SDSS-IV MaNGA: The kinematic-morphology of galaxies on the mass vs star-formation relation in different environments
MMNRAS , 1–20 (2020) Preprint 15 May 2020 Compiled using MNRAS L A TEX style file v3.0
SDSS-IV MaNGA: The kinematic-morphology of galaxies on themass vs star-formation relation in di ff erent environments Bitao Wang, , , (cid:63) Michele Cappellari, Yingjie Peng, † Mark Graham Department of Astronomy, School of Physics, Peking University, Beijing 100871, China Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China Sub-department of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
Accepted for publication on MNRAS on 2020 May 07
ABSTRACT
We study the link between the kinematic-morphology of galaxies, as inferred fromintegral-field stellar kinematics, and their relation between mass and star formation rate. Oursample consists of ∼ ff ective stellar angular momentum within the half-light radius λ R e . We findthat for star-forming galaxies, namely along the star formation main sequence (SFMS), the λ R e values remain large and almost unchanged over about two orders of magnitude in stellarmass, with the exception of the lowest masses M (cid:63) (cid:46) × M (cid:12) , where λ R e slightly decreases.The SFMS is dominated by spiral galaxies with small bulges. Below the SFMS, but above thecharacteristic stellar mass M crit ≈ × M (cid:12) , there is a sharp decrease in λ R e with decreas-ing star formation rate (SFR): massive galaxies well below the SFMS are mainly slow-rotatorearly-type galaxies, namely genuinely spheroidal galaxies without disks. Below the SFMSand below M crit the decrease of λ R e with decreasing SFR becomes modest or nearly absent:low-mass galaxies well below the SFMS, are fast-rotator early-type galaxies, and containfast-rotating stellar disks like their star-forming counterparts. We also find a small but clearenvironmental dependence for the massive galaxies: in the mass range 10 . − . M (cid:12) ,galaxies in rich groups or denser regions or classified as central galaxies have lower values of λ R e . While no environmental dependence is found for galaxies of lower mass. We discuss howthe above results can be understood as due to the di ff erent star formation and mass assemblyhistories of galaxies with varying mass. Key words: galaxies:evolution–galaxies:formation–galaxies:kinematics and dynamics
The diverse colour and morphology are probably the most twostriking and straightforward features of galaxies. Roughly at thetime when morphological classification systems more refined thanthe well-known Hubble scheme came out (e.g., de Vaucouleurs1959a; van den Bergh 1960), astronomers started to establish thatthese two properties of nearby galaxies actually correlate with eachother in the sense that elliptical galaxies are typically red whereasspiral galaxies are bluer (e.g., Holmberg 1958).In the following years, the advent of larger telescopes and theuse of charged coupled devices allowed for detailed study of lightprofiles (Sérsic 1963) and galaxy structure components such asbulges, disks, bars and rings (e.g., Kormendy 1977; de Vaucouleurset al. 1991; Caon et al. 1993). In parallel, the accumulation of stellar (cid:63)
E-mail: [email protected] † E-mail: [email protected] spectra deepened our understanding of galaxy integrated light andtheir stellar populations (e.g., Bruzual A. 1983; Faber et al. 1985;Worthey et al. 1994).But not until the new millennium had our knowledge aboutthis morphology-colour relation (hereafter T-C relation), i.e. “el-liptical galaxies are red and spiral galaxies are blue”, been dra-matically updated. Large sky surveys such as The Sloan DigitalSky Survey (SDSS) revealed the sharp bimodality of low-z galax-ies on colour-magnitude diagram (Strateva et al. 2001; Baldry et al.2004) which evolves to the form of two sequences of star-formingand quiescent / passive galaxies on a diagram of two more physicalparameters, the star formation rate-stellar mass (SFR − M (cid:63) ) dia-gram (Brinchmann et al. 2004; Noeske et al. 2007). Also thanksto observations at higher redshift z which clearly show the growth Though the passive sequence sometimes is less obvious as its correspon-dence red sequence on colour-magnitude diagram because SFR does notnecessarily saturates to the extent as much as colour index.c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a y B. Wang et al. of passive population (e.g., Bell et al. 2004; Faber et al. 2007),astronomers started picturing galaxy evolution tracks in this dia-gram. The “star formation main sequence” (SFMS) consists of ac-tively star-forming galaxies. For some reasons some of these leavethis sequence (the so-called quenching of star formation) and fi-nally join passive population (Martin et al. 2007; Salim et al. 2007;Schiminovich et al. 2007; Wong et al. 2012). Between the red se-quence and the blue cloud lies the "green valley" which is madeby galaxies believed to be transitioning from one sequence to theother. Therefore it has received much attention because of its po-tential for shedding light on the exact reasons why galaxies leaveSFMS (e.g., Mendez et al. 2011; Schawinski et al. 2014; Salim2014). Being a hot topic, much e ff ort has been made to understandgalaxy evolution on this SFR − M (cid:63) diagram and the quenching ofstar formation. And by looking for galaxy properties closest to starformation state, that T-C relation regained its significance and waspresented in a modern look.It has been extensively reported that the structure (in terms oflight concentration, bulge to total light ratio, Sérsic index, centraldensity etc.) of galaxies and their star formation state (indicated bythe position on colour-magnitude or SFR −M (cid:63) diagram) are closelyrelated in the same sense as that original T-C relation, both at low z (e.g., Kau ff mann et al. 2003a; Cameron et al. 2009; Gadotti 2009;Bluck et al. 2019) and at higher z (e.g., Wuyts et al. 2011; Bellet al. 2012; Cheung et al. 2012; Lang et al. 2014; Whitaker et al.2017). These results all showed that structure is a good indicatorof star formation rate and suggested a quenching mechanism con-nected to morphology. For example, a scenario has been proposedwhere a massive bulge can stabilise the disk against fragmenta-tion so that cessation of star formation is achieved (Martig et al.2009). And less directly, as bulge mass and the mass of galactic su-per massive black hole (SMBH) are connected via M − σ relation(Kormendy & Ho 2013), the influence from SMBH is also con-sidered a driver of the T-C relation. Wet compactions induced by,e.g., mergers, counter rotating streams or infall of galactic fountainraise mass concentration as well as feed the central SMBH, and itis followed by quenching in the form of stellar and active galacticnucleus (AGN) feedback resulting in a compact and passive galaxy(Dekel & Burkert 2014; Zolotov et al. 2015; Tacchella et al. 2016;Dekel et al. 2019). Regardless of whether bulges and AGNs directlyquench the entire galaxies or not (which so far have not been un-ambiguously observed), it has been reported that bulges have lowerspecific star formation rate than disks (e.g., Abramson et al. 2014;Lin et al. 2017).Morphology reflects the orbital composition of a galaxy.Galaxy spheroids have low angular momentum and higher randommotions while disky galaxies are dominated by stars in orderedrotation. By studying the kinematic properties of galaxies we getcomplementary and sometimes revolutionary results for light distri-bution based studies. As opposed to what people originally thought,long-slit spectragraphs revealed that fainter elliptical galaxies havehigher degree of rotation than the brighter ones (Bertola & Ca-paccioli 1975; Illingworth 1977; Kormendy & Illingworth 1982;Kormendy 1982; Davies et al. 1983). The advent of integral-fieldspectroscopy (IFS) with the SAURON (de Zeeuw et al. 2002), sug-gested a possible dichotomy between the kinematics of these twoclasses of galaxies that they called fast and slow rotators early-typegalaxies (Emsellem et al. 2007; Cappellari et al. 2007). This di-chotomy appeared closely related to the suggested one based on theinner surface brightness profiles (Kormendy & Bender 1996; Faberet al. 1997). Later, the volume-limited ATLAS IFS survey (Cap-pellari et al. 2011a) provided a proper census of the kinematic mor- phology in galaxies (Krajnovi´c et al. 2011; Emsellem et al. 2011).More recently, the evidence for a dichotomy was placed on firmground (Graham et al. 2018) using data from the Mapping NearbyGalaxies at Apache Point Observatory (MaNGA) survey (Bundyet al. 2015). See Cappellari (2016) for a review. This kinematiccensus has drawn attention to the similarity between intrinsic mor-phology of spiral galaxies and fast rotators, and has led to a revi-sion of the traditional Hubble morphological classification schemewhich ignores the wide range of bulge size of S0s (Cappellari et al.2011b).Part of the breakthrough is because classifications and quan-tifications based on kinematic maps are less a ff ected by projection.And this can also be taken as advantage to investigate T-C relation.Current studies have shown the di ff erence between fast and slowrotators in terms of current star formation and star formation his-tories (e.g., Shapiro et al. 2010; Smethurst et al. 2018). And echo-ing those studies suggesting the significance of central density inquenching galaxies, Cappellari et al. (2013b) and Li et al. (2018)found the important role of velocity dispersion in driving the varia-tion of stellar populations both of early-type and late-type galaxies.A full kinematic version of the T-C relation has been shown in vande Sande et al. (2018). The intrinsic shape of galaxies, as quantifiedin V /σ − (cid:15) (ordered over random motion versus ellipticity) diagramwith certain assumptions, clearly correlates with their luminosity-weighted age in the results.In this work, we attempt to link together the information in theSFR − M (cid:63) and ( λ, (cid:15) ) diagrams, two extensively exploited tools forunderstanding the star formation and kinematic aspects of galax-ies in the literature. The latter, firstly introduced in Emsellem et al.(2007) as an improved version of the ( V /σ, (cid:15) ) (with more intro-duction in Section 3), takes into account the spatial structure ofkinematic maps and has been shown able to di ff erentiate betweenkinematic classes (Cappellari 2016; Graham et al. 2018). In con-junction, we are able to revisit T-C relation from a new and infor-mative perspective. And by studying ∼ − M (cid:63) diagram can be well covered down toa stellar mass ∼ . M (cid:12) . Special attention will be paid to the de-pendence on stellar mass and environment, which have been shownto hold important leverage over the star formation (e.g., Kau ff mannet al. 2003a; Peng et al. 2010) and kinematic state (e.g., Cappellari2013; Choi & Yi 2017) of galaxies. Given that in ours study wewant to investigate the inter-dependence of a number of di ff erentparameters simultaneously, this can only be done using a sample ofthe size as that of the MaNGA survey.This paper is structured as follows. Section 2 presents anoverview of data sources, sample selections and measurements.Section 3 illustrates the interrelationship between star formationand kinematic state as seen from both SFR − M (cid:63) and λ − (cid:15) diagramand also the dependence on stellar mass, environment and visualmorphology. Section 4 discusses how to understand our results inthe context of a Λ CDM universe. Attempt of drawing implicationsfor quenching mechanisms and comparison with relevant IFS stud-ies are also made. Lastly, Section 5 lists our main conclusions.Throughout this paper we adopt a Chabrier IMF and standardvalues for cosmological parameters, H = km s − M pc − , Ω m = . Ω Λ = .
7, which are close to recent measurements (PlanckCollaboration et al. 2018).
MNRAS000
MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation The IFS data used in this study are taken from the SDSS Data Re-lease 15 (DR15) (SDSS15; Aguado et al. 2019). DR15 comprisesIFS data for 4597 unique galaxies observed via integral field units(IFUs) arranged in hexagon with e ff ective diameters ranging from12 to 32 arcsec (Drory et al. 2015). This corresponds to IFUs con-sisting of 19 to 127 fibres of 2 arcsec diameters that feed light intothe two dual-channel BOSS spectrographs (Smee et al. 2013). Thespectral range covers from 360 to 1030 nm with a median instru-ment broadening σ inst ∼
72 km s − (Law et al. 2016) and a result-ing typical spectral resolution R ∼ ∼ . < z < .
15. Two of the three MaNGAsubsamples, the Primary and Secondary sample which make upthe majority the sample, are targeted to have spectroscopic cover-age to 1.5 and 2.5 projected half-light radii ( R e ) respectively andare selected to have a flat number density distribution with re-spect to the − -band absolute magnitude M i (as a proxy for stellarmass). Another subsample, the Colour-Enhanced sample, increasesthe number of galaxies in the low-density regions of colourâ ˘A ¸S-magnitude diagram by extending the redshift limits of the Primarysample in appropriate colour bins. By such, the Primary plus theColour-Enhanced sample make up a sample with a smoother cov-erage in colour-magnitude diagram. There are also ancillary tar-gets included in DR15. These targets are those of special interestbut rare in a representative galaxy sample such as luminous AGNsand mergers. Especially, no cuts are made on colour, morphology,or environment so that the galaxies observed by MaNGA are fullyrepresentative of the local galaxy population.We adopt the same approach to data quality control as in Gra-ham et al. (2018). This excludes IFS data a significant fraction ofwhich are either flagged bad or show signs of being problematic. Italso excludes galaxies in a merger and too small galaxies as com-pared with the MaNGA beam size (See a detailed description inGraham et al. 2018). In addition, as also recommended in Wakeet al. (2017), galaxies in the ancillary sample are excluded as theyreduce the sample representativeness of the local galaxy popula-tion. Lastly, because of the limited spatial coverage, MaNGA dataalone are not enough for measuring the total SFR (Fig. 2 in Guoet al. 2019). Thus we cross match the sample with GALEX-SDSS-WISE Legacy Catalogue (GSWLC; references and more introduc-tion in Section 3.2) for total SFR of MaNGA galaxies. By doing thiswe only further put a limit that the sample is covered by the foot-print of GALEX All-sky Imaging Survey (see Section 3.2), whichoverlaps with the footprint of SDSS spectroscopic survey for about90 per cent. So finally we reach a MaNGA IFS sample of 3279galaxies, dubbed S MaNGA .To set up our "reference" of star formation for assessing thestar formation level of galaxies, in a following section (Section 4.1)we will define the SFMS by using local galaxy populations cata-logued in GSWLC. It includes ∼
700 000 SDSS galaxies within thefootprint of GALEX AIS with SDSS redshift below 0.3. And thissample is dubbed S GSWLC . In such a way, through out this work Colour index: GALEX NUV minus SDSS i band. Magnitude: absolutemagnitude in SDSS i band. there is only one source of SFR measurements so that the assessedstar formation level of galaxies is self-consistent.
The key parameters in this work are stellar mass, SFR, the spinparameter λ R e and ellipticity (cid:15) by which we quantify the star for-mation level and kinematic state of MaNGA galaxies. In this sec-tion we concisely describe how these are measured while leavingthe full-length description in the sources where we collected thesemeasurements. Together, we also describe the group identificationsand visual morphological classifications used in this work. They arerespectively for studying the environmental dependence and givinga glance at the interrelationship between kinematic state and visualmorphology. The measurements of ellipticity (cid:15) and the spin parameter are di-rectly taken from Graham et al. (2019b) with the methods describedin detail in Graham et al. (2018). (cid:15)
The spin parameter λ R e of each galaxy is measured within the half-light ellipse. The ellipse is defined by ellipticity and area A = π R e where R e is the circular e ff ective radius described in the following.Firstly, the SDSS r -band photometry from NASA-Sloan At-las (NSA; Blanton et al. 2011) is fitted using the Multi-Gaussian Expansion (MGE) method (Emsellem et al. 1994; Cap-pellari 2002), which models the surface brightness via the sum of acertain number (12 is used for every galaxy in Graham et al. 2018)of two-dimensional Gaussians.Then, the isophotal contour containing half the MGE to-tal luminosity is determined by making use of the routine mge _ half _ light _ isophote which implements steps (i) to (iv) foundbefore equation 12 in Cappellari et al. (2013a). And the ellipticity (cid:15) is calculated inside this half-light isophote as that of the inertiaellipse as (Cappellari et al. 2007)(1 − (cid:15) ) = q (cid:48) = (cid:68) y (cid:69)(cid:10) x (cid:11) = (cid:80) Pk = F k y k (cid:80) Pk = F k x k (1)where F k is the flux of the k th pixel, with coordinates ( x k , y k ) andthe summation extends to the pixels inside the isophote. The ef-fective radius R e is defined such that a circle of radius R e coversthe same area as the half-light isophote. An empirical factor of1.35 is further applied to R e in order to match the e ff ective radiusmeasurements from 2MASS (Skrutskie et al. 2006) and RC3 (deVaucouleurs et al. 1991) combined (see Fig. 7 of Cappellari et al.2013a). http: // This used the algorithm and M ge F it Python software package of Cappel-lari (2002) available at https: // pypi.org / project / mgefit / Included in the J am P y Python software package of Cappellari (2008)available at https: // pypi.org / project / jampy / MNRAS , 1–20 (2020)
B. Wang et al. λ R e In this work the spin parameter λ R e , a proxy for specific angularmomentum (angular momentum per unit mass) of stars , is usedas a diagnostic of galactic kinematic state.To calculate λ R e , Graham et al. (2019b) took stellar kinematicsfrom MAPS files which are the primary output of the Data AnalysisPipeline (DAP; Westfall et al. 2019a). Based on data products pro-duced by the Data Reduction Pipeline (DRP; Law et al. 2016), theDAP applies the Penalised Pixel-Fitting method (pPXF; Cappellari2017) to extract the line-of-sight velocity distribution (LOSVD)by fitting a set of 49 families of stellar spectra from the MILESstellar library (Sánchez-Blázquez et al. 2006; Falcón-Barroso et al.2011) to the absorption-line spectra. And then the data are spatiallyVoronoi binned (Cappellari & Copin 2003) to achieve a minimumsignal-to-noise ratio of ∼
10 per spectral bin of width 70 km s − before the mean stellar velocity V and velocity dispersion σ areextracted.With stellar kinematics maps ready, λ R e is calculated usingequation 5 and 6 of Emsellem et al. (2007): λ R ≡ (cid:104) R | V |(cid:105) (cid:68) R √ V + σ (cid:69) = (cid:80) Nn = F n R n | V n | (cid:80) Nn = F n R n (cid:112) V n + σ n (2)with the summation performed over N pixels within the radius R(for λ R e within the half-light ellipse determined before) and F n , V n , σ n , being the flux, mean velocity and velocity dispersion of thenth pixel respectively. By incorporating radial distance of pixels inaddition to flux, λ R e gives less weight compared with V /σ to centralpixels which usually have nearly zero velocity and high velocitydispersion. And this can also make λ R e sensitive to some spatialstructure like rings that locate at larger radii.The MaNGA beam size is sometimes non-negligible com-pared with the area of the half-light ellipse, and this tends to smearout the LOSVD and make the observed value of λ R e lower than theintrinsic one. To account for this Graham et al. (2019b) includesan analytic correction to observed λ R e which is derived in Grahamet al. (2018). Briefly, Graham et al. (2018) quantified the e ff ect ofatmospheric smearing by measuring λ R e of galaxy kinematic mod-els (JAM; Cappellari 2008) convolved with a Gaussian PSF for arange of PSF sizes. And this method of correction has been testedin Harborne et al. (2019) using realistic and independent modelsand shown to do a good job in recovering the intrinsic λ R e with nosystematic deviations for a range of PSF widths. Stellar mass and star formation rate of the MaNGA galaxies aretaken from the version X2 of GALEX-SDSS-WISE Legacy Cata-logue (GSWLC-X2, Salim et al. 2016, 2018). It is a value-addedcatalogue for SDSS galaxies in the redshift range 0 . < z < . Or more accurately, rotational velocity as a fraction of square root ofvelocity second moment weighted by flux and radius. Thus it indicates therelative importance of rotation in the overall motion and is similar to thespin parameter of halo (Bullock et al. 2001). http: // pages.iu.edu / ~salims / gswlc / frared bands and also one mid infrared band (22 microns or 12 mi-crons when the former is not available) from WISE (Wright et al.2010). In the footprint of GALEX All-sky Imaging survey, there arealso GALEX Medium Imaging Survey and Deep Imaging Surveynested with progressively longer exposure time. And GSWLC-X2has utilised the deepest available UV image for each galaxy fromthese sources. The complex nature of galaxy environment makes any one kindof environment definition insu ffi cient as a thorough description ofit. So in this work we will show the dependence of kinematicmorphology-star formation relation on several types of environ-ment indicators:– N : Group richness, i.e. number of member galaxies in a group.– Σ ( Σ ): Projected galaxy number density within a circle ofradius equal to the distance to the third (tenth) nearest neighbour.– Group identity: Central galaxy or satellite, depending on ifthe galaxy is the most massive galaxy in the group (central) or not(satellite).Group richness generally correlates with the total luminousmass of a group and thus also with the total dark mastter mass giventhe galaxy-halo connection (Wechsler & Tinker 2018). So a large N usually means a massive galaxy cluster with a massive dark mat-ter halo. In such a deep potential, strong tidal field as well as hotintracluster medium are able to significantly alter galaxy propertiesgravitationally and hydrodynamically (see a review in Boselli &Gavazzi (2006)). And the N used in this work is from a group cat-alogue for MaNGA galaxies constructed in Graham et al. (2019a)using the local group finder TD-ENCLOSER presented in Graham& Cappellari (2019).
TD-ENCLOSER is based on the kernel den-sity estimation (KDE) method and is optimised for obtaining thelocal galaxy environment. Descending from peaks in density filed,the algorithm assigns galaxies to these peaks so that galaxy groups"grow" around these peaks. A specified hard threshold is set to ex-clude outliers in underdense regions and at the group edges outliersare clipped below a soft (blurred) interior density level. In Gra-ham et al. (2019a)
TD-ENCLOSER is applied for each MaNGAgalaxy in a cylinder centered on the galaxy with hight rangingfrom 600 km s − by default up to 6000 km s − for large clusters.And galaxies falling in the cylinder are out of a sample obtainedby combining SDSS spectroscopic and photometric catalogues sothat incompleteness in the SDSS spectroscopic catalogue (e.g. dueto fiber collision) is accounted for.The second sort of environment indicator we use is the galaxysurface number density measured within a circle of radius the dis-tance to the nth nearest neighbour, which has been extensively cho-sen as gauge of environment in the literature (e.g., Dressler 1980;Baldry et al. 2006; Bamford et al. 2009; Peng et al. 2012). Specif-ically, in this work we make use of density based on 3rd ( Σ ) and10th ( Σ ) nearest neighbour provided by Graham et al. (2019a)defined as Σ n = N / ( π D n ) with D n in Mpc and calculation per-formed in a cylinder centered on the galaxies of hight 600 km s − ( ∆ V = ±
300 km s − ). Σ has been found to give a very smoothkinematic morphology-density relation in Cappellari et al. (2011b),suggesting it as a close proxy for the regulator of the relation. Thesame study has also shown that compared with Σ , Σ is a bet-ter indicator of environment on a larger scale so that it can clearlyseparate field and cluster galaxies.Lastly, we also adopt the central / satellite dichotomy defined MNRAS000
300 km s − ). Σ has been found to give a very smoothkinematic morphology-density relation in Cappellari et al. (2011b),suggesting it as a close proxy for the regulator of the relation. Thesame study has also shown that compared with Σ , Σ is a bet-ter indicator of environment on a larger scale so that it can clearlyseparate field and cluster galaxies.Lastly, we also adopt the central / satellite dichotomy defined MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation log ( / ) l o g S F R [ y r ] R e log ( / ) l o g S F R [ y r ] R e Figure 1.
Left: Projection of the spin parameter λ R e onto SFR − M (cid:63) plane for galaxies in sample S MaNGA . Background grey scale shows the volume correctedprobability density of galaxies in S GSWLC derived from kernel density estimation. White dotted lines mark ± .
35 dex from the star formation main sequence,the ridge line of the background density distribution, within which galaxies are defined star-forming galaxies. Red dotted line is one dex below the lower whitedotted line and galaxies beneath are considered passive / quenched galaxies. Right: LOESS smoothed version of the left (see more introduction in the text). by a group catalogue constructed for SDSS galaxies in Yang et al.(2012). This group catalogue is probably the most utilised oneamong studies of SDSS galaxies, and a large range of SDSS galaxyproperties bifurcate after galaxies are di ff erentiated under this di-chotomy (e.g., Catinella et al. 2013; Peng & Maiolino 2014;Woo et al. 2017). Instead of using a kernel-based finder, Yanget al. (2012) applied an iterative group finder based on friends-of-friends algorithm, which is an updated version of that in Yanget al. (2005). In short, halo properties inferred from tentative galaxygroups (identified using friends-of-friends method) are further usedto update group membership of galaxies, which in turn updates haloproperties. Yang et al. (2012) applied this algorithm to three galaxysamples with slightly increasing galaxy completeness but decreas-ing redshift reliability. Here we choose the "PetroB" version for atrade-o ff between the two. And more than 95% of MaNGA galaxiesin S MaNGA have group information therein.
For the purpose of comparing galaxy kinematic state with morphol-ogy, we take Galaxy Zoo 1 (GZ1) visual morphological classifica-tions of SDSS galaxies from the Galaxy Zoo citizen project (Lintottet al. 2008, 2011). Galaxies catalogued in GZ1 are classified intothree types - elliptical, spiral and indeterminate galaxies - deter-mined by weighted mean of votes with a threshold of 80 per cent. Afull description of the weighting scheme and the debiasing methodaccounting for e ff ects of size, luminosity, distance etc. are providedin Lintott et al. (2008) and Bamford et al. (2009) respectively.It is important to note that the GZ1 classification scheme has,by design, some important di ff erences with respect to the popularHubble classification which has been used by astronomers for acentury (Hubble 1926; Sandage 1961; de Vaucouleurs 1959b). Infact, spiral galaxies classified in GZ1 are defined as heaving ev-idence of disks, but not necessarily spiral arms. This means thatmost S0 galaxies will be included by GZ1 into the spiral galaxycategory. So in the following we directly refer to them as GZ1 el-lipticals (GZ1-E) and GZ1 spirals (GZ1-S). As for the indetermi-nate type in GZ1 (GZ1-I), they are galaxies whose morphology theproject volunteers do not know for sure. This includes those with too small apparent sizes or irregular morphology for example, andin many cases, composite bulge-disc systems in which neither thebulge nor disc clearly dominates (Schawinski et al. 2014).And, there are more than 95% of galaxies in sample S MaNGA catalogued in GZ1.
With this unprecedentedly large sample of galaxies with IFS data,now we are able to attain a thorough view of the kinematic state ofgalaxies on SFR − M (cid:63) diagram, down to a mass of ∼ . M (cid:12) . Theresults are shown in Fig. 1.Serving as a star formation benchmark, we have defined theso-called "star formation main sequence" (SFMS) as the ridge lineof the probability density distribution of galaxies in S GSWLC inredshift range 0 . < z < .
08 (see Appendix A for more de-tails). The upper limit of our redshift range was adopted by Gra-ham et al. (2019a) to have a more reliable kinematic classifica-tion and higher redshift completeness for the environmental esti-mate. But this makes our SFMS potentially not representative forMaNGA galaxies with M (cid:63) (cid:38) M (cid:12) . This is because under theMaNGA sample selection scheme (Wake et al. 2017), a limit inredshift z < .
08 implies a luminosity limit M i (cid:38) − . z > .
08. The two white dotted lines in thetwo panels mark the position 0.35 dex above / below SFMS and theyroughly define ± σ scatter which is consistent with results in the lit-erature (refer to a census in Speagle et al. 2014), and also with thestandard deviation of fitted Gaussians in stellar mass bin. We definethe galaxies within this band the star-forming galaxies hereafter andthose above it the star-bursting galaxies. While the red dotted linelies at one dex below the lower white dotted line so that galaxiesbelow the red have SFR at least one dex lower than star-forminggalaxies of the same stellar mass and we define these galaxies the MNRAS , 1–20 (2020)
B. Wang et al. R e M S ( d e x ) R e M S ( d e x ) Figure 2.
Upper: Projection of ∆ MS = SFR − SFR MS ( M (cid:63) ) onto λ R e − (cid:15) plane. The sample is split into three mass bins in which the data have good coverageacross SFR − M (cid:63) plane. In each panel, theoretical predictions based on tensor virial theorem for oblate rotators following a certain anisotropy relation β z = . × (cid:15) intr are shown: The solid magenta line corresponds to a edge-on view of the theoretical oblate rotators with di ff erent intrinsic ellipticity. The dottedmagenta lines are predictions for di ff erent fixed intrinsic ellipticity (zero to one as going above) seen at varying inclination (face-on to edge-on from left toright). And dashed magenta lines are predictions for the other way around, i.e. fixed inclination but varying intrinsic ellipticity. The region confined by theblack solid lines denotes where favoured by slow rotators. Lower: LOESS smoothed version the upper row. The orange peanut symbols denote galaxies withcounter-rotating disk components which feature two peaks away from center on velocity dispersion maps, i.e. two-sigma galaxies. And the arrows point to theregion populated by two-sigma galaxies. Note their higher star formation level compared with galaxies of similar λ R e at lower (cid:15) . passive galaxies. We define the galaxies in between the green valleygalaxies.In the left panel of Fig. 1, λ R e of about 3,200 MaNGA galaxiesin S MaNGA is mapped onto SFR − M (cid:63) plane. And in the right panel,we smooth the data using locally weighted regression methodLOESS by Cleveland & Devlin (1988) as implemented by Cap-pellari et al. (2013b). LOESS is designed to uncover underlyingmean trends by reducing observational errors and intrinsic scatter.Statistically, LOESS tries to estimate what one would infer by sim-ply averaging values in small bins, if the sample was much largerthan the present one. In application of LOESS smoothing, we adopta smoothing factor frac = ff erent scales of vertical and horizontal axes are accounted forby rotating and re-normalizing the coordinates so that the ellipse ofinertia of the galaxy distribution reduces to a circle in every projec-tion. LOESS reveals that star-forming galaxies on the SFMS aregenerally dynamically cold, except for very low-mass ones ( M (cid:63) ∼ M (cid:12) ) whose λ R e on average is comparable with some massive We used the Python package loess v2.0.11 available fromhttps: // pypi.org / project / loess / passive galaxies. The increase in λ R e at the lowest mass may be re-lated to the increased roundness of dwarf spheroidal (Sph) galaxiesillustrated in Fig. 24 of Cappellari (2016) which is generally at-tributed to tidal disturbances, as reviewed by Kormendy & Bender(2012). This may also be related to the signal of a decrease of coldorbit fraction at low mass end reported in Zhu et al. (2018).Above the SFMS we see a hint of λ R e drop. A possible expla-nation for this drop may be an inclination bias, i.e. galaxies beingpredominantly face-on making the SFR overestimated (less dust at-tenuation) and λ R e lower than a randomly oriented sample. In thatcase, these star-bursting galaxies can actually be just more face-onversion of the population on the SFMS. But, a visual check of theSDSS g-r-i composite images indicates some intrinsic di ff erencesand in particular a higher incidence of irregular features and bluestar-forming clumps among these star-bursting galaxies, as com-pared with a similar number of galaxies on the SFMS. This togetherwith another argument based on the distributions on ( λ − (cid:15) ) diagram(Appendix C) to a large extent rule out the above possibility. Andwe note that this drop of λ R e seems to be in line with an increaseof Sersic (1968) index (Wuyts et al. 2011) and bulge to total ratio(Morselli et al. 2017) found by works based on light distribution.Among galaxies below the SFMS, the mass trend is reversed. MNRAS000
Upper: Projection of ∆ MS = SFR − SFR MS ( M (cid:63) ) onto λ R e − (cid:15) plane. The sample is split into three mass bins in which the data have good coverageacross SFR − M (cid:63) plane. In each panel, theoretical predictions based on tensor virial theorem for oblate rotators following a certain anisotropy relation β z = . × (cid:15) intr are shown: The solid magenta line corresponds to a edge-on view of the theoretical oblate rotators with di ff erent intrinsic ellipticity. The dottedmagenta lines are predictions for di ff erent fixed intrinsic ellipticity (zero to one as going above) seen at varying inclination (face-on to edge-on from left toright). And dashed magenta lines are predictions for the other way around, i.e. fixed inclination but varying intrinsic ellipticity. The region confined by theblack solid lines denotes where favoured by slow rotators. Lower: LOESS smoothed version the upper row. The orange peanut symbols denote galaxies withcounter-rotating disk components which feature two peaks away from center on velocity dispersion maps, i.e. two-sigma galaxies. And the arrows point to theregion populated by two-sigma galaxies. Note their higher star formation level compared with galaxies of similar λ R e at lower (cid:15) . passive galaxies. We define the galaxies in between the green valleygalaxies.In the left panel of Fig. 1, λ R e of about 3,200 MaNGA galaxiesin S MaNGA is mapped onto SFR − M (cid:63) plane. And in the right panel,we smooth the data using locally weighted regression methodLOESS by Cleveland & Devlin (1988) as implemented by Cap-pellari et al. (2013b). LOESS is designed to uncover underlyingmean trends by reducing observational errors and intrinsic scatter.Statistically, LOESS tries to estimate what one would infer by sim-ply averaging values in small bins, if the sample was much largerthan the present one. In application of LOESS smoothing, we adopta smoothing factor frac = ff erent scales of vertical and horizontal axes are accounted forby rotating and re-normalizing the coordinates so that the ellipse ofinertia of the galaxy distribution reduces to a circle in every projec-tion. LOESS reveals that star-forming galaxies on the SFMS aregenerally dynamically cold, except for very low-mass ones ( M (cid:63) ∼ M (cid:12) ) whose λ R e on average is comparable with some massive We used the Python package loess v2.0.11 available fromhttps: // pypi.org / project / loess / passive galaxies. The increase in λ R e at the lowest mass may be re-lated to the increased roundness of dwarf spheroidal (Sph) galaxiesillustrated in Fig. 24 of Cappellari (2016) which is generally at-tributed to tidal disturbances, as reviewed by Kormendy & Bender(2012). This may also be related to the signal of a decrease of coldorbit fraction at low mass end reported in Zhu et al. (2018).Above the SFMS we see a hint of λ R e drop. A possible expla-nation for this drop may be an inclination bias, i.e. galaxies beingpredominantly face-on making the SFR overestimated (less dust at-tenuation) and λ R e lower than a randomly oriented sample. In thatcase, these star-bursting galaxies can actually be just more face-onversion of the population on the SFMS. But, a visual check of theSDSS g-r-i composite images indicates some intrinsic di ff erencesand in particular a higher incidence of irregular features and bluestar-forming clumps among these star-bursting galaxies, as com-pared with a similar number of galaxies on the SFMS. This togetherwith another argument based on the distributions on ( λ − (cid:15) ) diagram(Appendix C) to a large extent rule out the above possibility. Andwe note that this drop of λ R e seems to be in line with an increaseof Sersic (1968) index (Wuyts et al. 2011) and bulge to total ratio(Morselli et al. 2017) found by works based on light distribution.Among galaxies below the SFMS, the mass trend is reversed. MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation λ R e of these galaxies decreases with mass with the trend especiallysharp at the massive end. The red region at mass above ∼ . M (cid:12) is consistent with the previously found characteristic mass whereslow rotators starts dominating (Emsellem et al. 2011; Cappellari2013, 2016). Vertically, namely viewing T-C relation from a kine-matic perspective, there also exists an apparent mass trend. Consis-tent with what we expect from the original T-C relation, λ R e of mas-sive galaxies, especially the most massive ones, reduces drasticallyalong with their decreasing SFR. However at mass below 10 M (cid:12) ,on average λ R e only reduces by about 0.1 when SFR changes morethan two orders of magnitude. The same pattern can also be seen inthe original data on the left, although trends are more di ffi cult to seedue to the significant intrinsic scatter hiding the underlying meantrend. In Appendix E we compare the kinematics of low-mass andlow-spin galaxies to the kinematics of massive low-spin ones. Weconclude that those with lower mass generally indeed have com-plex velocity field while the low spin of the more massive systemsare to a significant extent due to their low inclination.Note that for individual galaxies, without the knowledge oftheir projected ellipticity, comparing alone their λ R e would bemeaningless given the obvious variation of λ R e with the galaxiesinclination. However here, given the sample size as well as the factthat the selection scheme for MaNGA galaxies does not bias themfor certain inclinations, the above results are meaningful and are in-deed confirmed when taking ellipticity into account in the ( λ R e , (cid:15) )diagram (Fig. 5).We note that the PSF to galaxy angular size ratio of low-masspassive galaxies are generally larger and this means larger smearingcorrection to them. However, this is only a small e ff ect. On average,because of dedicated sample selection and IFU allocation, MaNGAhas achieved a roughly similar PSF (full width at half maximum)to galaxy (in terms major axis of half light ellipse) angular sizeratio on SFR − M (cid:63) plane at the value ∼ .
25. This is only notthe case for part of region at low mass and low SFR region wherethe ratio can be ∼ .
4. And when translated to its e ff ect on λ R e ,the smearing correction can result in only ∼ .
05 di ff erence due todi ff erent PSF to galaxy angular size ratio between low mass star-forming and passive galaxies.Fig. 1 shows λ R e as a function of position on SFR − M (cid:63) planewhile a complementary view is provided by Fig. 2. The distance toSFMS ( ∆ MS = SFR − SFR MS ( M (cid:63) ) ) of galaxies are projected onto λ − (cid:15) plane with galaxies divided into three mass bins and againthe original data (upper row) and LOESS smoothed ones (lowerrow) are shown. The superposed magenta line is the anisotropy-shape boundary β z = . × (cid:15) intr of Cappellari et al. (2007), where β z = − σ z / σ R quantifies the vertical to radial velocity dispersionratio while (cid:15) intr is intrinsic ellipticity, i.e. ellipticity seen edge-on.This relation was first projected onto the ( V /σ, (cid:15) ) diagram us-ing the formalism of (Binney 2005) based on tensor virial theo-rem. Then it was transformed into the corresponding relation for( λ R e , (cid:15) ) using the empirical calibration of (Emsellem et al. 2007,2011). The solid magenta line corresponds to an edge-on view ofthe prediction with varying intrinsic ellipticity. While the dottedand dashed lines are predictions with fixed intrinsic ellipticity butvarying inclination and fixed inclination but varying intrinsic ellip-ticity respectively. The fact that the distribution of regular rotatorscan be well described by the solid magenta line and its projectionat di ff erent inclinations, their lack kinematic misalignment, com-bined with results from dynamical models, indicates these galaxiesare a family of galaxies with disks seen at di ff erent inclinations (seereview by Cappellari 2016). In addition, the black solid lines also shown define the region occupied by slow rotators (equation 19 inCappellari 2016).LOESS smoothed data show that in the most massive bin, thegalaxies with a certain star formation levels follow closely the pre-dicted tracks for oblate rotators of fixed intrinsic ellipticity, in factthe colour contours crudely follow the dotted lines in the ( λ R e , (cid:15) )diagram. This corresponds to the drastic λ R e reduction with de-creasing SFR among massive galaxies that is shown in Fig. 1. Andboth of them are reflection of the close relationship between stellarpopulations and kinematic state of massive galaxies. Toward lowermass, the stratification pattern becomes less clear which means therelationship is worse. This results from the fact that can be seen inFig. 1 that a growing number of galaxies with high λ R e reach lowSFR region while many with low λ R e appear on the SFMS. Such be-haviour makes the relation weaker and smears out the stratificationpattern we see for galaxies in the most massive bin.It is interesting to point out two features in the diagram. Thereis a group of galaxies mainly visible for the two low mass bins withunexpectedly low λ R e for their star formation levels. In the left twopanels, they start to appear at the high ellipticity tip of populationsof certain star formation levels making the tracks bending towardlow λ R e region. Among these "outliers" the most outstanding onesare located in the box 0 < λ R e < . . < (cid:15) < .
6. Thus weinspected the kinematic maps of galaxies in the two low mass binsin this region with a significantly larger star formation ( ∆ MS > − λ R e . There are 12 ofthese galaxies and their maps are shown in the Appendix D. Strik-ingly, at least 7 of them are "two-sigma" galaxies (Krajnovi´c et al.2011), with two symmetric peaks of velocity dispersion away fromthe centre, which indicate that they are actually galaxies with twocounterrotating stellar disk components (see Fig. 12 of Cappellari2016). The large star formation is due to the fact that "two-sigma"galaxies form a physically homogeneous class with the rest of thefast rotators ETGs (Sec. 3.5.3 of Cappellari 2016) and this explainswhy they also have similar star formation properties as their non-counterrotating counterparts. In fact we can argue that the star for-mation provides a way to recognize counterrotating disks on the( λ R e , (cid:15) ) diagram, even when the spatial resolution does not allowone to directly recognize the "two-sigma" kinematic feature. Thefact that not many massive galaxies show this feature shows thatcounterrotating disks are favoured in less massive systems. And weonly see them at the high ellipticity tips does not mean these coun-terrotating galaxies are only expected to have high ellipticity. Thisis only because their more face-on counterparts hide behind popu-lations of lower intrinsic ellipticity.Another feature here is that massive galaxies can hardly reachthe high ellipticity border of theoretical magenta lines, leavingsome uncovered regions on the right. This is probably the resultof the growing significance of bulges in massive galaxies. Whenviewed edge-on, their large bulges significantly reduce the elliptic-ity that you would measure out of their isophotes. This makes themmore inconsistent with the prediction of the magenta line, whichassumes constant ellipticity. Apart from stellar mass, galaxy environment is another importantdriver of variation of galaxy properties. In this section we inves-tigate how the previous kinematic-state vs star-formation relationdepends on environment indicated by a variety of environment di-agnostics.In left three columns of Fig. 3, we illustrate λ R e as a function MNRAS , 1–20 (2020)
B. Wang et al. R e Satellite Central R e LowMidHigh
Satellite Central R e < 6 6 R e LowMidHigh < 6 6 R e log < 0.5 log > 0.5 R e LowMidHigh log < 0.5 log > 0.5 R e log < 0.5 log > 0.5 R e LowMidHigh log < 0.5 log > 0.5 MS (dex) Figure 3.
Environmental dependence of λ R e as a function of ∆ MS in three stellar mass bins. From the first row downward shows the dependence on classificationin central / satellite dichotomy, group richness, galaxy surface number density calculated in a circle defined by the distance to the third and tenth nearestneighbours respectively ( Σ & Σ ). For the three columns on the left, in each panel the median λ R e and the band including inner 68% of data points aredisplayed. Only ∆ MS bins of 10 or more galaxies are shown. But all bins except the bin of star-bursting galaxies usually have data points much more than 10.In the last column, the median relations in certain mass and environment bins normalised to their own values on SFMS are compared, summarising the resultson the left. of ∆ MS for the same three mass slices, in which our data provide alarge dynamic range of star formation rate. From top down we showthe dependence respectively on group identity (central / satellite), N , Σ and Σ which are introduced in Section 3.3. The division ac-cording to group richness N is done by the median N of galaxies in groups ( N ≥ Σ andlog Σ was chosen because it crudely corresponds on average to theseparation between field ( N =
1) and cluster (
N ≥
20) galaxies.In each panel, the median λ R e and the band enclosing 68% of datapoints are shown. In the last column, the median relations normal- MNRAS000
20) galaxies.In each panel, the median λ R e and the band enclosing 68% of datapoints are shown. In the last column, the median relations normal- MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation P r o b a b ili t y D e n s i t y Figure 4.
Distributions of M (cid:63) (left column) and ∆ MS (middle column) and λ R e (right column) for massive galaxies below the SFMS in di ff erent envi-ronment (four indicators in the same row order as in Fig. 3). In each row, thetwo samples are matched in log M (cid:63) and ∆ MS with tolerance 0.02 and 0.1dex respectively. In each panel median values are marked by dashed linesand the p-value of KS test is also shown. ized to their values on SFMS are compared so that we get a sensehow λ R e varies with ∆ MS in di ff erent stellar mass and environmentbins.A first result we can infer from this plot is the similaritybetween red and black shaded regions in all panels of left threecolumns. This means at given stellar mass the decrease of λ R e to-ward low ∆ MS is not a strong function of environment. By contrast,just as what has been shown in Fig. 1, the relation varies substan-tially with mass. From low to high mass, the di ff erence between λ R e on the SFMS and at low level of star formation increases ap-parently. And in the highest mass bin, λ R e sharply falls with a sig-nificant fraction of them condensed in a narrow region of low ∆ MS and low λ R e (note how close are the median and 16th percentile inthe highest mass bin below ∆ MS = − λ R e overa large range of ∆ MS . This means environment may indeed play arole in a ff ecting kinematic properties of galaxies at least for mas-sive galaxies.Results described above is summarised in the last column ofFig. 3 where we see a monotonic change of relations with mass(from blue to red) while the split between galaxy populations in dif-ferent environment (solid and dashed lines) is not comparably obvi-ous. From medium to high mass, the dramatic drop of λ R e at a given ∆ MS suggests the existence of mass threshold for low λ R e systems. Note that the reliability of group catalogue reduces at higher z. Sowe also checked results by only looking at galaxies with z < . M (cid:63) (left) and ∆ MS (middle) and λ R e (right) for matched central and satellite galaxies, in the stel-lar mass range 10 . − . M (cid:12) and with distance to the SFMS ∆ MS < − .
35 (where we observe the continuous λ R e di ff erence dueto environment). During matching procedure, for each satellite werandomly match it with a central galaxy with log M (cid:63) and ∆ MS dif-fering less than 0.02 and 0.1 respectively. A more stringent masscontrol is given because the result that kinematics largely dependson mass. Note that every central galaxy can only go into the finalsample once. And lastly we get matched central and satellite sam-ples of 77 galaxies each. We do the same for the other three envi-ronment indicators and get matched samples of 173 (group richness N ), 179 (local density Σ ) and 137 ( Σ ) galaxies respectively, andthe resultant distributions are shown in the following rows.The left two columns show clearly that we have done well incontrolling stellar mass and star formation level, indicated by dif-ference of median values (marked by dashed lines) and the p-valueof Kolmogorov-Smirnov (KS) test (shown at the upper right corner)which is the probability that the two distributions are drawn fromthe same underlying continuous distribution. And last column con-firms the environmental dependence of λ R e for massive galaxies:the distribution of centrals or galaxies in larger groups or denserregions favours lower values of λ R e and the p-values suggest sta-tistical di ff erence with confidence higher than 90% for all exceptcentral / satellite dichotomy, for which we find a milder di ff erence(72.5% confidence).As discussed previously, given large enough sample size alongwith the fact that the sample is not biased toward certain inclina-tions, comparing between average λ R e alone is already informative.Here by further taking ellipticity into account, we show results inFig. 5 that are consistent with our aforementioned findings. Forbrevity, among those environment indicators we only show the re-sults with central / satellite dichotomy (upper and lower row respec-tively) and we confirmed that the conclusion remain the same forother environmental indicators. Again, galaxies are split into threemass bins and in each bin we plot on λ R e − (cid:15) plane the KDE de-rived probability density distribution of star-forming, green valleyand passive galaxies separately. The contour enclosing 68 per centof total probability is denoted as a solid line illustrating the positionof bulk distribution, and the one enclosing 10 percent as a dottedline marking the position of peak.For both rows, the distributions of star-forming galaxies alllook almost identical. When stellar mass increases, the distribu-tions of the green valley and in particular the passive galaxies, mi-grate to the region of small λ R e and (cid:15) . In the highest mass bin, forgreen valley and passive galaxies, the distributions of central galax-ies become more concentrated in the small λ R e and (cid:15) region than thesatellites, indicating an environmental dependence. While there isno obvious trend seen for the two bins of lower mass. All theseresults are consistent with those in Fig. 3. Here we check how visually classified morphology compares to theview from kinematics by taking a quick look at the distributions ofGZ1-S, GZ1-I and GZ1-E galaxies on λ R e − (cid:15) plane. Among S MaNGA
MNRAS , 1–20 (2020) B. Wang et al. R e PassiveGreen ValleyStar Forming
Centrals R e PassiveGreen ValleyStar Forming
Satellites
Figure 5.
Confirming the result in the first row of Fig. 3 by further taking ellipticity into account. The Upper and lower row are for central and satellite galaxiesrespectively. Each panel shows in a certain stellar mass bin the probability density distributions of galaxies with certain star formation levels (star-forming,green valley and passive) derived via kernel density estimation. Solid lines mark the contours enclosing 68 per cent of total probability illustrating the positionof bulk distribution, and the contours enclosing 10 percent are denoted as dotted lines showing the position of peaks. galaxies with mass falling into the range 10 . − . M (cid:12) , 37.6%,39% and 23.4% are GZ1-S, GZ1-I and GZ1-E respectively.The results are shown in Fig. 6 in the same manner as in Fig. 5with galaxies split into GZ1-S (top row), GZ1-I (mid row) andGZ1-E (bottom row). As there are only a handful of passive GZ1-Sand star-forming GZ1-E in S MaNGA , instead of showing their KDEderived density distribution we directly show each individual pointon the plane.First, we note that the distributions of GZ1-S and GZ1-E havelittle overlap which indicates that they are dynamically distinct pop-ulations. If LTGs evolve and become ETGs directly, then this canmean the change of their kinematics must be very fast. Alterna-tively, LTGs can first gradually evolve into a transitional phase, andthen become ETGs later without rapid change of their kinematics.Therefore, it is interesting to notice that the GZ1-I right occupy thetransition regions between GZ1-S and GZ1-E on the λ R e − (cid:15) plane.Though the physical nature of these GZ1-I is still unclear (partiallydue to the poor image quality of SDSS) they may indeed representa transitional population between GZ1-S and GZ1-E.On the other hand, we stress that within certain morphologicalpopulation and mass bin the distributions of galaxies with di ff erent star formation levels look very similar in general. This implies thatstar formation quenching processes are not necessarily accompa-nied by the change of morphology and kinematics. For instance, asthe top row suggests, the star-forming LTGs can be quenched andbecome passive LTGs with similar level of rotation. We will furtherexplore the interrelationship between star formation, morphologyand kinematics in our future work.The position of the distributions of GZ1-S, GZ1-I and GZ1-Eon the λ R e − (cid:15) plane indeed indicates a strong connection betweengalaxy morphology and kinematics. But it is clear that relativelyface-on passive disks are missed by visual classifications GZ1-Sas opposed to their edge-on counterparts. As the high λ R e and low (cid:15) region is barely populated by passive GZ1-S in top row wherewe expect those relatively face-on disks to be (see also the analytictracks of changing inclination in Fig. 2). And part of these face-ondisks have probably been classified as GZ1-E which can be foundin the high λ R e and low (cid:15) region in the bottom row. This echos theresult of ATLAS which shows that the vast majority of early-typegalaxies are actually fast rotating (Emsellem et al. 2011; Krajnovi´cet al. 2011). And it also shows the strong dependence of visualclassifications on inclination. MNRAS000
Confirming the result in the first row of Fig. 3 by further taking ellipticity into account. The Upper and lower row are for central and satellite galaxiesrespectively. Each panel shows in a certain stellar mass bin the probability density distributions of galaxies with certain star formation levels (star-forming,green valley and passive) derived via kernel density estimation. Solid lines mark the contours enclosing 68 per cent of total probability illustrating the positionof bulk distribution, and the contours enclosing 10 percent are denoted as dotted lines showing the position of peaks. galaxies with mass falling into the range 10 . − . M (cid:12) , 37.6%,39% and 23.4% are GZ1-S, GZ1-I and GZ1-E respectively.The results are shown in Fig. 6 in the same manner as in Fig. 5with galaxies split into GZ1-S (top row), GZ1-I (mid row) andGZ1-E (bottom row). As there are only a handful of passive GZ1-Sand star-forming GZ1-E in S MaNGA , instead of showing their KDEderived density distribution we directly show each individual pointon the plane.First, we note that the distributions of GZ1-S and GZ1-E havelittle overlap which indicates that they are dynamically distinct pop-ulations. If LTGs evolve and become ETGs directly, then this canmean the change of their kinematics must be very fast. Alterna-tively, LTGs can first gradually evolve into a transitional phase, andthen become ETGs later without rapid change of their kinematics.Therefore, it is interesting to notice that the GZ1-I right occupy thetransition regions between GZ1-S and GZ1-E on the λ R e − (cid:15) plane.Though the physical nature of these GZ1-I is still unclear (partiallydue to the poor image quality of SDSS) they may indeed representa transitional population between GZ1-S and GZ1-E.On the other hand, we stress that within certain morphologicalpopulation and mass bin the distributions of galaxies with di ff erent star formation levels look very similar in general. This implies thatstar formation quenching processes are not necessarily accompa-nied by the change of morphology and kinematics. For instance, asthe top row suggests, the star-forming LTGs can be quenched andbecome passive LTGs with similar level of rotation. We will furtherexplore the interrelationship between star formation, morphologyand kinematics in our future work.The position of the distributions of GZ1-S, GZ1-I and GZ1-Eon the λ R e − (cid:15) plane indeed indicates a strong connection betweengalaxy morphology and kinematics. But it is clear that relativelyface-on passive disks are missed by visual classifications GZ1-Sas opposed to their edge-on counterparts. As the high λ R e and low (cid:15) region is barely populated by passive GZ1-S in top row wherewe expect those relatively face-on disks to be (see also the analytictracks of changing inclination in Fig. 2). And part of these face-ondisks have probably been classified as GZ1-E which can be foundin the high λ R e and low (cid:15) region in the bottom row. This echos theresult of ATLAS which shows that the vast majority of early-typegalaxies are actually fast rotating (Emsellem et al. 2011; Krajnovi´cet al. 2011). And it also shows the strong dependence of visualclassifications on inclination. MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation R e PassiveGreen ValleyStar Forming
GZ1 Spirals R e PassiveGreen ValleyStar Forming
GZ1 Indeterminates R e PassiveGreen ValleyStar Forming
GZ1 Ellipticals
Figure 6.
The same as in Fig. 5 but for Galaxy Zoo 1 classified spirals (top), indeterminate-type (mid) and elliptical galaxies (bottom).
Probably the most striking result of this paper is Fig. 1. It shows thedramatic mass trend of the kinematic T-C relation and emphasizesthat relatively low-mass ( ∼ . M (cid:12) ) passive galaxies are generallydisk dominated systems. This is against the direct impression fromtheir images because when inclined and passive, in many cases they look roughly the same as spheroids (especially when the resolu-tion of images is low). Indeed there have been evidence showingthe mass dependence of rotation in elliptical galaxies as alreadymentioned in the introduction section, in this figure we take a stepforward by connecting together mass, star formation level and kine-matics. MNRAS , 1–20 (2020) B. Wang et al.
SFMS -2 MoreTurbulent?
Slow-rotator ETGsFast-rotator ETGsSpiral LTGsSpheroidals
Figure 7.
Schematic plot for Fig. 1. The blue band denotes the span of the SFMS ( ± .
35 dex). Above 10 . M (cid:12) galaxies with star formation are illustrated ina relatively face-on view and with spiral arms and di ff erent size of bulges (denoted “Spiral LTGs”). While star-forming galaxies at the very low mass end areshown by symbols with more irregular morphology which is hinted at by their lower values of λ R e . For passive galaxies, we show them as they are seen edge-onin order for a clearer view of disk significance. We emphasize the mass threshold of 10 . M (cid:12) beyond which the genuine slowly rotating ETGs (“Slow-rotatorETGs”) are preferentially found. And other passive galaxies with lower mass are denoted “Fast-rotator ETGs” and “Spheroidals” below 10 . M (cid:12) . The symbolsin this figure were chosen to be the same as in the related fig. 23 and 24 of Cappellari (2016), where one can find further details on the definitions. In Fig. 7 we present a cartoon version of Fig. 1 illustrating themain results and making a direct link between angular momentum λ R e and galaxy morphology. Galaxies are put on SFR − M (cid:63) dia-gram where we use a blue band to show the span of the SFMS. Todistinguish between passive galaxies and those with star formationand also to highlight the disk nature of relatively low-mass passivegalaxies, we use di ff erent types of symbols. We chose the symbolsto be the same as fig. 23 and 24 in the review by Cappellari (2016).This makes it easier for the reader to understand the connectionbetween galaxy properties on the SFR − M (cid:63) and in other relateddiagrams.For passive galaxies, we illustrate them as they are viewededge-on to make their structure recognizable. Except those at thevery low mass end, galaxies with star formation are shown as sys-tems with spiral arms with di ff erent size of bulges. While we putsymbols with more irregular morphology at the low mass end toillustrate the lower λ R e there and it is indeed supported by visualcheck of their SDSS images many of which reveal irregular fea-tures. Stronger turbulence may be the reason for their lower val-ues of λ R e and it will be discussed in the following section. Eventhough our data include almost no passive galaxies at this very low mass end (possibly due to the MaNGA magnitude-based selection),for completeness, we still put symbols for spheroidal galaxies inthis part of parameter space, based on previous results. As they aredominating the passive population at this low mass in the local uni-verse and there is convincing empirical evidence showing their con-nection with dwarf irregular galaxies (Kormendy & Bender 2012).Given the weak star formation dependence of λ R e among low-massgalaxies, the evolutionary link between spheroidals and not-so-coldlow-mass star-forming systems seems natural.Note that here, for the slight decrease of λ R e along the SFMSat the high mass end, we represent this as due to an increase ofthe bulges, following the known link between λ R e and bulge frac-tion (e.g., sec. 3.6.3 of Cappellari 2016). The fact that we observea slight decrease of λ R e only at the high mass of the SFMS is con-sistent with previous observations of a trend of increasing bulge tototal ratio with mass in that region of the diagram (e.g., Bluck et al.2019).To conclude, this figure highlights the similarity between low-mass star-forming and passive galaxies in terms of the significanceof disk components. While it is opposed to the progressively moredominating spheroid components in massive passive galaxies and MNRAS000
35 dex). Above 10 . M (cid:12) galaxies with star formation are illustrated ina relatively face-on view and with spiral arms and di ff erent size of bulges (denoted “Spiral LTGs”). While star-forming galaxies at the very low mass end areshown by symbols with more irregular morphology which is hinted at by their lower values of λ R e . For passive galaxies, we show them as they are seen edge-onin order for a clearer view of disk significance. We emphasize the mass threshold of 10 . M (cid:12) beyond which the genuine slowly rotating ETGs (“Slow-rotatorETGs”) are preferentially found. And other passive galaxies with lower mass are denoted “Fast-rotator ETGs” and “Spheroidals” below 10 . M (cid:12) . The symbolsin this figure were chosen to be the same as in the related fig. 23 and 24 of Cappellari (2016), where one can find further details on the definitions. In Fig. 7 we present a cartoon version of Fig. 1 illustrating themain results and making a direct link between angular momentum λ R e and galaxy morphology. Galaxies are put on SFR − M (cid:63) dia-gram where we use a blue band to show the span of the SFMS. Todistinguish between passive galaxies and those with star formationand also to highlight the disk nature of relatively low-mass passivegalaxies, we use di ff erent types of symbols. We chose the symbolsto be the same as fig. 23 and 24 in the review by Cappellari (2016).This makes it easier for the reader to understand the connectionbetween galaxy properties on the SFR − M (cid:63) and in other relateddiagrams.For passive galaxies, we illustrate them as they are viewededge-on to make their structure recognizable. Except those at thevery low mass end, galaxies with star formation are shown as sys-tems with spiral arms with di ff erent size of bulges. While we putsymbols with more irregular morphology at the low mass end toillustrate the lower λ R e there and it is indeed supported by visualcheck of their SDSS images many of which reveal irregular fea-tures. Stronger turbulence may be the reason for their lower val-ues of λ R e and it will be discussed in the following section. Eventhough our data include almost no passive galaxies at this very low mass end (possibly due to the MaNGA magnitude-based selection),for completeness, we still put symbols for spheroidal galaxies inthis part of parameter space, based on previous results. As they aredominating the passive population at this low mass in the local uni-verse and there is convincing empirical evidence showing their con-nection with dwarf irregular galaxies (Kormendy & Bender 2012).Given the weak star formation dependence of λ R e among low-massgalaxies, the evolutionary link between spheroidals and not-so-coldlow-mass star-forming systems seems natural.Note that here, for the slight decrease of λ R e along the SFMSat the high mass end, we represent this as due to an increase ofthe bulges, following the known link between λ R e and bulge frac-tion (e.g., sec. 3.6.3 of Cappellari 2016). The fact that we observea slight decrease of λ R e only at the high mass of the SFMS is con-sistent with previous observations of a trend of increasing bulge tototal ratio with mass in that region of the diagram (e.g., Bluck et al.2019).To conclude, this figure highlights the similarity between low-mass star-forming and passive galaxies in terms of the significanceof disk components. While it is opposed to the progressively moredominating spheroid components in massive passive galaxies and MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation beyond 10 . M (cid:12) , the disk-free genuinely spheroidal slowly rotat-ing ETGs are preferentially found.The spin parameter used throughout this work is measuredwithin the e ff ective (half-light) ellipse and it may vary using a largeraperture. The half-light ellipse is used because any classificationneeds to be define within a physical scale, and the λ R measuredwithin that radius was shown to be easy to measure for large sam-ples and to correlate well with other galaxy properties (see reviewby Cappellari 2016). However, given the relatively flat λ R profilesbeyond R e (See Fig.5 of Raskutti et al. 2014, Fig.5 of Foster et al.2016 and Fig.14 of Boardman et al. 2017), the kinematic classifica-tion in most cases does not changes when using di ff erent radii andour conclusions would have remained qualitatively the same if wehad adopted a less-optimal and larger aperture.The same dependence on the chosen aperture applies to ourdetermination of the SFR. For this, in Appendix B, we have shownthat the result stays qualitatively the same after we replace the totalSFR shown in Fig. 1 by a SFR measured in a completely di ff er-ent manner, using the H α fluxes derived directly from the MaNGAdata, within one R e .Galaxy populations produced by the state-of-the-art cosmo-logical hydrodynamic simulations have shown qualitatively similarbehaviour in terms of the lower level of rotation for star-forminggalaxies both at lower and higher mass end, and also the fact thatlowest spin is owned by the most massive passive galaxies (Correaet al. 2017; Lagos et al. 2018). But we note that simulated passivegalaxies with M (cid:63) ∼ M (cid:12) are more dispersion dominated thanthe observed ones.It is revealing to compare our Fig. 1 and Fig. 7 with the leftpanel of Fig. 1 of Wuyts et al. (2011), which visualizes the distri-bution of the Sersic (1968) index on the SFR − M (cid:63) diagram. Thatdiagram is often presented to demonstrate the connection betweengalaxy structure and SFR, with the passive galaxies having a indexclose to the de Vaucouleurs (1948) profile ( n =
4) while the starforming ones having exponential profiles ( n =
1) typical for disks.This is interpreted as galaxies generally becoming ellipticals whenthey quench and become passive.Our diagrams show a similar feature. However there is a cru-cial di ff erence. In fact, while in the Wuyts et al. (2011) figure theregion of “ellipticals” span the entire mass range from just above M (cid:63) ∼ M (cid:12) up to the largest masses of nearly M (cid:63) ∼ M (cid:12) ,in our diagrams there is a clear transition at a significantly largermass of M (cid:63) ∼ M (cid:12) . Only above that mass being passive is as-sociated to being slow-rotator “ellipticals”, while for lower massesquenching produces no more than a minor structural transformation(increasing bulges but retaining significant level of rotation). Thisis the key novelty we want to emphasize with this work.A transition around M (cid:63) ∼ M (cid:12) is not unexpected, giventhat only above that critical mass are slow-rotator ETGs starting todominate, while below that mass one only finds spiral galaxies andfast rotator ETGs (e.g. Cappellari 2016). However, in this paper wefirst illustrate this fact specifically in the context of the SFR − M (cid:63) diagram, where this fact is not yet universally appreciated.Beyond fitting the light distribution with single Sersic profiles,e ff orts have been made to decompose galaxies into multiple com-ponents including bulges and disks. A relevant result in Morselliet al. (2017) illustrating bulge to total ratio as a function of stel-lar mass and SFR shows overall consistency with what we foundusing the spin parameter. The same di ff erence appears in the pas-sive population for which the spin reveals a sharp transition amongmassive galaxies whereas Fig. 5 of Morselli et al. (2017) by con- trast indicates very close bulge to total ratio over a large range ofmass.In the following section, we discuss the implications of ourresults in the context of a Λ CDM universe in order to understandthe trend of λ R e with stellar mass and star formation level. Λ CDM universe / late star formation and in / ex situ mass assembly To understand the current kinematics of galaxies, we need to knowwhat factors are key to determining their kinematic state. In princi-ple, whether a galaxy is mainly in ordered rotation or random mo-tion (that is disk-dominated or spheroid-dominated) will depend on1) the angular momentum of gas used as raw material for makingstars and 2) how these stars are assembled. Just as shown in Bucket al. (2019) for a Milky Way like disk galaxy in a cosmologicalhydrodynamical simulation, stars with lower initial birth angularmomentum end up in a non-rotating spherical bulge. But even starsare born with high angular momentum, if they are assembled viaviolent mergers, the final aggregate is still likely to be dominatedby random motion.These two aspects are translated into two crucial factors ofgalaxy formation: 1) formation time of stars of the galaxy and 2) thefractional stellar mass assembled in situ and ex situ. Note that theformation time of stars of the final galaxy is not necessarily closeto the assembly time of this galaxy. As stars can form in separategalaxies at higher redshift while they merger at low redshift to makeup the final galaxy (Oser et al. 2010).The origin of angular momentum of galaxies remains a hottopic in the field. To first order, it is believed that protohalos (in-cluding their gas) gain angular momentum through tidal torquesfrom their environment until maximum expansion (turnaround),and subsequently detach with Hubble flow and collapse into viri-alized structures that preserve their angular momentum (Pee-bles 1969; Doroshkevich 1970; White 1984; Catelan & Theuns1996a,b). Before turnaround, angular momentum in protohalosgrows linearly with time. Therefore, stars formed earlier thanturnaround can have lower specific angular momentum than thoseformed later, contributing to spheroidal component (Zavala et al.2016; Peng & Renzini 2019; Renzini 2020). On the other handmergers, i.e. ex situ mass assembly, tend to randomise the stellarkinematics via violent relaxation and result in a transfer of angularmomentum from galaxies to outer halos (Toomre 1977; Hernquist1992; Naab et al. 2006b). Thus, the angular momentum gained viatidal torques during the linear growth stage can only be preservedwhen stars are assembled in situ, i.e. star formation on the cold gasdisks (Fall & Efstathiou 1980; Mo et al. 1998). This explains theimportance of the second factor put forward in last paragraph. Onething that has not been included explicitly in the second factor isthe wetness of mergers. A significant amount of gas involved indissipative mergers can suppress growth of boxy orbits (Naab et al.2006a) and can also re-build a disk (Hopkins et al. 2009). But giventhat the subsequent stellar disk builds out of the survived gas diskby in situ star formation, the second factor has already implicitlytaken this into account. This means when we say a galaxy has alarge fraction of stars assembled ex situ, it directly rules out thecase where much of its stellar mass is formed out of gas brought bya wet merger and it indicates that dry mergers dominate.As a result, a galaxy is more likely to be disk-dominated when
MNRAS , 1–20 (2020) B. Wang et al. most of its stars are assembled in situ at lower redshift whichechos what is concluded for disk formation in Naab & Ostriker(2017) that to form a disky galaxy in simulation early star formationshould be suppressed by e ff ective feedback so that ejected gas canfall back to the galaxy with higher angular momentum (Governatoet al. 2007; Übler et al. 2014). While a galaxy that either assemblesmuch mass via accreting existing stars or converts gas into starsat early universe tends to end up being spheroid-dominated. Whatoutlined here is much in line with the conclusion in Lagos et al.(2017). Using state-of-the-art cosmological hydrodynamical simu-lation, they found galaxy mergers and early star formation quench-ing (thus most of stars form at high redshift) as two primary chan-nels to galaxies with low specific angular momentum. With these two factors in mind, now we attempt to understand theresult that among massive galaxies star-forming ones are rotatingwhereas passive ones are not and low mass galaxies are mainlydisk-dominated regardless of star formation.In the currently accepted paradigm of the Λ CDM universe,gas cools and condenses into stars at the bottom of dark matterhalos which are the result of gravitationally amplified primordialdensity perturbations. Highest density peaks grow rapidly towardmassive halos and they later form the central part of clusters afterhierarchical merging. Within these most massive halos, the evo-lution of the galaxies proceeds clearly in two phases (Naab et al.2007; Feldmann et al. 2010; Oser et al. 2010; Johansson et al. 2012;Qu et al. 2017). At high redshifts ( z (cid:38) ff ective (Kormendy& Ho 2013). At this stage mass assembly is switched to ex situmode and galaxies further grow by accreting stars formed in othergalaxies (mergers tend to be dry due to massive halos). And it hasbeen reported that accreted mass on average makes up a half ofthese massive galaxies (Conselice 2014). This two-phase charac-teristic is particularly true for passive galaxies because they residein more massive halos than their star-forming counterparts, whichhas been shown by weak gravitational lensing (Mandelbaum et al.2006, 2016). Therefore, it can be understood why present-day mas-sive passive galaxies have their spheroid-dominated kinematics ac-cording to the two factors discussed previously.For galaxies with lower mass, cosmological simulationsclearly indicate that stellar accretion is less important (Oser et al.2010; Lackner et al. 2012) so that in situ star formation prevails. But rarer cases do happen where a minor merger completely destroys thepre-existing disk (Jackson et al. 2019) or where a significant fraction ofaccreted gas has largely misaligned angular momentum (Sales et al. 2012).And in these cases though little mass is assembled ex situ, galaxies can endup with spheroids.
On the other hand, low-mass systems form later (i.e. with youngerage; Gallazzi et al. 2005). This so-called downsizing (Cowie et al.1996; Neistein et al. 2006) is partly due to more e ff ective feedbackthat delays star formation in shallower potential wells (Maller &Dekel 2002). Together, ubiquitous disks shown among low-massMaNGA galaxies are expected because of both more disk con-struction (later gas infall) and less disk destruction (fewer mergers).However, exception exists at the very low mass end of the SFMS( M (cid:63) ∼ . M (cid:12) ). Just like their more massive star-forming coun-terparts, these low-mass star-forming galaxies assembled most ofmass at low redshifts (Asari et al. 2007; Peng et al. 2010; Leitner2012) via gas accretion. But they do not show significant rotationas more massive star-forming galaxies do, which is likely due totheir large cold gas reservoir. For these systems, the mass of coldatomic gas is already about three times the mass of stars (Huanget al. 2012). And the strong specific gas accretion rate responsiblefor this into a shallow potential well may disturb disks and booststurbulence, reminiscent of high-redshift turbulent galaxies (Genzelet al. 2008; Law et al. 2012). Supernova feedback can also play animportant role in disrupting existing gas disks as well as prevent-ing the supply of high angular momentum gas for disk construction(Dekel et al. 2020). This suggests a di ff erent assembly mode amongthese less massive systems (Clauwens et al. 2018). Above arguments qualitatively explains the relation of kinematicsand star formation we observe as a function of stellar mass. Never-theless, kinematic and morphological evolution of galaxies involvemuch more than what is discussed above.There are other important internal processes that also play arole. Large Jeans mass on high-redshift turbulent disks causes frag-mentation into massive clumps which migrate toward central regionunder dynamical friction and contribute to classical bulge growth(Dekel & Burkert 2014; Zolotov et al. 2015). This may be alsopartly responsible for kinematics of present-day massive passivegalaxies.Kormendy & Kennicutt (2004) argues while hierarchicallydriven galaxy evolution is more dominant in the past, now secu-lar internal evolution is gradually taking over. Among large non-axisymmetric structures, bars are known to enhance galaxy massconcentration and buckle to make disks thicker (Kormendy & Ken-nicutt 2004). But these instabilities usually serve as mild negativefeedback to adjust galaxies rather than altering them completely.For example, bars grow in systems that are dynamically too coldand with mass concentration too low. They fuel central star forma-tion by funnelling gas in and heat the disk vertically under buck-ling instability but increased mass concentration in turn dissolvesthe bar (Hasan & Norman 1990; Friedli & Benz 1993; Sellwood &Moore 1999; Shen & Sellwood 2004), which renders the e ff ects ofbar less overwhelming.Externally, it is also reported that tidal interaction with neigh-bours in group environment can modify the shape of galaxies (Bin-ney & Silk 1979; Boselli & Gavazzi 2006). However, except themost massive galaxies we do not see apparent dependence of λ R e on environment at a given star formation level. Though we cannotexclude the possibility that these tidal interactions move galaxiesalong the median relation, i.e. reducing λ R e and SFR together alongthe track of central galaxies. For the most massive galaxies, wedo identify a trend that random motion dominates more if galax-ies are central / in denser environment / in richer groups, at the samestar formation level. This is qualitatively consistent with merging is MNRAS000
On the other hand, low-mass systems form later (i.e. with youngerage; Gallazzi et al. 2005). This so-called downsizing (Cowie et al.1996; Neistein et al. 2006) is partly due to more e ff ective feedbackthat delays star formation in shallower potential wells (Maller &Dekel 2002). Together, ubiquitous disks shown among low-massMaNGA galaxies are expected because of both more disk con-struction (later gas infall) and less disk destruction (fewer mergers).However, exception exists at the very low mass end of the SFMS( M (cid:63) ∼ . M (cid:12) ). Just like their more massive star-forming coun-terparts, these low-mass star-forming galaxies assembled most ofmass at low redshifts (Asari et al. 2007; Peng et al. 2010; Leitner2012) via gas accretion. But they do not show significant rotationas more massive star-forming galaxies do, which is likely due totheir large cold gas reservoir. For these systems, the mass of coldatomic gas is already about three times the mass of stars (Huanget al. 2012). And the strong specific gas accretion rate responsiblefor this into a shallow potential well may disturb disks and booststurbulence, reminiscent of high-redshift turbulent galaxies (Genzelet al. 2008; Law et al. 2012). Supernova feedback can also play animportant role in disrupting existing gas disks as well as prevent-ing the supply of high angular momentum gas for disk construction(Dekel et al. 2020). This suggests a di ff erent assembly mode amongthese less massive systems (Clauwens et al. 2018). Above arguments qualitatively explains the relation of kinematicsand star formation we observe as a function of stellar mass. Never-theless, kinematic and morphological evolution of galaxies involvemuch more than what is discussed above.There are other important internal processes that also play arole. Large Jeans mass on high-redshift turbulent disks causes frag-mentation into massive clumps which migrate toward central regionunder dynamical friction and contribute to classical bulge growth(Dekel & Burkert 2014; Zolotov et al. 2015). This may be alsopartly responsible for kinematics of present-day massive passivegalaxies.Kormendy & Kennicutt (2004) argues while hierarchicallydriven galaxy evolution is more dominant in the past, now secu-lar internal evolution is gradually taking over. Among large non-axisymmetric structures, bars are known to enhance galaxy massconcentration and buckle to make disks thicker (Kormendy & Ken-nicutt 2004). But these instabilities usually serve as mild negativefeedback to adjust galaxies rather than altering them completely.For example, bars grow in systems that are dynamically too coldand with mass concentration too low. They fuel central star forma-tion by funnelling gas in and heat the disk vertically under buck-ling instability but increased mass concentration in turn dissolvesthe bar (Hasan & Norman 1990; Friedli & Benz 1993; Sellwood &Moore 1999; Shen & Sellwood 2004), which renders the e ff ects ofbar less overwhelming.Externally, it is also reported that tidal interaction with neigh-bours in group environment can modify the shape of galaxies (Bin-ney & Silk 1979; Boselli & Gavazzi 2006). However, except themost massive galaxies we do not see apparent dependence of λ R e on environment at a given star formation level. Though we cannotexclude the possibility that these tidal interactions move galaxiesalong the median relation, i.e. reducing λ R e and SFR together alongthe track of central galaxies. For the most massive galaxies, wedo identify a trend that random motion dominates more if galax-ies are central / in denser environment / in richer groups, at the samestar formation level. This is qualitatively consistent with merging is MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation strongest for central galaxies in galaxy clusters (Ostriker & Haus-man 1977; De Lucia & Blaizot 2007). And it confirms that at givenstellar mass, kinematic state indeed depends on environment as op-posed to the purely mass-driven kinematic trend in some studiesbased on smaller dataset (e.g., Greene et al. 2017; Brough et al.2017).One may also resort to the properties of dark matter halos tounderstand galaxies considering the close connection between thehalo and the baryonic component (Wechsler & Tinker 2018). As-suming that dark matter halo and gas share the same specific an-gular momentum, galaxy populations with realistic properties canbe reproduced with the knowledge of spin distribution from nu-merical simulations (Dalcanton et al. 1997; Jimenez et al. 1997;Mo et al. 1998; van den Bosch 1998). And those low spin halosmay partly responsible for the formation of bulges and spheroidalgalaxies. But clearly there is gap between the numbers of dispersionsupported galaxies and halos at the low spin tail of distribution (Ro-manowsky & Fall 2012). And the spin distribution of halos fromsimulations does not depend on the mass of halos (e.g., Maller et al.2002) , in contrast with the dramatic mass trend that we found forgalactic spin parameter. These suggest more roles played by bary-onic physics, such as the heating from stellar feedback that pre-vents over-cooling and its subsequent massive transfer of angularmomentum from baryons to halo particles (Maller & Dekel 2002),which can lead to a mass dependence of stellar angular momentum. From our results we may also be able to draw some implicationsfor how star formation is getting or has got quenched.For massive galaxies, as discussed above the decrease of SFRtogether with the shrinking significance of stellar disk can be linkedby progressively more massive dark matter halos. Presence of amassive halo implies a merger-rich assembly history as well assuggesting the absence of cold streams. And an extremely supermassive black hole as the outcome of abundant mergers keeps thecircumgalactic medium hot.By contrast, the disk dominance present even among thereddest low-mass galaxies implies that those contributing fac-tors to the quenching of low-mass galaxies do not severely a ff ecttheir kinematics. Without doubt, one would immediately think ofenvironment-related mechanisms which are believed to be e ff ectiveamong low-mass galaxies. For instance, various kinds of hydrody-namical interaction with hot intergalactic medium such as ram pres-sure stripping (e.g., Gunn & Gott 1972; Abadi et al. 1999; Quiliset al. 2000) and strangulation (e.g., Larson et al. 1980; Peng et al.2015) can largely a ff ect gas disks while leaving stellar disks almostintact. However, considering that these mechanisms are mainly ef-ficient in massive halos there comes a question that why median λ R e at a given star formation level does not di ff er for low-mass galax-ies in di ff erent environment. A straightforward solution would bethat the quenching mechanisms responsible for star formation ces-sation in relatively isolated galaxies also do little on the kinematics.Thus commonly proposed reionization and stellar feedback (Dekel& Silk 1986; Bullock et al. 2000; Somerville 2002) as primaryquenching mechanisms for low-mass galaxies are indeed feasiblefrom this stand point. Despite of some observational evidence against this (Cervantes-Sodiet al. 2008; Berta et al. 2008).
So far the extraction of conclusion for many of our results has reliedon the statistical significance given by MaNGA data release 15. Forexample, such large sample allows for a fairly good coverage onSFR − M (cid:63) plane down to a relatively low mass which has helpedto reveal the striking mass trend of kinematics. Additionally, it alsosheds light on those straggling counter-rotating populations on λ − (cid:15) plane that would otherwise be missed by smaller samples due to therarity. In this section, we briefly compare our Fig. 2 and Fig. 3 withthe main results in van de Sande et al. (2018) and Cortese et al.(2019) respectively given they are highly relevant.van de Sande et al. (2018) illustrates a good correlation be-tween intrinsic ellipticity (as inferred on V /σ − (cid:15) diagram) andluminosity-weighted age of ∼
800 galaxies from Sydneyâ ˘A ¸SAus-tralian Astronomical Observatory Multi-object Integral field spec-trograph (SAMI) Galaxy Survey (Croom et al. 2012), which is sim-ilar to what we observe for intrinsic ellipticity and star formationlevel. The consistency is marked especially considering that howmuch the di ff erence is between their stellar age and the SFR that weuse. They take the age of a representative single stellar populationmodel that best reproduces the measured Lick indices within aper-ture of radius one R e (Scott et al. 2017), while SFR here is the oneaveraged over the past 100-Myr star formation history of the best fitstellar population synthesis model, fitted to total light (rather thanin an aperture). The "stragglers" we found on λ − (cid:15) plane barelyhave counterparts on V /σ − (cid:15) plane in van de Sande et al. (2018),which is very likely due to their relatively small sample size.The main result of Cortese et al. (2019) (their Fig. 3) showsthe variation in stellar V /σ as a function of star formation level for ∼
170 satellite galaxies with SAMI IFS data, resembling what wehave done for MaNGA satellite galaxies in the first row of Fig. 3.Because in their result the average change is not far from zero fora large range of star formation level, they conclude that satellitegalaxies undergo little structure change during quenching phase.However, from our results the structure change as indicated by λ R e does not highly depend on environment but stellar mass. And in-deed when looking at Fig. 3 of Cortese et al. (2019), there is de-tectable mass trend at a given star formation level in the same senseas we found in our data. So their mean relation being close to zerois due to the fact that the result is relatively dominated by less mas-sive galaxies ( M (cid:63) (cid:46) . M (cid:12) ). It is true that we have analyzedin a slightly di ff erent way and particularly they match ellipticitywhen getting ∆ V /σ . But as we have shown that our conclusion doesnot change when further taking ellipticity into account (Fig. 5), thisdi ff erence should not be a key point. In this work, using the spin parameter λ R e as a kinematic indicatorof disk significance we have studied the correlation between mor-phology and star formation level and its dependence on stellar massand environment for ∼ −M (cid:63) plane down to about10 . solar mass. And our findings are summarized as follows:(i) The SFMS is approximately a ridge of maximum valuesfor the specific angular momentum λ R e distribution on theSFR − M (cid:63) plane. In fact, λ R e decreases toward both lowand high SFR, at given stellar mass. On the SFMS galaxieshave large specific angular momentum ( λ R e ∼ . MNRAS , 1–20 (2020) B. Wang et al. alently are dominated by rotation, and there is little changein λ R e with mass, with the exception of the lowest masses( M (cid:63) (cid:46) . M (cid:12) ), where λ R e decreases.(ii) Below the SFMS, and for M (cid:63) (cid:38) M (cid:12) , there is a dramaticchange in λ R e with SFR ( ∆ λ R e ∼ .
5) and passive galaxiesare dominated by slow-rotator ETGs. When M (cid:63) (cid:46) M (cid:12) the variation of λ R e with SFR becomes more marginal andpassive galaxies are mainly fast-rotator ETGs, which have asignificant amount of rotation. And particularly at low masses( M (cid:63) ∼ . M (cid:12) ) on average ∆ λ R e has a value of only about0.1.(iii) Such progressively tighter relation between λ R e and SFR to-ward high stellar mass displays as clearer stratification patternon the ( λ R e , (cid:15) ) plane, in the sense that galaxy population witha certain star formation level matches the theoretical track, fordi ff erent inclinations, of galaxy population of certain intrinsicellipticity. This means for massive galaxies intrinsic morphol-ogy is a good indicator of star formation state.(iv) Counterrotating stellar disks are clear outliers on the ( λ R e , (cid:15) )plane in the lower right region (relatively high apparent el-lipticity but low λ R e ). They stand out for their star formationlevel larger than what one would expect given their λ R e . Thisis because their low λ R e is due to counterrotating stellar disksand not to a spheroidal non-rotating morphology.(v) The environmental dependence of λ R e − SFR relation is muchweaker than its mass dependence but it is unambiguous for themassive galaxies. In our highest mass bin 10 . − . M (cid:12) ,central galaxies or the galaxies in dense regions or rich groupson average have a lower value of λ R e . While no obvious envi-ronmental dependence is found for low-mass galaxies.(vi) The position of the distributions of spiral, elliptical andindeterminate-type galaxies (according to Galaxy Zoo 1 vi-sual classifications) on ( λ R e , (cid:15) ) plane suggests a strong con-nection between galaxy morphology and kinematics. In par-ticular, the indeterminate-type galaxies right occupy the re-gion between spiral and elliptical galaxies and hence may rep-resent an transitional population between the two. Togetherthey form a continuous sequence which may also imply anevolutionary track of galaxies in their morphology and kine-matics. However it is clear that a fraction of relatively face-on passive disks are visually classified into a di ff erent cate-gory compared with their edge-on counterparts. This showsthe strong dependence of visual morphological classificationson inclination and reflects the advantage of using IFS data toprobe galactic structure.These results have shown that a good correspondence be-tween star formation level and intrinsic morphology is only seenfor massive galaxies ( M (cid:63) (cid:38) . M (cid:12) ). And the traditional picturethat galaxies below the SFMS are generally spheroidal or bulge-dominated has been shown not to apply for galaxies with lowermass (10 . (cid:46) M (cid:63) (cid:46) M (cid:12) ). As among them, even the red-dest (with oldest stellar populations and lowest SFR) are still disk-dominated fast-rotator ETGs. This concurs with the fact found byATLAS survey that two thirds of visually classified ellipticalgalaxies (which are thought to be spheroidal or ellipsoidal in 3Dspace) are fast rotators thus with significant disk component.We have discussed that this mass and star formation depen-dence of disk significance can be qualitatively understood in thecontext of formation time of stars and mass assembly mode. Agalaxy that either assembles much mass via accreting existing starsor has most of its stars formed at early universe tends to end up being spheroid-dominated. While a galaxy is more disk-dominatedif it assembles mainly via in situ star formation fuelled by gas ac-cretion at later time. And the flat λ R e − SFR relation of less massivegalaxies together with its negligible dependence on environmentsuggest that though the quenching mechanisms are likely to be dif-ferent for group and field low-mass galaxies, they all have littlee ff ect on galaxy kinematics. ACKNOWLEDGEMENTS
BW is grateful for the financial support from China ScholarshipCouncil during his stay in Oxford. YP acknowledges the NationalKey R&D Program of China, Grant 2016YFA0400702 and NSFCGrant No. 11773001, 11721303, 11991052.Funding for the Sloan Digital Sky Survey IV has been pro-vided by the Alfred P. Sloan Foundation, the U.S. Department ofEnergy O ffi / University of Tokyo, the Ko-rean Participation Group, Lawrence Berkeley National Labora-tory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institutfür Astrophysik (MPA Garching), Max-Planck-Institut für Extrater-restrische Physik (MPE), National Astronomical Observatories ofChina, New Mexico State University, New York University, Uni-versity of Notre Dame, Observatário Nacional / MCTI, The OhioState University, Pennsylvania State University, Shanghai Astro-nomical Observatory, United Kingdom Participation Group, Uni-versidad Nacional Autónoma de México, University of Arizona,University of Colorado Boulder, University of Oxford, Universityof Portsmouth, University of Utah, University of Virginia, Univer-sity of Washington, University of Wisconsin, Vanderbilt University,and Yale University.
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APPENDIX A: STAR FORMATION MAIN SEQUENCE
Following Renzini & Peng (2015), the star formation main se-quence (the dark blue dashed line in Fig. A1 labeled as "SDSS")used in this work is defined by the ridge line of probability den-sity distribution (illustrated by gray scale and contours) of SDSSgalaxies in sample S GSWLC in redshift range 0 . < z < . M (cid:63) are binned at reso-lution about 0.12 and 0.06 dex respectively. And in the estimationeach galaxy is weighted by V total / V max , the co-moving volume ratiobetween total volume in our redshift range and the volume in range0 . < z < z max where z max is the maximum redshift at which acertain galaxy can still be included in SDSS spectroscopic survey(given the r band apparent magnitude limit 17.77), or z max = . M (cid:63) bin. We fit it with a second-order polynomial and get:log SFR = − . + .
76 log M (cid:63) − .
21 (log M (cid:63) ) (A1) MNRAS000
21 (log M (cid:63) ) (A1) MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation Figure A1.
The V max corrected probability density distribution and its ridge(the dark blue dashed line labeled as "SDSS") of SDSS galaxies in sample S GSWLC in redshift range 0 . < z < .
08 on SFR − M (cid:63) plane. Gray scalereflects the contour level with a decreasing order from dark to light. TheSFMS defined by S MaNGA (lebeled by "MaNGA") and its subsample offast rotating galaxies with λ R e > . λ R e > . And this analytic line is used throughout the work.Just for comparison, the SFMS defined in the same way by us-ing much smaller sample S MaNGA and its subsample of fast rotatinggalaxies with λ R e > . ff erence is markedly small. APPENDIX B: REPRODUCTION OF FIG. 1 WITH SFRMEASURED IN EFFECTIVE RADIUS
In this section we test the robustness of the qualitative trend wepresented in Fig. 1, by using a completely di ff erent approach to in-fer the SFR. For this we use the SFR derived using the H α fluxeswithin one e ff ective radius SFR R e in the MaNGA data. Our alter-native version of Fig. 1, when using the MaNGA SFR is shown inFig. B1.To obtain SFR R e , we took MAPS files (the ones used for mea-suring the spin parameter) for MaNGA galaxies in our sample, asproduced by the MaNGA DAP (Westfall et al. 2019b). The ap-proach used for the extraction of the gas fluxes from the MaNGAcubes was described in Belfiore et al. (2019). For spaxels that fallinto one elliptical e ff ective radius (defined by r-band elliptical Pet-rosian e ff ective radius, axial ratio and position angle catalogued inthe NSA), we used BPT diagram (Baldwin et al. 1981) to clas-sify them into star-forming and non-star-forming according to thedefinition of Kau ff mann et al. 2003b. And then we corrected the H α flux of star-forming spaxels for dust extinction assuming aHowarth (1983) Galactic extinction curve with R V = . H α/ H β = .
86. Lastly we summed all dust-corrected H α flux of star-forming spaxels within one R e and converted it to SFRusing the calibration in Calzetti 2013:SFR H α / ( M (cid:12) yr − ) = . × − × L H α / (erg s − ) (B1)A factor of 95% was then applied to adjust from Kroupa to ChabrierIMF (Salim et al. 2007). APPENDIX C: TESTING HOW THE DISTRIBUTIONS ON λ − (cid:15) PLANE CHANGE WITH INCLINATION
In this appendix, we show how the distribution on λ − (cid:15) plane ofa sample of models change with their inclination angles. Such thatwe prove star-bursting MaNGA galaxies are not merely the face-onversion of star-forming MaNGA galaxies.In Fig. C1, the red and blue line denote the probability densitycontour enclosing 68% of total, respectively for the star-burstingand star-forming galaxies in our MaNGA sample in stellar massrange 10 − M (cid:12) . The probability density distributions are de-rived in the same manner as in the main text. And the stellar massbin is chosen to be the range for which we observe the drop of λ R e when going beyond the SFMS. Compared with star-forming galax-ies it is clear that the distribution of star-bursting galaxies populateslower left, consistent with their lower λ R e on average. However, itmay not be trivial to convince one that this is due to their smallerintrinsic ellipticity rather than lower inclination angles. As whencutting o ff the high inclination tip of the star-forming distribution,the remaining distribution may resemble the star-bursting one.To investigate this we created a sample of 3000 model galax-ies based on tensor virial theorem. For each model the intrinsic el-lipticity (cid:15) intr was randomly drawn from a Gaussian distribution withmean 0.95 and standard deviation 0.25 trimmed between (0 , , . × (cid:15) intr ] and with a randomorientation. So that, as shown by the black solid line in Fig. C1, weget a density contour of model galaxies similar to the MaNGA star-forming one. We further assembled two samples of models with thesame parameter configurations but restricted in certain inclinationrange [0 ,
70] and [0 ,
50] degrees. Their density contours enclosing68% of total are illustrated by black dashed and gray dotted lineseparately.The result shows that when restricting models to be more face-on, the distributions still reach the high λ R e envelope of the dis-tribution without restriction. This will be a key discrepancy if onethinks the star-bursting galaxies are only more face-on than the star-forming galaxies. Because the star-bursting galaxies have lower λ R e not only due to their distribution having lower bottom boundary butalso the lower top boundary, suggesting intrinsically lower elliptic-ity. APPENDIX D: IMAGES AND KINEMATIC MAPS OF THE"STRAGGLERS"
In this appendix, from the perspective of line-of-sight velocity andvelocity dispersion maps, we show that those "stragglers" on λ R e − (cid:15) plane, i.e. galaxies with star formation level mismatched with theirmeasured λ R e discussed in Section 4.1, are mostly galaxies withsignificant counterrotating stellar components.Like already mentioned in the main text, the maps shown inFig. D1 are for 12 galaxies in the two lower mass bins in the box0 < λ R e < . . < (cid:15) < . ∆ MS > −
1. For each galaxy,from left to right its SDSS g-r-i composite image, line-of-sight ve-locity map and line-of-sight dispersion map is displayed respec-tively. Noteworthily, many of them do not have clear hourglass-likevelocity field and centrally peaked dispersion field, both of whichare features of normal rotators. Instead, there are a large fraction ofvelocity maps indicating flipped rotating axis (e.g. the first, fifthand sixth of the second column) and also dispersion maps withtwo peaks away from center (the so-called "two-sigma" feature).These are signals that galaxies have significant counterrotating stel-lar components. By counting the "two-sigma" feature in dispersion
MNRAS , 1–20 (2020) B. Wang et al. log ( / ) l o g S F R R e [ y r ] R e log ( / ) l o g S F R R e [ y r ] R e Figure B1.
Reproduction of Fig. 1 using SFR measured from the MaNGA IFS data, using the H α fluxes within one half-light radius. R e MaNGA SBMaNGA SFTVT inc [0, 90]TVT inc [0, 70]TVT inc [0, 50]
Figure C1.
Probability density contours enclosing 68% of total for MaNGAstar-forming (blue), MaNGA star-bursting (red) galaxies and models basedon tensor virial theorem (TVT) with di ff erent inclination restrictions. maps, which is most sensitive to counterrotating disks, here weidentify at least 7 out of 12 are counterrotating galaxies. APPENDIX E: LOW-SPIN GALAXIES ON THE SFMS
Galaxies on the SFMS are generally fast rotating while there arestill systems with apparently low values of λ R e .We have visually checked the velocity and dispersion maps ofall galaxies on the SFMS with λ R e < .
2, in low (10 − M (cid:12) ; 24galaxies) and high stellar mass (10 − . M (cid:12) ; 16 galaxies) binsrespectively. A randomly chosen sample of 10 galaxies of each sortare shown in Fig. E1.As can be seen from the upper section, most of these low-mass galaxies display complex velocity field, suggesting they be-ing intrinsically slowly rotating systems. Many of them have lowangular size but are still well resolved by the MaNGA IFU. In thelower section, it shows that among these massive galaxies thereare also two with complex velocity field (the first and the last).But clearly, di ff erent from the low-mass systems, six of these mas- sive galaxies display normal rotation velocity field (even thoughsome of these galaxies are also small) and feature very open ve-locity contours which is the signal of face-on disks (see also Fig.3 of Cappellari (2016) for an illustration). A representative is thefirst galaxy in the right column. This suggests a significant frac-tion of them have apparently low spin primarily because they areviewed relatively face-on. We note that the apparent red colour ofthese massive star-forming galaxies is partly due to their lower spe-cific SFR and higher dust attenuation than star-forming galaxiesof lower mass. And five of these ten massive galaxies, for whichwe collected GALEX NUV and WISE 24 microns data, are all onthe SFMS according to SFRs derived from NUV plus 24 micronsluminosity.This di ff erence between low- and high-mass galaxies accordsthe decreasing λ R e trend toward low mass end that we see on theSFMS in Fig. 1. This paper has been typeset from a TEX / L A TEX file prepared by the author.MNRAS000
2, in low (10 − M (cid:12) ; 24galaxies) and high stellar mass (10 − . M (cid:12) ; 16 galaxies) binsrespectively. A randomly chosen sample of 10 galaxies of each sortare shown in Fig. E1.As can be seen from the upper section, most of these low-mass galaxies display complex velocity field, suggesting they be-ing intrinsically slowly rotating systems. Many of them have lowangular size but are still well resolved by the MaNGA IFU. In thelower section, it shows that among these massive galaxies thereare also two with complex velocity field (the first and the last).But clearly, di ff erent from the low-mass systems, six of these mas- sive galaxies display normal rotation velocity field (even thoughsome of these galaxies are also small) and feature very open ve-locity contours which is the signal of face-on disks (see also Fig.3 of Cappellari (2016) for an illustration). A representative is thefirst galaxy in the right column. This suggests a significant frac-tion of them have apparently low spin primarily because they areviewed relatively face-on. We note that the apparent red colour ofthese massive star-forming galaxies is partly due to their lower spe-cific SFR and higher dust attenuation than star-forming galaxiesof lower mass. And five of these ten massive galaxies, for whichwe collected GALEX NUV and WISE 24 microns data, are all onthe SFMS according to SFRs derived from NUV plus 24 micronsluminosity.This di ff erence between low- and high-mass galaxies accordsthe decreasing λ R e trend toward low mass end that we see on theSFMS in Fig. 1. This paper has been typeset from a TEX / L A TEX file prepared by the author.MNRAS000 , 1–20 (2020) inematic-morphology vs star-formation relation Figure D1.
Images and kinematic maps of the 12 "stragglers". For each galaxy, the panels from left to right represent, respectively (1) SDSS g-r-i compositeimage with MaNGA bundle superimposed, (2) line-of-sight velocity and (3) line-of-sight velocity dispersion. In each image, the MaNGA plate-ifu ID forthe galaxy is shown at the bottom together with its stellar mass and star formation level (SB, SF, GV corresponding to ∆ MS > . − . < ∆ MS < . − . < ∆ MS < − .
35) shown on the top left. For velocity and dispersion maps, FWHM of MaNGA beam is denoted at bottom left. Colour bars indicate thedynamic range in unit km / s and note that the range of velocity map is symmetric with respect to zero. Black dashed ellipses mark the boundary within whichthe spin parameter λ R e is measured.MNRAS , 1–20 (2020) B. Wang et al.
Low-mass low-spin star-forming galaxies
High-mass low-spin star-forming galaxies
Figure E1.
Low-spin ( λ R e < .
2) star-forming galaxies with low mass (upper section; 10 − M (cid:12) ) and high mass (lower section; 10 − . M (cid:12) ).Additional to the maps shown in Fig. D1, here we also show H α flux density maps in erg / ( s cm spaxel) in log scale at the end of row for each galaxy. Thevalue of λ R e and ellipticity are attached at the bottom of SDSS images. MNRAS000