Planetary Nebula Spectrograph survey of S0 galaxy kinematics. II. Clues to the origins of S0 galaxies
A. Cortesi, M. R. Merrifield, L. Coccato, M. Arnaboldi, O. Gerhard, S. Bamford, N. R. Napolitano, A. J. Romanowsky, N. G. Douglas, K. Kuijken, M. Capaccioli, K. C. Freeman, K. Saha, A. L. Chies-Santos
aa r X i v : . [ a s t r o - ph . C O ] A p r Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 2 September 2018 (MN L A TEX style file v2.2)
Planetary Nebula Spectrograph survey of S0 galaxykinematics. II. Clues to the origins of S0 galaxies
A. Cortesi , , ⋆ , M. R. Merrifield , L. Coccato , M. Arnaboldi , O. Gerhard ,S. Bamford , N. R. Napolitano , A. J. Romanowsky , N. G. Douglas ,K. Kuijken , M. Capaccioli , K. C. Freeman , K. Saha , and A. L. Chies-Santos University of Nottingham, School of Physics and Astronomy, University Park, NG7 2RD Nottingham, UK European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany Max-Planck-Institut f¨ur Extraterrestrische Physik, Giessenbachstrasse, 85741 Garching, Germany Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Naples, Italy Department of Physics and Astronomy, San Jos´e State University, One Washington Square, San Jose, CA, 95192, USAand University of California Observatories, 1156 High St., Santa Cruz, CA 95064, USA Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands Dipartimento di Fisica, Universit`a “Federico II”, Naples, Italy Research School of Astronomy and Astrophysics, Australian National University, Canberra, Australia ; ABSTRACT
The stellar kinematics of the spheroids and discs of S0 galaxies contain clues totheir formation histories. Unfortunately, it is difficult to disentangle the two compo-nents and to recover their stellar kinematics in the faint outer parts of the galaxiesusing conventional absorption line spectroscopy. This paper therefore presents thestellar kinematics of six S0 galaxies derived from observations of planetary nebulae(PNe), obtained using the Planetary Nebula Spectrograph. To separate the kinemat-ics of the two components, we use a maximum-likelihood method that combines thediscrete kinematic data with a photometric component decomposition. The results ofthis analysis reveal that: the discs of S0 galaxies are rotationally supported; however,the amount of random motion in these discs is systematically higher than in compa-rable spiral galaxies; and the S0s lie around one magnitude below the Tully–Fisherrelation for spiral galaxies, while their spheroids lie nearly one magnitude above theFaber–Jackson relation for ellipticals. All of these findings are consistent with a sce-nario in which spirals are converted into S0s through a process of mild harassment or“pestering,” with their discs somewhat heated and their spheroid somewhat enhancedby the conversion process. In such a scenario, one might expect the properties of S0sto depend on environment. We do not see such an effect in this fairly small sample,although any differences would be diluted by the fact that the current location doesnot necessarily reflect the environment in which the transformation occurred. Similarobservations of larger samples probing a broader range of environments, coupled withmore detailed modelling of the transformation process to match the wide range ofparameters that we have shown can now be measured, should take us from these firststeps to the definitive answer as to how S0 galaxies form.
Key words: galaxies: elliptical and lenticular – galaxies: evolution – galaxies: kine-matics and dynamics. ⋆ email:[email protected] (cid:13) Cortesi et al.
The origin of lenticular, or S0, galaxies, and in particularwhether they are more closely related to spiral galaxies orelliptical galaxies, remains obscure. They display the bulge-plus-disc morphology that we associate with spiral galaxies,but they lack the young stars in spiral arms that we asso-ciate with such systems, and tend to be more dominated bytheir spheroidal bulge components, making it tempting toassociate them with elliptical galaxies.Moving away from purely morphological considerations,we might hope that kinematic information can help to ascer-tain which other galaxies are S0s closest cousins, since thetraditional view is that disc-dominated spiral galaxies willreflect that morphology in rotationally-dominated kinemat-ics, while elliptical galaxies are largely supported by ran-dom motions. However, more recent data suggests that thesituation is somewhat subtler. The importance of rotationwas quantified by Emsellem et al. (2007), who defined thequantity λ R , the cumulative specific angular momentum ofgalaxies as a function of radius, seeking to draw a distinc-tion between disc- and bulge-dominated systems via thisparameter. Unfortunately, they show that there is no cleardichotomy in this quantity, with a broad spectrum of de-grees of rotational support. Coccato et al. (2009) calculatethe same quantity for a sample of elliptical galaxies, but us-ing PNe as tracers of the velocity field and, in this way, ex-ploring a wider range of radii. They show that the recovered λ R smoothly join the quantity obtained with the SAURONdata, which describe the central regions of the galaxies,where PNe are not detectable. This radially-extended recon-struction of the specific angular momentum for a sample ofelliptical (Coccato et al. et al. et al. et al. Figure 1.
Plot showing a measure of specific angular momentumas a function of radius for a sample of early-type galaxies. Blacksolid lines are S0s from Cortesi et al. (2011), black dashed linesare S0s from Coccato et al. (2009), and red lines are ellipticalsfrom Coccato et al. (2009). The dotted line shows the suggestedseparation between slow and fast rotators as a kinematic classifi-cation scheme (Emsellem et al. ply spiral galaxies that have quietly ceased forming stars,one would expect their stellar discs to have the same kine-matic properties as those in spirals; if, on the other hand, amore violent event such as a minor merger led to the tran-sition from spiral to S0, one might expect the disc, if notdestroyed in the process, to at least have had its randommotions increased significantly (Bournaud, Jog & Combes2005). Equally, with reliable kinematic parameters for theindividual components, we can see where they lie relative tothe usual kinematic scaling relations followed by spirals andellipticals, to see if they could plausibly have evolved fromsuch progenitors.In this paper, we therefore apply the kinematic bulge–disc decomposition technique developed in Cortesi et al. (2011) to the sample of six S0s with suitable PNe data pre-sented in Cortesi et al. (2013). This sample was selected tospan a range of environments in order to see if the evolu-tionary properties depend systematically on surroundings:NGC 7457 and NGC 3115 are isolated; NGC 1023 andNGC 2768 are the dominant galaxies of two small groups(5-6 members); while NGC 3384 and NGC 3489 are satellitegalaxies of the Leo Group (30 members). The Hubble typesof these galaxies and the adopted distance moduli are listedin Table 1.The remainder of this paper is laid out as follows. InSection 2, we present the photometric bulge–disc decompo-sition that underlies the analysis, and confirms the nature ofthese galaxies as composite S0 systems. Section 3 then usesthis decomposition to model the spheroid and disc kinemat-ics of each system, and Section 4 looks at the characteristickinematics of the separate components for indications asto their origins. Section 5 brings this evidence together topresent the emerging picture as to the steps leading to theformation of a lenticular galaxy. c (cid:13) , 000–000 inematic clues to the origins of S0s In order to correctly assign each PN’s observed velocity todisc or bulge kinematics, we must first calculate the rela-tive contributions of disc and bulge to the total light at itslocation. To do so, we follow the same photometric decom-position procedure described in Cortesi et al. (2011), brieflysummarised here for completeness.Where possible, the galaxies’ images used for the de-composition are K -band data from the 2MASS survey(Skrutskie et al. et al. et al. et al. n = 4, but in the case of NGC 2768 this pro-duced a poor fit, so the index was left as a free parameter.The resulting fits to the images are presented in Figure 2,and the associated values for the best fit parameters aregiven in Table 2. As is apparent from Figure 2, in somecases this simple two component model fits the galaxy verywell, while in others systematic residuals indicate that thesystem is somewhat more complex. In particular, we find: • NGC 3115 contains an additional very thin disc-likestructure as well as the thicker disc component that we havefitted. In addition, the de Vaucouleurs fit is not perfect forthe bulge at very small radii. • NGC 3489 contains a faint but significant ring struc-ture. • NGC 3384 shows a central dipolar structure in the resid-uals, seemingly indicative of an off-centre nucleus.Although all these features are interesting, and tell us thateven the plainest looking S0 galaxy can be quite complex,they are all either localized in regions of high surface bright-ness where we do not detect the PNe used in this kinematicanalysis, or they are of low surface brightness compared tothe main bulge and disc components. Accordingly, they donot compromise our ability to use the simple two compo-nent fit to determine the relative contributions of disc andspheroid to the light at each point in the galaxy.To illustrate the assignment of PNe to the two com-ponents, Figure 3 shows a greyscale image of the spheroid-to-total light at each point in the model. The PNe are alsoplotted and identified by whether they lie in a region wherespheroid or disc dominates, but note that, in the kinematiclikelihood analysis below, each is assigned an exact value f i from this image, such that it has a probability f i thatit comes from the spheroidal component and 1 − f i that itcomes from the disc component (Cortesi et al. Having obtained the disc–spheroid light decomposition foreach galaxy, we can now fit all the line-of-sight velocitiesfor the PNe shown in Figure 3 using a maximum likelihoodfit. The method, described in detail in Cortesi et al. (2011),essentially involves fitting in radial bins using a model com-prising a simple Gaussian spheroid line-of-sight velocity dis-tribution plus a similar Gaussian velocity distribution forthe disc component. For the disc component, we allow anon-zero mean velocity to fit rotation, varying with azimuthas geometrically required for a rotating disc, and also incor-porate the fact that its line-of-sight velocity dispersion is adifferent projection of the disc’s coupled radial and tangen-tial velocity dispersions, σ r and σ φ respectively, at differentazimuths. We neglect the contribution of the z -componentof the velocity dispersion: it is intrinsically smaller, and itsmodest projection along the line of sight further reduces itssignificance in these inclined systems. We also assume thatthe disc is not too hot, so we can invoke the epicycle ap-proximation to couple the values of σ r and σ φ . This fittingprocess thus solves for a simplified model of both disc andspheroid kinematics, and also allows us to identify and re-ject PNe that do not fit the model, based on their individualcontributions to the total likelihood.Any PNe rejected in this process are highlightedin Figure 3, and the final resulting best-fit kinematicparameters as a function of radius are shown in Fig-ure 4. In each case, the radial bins have been chosen toensure that each contains at least 30 PNe, as found tobe a suitable minimum in Cortesi et al. (2011), whichis why the bin sizes and number vary from galaxy togalaxy. The resulting elliptical bin boundaries are shownin Figure 3. For comparison, Figure 4 also shows conven-tional absorption-line kinematics along the major axesfrom various sources (Caon, Macchetto & Pastoriza 2000;Simien & Prugniel 1997; Norris, Sharples & Kuntschner2006; Debattista, Corsini & Aguerri 2002). Since the disclight dominates in this region, we compare these data to thederived disc kinematics. In one case there is also publishedminor-axis data (Norris, Sharples & Kuntschner 2006)where the bulge light dominates, so the absorption-linedispersion profile is compared to the bulge kinematics thatwe derive. In all cases, the agreement between the twomethods is good, but the comparison underlines how con-ventional absorption-line spectroscopy is typically limitedto the bright inner parts of each galaxy.One simplification that we have made in this analy-sis is in assuming that the spheroidal component is non-rotating. In general, there is not sufficient data to allowus to relax this assumption, but in the case of NGC 2768Forbes et al. (2012) found that the larger number of PNeallowed this extra degree of freedom to be introduced. How-ever, the resulting spheroidal component was found to becompletely dominated by random motions, so the differ-ence was negligible, justifying the assumption in the caseof this galaxy and rendering it plausible for the other galax-ies where there were not sufficient data to test it directly.This assumption also fits with the findings in spiral galax-ies, where classical bulges tend to be very slowly rotat-ing (MacArthur, Gonz´alez & Courteau 2009) while pseudo- c (cid:13) , 000–000 Cortesi et al.
Name Type Distance modulus Archive Band Angular scale Zero point[mag] [” per pixel] [mag]NGC 3115 S0-edge-on 29 .
77 2MASS K . − .
45 2MASS K . .
59 2MASS K . − .
13 2MASS K . + .
25 SDSS z . . − .
16 2MASS K . Table 1.
Basic data on the sample and images analysed. From left to right: galaxy name, galaxy type, distance modulus from Tonry et al. (2001) shifted by 0.16 magnitudes (see text for details), archive, band, angular scale, zero pointDisc Spheroid B/TName m D R d b/a incl P A m B R e n b/a P A [mag] [arcs] [deg] [deg] [mag] [arcs] [deg]NGC 3115 8 .
34 53 .
69 0 .
39 67 45 .
00 7 .
17 26 .
19 4 0 .
31 45 .
00 0 . .
56 27 .
07 0 .
48 62 − .
28 9 .
49 11 .
62 4 0 . − .
04 0 . .
19 42 .
93 0 .
29 73 − .
25 7 .
23 50 .
46 4 .
65 0 . − .
39 0 . .
02 59 .
08 0 .
26 74 84 .
12 6 . .
86 4 0 .
75 75 .
59 0 . .
18 24 .
98 0 .
49 61 − .
05 8 .
05 7 .
64 4 0 . − .
50 0 . .
92 63 .
73 0 .
34 70 52 .
50 7 .
29 15 .
20 4 0 .
83 60 .
51 0 . Table 2.
Results from GALFIT fit. From left to right: galaxy name [1], disc apparent magnitude [2], disc scale length [3], disc axes ratio[4], used to obtain the galaxy inclination [5], disc position angle [6], spheroid apparent magnitude [7], effective radius [8], Sersic index,equal to 4 where this value fitted well, [9], spheroid axes ratio [10], spheroid position angle [11] and bulge-to-total light ratio [12]. ForNGC 3489 the recovered magnitudes in z-band have been colour corrected. bulges with low Sersic indices display more rotational sup-port (Fabricius et al. et al. (2011).As is apparent from Figure 4, this analysis reveals a re-markably consistent kinematic picture amongst these galax-ies. The one exception seems to be NGC 3489, althoughit is notable that this galaxy contains the smallest numberof available kinematic tracers, which may be compromis-ing the results somewhat. However, apart from this galaxy,all the systems here display kinematics with many featuresin common: the spheroidal components have a dispersionthat varies very little with radius, and the disc componentsrise to flat rotation curves with ordered motions dominat-ing over random velocities at all radii. It is interesting tocompare this situation with the much more heterogeneouspicture presented in Figure 1; it would appear that at leastsome of the variety in that plot arose from the net effectof superimposing multiple kinematic components whose re-spective contributions vary from galaxy to galaxy. This newconsistency provides some confidence in the analysis, but also offers at least the possibility that these galaxies aresufficiently homogeneous for some common underlying for-mation mechanism to exist.
Having determined the kinematic profiles of the spheroidand disc components of these S0 galaxies, we can now startto use these data to seek archaeological evidence as to howthey formed. As a starting point, we translate these profilesinto characteristic values for the kinematics of each compo-nent. For the disc, we determine the mean streaming mo-tion, V ∗ , and the two components of velocity dispersion, σ φ and σ r , at three disc scale lengths as determined by thephotometric parameters (see Table 2), since by this radiusthey seem to have settled to their asymptotic values. Theonly exception is NGC 3489, where the limited amount ofkinematic data restricts us to calculating these quantitiesat 2 R d ; in practice this makes little difference, as in theother galaxies the parameters do not change significantlyover this radial range. The resulting values are presented inTable 3. In the spheroids, the velocity dispersion does notchange significantly with radius, so we simply calculate aluminosity-weighted average value,ˆ σ sph = P i L sph,i σ sph,i P i L sph,i , (1)where L sph,i is the luminosity of the spheroid in each radialbin, as ascertained from the photometric fit. The resultingvalues of ˆ σ sph are also listed in Table 3.The other kinematic quantity we need to derive is thecharacteristic circular speed of each galaxy, V c , which pro- c (cid:13)000
Having determined the kinematic profiles of the spheroidand disc components of these S0 galaxies, we can now startto use these data to seek archaeological evidence as to howthey formed. As a starting point, we translate these profilesinto characteristic values for the kinematics of each compo-nent. For the disc, we determine the mean streaming mo-tion, V ∗ , and the two components of velocity dispersion, σ φ and σ r , at three disc scale lengths as determined by thephotometric parameters (see Table 2), since by this radiusthey seem to have settled to their asymptotic values. Theonly exception is NGC 3489, where the limited amount ofkinematic data restricts us to calculating these quantitiesat 2 R d ; in practice this makes little difference, as in theother galaxies the parameters do not change significantlyover this radial range. The resulting values are presented inTable 3. In the spheroids, the velocity dispersion does notchange significantly with radius, so we simply calculate aluminosity-weighted average value,ˆ σ sph = P i L sph,i σ sph,i P i L sph,i , (1)where L sph,i is the luminosity of the spheroid in each radialbin, as ascertained from the photometric fit. The resultingvalues of ˆ σ sph are also listed in Table 3.The other kinematic quantity we need to derive is thecharacteristic circular speed of each galaxy, V c , which pro- c (cid:13)000 , 000–000 inematic clues to the origins of S0s Figure 2.
GALFIT analysis of the S0 sample.
Left panels : galaxy image; middle panels : GALFIT model image; right panels : differenceimage, scaled to emphasize any residuals in the fit. The ratio between the flux in the residual image and in the scientific image is around5%. From top to bottom: NGC 3115 in a [800 ′′ × ′′ ] box, NGC 7457 in a [600 ′′ × ′′ ] box, NGC 2768 in a [800 ′′ × ′′ ] box,NGC 3489 in a [ ≃ ′′ × ′′ ] box and NGC 3384 in a [ ≃ ′′ × ′′ ] box. The dimension of the box corresponds to the dimensionof the image in which the fit was performed, apart from NGC 3384, which was fitted simultaneously with the two companion galaxiesappearing in the 2MASS [1200 ′′ × ′′ ] image, in order to remove any residual contamination. vides a measure of the system’s mass. Because of the pres-ence of significant random motions, we cannot simply usethe mean streaming speed of the stars, but must correctthese motions for asymmetric drift via the equation V c = V ⋆ + σ φ − σ r (1 + d ln νd ln r + d ln σ r d ln r ) (2) (Binney & Tremaine 1987). If the random motions are nottoo large and the rotation curve is close to flat, then theepicycle approximation implies that σ r = √ σ φ . If we fur-ther use the photometrically-derived exponential disc pro-file (see Section 2) to determine ν ( r ) and fit the observedvariation in velocity dispersion with radius using a furtherexponential with its own scalelength, c (cid:13) , 000–000 Cortesi et al.
Figure 3.
Probability map that a PN belongs to the disc (darker areas) or spheroid (lighter areas). The locations of detected PNe arealso shown, with those more likely to belong to the disc shown as triangles, and those more likely to belong to the spheroid as squares.Colours indicate the line-of-sight velocities of the PNe. Open circles are drawn around PNe rejected by the likelihood fit to the kinematics.c (cid:13) , 000–000 inematic clues to the origins of S0s Figure 4. disc and spheroid kinematics of the sample galaxies assuming a spheroid+disc model. For each galaxy, we show the rotationvelocity of the disc (top panel), its coupled tangential, σ φ , and radial, σ r dispersions (middle panel), and the velocity dispersionof the spheroid (bottom panel). Vertical error bars indicate uncertainty, while horizontal error bars show the radial binning. Whereavailable, we also show kinematics derived from conventional absorption-line spectra (open circles) (Caon, Macchetto & Pastoriza 2000;Simien & Prugniel 1997; Norris, Sharples & Kuntschner 2006; Debattista, Corsini & Aguerri 2002).c (cid:13) , 000–000 Cortesi et al.
Name ( V ∗ ) disc ( V ∗ /σ φ ) disc ( V c ) disc ˆ σ sph [km/s] [km/s] [km/s]NGC 3115 220 +41 − . +0 . − . +67 − +36 − NGC 7457 113 +18 − . +0 . − . +23 − +85 − NGC 2768 232 +39 − . +0 . − . +79 − +11 − NGC 1023 244 +37 − . +0 . − . +47 − +42 − NGC 3489 144 +37 − . +0 . − . +38 − +36 − NGC 3384 179 +22 − . +0 . − . +37 − +53 − Table 3.
Kinematic results. From left to right: galaxy name [1], rotation velocity in the disc at 3 R d [2], ratio between rotation andvelocity dispersion along the tangential direction for the galaxy disc calculated at 3 R d [3], circular speed in the disc at 3 R d [4], lightweighted spheroid dispersion velocity [4]. Figure 5.
Ratio of stellar rotation velocity in the disc to thedisc velocity dispersion for the S0 galaxies of this sample (filled),and the corresponding quantity for a comparison sample of spiralgalaxies from the literature (diagonally shaded) (Bottema 1993;Herrmann & Ciardullo 2009), normalised to the same number asthe S0 galaxies. σ r = σ r (0) exp( − rR ) , (3)the asymmetric drift equation simplifies to V c ( r ) = V ⋆ + σ φ ( −
12 + rR d + rR ) , (4)We can hence estimate V c at any radius using this equa-tion; Table 3 lists the derived characteristic value of thisquantity for each galaxy at 3 R d , which matches the fiducialradius used for the other kinematic parameters; it is alsoat large enough radii that the circular speed will have con-verged to its characteristic asymptotic value. A check on thevalidity of this simplified equation is provided by comparingour results to those of Davis et al. (2011), who carried outfull anisotropic Jeans modelling (Cappellari 2008) on twoof the sample galaxies. They obtained circular velocities of310 km s − for NGC 2768 and 160 km s − for NGC 3489, ingood agreement with the values derived here. As previously mentioned, one key diagnostic of the evo-lutionary past of a disc is provided by the ratio betweenits ordered and random motions: if they are simply spiralgalaxies that have ceased forming stars, then they shouldbe dominated by mean streaming motions in the same wayas their progenitors, whereas any more violent transitionsuch as one precipitated by a merger would tend to heatthe disc and hence decrease the dominance of the rotation.Table 3 lists the characteristic values of V ∗ /σ φ for these S0systems, yielding a mean value of 4.2, with an RMS scatterof 0.8. These values contrast with the V ∗ /σ φ ∼ V ∗ /σ φ than at our adopted ra-dius of 3 R d . The comparison is more direct with the datafrom Herrmann & Ciardullo (2009), as we can interpolatea value at 3 R d from the kinematic profiles they present. Inboth cases, we again use the epicycle approximation to in-terchange between σ r and σ φ . Figure 5 shows the resultingestimates of V ∗ /σ φ for both the spiral comparison sampleand the current sample of S0s. Although there is a reason-able degree of overlap, implying that these S0s could haveformed passively from spirals, there are also strong indica-tions that the values are systematically lower for the S0s,which is not the sense one would expect if it arose from thepossible bias in the smaller fiducial radii used by Bottema(1993). Thus, if these S0s formed from a random selectionof comparable present-day spirals, it would seem that someheating of their discs must have occurred during the transi-tion.Although the sample becomes small when divided inthis way, there is no evidence that the degree of heatingof the disc depends on environments, since the S0s fromisolated, small group and large group surroundings (as de- c (cid:13) , 000–000 inematic clues to the origins of S0s Figure 6. K -band Tully–Fisher relation for the S0 galaxies an-alyzed here, compared to the relation for spiral galaxies (bluecircles and line of best fit) from (Tully & Pierce 2000) andRothberg et al. (2000) scribed in Section 1) do not display systematically differentvalues of V ∗ /σ φ . We are thus left with a developing pic-ture in which the formation of an S0 from a spiral appearssomewhat more violent than a simple shutdown of star for-mation, but not as extreme as a merger-induced transition,with no indication that the mechanism depends strongly onenvironment. We can seek further insight into the possible scenario fortransformation, and also try to address the question ofwhether S0s are more closely related to spirals or ellipti-cals, by looking at where these systems lie on the scalingrelations respected by the other galaxy classes.
The simplest test we can carry out is to place these S0galaxies on the Tully–Fisher relation, which displays a verytight correlation between a spiral galaxy’s luminosity andits circular rotation speed (Tully & Fisher 1977). Such com-parisons have previously been carried out by various au-thors, with somewhat mixed results (Arag´on-Salamanca2008; Neistein et al. K -band photometry introduced inSection 2 to minimise the impact of dust obscuration. Thereis a risk that the relatively shallow 2MASS exposures mightmiss some of the flux from the outer parts of the galaxy,so we use the magnitudes derived from the full GALFITmodels obtained in Section 2 rather than the values quotedin the published 2MASS catalogue; in fact, this effect turnsout to be rather small, with an average offset of only 0.05magnitudes. For NGC 3489, we had to use an SDSS z -bandimage to carry out the GALFIT modeling, so for this galaxywe calculate a total z -band magnitude from the model, thenuse the SDSS/2MASS integrated colours to convert it to a K -band magnitude, which implicitly assumes that there areno strong colour gradients in this galaxy.To convert these values to absolute magnitudes, weuse the distance moduli derived from surface brightnessfluctuations from Tonry et al. (2001), systematically de-creased by 0 .
16 mag to take into account the updatedCepheid zero point of Freedman et al. (2001), as discussedin Coccato et al. (2009) and Cortesi et al. (2013). Here, itis important to use a distance scale that has not itself beenbased on Tully–Fisher or other kinematic scaling relations,to avoid introducing a circularity into the analysis.Figure 6 shows the resulting Tully–Fisher relation forthe S0 galaxies analyzed here, compared to the relation forspiral galaxies (Tully & Pierce 2000; Rothberg et al. c (cid:13) , 000–000 Cortesi et al.
Figure 7. K -band Faber–Jackson relation plotting spheroid ab-solute magnitude as a function of its dispersion for the S0galaxies studied here. Comparable kinematic data for ellipti-cal galaxies from Mobasher et al. (1999) (filled red circles) andMatkovi´c & Guzm´an (2005) (open red circles) are also shown.The line shows a fit to the brighter elliptical galaxy data. Having separated spheroid and disc components, we arealso in a position to look at connections in the other di-rection along the Hubble sequence to see how closely S0smight be related to elliptical galaxies. For these systems,the equivalent scaling is the Faber–Jackson relation betweenthe spheroidal component velocity dispersion and its abso-lute magnitude.Accordingly we have plotted these quantities for theS0 galaxy spheroids in Figure 7, using the spheroid disper-sions calculated in Section 4.1, and spheroid absolute magni-tudes derived as described above. For comparison, we havealso plotted the relation followed by elliptical galaxies asderived by Mobasher et al. (1999). These latter data arebased on velocity dispersions measured at an effective ra-dius, away from any central spike in velocity dispersion, soshould be directly comparable to the dispersions determinedfor the S0 spheroids. These elliptical data do not span thefull range of magnitudes seen for the S0 spheroids, so wesupplement them with kinematic data on fainter early-typegalaxies in the Coma Cluster (Matkovi´c & Guzm´an 2005)using K -band magnitudes from Skrutskie et al. (2006). Forthese fainter galaxies, the kinematics were derived from fibrespectra, but the large three-arcsecond fibres used will covermost of these small faint galaxies at the distance of Coma, so Figure 8.
Plot showing how the S0 galaxies are offset in mag-nitude from the mean Tully–Fisher and Faber–Jackson relationsfor spiral galaxies and elliptical galaxies respectively. should again be comparable to the luminosity-weighted aver-age values of ˆ σ sph derived for the S0 spheroids. To obtain theabsolute magnitude for the Coma galaxies, we placed the ap-parent magnitudes tabulated in Mobasher et al. (1999) andSkrutskie et al. (2006) at a distance modulus of m − M =35 .
06, as also found using surface brightness fluctuations(Thomsen et al.
In this paper, we have analysed the kinematics of a sam-ple of six lenticular galaxies using the planetary nebulaedata presented in Cortesi et al. (2013) to determine theirdynamical properties out to large radii. This analysis hasemphasised the importance of treating the spheroidal anddisc components of these systems as distinct entities bothphotometrically and kinematically, and doing a careful job c (cid:13)000
In this paper, we have analysed the kinematics of a sam-ple of six lenticular galaxies using the planetary nebulaedata presented in Cortesi et al. (2013) to determine theirdynamical properties out to large radii. This analysis hasemphasised the importance of treating the spheroidal anddisc components of these systems as distinct entities bothphotometrically and kinematically, and doing a careful job c (cid:13)000 , 000–000 inematic clues to the origins of S0s of separating them. Through this process, the rather hetero-geneous properties of S0s over-all start to be resolved intomore consistent sub-components, and a reasonably coherentpicture begins to emerge.The common factors we have uncovered are that:(i) The discs of S0 galaxies are comparable to those ofspirals, with similar flat rotation curves and falling veloc-ity dispersion profiles, but with a larger amount of randommotions.(ii) The spheroids of S0 galaxies show flat dispersion pro-files, similar to what is found in some ellipticals.(iii) S0 galaxies follow the Tully–Fisher relation, but off-set to fainter magnitudes than spiral galaxies, with a greateroffset for more massive galaxies.(iv) S0 galaxy spheroids follow the Faber–Jackson rela-tion, somewhat offset to brighter magnitudes than ellipticalgalaxies.(v) There is no strong evidence that any of these effectsdepend on the current environment of the galaxy.The Tully–Fisher and Faber–Jackson findings are sum-marised in Figure 8, which shows the offset from each re-lation for the S0 sample. In the absence of any systematiceffect, we would expect these points to appear equally in allfour quadrants, but in fact they appear strongly clusteredin the region of the plot where the spheroids are too brightbut the overall galaxies are too faint.With this level of detail starting to become available,we can begin to sketch out a plausible evolutionary sequenceleading to the formation of S0 galaxies. If these systems be-gan their lives as spiral galaxies, at some point they under-went a transition that removed their gas supply and hencecut off star formation. The process responsible does not de-pend strongly on current environment, but does seem tohave acted earlier on more massive galaxies as another exam-ple of downsizing. The hotter discs of S0s could indicate thattheir high-redshift spiral progenitors had less ordered discs(Kassin et al. et al. et al. (1996) as a process for transforming galaxiesin clusters. In their paper, they demonstrated that this pro-cess of repeated high-speed encounters could strip gas froma galaxy while dumping some at the centre of the systemunder transformation as we require here. However, we alsoknow that the process needs to be somewhat gentler thanthey modelled because we need to preserve the disc structure of the galaxy with only a fairly modest amount of heating. Itremains to be seen whether such mild harassment, perhapsbetter thought of as “pestering,” could be made to workacross the range of environments in which S0s are found,but we do at least now have a growing number of obser-vational constraints against which any such model can betested. ACKNOWLEDGEMENTS
AC acknowledges the support from both ESO (during herstudentship in 2011 and the visitor program in 2012) andMPE (visitor program 2012). LC acknowledges funding fromthe European Community Seventh Framework Programme(FP7/2007-2013/) under grant agreement No 229517. AJRwas supported by National Science Foundation grant AST-0909237. We thank the referee for the supportive and con-structive report. The PN.S team thanks both the UK andNL time allocation committees and the staff of the WHT fortheir strong support in acquiring the data used in this re-search. This research has also made use of the 2MASS dataarchive, the NASA/IPAC Extragalactic Database (NED),and of the ESO Science Archive Facility, for which we aregrateful.
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