RXG597 6 223.2440 16.7010 0.044 1.46 1.17 0.77 502.9 0.66 0.0030 - 109 -RXG615 3 228.1770 7.4190 0.046 1.25 1.11 0.73 477.7 0.66 0.0029 - 104 -RXG62 3 18.2650 15.4990 0.043 1.26 1.11 0.73 478.7 0.66 0.0029 - 104 -RXG632 4 233.1070 4.7720 0.039 1.62 1.20 0.79 520.6 0.66 0.0031 - 112 -RXG651 6 241.2110 17.7320 0.035 1.93 1.26 0.83 553.0 0.66 0.0033 - 119 -RXG653 3 241.3810 16.4410 0.042 0.76 0.94 0.61 404.4 0.66 0.0027 - 88 -RXG931 7 333.7340 13.8340 0.026 0.46 0.77 0.51 341.8 0.66 0.0027 - 72 - Table 1. Cluster properties.
Column (1): name. Column (2): number of galaxies included in our main sample.Column(3)-(6): RA, DEC, z , M and R of the cluster centers; high-mass cluster values are taken from Reiprich & B¨ohringer (2002),and low-mass cluster values from Xu et al. (2018). Column (7), (9) (12) and (13): R and (double-)beta model parameters β , and r c ( r c, ); high-mass cluster values are taken from Eckert et al. (2011), and low-mass values from Xu et al. (2018). Whenonly a single-beta model is available, the parameters for the second beta component are written as -. Column (7): velocitydispersion of the clusters, estimated from M (see Sec. 2.1.1 ). Column (10) and (11): central density of ICM for (double-)betamodels, estimated from M gas, and the (double-)beta models (see. Sec. 3.1); ρ H = 1 . N H m p , where m p is the mass of proton. disk for the stars, so that the central stellar surface den-sity Σ ∗ , = M ∗ / πR d , and Σ ∗ ,r = Σ ∗ , e − r/R d , where R d is the r -band scale-length.There are also a few uncertainties related to the aboveestimates. • Assumption of universal H i radial profiles in theouter disks. Galaxies in clusters may have per-turbed H i profiles. Luckily, Wang et al. (2016)found that galaxies from the VIVA (VLA Imag-ing of Virgo Spirals in Atomic Gas, Chung et al.2009) survey lie on the same H i size-mass relationas other galaxies. We further test our method of estimating Σ HI ,R with the VIVA data. Whengalaxies are selected in the same M ∗ and R HI /R range as our main sample (in total 16 galaxies), themedian offset between the predicted and observedvalues of Σ HI ,R is 0.08 ± HI ,R hasa scatter of 0.31 dex, so the prediction indeed helpsconstrain the value. • Only disc stars and H i gas are considered in thegravitational potential. We ignored gravity fromthe bulge stars, molecular gas and dark matter.Because we are considering the anchor forces in a relatively distant outer region, the gravity froma central spheroidal bulge is usually small (Abadiet al. 1999). The molecular disks usually do notextend beyond R and should contribute little tothe disk gravity. The contribute of the dark matterto the gravity that holds gas in the disc mid-planeshould be negligible due to the low volume density,which was confirmed in Jaff´e et al. (2018). • Over-estimates of the disk masses. By ignoringthe bulge, we may over-estimate Σ ∗ , , and there-fore over-estimate the anchor force. We use thelinear equation of Catinella et al. (2013) whichwas based on the galactic decomposition catalogof Gadotti (2009) to roughly convert the concen-tration index R /R to the bulge-to-total massratio B/T . We test by using the derived 1 − B/T to scale down Σ ∗ ,r and recalculating the anchorforces. We do not find the results presented laterin Sec. 4 to significantly change after this treat-ment. This is because by selection our galaxiesare disk-dominated, with R /R having 10, 50and 90 percentiles of 1.97, 2.31 and 2.73, corre-sponding to estimated B/T of 2%, 17% and 36%.However, we note that estimating
B/T in this wayis crude, particularly because our galaxies extendto much lower M ∗ than the limit ( > M (cid:12) ) ofGadotti (2009). • We ignored the protection / pressure from thecircum-galactic hot gas halo, which needs tobe stripped before the H i gas directly feels theram pressure. As previous studies suggested thatstrangulation of galaxies due to halo gas removalstarts at 5 R from the cluster center (Bah´e et al.2013), the problem of ignoring pressure from thehalo gas is mitigated.3.3. The strong, weak, and no-RPS galaxies
We can view the ratio between the ram pressure andthe anchor force as a measure of RPS strength. Wedivided our sample of galaxies into 3 types with the fol-lowing criteria: • Strong-RPS:
P > F R , including 17 (13%) and3 (3%) galaxies in high-mass and low-mass clus-ters, respectively. • Weak-RPS: F RHI < P < F R , including 70(52%) and 33 (30%) galaxies in high-mass and low-mass clusters, respectively. • No-RPS:
P < F
RHI , including 48 (35%) and 73(67%) galaxies in high-mass and low-mass clusters,respectively. Atlases of SDSS images and ALFALFA H i spectrumof the 20 strong-RPS galaxies can be found in Sec. A.1and A.2 in the Appendix.By definition we expect that on average the strong-RPS galaxies are strongly stripped by ram pressure nearor on the stellar disks, the weak-RPS galaxies just startto feel the ram pressure in the very outer region of theirH i disks, and no-RPS galaxies are not strongly affectedby ram pressure in either the H i or stellar disks.Because both ram pressure and anchor force have un-certainties in the estimates, the division into these threegroups should be viewed as being statistically represen-tative instead of being absolutely accurate. We also re-mind that all the galaxies in the main sample are AL-FALFA detected, H i -rich galaxies, and do not representthe general galaxy population. The sample should havealso significantly missed the galaxies which suffer fromstrong RPS and become highly deficient in H i . Thegalaxies in this sample are thus selected to search forcandidates under relatively weak RPS on the H i and ata relatively early stage of being processed by the envi-ronment, when they are moving through the clusters. RESULTS4.1.
Projected PSD positions versus internal surfacedensities and the determination of RPS strength
Previous studies have demonstrated that the pro-jected PSD is not only reliable for identifying clustermembers, but also useful to statistically assign clustermembers to different infall stages (Oman et al. 2013).Virialized galaxies tend to lie in a triangular regionaround the cluster center in the projected PSD, whilegalaxies that are infalling for the first time tend to havehigher ∆ v at a given d proj . For convenience, we callthem virialized and infalling galaxies respectively. Wekeep in mind that galaxies may transport between thepericentre and apocentre (the “back-splash” galaxies)several times before finally virialized. According to theliterature, nearly half of the galaxies at small | ∆ v rad | (e.g. < σ C ) and slightly beyond the virialized region(1-2 R ) can be back-splash objects (Mahajan et al.2011).In the bottom row of Fig. 2, the different RPS typesseparate well on the projected PSD. We further dividethem into infalling and virialized types, and summarizetheir numbers in Tab. 2. In Tab. 2, the strong-RPSgalaxies are not divided according to their infall sta-tus, because they are found continuously across the pro-jected PSD. Most of the strong-RPS galaxies are foundin the high-mass clusters, and in the infalling region.They dominate the H i -rich galaxy population of high-mass clusters when d proj < . R . The weak-RPSgalaxies are also found mainly in the infall region, butextend further in high-mass clusters than in low-massclusters. They are rarely found beyond d proj /R ∼ . ∼
40% among thethree RPS types, top row of Fig. 2) at d proj /R ∼ d proj > R and∆ v rad /σ C <
1) in high-mass clusters. They are dom-inantly found in two regions of the low-mass clusters:the outskirts where d proj > . R , and the virializedregion where d proj > . R .In other panels of Fig. 2, we can see that the strong-RPS galaxies tend to have low Σ ∗ ,R + Σ HI , R25 andlow Σ HI , R25 , hence low anchor forces at R . The weakand no-RPS galaxies are less different from each otherin these properties.In summary, the RPS strength strongly depends onthe cluster mass and the projected PSD position. Suchstrong dependence on PSD positions were noticed be-fore (Jaff´e et al. 2018; Yun et al. 2019). Although theRPS strength is determined by both the ram pressureand the anchor force, the former (reflecting the externalenvironments) seems to play a dominant role in regulat-ing the evolution of H i -rich galaxies. The regulating roleof anchor forces (reflecting the internal properties) risesonly when the RPS is strong, probably after an earlierstage of weak RPS, which has reduced Σ HI , R25 and thusthe anchor forces.4.2.
HI mass and central SFR compared to controlgalaxies
As the reservoir of material for star formation, theH i richness is strongly correlated with the star-formingstatus of field galaxies, and determines the future poten-tial of forming stars. A lower M HI than control galaxieswhich have similar integral SFR would be the signatureof recent, violent removal of the H i gas, and predictiveof a drop in SFR in the near future.Past studies (Kauffmann et al. 2003; Li et al. 2015)showed that some spectral indices are good tracers ofthe recent star forming activities. Higher specific SFRsare typically associated with lower D and higher EW ( Hα ). We remind that the control galaxies arematched in the global SFR to the main sample, and theSDSS spectral indices are measured for the galactic cen-tral regions. So if the main sample galaxies have lowercentral D and higher central EW ( Hα ) than the con-trol galaxies, it can be interpreted as these galaxies hav-ing higher central SFR, but lower SFR in the outer re-gions when compared to the control galaxies. Such anoutside-in star formation cessation is often linked to gasstripping (Koopmann & Kenney 2004b,c; Boselli et al. 2006a,b; Fossati et al. 2013; Fabello et al. 2012). Onthe other hand, if strong central starbursts happened inthe past 10 Myr, galaxies are expected to have highercentral EW ( Hα ) for their central D (Li et al. 2015).We compare the M HI and central SFR of main andcontrol samples in Fig. 3 and 5. We focus on the extentof differences each of the RPS sub-samples (strong, weakand no) shows with respect to their control galaxies.However, we will refrain from interpreting the appar-ent differences between the three sub-samples, because M HI and SFR depends on several additional parameters(e.g. M ∗ , disk-bulge structure) which are not matchedbetween the sub-samples.Strong-RPS galaxies are shown in the third row ofFig. 3, which are mostly observed in the high-massclusters. They tend to have on average higher cen-tral EW ( Hα ) but similar central D , indicative ofenhanced central starbursts compared to their controlgalaxies. They also have lower M HI than the controlgalaxies.Three strong-RPS galaxies in the high-mass clus-ters have been excluded from this analysis because notenough control galaxies could be found (atlas in Fig. 10in the appendix). Two of these galaxies have signifi-cantly higher SF R than all other galaxies with similar z , M ∗ and µ ∗ in the control galaxy pool. The abnor-malities in SFR are consistent with the enhanced central Hα emission in the strong-RPS galaxies which have con-trol galaxies. The remaining galaxy without a controlgalaxy is an elliptical galaxy from the SDSS image. Ithas low integral SF R ∼ − . M (cid:12) yr − , but significant M HI ∼ . M (cid:12) , which is 0.46 dex higher than expectedfor its M ∗ ∼ . M (cid:12) and SFR (Saintonge et al. 2016).Like in other H i -rich early-type galaxies, its H i may havebeen obtained through mergers and maintained in theform of an extended disk, which does not easily flow tothe galaxy center to fuel the star formation there (Serraet al. 2012).The weak-RPS galaxies in the high-mass clusters haveon average slightly higher central EW ( Hα ) than thecontrol samples (second row of Fig. 3). We find similarresults when only selecting the infalling galaxies (sec-ond row of Fig. 4), but do not have a large enough sam-ple to conclude anything about the virialized weak-RPSgalaxies. Similar results are found in the low-mass clus-ters (second row of Fig. 5, and second row of Fig. 6 ).None of the weak-RPS subsets show significantly differ-ent M HI distribution compared to the control galaxies.The no-RPS galaxies do not significantly differ fromtheir control galaxies in the distributions of central EW ( Hα ), central D , or M HI . This result holdswhen selecting either virialized or infalling galaxies, in0 Cluster type Galaxy typeInfalling Virializedno-RPS Weak-RPS Strong-RPS Weak-RPS no-RPS(1) (2) (3) (4) (5) (6)High-mass 42 63 17 7 6Low-mass 51 24 3 9 22
Table 2. Galaxy numbers in different types.
Column (1): type of clusters where the galaxies are found. Column (2)-(7):galaxy type. Column (2)-(4): Numbers of weak, strong and no-RPS galaxies within the virialized regions. Column (5)-(7):numbers of weak, strong and no-RPS galaxies beyond the virialized regions. f r a c H I , R H I , R + * , R d proj / R | v r a d |/ C high-mass clusters f r a c H I , R H I , R + * , R d proj / R | v r a d |/ C low-mass clusters Figure 2.
Distribution of galactic properties as a function of cluster centric radius. Galaxies have been identified as weak(green), strong (red) and no-RPS (purple) types, and further classified as within (tri-down markers) and beyond (circles) thevirialized regions of clusters. From top to bottom, we plot the fraction of galaxies in each RPS type, the H i surface densityat R (Σ HI ,R , in unit of M (cid:12) pc − ), the sum of H i and stellar mass surface density at R (Σ HI ,R + Σ ∗ ,R , in unit of M (cid:12) pc − ), and the projected PSD. In the projected PSDs, v esc assuming an NFW potential and the border of the virializedregion (Mahajan et al. 2011; Jaff´e et al. 2015) are plotted as dashed lines. both low-mass and high-mass clusters (Fig. 5, Fig. 3 andFig. 6). DISCUSSIONCombining HI data of galaxies with extended X-raydata of clusters was conducted for individual clusters(e.g. Jaff´e et al. 2015) before, but this paper for thefirst time works on a relatively complete overlap between the largest H i blind survey ALFALFA and the largestX-ray blind survey ROSAT. The galaxies were selectedfrom two complete catalogs of clusters with extended X-ray emissions; particularly the RXGCC sample is latelybuilt with a noval algorithm to search for faint clustersfrom the whole ROSAT dataset. The extended X-rayfluxes ensures M , R and n ICM to be derived inrelatively accurate ways. The results presented in this1 f r a c no-RPS (N=48) f r a c weak-RPS (N=70) D f r a c log EW ( H )( Å )0.04 strong-RPS (N=17) log M HI ( M )0.02 Figure 3.
Comparison of star formation status and H i masses with control galaxies in high-mass clusters. Fromthe left to the right, the histograms of central D , central EW ( Hα ) and log M HI are plotted in each column. From thetop to the bottom, we show histograms for the No- (ma-genta), weak- (green), and strong- (red) galaxies, respec-tively. The corresponding control sample for each sub-sampleof cluster galaxies is plotted as black histograms, and the K-Stest probability for the comparison between cluster and con-trol galaxies are denoted in each panel. The median valuesare marked by the dashed lines. study can thus be compared to simulations in a rela-tively convenient way in the future, by producing mockcatalogs with similar survey parameters as ALFALFAand ROSAT.We point out that, the major goal of this study isneither characterizing galactic features under RPS, norproviding a census of galaxies under strong RPS, for thesample is strongly biased against H i deficient galaxies.Instead, we examine whether the observed H i and SFRproperties are consistent with expectations when galax-ies are under RPS, as a test of our classification method(Sec. 5.2); we discuss the role that weak RPS might playin cluster galaxy evolution, based on the PSD distribu-tion and frequency of weak-RPS galaxies in our sample(Sec. 5.3).5.1. Past studies on HI and SFR properties of galaxiesin the Coma and A1367 clusters
We note that a considerable fraction of the main sam-ple galaxies come from the Coma and A1367 clusters. f r a c no-RPS:infalling (N=42) D f r a c log EW ( H )( Å )0.01 weak-RPS:infalling (N=63) log M HI ( M )0.64 Figure 4.
Distribution of star formation status and H i masses with control galaxies in high-mass clusters. Similarto Fig. 3, but only for infalling galaxies. We do not presentfigures for the virialized, weak- or no-RPS types, because ofsmall sample sizes. f r a c no-RPS (N=73) D f r a c log EW ( H )( Å )0.01 weak-RPS (N=33) log M HI ( M )0.81 Figure 5.
Distribution of star formation status and H i masses with control galaxies in low-mass clusters. Similarto Fig. 3, but for galaxies in low-mass clusters. We do notpresent figures for the strong-RPS galaxies because of smallsample size. The H i and SFR properties of galaxies in these two clus-ters have been extensively studied before.Studies based on wide-field, blind H i surveys foundthat, the distribution of HI detected galaxies is muchless concentrated on the cluster centers than opticallydetected galaxies (Cortese et al. 2008), and galaxies aremore H i -deficient when the local densities are higher(Gavazzi et al. 2013). Studies based on ultraviolet, in-frared and H α images consistently found the outside-2 f r a c no-RPS:infalling (N=51) f r a c weak-RPS:infalling (N=24) D f r a c log EW ( H )( Å )0.30 no-RPS:virialized (N=22) log M HI ( M )0.99 Figure 6.
Distribution of star formation status and H i masses with control galaxies in low-mass clusters. Similarto Fig. 5, but no-RPS galaxies are further classified into in-falling and virialized types, and we also present the infalliing,low-RPS galaxies. We do not present figures for the virial-ized, low-RPS galaxies because of small sample size. in suppression of SFR at high local densities (Cybulskiet al. 2014; Gavazzi et al. 2013). These statistical resultssupport a picture where ram pressure plays an effectiverole in removing H i from galaxies.Interferometric H i images further confirmed the on-going RPS for a number of galaxies. The H i disks ofobserved galaxies in the Coma and A1367 clusters oftendisplay lopisided morphologies, displaced center fromthe optical counterparts, and / or smaller extension thanthe optical disks (Bravo-Alfaro et al. 2000b, 2001a; Scottet al. 2010, 2018). The ubiquitous RPS in the Comacluster was also confirmed from observing the warm ion-ized gas with deep H α images (Gavazzi et al. 2018; Yagiet al. 2017, 2010).5.2. Relating the observed trends in this study to RPS
We find that, only the strong-RPS galaxies show ev-idence for a significant reduction in M HI compared tothe control galaxies; strong- and weak-RPS galaxiesshow higher central EW ( Hα ) in the galactic center thanthe control galaxies; no-RPS galaxies are no differentfrom the control galaxies in either M HI or the central EW ( Hα ). We discuss possible physical mechanisms re-lating RPS to these observed differences. 5.2.1. Differences in M HI The strong-RPS galaxies have on average lower M HI than the control galaxies, suggesting a fast removal ofH i . H i does not directly form stars, but fuels star for-mation as part of the circle of gas accretion, gas inflow,star formation and outflow (Krumholz et al. 2018; Wanget al. 2020). So at a given M ∗ , SFR is adjusted to theavailable H i on a timescale longer than the free fall timeof molecular gas (Krumholz et al. 2012), but shorterthan the H i depletion time (Saintonge et al. 2017). Un-der strong RPS, the gas removal can be much quickerthan the capability for SFR to be adjusted to M HI . Forextreme cases of galaxies in the stripping region of theprojected PSD, gas removal has a timescale of a few 10 yr (Abadi et al. 1999). Our result is consistent with pre-vious findings that the detection rate and mass fractionof H i drops much more quickly than the specific SFRnear the cluster centers (Fabello et al. 2012; Jaff´e et al.2015). Cross-matching with nearby galaxies which areknown to display RPS gas tails, we confirm that at least4 out of the 17 strong-RPS galaxies are indeed amongthose with tails (see Sec. A.3 of Appendix). This confir-mation rate should be viewed as a lower limit, for not allour clusters have been searched for RPS features in themorphology before. Gas removal in low- and no-RPSgalaxies seems to be much slower. One direct reasonis likely that a smaller radial range of H i is affected inlow-RPS galaxies than in high-RPS galaxies. Addition-ally, there is a time lag between gas being stripped offthe disk plane and reaching the escape velocity of thegalaxy, which is longer when the ram pressure is weaker(Roediger & Br¨uggen 2007). In addition to RPS, tidalstripping or harassment may also contribute to reduc-ing M HI in the weak- and no-RPS galaxies because theirvelocities are lower than those of the strong-RPS galax-ies. Yet the combined efficiency of removing H i is notas high as in the strong-RPS galaxies.5.2.2. Differences in the central SFR
The strong-RPS and low-RPS galaxies show highercentral EW ( Hα ) in the center when compared to theircontrol galaxies, consistent with the consequence ofRPS. Higher values of central EW ( Hα ) compared to thecontrol sample could indicate either recently enhancedcentral SFRs, or suppressed SFRs in the outer disks.If the strong-RPS or low-RPS galaxies had on averagelower central D values than their control galaxies,then it would be strong evidence for suppressed SFR inthe outer region. But we observed no significant dif-ference in central D between the low-RPS (strong-RPS) galaxies and their control galaxies. Consideringthe fact that D may not be as sensitive as EW ( Hα )3to small changes in the sSFR, we discuss both possibil-ities regarding whether SFR is suppressed in the outerdisks.If the SFR is indeed suppressed in the outer regionof strong- and low-RPS galaxies, then it strongly sup-ports a scenario of outside-in quenching as a result ofoutside-in gas stripping. Such a stripping scenario isconsistent with the nature of RPS, because the anchorforce is weaker at larger galactic radius. RPS couldthen perfectly explain the central EW ( Hα ) enhance-ments in strong- and weak-RPS galaxies compared tono-RPS galaxies.It is also plausible that the strong- and weak-RPSgalaxies have enhanced central SFR instead of (or inaddition to) suppressed outer SFR. Theoretical stud-ies predicted the enhancement of SFR when pressurefrom the ICM or shocks at the ICM-disk interface com-press the cold gas, before the gas is severely stripped(Ramos-Mart´ınez et al. 2018; Safarzadeh & Scannapieco2017; Steinhauser et al. 2016). In several simulationsthe process is accompanied by significant gas inflows,generated directly by oblique shocks (Ramos-Mart´ınezet al. 2018), or loss of angular momentum in interac-tion with the ICM (Tonnesen & Bryan 2009), which re-sults in enhanced central SFR (Bekki 2014; Tonnesen& Bryan 2012; Kronberger et al. 2008). Observationalstudies also found enhanced SFR prevalent in galaxiesundergoing ram pressure (Roberts & Parker 2020; Vul-cani et al. 2018; Jaff´e et al. 2016). But the preferredlocation within galaxies for SFR to be enhanced is de-bating, which can be in the ICM-disk interface (Ramat-soku et al. 2019; Lee et al. 2017; Ebeling et al. 2014),in the center (Mok et al. 2017), and at all galactic ra-dius (Vulcani et al. 2020). The enhanced central SFRin strong-RPS galaxies is thus not against the literaturefindings.But the mechanism of enhancing central SFR mightbe more complex in the weak-RPS galaxies. As the low-RPS galaxies tend to be in the relatively outer regionof the cluster, tidal interactions with both the cluster(Byrd & Valtonen 1990) and surrounding galaxies (Mi-hos et al. 1992) might also play a role by driving gasinflows. However, interestingly, in low-mass clusters,the virialized, no-RPS galaxies do not show enhancedcentral SFR, although they are in a similar d proj rangeand thus similar cluster gravities and local densities asthe infalling, low-RPS galaxies. These virialized, no-RPS galaxies should even suffer from more effective tidalinteraction with the surrounding galaxies, due to theirlower velocities than the infalling, low-RPS galaxies. Yetthey do not show as much enhanced central SFR as theinfalling, low-RPS galaxies. It is possible that galactic tidal effects even in the outer region of these massiveclusters are generally weak (Boselli et al. 2006a), andtake the form of harassment (Moore et al. 1996, 1998)instead of interactions, which heat the disks but do notefficiently drive gas inflows. Meanwhile, tidal interac-tion with the cluster may not be so efficient at theserelatively large distances, and indeed we find that allof the infalling, low-RPS galaxies have a cluster pertur-bation strength ( M /M ∗ )(( π/ ∗ ( R /d proj )) lowerthan the critical value of 0.1 for triggering nuclear ac-tivities (Byrd & Valtonen 1990). It implies that rampressure may be the mechanism that enhanced the cen-tral SFR in the weak-RPS galaxies.5.2.3. Feasibility of the RPS strength parameter
As discussed above, cluster galaxies under strongerRPS exhibit more significant difference in M HI and cen-tral SFR from their control galaxies. It is worth notingthat the three RPS types occupy different regions ofthe projected PSD in high-mass and low-mass clusters.The difference is expected because σ C of the high-massclusters is higher, leading to higher ∆ v rad at a givenprojected PSD position than in the low-mass clusters.But, the low-mass and high-mass clusters show consis-tent results when comparing the different RPS typesto control galaxies. It implies that the RPS strengthparameter has captured a fundamental property of theenvironmental processing. Although the RPS strengthparameter combined several observables of external andinternal properties, the way these observables are com-bined is not arbitrary but motivated by the RPS theory.Although the way of inputting the observables to thecalculation of PRS strength has uncertainties, it seemsthat the physical effect of RPS is strong enough in themassive clusters to override many of the uncertainties.Thus, we conclude that our classification of galaxiesinto the three RPS types is statistically successful.The way we define the three populations can be effec-tively used to combine galaxies from different clusters.In statistical analysis, cluster galaxies were often binnedinto sub-sample by more directly observed parameterslike d proj /r ; here we have introduced P/F R as a This critical value of 0.1 assumes that the galaxy preserves itsdark matter halo (Byrd & Valtonen 1990), which is reasonable as90% of the infalling, weak-RPS galaxies have tidal radius r tid ∼ . W /σ C > R (Merritt 1984) in both low and high-massclusters. The tidal radius has been defined as the galactic radiusbeyond which material is effectively removed by tidal effects. Forreference, if we assume that no dark matter remains, the criticalvalue of cluster tidal perturbation strength drops to 0.006 (Byrd& Valtonen 1990), and 70% (38%) of infalling, weak-RPS galaxiesin high-mass (low-mass) clusters are perturbed according to thiscriteria. / parameters that influence galaxy evolution.5.3. Radial extension of RPS in the massive clusters
Early statistical studies on environmental effects ingroups / clusters focused on the cluster centric trend ofgalaxy properties (or similarly, galaxy properties asa function of local densities). Those studies foundthat galaxies on averaged become more H i -deficient andpassive toward the cluster center (Brown et al. 2017;Odekon et al. 2016; Yoon & Rosenberg 2015; von derLinden et al. 2010; Gavazzi et al. 2010, 2006; Weinmannet al. 2006), implying accelerated galaxy evolution inclusters. Such a trend is found to be steeper in high-mass clusters than in low-mass clusters (Brown et al.2017; Yoon & Rosenberg 2015; Hess & Wilcots 2013;Woo et al. 2013), more significant for low-mass galax-ies than for high-mass galaxies (Woo et al. 2017; Zhanget al. 2013; Woo et al. 2013; Wetzel et al. 2013), consis-tent with the way that RPS is predicted to work. Later,it was found that galaxy properties also vary as func-tion of radial velocity offsets from the cluster center at agiven projected distance (Nascimento et al. 2019; Baylisset al. 2017; Barsanti et al. 2016; Mahajan et al. 2011;Pimbblet et al. 2006). With the aid of cosmological sim-ulations, it becomes clear that positions on the PSD areassociated with galaxies at different infall stages, thusshow correlation with the averaged galactic properties(Haines et al. 2015; Boselli et al. 2014b; Gill et al. 2005).The PSD becomes an excellent tool to study RPS, notonly because it can identify infalling galaxies which mayhave more gas to be stripped (Rhee et al. 2017; Haineset al. 2015; Oman et al. 2013), but also because its twoaxes almost fully determine the ram pressure for a givencluster (Gunn & Gott 1972). In observations, only theprojected PSD is available, but has been proven to bestatistically powerful in linking infall stages, strippingevents, gas-richness and star-forming status of galaxies(Yoon et al. 2017; Oman & Hudson 2016; Boselli et al.2014b; Muzzin et al. 2014).The pioneer studies utilizing the projected PSD tostudy RPS of H i in galaxies found remarkable con-sistency between observed and predicted H i -richness.These studies typically assume exponentially radial dis-tributions for both the H i and stars, and the scale-lengthof an H i disc is set to be a fixed factor of that of the stel-lar disk. Then, basing on the equation of Gunn & Gott(1972) and setting the relative velocity to be σ C , a limit-ing “stripping region” could be defined in the projectedPSD where the ram pressure becomes stronger than the anchor force at all galactic centric radii, and thus the gasin galaxies is expected to be significantly removed withinthis region. The detection rates of galaxies in blind H i surveys abruptly drop, and the fractions of red galax-ies significantly increase after passing that limit (Jaff´eet al. 2015, 2016; Yoon et al. 2017; Jaff´e et al. 2018).These results lent strong support to RPS driving galaxyevolution in massive clusters, in a more direct way thanpreviously using cluster centric radial trends.Our work is built upon these previous analyses withtwo new components added to the method. The firstnew component is that we use a more realistic radialdistribution of H i when estimating the anchor forces.Compared to the exponential model often assumed inthe previous studies, a real H i disk tends to have a flat-tened surface density distribution, and sometimes a cen-tral hole in the inner region. Thus for the same M HI and scale-length, a real disc tends to have more massand hence higher surface densities in the outer region,resulting in higher anchor forces. Additionally, statis-tical analysis based on H i images found that the H i scale-length ∼ . R HI (Wang et al. 2014, 2020), whichstrongly depends on M HI but not on the optical scale-length. The ratio between the H i and r − band scale-lengths of our main sample galaxies ranges from 0.7-1.9in both high-mass and low-mass clusters. Assuming afixed ratio of the scale-lengths as in the previous studieswill thus introduce additional uncertainties in H i sur-face densities at a given galactic radius. The second newcomponent of the method is that we focus on an earlierphase of stripping, when ram pressure is just enough tostrip the H i at R and R HI . The selection of galaxieswith R HI > R also ensures that most galaxies have notentered the classical “stripping region” yet. We thus in-cluded the self-gravity of H i when calculating the anchorforces, which is usually ignored when discussing strip-ping of the inner disks where stars dominate the gravity.We also used ∆ v rad instead of σ C when calculating theram pressure, to better reflect the fact that during infallgalaxies are accelerated while approaching the pericen-tre. A few interesting features show up with this newscheme of classifying galaxies into strong-, weak- and no-RPS populations. We summarize the scenario in Fig. 7and discuss a few key points below.First, strong-, weak- and no-RPS galaxies overlap sig-nificantly in d proj . Thus the scatter in the previouslyquantified cluster centric radial trends of gas richness(Brown et al. 2017; Odekon et al. 2016; Hess & Wilcots2013) can be explained at least partly by this feature.As already mentioned, at a given M , the projectedPSD position traces the ram pressure of different levelsmuch more closely than d proj . The higher incidence of5 Figure 7.
Toy scheme of an H i -rich galaxy passing different RPS regions while traveling through a massive cluster. Like inFig. 2, the black, dashed curves mark the escape velocity and the virialized region. The arrowed blue curve is the trajectoryof the galaxy starting from d proj ∼ R , shrinking due to dynamic friction until getting virialized. The purple, green andred regions are divided by curves of equivalent ram pressure, and approximately correspond to the no, weak and strong-RPSregions, because RPS strengths are largely determined by the relative velocity of the galaxy and the density of the ICM. Butthe gradually reduced anchor force due to the drop of Σ HI ,R also enhances the RPS strength, particularly when the galaxyenters the strong-RPS region. RPS for the infalling galaxies (with respect to the virial-ized galaxies) was also noticed in previous studies (Jaff´eet al. 2018; Yun et al. 2019). Whether the RPS is ef-fective further depends on the anchor force determinedby the gas and stellar surface densities in the galaxy.The RPS strength (the ram pressure over the anchorforce) as one parameter puts together these factors in aphysically motivated way. Despite the projection effectsand other uncertainties discussed in Sec 3, their statisti-cal correctness is supported by the distinct H i and SFRproperties of the three RPS populations.More importantly, the strong- and particularly weak-RPS galaxies make a significant fraction ( ∼ half) of theH i -rich sample with d proj extending out to at least R ,and even to 2 R in high-mass clusters. Evidence forwidely distributed RPS out to at least R was reportedin the Coma Cluster (Gavazzi et al. 2018; Roberts &Parker 2020). Jellyfish galaxies from the project GASPare also found out to R (Jaff´e et al. 2018). How-ever, limited by imaging efficiencies (and the possibilitythat weak-RPS only produces weak signatures), therewas no observational census yet regarding the fractionof gas-rich galaxies undergoing RPS. The significanceof RPS in the outskirts of clusters has therefore been rarely discussed in observations. The weak RPS mayremove H i much more slowly than strong-RPS (whichhas produced observable reduction in M HI at a givenSFR), so their SFR can catch up with the change in M HI . But weak RPS is not necessarily much slowerthan the tidal stripping from the cluster which has atimescale similar to the crossing time of the cluster ( ∼ R and 1 / R can account for one third of the total gas loss in a galaxyduring the infall process between R and the pericen-tre (Steinhauser et al. 2016, their Fig.2 and 4). At thispoint, we are still unable to directly compare in observa-tions the relative importance of RPS to tidal stripping ofthe cluster and other environmental effects (harassment,viscosity stripping, thermal evaporation, etc.), but we6showed that for a significant fraction of gas-rich galax-ies at and beyond R of massive clusters, ram pressureis likely already causing H i loss. The high incidence ofRPS in H i -rich galaxies at R is consistent with theprediction of the simulation IllustrisTNG-100 (Yun et al.2019). Environmental processing beyond R is com-monly termed pre-processing and attributed to effectsin groups (Bah´e et al. 2019; Bah´e & McCarthy 2015;Bah´e et al. 2013), but our results suggest that part ofthe “pre-processing” around the most massive clusterscould actually be processed by the cluster itself throughweak RPS.5.4. Uncertainties and future perspective
We warn readers again about the uncertainties re-lated to the estimates of the RPS parameter. Amongthose discussed in the paper, the most obvious one is theprojection effect. Luckily, as massive clusters stronglyconcentrate galaxies, a d proj is associated with a rel-atively narrow distribution d with the median valueslightly larger than but close to d proj (in contrast, inthe field d proj and d are much more different). Simi-larly, ∆ v rad is much closer to ∆ v than they would be inlooser environment. We roughly quantify the differencebetween d proj and d by selecting all the 280 clusters with M > M (cid:12) (having in total 23295 galaxies withmass > M (cid:12) ) from the TNG300 run in the suite of Il-lustrisTNG cosmological simulations (Nelson et al. 2019;Springel et al. 2018). From Fig. 8, we can see that at all d proj , the majority ( > d differ by less than 40% from d proj (see also Mahajanet al. 2011). This is one important reason why with pro-jected distances, the estimated ram pressure still statis-tically select galaxies with SFR and H i properties con-sistent with the expected RPS. We roughly assess theuncertainty of approximating d with d proj , by replacing d proj with 1 . d proj when estimate ρ . Then, ∼
45% of themain sample galaxies are under weak RPS at 1 . R inthe high-mass clusters; only 25% of the main samplegalaxies, but nearly half of the infalling subset are un-der weak RPS at R in the low-mass clusters. Because∆ v rad is an under-estimate of ∆ v , the real ram pressureis likely stronger, and more galaxies may be under weakRPS at these distances than classified with ∆ v rad . Soour main result that weak-RPS affects a significant frac-tion of galaxies near and beyond R is likely robust.We emphasize that application of the method shouldalways be limited to statistical analysis, and future com-parison with hydro-dynamic and semi-analytical simu-lations may help us quantify and correct for the limi-tations. Most previous comparisons between the obser-vation and the simulation were in the form of compar- d proj / R d / d p r o j Figure 8.
Violin plot of the difference between d and d proj of galaxies in clusters selected from the TNG300 run inthe IllustrisTNG project. Only galaxies with mass > M (cid:12) are selected. The three bars of each violin represent the 10,50 and 90 percentiles of the distribution. The distributionsdo not change much if we only select infalling galaxies, orexclude the backsplash galaxies. ing scaling relations and cluster centric radial distribu-tion of observable parameters, which reflect the resultof complex physical processes mixed together. Our RPSstrength parameter provides an opportunity to (at leastpartly) separate RPS from other environmental and in-ternal processes, in such comparisons. For example, re-cent ΛCDM semi-analytical models (SAM) found thatRPS of cold gas is a necessary component in the modelto reproduce the observed level of H i mass fractions inrelatively high-mass satellite galaxies, but the H i massfraction of low-mass satellite galaxies, and the offsets ofH i related scaling relations between central and satel-lite galaxies are difficulty to reconcile (Cora et al. 2018;Stevens & Brown 2017; Luo et al. 2016; Henriques et al.2015; Gonzalez-Perez et al. 2014). Directly comparingto the observed distribution of RPS strength, and to theobserved H i property as a function of RPS strength mayhelp identify whether and which part of the RPS recipein SAMs need to be improved.The sample used in this study is still relatively small,thus the differences between strong / weak-RPS and con-trol galaxies are marginal in each individual figure ofFig.3-6. The differences remain consistent in all thesefigures, adding strength to their statistical significance,but they need confirmation with larger samples in thefuture.Finally, as in many other studies utilizing ALFALFAdata (e.g., Odekon et al. 2016), we are limited by thedepth of H i data, which biased the sample against low-mass galaxies. We look forward to deeper and more H i detections with the up-coming CRAFTS (Zhang et al.72019), Apertif (Verheijen et al. 2009), and WALLABY(Koribalski et al. 2020) surveys. H i images are usuallyused to search for RPS tails, but as the observability oftails depends on the angle of the line of sight from thedirection of infall as well as the image resolution, ourmethod can be used to select RPS candidates that donot show obvious tails. Such an application is particu-larly useful when considering that the majority (90%)of galaxies going to be detected in those new H i surveywill not be well resolved (Staveley-Smith & Oosterloo2015). SUMMARY AND CONCLUSIONSo far as we know, this is the first statistical study onALFALFA detected galaxies in more than ten clusterswith well parametrized extended X-ray emissions (i.e.with resolved X-ray surface brightness radial profiles).The sample of clusters extends to M ∼ × M (cid:12) thanks to the new RXGCC catalog (Xu et al. 2018, Xuet al. in prep) built with the state-of-art algorithmssearching for faint and extend X-ray sources.We described a promising method to parametrize theRPS strength in clusters, based on the theory of Gunn& Gott (1972) and improved upon the previous observa-tional achievements. We compared the M HI and centralSFR of over 200 H i -rich cluster galaxies to a controlsample of field galaxies which are matched in the totalSFR, M ∗ , stellar surface density and redshift.We showed that galaxies under stronger RPS also havefaster H i removal and more enhanced central SF R (com-pared to general galaxies with similar global
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SDSS false-color ( g , r and i -band) atlas of strong-RPS galaxies in the main sample. The first 17 galaxies are inhigh-mass clusters and the last 3 galaxies are in low-mass clusters. All images are 100 arcsec in width. APPENDIX A. MORE INFORMATION ABOUT THE STRONG-RPS GALAXIESA.1.
The SDSS atlas
We present in Fig. 9 the SDSS (DR7) false-color atlas for all strong-RPS galaxies in the main sample. We alsopresent in Fig. 10 the false-color atlas for the 3 galaxies which can be classified as the strong-RPS type, but excludedfor not having enough control galaxies. We find asymmetric distribution of blue light indicative of perturbation onthe gas in a few extreme galaxies, e.g. galaxy with ID = 1 in Fig. 9, and the first galaxy in Fig. 10. In general itis hard to see morphological features indicative of RPS from these images, for the ( g , r , and i -band) optical light isdominated by the old stars which are little influenced by the RPS. The clearest characteristic in the morphology isthat these galaxies are disc-dominated (except for the galaxy in the right panel of Fig. 10, see discussion in Sec. 4),consistent with the sample selection for H i -rich galaxies.2 Figure 10.
SDSS false-color ( g , r and i -band) atlas of galaxies in high-mass clusters which satisfy the selection criteria ofthe strong-RPS type, but were excluded from the main sample due to insufficient control galaxies. All images are 100 arcsec inwidth. F l u x d e n s i t y ( m J y ) F l u x d e n s i t y ( m J y ) F l u x d e n s i t y ( m J y ) kms )505 F l u x d e n s i t y ( m J y ) kms )50510 kms )010 kms )10010 kms )010 Figure 11.
ALFALFA H i spectrum of strong-RPS galaxies in the main sample. Each spectrum is centered on the radialvelocity of the galaxy and has a width of 1600 km s − . We have smoothed each spectrum using a hanning kernel with a widthof 5 channels. The measurements of W (width at half the peak flux density) are marked as the dotted blue lines. The ID ineach panel is consistent as that in Fig. 9. A.2.
The ALFALFA HI spectrum
We present in Fig. 11 the H i spectrum from ALFALFA for all strong-RPS galaxies in the main sample. There aresome galaxies with strongly lopisided H i emission lines (e.g. ID =14, 18, 20), but there are also symmetric ones (e.g. ID =1, 2, 3). Whether the asymmetry of an integral H i line shape reflects the perturbation of the disk dependson the galactic inclination and the signal-to-noise ratio of the spectrum (Watts et al. 2020). Calibration against asample of solidly confirmed RPS galaxies (either in observation or in simulation) may be needed in the future regardingwhether / how information about RPS can be drawn from the integral spectral shape.3A.3. Cross-matching to nearby galaxies known with RPS tails
Among the 17 strong-RPS galaxies in the main sample, 4 galaxies indeed show RPS features in various imageobservations (H i , Hα , and u -band optical images, Gavazzi et al. 2001; Scott et al. 2010; Yagi et al. 2017; Roberts &Parker 2020). Particularly, CGCG 097-073 in Abell 1367 cluster (No. 1 in Fig. 9) has long, extended ionized ( Hα )gas tail due to ram pressure (Gavazzi et al. 2001; Yagi et al. 2017). In addition, the asymmetric H i distribution ofCGCG 097-073 suggests that this galaxy is undergoing strong RPS (Scott et al. 2010). Three galaxies (GMP 5821,GMP 3253, GMP 597, corresponding to No. 10, 12, and 14 in Fig. 9) in Coma cluster are visually classified intopotential RPS galaxies, based on CFHT u -band images. The u -band images of three galaxies show RPS features suchas asymmetric star formation and tails (Roberts & Parker 2020).Among the three strong-RPS galaxies in high-mass clusters excluded due to insufficient number of control galaxies(Fig. 10), J114313.3+200017 (CGCG 097-079 in Abell 1367 cluster) also has an extended ionized gas tail (Gavazziet al. 2001; Yagi et al. 2017), as CGCG 097-073 does. Its H i peak is off from the optical center toward the ionizedgas tail (Scott et al. 2010). J130354.4+281837 (GMP 713 in Coma cluster) has been reported as an RPS candidateby visual inspection of the u -band image (Roberts & Parker 2020). However, J125629.79+275622.9 (NGC 4817), anearly-type galaxy, has no signature of the RPS effect reported so far.We note that, not all the galaxies displaying RPS tails in the literature are identified by our method as strong-RPSgalaxies, mostly due to our selection criteria. For example, source J125628.57+271728.6, J125809.23+284230.9 andJ125839.95+264534.3 in the Coma cluster are identified as RPS candidates by Roberts & Parker (2020). The formertwo galaxies also show marginally asymmetric H i disks (Bravo-Alfaro et al. 2001b). They were excluded from ourmain sample because they have R HI < R , and should be at a relatively later stage of gas depletion. Another knownexample galaxy of this type is NGC 4569 in the Virgo cluster (Boselli et al. 2018; Chung et al. 2009).The last galaxy among the three literature candidates was identified as a weak-RPS galaxy by our method. B. TEST THE CLASSIFICATION METHOD WITH VIVA HI IMAGESWe take the H i interferometric data of Virgo cluster galaxies observed in the VIVA project (Chung et al. 2009). Wederive Σ HI radial profiles and R HI from these H i images. We also use the SDSS photometric measurements from theExtended Virgo Cluster Catalog (Kim et al. 2014), to derive M ∗ and the optical scale-length R d . M ∗ is estimated fromthe r band luminosity and the g − r color, using the formula from Zibetti et al. (2009). R d is estimated as R /1.678,assuming an exponential radial distribution.We select galaxies with M ∗ < M (cid:12) , R HI > R , and R > b maj as for the main sample, but we do not applythe selection criteria on ∆ v rad or d proj . It results in 16 galaxies. We note that due to the lower distance of Virgo,VIVA reaches lower M HI and M ∗ limits than our main sample. We use the same set of cluster parameters as in Yoonet al. (2017) to derive ram pressure and the PSD.A figure of comparing the predicted to the real R HI of the VIVA galaxies can be found in Wang et al. (2016, W16).The two types of R HI are close to each other, with a median offset of 0.05 ± .
09 dex. We present in Fig. 12 thecomparison between real and predicted Σ HI , R25 , along with that of normal late-type galaxies from the sample of W16.Despite the good correlation (with Pearson correlation coefficients of 0.8 and 0.89 for the W16 sample and VIVAsample respectively) and relatively small scatter in the offsets between the measured and predicted Σ HI , R25 (0.12 dexand 0.16 dex for the W16 sample and VIVA sample respectively), we notice a saturation of the predicted Σ HI , R25 at ∼ . M (cid:12) pc − . Such a saturation typically happens when the galaxy is highly H i -rich and the ratio of R HI /R > R reaches the inner non-exponential part of the median Σ HI profile which has a much larger scatter thanthe outer part (see Fig. 2 of W16, and Fig. 1 of Wang et al. 2020). The saturation tends to under-estimate Σ HI , R25 and thus the anchor force at R , potentially rendering galaxies to be mistakenly identified into the strong-RPS type.Luckily, because H i -richness tends to drop while RPS strength grows, this type of H i -rich galaxies are rare withinmassive clusters when the ram pressure starts to work, and none of our strong-RPS galaxies have R HI /R >
2. Sothis problem of saturation in the predicted Σ HI , R25 does not significantly affect the estimate of RPS strengths or theresults in this paper.We use the directly measured and predicted Σ HI radial distributions respectively, and make two sets of classificationsthat divide galaxies into the strong, weak and no-RPS types. We compare the two sets of classifications on the PSDof the Virgo cluster (Fig. 13), and find them to be identical. It strongly supports our classification based on predictedΣ HI . We also see from Fig. 13 that most of the galaxies (12/19) are classified into the strong-RPS type, consistentwith the overally perturbed H i morphologies reported before for the sample (Chung et al. 2009). As discussed in4 HI , R real ( M pc )0.20.00.20.40.60.81.01.2 l o g H I , R , p r e d ( M p c ) W16, R HI / R > 2W16, R HI / R < 2VIVA Figure 12.
Comparing the predicted and measured Σ HI , R25 . The stars mark galaxies selected from Wang et al. (2016, W16),by requiring R HI > R , R > b maj , and availability of Σ HI radial profiles. The W16 sample is further divided by whetherthe value of R HI /R is > < | v r a d |/ C With predicted HI distribution d proj / R | v r a d |/ C With real HI distributionVirgo Figure 13.
VIVA galaxies in the PSD. Similar as the bottom panels of Fig. 2, but for galaxies from the VIVA sample. Theclassification of galaxies into strong (red), weak (green) and no (purple)-RPS types is based on predicted and observed Σ HI radial distributions in the top and bottom panel, respectively. Sec. 3.1 and 5.3, our classification method is only applicable to statistical samples, but inappropriate to discussionof individual sources. We refer the readers to Yoon et al. (2017) for a comprehensive discussion about the statisticalcorrespondence between the perturbed H ii