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Mon. Not. R. Astron. Soc. 376, 1033­1046 (2007)

doi:10.1111/j.1365-2966.2007.11549.x

Kinematics and stellar populations of the dwarf elliptical galaxy IC 3653
I. V. Chilingarian,1
1 2

,2,3

P. Prugniel,

2,4

O. K. Sil'chenko1 and V. L. Afanasiev

5

Sternberg Astronomical Institute of the Moscow State University, Universitetsky pr. 13, Moscow 119992, Russia ´ ´ Universite de Lyon, Lyon F-69000, France; Universite Lyon 1, Villeurbanne, F-69622, France; Centre de Recherche Astronomique de Lyon, Observatoire de ´ ´ Lyon, 9 Av. Charles Andre, Saint-Genis Laval, F-69561, France; CNRS, UMR 5574; Ecole Normale Superieure de Lyon, Lyon, France 3 LERMA Observatoire de Paris-Meudon, 61 Av. de l'Observatoire, Paris 75014, France 4 GEPI Observatoire de Paris-Meudon, 5 place Jules Janssen, Meudon 92195, France 5 Special Astrophysical Observatory of the Russian Academy of Sciences, Nizhniy Arkhyz, Karachaevo-Cherkesia 369167, Russia

Accepted 2007 January 24. Received 2007 January 15; in original form 2006 August 3

ABSTRACT

We present the first 3D observations of a diffuse elliptical galaxy (dE). The good quality data (S/N up to 40) reveal the kinematical signature of an embedded stellar disc, reminiscent of what is commonly observed in elliptical galaxies, though similarity of their origins is questionable. Colour map built from Hubble Space Telescope Advanced Camera for Surveys (ACS) images confirms the presence of this disc. Its characteristic scale (about 3 arcsec =250 pc) is about a half of galaxy's effective radius, and its metallicity is 0.1­0.2 dex larger than the underlying population. Fitting the spectra with synthetic single stellar populations (SSP), we found an SSPequivalent age of 5 Gyr and nearly solar metallicity [Fe/H] =-0.06 dex. We checked that these determinations are consistent with those based on Lick indices, but have smaller error bars. The kinematical discovery of a stellar disc in dE gives additional support to an evolutionary link from dwarf irregular galaxies due to stripping of the gas against the intracluster medium. Key words: galaxies: dwarf ­ galaxies: elliptical and lenticular, cD ­ galaxies: evolution ­ galaxies: individual: IC 3653 ­ galaxies: stellar content.

1 INTR ODUCTION Giant elliptical galaxies (E) were believed to be simple objects, rotationally supported and featureless until the kinematical observations of NGC 4697 by Bertola & Capaccioli (1975) made realize that at least some of them were supported by anisotropic velocity dispersions (Binney 1976; Illingworth 1977). In parallel, new imaging and processing techniques revealed the presence of dust lanes (Bertola & Galletta 1978; Sadler & Gerhard 1985) and fine structures (e.g. shells; Malin & Carter 1983) in many Es. Diffuse elliptical galaxies (dE, also called dwarf elliptical or dwarf spheroidal galaxies) followed the same line more recently when high-quality images revealed fine structures, in particular presence of a spectacular and intriguing stellar spiral in IC 3328 (Jerjen, Kalnajs & Binggeli 2000) and IC 783 (Barazza, Binggeli & Jerjen 2002) or broader structures, like embedded discs or bars in a number of dEs (Barazza et al. 2002). Evidence for ubiquity of discs in bright dE galaxies in the Virgo cluster, based on multicolour photometry, has been shown by Lisker, Grebel & Binggeli (2006). A number of recent papers presented also long-slit spectroscopic data (De Rijcke et al. 2001; Geha, Guhathakurta & van der Marel 2002, 2003; Pedraz et al. 2002; Simien & Prugniel 2002; van Zee, Skillman & Haynes 2004a; van Zee, Barton & Skillman 2004b) revealing a diversity

E-mail: chil@sai.msu.su
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of degree of rotational support and even some complex structures (De Rijcke et al. 2004; Thomas et al. 2006). The stellar population may also be inhomogeneous (Michielsen et al. 2003) and an ionized interstellar medium (ISM) has been detected in some objects (Michielsen et al. 2004). The complexity of elliptical galaxies put severe constraints on the scenario of their formation and evolution. Ellipticals are thought to form at high redshifts from collapse and hierarchical mergers and accidentally lately evolve through major mergers. For what concerns dEs, the main classes of physical mechanisms intervening in the formation and evolution are (i) the feedback of the star formation on the ISM and (ii) the environment. The stellar population of most present dEs may not have formed in large galaxies, because the metallicity, [Fe/H] -0.3 (Geha et al. 2003; van Zee et al. 2004b), is typically smaller than that of large bulges or Es. It is thought to have formed in small galaxies where the supernova-driven winds certainly play an important role in controlling star formation rate and metal enrichment. In the smallest galaxies, the major part of gas and produced metals will be spread to the intergalactic medium. However, duration of star formation should be long enough, because recent studies (Geha et al. 2003; van Zee et al. 2004b) demonstrate that dE galaxies exhibit solar [Mg/Fe], while in the case of short star formation episode they would have been iron-deficient. The environment also obviously plays a major role through three phenomena:

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most luminous dE in Virgo and has a relatively high surface brightness. It is located 2 7 from the centre of the cluster, i.e. 0.8 Mpc in . projected distance. Its radial velocity 588 ± 4 km s-1 (this work) confirms its membership to the Virgo cluster, the velocity difference from the mean velocity of Virgo (1054 km s-1 , HyperLeda; Paturel et al. 20031 ) is nearly -470 km s-1 . IC 3653 is located some 100 kpc in the projected distance from NGC 4621, a giant elliptical galaxy having a similar radial velocity value (410 km s-1 , HyperLeda). With other low-luminosity Virgo cluster members, in particular IC 809, IC 3652 for which the radial velocities have been measured, they may belong to a physical substructure of Virgo, crossing the cluster at 500 km s-1 . Velocity and velocity dispersion profiles from Simien & Prugniel (2002) show some rotation. Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) archival images from the Virgo cluster ACS survey (Cote et al. 2004) are also available and will be ^´ discussed here. In Section 2, we describe the observations and the data reduction. In Section 3, we derive the age and the metallicity using spectrophotometric indices, and in Section 4 we introduce and use a new method for measuring the internal kinematics and the population parameters by fitting directly the spectra against high spectral resolution population models. The analysis of the ACS images is presented in Section 5. Section 6 is the discussion. 2 SPECTR OSCOPIC OBSER VA TIONS AND D A T A REDUCTION The spectral data we analyse were obtained with the Multi-Pupil Fiber Spectrograph (MPFS) integral-field spectrograph. The MPFS, operated on the 6-m telescope Bolshoi Teleskop Al'tazimutal'nij (BTA) of the Special Astrophysical Observatory of the Russian Academy of Sciences, is a fibre-lens spectrograph with a microlens raster containing 16 â 16 square spatial elements together with 17 additional fibres transmitting the sky background light, taken 4-arcmin away from the object. The size of each element is 1 â 1 arcsec2 . We used the grating 1200 g mm-1 providing the reciprocal dispersion of 0.75 å pixel-1 with an EEV CCD42-40 detector in the spectral range 4100­5650 å. Observations of IC 3653 were made on 2004 May 24 under good atmosphere conditions (seeing FWHM = 1.4 arcsec). The total integration time was 2 h. The spectral resolution R = / , where is the FWHM (full width at half-maximum) resolution (width of the line-spread function), as determined by analysing twilight spectra, varied from R = 1300 to 2200 (between 2.5 and 3.3 å) over the field of view and wavelength. R is lower in the centre of the field and increases towards top and bottom and also in the red end of the wavelength range (Moiseev 2001). The following calibration frames were taken during the observations of IC 3653 with MPFS. (i) BIAS, DARK. (ii) `Etalon': 17 night-sky fibres illuminated by the incandescent bulb. This frames are used to determine positions of spectra on the frame. (iii) `Neon' (arc lines): by exposing the spectral lamp filled with Ar­Ne­He to perform a wavelength calibration. (iv) The internal flat-field lamp. (v) A spectrophotometric standard (Feige 56 for our observations) used to turn the spectra into absolute flux units.
1

(i) the ram pressure stripping against the intracluster medium (Marcolini, Brighenti & D'Ercole 2003), (ii) the tidal harassment due to distant and repeated encounters with other cluster members (Moore, Lake & Katz 1998) and (iii) the collisions involving large gas-rich objects that may disrupt gas clouds from which a dwarf galaxy may born (tidal dwarfs) and evolve into a dE after fading of the young stellar population (Duc & Mirabel 1999). The latter possibility may probably not be the main scenario because dEs are one order of magnitude more numerous than large galaxies which in average have suffered one major collision in their lifetime, while the merger remnants in the local Universe are only accompanied by a few tidal dwarfs candidates which have generally much smaller mass than bright ellipticals (Weilbacher et al. 2000). The first two mechanisms are undoubtedly the major ingredients. Ram pressure stripping is an accepted explanation for the H I depletion of spiral galaxies in clusters and any type of gas-rich galaxies will experience it. It may well explain the relation between the morphology of dwarfs and the density of the environment (Binggeli, Tarenghi & Sandage 1990; van den Bergh 1994): low-density environment is mostly populated by dIrrs, while dEs reside mostly in clusters where ram pressure stripping is expected to be the most efficient. Recently, Conselice et al. (2003) discovered H I in two dEs in the Virgo cluster, which they interpret as transition objects on their way in the morphological transformation from dIrr to dE. Conselice, Gallagher & Wyse (2001) argue that dEs are recently accreted galaxies which morphologically evolve from late-type galaxies when they cross the centre of the cluster. There is yet no decisive test to disentangle the roles of each mechanism. In this paper, we present 3D spectroscopic observations in order to bring further observational constraints. Velocity fields and spatial distribution of the stellar population are most needed to check if counterparts of the observed kinematical substructures can be detected. We are presenting here the first 3D observations of a dE. IC 3653 is a bright dE galaxy belonging to the Virgo cluster (Binggeli, Sandage & Tammann 1985). In Table 1, we summarize its main characteristics. IC 3653 was chosen because it is amongst the
Table 1. General characteristics of IC 3653. Sersic exponent, ´ kinematical and stellar population parameters are obtained in this paper, other properties are taken from HyperLeda and Goldmine (Gavazzi et al. 2003; http://goldmine.mib.infn.it/) data bases, and from Ferrarese et al. (2006). Uncertainties given for age and metallicity correspond to the measurements on co-added spectra. Name Position B Distance modulus A(B) M(B)corr Spatial scale Effective radius, Re B , mag arcsec-2 Ellipticity, S´ ersic exponent, n Heliocentric cz, km s-1 cent , km s-1 Vmax , km s-1 Vmax / t, Gyr (lum. weighted) [Z/H], dex (lum. weighted) IC 3653, VCC1871 J124115.74+112314.0 14.55 31.15 0.13 -16.78 82 pc arcsec-1 6.7 arcsec 550 pc 20.77 0.12 1.2 588 ± 4 80 ± 3 18 ± 2 0.27 ± 0.08 5.2 ± 0.2 -0.06 ± 0.02

http://leda.univ-lyon1.fr/
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(vi) A standard for Lick indices and radial velocity (HD 137522 and HD 175743), used also to measure instrumental response: asymmetry and width of the line-spread function. (vii) `SunSky': twilight sky spectra for additional corrections of the systematic errors of the dispersion relation and transparency differences over the fibres.
Table 2. Parameters of the `3-points' binning: number of spatial elements, mean AB magnitude, mean AB surface brightness (mag arcsec-2 ) and mean signal-to-noise ratio at 5000 å. Bin P1 P2 P3 N
spax

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m(AB) 16.3 15.2 15.7

(AB) 18.7 19.9 20.9

S/N 69 49 21

2.1 Data reduction We use the original IDL software package created and maintained by one of us (VLA) that we modified for this work: error frames are created using photon statistics and then processed through all the stages to have realistic error estimates for the fluxes in the resulting spectrum. The primary reduction process (up to obtaining flux-calibrated data cube) consists of: (i) Bias subtraction, cosmic ray cleaning. Cosmic ray cleaning implies the presence of several frames. Then they are normalized and combined into the cube (x, y, Num). The cube is then analysed in each pixel through `Num' frames. All counts exceeding some level (5 ) are replaced with the robust mean through the column. Then the individual cleaned frames are summed. This procedure assumes that all the frames have the same atmospheric conditions and cleans only the brighter spikes, though it was found sufficient for our purpose. (ii) Creation of the traces of spectra in the `etalon' image. Accuracy of the traces is usually about 0.02 or 0.03 pixel. (iii) Flat-field reduction and diffuse light subtraction. Flat-field is applied to the CCD frames before extracting the spectra. The scattered light model is also constructed and subtracted from the frames during this step. It is made using parts of the frames not covered by spectra and then interpolated with low-order polynomials. (iv) Creation of the traces for every fibre. On this step the traces are determined for each fibre in the microlens block (presently 256 fibres) using the night-sky fibre traces created on the second step and interpolation between them using the tabulated fibre positions. (v) Spectra extraction. Using the fibre traces determined in the previous steps, spectra are extracted from science and calibration frames using fixed-width Gaussian (usually with FWHM = 5 pixel for the present configuration of the spectrograph). The night-sky spectra are also extracted from the science frames. (vi) Creation of dispersion relations. Spectral lines in the arc lines frame are identified and dispersion relations are computed independently for every fibre. (vii) Wavelength rebinning. All the spectra of night sky, object and standard stars are rebinned independently into logarithm of wavelength (as required for the kinematical analysis). The sampling on the CCD varies between 0.65 and 0.85 å (FWHM resolution 3­5 pixel) and we rebinned to a step of 40 km s-1 , i.e. 0.55­0.75 å, corresponding to the mean oversampling factor of 1.2 (we checked that this oversampling was high enough to have no measurable effect on the result of the analysis). (viii) Sky subtraction. The sky spectrum, computed as the median of the 17 night-sky fibres, is rescaled using flat-field to account for the twice larger aperture of the night fibres compared to object fibres. Then it is subtracted from each fibre. (ix) Determination of the spectral sensitivity and absolute flux calibration. Using the spectrophotometric standard star, the ratio between counts and absolute flux is calculated and then approximated with a high-order polynomial function over the whole wavelength
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range. Finally, the values in the data cube are converted into F [erg cm-2 s-1 å-1 ]. 2.2 Spatial adaptive binning



In our data, the surface brightness, B , changes from 18.5 mag arcsec-2 in the centre down to 21.2 mag arcsec-2 in the outer parts of the field of view. Though the signal-to-noise ratio at the central part is high enough (30) for detailed analysis, the accuracy of kinematics and Lick indices measurements in individual decreases dramatically at the largest radii. To increase the signal-tonoise ratio in the outer parts, without degrading the resolution in the centre, we applied the Voronoi adaptive binning procedure proposed by Cappellari & Copin (2003) for this exact purpose. It uses variable bin size to achieve equal signal-to-noise ratio over the field of view. The Voronoi 2D-binning produces a set of 1D spectra that are then analysed independently. For the kinematical analysis, we will use a target signal-to-noise ratio of 15, and for stellar population analysis we will use 30. Besides we will also use a tessellation of the data set containing only three bins (3-points binning hereafter): central condensation (3 â 3 arcsec2 region around the centre of the galaxy), elongated discy substructure (14 â 7 arcsec2 ) oriented according to kinematics (see Section 4, Fig. 1, illustrating locations of bins and demonstrating spectra integrated in them) with the central region excluded, and the rest of the galaxy. The location of these three bins is shown in Fig. 1, and their characteristics in Table 2. Such a physically stipulated tessellation allows us to gain high signal-to-noise ratios in the bins in order to have high-quality estimations of the stellar population parameters in the regions where they are expected to be homogeneous. 3 SSP A G E AND MET ALLICITY DERIVED FR OM LICK INDICES A classical and effective method of studying stellar population properties exploits diagrams for different pairs of Lick indices (Worthey et al. 1994). A grid of values, corresponding to different ages and metallicities of single stellar population models (instantaneous burst, SSP), is plotted together with the values computed from the observations. A proper choice of the pairs of indices, sensitive to mostly age or metallicity like H and Mgb, allows us to determine SSP-equivalent age and metallicity. We use a grid of models computed with the evolutionary synthesis code: PEGASE.HR (Le Borgne et al. 2004). These models are based on the empirical stellar library ELODIE.3 (Prugniel & Soubiran 2001, 2004) and are therefore bound to the [Mg/Fe] abundance pattern of the solar neighbourhood (see Wheeler, Sneden & Truran 1989). To show that this limitation is not critical for our (low-mass) galaxy, Fig. 2(a) presents the Mgb versus Fe diagram with the models

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(a) (c)

(b)

Figure 1. (a) The radial velocity field with three bins overplotted (3-points binning, see the text); (b) fit of the `P1' bin, representing the spectrum, `PEGASE.HR' marking the template spectrum (shifted by -0.3 on the flux axis from its real position, and `residuals' showing the difference between the fit and observed spectrum; (c) `P1', `P2' and `P3': co-added spectra for the 3-points binning.

by Thomas, Maraston & Bender (2003) for different [Mg/Fe] ratios overplotted. These data allow us to conclude that IC 3653 has solar [Mg/Fe] abundance ratio with a precision of about 0.05 dex. A critical limitation of Lick indices is their sensitivity to missed/wrong values in the data, for example, due to imperfections of the detector, or uncleared cosmic ray hits. A simple interpolation of the missed values is a poor solution, because if some important detail in the spectrum, e.g. absorption line, is affected, the final measurement of the index will be biased. In addition, the definition of the indices (see equations 1­3 in Worthey et al. 1994) does not allow us to flag or to decrease the weight of low-quality values. Due to a defect of the detector, our data have a 3-pixel wide bad region (hot pixels) in the middle of the blue continuum of Mgb. Therefore, strictly speaking, we could not measure Mgb at all, neither H on a significant part of the field of view.
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As a workaround, we replaced all the missing or flagged values in the data cube by the corresponding values of the best-fitting model determined as explained in the next section. Therefore, instead of a mathematical interpolation of missing values, we are using model predictions. We measured Lick indices as defined in Trager et al. (1998), and we also derived the combined iron index Fe = 0.72Fe5270 + 0.28Fe5335 , and `abundance-insensitive' [MgFe] = Mg Fe (Thomas et al. 2003). A good intermediate resolution age tracer, H +Mg+Fe125 (Vazdekis & Arimoto 1999) cannot be used, because the required signal-to-noise ratio of about 100 at around = 4340 å cannot be achieved even after co-adding all the spectra in the data cube due to lower S/N in the blue end of the spectral range. The statistical errors on the measurements of Lick indices were computed according to Cardiel et al. (1998). Table 3 presents the measurements of selected Lick indices for the 3-points binning,
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Table 3. Measurements of selected Lick indices for the 3-points binning. All values are in å. The first line for each index corresponds to the measurements made on the real spectra and the second on the best-fitting optimal templates (see the text). (Note that the Fe indices Fe4531 and Fe5015 are essentially sensitive to titanium; see Sil'chenko & Shapovalova 1989.) Name Ca4227 G4300 Fe4383 Ca4455 Fe4531 Fe4668 H Fe5015 Mgb Fe5270 Fe5335 Fe5406 Fe [MgFe] Bin 1 1.062 1.096 5.106 4.995 5.794 4.861 1.187 1.336 2.858 3.499 6.070 5.114 1.841 1.908 5.121 5.491 3.575 3.361 3.016 3.059 2.708 2.675 1.687 1.840 2.930 2.952 3.236 3.150 ± 0.080 ± 0.135 ± 0.176 ± 0.089 ± 0.125 ± 0.181 ± 0.067 ± 0.138 ± 0.065 ± 0.072 ± 0.084 ± 0.065 ± 0.075 ± 0.070 Bin 2 0.874 1.020 5.042 4.820 4.940 4.458 1.096 1.235 2.326 3.367 5.776 4.602 1.823 1.966 4.767 5.211 3.550 3.203 2.969 2.886 2.551 2.524 1.667 1.720 2.852 2.785 3.182 2.987 ± 0.190 ± 0.313 ± 0.389 ± 0.186 ± 0.260 ± 0.361 ± 0.122 ± 0.246 ± 0.116 ± 0.132 ± 0.155 ± 0.121 ± 0.138 ± 0.127 Bin 3 0.689 1.092 6.923 4.979 6.251 4.696 0.750 1.313 1.595 3.457 5.685 4.808 1.800 1.878 4.912 5.292 3.771 3.334 3.362 2.963 2.526 2.598 1.542 1.779 3.128 2.861 3.435 3.089 ± 0.700 ± 1.040 ± 1.243 ± 0.561 ± 0.777 ± 1.025 ± 0.304 ± 0.584 ± 0.278 ± 0.309 ± 0.367 ± 0.286 ± 0.325 ± 0.301

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Table 4. Comparison of age and metallicity measurements for the 3-points binning obtained with pixel fitting and based on different pairs of Lick indices grids: measured on real spectra and on best-fitting templates. `P1' tfit , Gyr tH ­Mgb tH - Fe tH ­[MgFe] t t t
H ­Mgbmod H - Fe mod H ­[MgFe]mod

`P2' 4.95 6.97 7.28 6.88 ± ± ± ± 0.30 1.47 2.20 1.89

`P3' 4.97 ± 0.70 11.25 ± 6.02 6.08 ± 3.94 6.70 ± 5.11 4.85 ± 6.02 4.23 ± 3.94 4.15 ± 5.11 -0.17 ± 0.05 -0.34 ± 0.24 0.03 ± 0.13 -0.11 ± 0.15 -0.16 ± 0.24 -0.17 ± 0.13 -0.16 ± 0.15

4.93 7.04 7.02 7.11

± ± ± ±

0.20 1.56 1.33 1.65

5.27 ± 1.56 5.15 ± 1.33 5.22 ± 1.65 0.03 ± 0.01 -0.05 ± 0.09 -0.02 ± 0.04 -0.04 ± 0.05 -0.02 ± 0.09 0.02 ± 0.04 0.00 ± 0.05

5.13 ± 1.47 4.30 ± 2.20 4.12 ± 1.89 -0.14 -0.18 -0.10 -0.14 ± ± ± ± 0.02 0.08 0.05 0.06

Zfit , dex Z H ­Mgb Z H - Fe Z H ­[MgFe] Z H ­Mgbmod Z H - Fe mod Z H ­[MgFe]mod

-0.14 ± 0.08 -0.14 ± 0.05 -0.13 ± 0.06

The median value for age using [MgFe]­H pair is 6 ± 2.5 Gyr, without significant spatial variation. [MgFe] and Fe indices are not very age sensitive, thus the age estimations depend mostly on values of H , and are almost equal for all three pairs of indices.

4 STELLAR POPULA TIONS AND INTERN AL KINEMA TICS USING PIXEL FITTING Various methods have been developed to determine the star formation and metal enrichment history (SFH) directly from observed spectra (Ocvirk et al. 2006a,b; De Rijcke et al. 2004; Moultaka et al. 2004). The procedure that we are proposing here, population pixel fitting, is derived from the penalized pixel-fitting method developed by Cappellari & Emsellem (2004) to determine the line-of-sight velocity distribution (LOSVD). The observed spectrum is fitted in pixel space against the population model convolved with a parametric LOSVD. The population model consists of one or several starbursts, each of them parametrized by some of their characteristics, typically age and metallicity for a single burst while the other characteristics, like initial mass function, remain fixed. A single minimization returns the parameters of LOSVD and those of the stellar population. Ideally, we would like to reconstruct SFH, over all the life of the galaxy. This means, disentangle internal kinematics and distribution in the Hertzsprung­Russell diagram from the integratedlight spectrum. This problem has been discussed in several places (e.g. Ocvirk et al. 2006a,b; De Rijcke et al. 2004), it is clearly extremely degenerated and solutions can be found only if a simplified model is fitted. In this paper, we discuss only the simplest case of SSP characterized by two parameters: age and metallicity. We do not discuss complex SFH, because signal-to-noise ratio of our data is not sufficient. The 2 value (without penalization) is computed as follows: 2 =
N

and Fig. 2(c) presents the main index­index pairs that are used to determine age and metallicity. We see almost no population difference among three bins within the precision we reach. The age (see Table 4) is around 6 Gyr, metallicity is about solar for `P1' and slightly subsolar for `P2' and `P3'. The large scatter of the measurements, seen in Fig. 2, results in a spread of age estimations from 4 to 13 Gyr. It is mainly caused by an imperfect cleaning of the spikes and dark pixels but also weak nebular emission may alter these indices: H index might be affected by emission in H , Mgb ­ by [N I] ( = 5199 å) laying in the red continuum region. Though we do not see any significant emission line residuals when we subtract the best-fitting model, we cannot exclude completely this effect. To reduce the scatter, we measured Lick indices on the optimal templates fitted to the data. This approach may produce biased results in case of model mismatch, due for example to inconsistent abundance ratios between the models and the real stellar population. However, we believe it is not the case, since IC 3653 exhibits solar Mg/Fe abundance ratio (see Fig. 2a). We made inversions of the bi-index grids for three combinations of indices: Mgb­H , [MgFe]­H and Fe ­H . The maps shown in Fig. 3 represent interpolated values of the parameters between intensity-weighted centres of the bins. The metallicity distribution shows slight gradient from -0.15 dex at the periphery to +0.10 in the very centre (the average error bar on the metallicity measurements using [MgFe]­H is 0.15 dex).
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{ Fi - P1 p [Ti (t , Z ) L(v, , h 3 , h 4 ) + P2q ]}2 , Fi2

(1)

where L is LOSVD; Fi and Fi are observed flux and its uncertainty; Ti is the flux from a SSP spectrum, convolved by the

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(a) (b)

(c)

(d)

Figure 2. The Mgb­ Fe (a), H ­[MgFe] (b), H ­Mgb (c) and H ­ Fe (d) diagrams. On (a) the models from Thomas et al. (2003) are plotted. On (b), (c) and (d) the displayed grid is constructed of the values of the Lick indices for PEGASE.HR synthetic spectra (SSP) for different ages and metallicities. Bold crosses with pointers represent measurements for three regions of the galaxy (see the text), thin crosses are for individual bins for Voronoi tessellation with target S/N = 30.

line-spread function of the spectrograph (LSF; see the next section); P1p and P2q are multiplicative and additive Legendre polynomial of the order of p and q for correcting a continuum; t is the age, Z is the metallicity, v , , h3 and h4 are radial velocity, velocity dispersion and Gauss­Hermite coefficients, respectively (van der Marel & Franx 1993). Normally we used no additive polynomial continuum, and fifth-order multiplicative one, and for IC 3653, which has a low velocity dispersion resulting in insufficient sampling of the LOSVD, we did not fit h3 and h4 . The problem can be partially linearized: in particular, fitting of additive polynomial continuum, and relative contributions of subpopulations Ti is done linearly on each evaluation of the non-linear functional. Thus we end up with 10 free parameters: t, Z, six coefficients for Pmult5 , v and .
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The main technical part of our method is a non-linear minimization procedure for 2 difference between the observed and modelled spectra. The latter is made by interpolating a grid of SSP spectra computed with PEGASE.HR and degraded to match the LSF of the observed spectrum. This grid has 25 steps in age (10 Myr to 20 Gyr) and 10 steps in metallicity ([Fe/H] from -2.5 to 1.0). Because the minimization procedure requires that the derivatives of the functions are continuous, we used a two-dimensional spline interpolation. The non-linear minimization is made with the MPFIT package (by Craig B. Markwardt, NASA2 ) implementing constrained variant of Levenberg­Marquardt minimization.

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http://cow.physics.wisc.edu/craigm/idl/fitting.html ~
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Figure 3. Maps for age and metallicity obtained by inverting bi-index grids for indices measured on optimal template spectra: (a) Mgb­H , (b) [MgFe]­H , (c) Fe ­H ; and on real data: (d) Fe ­H .

4.1 Line-spread function of the spectrograph Before comparing a synthetic spectrum to an observation, it is required to transform it as if it was observed with the same spectrograph and setup, i.e. to degrade its resolution to the actual resolution of the observations. Actually the spectral resolution changes both with the position in the field of view and with the wavelength (thus it is not a mere operation of convolving with the LSF). Taking into account these effects is particularly critical when, as it is the case here, the physical velocity dispersion is of the same order or smaller than the instrumental velocity dispersion. The procedure for properly taking into account the LSF goes in two steps. First, determine the LSF as a function of the position in the field and of the wavelength. Secondly, inject this LSF in the grid of SSP. Therefore we made an exhaustive analysis of the LSF of our observations. A previous study of the change of the resolution of the MPFS over the field of view (Moiseev 2001) qualitatively agrees with our results. To measure the LSF change over the field of view we used the spectra of standard stars (HD 135722 and HD 175743) and twilight sky that we analysed with our fitting procedure. The highresolution spectra ( = 0.55 å; R 10 000) for the corresponding stars (the Sun for the twilight spectra) taken from the ELODIE.3 library (Prugniel & Soubiran 2001, 2004) were used as templates. Since these spectra have exactly the same resolution as the PEGASE.HR SSPs, the `relative' LSF that we determined in this way can be directly injected to the grid of SSP to make it consistent with the MPFS observations. We parametrize the LSF using v , , h3 and h4. The whole wavelength range (4100­5650 å) was split into five parts, overlapping by 10 per cent, and the LSF parameters w