The SAURON Project - XIV. No escape from V esc : a global and local parameter in early-type galaxy evolution
Nicholas Scott, Michele Cappellari, Roger L. Davies, R. Bacon, P. T. de Zeeuw, Eric Emsellem, Jesus Falcon-Barroso, Davor Krajnovic, Harald Kuntschner, Richard M. McDermid, Reynier F. Peletier, Antonio Pipino, Marc Sarzi, Remco C. E. van den Bosch, Glenn van de Ven, Eveline van Scherpenzeel
MMon. Not. R. Astron. Soc. , 1–23 (2009) Printed 6 November 2018 (MN LaTEX style file v2.2)
The SAURON Project - XIV. No escape from V esc : a global and localparameter in early-type galaxy evolution
Nicholas Scott, (cid:63) Michele Cappellari , Roger L. Davies , R. Bacon , P. T. de Zeeuw , ,Eric Emsellem , , J´esus Falc ´on-Barroso , Davor Krajnovi´c , Harald Kuntschner ,Richard M. McDermid , Reynier F. Peletier , Antonio Pipino , Marc Sarzi ,Remco C. E. van den Bosch , , Glenn van de Ven † and Eveline van Scherpenzeel Sub-Department of Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH Universit´e de Lyon, France; Universit´e Lyon 1, F-69007; CRAL, Observatoire de Lyon, F-69230 Saint Genis Laval; CNRS, UMR 5574;ENS de Lyon, France European Southern Observatory, Karl-Schwarzschild-Str 2, 85748 Garching, Germany Sterrewacht Leiden, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, the Netherlands European Space and Technology Centre (ESTEC), Keplerlaan 1, Postbus 299, 2200 AG Noordwijk, the Netherlands Space Telescope European Coordinating Facility, European Southern Observatory, Karl-Schwarzschild-Str 2, 85748 Garching, Germany Gemini Observatory, Northern Operations Centre, 670 N. A’ohoku Place, Hilo, Hawaii 96720, USA Kapteyn Astronomical Institute, Postbus 800, 9700 AV Groningen, the Netherlands Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484 Centre for Astrophysics Research, University of Hertfordshire, Hatfield, Herts AL1 09AB McDonald Observatory, The University of Texas at Austin, TX 78712, Austin, USA Institute for Advanced Study, Peyton Hall, Princeton, NJ 08544, USA
ABSTRACT
We present the results of an investigation of the local escape velocity (V esc ) - line strengthindex relationship for 48 early type galaxies from the SAURON sample, the first such studybased on a large sample of galaxies with both detailed integral field observations and extensivedynamical modelling. Values of V esc are computed using Multi Gaussian Expansion (MGE)photometric fitting and axisymmetric, anisotropic Jeans’ dynamical modelling simultaneouslyon HST and ground-based images. We determine line strengths and escape velocities at mul-tiple radii within each galaxy, allowing an investigation of the correlation within individualgalaxies as well as amongst galaxies. We find a tight correlation between V esc and the line-strength indices. For Mgb we find that this correlation exists not only between different galax-ies but also inside individual galaxies - it is both a local and global correlation. The Mgb-V esc relation has the form: log(Mgb / ˚ A) = (0 . ± .
03) log(V esc / / s) − (0 . ± . with an rms scatter σ = 0 . . The relation within individual galaxies has the same slope andoffset as the global relation to a good level of agreement, though there is significant intrinsicscatter in the local gradients. We transform our line strength index measurements to the singlestellar population (SSP) equivalent ages (t), metallicity ([Z/H]) and enhancement ([ α /Fe]) andcarry out a principal component analysis of our SSP and V esc data. We find that in this four-dimensional parameter space the galaxies in our sample are to a good approximation confinedto a plane, given by log ( V esc / / s) = 0 . / H]+0 .
43 log(t / Gyrs) - 0.20. It is surpris-ing that a combination of age and metallicity is conserved; this may indicate a ‘conspiracy’between age and metallicity or a weakness in the SSP models. How the connection betweenstellar populations and the gravitational potential, both locally and globally, is preserved asgalaxies assemble hierarchically may provide an important constraint on modelling.
Key words: galaxies: elliptical and lenticular, cD - galaxies: abundances - galaxies: formation- galaxies: evolution. (cid:63)
E-mail: [email protected] † Hubble Fellow
In the Hubble classification (Hubble 1936) scheme elliptical andlenticular (or S0) galaxies are collectively known as early-type c (cid:13) a r X i v : . [ a s t r o - ph . GA ] J un N. Scott et al. galaxies, and are thought to represent the end-point of many bil-lions of years of evolution. Early-type galaxies exhibit smooth mor-phologies, appearing as essentially featureless collections of starson the sky. For many years this simple appearance was thought toreflect a straightforward and homogeneous behaviour, both dynam-ically and in terms of their stellar populations, across a broad rangein luminosity and size. More recently observations have shown thatwhile in many ways the structure of early-type galaxies is intrinsi-cally simple there is a rich diversity in their properties that requiresa more complex understanding of these objects. Such an under-standing will yield important information about the formation andevolution of structure in the Universe.Many different properties of early-type galaxies are found tobe well correlated with their luminosities. The earliest correlationsdiscovered were those relating global quantities of these galaxies.The most luminous galaxies were found to have large half-lightradii R e (Kormendy 1977), low surface brightnesses within R e , (cid:104) I e (cid:105) and large central velocity dispersions σ e (Faber & Jackson1976). These correlations can be combined if we plot the mea-surements in log σ e , log R e , log (cid:104) I e (cid:105) space. In this variable spaceit is found that galaxies are confined to a tight plane, known asthe Fundamental Plane (Djorgovski & Davis 1987; Dressler et al.1987). In this case the value of any one of the variables can becalculated once the other two are known - early-type galaxies are atwo-parameter family. The most luminous galaxies were also foundto be predominantly pressure-supported (low V/ σ , Bertola & Ca-paccioli 1975; Illingworth 1977; Binney 1979), have core surfacebrightness profiles (Kormendy 1987; Lauer et al. 1995; Ferrarese etal. 1994, 2006; Faber et al. 1997; Kormendy et al. 2008) and boxyisophotes (Bender et al. 1988). In contrast the less luminous galax-ies are predominantly rotationally supported (Davies et al. 1983)with cuspy surface brightness profiles and discy isophotes. Theseobservations hinted at a dichotomy in the early-type population(Faber et al. 1997; Kormendy & Bender 1996) but the inclusion oftwo-dimensional kinematics reveals a different, more marked sepa-ration into two distinct populations (Emsellem et al. 2007; Cappel-lari et al. 2007, hereafter Paper IX and Paper X). Another quantitythat is found to correlate well with σ e is the mass of the galaxy’scentral black hole M • (Ferrarese & Merritt 2000; Gebhardt et al.2000), which also correlates with many other galaxy properties in-cluding bulge mass M bulge (Magorrian et al. 1998; Mclure & Dun-lop 2002; Marconi & Hunt 2003; H¨aring & Rix 2004).As well as relationships between these global, predominantlydynamical quantities there are tight correlations relating stellarpopulation parameters. The first known of these was the colour-magnitude relation relating the total luminosity of a galaxy to its B-V colour (Visvanathan & Sandage 1977). Global colours werealso found to be well correlated with other galaxy properties, mostnotably central velocity dispersion σ e and central absorption linestrengths for a number of commonly observed absorption indices(Bender et al. 1992). That colour and line strength should be tightlyrelated is not entirely surprising. The fact that a quantity measur-ing a global property of the galaxy (in this case the global colour)which is dominated by light from the outer parts of the galaxyshould be closely related to a quantity measured only in the verycentre (true for both σ and the absorption indices) suggests that thebehaviour of these properties within a galaxy, as well as betweendifferent galaxies, must also be confined to a relatively narrow re-gion in parameter-space. We shall explore further evidence for thisidea and it’s consequences later in this work.There is one further relation most closely related to this work,that linking σ and the magnesium line strength index (either Mgb or Mg ) measured in a central aperture (Burstein et al. 1988). Thisis the tightest and best-studied relation linking a dynamical quan-tity σ with a quantity depending only on the stellar population, theMg index. Many authors have measured this relation for many hun-dreds of early-type galaxies (see e.g. Colless et al. 1999), and whilethe precise gradient and zero-point found for the relation vary fromauthor to author the tightness of the relation is common to all stud-ies. Any successful model of early-type galaxy formation must ex-plain this and the other relations discussed above before it can beaccepted as accurately describing the formation histories of theseobjects.The previously discussed relations are all global ones; somelocal relations have also been studied but only with small samples.Franx & Illingworth (1990) found that the local colour in ellipti-cal galaxies correlated well with the local escape velocity, V esc ,whereas the local colour - local σ relation has significantly largerscatter. A similar result for the local Mg -V esc relation was foundby Davies, Sadler & Peletier (1993), hereafter DSP93. This depen-dence on local parameters, which holds both within a single galaxyand between a sample of early-type galaxies begins to suggest thata key parameter in the formation and evolution of early-type galax-ies is the gravitational potential Φ , for which V esc is a proxy.In this work we explore the line strength - V esc relation forthe SAURON sample of galaxies (de Zeeuw et al. 2002) for whichintegral-field spectroscopy obtained on the SAURON integral-fieldunit (Bacon et al. 2001) and extensive photometry are available. InSection 2 we give details of the SAURON sample, the observationsand the data reduction process for the photometry and the spec-troscopy. In Section 3 we discuss the dynamical modelling of thesample from which we derive the potential Φ and the escape veloc-ity V esc . In Section 4 we present the resulting line strength-V esc re-lations and translate these to the physical properties age, metallicityand alpha enhancement. In Section 5 we consider the implicationsof our results in the context of galaxy formation scenarios. Finally,our conclusions are summarised in Section 6. The sample of galaxies used in this investigation is the SAURONsample of 48 early type galaxies (de Zeeuw et al. 2002), dividedequally between E and S0 morphologies (where the classificationis taken from de Vaucouleurs et al. 1991). This sample is repre-sentative of nearby bright early-type galaxies ( cz (cid:54) − ; M B (cid:54) −
18 mag ) and is fully described in de Zeeuw et al. (2002).The sample consists of an equal number of ‘cluster’ and ‘field’ ob-jects (where cluster objects are defined as those belonging to theVirgo cluster, the Coma I cloud and the Leo group) uniformly cov-ering the ellipticity- M B plane. The photometric data consists of ground-based photometry ob-tained in the F555W filter on the 1.3-m McGraw-Hill Telescopeat the MDM observatory on Kitt Peak (Falc´on-Barroso et al. inpreparation), supplemented by HST observations where available(see Table 1 for the complete list.) A relatively large field of view of17.1 × arcmin was used for the MDM observations in orderto provide accurate sky-subtraction from the images. The space-based observations consist primarily of HST/WFPC2 imaging or c (cid:13) , 1–23 he SAURON Project - XIV Table 1.
Properties of the 48 E and S0 galaxies from the SAURON sample used in this paperGalaxy Type R e Dist Rotator i (M/L) X Band M I X − I (M/L) I HST Quality d (log Mgb) d (log V esc ) Name (arcsec) (Mpc) ( ◦ ) X (mag) (mag) Imaging of fit(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)NGC 474 S0 (s)
29 32.0 F 37 2.86 I -21.94 – 2.86 814W 3 0.66NGC 524 S0 + (rs)
51 23.3 F 20 5.36 I -22.99 - 5.36 814W 1 0.19NGC 821
E6?
39 23.4 F 79 3.58 I -22.32 - 3.58 814W 1 0.43NGC 1023
SB0 − (rs)
48 11.1 F 73 2.90 I -21.97 - 2.90 814W 2 0.09NGC 2549 S0 (r)sp
20 12.3 F 90 4.84 R -20.49 0.65* 3.64 702W 1 0.41NGC 2685 (R)SB0 + pec
20 15.0 F 76 1.74 I -20.65 - 1.74 814W 2 0.47NGC 2695
SAB0 (s)
21 31.5 F 48 5.64 V -21.63 1.18 3.80 - 1 0.30NGC 2699
E :
14 26.2 F 46 3.21 R -20.81 0.61 2.48 702W 2 0.51NGC 2768
E6 :
71 21.8 F 90 5.32 I -22.73 - 5.32 814W 1 0.39NGC 2974 E4
24 20.9 F 56 4.79 I -21.94 - 4.79 814W 1 0.39NGC 3032
SAB0 (r)
17 21.4 F 38 1.99 I -20.41 - 1.99 814W 1 -1.46NGC 3156
S0 :
25 21.8 F 67 1.46 I -20.43 - 1.46 814W 1 -0.07NGC 3377 E5 −
38 10.9 F 90 2.31 I -21.19 - 2.31 814W 1 0.74NGC 3379 E1
42 10.3 F 68 3.43 I -22.11 - 3.43 814W 1 0.32NGC 3384
SB0 − (s) :
27 11.3 F 66 1.89 I -21.45 - 1.89 814W 3 0.31NGC 3414
S0pec
33 24.5 S 60 4.23 I -22.23 - 4.23 814W 2 0.75NGC 3489
SAB0 + (rs)
19 11.8 F 60 0.99 I -20.99 - 0.99 814W 2 0.25NGC 3608 E2
41 22.3 S 60 3.73 I -22.22 - 3.73 814W 1 0.47NGC 4150 S0 (r)?
15 13.4 F 51 1.43 I -19.91 - 1.43 814W 1 -0.37NGC 4262
SB0 − (s)
10 15.4 F 26 8.84 B -20.51 2.24 4.08 ACS/475W 3 0.52NGC 4270 S0
18 33.1 F 70 4.01 V -21.27 1.06 3.01 606W 1 0.02NGC 4278 E1 −
32 15.6 F 40 4.86 I -22.08 - 4.86 814W 1 0.47NGC 4374 E1
71 18.5 S 60 4.08 I -23.46 - 4.08 814W 1 0.34NGC 4382 S0 + (s)pec
67 17.9 F 78 2.58 I -23.39 - 2.58 814W 3 -0.29NGC 4387 E
17 17.9 F 65 5.23 B -20.19 2.22 2.46 ACS/475W 1 0.21NGC 4458 E0 −
27 16.4 S 76 2.43 I -20.42 - 2.43 814W 1 0.44NGC 4459 S0 + (r)
38 16.1 F 46 2.86 I -21.86 - 2.86 814W 1 0.31NGC 4473 E5
27 15.3 F 73 3.38 I -21.87 - 3.38 814W 1 0.42NGC 4477
SB0(s) :?
47 16.5 F 26 6.66 V -21.66 1.28 4.09 606W 3 0.08NGC 4486 E0 − + pec
105 17.2 S 60 4.90 I -23.43 - 4.90 814W 1 0.50NGC 4526
SAB0 (s)
40 16.4 F 78 3.54 I -22.54 - 3.54 814W 1 0.09NGC 4546
SB0 − (s) :
22 13.7 F 70 6.12 V -21.17 1.15 4.23 606W 1 0.46NGC 4550
SB0 : sp
14 15.5 S 82 3.38 I -20.50 - 3.38 814W 1 0.41NGC 4552 E0 −
32 15.8 S 60 4.33 I -22.45 - 4.33 814W 1 0.28NGC 4564 E
21 15.8 F 74 4.29 R -21.03 0.65* 3.22 702W 1 0.48NGC 4570
S0sp
14 17.1 F 90 3.39 I -21.42 - 3.39 814W 1 0.40NGC 4621 E5
46 14.9 F 90 3.95 I -22.80 - 3.95 814W 1 0.42NGC 4660 E
11 15.0 F 68 3.16 I -20.20 - 3.16 814W 1 0.56NGC 5198 E1 −
25 37.4 S 60 6.48 R -22.04 0.65* 4.87 702W 1 0.41NGC 5308 S0 − sp
10 34.1 F 90 3.56 I -22.13 - 3.56 814W 1 0.28NGC 5813 E1 −
52 31.3 S 60 4.23 I -23.28 - 4.23 814W 1 0.19NGC 5831 E3
35 26.4 S 60 3.94 R -21.85 0.58 3.16 702W 3 0.64NGC 5838 S0 −
23 19.8 F 70 5.22 I -21.73 - 5.22 814W 1 0.26NGC 5845
E : E0 −
81 24.2 S 60 5.09 I -23.34 - 5.09 814W 1 0.30NGC 5982 E3
27 46.4 S 60 3.51 I -23.18 - 3.51 814W 1 0.30NGC 7332
S0 pec sp
11 22.4 F 83 2.78 V -21.44 1.11 2.00 WF1/555W 1 0.16NGC 7457 S0 − (rs)?
65 12.9 F 64 1.89 I -20.73 - 1.89 814W 1 0.07Notes: Column (1): NGC number. Column (2): Morphological type from RC3. Column (3): Effective (half-light) radius R e measured in the I band (see PaperIV). Column (4): Distances were taken from preferentially from Mei et al. (2007) or Tonry et al. (2001). Virgo galaxies without other distance determinationswere assigned the mean Virgo distance of 16.5 Mpc from Mei et al. (2007). Distances for other galaxies were taken from Paturel et al. (2003). Column(5): Galaxy classification from Paper IX: F = fast rotator ( λ R > . ), S = slow rotator ( λ R (cid:54) . ). Column (6): The best-fitting inclination determinedfrom axisymmetric Jeans Anisotropic MGE (JAM) modelling. For slow rotators an inclination of 60 ◦ is assumed (except NGCs 4458 and 4550 which haveindependent determinations of their inclination). Column (7): The M/L of the best-fitting JAM model, in the given band. Column (8): Photometric band the M/Lwas determined in. Column (9): Total magnitude determined from the MGE models and converted to I -band using colours from the literature. Column (10):Galaxy colour, where X is the band of the HST imaging. Colours were taken preferentially from Tonry et al. (2001) or from Prugniel & Heraudeau (1998). Forthose galaxies marked with a * no colour was available and an average early-type colour from Prugniel & Heraudeau (1998) was used. Column (11): The M/Lof the best-fitting JAM model, converted to I -band. Column (12): The instrument and filter on the HST from which the photometry is taken. Unless otherwisestated data was taken using HST/WFPC2. Column (13): The quality of fit of the MGE model. For galaxies ranked 1 a good fit was achieved. For galaxiesranked 2 the fit achieved was still good apart from minor discrepancies or dust absorption. For those ranked 3 significant discrepancies had to be taken intoaccount in the fitting process and the MGE model does not closely follow the isophotes (mostly due to bars) but still reproduces reasonable second-momentvelocity maps. Column (14): Mgb - V esc gradient determined as described in Section 4.2.c (cid:13)000
65 12.9 F 64 1.89 I -20.73 - 1.89 814W 1 0.07Notes: Column (1): NGC number. Column (2): Morphological type from RC3. Column (3): Effective (half-light) radius R e measured in the I band (see PaperIV). Column (4): Distances were taken from preferentially from Mei et al. (2007) or Tonry et al. (2001). Virgo galaxies without other distance determinationswere assigned the mean Virgo distance of 16.5 Mpc from Mei et al. (2007). Distances for other galaxies were taken from Paturel et al. (2003). Column(5): Galaxy classification from Paper IX: F = fast rotator ( λ R > . ), S = slow rotator ( λ R (cid:54) . ). Column (6): The best-fitting inclination determinedfrom axisymmetric Jeans Anisotropic MGE (JAM) modelling. For slow rotators an inclination of 60 ◦ is assumed (except NGCs 4458 and 4550 which haveindependent determinations of their inclination). Column (7): The M/L of the best-fitting JAM model, in the given band. Column (8): Photometric band the M/Lwas determined in. Column (9): Total magnitude determined from the MGE models and converted to I -band using colours from the literature. Column (10):Galaxy colour, where X is the band of the HST imaging. Colours were taken preferentially from Tonry et al. (2001) or from Prugniel & Heraudeau (1998). Forthose galaxies marked with a * no colour was available and an average early-type colour from Prugniel & Heraudeau (1998) was used. Column (11): The M/Lof the best-fitting JAM model, converted to I -band. Column (12): The instrument and filter on the HST from which the photometry is taken. Unless otherwisestated data was taken using HST/WFPC2. Column (13): The quality of fit of the MGE model. For galaxies ranked 1 a good fit was achieved. For galaxiesranked 2 the fit achieved was still good apart from minor discrepancies or dust absorption. For those ranked 3 significant discrepancies had to be taken intoaccount in the fitting process and the MGE model does not closely follow the isophotes (mostly due to bars) but still reproduces reasonable second-momentvelocity maps. Column (14): Mgb - V esc gradient determined as described in Section 4.2.c (cid:13)000 , 1–23 N. Scott et al.
Figure 1.
Photometry of NGC4570 with the MGE model contours over-plotted. From top to bottom the figures are: HST/PC1 field, HST/WFPC2mosaic image, wide-field MDM image. The MDM image is oriented withnorth to the top and east to the left. The WFPC2 mosaic field is shownon the MDM image. As can be seen the MGE contours closely follow theisophotes at all radii. imaging from ACS or WPFC where WFPC2 data was not avail-able.The HST data were used as reference for the photometric cal-ibration and the MDM images were rescaled to the same level. Themethod of photometric calibration is described in detail in Cappel-lari et al. (2006, hereafter Paper IV), but in summary we measuredlogarithmically sampled photometric profiles using circular aper-tures for each image after masking bright stars or galaxies. We donot expect or observe strong colour gradients between the F555W,F814W and intermediate filters, allowing us to match the MDMand HST photometry. The photometric profiles were then fitted byminimising the relative error between the two profiles in the regionof overlap. The HST and MDM images were then merged to forma single photometric profile for each object.The spectroscopic information was obtained using theSAURON integral-field unit on the 4.2-m William Herschel Tele-scope at the Roque de los Muchachos observatory on La Palma. Fordetails of the instrument and the data reduction pipeline see Baconet al. (2001). The SAURON field of view covers objects out to typ-ically 1 R e and at least . R e . The data reduction steps includebias and dark subtraction, extraction of the spectra using a fittedmask model, wavelength calibration, flat fielding, cosmic-ray re-moval, sky subtraction and flux calibration. The flux calibration isdescribed in detail in Kuntschner et al. (2006, hereafter Paper VI).The stellar absorption lines are also properly corrected for nebularemission. The SAURON wavelength range allows us to measurefour Lick indices (Trager et al. 1998): H β , Fe5015, Fe5270 andMgb (see Worthey et al. 1994, for a full definition of these indices).In this work we consider only H β , Fe5015 and Mgb as the Fe5270line lies at the edge of SAURON’s spectral range and so has incom-plete spatial coverage in some objects. The measurement of the linestrength indices from the final data cubes is described in Paper VIwhere line strength maps for the whole sample are presented. Thestellar kinematics we use in this paper is the same that was usedin Paper IV which was presented in Emsellem et at. (2004). Thismakes our M/L values directly comparable with those of paperIV, when scaled to the same distances.
Photometric models for all 48 galaxies in the sample were con-structed using the Multi-Gaussian Expansion (MGE) parametriza-tion of Emsellem, Monnet & Bacon (1994). The observed sur-face brightness profile is described in terms of the sum of two-dimensional Gaussians, which allows the reproduction of ellipticityvariations and strongly non-elliptical isophotes. The MGE fittingmethod of Cappellari (2002) was used to facilitate fitting of a largesample of galaxies. The MGE models were constrained to haveconstant position angle (PA) to enable axisymmetric Jeans mod-elling to be used in determining the underlying potential.Twenty four of the MGE models used in this investigationwere discussed in Paper IV and will not be discussed further here.The remaining 24 early-type galaxies of the SAURON sampleare those for which either accurate Surface Brightness Fluctua-tion (SBF) distances were unavailable, WFPC2/F814W data wasunavailable or the objects show strong non-axisymmetric features. (cid:13) , 1–23 he SAURON Project - XIV While accurate distances are required to estimate mass to light ra-tios they are not required for this investigation and by relaxing therequirement for WFPC2/F814W data we can now model the entireSAURON early-type sample. MGEs for those galaxies not alreadypresented in Paper IV are listed in the appendix. Note that severalof the galaxies already modeled in Paper IV are triaxial objects.The MGE models were fitted simultaneously to the wide-field MDM images and the higher resolution HST images. WhereWFPC2 imaging was available the models were fitted simultane-ously to the ground based, lower resolution mosaic and higher res-olution WFPC2/PC1 images. The MGE fits were performed bykeeping the position angle (PA) of the Gaussians constant and alsotaking the point spread function (PSF) into account. PSFs were cal-culated using TinyTim (Krist 1993) and modeled using the aboveMGE fitting method. The PSFs used are presented in Table B1.The resulting analytically deconvolved MGE models are all cor-rected for galactic extinction following Schlegel, Finkbeiner &Davis (1998), as given by the NASA/IPAC Extragalactic Database(NED). They are then converted to a surface density in solar unitsin the Johnson-Cousins magnitude system using the calibration rel-evant to each instrument (WFPC1 - Harris et al. (1991); WFPC2 -Dolphin (2000); ACS - Sirriani et al. (2005).) Absolute magnitudesfor the Sun (M B = 5 . ,M V = 4 . , M R = 4 . , M I = 4 . ,)are taken from Table 2.1 of Binney & Merrifield (1998). The val-ues of the MGE parameterizations are presented in the Appendixin Table D1 and D2.Because the SAURON field-of-view is relatively small whencompared to our imaging we are principally interested in fitting thecentral regions of each galaxy, while the MDM imaging is usedto provide additional constraints on the MGE model. We do notattempt to accurately model structure such as shells or isophotaltwists in the outer parts of these galaxies but we do seek to repro-duce the overall shape of the object. As discussed in Cappellari(2002) the models were regularized by requiring the axial ratio ofthe flattest Gaussian to be as round as possible while still repro-ducing the observations. This is important so as not to artificiallyconstrain the possible inclinations of the models and to reproducerealistic densities. We also masked dusty regions in the images; inthe small number of galaxies in our sample that exhibit dust, thedust is only visible in one half of the galaxy image and so does notreduce the quality of our MGE fits.The quality of the resulting models with respect to the pho-tometry was visually inspected for all galaxies to ensure a reason-able fit had been achieved. We also compared the resulting kine-matics (see Section 3.2) to the SAURON kinematics presented inEmsellem et al. (2004) and adapted the MGEs (within the rules out-lined below) where necessary to obtain a match to the SAURONobservations. The models were refined until a satisfactory qualita-tive fit was achieved for all galaxies. For those galaxies with regularphotometry this was easily achieved. An example of the model anddata photometry for such a galaxy, NGC4570 is given in Fig. 1. For those galaxies with non-axisymmetric features such as bars orisophotal twists achieving a good match proved more challenging.This is because by simply fitting the two-dimensional isophotes weinfer a three-dimensional distribution of matter than does not re-flect that in the real object. In these cases a simple prescription wasfollowed to produce our MGE models.We note that bars are always associated with a discy structurewhich is to first order axisymmetric and of which the bar repre-
Figure 2.
HST/PC1 photometry on NGC3384 showing two different MGEmodel contours overplotted. In the upper figure we have allowed the modelto follow the isophotes such that the effect of the bar is included in theMGE model. In the lower image we have constrained the axial ratios ofthe Gaussians as described in the text in order to reduce the influence ofthe bar on the MGE model. Despite being a superficially poorer fit to thephotometry the MGE model from the lower figure reproduces a better fit tothe observed kinematics than that from the upper figure (see Fig. 3). sents a perturbation. Because of this we assume that a reasonableaxisymmetric mass model of a barred galaxy is found when the el-lipticity over the barred region is fixed at the global ellipticity. Ingalaxies where there is an obvious bar we constrained the MGEmodel such that the axial ratio of the Gaussians over the barredregion was consistent with the axial ratios of the inner and outerregions where the impact of the bar on the photometry was negligi-ble. An example of a model for a barred galaxy is given in Figs. 2and 3. With the barred MGE the axisymmetric JAM model fails toreproduce the kinematics, we find a significant improvement whenusing our bar-less MGE. Moreover, the recovered inclination of the c (cid:13)000
HST/PC1 photometry on NGC3384 showing two different MGEmodel contours overplotted. In the upper figure we have allowed the modelto follow the isophotes such that the effect of the bar is included in theMGE model. In the lower image we have constrained the axial ratios ofthe Gaussians as described in the text in order to reduce the influence ofthe bar on the MGE model. Despite being a superficially poorer fit to thephotometry the MGE model from the lower figure reproduces a better fit tothe observed kinematics than that from the upper figure (see Fig. 3). sents a perturbation. Because of this we assume that a reasonableaxisymmetric mass model of a barred galaxy is found when the el-lipticity over the barred region is fixed at the global ellipticity. Ingalaxies where there is an obvious bar we constrained the MGEmodel such that the axial ratio of the Gaussians over the barredregion was consistent with the axial ratios of the inner and outerregions where the impact of the bar on the photometry was negligi-ble. An example of a model for a barred galaxy is given in Figs. 2and 3. With the barred MGE the axisymmetric JAM model fails toreproduce the kinematics, we find a significant improvement whenusing our bar-less MGE. Moreover, the recovered inclination of the c (cid:13)000 , 1–23 N. Scott et al.
Figure 3.
Bi-symmetrized and linearly interpolated maps of the second velocitymoment µ (cid:48) ≡ √ V + σ (left) and velocity field V (right) of NGC3384. Thetop image shows the observed µ (cid:48) and V extracted from the SAURON stellarkinematics. The centre and bottom images show the predicted µ (cid:48) and V fromthe two MGE models described in the caption to Fig. 2. The centre image showsthe predictions for an MGE that follows the isophotes of the bar whereas thebottom image shows the predictions for an MGE that attempts to avoid theeffect of the bar. As can be clearly seen the ‘bar-less’ MGE is a much betterfit to the observed µ (cid:48) and V. The contours shown are the isophotes from thereconstructed SAURON image. model becomes closer to the one inferred from the disc. This sug-gests that our bar-less MGEs is a better approximation to the globalgalaxy structure.For galaxies where the photometric and kinematic PA (see ta-ble 1, Paper X) differ significantly the kinematic PA was used forthe MGE models as being more representative of the galaxy overthe SAURON field of view. Although in this way we do not rep-resent the isophotal twists in the photometry the stellar kinematicsare fitted better leading to a significant improvement in the χ valueof the fit. We checked the kinematics produced by the axisymmet-ric Jeans modelling and in all cases a reasonable agreement wasfound with the observed kinematics. Further examples of the ob-served and modelled first and second velocity moments are shownin the Appendix in Fig. C1. In order to compute V esc we constructed Jeans Anisotropic MGE(JAM) axisymmetric models (Cappellari 2008) of all the galax-ies in the sample. For a given inclination i , the MGE surface den-sity can be deprojected analytically (Monnet, Bacon & Emsellem ∼ mxc/idl/ ρ ( R, z ) in the galaxy merid-ional plane, still expressed in terms of Gaussians. This deprojectionis non-unique but represents a reasonable choice as the resulting in-trinsic density resembles observed galaxies for all lines of sight. Wethen apply JAM modelling to the resulting deprojected densities todetermine the underlying potential.The method is described fully in Cappellari (2008) but we willbriefly summarise the key points here. The positions x and veloci-ties v of a large system of stars can be described by a distributionfunction f ( x , v ) which in a steady state must satisfy the collision-less Boltzmann equation. In order to make use of this equation fur-ther simplifying assumptions must be made. A typical first choice isto assume axial symmetry, which leads to the two Jeans equations(Jeans 1922) , but this is not sufficient to specify a unique solution.We make the further assumptions that the velocity dispersion ellip-soid is aligned with the cylindrical coordinate system ( R, z, φ ) andthat the anisotropy is constant. We also assume that mass followslight, but allow for a constant dark matter fraction. Under these as-sumptions the Jeans equations reduce to: bνv z − νv φ R + ∂ ( bvv z ) ∂R = − ν ∂ Φ ∂R (1) ∂ ( νv z ) ∂z = − ν ∂ Φ ∂z (2)where b quantifies the anisotropy, v R = bv z , ν is the luminositydensity and v i the components of the velocity. They provide thesecond moments of the line-of-sight velocity v z (cid:48) ≡ v los , which aregenerally considered to be good approximations to the observedquantity V rms = V + σ . By comparing the observed and Jeansmodelled second moments we determined the best fitting inclina-tion, anisotropy and constant mass-to-light ratio M/L for all 48galaxies in our sample.Determining the inclination is difficult but we apply severalindependent checks which validate our fitted results. For highlyflattened objects they must be close to edge on (16 objects). Sixgalaxies have an obvious embedded gas disk or dust lane, inclina-tions were estimated assuming these are thin discs. In all cases ourinclinations were consistent with the independent determination.For the remaining 26 galaxies the inclinations are determined basedpurely on the model and may not always be accurate. The accu-racy of these inclinations is discussed further in Cappellari (2008).Our V esc is only weakly dependent on the inclination used and sothis uncertainty does not significantly affect the conclusions of thiswork. As an extreme test of the dependence of our modeled V esc on inclination we artificially set the inclinations for the models ofall our galaxies to 90 ◦ (i.e. edge-on) and re-calculated the V esc .The effect on V esc was small, only a 5 percent change in the mostextreme cases..As mentioned above some of the objects in our sample areclearly not axisymmetric systems and so the use of axisymmetricmodels requires some justification. The alternative would be to usethe more general Schwarzschild (1979) models. In Paper IV wecompared the mass-to-light ratios (M/L) derived from axisymmet-ric Jeans and Schwarzschild modelling and find an excellent agree-ment between the two (see particularly Fig. 7 from that paper.) Ad-ditionally, the slow-rotators, while likely to be triaxial objects arealso very round (see Paper X, van den Bosch et al. 2008) and so anydeviations from axisymmetry in their intrinsic shapes are relativelysmall. From this one should not expect major biases in the M/Lwe derive with axisymmetric models. We explicitly tested whetherthis is the case, using the M/L derived via more general triaxial c (cid:13) , 1–23 he SAURON Project - XIV Figure 4. V esc and Mgb maps for several galaxies with the elliptical annuli used to extract the profiles shown. Here we show only a few of the ellipses to avoidcluttering the plot. The numbers to the bottom right of each plot indicate the range of values displayed. As can be seen the modelled V esc field (or equally thepotential Φ ) closely traces the ellipses but the observed Mgb maps are less regular. models by van den Bosch (2008) for eight slow-rotators in com-mon with our sample. We found good agreement between our M/Ldeterminations with JAM and the triaxial models. A more detailedcomparison will be presented elsewhere. As for the M/L, we expectV esc to be only weakly affected by the assumption of axisymmetryand the use of Jeans models. This can be understood by noting thatwhile there are many more possible orbits in a triaxial system thanin an axisymmetric one this does not affect the potential and henceV esc . It is the distribution of the mass, not the structure of the or-bits, that affects Φ , and this is largely unchanged between triaxialand axisymmetric systems, apart from a small geometric factor. esc In order to study the index-V esc relations we must extract the in-trinsic line strength indices from the SAURON maps and the V esc from our JAM models in a consistent fashion. The potential Φ iscalculated as in Emsellem, Monnet & Bacon (1994) and the V esc issimply related to this by the expression: V esc = (cid:112) | Φ( R, z ) | (3)The observed indices on the sky plane are the luminosity-weighted average of the local values in the galaxy along the line-of-sight. We make the quite general assumption that the indices arerelated to V esc by a simple power-law relationship of the form: Index ∝ V γ esc (4)This leads to: Σ( x (cid:48) , y (cid:48) )Mgb p ∝ Σ( x (cid:48) , y (cid:48) )V γ esc , p ( x (cid:48) , y (cid:48) )= (cid:90) ∞−∞ ρ ( R, z )V γ esc ( R, z ) dz (cid:48) = (cid:90) ∞−∞ ρ ( R, z ) | R, z ) | γ/ dz (cid:48) (5)With this assumption it is possible to extract the luminosity-weighted average, V esc , p of the local V esc along the line-of-sight.In practice the V esc values depend only weakly on the parameter γ and our conclusions hold for any reasonable choice of the parame-ter. To form profiles we sum the local line-of-sight integrated val-ues over elliptical annuli aligned with the kinematic major axis ofthe galaxy and evenly spaced in radii over the entire SAURON field,where the ellipticity used is the global ellipticity as given in table1 of Paper X. The noise in each profile is minimised by choos-ing the photometric ellipticity (cid:15) for the profile extraction ellipses.Several examples of the Mgb and V esc maps with the elliptical an-nuli used to extract the profiles overplotted are shown in Fig. 4.Before this was done the individual SAURON line strength mapswere inspected for irregular bins. These occasionally occur in theouter parts of the SAURON field due to the continuum effects de-scribed in Paper VI. Masks were constructed for several of the mostaffected maps. Only the outer few elliptical annuli are affected bythis issue and the use of un-masked maps does not significantly ef-fect the Index-V esc profiles. Bright stars and obvious dust featureswere also masked on the line strength maps. The error in the linestrength for each data point is the rms sum of the measurement errorfrom Paper VI and the rms scatter within an annulus. We adoptedan error of 5 per cent in V esc (see Paper IV). In this section we present the Index-V esc relations determined us-ing the method described above. The profiles are presented in Fig. c (cid:13) , 1–23 N. Scott et al.
Figure 5.
The line strength index versus V esc relations. All indices are measured in ˚A of equivalent width. In each figure all the points for an individual galaxyare represented by a single combination of colour and symbol. In all three cases the correlation is remarkably tight. The black line in each panel is a fit tothe central Re/8 aperture values, excluding outlying galaxies. The profiles with their NGC numbers shown are those galaxies showing evidence of recent starformation. Typical error bars are shown in each figure. c (cid:13) , 1–23 he SAURON Project - XIV Table 2.
Linear fit parameters for the Index-V esc relations from Re/8 circular aperture values.Sample Index a b
StandardDeviationMgb -0.30 ± ± ± ± β ± ± ± ± ± ± β ± ± ± ± ± ± β ± ± ± ± ± ± β ± ± log Index = a + b × log V esc . The linear fit parameters were calculated using a χ minimisation technique asdescribed in the text.
5. Mgb and Fe5015 show a remarkably tight correlation, with theMgb-V esc relation having the tightest correlation. The H β -V esc correlation is less tight. In this and all following linear fits we fitteda linear relation to the Re/8 circular aperture values for each of theobserved correlations by minimizing the χ parameter using theFITEXY routine taken from the IDL Astro-Library (Landsman1993), which is based on a similar routine by Press et al. (1992)and adding quadratically the intrinsic scatter to make χ /ν = 1 ,where ν is the number of degrees of freedom. For a discussion ofthe technique and its merits see Tremaine et al. (2002). Four out-lying galaxies were excluded from these fits (see Section 4.2 for adescription of how outliers were selected). The results of these fitsare plotted as the straight line on each figure, and the zero-point,slope and rms scatter for each relation are shown in Table 2. Mgband Fe5015 rise with increasing V esc , with Mgb having the steeperslope. In contrast H β shows the opposite trend, in the sense that theareas of deepest potential Φ have the weakest H β absorption.It is known that some early type galaxies may be weakly triax-ial (Kormendy & Bender 1996, Paper IX; Paper X) and an axisym-metric model may not reliably reproduce the intrinsic kinematicsand potential. Galaxies where this is the case typically show a largekinematic and photometric misalignment; barred galaxies are alsonot fully axisymmetric systems. Some of the scatter observed inthe Index-V esc relations may be due to axisymmetric models notproperly reproducing the intrinsic V esc . In order to investigate thiswe define a ‘clean’ sample in which all galaxies that show evidencefor a non-axisymmetric distribution have been removed (see Table1, column (13), only galaxies graded 1 were included in this cleansample.) The best-fitting linear fit parameters for the clean sampleare given in Table 2. There is little change in the gradients betweenthe full and axisymmetric samples, though the scatter is slightly re-duced by ∼
10 per cent. This suggests that while imperfect fittingof Φ due to the assumption of axisymmetry accounts for some ofthe scatter observed in the relations it is only a small effect.In Emsellem et al. (2007) a classification schemewas described for galaxies based on a parameter λ R ≡(cid:104) R | V |(cid:105) / (cid:104) R √ V + σ (cid:105) which is related to the angular mo-mentum per unit mass of the stars integrated within 1 R e . Withinthis classification galaxies with λ R (cid:54) . are described as slow rotators and those with λ R > . as fast rotators. Emsellem etal. (2007) and Cappellari et al. (2007) speculated that slow andfast rotators represent two different families of galaxies withsignificantly different formation histories (in terms of interactionor merger events, cold gas accretion episodes, secular evolutionetc.). If this is the case we might expect the stellar populations ofthe two galaxies to have experienced different histories and forsignatures of this to show up in the line strength-V esc relations.Definite predictions of these differences are beyond the scope ofthis work but it is thought that dry merger processes are moreimportant in the formation of slow rotators whereas the role ofgas is more prominent in fast rotators. Mergers would tend toalter V esc while leaving the stellar population (and thereforethe line strengths) unchanged whereas gaseous processes willalter the line strengths. In order to explore this we separate oursample into fast- and slow-rotators and again perform linear fitsto the two sub-populations; the best fitting parameters are againshown in Table 2. For the case of Mgb the fast- and slow-rotatorsfollow the same relationship. In the case of H β and Fe5015 thereis some suggestion that fast- and slow-rotators follow differentrelationships, though when only ‘clean’ galaxies are consideredthis disappears.We also explored the dependence on the traditional divi-sion into ellipticals/S0s based on their RC3 classifications (thoughEmsellem et al. (2007) and Cappellari et al. (2007) suggest theslow/fast rotator classification is more physically relevant) with 24of each in our sample and found no significant difference in theIndex-V esc relations between the two sub-samples. We also splitour sample into field galaxies and those belong to a cluster or group(again with 24 galaxies lying in each sub-sample) and again foundno significant differences but it important to remember that the en-vironmental classification used here is a simple one. The number of studies that have looked at the local Mg- σ and Mg-V esc relations is surprisingly small given the well known tightnessof the global relation. The two main studies in the area are DSP93and Carollo & Danziger (1994). Both have much smaller samplesthan our current work (8 galaxies and 5 galaxies with V esc respec-tively). The DSP93 sample has four galaxies in common with the c (cid:13)000
10 per cent. This suggests that while imperfect fittingof Φ due to the assumption of axisymmetry accounts for some ofthe scatter observed in the relations it is only a small effect.In Emsellem et al. (2007) a classification schemewas described for galaxies based on a parameter λ R ≡(cid:104) R | V |(cid:105) / (cid:104) R √ V + σ (cid:105) which is related to the angular mo-mentum per unit mass of the stars integrated within 1 R e . Withinthis classification galaxies with λ R (cid:54) . are described as slow rotators and those with λ R > . as fast rotators. Emsellem etal. (2007) and Cappellari et al. (2007) speculated that slow andfast rotators represent two different families of galaxies withsignificantly different formation histories (in terms of interactionor merger events, cold gas accretion episodes, secular evolutionetc.). If this is the case we might expect the stellar populations ofthe two galaxies to have experienced different histories and forsignatures of this to show up in the line strength-V esc relations.Definite predictions of these differences are beyond the scope ofthis work but it is thought that dry merger processes are moreimportant in the formation of slow rotators whereas the role ofgas is more prominent in fast rotators. Mergers would tend toalter V esc while leaving the stellar population (and thereforethe line strengths) unchanged whereas gaseous processes willalter the line strengths. In order to explore this we separate oursample into fast- and slow-rotators and again perform linear fitsto the two sub-populations; the best fitting parameters are againshown in Table 2. For the case of Mgb the fast- and slow-rotatorsfollow the same relationship. In the case of H β and Fe5015 thereis some suggestion that fast- and slow-rotators follow differentrelationships, though when only ‘clean’ galaxies are consideredthis disappears.We also explored the dependence on the traditional divi-sion into ellipticals/S0s based on their RC3 classifications (thoughEmsellem et al. (2007) and Cappellari et al. (2007) suggest theslow/fast rotator classification is more physically relevant) with 24of each in our sample and found no significant difference in theIndex-V esc relations between the two sub-samples. We also splitour sample into field galaxies and those belong to a cluster or group(again with 24 galaxies lying in each sub-sample) and again foundno significant differences but it important to remember that the en-vironmental classification used here is a simple one. The number of studies that have looked at the local Mg- σ and Mg-V esc relations is surprisingly small given the well known tightnessof the global relation. The two main studies in the area are DSP93and Carollo & Danziger (1994). Both have much smaller samplesthan our current work (8 galaxies and 5 galaxies with V esc respec-tively). The DSP93 sample has four galaxies in common with the c (cid:13)000 , 1–23 N. Scott et al.
Figure 6.
Comparison of the results of our sample with those galaxies wehave in common with DSP93. The Mg index values of DSP93 and CD94were converted to Mgb index values using Equation 6. The open symbolsare the values from DSP93 and the closed symbols are the results from thiswork. The solid line is the fit to the SAURON sample, the dotted line to theDSP93 sample and the dashed line the CD94 sample. SAURON sample ( NGC 3379, 4278, 4374 and 4486) for three ofwhich DSP93 have V esc (the exception is NGC 4374) whereas wehave no galaxies in common with the CD94 sample.Both DSP93 and CD94 looked at the Mg -V esc relation,rather than Mgb-V esc relation. Mg is a broader molecular indexbut is tightly correlated with the Mgb index (Jørgensen 1997). Weconvert their Mg index values to Mgb using: log Mgb = 1 .
57 Mg + 0 . (6)DSP93 and CD94 are also based upon long-slit spectroscopyrather than integral-field data. In order to fairly compare our data tothe previous work we re-extract our V esc , σ and Mgb profiles usinga rectangular aperture 2.5 arcseconds wide (as used in the DSP93observations) aligned with the major axis of the SAURON maps,and sampling linearly in distance along the slit from the centre ofeach galaxy.For the three galaxies in common with the DSP93 samplewe find reasonable agreement with our Mgb-V esc result (see Fig.6). While the individual measurements are in broad agreementthe slope for our sample is significantly different to that foundby DSP93 and CD94. This is largely because we sample a muchbroader range in V esc , approximately twice that in DSP93 andCD94. The Mgb-V esc relation is particularly interesting, partly because itis the tightest correlation but also because the profiles for individualgalaxies follow the global relation remarkably closely. This agreeswith the results found by DSP93 and CD94. To better illustrate thisimportant point we performed a linear fit to each of the individ-ual galaxy profiles. In Fig. 7 we show the gradients determined bya linear fit for each galaxy, along with the global gradient deter-mined from a linear fit to the Re/8 circular aperture value for all thegalaxies. The global gradient is . ± . . The distribution of theindividual galaxy gradients has a biweight mean of 0.34 and robust σ of 0.2 (see Hoaglin, Mosteller & Tukey 1983, for a description of Figure 7.
Upper panel: Mgb vs. V esc measured within circular Re/8 aper-tures. The solid line is a linear fit to the data. The solid symbols mark theoutlying galaxies which have been excluded from the fit. Lower panel: Thegradients of the Mgb-V esc relations for each individual galaxy profile, de-termined by fitting a straight line to the galaxy profiles in the same wayas for the global relation. The histogram shows the individual galaxy gra-dients. The dotted line is a continuous distribution with the same mean, σ and total area as the individual gradients. The vertical solid line shows theglobal gradient determined from fitting to Re/8 values only, with the dashedlines indicating the 2 σ error. robust statistics). The typical error in the individual galaxy gradi-ents is 0.04. The mean of the individual gradients is consistent withthe global gradient within the errors, but the distribution is con-siderably broader. The additional observed scatter in the individualgradients implies an intrinsic scatter of 0.16. The Fe5015 and H β relations behaves quite differently. In the case of Fe5015 the localgradients are typically steeper than the global gradient. The localgradients in Mgb and Fe5015 vs V esc appear the same, whereasthe global gradient is significantly flatter in the case of Fe5015.Galaxies typically show H β to be flat or slightly rising with V esc ,whereas (as mentioned above) the global trend is that H β falls withincreasing V esc . This is in line with studies of radial gradients in c (cid:13) , 1–23 he SAURON Project - XIV Figure 8.
The residuals of the Mgb-V esc relation plotted against H β . Thereis a clear trend with H β , in the sense that the residuals are larger (in theabsolute sense) as H β increases. This trend is largely driven by those galax-ies that stand out in the Index-V esc relations, shown as red symbols. Themajority of galaxies cluster around a small region centred on zero residual.The straight line is a fit to the red points only. early-type galaxies (e.g. Mehlert et al. 2003) which find galaxieshave typically very uniform H β indices and hence characteristicages.Taking a 2 σ cut in Fig. 7 we note that 3 galaxies have signif-icantly different gradients from the mean: NGCs 3032, 4150 and4382. These three galaxies also stand out in the Mgb-V esc relation,deviating significantly from the mean relation. NGC 3156 also de-viates significantly from this relation, and even though its local gra-dient lies within our 2 σ cut it has the 2nd largest error on it’s localgradient due to it’s U-shaped profile. For this reason we also con-sider NGC 3156 as an outlier. These four galaxies are labelled inFig. 5 with their NGC numbers. Three of these galaxies have thehighest values of H β in our sample, indicative of recent star forma-tion (see Paper VI). The fourth, NGC4382, is a peculiar galaxy inboth the kinematic and line strength maps, showing a central dip in σ and Mgb as well as a disturbed morphology. It also has signif-icantly higher H β than galaxies of a similar V esc , associated withstar formation in a central disc. While these galaxies stand out no-ticeably in Mgb and H β they lie much closer to the Fe5015 relation,with only NGC3156 showing a significant deviation.Three of these outliers also have the lowest values of V esc inour sample. It is possible that there is a break in the Mgb-V esc re-lation at these low values of V esc but we cannot make a definitivejudgement on this, given the limited number of galaxies in our sam-ple that occupy this regime. Either low-V esc galaxies are simply theleast massive galaxies, expected to have experienced more recentstar formation in a downsizing scenario, in which case we mightexpect them to return to the observed relations, or the Mgb-V esc relation breaks down at these low values of V esc , suggesting dif-ferent processes determine the stellar population characteristics ofgalaxies in this regime. A sample with more galaxies in this regimewould be required to decide between these two hypotheses. β -strong galaxies We mentioned above that those galaxies that deviate significantlyfrom the Mgb-V esc relation also have high values of H β . We Figure 9.
The Index-V esc relation corrected using the relationship betweenthe Mgb residuals and H β shown in Fig. 8. The remaining scatter in thisrelation is consistent with the measurement errors. quantify this in Fig. 8 by plotting the Mgb residuals, ∆ Mgb =Mgb(observed) - Mgb(fitted), against H β . While most galaxiescluster in a large clump centred on ∆ Mgb = 0 there is a signif-icant tail of points with large residuals which appear to correlatewith H β . A linear fit to only those galaxies with high values of H β gives the relationship: ∆ log Mgb = ( − . ± .
05) log H β + (0 . ± . (7)We can use this relationship to modify our Mgb-V esc relation forH β -strong galaxies. In Fig. 9 we plot the ‘corrected’ index givenby: Index = log Mgb + 0 .
36 log H β − . (8)against V esc and again perform a linear fit to these data. The result-ing fit is given by: log(V esc / − ) = 0 .
16 + 3 .
57 log(Mgb / ˚ A)+1 .
29 log(H β/ . ˚ A) (9)We find that this fit has a scatter of only σ = 0 . in log V esc , re-ducing the scatter by 22 percent compared to the uncorrected Mgb-V esc relation. This scatter is now consistent with the measurementerrors. Even with the four galaxies with strongest H β removed thereduction in scatter is significant, σ changes from 0.033 to 0.026,a reduction of 20 percent. As a specific example the two galaxiesat low V esc lying above the Mgb-V esc relation fall on the relationafter this correction is applied. esc as an alternative to σ and Σ M While σ is related to the depth of the potential it is also depen-dent on the details of the orbital structure of the galaxy; in galaxieswith significant rotation or other anisotropy σ is a poor tracer of Φ , whereas the true line-of-sight V esc is always a reliable measure.As an example to support the idea that V esc is a better predictor oflocal galaxy properties than σ we need only look at Emsellem et al.(1996). Here the authors study NGC 4594, the Sombrero galaxy, adiscy edge-on galaxy. In their Fig 21. they show both Mgb vs log σ and Mgb vs log V esc . They clearly demonstrate that the local val- c (cid:13) , 1–23 N. Scott et al.
Figure 10.
Upper figure: Mgb - V esc profiles for five galaxies from the sam-ple. The individual galaxy profiles closely follow the global relation (shownas the dotted line). Lower figure: Mgb - σ profiles for the same four galax-ies. The individual profiles show little resemblance to the global relation(again shown as the dotted line), and in some cases exhibit essentially notrend with σ at all. This illustrates the improvement in using V esc insteadof σ as a tracer of a galaxies dynamical properties. ues of Mgb are not significantly correlated with σ but are tightlycorrelated with V esc .In our own work we find a similar result. While σ is a rea-sonable predictor for some galaxies it is generally worse than V esc ,and in some cases fails spectacularly to reproduce the line strengthtrends observed with V esc . This is particularly true of galaxies withatypical σ maps (central dips in σ , counter-rotating discs etc.) InFig. 10 we show the Mgb-V esc and Mgb- σ relations for a selec-tion of galaxies from our sample. As can be clearly seen, while σ produces a reasonable trend for some galaxies, in others there is noobservable trend whatsoever yet in these cases the trend with V esc is still quite obvious. We choose to use V esc because it is a directmeasure of the potential.We also investigated whether Mgb correlates with the localsurface mass density Σ M (upper panel, Fig. 11). Σ M was calcu-lated directly from the MGE models and then scaled using the M/Lderived from the JAM models. We find that within each galaxythere is a tight relationship between Mgb and Σ M with consistent Figure 11.
Upper panel: the Mgb - Σ M relation for all 48 galaxies. For eachgalaxy the mean Mgb and mean Σ M of that galaxy has been subtractedfrom each profile. The colour and symbol combination is the same as inFig. 5. Galaxies have the same internal gradients but have very differentoffsets - this relation is local rather than global. The lower panel showsthe tight relation between V esc and Σ M within a galaxy and the lack of aconnection between different galaxies. gradients between galaxies, however, there is no relation betweenthe central Σ M and central Mgb. In this case we find only a lo-cal relation; no global relation is apparent. It is interesting to notethat this implies a constant gradient for V esc vs Σ M , but the off-set between galaxies shows no such correlation (lower panel, Fig.11). This suggests that Σ M is not physically related to Mgb; the lo-cal correlation arising simply because both Σ M and Mgb decreasewith galactic radius. Again V esc appears to be a more significantparameter because it shows both a local and global correlation. As mentioned above we made the assumption that mass followslight in order to calculate our V esc . If the dark matter distributionfollows that of the stellar mass then this assumption is valid, butin general the dark matter profile may be different. The effect ofa dark halo on the local potential was first explored by Franx & c (cid:13) , 1–23 he SAURON Project - XIV Figure 13.
Mgb and V esc maps for NGC 3377. The solid lines show the ellipses used for extraction of the profiles. Panel a) log Mgb. Panel b) log V esc derivedfrom our best-fitting models. Panel c) log V esc derived from our thin disc model. As can be seen the isocontours of V esc produced from the thin disc modelare significantly flatter than the isophotes or the isocontours of Mgb shown in panel a)..
Figure 12.
Circular velocity (top panel) and escape velocity (bottom panel)as a function of radius. The yellow line indicated the total value while thered and blue lines represent the contributions due to dark and stellar massrespectively. The dashed vertical lines represent the position of 1, 2, 3, 4and 5 R e . The change in the gradient of V esc , between total and stellarcontribution only, over the region 0-1 R e is 0.07 dex. Illingworth (1990). In order to investigate this issue we considerthe effect of a dark matter halo on a simple galaxy model. We takethe stellar density to be given by a Hernquist (1990) profile withscale radius a = 1 and embed this in a dark halo also representedby a Hernquist profile with a = 10 : ρ ( r ) = M π ar r + a ) (10)The mass of the dark matter halo was fixed to give a dark mat-ter fraction of 50 percent within 5 R e which is consistent with themeasurements from dynamical studies (see Paper IV, Gerhard et al.2001; Thomas et al. 2007) and from lensing (Rusin & Kochanek2005; Koopmans et al. 2006). This is similar to the NFW profile(Navarro, Frenk & White 1996) in that it has a slope of ρ ∼ r − for r < a , but the Hernquist halo has finite total mass. Recalcu-lating our V esc with this new halo we find that the V esc gradientdecreases by 0.07 dex in the interval 0-1 R e (see Fig. 12) betweenthe model with a dark halo and that with only a stellar contribu-tion. This shows that with these assumptions the dark matter haloproduces a small but detectable change in V esc . Over the limited ra-dial range covered by our SAURON observations a reasonable halomodel produces only a modest change of slope. Over a larger ra-dial range the dark matter halo can significantly change the slope asillustrated for NGC821 and NGC3379 by Weijmans et al. (2009). esc maps While there is a clear correlation between Mgb and V esc in both aglobal and local sense this is not as obvious when comparing theSAURON and V esc maps. In 18 of the 48 SAURON galaxies theisocontours of Mgb are more flattened than those of V esc (see PaperVI. Note, this mostly applies to the Mgb maps. For Fe5015 theisocontours are typically rounder than the Mgb contours and so theproblem is less pronounced if present at all, while for H β the mapsare essentially flat and so not affected by the choice of aperture.)Moreover, the Mgb maps show some structure whereas the V esc maps, which trace the potential, are smooth by construction. A lotof this difference comes down to rms scatter in the observationaldata which is absent in the modeled V esc , but the flattening of theMgb isocontours is a significant effect. In particular some galaxies(for example NGC3377, see Fig. 13) exhibit a pronounced Mgbdisc. c (cid:13) , 1–23 N. Scott et al.
Figure 14.
Edge-on and face-on views of the hyperplane. The directionsof V esc and the SSP parameters are shown in the face on view. The redsymbols on the lower panel show the four galaxies singled-out earlier aslying off the Mgb-V esc relation. The arrows indicate the directions of theV esc and the SSP parameters within the hyperplane.
Table 3.
Principle components analysisV esc ’ Age’ [Z/H]’ [ α /Fe]’ Eigen- % ofvalue variancePC1 0.581 0.286 -0.214 -0.731 2.49 62PC2 0.531 -0.388 -0.606 0.447 1.10 28PC3 0.399 0.708 0.275 0.514 0.30 8PC4 0.471 -0.516 0.715 -0.037 0.10 2Notes: The primed variables are standardised versions of the correspondingvariables with zero mean and unit variance. The coefficients of the principalcomponents are scaled to the variance and sensitive to the range of eachvariable, in the sense that vairables that only vary by a small amount tendto have a large coefficient. We considered whether the galaxies which exhibit these Mgbdisc structures would be better fitted by assuming all the Mgbcomes from a thin disc rather than being uniformly distributed foreach galaxy. This resulted in only a small change in the determinedV esc for these galaxies. The Mgb-V esc relation derived from thedisc-based models has a slightly larger scatter than for our best-fitting models ( σ ∼ . for the disc-based values compared to σ ∼ . for the best-fitting models) but the relation is still atight one (see Fig. 17). We also considered the effect of extractingour Mgb index and V esc from the maps using a long slit aperture -again we recover the tight local and global correlation with similarscatter as we found using elliptical apertures.While a pure-disc model is clearly unrealistic even this ex-treme assumption does not change our main results. We favour ascenario of a disc-like structure embedded in a spheroid (see PaperVI for further discussion of this idea) to account for the flattenedMgb contours and the structure observed in the Mgb maps. Still,the key issue here is the link between line strengths and the localV esc , which appears robust against the differing assumptions testedabove. esc and single stellar population (SSP) parameters While the line strength-V esc relations are interesting it is not en-tirely clear what they tell us about the formation of local early-typegalaxies. The measured line strengths are a synthesis of the age,metallicity and chemical abundance distributions of the stellar pop-ulation. In order to study these more fundamental properties of thestellar populations we transform our line strengths into the physi-cal parameters, age (t), metallicity ([Z/H]), and alpha enhancement([ α /Fe]) using the single stellar population models of Schiavon(2007). These are not true ages, metallicities and abundances butSSP-equivalent parameters assuming each galaxy formed its starsin a single burst. While this assumption is clearly unrealistic and weshould not believe the precise values returned by the model it stillallows us to make comparisons between the SSP-equivalent valuesfor our galaxies.The models predict the Lick line strength indices for a widerange in age, [Z/H] and [ α /Fe] based upon accurate stellar parame-ters from library stars and fitting functions describing the responseof the Lick indices to changes in stellar effective temperature, sur-face gravity and iron abundance. The models produce a grid of age,[Z/H] and [ α /Fe] iso-contours in the Mgb-Fe5015-H β space of ourdata. For each data point we find the nearest point on the modelgrids, which gives us the best-fitting age, [Z/H] and [ α /Fe] and fromthis we construct age, [Z/H] and [ α /Fe] maps. These maps are thenused to produce the age-, metallicity- and alpha enhancement- V esc profiles using the same method used to construct the line strengthindex-V esc profiles. This process, along with a more general discus-sion of the results is presented in Kuntschner et al. (in preparation).Here we confine ourselves to a discussion of the SSP parameters inthe context of V esc .We search for correlations in this four-dimensional V esc , age,[Z/H], [ α /Fe] space using principal components analysis (PCA; seee.g. Francis & Wills 1999; Faber 1973) the results of which areshown in Table 3. As can be seen the first two principal componentsaccount for 90 per cent of the variance. The properties of local el-lipticals are therefore confined to a two-dimensional hyperplane,similar to the result found by Trager et al. (2000) but for σ insteadof V esc . Face-on and edge-on views of this hyperplane are shownin Fig. 14. There is a lack of points in the bottom right quadrant ofthe face-on view of the plane, due to the upper cut-off in age of 18 c (cid:13) , 1–23 he SAURON Project - XIV Figure 15.
Upper panels and bottom left: the V esc vs. [Z/H], Age and [ α /Fe]. There is a strong correlation between [Z/H] and V esc , though not as tight as withthe individual line strength indices. There is a weaker correlation with age and essentially no correlation with [ α /Fe]. None of the figures exhibit the local andglobal correlation observed in the Mgb- and Fe5015-V esc relations. The sharp cutoff at the top of the upper right and lower left figures is due to the limitedrange of the SSP model. Lower right panel: Edge-on view of the plane connecting [Z/H], age and V esc , derived from a linear fit to the three variables. Therelationship between the combination of these three variables is much tighter than in the other three panels. Colours and symbols are as described in Fig. 5. Gyrs imposed by the SSP model. We checked this result by usingthe models of Thomas, Maraston & Bender (2003) to calculate theSSP parameters of our sample and while the precise values in Table3 change by ∼ percent the conclusion that galaxies are confinedto a hyperplane is independent of the SSP model used.Assuming the hyperplane to be infinitely thin (i.e. the contri-butions from PC3 and PC4 are zero) then we can express two ofour variables in terms of the other two variables. The choice of de-pendent and independent variables is entirely arbitrary, but in theinterests of physical insight we choose [Z/H] and age as our twoindependent variables and seek to express V esc in terms of them.Performing a linear fit to the three-dimensional age, [Z/H], V esc space we find that the variables are related by: log (cid:16) V esc − (cid:17) = 0 . (cid:104) ZH (cid:105) + 0 .
43 log (cid:18) tGyrs (cid:19) − . (11)It is important to bear in mind that these are not true ages and metal-licities but SSP-equivalent values. This combination of variables isshown in the lower panel of Fig. 15. The scatter in this relation isgreatly reduced from that of any relation between just two of the four variables we are considering here as shown in Fig. 15. In Fig.16 we show that the local gradients within a galaxy again followthe global gradient, though this result is not as tight as the local-and-global relation for Mgb-V esc . The global gradient, determinedfrom fitting to Re/8 values is . ± . . The mean of the individ-ual gradients is 0.78, with the width of the distribution given by a σ of 0.40. The typical error on the individual gradients is 0.11. Theglobal gradient is consistent with the local gradient well within theerrors. The local gradients again show a broader distribution, im-plying an intrinsic scatter of 32 per cent. This is not the case for[Z/H] alone; here the local gradients are significantly steeper thanthe global one. The specific combination of age and [Z/H] dependson the SSP model used, but the tightness of the plane and the localand global connection do not. c (cid:13)000
43 log (cid:18) tGyrs (cid:19) − . (11)It is important to bear in mind that these are not true ages and metal-licities but SSP-equivalent values. This combination of variables isshown in the lower panel of Fig. 15. The scatter in this relation isgreatly reduced from that of any relation between just two of the four variables we are considering here as shown in Fig. 15. In Fig.16 we show that the local gradients within a galaxy again followthe global gradient, though this result is not as tight as the local-and-global relation for Mgb-V esc . The global gradient, determinedfrom fitting to Re/8 values is . ± . . The mean of the individ-ual gradients is 0.78, with the width of the distribution given by a σ of 0.40. The typical error on the individual gradients is 0.11. Theglobal gradient is consistent with the local gradient well within theerrors. The local gradients again show a broader distribution, im-plying an intrinsic scatter of 32 per cent. This is not the case for[Z/H] alone; here the local gradients are significantly steeper thanthe global one. The specific combination of age and [Z/H] dependson the SSP model used, but the tightness of the plane and the localand global connection do not. c (cid:13)000 , 1–23 N. Scott et al.
Figure 16.
Local gradients for [Z/H] and 0.85 [Z/H] + 0.43 log t . The histograms show the individual galaxy gradients determined from a linear fit to eachgalaxy’s profile. The dotted line shows a distribution with the same mean, σ and total area as the individual gradients. The vertical solid line shows the globalgradient determined from fitting to Re/8 values only, with the dashed lines indicating the 2 σ error. As can be seen the local and global gradients are the samefor our combination of Z and age but not for Z alone. We have already mentioned a few caveats to consider whenanalysing our results. While these points have been discussed morefully elsewhere in the text we summarise them here in the interestof showing that none of these issues threaten our conclusions. Thefour principal caveats in this work are: triaxiality, inclination, darkmatter and the shape of the Mgb isophotes. The first three of theseaffect our determination of the V esc of our galaxies whereas thefourth affects the extraction of our Mgb-V esc profiles. i) Bars and triaxiality:
Several of our galaxies are triaxial orbarred systems. While triaxial objects can have very different or-bit families to axisymmetric systems the distribution of the matterand hence Φ will not be significantly different. Furthermore triax-ial systems tend to be rounder so the deviations in shape are typi-cally small. The M/L is also relatively robust against the assump- tion of axisymmetry, which is expected due to the Virial Theoremand the tight scaling relations followed by fast and slow rotators,e.g. the Fundamental Plane (Djorgovski & Davis 1987). Becauseof this we are able to produce reasonable values for the second mo-ments and velocity fields and hence the V esc of triaxial or barredobjects under the assumption of axisymmetry. Therefore we do notexpect that more detailed triaxial modelling (de Lorenzi et al. 2007;van den Bosch et al. 2008) will significantly alter our conclusions.There is no systematic dependence of the residuals from the Index-V esc relations on bar strength (determined qualitatively by eye forour sample) and that our ‘clean’ axisymmetric sample discussed inSection 4 shows no significant improvements in the tightness of therelations. ii) Dark matter: Our determination of V esc is based on modellingof the photometry and so we are assuming that mass follows light,while allowing for a constant dark matter fraction. We note thatdark matter makes up only a small fraction of the total density in the c (cid:13) , 1–23 he SAURON Project - XIV Figure 17.
The Mgb-V esc relation derived under three different assumptions. Panel a) shows the relation derived assuming all our galaxies are seen with aninclination i = 90 ◦ . Panel b) shows the results of assuming that all the absorption arises from the equatorial plane of our galaxies, i.e. in a disc. The solid linein both panels is taken from Table 2, using the complete sample. As can be seen when comparing this figure with the top panel of Fig. 5 the assumptions madein deriving panels a) and b) do not significantly affect our results. central regions and hence doesn’t significantly affect the potentialin the region we are studying. There is much observational evidencefrom dynamical studies and from lensing to support this view. InSection 4.5 we consider the effect of a dark halo and note that whilethe local gradients in V esc do change the effect is modest over theSAURON field of view. iii) Inclination: For many of our galaxies it was possible to esti-mate the inclination from methods other than our JAM modelling(6 with embedded discs, 16 edge-on objects) and in these cases ourJAM inclinations fall within the errors on our independent esti-mates. For our other galaxies, while we expect that our inclinationestimates are accurate in most cases (see also Cappellari 2008) wealso show in Fig. 17 that our V esc values do not depend strongly oninclination. In panel a) of this figure we show the Mgb-V esc rela-tion for our galaxies under the assumption that they are all edge-on.As can be seen there is little difference between this panel and thetop panel of Fig. 5 which shows our Mgb-V esc relation using ourbest estimates for the inclinations. iv) Mgb discs:
Finally, as noted in Paper VI, the Mgb isocontoursdo not always follow the isophotes which we are using to extractour Mgb-V esc profiles. We investigated this issue by consideringthe idea that our Mgb absorption comes entirely from a disc andre-calculated our V esc based on this assumption. In panel b) of Fig.17 we show the results of this, again, there is little difference be-tween panel b) and the upper panel in Fig. 5, though the scatteris slightly larger. We also investigated the effect of using differ-ent apertures to extract V esc and Index profiles from the maps byvarying the ellipticity of our apertures. While the scatter increasedslightly when circular apertures were used the relations did not sig-nificantly change. esc relations
It is clear from the tightness of the correlations shown in Fig. 5 thatthe stellar populations of early-type galaxies are closely linked withthe depth of the local potential they reside in (characterised in thisstudy by V esc ). That this should be the case is by no means obvious.While we might expect that the formation of a star is influenced bythe potential that it forms in it is perfectly possible for that potential to have changed significantly between the star’s formation and thepresent day. We expect that the availability of gas and it’s abilityto cool will also play a role. The tight correlation observed is moreeasily accommodated in a monolithic collapse scenario for star for-mation in which the gravitational potential Φ is largely unchanged,but it is clear that galaxies do not form in this way - we need toaddress how mergers fit into this picture.While in the monolithic collapse scenario the potential doesnot change the same is not true of mergers; in this case the potentialcan be significantly altered as more mass is added to the galaxy andthe distribution of that mass can also be changed. In this case it isclear that the potential a star forms in and the potential we observeit in several billions years later are different. It has been known forsome time (White 1978; Barnes 1988) that during a merger the starsare preserved in their rank-order of binding energy, in the sense thatthe most deeply bound stars before the merger are also most deeplybound after the merger. This suggests a possible link between thepotential a star formed in and the potential it finds itself in afterthe merger. More recent work by Hopkins et al. (2008) has arguedthat in both wet and dry mergers the radial gradients of metallicityare preserved, again suggesting that the tightness of the observedline strength-V esc relationships can be compatible with hierarchicalmerging. However it is the detail that the local and global relationsare the same that is our key result and more detailed modelling isrequired before we can properly compare model predictions to ourresult.Four galaxies in our sample show signs of recent star forma-tion, and these galaxies are significant outliers in the Mgb- and H β -V esc relations. But, when we convert our line strength indices intoSSP-equivalent parameters we find that these four galaxies are con-fined to the same region in the four-dimensional parameter spaceof V esc , t, [Z/H] and [ α /Fe] as those galaxies which lie on theIndex-V esc relations. As these objects all have unusually high H β they are all likely to be relatively young objects. This suggests thateven recently disrupted objects have some regular properties con-nected with the potential Φ that survive whatever process movedthe galaxy off the Index-V esc relation. It seems likely that as theseobjects age they will return to the Index-V esc relations.It is interesting to ask why we observe a tight local and global c (cid:13) , 1–23 N. Scott et al.
Figure 18.
The line strength - V esc relations predicted by re-inverting theSSP model of Schiavon (2007) and applying the constraint of Equation 11at constant [ α /Fe/] = 0.33 and minimum age, t > β -V esc relations but thecondition of fixed [ α /Fe] is required to reproduce the Fe5015-V esc relation. relation in the Mgb-V esc relation but not in the case of the other twoindices. In order to investigate this issue we begin with our SSP hy-perplane equation, Equation 11. We re-invert the SSP model grid ofSchiavon (2007) and consider the constraints on the line strength-V esc relations implied by Equation 11, using a constant [ α /Fe] of0.33, the mean value for galaxies in our sample. We also imposea minimum age of t > esc relation produced in this way tightly follows theobservations. In the case of H β the region allowed by the model(the grid of points) is well matched to the region occupied by theobservations (shaded area). The observed local gradients broadlyfollow the lines of constant age in the modeled region, which maysuggest why the local and global connection is not observed be-tween H β and V esc . In the case of Fe5015 the model predicts atight correlation with V esc but one that is somewhat steeper thanthe observed relation. Allowing other values of [ α /Fe] is requiredto match the observations; this is consistent with the SSP hyper-plane having a small thickness. We again note that the steeper localgradients in Fe5015 appear to follow lines of constant age. Theseresults suggest two possible conclusions; either the local and globalcorrelation in Mgb is a conspiracy of the interaction between ageand metallicity in producing stellar absorption indices or that therestill remain weaknesses in the SSP models used to derive Equation11. We find essentially no difference between the relations forfast- and slow-rotators, which are thought to have significantly dif-ferent assembly histories. There are clear differences between thetwo classes of galaxies in many of their properties (see Emsellem etal. 2007, for a discussion of these differences) but not in the Index-V esc relation. What does this tell us about the assembly of thesegalaxies? If fast rotators are the progenitors of slow rotators andwe assume that fast rotators lie naturally upon the Index-V esc rela-tions we have observed whatever process leads to these differencesbetween fast- and slow-rotators must preserve the links betweenstellar population properties and the gravitational potential. If, asDi Matteo et al. (2009) suggest, equal mass dry mergers betweengiant elliptical galaxies can significantly alter the metallicity gradi-ents of the remnant, the lack of a difference between the relationsfor fast- and slow-rotators may provide a significant constraint onthe modelling of the formation of these galaxies. In this work we have examined the link between the local escapevelocity, V esc (determined from photometric observations and dy-namical modelling) and the local line strength indices. We discussthe impact on our results of non-axisymmetry, dark matter, inclina-tion and substructure within the line strength maps. Single stellarpopulation models were used to convert our line strength measure-ments into representative values for the age t, metallicity [Z/H],and alpha enhancement [ α /Fe]. We then used some simple modelsto explore the impact of the observed correlations on the formationhistory of early-type galaxies. The main findings of this work areas follows:i) The line strength indices Mgb and Fe5015 are correlated withV esc (both with rms scatters of 0.033) while H β is anti-correlatedwith V esc (with an rms scatter of 0.049). Using the models of Schi-avon (2007) the scatter in the Mgb relation corresponds to a spread ∆[Z / H] ∼ . at a fixed age of 9 Gyrs. The scatter in the H β re-lation corresponds to a spread ∆t ∼ . Gyrs with [Z/H] fixed at c (cid:13) , 1–23 he SAURON Project - XIV solar metallicity. The tightness of these relations provide an impor-tant check for simulations of early-type galaxy formation. (In com-parison the index - σ e relations have rms scatters of 0.028, 0.030and 0.046 for Mgb, Fe5015 and H β ).ii) For Mgb the correlation within a galaxy (the local relation) isthe same as that between the central values of different galaxies(the global relation). This is the key difference when consideringV esc compared to using σ .iii) For outliers characterised by high H β the residuals in the Mgb-V esc relation correlate with H β . We use this correlation to mod-ify our Index-V esc relation such that log(V esc / − ) =0 .
16 + 3 .
57 log(Mgb / ˚ A) + 1 .
29 log(H β/ . ˚ A) . The scatter ofthis corrected relation is consistent with the measurement errors.iv) We divided our sample into several sub-populations: S0s andellipticals, field and group/cluster objects and fast- and slow-rotators. The Index-V esc relations for each of these sub-populationsare consistent with the relations for the entire sample. We find nodependence on these simple divisions into morphological type andenvironment. We also find no significant difference between fast-and slow-rotators.v) When converting these line strength measurements to SSP pa-rameters we find that all the galaxies are confined to a two-dimensional plane within the four-dimensional space of V esc ,age [Z/H] and [ α /Fe]. This plane is described by the equation: log ( V esc / − ) = 0 . / H] + 0 .
43 log(t / Gyrs) - 0.29.Those galaxies that were outliers in the Index-V esc relations do notstand out in this SSP-hyperplane.vi) We find that in the Z-V esc diagram the local gradients are sig-nificantly steeper than the global relation. When we consider theabove combination of Z and age we recover the local and globalrelation, in that the local gradients are the same as the global one.This tight relation does not depend on the SSP model used.How the connection between stellar populations and the gravi-tational potential, both locally and globally, is preserved as galaxiesassemble hierarchically presents a major challenge to models.
We thank Anne-Marie Weijmans for useful discussion on theinfluence of dark matter. The SAURON project is made pos-sible through grants 614.13.003, 781.74.203, 614.000.301 and614.031.015 from NWO and financial contributions from the In-stitt National des Sciences de l’Univers, the Universit Lyon I,the Universities of Durham, Leiden and Oxford, the ProgrammeNational Galaxies, the British Council, PPARC grant ’Observa-tional Astrophysics at Oxford 20022006’ and support from ChristChurch Oxford, and the Netherlands Research School for Astron-omy NOVA. NS is grateful for the support of an STFC studentship.MC acknowledges support from a STFC Advanced Fellowship(PP/D005574/1). RLD is grateful for the award of a PPARC SeniorFellowship (PPA/Y/S/1999/00854), postdoctoral support throughPPARC grant PPA/G/S/2000/00729, STFC grant PP/E001114/1and from the Royal Society through a Wolfson Merit Award. ThePPARC Visitors grant (PPA/V/S/2002/00553) to Oxford also sup-ported this paper. GvdV acknowledges support provided by NASAthrough Hubble Fellowship grant HST-HF-01202.01-A awarded bythe Space Telescope Science Institute, which is operated by theAssociation of Universities for Research in Astronomy, Inc., forNASA, under contract NAS 5-26555. This paper is based on ob-servations obtained at the William Herschel Telescope, operated bythe Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofsica de Canarias. It is alsobased on observations obtained at the 1.3m Mcgraw-Hill Telescopeat the MDM observatory on Kitt Peak, which is owned and oper-ated by the University of Michigan, Dartmouth College, the OhioState University, Columbia University and Ohio University. Thisproject made use of the HyperLeda and NED data bases. Part ofthis work is based on HST data obtained from the ESO/ST-ECFScience Archive Facility.
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Figure A1.
M/L - σ e relation. Solid symbols are those galaxies ranked ashaving a good fitting MGE in Table 1 (rank 1), open symbols represent thosegalaxies having discrepancies between the MGE models and the photome-try, typically due to bars (rank 2 or 3). Blue symbols indicate fast rotatorsand red symbols indicate slow rotators. The solid line is a fit to the data,excluding the galaxy with the lowest M/L, NGC3489. Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, 525Schwarzschild M., 1979, ApJ, 232, 236Sirianni M., Jee M. J., Bentez N., Blakeslee J. P., Martel A. R.,Meurer G., Clampin M., De Marchi G., Ford H. C., Gilliland R.,Hartig G. F., Illingworth G. D., Mack J., McCann W. J., 2005,PASP, 117, 1049Thomas D., Maraston C., Bender R., 2003, MNRAS¡ 339, 897Thomas J., Saglia R. P., Bender R., Thomas D., Gebhardt K.,Magorrian J., Corsini E. M., Wegner G., 2007, MNRAS 382,657Tonry J. L. et al., 2001, ApJ, 546, 681Trager S. C., Faber S. M., Worthey G., Gonz´alez J. J., 2000, ApJ,120, 165Trager S. C., Worthey G., Faber S. M., Burstein D., Gonzalez J.J., 1998 ApJS, 116, 1Tremaine S. et al., 2002, ApJ, 574, 740van den Bosch R. 2008, PhD thesis, Leiden Universityvan den Bosch R.,van de Ven G., 2008, submittedVazdekis A., Casuso E., Peletier R. F., Beckham J. E., 1996, ApJS,106, 307Vazdekis A., 1999, ApJ, 513, 224Visvanathan N., Sandage A., 1977, ApJ, 216, 214Weijmans A., et al, 2009, to be submittedWhite S. D. M., 1978, MNRAS, 184, 185Worthey G., Faber S. M., Gonzalez J. J., Burstein D., 1994 ApJS,94, 687Young L. M., Bureau M., Cappellari M., 2008, ApJ, 676, 317
APPENDIX A: MASS-TO-LIGHT RATIOCORRELATIONS
In Paper IV we examined the correlation between the dynamicalmass-to-light ratio (M/L)
Jeans , and several other properties of lo-cal early-type galaxies, including σ e , H β and the virial mass-to-light ratio, (M/L) Virial . Here we revisit those correlations with theadditional 24 galaxies contributed by this work. The analysis was c (cid:13) , 1–23 he SAURON Project - XIV Figure A2. (M/L)
Jeans vs (M/L)
Virial . The solid line is a fit to the datawhile the dotted line shows a one-to-one correlation. Symbols as in Fig.A1.
Figure A3.
Dynamical M/L versus the observed line strength index, H β .Symbols as in Fig. A1. The shaded region indicates the predictions of theSSP models of Vazdekis et al. (1996) and Vazdekis (1999) using a SaltpeterIMF. carried out precisely as described in Section 4.2 of Paper IV, us-ing mass-to-light ratios derived from JAM modelling rather thanSchwarzschild modelling. Where available we used surface bright-ness fluctuation distances, otherwise distances are redshift only andhave a significantly larger error (Tonry et al. 2001; Paturel et al.2003; Mei et al. 2007). All mass-to-light ratios were converted to I -band using galaxy colours obtained from Tonry et al. (2001) andPrugniel & Heraudeau (1998). As in Paper IV we adopted an errorin σ e of 5 percent and a 6 percent modelling error in (M/L) Jeans to which we quadratically co-added the distance errors. The fitwas carried out by quadratically adding an intrinsic error to make χ /ν = 1 , where ν is the degrees of freedom. To preempt our con-clusions we find no significant change from the results presented inPaper IV.We find a tight correlation with σ e , with an observed rms scat- ter of 30 percent, shown in Fig. A1. This implies an intrinsic scatterof 11 percent. The best fitting relation has the form: (M / L) Jeans = (3 . ± . (cid:16) σ e
200 km s − (cid:17) . ± . (A1)We also compared our dynamical (M/L) Jeans to the observed virial(M/L)
Virial = βR e σ e /G L (where we adopt β = 5 as found inPaper IV), shown in Fig. A2. With our adopted modelling errorof 6 percent in the (M/L) Jeans the scatter in (M/L)
Virial requiredto make χ /ν = 1 is 26 percent. The best fitting relation has theform: (M / L) Jeans ∝ (M / L) . ± . (A2)We also present the relation with H β (see Fig. A). This is closelyrelated to the population mass-to-light ratio (M/L) Pop , which islargely driven by variations in H β . We again reproduce the trendfound in Paper IV. We also indicate the predictions of the SSP mod-els of Vazdekis et al. (1996) and Vazdekis (1999) as shown in fig.16 of Paper IV. APPENDIX B: PSF PARAMETERS USED IN THE MODELMGES
Table B1 contains the details of the point spread functions usedwhen evaluating our model MGEs. These PSFs were calculated byfitting circular Gaussians to PSFs produced using the TinyTim soft-ware. The PSFs have the form:
PSF = Σ nk =1 G k exp[ − R / σ k ] / πσ k . APPENDIX C: FURTHER EXAMPLES OF VELOCITYFIELDS CALCULATED FROM JAM MODELLING
In Fig. C we show the results of JAM modelling for eight galaxiesfrom our sample. Further examples are shown in Cappellari (2008).Details of the JAM modelling can be found in Section 3.2. We showthe observed and modeled results for both the first and second mo-ments of the velocity for each galaxy. As can be seen in all cases weachieve good agreement between the observations and our models.
APPENDIX D: MULTI-GAUSSIAN EXPANSIONPARAMETERS FOR 24 GALAXIES IN OUR SAMPLE
In Appendix B of Paper IV we presented the (distant-independent)MGE parameters for 23 galaxies from the SAURON sample . InTable D1 and D2 we present the MGE parameters for the remaining23 galaxies. The constant-PA models were obtained by fitting theHST photometry (where available) at small radii and the ground-based MDM photometry at large radii. They provide an accuratedescription of the surface brightness of the galaxies from R ≈ . arcsec to about twice the maximum σ j used in each galaxy (usu-ally corresponding to − R e ). Dust and bright foreground starswere excluded from the fit. The matching of the different images isdescribed in Section 3.1. The deconvolved surface brightness Σ isdefined as follows: The MGE parameters for NGC 2974 were given in Krajnovi´c et al.(2005). Those for NGC 3032 were given in Young, Bureau & Cappellari(2008).c (cid:13) , 1–23 N. Scott et al.
Figure C1.
Examples of the first and second moments of the velocity fields, v ( µ ) and √ v + σ ( µ ) derived from our JAM models alongside the bi-symmetrised measured µ and µ from the SAURON kinematics. From top to bottom for each galaxy the figures show: observed µ , model µ , observed µ ,model µ . We show here a selection of galaxies from our sample to illustrate the range in the quality of fits we achieved. c (cid:13) , 1–23 he SAURON Project - XIV Table B1.
Parameters of the model MGE PSFsInstrument/Filter k G k σ k (arcsec)1 0.226 0.022 0.573 0.05WFPC2/F606W 3 0.092 0.144 0.071 0.335 0.038 0.881 0.254 0.022 0.560 0.06WFPC2/F702W 3 0.083 0.164 0.070 0.385 0.033 1.051 0.280 0.022 0.546 0.06WFPC2/F814W 3 0.073 0.184 0.071 0.455 0.030 1.391 0.061 0.032 0.089 0.09WFPC1/F555W 3 0.145 0.194 0.637 1.005 0.066 1.911 0.445 0.052 0.303 0.15ACS/F475W 3 0.101 0.374 0.081 1.045 0.061 3.38Notes: The model PSFs are formed from the sum of circularGaussians fitted to TinyTim PSFs and have the form: PSF =Σ nk =1 G k exp[ − R / σ k ] / πσ k . The numerical weights are normalisedsuch that Σ nk =1 = 1 Σ( x (cid:48) , y (cid:48) ) = N (cid:88) j =0 L (cid:48) j πσ (cid:48) j q (cid:48) j exp (cid:26) − σ (cid:48) j (cid:18) x (cid:48) j + y (cid:48) j q (cid:48) j (cid:19)(cid:27) (D1)where the model is composed of N Gaussian components of dis-persion σ j , axial ratio q j and peak intensity I j . The coordinates( x (cid:48) , y (cid:48) ) are measured on the sky plane, with the x (cid:48) -axis correspond-ing to the galaxy major axis. The total luminosity of each Gaussiancomponent is given by L j = 2 πI j σ j q j . See Cappellari (2002) fordetails. The obscured areas in each figure were masked in the fittingprocess. c (cid:13) , 1–23 N. Scott et al.
Table D1.
MGE parameters for the deconvolved I -band surface brightnessj log I j log σ j q j log I j log σ j q j log I j log σ j q j log I j log σ j q j (L (cid:12) pc − ) (arcsec) (L (cid:12) pc − ) (arcsec) (L (cid:12) pc − ) (arcsec) (L (cid:12) pc − ) (arcsec)NGC 474 NGC 1023 NGC 2549 NGC 26851 5.224 -1.762 0.922 6.084 -1.645 0.800 5.775 -1.593 0.753 5.278 -1.363 0.5002 4.697 -1.097 0.989 5.214 -1.012 0.747 4.760 -0.877 0.646 4.657 -0.845 0.5003 4.089 -0.652 0.978 4.837 -0.637 0.613 4.260 -0.363 0.811 4.261 -0.335 0.3924 4.005 -0.192 0.965 4.288 -0.383 0.800 4.078 0.062 0.732 4.110 0.145 0.3455 3.595 0.043 0.992 4.366 -0.152 0.474 3.512 0.538 0.554 3.689 0.450 0.4226 3.391 0.283 0.922 4.328 -0.015 0.800 2.981 0.778 0.742 2.949 0.684 0.6007 3.028 0.435 0.997 4.180 0.261 0.800 3.239 0.801 0.233 3.101 0.903 0.2938 3.029 0.621 0.900 3.869 0.580 0.800 5.666* 1.248 0.434 2.609 1.033 0.6009 2.680 0.857 0.900 3.539 0.896 0.757 5.666 1.248 0.434 2.653 1.308 0.26110 2.161 1.322 0.931 3.091 1.320 0.634 3.122 1.595 0.421 1.950 1.340 0.60011 1.566 1.661 1.00 1.637 1.655 0.800 3.186* 1.602 0.430 1.902 1.599 0.60012 - - - 2.441 1.827 0.300 2.549 1.702 0.409 0.985 1.914 0.60013 - - - 2.061 2.033 0.3828 2.865* 1.911 0.403 - - -14 - - - 0.648 2.255 0.800 2.829 1.920 0.404 - - -NGC 2695 NGC 2699 NGC 2768 NGC 33841 3.870 -0.009 0.710 5.388 -1.762 0.810 4.801 -1.337 0.750 5.093 -1.762 0.7002 3.575 0.293 0.710 4.549 -1.241 0.900 4.532 -0.721 0.482 5.203 -1.222 0.7003 3.103 0.586 0.710 4.072 -0.484 0.900 4.370 -0.544 0.750 5.064 -0.884 0.7004 2.673 0.948 0.701 3.541 -0.323 0.866 4.084 -0.178 0.750 4.640 -0.486 0.6655 1.940 1.375 0.710 3.775 -0.067 0.884 3.654 0.182 0.750 4.071 -0.170 0.7006 0.921 1.720 0.710 3.347 0.338 0.700 3.458 0.512 0.674 4.094 0.261 0.7007 - - - 2.893 0.573 0.798 3.204 0.862 0.689 4.113 0.273 0.4368 - - - 2.704 0.815 0.900 2.792 1.225 0.504 3.909 0.513 0.7009 - - - 1.603 1.152 0.900 2.545 1.449 0.553 3.657 0.827 0.70010 - - - 1.384 1.241 0.700 2.021 1.797 0.305 3.019 1.162 0.70011 - - - 1.324 1.357 0.900 1.923 1.910 0.523 1.927 1.775 0.69612 - - - 0.657 1.878 0.724 1.182 2.139 0.544 2.300 1.781 0.41513 - - - - - - - - - 1.04279 2.127 0.537NGC 3489 NGC 4262 NGC 4270 NGC 43821 6.070 -1.624 0.500 5.410 -1.422 0.910 5.049 -1.589 0.692 4.148 -0.728 0.7702 5.466 -0.950 0.500 4.459 -0.903 0.910 3.961 -0.721 0.700 4.195 -0.344 0.7803 4.790 -0.573 0.625 4.119 -0.570 0.910 3.630 -0.301 0.606 4.337 -0.001 0.7804 4.726 -0.181 0.500 4.006 -0.235 0.910 3.551 -0.025 0.682 3.994 0.383 0.7805 4.363 0.109 0.700 3.780 0.251 0.906 3.145 0.250 0.700 3.591 0.707 0.7706 3.831 0.397 0.700 3.312 0.518 0.910 2.839 0.550 0.676 3.194 0.962 0.7807 3.702 0.722 0.700 2.266 0.747 0.910 2.570 0.877 0.500 2.802 1.252 0.7808 3.010 1.103 0.700 2.259 1.024 0.910 2.412 1.151 0.500 2.303 1.460 0.7709 2.623 1.515 0.505 1.858 1.358 0.910 1.693 1.444 0.500 2.551 1.752 0.78010 1.445 1.876 0.694 0.439 1.743 0.910 0.636 1.750 0.700 1.818 2.154 0.780Note: * indicates where a negative Gaussian was used to achieve a satisfactory fit. This only occurs in the most discy objects.c (cid:13) , 1–23 he SAURON Project - XIV Table D2.
MGE parameters for the deconvolved I -band surface brightnessj log I j log σ j q j log I j log σ j q j log I j log σ j q j log I j log σ j q j (L (cid:12) pc − ) (arcsec) (L (cid:12) pc − ) (arcsec) (L (cid:12) pc − ) (arcsec) (L (cid:12) pc − ) (arcsec)NGC 4387 NGC 4477 NGC 4546 NGC 45641 4.793 -1.422 0.750 4.785 -1.337 0.910 6.012 -1.707 0.770 5.304 -1.482 0.8002 4.120 -0.959 0.804 4.203 -0.918 0.910 5.028 -1.063 0.773 4.876 -0.993 0.8003 3.274 -0.679 0.750 4.126 -0.377 0.900 4.639 -0.682 0.732 4.521 -0.586 0.8004 3.311 -0.492 0.740 3.441 0.141 0.910 4.251 -0.397 0.753 4.224 -0.242 0.8005 3.201 -0.261 0.718 3.453 0.431 0.910 4.107 -0.160 0.592 3.873 0.097 0.7126 3.166 -0.037 0.850 3.154 0.779 0.910 3.940 0.050 0.780 3.521 0.348 0.7417 2.980 0.279 0.773 2.567 1.081 0.910 3.750 0.304 0.812 3.270 0.638 0.7018 2.860 0.591 0.647 2.184 1.604 0.910 3.465 0.582 0.918 2.270 0.929 0.8009 2.573 0.848 0.592 0.421 1.892 0.910 2.917 1.031 0.473 2.852 1.063 0.35010 2.229 1.128 0.546 - - - 2.723 1.345 0.400 2.347 1.333 0.35011 1.558 1.388 0.638 - - - 2.003 1.602 0.451 2.111 1.461 0.41312 0.732 1.634 0.756 - - - 1.378 1.859 0.641 1.711 1.630 0.48913 - - - - - - - - - 1.150 1.840 0.712NGC 4570 NGC 5198 NGC 5308 NGC 58311 6.101 -1.762 0.550 4.387 -1.008 0.867 5.922 -0.931 0.405 4.843 -1.585 0.7002 5.009 -0.944 0.580 4.196 -0.634 0.900 5.955* -0.917 0.411 4.518 -1.044 0.8133 4.646 -0.585 0.537 3.860 -0.270 0.900 4.875 -0.654 0.605 4.314 -0.708 0.8694 4.392 -0.327 0.752 3.525 0.050 0.900 4.337 -0.298 0.0869 3.714 -0.393 0.7005 4.207 0.015 0.804 3.013 0.406 0.875 4.250 -0.218 0.649 3.779 -0.295 0.9006 3.866 0.405 0.644 2.676 0.729 0.850 3.889 0.166 0.095 3.649 -0.020 0.7007 3.522 0.638 0.665 2.494 1.051 0.850 3.835 0.198 0.590 3.480 0.238 0.7008 3.138 1.042 0.471 1.861 1.359 0.900 3.325 0.385 0.194 3.202 0.474 0.7009 2.723 1.397 0.150 1.049 1.743 0.900 3.520 0.595 0.547 2.877 0.801 0.70010 2.544 1.588 0.236 - - - 3.201* 0.854 0.331 2.506 1.048 0.90011 1.684 1.746 0.326 - - - 3.235 0.906 0.509 1.969 1.367 0.90012 0.847 1.954 0.768 - - - 2.953 1.338 0.118 1.470 1.630 0.90013 - - - - - - 2.516 1.512 0.193 0.804 1.952 0.90014 - - - - - - 1.494 1.740 0.241 - - -15 - - - - - - 0.786 1.805 0.700 - - -NGC 5838 NGC 5982 NGC 73321 5.583 -1.637 0.950 4.019 -0.719 0.850 6.192 -1.721 0.2812 4.752 -1.091 0.950 4.192 -0.405 0.850 4.815 -1.054 0.5893 5.075 -0.779 0.530 4.138 -0.080 0.850 4.580 -0.709 0.3514 4.371 -0.205 0.950 3.647 0.319 0.650 4.337 -0.591 0.7005 4.041 0.264 0.780 3.444 0.577 0.708 4.133 -0.263 0.7006 3.556 0.625 0.890 2.837 0.806 0.706 3.798 0.041 0.6027 2.954 0.989 0.466 2.728 1.039 0.650 3.551 0.254 0.7008 2.886 1.087 0.835 2.346 1.345 0.650 3.245 0.479 0.2469 1.091 1.450 0.793 1.396 1.685 0.709 3.125 0.684 0.66510 2.286 1.684 0.350 1.282 1.843 0.850 2.606 1.144 0.51611 0.998 2.018 0.350 - - - 2.395 1.512 0.15212 - - - - - - 1.197 1.516 0.70013 - - - - - - 1.845 1.656 0.23214 - - - - - - 1.026 1.821 0.27415 - - - - - - 0.160 1.906 0.700Note: * indicates where a negative Gaussian was used to achieve a satisfactory fit. This only occurs in the most discy objects.c (cid:13)000