Formation and evolution of dwarf early-type galaxies in the Virgo cluster I. Internal kinematics
E. Toloba, A. Boselli, A. J. Cenarro, R. F. Peletier, J. Gorgas, A. Gil de Paz, J. C. Munoz-Mateos
aa r X i v : . [ a s t r o - ph . C O ] D ec Astronomy&Astrophysicsmanuscript no. toloba˙v2 c (cid:13)
ESO 2018October 23, 2018
Formation and evolution of dwarf early-type galaxies in the Virgocluster
I. Internal kinematics
E. Toloba , A. Boselli , A. J. Cenarro , R. F. Peletier , J. Gorgas , A. Gil de Paz , and J. C. Mu˜noz-Mateos Departamento de Astrof´ısica y CC. de la Atm´osfera, Universidad Complutense de Madrid, 28040, Madrid, Spaine-mail: [email protected] e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] Laboratoire d’Astrophysique de Marseille, UMR 6110 CNRS, 38 rue F. Joliot-Curie, F-13388 Marseille, Francee-mail: [email protected] Centro de Estudios de F´ısica del Cosmos de Arag´on, E-44001, Teruel, Spaine-mail: [email protected] Kapteyn Astronomical Institute, Rijksuniversiteit Groningen, Postbus 800, 9700 AV Groningen, the Netherlandse-mail: [email protected] National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475Received ; accepted
ABSTRACT
We present new medium resolution kinematic data for a sample of 21 dwarf early-type galaxies (dEs) mainly in the Virgo cluster,obtained with the WHT and INT telescopes at the Roque de los Muchachos Observatory (La Palma, Spain). These data are usedto study the origin of the dwarf elliptical galaxy population inhabiting clusters. We confirm that dEs are not dark matter dominatedgalaxies, at least up to the half-light radius. We also find that the observed galaxies in the outer parts of the cluster are mostlyrotationally supported systems with disky morphological shapes. Rotationally supported dEs have rotation curves similar to those ofstar forming galaxies of similar luminosity and follow the Tully-Fisher relation. This is expected if dE galaxies are the descendant oflow luminosity star forming systems which recently entered the cluster environment and lost their gas due to a ram pressure strippingevent, quenching their star formation activity and transforming into quiescent systems, but conserving their angular momentum.
Key words.
Galaxies: clusters: individual: Virgo Galaxies: dwarf Galaxies: elliptical and lenticular, cD Galaxies: kinematics anddynamics Galaxies: evolution Galaxies: dark matter
1. Introduction
The processes involved in galaxy formation and evolutionthrough cosmic time are still poorly understood. It is indeed stillunclear how matter assembled to form the present day galaxypopulation, whether it followed a passive evolution after thecollapse of the primordial density fluctuations (secular evolu-tion), through a subsequent merging of growing structures (hi-erarchical formation) or a combination of the two. A way ofquantifying the relative role of these di ff erent mechanisms isto study dwarf galaxies, the most numerous objects in the uni-verse (Ferguson & Binggeli 1994). Their importance resides inthe fact that these low-luminosity systems are expected to be thebuilding blocks of massive galaxies in lambda cold dark mat-ter ( Λ CDM) hierarchical merging scenarios (e.g., White & Rees1978; White & Frenk 1991).Among dwarf galaxies, quiescent dwarfs (which we heredefine to be all quiescent galaxies with M B > −
18, includingboth dwarf ellipticals and spheroidals, hereafter indicated asdEs) are of particular interest since they are the most numer-ous population in clusters (Ferguson & Binggeli 1994). Theseobjects were originally thought to be the low luminosity ex-tension of giant ellipticals (Es). Since the 1990s it is knownthat dEs are composed of several families of objects (e.g. com- pact and low surface brightness dwarfs) (Bender et al. (1992);Kormendy et al. (2009). Later on, it was shown that dEs wereno longer small Es with simple, old and metal-poor stellar pop-ulations, but much more complex objects exhibiting a widerange of stellar contents. For example, in the Virgo cluster, theyhave stellar populations ranging from very young (around 1 Gyrold) luminosity-weighted ages to as old as the oldest Es galax-ies (14 Gyr) (Michielsen et al. 2008). Their proximity alloweddetailed studies of their structural properties which indicatedthat, behind their elliptical appearance, dEs show a great varietyof underlying structures, like discs, spiral arms, irregular fea-tures, etc, making them a very heterogeneous class of galaxies(Lisker et al. 2006a,b, 2007).These evidences indicate a complex formation process shap-ing the evolution of dEs in clusters. Two main di ff erent pro-cesses have been proposed in the literature: the first mecha-nism is based on the idea that dEs are formed through in-ternal processes, like supernova feedback, where the interstel-lar medium (ISM) of the progenitor star forming galaxy isswept away by the kinetic pressure generated by supernovae(Yoshii & Arimoto 1987), although it seems highly unlikely indark-matter dominated systems (Silich & Tenorio-Tagle 2001);the second mechanism rests upon external processes induced bythe interaction with the hostile environment in which dEs reside E. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster (Sandage et al. 1985; Blanton et al. 2005). In a dense environ-ment several mechanisms are a ff ecting galaxies. This might hap-pen through interactions with the intergalactic medium (IGM),as ram-pressure stripping (Boselli et al. 2008a,b), galaxy-galaxyinteractions (e.g., Byrd & Valtonen 1990) and galaxy harass-ment (e.g., Moore et al. 1998; Mastropietro et al. 2005). It hasbeen shown that all these interactions are able to reproducesome of the observational properties of local dEs in clusters,like their structural parameters (Lisker et al. 2006b, 2007) ortheir stellar populations (Geha et al. 2002, 2003; van Zee et al.2004b; Michielsen et al. 2008; Paudel et al. 2010), but none ofthem have been tested versus the kinematic properties. In thisregard, whereas in the harassment scenario the system is rapidlyheated, leading to an increase of the velocity dispersion of thegalaxy and a decrease of its rotation (Mastropietro et al. 2005),in a ram-pressure stripping event the angular momentum is con-served (Boselli et al. 2008a,b).With the aim of using kinematic data to constrain dwarfgalaxy evolution, we recently started an ambitious observationalprogram at the Observatory El Roque de los Muchachos (LaPalma, Spain) to gather medium resolution spectroscopic data ofdEs in the Virgo cluster. In this paper we present a detailed analy-sis of the internal kinematics focusing our attention into the mostrapidly rotating systems. In Toloba et al. (2009) we have stud-ied the kinematics as a function of local environment inside theVirgo cluster. Several typical scaling relations of pressure sup-ported systems, such as the Fundamental Plane as well as theirstellar population properties will be analysed in a forthcomingcommunication.This paper is structured as follows: in Sections 2, 3 and 4we describe the sample selection, the observations and the datareduction process. In Section 5 we report the kinematic measure-ments paying special attention to the method employed and thestellar templates used. We also describe the procedure followedto obtain the radial kinematic profiles (Section 5.1), the centralvelocity dispersion and the maximum rotational speed of the se-lected galaxies (Section 5.2), making comparisons with previousworks (Section 5.3). Combined with photometric data (Section6), the present kinematic observations are used to study the prop-erties of rotationally supported systems in the framework of var-ious models of galaxy evolution (Sections 7, 8 and 9).
2. The sample
The sample analysed in this work is composed of galaxies with M r > −
16 classified as dE or dS0 in the Virgo Cluster Catalog(VCC) by Binggeli et al. (1985). All galaxies have been selectedto have SDSS imaging and to be within the GALEX MIS fields(Boselli et al. 2005), thus to have a measured UV magnitude oran upper limit. To these we added a few field quiescent dwarfs(originally used as fillers in our observing runs) useful for com-parison in a statistical study. Out of the 43 Virgo galaxies satis-fying these requirements in the VCC, 18 have been observed forthis work. To make the observations accessible to 2.5-4.2m tele-scopes, we chose those objects with the highest surface bright-ness.The field sample consists of early-type dwarfs in low den-sity regions with magnitudes between − < M r < − − < v < − , 5-25Mpc). Quiescent objects have been selected assuming the colourcriterion FUV-NUV > u − g >
3. Observations
The observing time that we obtained for this work was part ofthe International Time Program (ITP 2005-2007) at El Roquede los Muchachos Observatory. Here we focus on the mediumresolution ( R ≃ in our case) to split the light into twobeams to observe simultaneously two wavelength ranges, one inthe blue optical part of the spectra and another in the red. Thistechnique allowed us to cover, in 3 settings in the first run, thefull wavelength range from 3500 Å to 8950 Å, using a mirrorto cover 5000-5600 Å, the only range that we could not coverwith this dichroic. In the third run we used 2 settings to coverthe same wavelength range except for the dichroic gap.The wavelength range covered by the IDS was smaller(4600-5960 Å), since detector and grating are the same as on theblue arm of ISIS, the data obtained had similar resolution. Thespectral resolution ( R ≃ / or a bar) or other struc-tures (such as irregular central features (VCC21)); dE(bc) refersto galaxies with a blue center; dE to galaxies with no evident un-derlying structure. Four out of our 21 dwarf galaxies were not inthe Lisker et al. sample (NGC3073, PGC1007217, PGC1154903and VCC1947), therefore we classified them as described inSection 6 attending only to their boxyness / diskyness. Column 6gives the Virgo substructure to which the galaxy belongs, takenfrom GOLDMine Database (Gavazzi et al. 2003) and defined asin Gavazzi et al. (1999). Columns 7 and 8 refer to the observa-tional campaign (see Table 1) and the exposure time for eachsetting, which allowed us to get a typical signal-to-noise ratio for the central spectra of ∼
60 Å − , enough to obtain reliable cen-tral kinematics. The galaxies were observed along their majoraxis. Their position angles (PA) from the HyperLEDA Database(Paturel et al. 2003) are given in column 9. Column 10 gives theGalactic colour excess from Schlegel et al. (1998).A total of 37 B to M stars in common with the MILESlibrary (S´anchez-Bl´azquez et al. 2006) and the CaT library(Cenarro et al. 2001) were observed to flux-calibrate our dataand to use them as templates for velocity dispersion measure-ments. The S / N per Å − is obtained dividing the S / N per pixel by thesquare root of the spatial scale along the slit. These measurement istherefore independent of the instrument used.. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 3
Table 1.
Observational configurations
Run 1 Run 2 Run 3Date Dec.24-27 2005 Jan.21-23 2007 Feb.10-12 2007Telescope WHT 4.2m INT 2.5m WHT 4.2Spectrograph ISIS IDS ISISDetector EEV12(blue) Marconi(red) EEV10 EEV12(blue) RedPlus(red)Grating R1200B(blue) R600R (red) R1200B R1200B(blue) R600R(red)Wavelength range 1 (Å) 3500-4300 5500-6700 3700-4790 3500-4300 5500-6700Wavelength range 2 (Å) 4100-4900 7750-8950 4600-5690 4100-4900 7750-8950Wavelength range 3 (Å) 4800-5600 — — — —Dispersion (Å / pixel) 0.44 0.87 0.48 0.44 0.97Spectral Resolution (FWHM, Å) 1.56 3.22 1.80 1.56 3.23Instrumental Resolution (km s − ) 40 58 46 40 58Spatial scale (” / pix) 0.40 0.44 0.40 0.40 0.44Slit width (”) 1.95 1.95 1.94 1.91 1.91 Table 2.
The observed galaxies.
Galaxy Other name RA(J2000) Dec.(J2000) Type Env. Run t exp
PA E(B-V)(h:m:s) ( ◦ :’:”) (sec) ( ◦ ) (mag)M 32 NGC 221 00:42:41.84 + + + + + + + + + + + + + + + + + + + + + +
4. Data reduction
The data reduction was performed with REDucmE (Cardiel 1999),a package specially designed to reduce long-slit spectroscopywith particular attention to the treatment of errors. This packageis ideal for treating in parallel the data and error frames, pro-ducing an error spectrum associated with each individual dataspectrum, which means that the errors are controlled at all times.Due to the similar instrumental configurations used on all ob-serving runs, the reduction process for both telescopes was thesame. The standard procedure for long-slit spectroscopy data re-duction consists of bias and dark current subtraction, flat-fielding(using observations of tungsten lamps and twilight sky to cor-rect for high and low frequency variations respectively), cos-mic ray cleaning, C-distortion correction, wavelength calibra-tion, S-distortion correction, sky subtraction, atmospheric andinterstellar extinction correction and flux calibration. We givebelow some comments on steps of particular importance:
Flat-fielding.
The flat-fielding correction is a delicate stepat near infrared wavelengths due to the fringing e ff ects. In thefirst run, the Marconi CCD su ff ered from significant fringingthat varied with the telescope position. Since complete removalof the fringing in run 1 was not possible, we did not use thered Marconi-CCD data to determine the galaxy kinematics. Thefringing produced by RedPlus, the new CCD optimised to avoidthese patterns, was much lower, with an amplitude of only ∼ Wavelength calibration.
The wavelength calibration was per-formed using between 65-100 arc lines depending on the instru-mental configuration. They were fitted with a 5 th order polyno-mial that led to a typical RMS dispersion of 0.1-0.25 Å. S-distortion, alignment of the spectra.
During the spectro-scopic observations, the galaxies were not perfectly aligned withthe rows of the detector. This e ff ect is crucial when measuringgradients of any type (rotation curves, velocity dispersion pro-files or line-strength indices). The correction of this e ff ect was E. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster performed using a routine that found the position of the galaxycenter as a function of wavelength, fitted all these positions witha low order polynomial and straightened the spectra using thatpolynomial. This alignment was done with a technique that min-imised the errors due to the discretization of the signal. Thistechnique consists of adopting a more realistic distribution ofthe light in each pixel than just assuming it to be constant. Toachieve this the signal in each pixel is fitted with a second or-der polynomial using the available information in the adjacentpixels.
Sky subtraction.
The sky subtraction is critical for studieswhere the spectra are analysed at light levels corresponding toonly a few per cent of the sky signal, as in our case. For eachgalaxy observation a sky image was generated fitting the dataat each wavelength with a first order polynomial in regions atboth sides of the galaxy close to the ends of the slit (which hasa length of 3.7 arcmin on the WHT and 3.3 arcmin on the INT).This was possible since for all targets except M32 the galaxyfilled only a small region of the slit, so this synthetic sky im-age was free from contamination from the galaxy. For M32, weobserved a separate sky frame moving the telescope from thecoordinates of the galaxy to a position ∆ α = -416” (West), ∆ δ = -459” (South) far enough from M32 to avoid its light but with thesame level of contamination from M31. Extinction correction. / Astronomy / observing / manuals / ps / tech notes / tn031.pdf). The Galactic extinction was corrected usingthe curve of Fitzpatrick (1999) and the reddening fromSchlegel et al. (1998) listed in Table 2. Flux calibration.
The relative flux calibration of the spec-tra was performed using the observed stars in common with theMILES library (S´anchez-Bl´azquez et al. 2006) for the opticalspectra, and with the CaT library (Cenarro et al. 2001) for thenear infrared. For each observed star we obtained a flux calibra-tion curve. All of them were averaged to obtain one unique fluxcurve for each run and instrumental configuration. The devia-tions of each flux calibration curve from the averaged one wereintroduced as uncertainties in the error spectra. The typical de-viation was of 2% reaching ∼
7% in the first and last ∼
150 Å ofeach setup spectra where the noise is the highest.
5. Measurement of the kinematic parameters
The stellar kinematics of galaxies (radial velocities and velocitydispersions) were calculated using the routine MOVEL includedin REDucmE package (Cardiel 1999). This routine is based on theFourier quotient method described by Sargent & Turner (1977)and refined with the OPTEMA algorithm (Gonz´alez 1993) thatallows us to overcome the typical template mismatch problem.In order to do this, a number of stars of di ff erent spectral typesand luminosity classes were introduced in the program to cre-ate a model galaxy. These stars were of spectral type B9, A0,A3V, G0, G2III, G5III, G8III, G9III, K0III, K0I, K2III, K3III,M0III and M2III. The model galaxy was created and processedin parallel to the galaxy spectrum. To build the model galaxy allthe template spectra were scaled, shifted and broadened accord-ing to a first guess of γ (mean line-strength), v (radial velocity)and σ (velocity dispersion). Then the algorithm looked for thelinear combination of these template stars that best matched theobserved galaxy spectrum. The best linear combination of ob-served stars was chosen as the one that minimises the residuals between the galaxy spectrum and the broadened optimal tem-plate. This provided a first model galaxy with a first kinematicoutput ( γ , v and σ ). This model galaxy was then improved us-ing this new guess of kinematic parameters. The process wasiterated until it converged. The emission lines, found only forthe field dwarf galaxies, and some large sky line residuals, onlypresent in some cases, were masked, so that the program did notuse them for the minimisation of the residuals.To minimize template mismatch e ff ects, it is essential to useas templates a variety of spectral types and luminosity classeswhich are representative of the stellar population of the observedgalaxy; as we will discuss in Section 5.3.1, small di ff erences inages and metallicities could lead to a partial fit of the strongestlines and therefore a ff ect the derived velocity dispersion of thegalaxy.It is also important to check whether the observed stars werefilling the slit during the observation. If they were not, the instru-mental profile would not a ff ect them in the same way as in thegalaxies, and as a consequence, the σ that one would measurefor the galaxy would be q σ inst + σ gal , where σ gal is the intrin-sic velocity dispersion of the galaxy and σ inst , in this case, is thequadratic instrumental di ff erence between the galaxies and thestars.To correct for this e ff ect the physical slit width is required.We calculated it from the spatial scale and the FWHM (in pixels)of the arc lines, which illuminate homogeneously the slit. To seewhether the stars were filling the slit completely we checked thatthe FWHM of their spatial profile was larger than the physicalslit width. If this was not the case, the spatial profile of the starwas broadened accordingly. Although this introduced some un-certainties, the data quality improved by making this correction.The value of σ measured and adopted in this work is thus theintrinsic velocity dispersion of the galaxy corrected for possibleinstrumental e ff ects.Figure 1 shows a typical fit of the observed central spectralof a galaxy and the corresponding optimal template broadenedwith a gaussian with the derived dynamical parameters. The er-rors in velocity and σ were computed through Monte-Carlo sim-ulations, repeating the whole process (including the derivation ofthe optimal template) for 100 simulated galaxy spectra createdusing the error spectra obtained during the reduction process.The observed and simulated spectra perfectly match. To measure kinematic gradients it is important to determine theminimum S / N needed to measure reliable radial velocities andvelocity dispersions. To do that we have designed and carried outa test exercise based on Monte-Carlo simulations that constraintsthe errors and systematic e ff ects in the measurement of radialvelocities and velocity dispersions on fake galaxy spectra withknown input kinematic parameters and di ff erent ages, metallici-ties and S / N ratios. This can be outlined in the following steps:i) from the simple stellar population models from PEGASE.HR(FWHM ∼ Z = Z = − Z = − ∼ During the observation an indicative width of the slit is selected bythe user through a web interface.. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 5
Fig. 1.
Example of the fit computed by MOVEL. Upper panel: inblack, the central spectrum of VCC523. The spectrum has beencontinuum subtracted and normalised. The optimal template thatfits the galaxy is shown in red, a linear combination with di ff er-ent weights of the stars observed with the same configurationas the galaxy. Bottom panel: residuals of the galaxy-compositetemplate fit.resolution, each model was broadened and redshifted to matcha set of input velocity dispersions, σ i , (9 values between 20 kms − and 60 km s − in steps of 5 km s − ) and radial velocities, v i , (800 km s − and 1500 km s − , typical values of Virgo clustermembers). This amounts a total of 162 model spectra. iii) Foreach one of the above spectra we added di ff erent levels of ran-dom noise to match S / N ratios of 10, 15, 20, 25, 30 and 50, henceending up with 972 model galaxy spectra. iv) For each simulatedgalaxy spectrum we run exactly the same MOVEL procedureas we did for our dE galaxy sample, using the same templatestars and MOVEL parameters. 100 Monte-Carlo simulations foreach model galaxy were carried out to get reliable errors of thederived kinematic parameters, σ o and v o obtained as the meanvalue of the 100 Monte-Carlo simulations in each case. Sincethe input kinematics σ i and v i are set by construction, compar-isons and reliability analysis are immediate to perform.The above procedure was carried out for each instrumentalconfiguration in each of the 5 di ff erent spectral regions. The re-sults obtained are shown in Figures 2, 3 and 4.After correcting for any systematic o ff sets in radial veloc-ity and velocity dispersion due to small intrinsic di ff erences be-tween PEGASE.HR models and our observed stars, we haveanalysed the simulations looking at the relative di ff erences be-tween the measured values and the parameters introduced in thesimulated galaxies ( ∆ v / v = ( v o − v i ) / v i and ∆ σ/σ = σ o − σ i ) /σ i ).Figures 2, 3 and 4 show these di ff erences as a function of S / Nin the wavelength range 4100-4900 Å, a range in common be-tween the WHT and INT observations and where lines as impor-tant as the G-band are located. The error bars in these 3 Figuresshow the relative uncertainties obtained by MOVEL as the RMSscatter resulting from the 100 Monte-Carlo simulations for eachmodel galaxy.In Figure 2 we study the influence of the S / N ratio and theinstrumental resolution on the measurement of the velocity dis-persion of a galaxy. Each point represents a galaxy of similarstellar populations (age 4 Gyr and metallicity − ff er-ent velocity dispersion (from 20 to 60 km s − ). As expected, theerrors increase dramatically at the lowest S / N ratios. For low
Fig. 2.
Simulations to study the minimum S / N ratio to obtainreliable measurements of the velocity dispersion. It is plotted ∆ σ/σ (defined as ( σ o − σ i ) /σ i ), the relative error introducedwhen measuring the σ of a galaxy as a function of S / N ratio.Di ff erent colours show di ff erent σ for the simulated galaxies.Done assuming a stellar population of 4 Gyr and Z = − / N ratios (S / N =
10) o ff sets are found even for galaxies withhigh σ ’s, so the velocity dispersions derived at this S / N cannotbe trusted. On the contrary, for S / N ratios higher than or equalto 15 we do not find statistically significant o ff sets, with the ex-ception of measurements below half the instrumental resolution( σ =
20 km s − ) where special care must be taken. Only for S / Nlarger than 20 the measured σ can be fully trusted for velocitydispersions as low as half the instrumental resolution.Figure 3 presents the influence of the stellar populations onthe measurement of the velocity dispersion of a galaxy. In theupper panel we show the e ff ect of the age on a dwarf galaxy of σ =
40 km s − and Z = − ff ect of the metallicity for a galaxy with σ =
40 km s − and4 Gyr old. In this case, although the errors barely depend onmetallicity, the age-dependence is crucial, and for populationsas young as 1 Gyr the σ measurements are underestimated for aS / N ratio below 15.In Figure 4 we analyse the e ff ect of the stellar populationson the computation of the radial velocity. Neither a change inthe velocity dispersion nor in the metallicity have appreciablee ff ects on this variable. Only the age of the stellar populationhave appreciable influence on the determination of the radial ve-locity whenever the age is young, around 1 Gyr. The uncertaintyinduced by age variations, however, is small, ≤ / N ∼ / N ratio in orderto have a statistical estimate of the uncertainty. The average of allthe simulations (corresponding to di ff erent velocity dispersions,ages and metallicities) for each S / N, takes into account that for atarget galaxy we do not have a priori information about either itsvelocity dispersion or the parameters of the stellar population.Figures 2-5 clearly show that data with S / N ratios below 15might induce errors as large as 22% in the determination of σ , inparticular for small velocity dispersions ( σ ∼
20 km s − ), whileonly 0.4% for radial velocities.All these tests have been computed for the di ff erent wave-length ranges covered by our survey and the results obtained are E. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster
Fig. 3.
Simulations to study the dependence of the stellar popula-tion of the galaxy on the measurement of its velocity dispersion.We plot the relative o ff sets found between the measured σ andthe velocity dispersion introduced in the simulated galaxy as afunction of the S / N ratio. In both panels a typical σ of 40 kms − has been considered. In the upper panel we fix the metallic-ity of the galaxy to − σ . Fig. 4.
Simulations to study the influence of the stellar popula-tions and the S / N ratio on the measurement of the radial veloci-ties. We plot the relative uncertainty when measuring the radialvelocities ( ∆ v / v , defined as ( v o − v i ) / v i ) as a function of the S / Nratio. Only the results for the radial velocity v = − are shown because the o ff sets and errors found are independentof the radial velocity of the galaxy. The results plotted are for atypical dwarf galaxy with velocity dispersion of 40 km s − andmetallicity -0.4. The velocity dispersion does not have any ef-fect on the measurement of radial velocities nor the metallicities.Note the di ff erent scale in the y-axis compared to Figures 2 and3. Fig. 5.
Total scatter in the di ff erences found for the 972 simula-tions computed as a function of the S / N ratio. In this Figure allmodels for all stellar populations and velocity dispersion param-eters have been used.rather similar. For the red arm of ISIS, where the instrumentalresolution is larger, we obtain similar results as those shown inthe blue arm (Figures 2-5) but with slightly larger uncertainties.These simulations show that radial velocities can be com-puted with spectra of S / N as low as 10 given that the uncertaintyis always below 1%. However, in the study of velocity disper-sions, we must discard any measurement with S / N below 15 be-cause σ is, in this case, highly dependent on age and not reliablefor σ as low as half the instrumental resolution.When running the MOVEL algorithm as a function of galaxyradius, we fitted the optimal template at every radius, rather thanusing the central optimal template, in order to improve the fit.As a result, the optimal templates turn out to be radial depen-dent. The di ff erences, however, are not very large, because inthe linear combination of templates, G-stars always contributewith the highest weight.Due to the di ff erent instrumental configurations used in theobservation campaigns (see Table 1), more than one kinematicprofile per galaxy was obtained. These profiles, consistent withinthe errors, were averaged to produce a single, high S / N profileper galaxy (see Figure 6).The recessional velocity of each single galaxy, removed forthe determination of the rotation curve (Figure 6), has been de-termined by averaging, with a weighted mean, the recessionalvelocity measured in each single position along the radius. Thisimproved technique for measuring recessional velocities (listedon Table 4) can be applied since the rotation curves are symmet-rical. Table 3 gives an example of the tables electronically avail-able with the values of the kinematic profiles.
To compute the central velocity dispersion ( σ ) we shifted all thespectra to the same wavelength scale using the rotation curvesdisplayed in Figure 6, and we coadded all the individual spectra Note that galaxies as VCC856, those with the poorest quality, havea non-zero central velocity.. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 7
Fig. 6.
Kinematic profiles of the galaxy sample. Each diagram shows in the left upper panel the folded rotation curve of the galaxyand in the left bottom panel the folded velocity dispersion profile. The di ff erent sides of the galaxy are indicated with red squaresand black dots. On the upper x-axis the radius is given as a fraction of the e ff ective radius ( R e f f ) of each galaxy in the I band (seeSection 6). The purple open squares show the points used to calculate the maximum rotation for each galaxy and the purple lineindicates this v max . The dashed line in the velocity dispersion profiles indicate the central σ computed up to the R e f f (see Table 4).In the right panels the not-folded kinematical profiles are plotted. E. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster
Table 3.
Kinematic profiles for VCC990. R v ( ′′ ) v (km s − ) R σ ( ′′ ) σ (km s − )-5.43 1.8 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± up to one e ff ective radius. The typical S / N ratio for the spectrumwhere the central σ is computed is ∼
60 Å − . These results areshown in Table 4.The maximum rotational velocity ( v max ) was calculated asthe weighted average of the two highest velocities along themajor axis on both sides of the galaxy at the same radius (fornon-symmetric profiles at least three values were required). Asa consequence values with larger errors weight less than thosewith smaller errors. For each galaxy these values are presentedin Figure 6 as purple squares. We show in Appendix A that, giventhe uncertainty, all galaxies with v max < − can be consid-ered non-rotators.The ratio between these two kinematic measurements, themaximum rotation velocity v max and the velocity dispersion σ ,is called anisotropy parameter, v max /σ , and it is used to studythe rotational / pressure support of the galaxies. In Table 4 weshow ( v max /σ ) ∗ , the anisotropy parameter corrected from theinclination. This correction is done following the expression( v max /σ ) ∗ = v max /σ √ ǫ/ (1 − ǫ ) , where ǫ is the ellipticity. Note that forthose galaxies with ellipticity close to zero, no correction canbe done because they are nearly face on. We choose a conserva-tive value of ( v max /σ ) ∗ = . v max is a lower limit since the rotation curves are still rising. Displaying simultaneously the kinematic profiles measured inthis work with those of other authors (Figure 7), one sees thatthe radial extent of the kinematic curves varies from one work toanother. In addition, the o ff sets found in the velocity dispersionsare not always consistent within the errors (Figure 8). These twodi ff erences are important, because di ff erent radial extents lead todi ff erent maximum rotation velocities and o ff sets in the velocitydispersion profiles lead to di ff erent central σ values. Table 4.
Kinematic parameters.
Galaxy σ (km s − ) v max (km s − ) ( v max /σ ) ∗ v rad (km s − )PGC1007217 35.2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± R ef f . Column 3: maximum rotation veloc-ities. The v max adopted for VCC0856, VCC0990 and VCC1183 havebeen measured in the rotation curves of Chilingarian (2009) due totheir larger extent (see Section 5.3). Column 4: anisotropy parametercorrected from inclination. Column 5: mean radial velocity observed.Values in agreement with those of NED database. There are two factors that critically a ff ect the measurements ofthe velocity dispersion of the galaxies: the not identical instru-mental σ for the stars and the galaxies and the spectral types ofthe stars used to fit the width of the galaxy lines.Caldwell et al. (2003) made their observations with a σ inst =
100 km s − , too high to accurately measure velocity dispersionsof typical dwarf galaxies, below 50 km s − .Concerning the equality of the instrumental resolutionin the templates and in the galaxies Chilingarian (2009)used simple stellar population (SSP) models of PEGASE.HR(Le Borgne et al. 2003), based on ELODIE (Prugniel et al.2007) ( R = σ inst of the galaxies must be cautiously done because σ inst of the models is based on the mean value of the spectral resolu-tion of the library they are based on, therefore small di ff erencesafter the broadening between the SSP models and the galaxiescan arise.Continuing with the same e ff ect, in the works of Pedraz et al.(2002) and van Zee et al. (2004b) the stars observed were notfilling the slit because they were not defocused and the seeingwas smaller than their slit width. But in the case of Geha et al.(2003) and Beasley et al. (2009), where their slit widths were0.75” and 1.0” respectively, it is possible that some stars werefilling the slit thanks to the seeing. However, in none of theseworks a correction was made to assure that the instrumental pro-file in the stars was the same as in the galaxies.In reference to the templates used to perform σ , some ofthe authors mentioned above used only one star to fit the galaxyspectrum, and in such a case the fact that the template is notrepresentative of the stellar population of the galaxy might lead . Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 9 Table 5.
Uncertainties introduced when di ff erent templates areused to calculate the velocity dispersion of a dwarf galaxy withdi ff erent stellar populations. ∆ σ/σ , defined in Figure 2, uses as σ i
40 km s − . ∆ σσ x100Age (Gyr) Z =+ = -0.4 Z = -0.7Linear combination of B to M stars1 15% 19% 1%4 8% 18% 19%10 7% 14% 23%G8III1 32% 54% 71%4 15% 18% 20%10 17% 13% 11%K1III1 29% 47% 59%4 19% 18% 20%10 17% 13% 11% to large errors. We have computed Monte-Carlo simulations tosee the di ff erences between fitting the galaxy spectrum with onlyone star and a linear combination of stars of spectral types fromB to M, with di ff erent luminosity classes. The simulations con-sisted of a selection of PEGASE.HR models of 3 di ff erent ages(1 Gyr, 4 Gyr and 10 Gyr) and 3 di ff erent metallicities ( Z = Z = − Z = − = = σ = − when running MOVEL, thereby showingthat there was no zero point o ff set. Secondly, we broadened themodels to 40 km s − to simulate dwarf galaxies of di ff erent stel-lar populations. And finally, we ran MOVEL using 3 di ff erentkinds of templates: only one K1III star (as in Geha et al. (2003)), only one G8III star (as in van Zee et al. (2004b)), and a linearcombination of B to M stars with di ff erent luminosity classes (asin this work). To measure σ we have masked the Balmer lines,especially those bluer than H δ to avoid possible problems due toemission lines. Our simulations show that a linear combinationof di ff erent stars is the most accurate method to obtain the veloc-ity dispersion of the galaxies, never finding an error above 25%,independent of the stellar population considered. Note that if ayoung population dominates the light of the galaxy (for ages of1 Gyr and below), and a single G or K star is used as a template,an error up to 70% can be done. When a single star is used astemplate, a dependence on metallicity for young populations (1or 4 Gyr) is also found, in the sense that decreasing the metal-licity increases the uncertainty. This dependence is likely due too ff sets introduced by the method employed to compute σ . Theresults obtained have been summarised in Table 5. Di ff erent criteria have been used in the literature to measurethe maximum rotation velocity. The main di ffi culty here is tohave an extended rotation curve that reaches a clear plateauwhere the maximum rotation can be measured. As this is notso easy for dEs, an objective criteria, independent of the shapeof the rotation curve in each case, must be adopted. The di ff er-ent criteria used by the various authors have led to maximum Fig. 8.
Comparison between the velocity dispersions measuredin this work versus those of other authors. The colours and sym-bols are the same as in Figure 7. We add a comparison withCaldwell et al. (2003) (solid red points), who only measuredcentral values and no kinematical profiles.rotational velocities that are nevertheless in the majority of thecases nearly consistent within the errors (Figure 9). The criterionused by Pedraz et al. (2002) is the same as the one adopted here.Although we achieved a radial extent of 23 ′′ for VCC1122 andPedraz et al. (2002) only 8 ′′ , the latter value was enough to reachthe flat part of the rotation curve, and, as a consequence, bothmeasurements of the maximum rotation are identical. The expla-nation for the di ff erences found with Simien & Prugniel (2002)are mainly based on the fact that only two points were consideredto obtain the maximum rotation in that paper. The di ff erenceswith Geha et al. (2003) are due to the limitation of their datato the core of the galaxies, never reaching radii larger than 6 ′′ (see Figure 7). The di ff erences with van Zee et al. (2004b) andChilingarian (2009) are related to a di ff erent radial extent of therotation curves. Note that Chilingarian (2009) does not calculatethe maximum rotation, but we have applied our criterion to hisrotation curves. Finally, the di ff erences found with Beasley et al.(2009) are due to the fact that v max is obtained from the anal-ysis of Globular Clusters located up to ∼ R e f f . When theirkinematic determined from the stellar component using long slitspectroscopy along the major axis of the galaxy is compared toour data, the agreement is evident (Figure 7). The maximumrotation values adopted for the analysis (see Table 4) are ourown values, except for VCC856, VCC990 and VCC1183, wherethe data come from Chilingarian (2009) since he obtained largerradii than us. Note that the values from Beasley et al. (2009) cannot be adopted here because our work is dedicated to the analysisof the stellar component of dEs.The comparison with Beasley et al. (2009), who finds rota-tion speeds much larger at 7 R e f f (100 and 50 km s − higher forVCC1087 and VCC1261, respectively) than our data at the R e f f ,indicate that the rotation curves of these galaxies are still rising.
6. Photometric parameters
In order to make a complete analysis of the kinematics, compar-ison with some photometric parameters is needed. For our study,we require I-band (Johnson-Cousins) total magnitudes and opti-cal radii ( R opt , radius containing 83% of the total I-band lumi-nosity (Catinella et al. 2006)) to study the shape of the rotation Fig. 9.
Comparison between the maximum rotational velocitymeasured in this work and those measured by other authors.Symbols and colours are the same as in Figure 7. VCC1261from Beasley et al. (2009) is nearly outside the plot due to itsenormous rotation: 105 ±
44 km s − .curves. E ff ective radii ( R e f f , radius containing 50% of the to-tal light) is needed to measure the extent of the radial profilesin physical units of the galaxy. Ellipticities ( ǫ ) are needed tomake the appropriate corrections due to inclination. A param-eter to measure the boxyness / diskyness of the isophotes ( C ) isalso required to study the possible late-type origin of these dwarfearly-type galaxies.All these parameters have been obtained from i -band SloanDigital Sky Survey (SDSS, York et al. (2000)) data release 6(DR6, Adelman-McCarthy et al. (2008)) photometry. They havebeen calculated using the IRAF task ellipse as described inAppendix B. The transformation from i -band (SDSS) to I -band(Johnson-Cousins) has been done assuming m I = m i − . ± . C : boxyness/diskyness parameter The boxyness / diskyness ( C ) parameter measures the deviationsof the isophotes from a perfect ellipse. If C > C ≤ parameter,determined for our galaxies as described in Appendix D, is pro-vided in Table 6.Our C classification for disky isophotes agrees in generalwith the morphological classification of Lisker et al. (2006a) ascan be seen in Figure 10. Note that Lisker et al. (2006a) clas-sified a galaxy as disky when disk features (spiral arms, edge-on disks, or bars) were detected after subtracting an axisym-metric light distribution from the original image or after un-sharp masking. In this Figure we can see that the red dots,those galaxies classified as being without underlying structuresin Lisker et al. (2006a), are grouped around C ≤ IRAF is distributed by the National Optical AstronomyObservatory, which is operated by the Association of Universitiesfor Research in Astronomy, Inc., under the cooperative agreement withthe National Science Foundation.
Fig. 10.
Correlation between the anisotropic parameter( v max /σ ) ∗ and C x100. Colours indicate Lisker et al. (2006b)classification. The galaxies with v max measured inside the cen-tral 6” are considered lower limits and are indicated with arrows.The horizontal dashed line at ( v max /σ ) ∗ = C > C parameter todetect the presence of an underlying disk. Three exceptions arefound and discussed in Appendix D.In this respect, it is important to underline the correlationbetween C and the anisotropic parameter evident in Figure 10,first found by Bender et al. (1988) for more massive ellipticalgalaxies.
7. Analysis
The analysis presented in this work is primarily focused on therotationally supported systems. Although the majority of thedwarf galaxies (15 out of 21) show some rotation ( v max > − , Table 4), only 11 are rotationally supported (( v max /σ ) ∗ > Catinella et al. (2006) made a systematic study of the shape ofthe rotation curves of late-type spiral galaxies as a functionof luminosity based on the method described in Persic et al.(1996). They fitted the rotation curves following the Polyexmodel (Giovanelli & Haynes 2002) which has the form: V PE ( r ) = V (cid:18) − e − r / r PE (cid:19) + α rr PE ! (1)This analytical function depends on 3 parameters: V , r PE and α ,which represent the amplitude, the exponential scale of the innerregion and the slope of the outer part of the rotation curve, re-spectively. The mean fitted rotation curves from Catinella et al. . Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 11 Table 6.
Derived parameters.
Galaxy d (Mpc) M I (mag) ǫ R ef f (”) C x100 Disk classification (L06b)PGC1007217 20.23 ± ± ± ± ( ∗ ) ± ± ± ± ± ± ± ± ± ± ( ∗ ) ± ± ± ± ± ( ∗ ) ± ± ± ± ± ± ± ± ± ± ( ∗ ) ± ± ± ± ± ( ∗ ) ± ± ± ± ± ± ± ± ± ± ( ∗ ) ± ± ± ± ± ( ∗ ) ± ± ± ± ± ± ± ± ± ± ( ∗ ) ± ± ± ± ± ( ∗ ) ± ± ± ± ± ( ∗ ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ( ∗ ) ± ± ± ± ± ( ∗ ) ± / B Cluster distance from Mei et al. (2007) for the rest of them (note that E, N and S Clouds are East,North and South areas of Cluster A). The distance for NGC3073 from SBF by Tonry et al. (2001) and PGC1007217 and PGC1154903 distancesare from NED / IPAC Database derived from redshift with H = ± − Mpc − (these two distances must be used cautiously). Column 3:Absolute magnitudes in I -band (Johnson-Cousins in AB system) converted from i -band measured in SDSS images using m I = m i − .
52 mag.Column 4: ellipticities from i -band (SDSS) images. The quoted errors indicate the RMS scatter in the ellipticity between 3 ′′ and the R ef f . Column5: E ff ective radius from i -band (SDSS) images. Column 6: Diskyness / Boxyness parameter from i -band (SDSS) images. The asterisks indicate C measured as the maximum in the region 3 ′′ - 3 R ef f if prominent disky features are found; in the rest of the cases the quoted values are the averagein this same radial range and the errors the RMS scatter (see Appendix D). Column 7: Disk / No Disk classification by Lisker et al. (2006b) (L06b)(no values indicate that these galaxies are not included in their analysis). (2006) are normalised to the optical radius ( R opt , radius contain-ing 83% of the total I -band luminosity), and the velocities arecorrected from inclination. To compare them with our rotation-ally supported galaxies, we have calculated the inclinations as inGiovanelli et al. (1997a): cos i = (1 − ǫ ) − q − q (2)where i is the inclination, ǫ is the ellipticity and q is a constantvalue that depends on the thickness of the disk. Here we assume q = .
3, a conservative value for dwarf galaxies shaped as thickdisks (Lisker et al. 2007). The comparison between the mean rotation curves ofCatinella et al. (2006) and those of our rotationally supportedobjects must be done in the same luminosity regime since thederived parameters of the Polyex model are luminosity depen-dent. As the dwarf galaxies analysed in this work have magni-tudes below the minimum magnitude in Catinella et al. (2006)( M I = − M I = − I -band magnitude of the galaxies here analysed. Theparameters used to construct this curve are V = − , r PE = α = For early-type spirals q = . q = . − .
35 (S´anchez-Janssen et al. 2010). The di ff erence in v max afterthe correction for inclination between using q = . q = .
35 isof 4.4%, insignificant.
In Figure 11 we compare the mean fitted rotation curves ofCatinella et al. (2006) for late-type spirals (obtained from emis-sion lines, black solid curves) with the rotation curves of our ro-tationally supported dEs determined from absorption lines (greysymbols). Of the 11 rotationally supported dEs, only 7 have beenconsidered for this analysis because 3 of them, VCC21, VCC917and NGC3073, have poor quality rotation curves ( ∆ v max v max largerthan 25%), and VCC308 has ǫ lower than 0.1, implying that thegalaxy is nearly face on. The blue dots in Figure 11 show themedian rotation curve of our dEs in bins of rR opt = .
1. The greyarea contains the 1 σ deviation from this median value (68% ofthe values are inside this area). The blue dashed line is the ex-trapolated Polyex model for M I = − ff erent kinematic be-haviour, they can be either pressure or rotationally supported.Furthermore, rotationally supported dEs have rotation curvessimilar to those late-type spirals despite the fact that these lat-ter objects are gas dominated systems. Fig. 11.
The observed rotation curves of rotationally supporteddEs (grey symbols) are compared to the mean rotation curvesof late-type spiral galaxies (black solid and blue dashed lines)from Catinella et al. (2006). Blue filled dots represent the me-dian observed rotation curve of rotationally supported dE in binsof r / R opt = .
1. The last bin contains all data for r / R opt ≥ . σ from themedian. Given the similarity in the kinematic properties of rotation sup-ported dEs with those of late-type spirals we expect that thesesystems follow the Tully-Fisher relation, as firstly proposed byvan Zee et al. (2004b). The Tully-Fisher relation is a typicalscaling relation valid for star forming, rotating systems, link-ing the total luminosity to the maximal rotation velocity of thegalaxy.In Figure 12 we compare the Tully-Fisher relation for our(dark blue) and van Zee et al. (2004b) (light blue) dEs to thatof normal late-type galaxies of Giovanelli et al. (1997b) (greysymbols) and De Rijcke et al. (2007) (red dashed area), respec-tively. Figure 12 clearly shows that these rotationally supporteddEs follow the Tully-Fisher relation with a similar scatter as thenormal spirals of De Rijcke et al. (2007) and thus kinematicallybehave as late-type spirals. The v max of dEs plotted in Figure 12is probably a lower limit since it is generally measured wherethe rotation curve is still rising, as suggested by the kinematicsof the globular clusters. It is thus conceivable that the agreementbetween the Tully-Fisher relation of rotationally supported dEsand late-type spirals of similar luminosity is even better than thatdepicted in Figure 12. The shape of the rotation curves gives information about thedark matter content and distribution of late-type galaxies (e.g.,Catinella et al. 2006). Similarly, σ can be used to measure thedark matter content of pressure supported systems. FollowingBeasley et al. (2009) we estimate the total dynamical mass ofour sample galaxies using the relation: M tot = M press + M rot (3) No asymmetric drift is applied neither to our dEs nor to those ofvan Zee et al. (2004b). This correction would increase v max by 2.5 ± Fig. 12.
Tully-Fisher relation for 7 of our rotationally sup-ported dEs (in dark blue), the dEs from van Zee et al. (2004a,b,VZ04, in light blue), the normal spirals from Giovanelli et al.(1997b, G97, in grey) and De Rijcke et al. (2007, DR07, redlimited area). Absolute magnitudes of dEs have been obtainedusing distances from Mei et al. (2007) (criterion described inTable 6). For Giovanelli et al. data we use H =
73 kms − Mpc − (Mei et al. (2007)). The arrows indicate lower lim-its of v max (those obtained in the inner 6”). Fits of the Tully-Fisher relation are indicated in black for the normal spirals ofGiovanelli et al. (1997b) and in red for De Rijcke et al. (2007,DR07). DR07 fit has been transformed to I band using thecolour-morphology relation from Fukugita et al. (1995) and us-ing H =
73 km s − Mpc − and M I ⊙ = .
08 and M B ⊙ = . M press is the mass inferred from the velocity disper-sion after the contribution from rotation has been removed and M rot is the mass deduced by the intrinsic rotation velocity ofthe galaxies. M press inside the half-light radius is defined as inCappellari et al. (2006): M press ≃ . G − σ R e f f ≃ σ km s − ! R e f f pc ! M ⊙ (4)The rotation curves of rotationally supported systems arecharacterised by an approximately constant gradient suggestingsolid body rotation up to the R e f f . In this case M rot is given bythe relation: M rot = R e f f v max G = R e f f pc ! v max km s − ! . × − ! M ⊙ (5)Dynamical mass-to-light ratios ( Υ I , Table 7) are then mea-sured using the I -band luminosities and equation 4 for pressuresupported systems and the sum of equations 4 and 5 for rotation-ally supported objects . Stellar mass-to-light ratios ( Υ ∗ I , Table7) are computed using the models of single stellar populations Note that this method to obtain M tot is equivalent to introducing theasymmetric drift.. Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 13 Table 7.
Dynamical and stellar mass-to-light ratios in I-band insolar units.
Galaxy ( Υ I ) ⊙ ( Υ ∗ I ) ⊙ PGC1007217 4.0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Υ ∗ I ) ⊙ is only indicative, the large errors in the stellar popu-lations (Michielsen et al. 2008) make the uncertainties of ( Υ ∗ I ) ⊙ of thesame order as the values. (SSP) of Vazdekis et al. (2010) and the ages and metallicitiesfrom Michielsen et al. (2008).Figure 13 presents the relation between the dynamical mass-to-light ratio and the absolute I-band magnitude for our galax-ies (red and blue dots), the sample of classical elliptical galax-ies from Cappellari et al. (2006, Υ Jeans in I-band), the dEs fromGeha et al. (2002) and the Milky Way dwarf spheroidals (dSphs)from Wolf et al. (2010) . Consistently with Zaritsky et al. (2006)and Wolf et al. (2010), we observe that the total mass-to-lightratio within the R e f f of dEs is the lower limit of the decreas-ing and increasing Υ I vs. luminosity relations observed in giantellipticals (Cappellari et al. 2006) and dSphs (Wolf et al. 2010),respectively. Dwarf early-type galaxies have on average Υ I = . ± . Υ I ⊙ , with a slightly higher dispersion in rotatingsystems ( RMS = . Υ I ⊙ ) than in pressure supported systems( RMS = .
04 l Υ I ⊙ ) .Our sample of dEs have on average M dyn / M ∗ = . ± . Υ I and Υ ∗ I , respectively, Table 7), thus they arenot dominated by dark matter within the R e f f (as previously sug-gested by Geha et al. (2002); Forbes et al. (2008)), consistentlywith what is found is massive ellipticals (Cappellari et al. 2006)but contrary to dSphs (Wolf et al. 2010).
8. Discussion
How does this observational evidence compare with the di ff erentscenarios of galaxy formation? In a more general context we re-call that in the most recent hierarchical models of galaxy forma-tion only the most massive ellipticals have been formed throughmajor merging events (De Lucia et al. 2006). The strong mor-phological segregation observed in high density environments(Sandage et al. 1985; Ferguson & Binggeli 1994; Blanton et al. The Υ I values of Wolf et al. (2010) have been converted to equation4 for consistency. Fig. 13.
Dynamical mass-to-light ratio as a function of the ab-solute magnitude in I-band. Red and blue dots are our pres-sure and rotationally supported dEs respectively. For compari-son open circles are dEs by Geha et al. (2002, G02), grey as-terisks are dSphs from Wolf et al. (2010, W10) and dark andlight grey triangles are slow and fast rotators respectively fromCappellari et al. (2006, C06). The transformation to I bandhas been performed using the colour-morphology relation byFukugita et al. (1995) for Es. For the dwarf galaxies we haveused V − I = . ± .
04 as calculated by van Zee et al. (2004a).Note that NGC3073 in not a dE given its high luminosity ( M I = − . (Fundamental Plane) will be the subject of a future communica-tion.It is indeed possible that, as for the massive galaxies, gravita-tional interactions played a major role at early epochs, when thevelocity dispersion of the cluster was lower since galaxies wereaccreted through small groups (preprocesing) than at the presentepoch (Boselli & Gavazzi 2006).
9. Conclusions
We present medium resolution (R ∼ ff erent wavelength ranges correspond-ing to those used during the observations, and we have run, foreach simulated galaxy, 100 Monte-Carlo simulations. The com-parison between observed data and simulations shows that theadopted data extraction technique is appropriate for measuringthe kinematic parameters of the target galaxies. We have alsoshown that velocity dispersions can not be measured for S / N ra-tios below 15, while for radial velocities with S / N ≥
10 accurateresults are obtained.Our analysis has shown that dEs have on average dynami-cal M / L ratios within the e ff ective radius smaller than those ofmassive ellipticals and dSphs (in average log ( Υ I ) = . ± . Υ I ⊙ )). We thus confirm that, within the e ff ective radius, dEsare not dark matter dominated objects.We have found that rotationally supported dEs have rotationcurves similar to those of star forming systems of similar lu-minosity and follow the same Tully-Fisher relation. Combinedwith the evidence that these systems are young objects withdisk-like structures generally located in the outskirts of the clus-ter (Toloba et al. 2009), these observations are consistent with apicture where these rotationally supported dEs result from thetransformation of star forming systems that recently entered thecluster and lost their gas through their interaction with the envi-ronment. The observed conservation of the angular momentumin the rotationally supported dEs suggests that a milder ram pres-sure stripping event as the responsible of the gas removal hasto be preferred to more violent gravitational interactions (ha-rassment) which would rapidly heat up the perturbed systems.Therefore, all these evidences suggest that dEs are not the lowluminosity end of massive early-types because if that was thecase all dEs would be rotating with v max /σ higher than those ofEs, but a population of non-rotators has also been found and,in addition, the evidences of being stripped late-type spirals arestrong enough as to consider it as a possible origin of dEs inclusters. Acknowledgements.
We thank the MAGPOP EU Marie Curie Training Networkfor financial support for the collaborating research visits and observations that al-lowed to make this paper. ET thanks the financial support by the Spanish researchproject AYA2007-67752-C03-03. We thank Consolider-GTC project for partialfinancial support. This paper made use of the following public databases: SDSS,NED, HyperLEDA, GOLDMine. We are grateful to the anonymous referee for acritical report that has improved the quality of the paper.
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Fig. A.1.
Simulations performed to quantify the bias that canbe introduced in the measurement of v max . Plotted are the 100folded rotation curves computed with random numbers dis-tributed as a Gaussian with width the typical errors of the targetgalaxies for that radius. Red squares and black dots are the leftand right arms of the unfolded rotation curves respectively. Thethick black line is the mean v max for all the simulations. The greyshaded area is the scatter for this mean. Vazdekis, A., S´anchez-Bl´azquez, P., Falc´on-Barroso, J., et al. 2010, MNRAS,404, 1639White, S. D. M. & Frenk, C. S. 1991, ApJ, 379, 52White, S. D. M. & Rees, M. J. 1978, MNRAS, 183, 341Wolf, J., Martinez, G. D., Bullock, J. S., et al. 2010, MNRAS, 406, 1220York, D. G., Adelman, J., Anderson, Jr., J. E., et al. 2000, AJ, 120, 1579Yoshii, Y. & Arimoto, N. 1987, A&A, 188, 13Zaritsky, D., Gonzalez, A. H., & Zabludo ff , A. I. 2006, ApJ, 638, 725 Appendix A: Quantification of the bias introducedin v max Using the technique described in Section 5.2 to measure themaximal rotation speed, it seems that none of the galaxies havezero rotation (look at the v max presented in Table 4). However,rotation curves like PGC1154903 or VCC1087 (Figure 6) ap-pear to be statistically consistent with no rotation. The fact thatwe always find positive maximum velocities is a consequence ofthe method used to measure it. To quantify the bias introducedby using this technique we have run some simulations. We havetaken a zero-rotation object with errors typical of those galaxiesthat statistically are non-rotators. We have taken a typical rota-tion curve with 11 bins, at 0, 2 ′′ , 4 ′′ , 7 ′′ , 12 ′′ and 16 ′′ , with sym-metrical errors of 2, 5, 7, 10, 12 and 15 km s − respectively. Fromthese errors we have generated 100 simulated rotation curves as-signing to each radius a random number with a Gaussian distri-bution, of which the width is the error associated to that radius.After folding these simulated rotation curves, shown in FigureA.1, we calculated v max following exactly the same technique asthe one we used for the target galaxies. We then obtained a meanvalue for the 100 values of v max and its scatter, 9 ± − ,shown as a thick black line and a grey shaded area in Figure A.1.As a result, we consider that those galaxies with v max < − are not rotating, based on our data. For the other galaxies therotation is significant (three times above the standard deviation,except for VCC1122 and VCC1261, see Table 4, 3rd column),so that the systematic bias described here is much less relevant.For VCC1122 (17.3 ± − ) and VCC1261 (13.9 ± − ) the rotation is marginal, as also shown by their low v max /σ . Appendix B: Absolute I band magnitudes, opticaland half-light radii and ellipticity
The I -band images for our sample of 21 dwarf galaxies weredrawn from Sloan Digital Sky Survey (SDSS, York et al. (2000))data release 6 (DR6, Adelman-McCarthy et al. (2008)) and con-verted to Johnson-Cousins systems following Appendix C. Thephotometric parameters were calculated using the IRAF task el - lipse .To remove the stars from the images we used the IRAF task fixpix . This task allows us to remove the stars interpolating thesurrounding galaxy area. To improve the final outcome, we av-eraged the results of interpolating along the horizontal and ver-tical directions for each star. For those galaxies that were onthe edge of the FITS images or had a very bright nearby star, amore careful procedure was implemented. Taking advantage ofthe fact that the galaxies are ellipticals, so that they have smoothand axisymmetric surface brightness profiles, the bmodel task ofIRAF can be used to replace the a ff ected areas of the galaxy bythe azimuthal average of the una ff ected ones. The output from bmodel was used only to replace a small fraction of pixels, sothis procedure was not a ff ected by the possible presence of moresubtle features, such as bars or spiral arms, which could not bereproduced by the model provided by the bmodel task. Once ex-tremely bright nearby stars had been removed the same proce-dure as above was followed with ellipse and fixpix .The procedure followed to run ellipse is dependent on theparameters we want to measure. First of all we run ellipse fixingonly the center of the galaxy assuming a step between isophotesof 1 pixel, the rest of the parameters were left free. We also madethe masks for the stars to be removed as described above. Withthe aim of measuring the absolute magnitude, R opt and R e f f werun ellipse again fixing, the center of the galaxy, the ellipticityand the position angle (PA) to avoid overlap between consecu-tive isophotes. The adopted ǫ and PA in this case are the typicalvalues in the outer parts of the galaxy (beyond 1.5-2 R e f f , regionwhere these two parameters stabilise). To measure ǫ and C werun again ellipse after removing the stars leaving fixed only thecenter of the galaxy.Asymptotic magnitudes and the radii were derived as inGil de Paz et al. (2007). We first computed the accumulated fluxand the gradient in the accumulated flux (i.e., the slope of thegrowth curve) at each radius, considering as radius the major-axis value provided by ellipse . After choosing an appropriateradial range, we performed a linear fit to the accumulated flux asa function of the slope of the growth curve. The asymptotic mag-nitude of the galaxy was the Y-intercept, or, equivalenly, the ex-trapolation of the growth curve to infinity. Once the asymptoticmagnitude was known, the optical and e ff ective radii of eachgalaxy were obtained as the major-axis of an elliptical isophotecontaining 83% and 50% of the total flux respectively. For theasymptotic magnitudes di ff erent sources of error have been con-sidered (see Appendix C). The resulting uncertainty is ∼ ǫ ) were measured as the mean value be-tween 3” and the R e f f , the galaxy region covered by our spectro-scopic observations. Appendix C: Errors in magnitudes
The zero points (ZP) and the errors in the i -band magnitudeshave been computed as described in SDSS documentation. TheZP have been obtained from F , the flux a source produces in counts per second in the image, calculated as a function of threeparameters ( aa , kk and airmass ) defined as: F = t exp . aa + kk × airmass ) (C.1)where the exposure time ( t exp ) is the same for all the SDSS im-ages (53.91 seconds). The uncertainties in the i -band magnitudesare a ff ected by di ff erent sources of error: firstly, the errors in theflux, that can be calculated following the equation: ∆ F = s F + skygain + N pix ( dark variance + ∆ sky ) (C.2)where F is the total flux in counts, the sky and ∆ sky are thebackground sky and its error (in counts), the gain and the dark variance are given in the header and N pix is the numberof pixels in the largest aperture where the flux is measured. Thiserror was typically 10 − mag. Other error sources are the errorintroduced in the fit to the growth curve (between 10 − mag and6 × − mag), and the error due to photometric zero point dif-ferences between the di ff erent scans of SDSS, which might leadto an error of 0.01 mag. SDSS i -band magnitudes are not ex-actly in the AB system, so an error of 0.01 mag might alsobe introduced (see SDSS documentation about the photomet-ric flux calibration). And finally, we have transformed our datafrom the SDSS i -band to the Johnson-Cousins I -band assuming m I = m i − . ± .
01 mag Fukugita et al. (1995) given that their r − i colour ranges from 0.23 mag to 0.57 mag.Adding quadratically all these sources of error, the final esti-mated error is 0.02 mag for the apparent I -band magnitudes. Appendix D: The C Boxyness/Diskynessparameter
The boxyness / diskyness parameter is defined as the fourth mo-ment in the Fourier series as follows I ( Φ ) = I + X k [ S k sin ( k Φ ) + C k cos ( k Φ )] (D.1) I ( Φ ) is the intensity measured in each isophote. The first twomoments in this series describe completely an ellipse. Higherorder moments ( k ≥
3) define deviations of the isophotes from el-lipses. The third order moments ( S and C ) represent isophoteswith three fold deviations from ellipses (e.g. egg-shaped orheart-shaped), while the fourth order moments ( S and C )represent four fold deviations. Rhomboidal or diamond shapedisophotes have nonzero S . For galaxies that are not distortedby interactions, C is the most meaningful moment indicat-ing the disky / boxy shapes of the isophotes (see Figure 1 fromPeletier et al. (1990) for an example of these di ff erent shapes). C is measured in i -band SDSS images using ellipse thatperforms equation D.1 along the radius of the galaxy fixing onlythe center of the galaxy and leaving the rest of ellipse parametersfree, as described in Section 6.1. Figure D.1 shows C as a func-tion of radius for 3 dEs. Due to the large changes of C with radiitaking an averaged value is therefore not the best way to detectdisks in these galaxies, especially if they cover only a limitedrange in radius. We have thus adopted the following procedure:If at least one prominent bump is detected, which has a widthlarger than ∼
6” inside three e ff ective radii (above this radius thescatter of C and its error becomes too large as to be reliable),we consider the galaxy to be disky, and assign the maximum C Fig. D.1.
Examples of C vs. radius for three galaxies: VCC397,VCC308 and VCC1695. The dashed purple lines indicate theregion between 3” and the 3 R e f f . The dotted purple line showsthe R e f f . In the upper panel one can see that if an average valueis used between the dashed lines, C will be compatible withzero and as a consequence, the prominent disky structure will besmeared out by the adjacent regions. In contrast, in the middlepanel a galaxy with no clear disky structures is shown. In thislatter case the errors are larger. The bump in C only covers ∼ C and its scatter is more representative. In the lowerpanel VCC1695 is an example of a typical boxy shaped galaxy.between 3” and 3 R e f f to the global C . The error in this mea-surement has been estimated by dividing the photometric errorof the maximum of C by the square root of the number of pointsthat describe the disky structure in order to quantify the reliabil-ity of the bump considered. If the bump is described by a largenumber of points it is highly likely that the bump is truly thereand as a consequence the error will be small, but if the numberof points is small but the photometry is of high quality then theerror will be small again. In any other case the error will be largeand the result must be used cautiously.Otherwise, if the values oscillate around C ∼ R e f f to the global C . In this case, the RMS quantifies simultaneously the quality . Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 17 of the photometry and the possible presence of small bumps (asit is the case of VCC308, middle panel of Figure D.1).The results obtained for this parameter are listed in Table 6and plotted vs. the anisotropic parameter, ( v max /σ ) ∗ , in Figure10. The agreement between the C classification in disky / boxygalaxies and the morphological classification from Lisker et al.(2006b) is evident but apart from three red dots. These filledcircles correspond to VCC917, a rotationally supported galaxy(above the horizontal dashed line) with strong disky isophotesbut no structure found by Lisker et al. (2006a)); VCC1122, anot rotationally supported dE but with an appreciable rotation inFigure 6 and very important disky structures in the inner R e f f notdetected by Lisker et al. (2006a)); and VCC1912, inside half thee ff ective radius a moderate rotation is found in this system witha clear disky feature that peaks at 1.5 R e f f . For this galaxy, how-ever, no underlying structure was found by Lisker et al. (2006a).More importantly VCC308 and VCC856, two rotationally sup-ported galaxies with boxy C , present prominent spiral arms inLisker et al. (2006a). In Ferrarese et al. (2006), based on ACS-HST images, VCC856 also shows spiral arms but their analysisof the isophotes’ shapes shows that they are boxy too. Lookingat Table 6 we see that both galaxies are nearly face-on, whichmeans that the isophotes are boxy since face-on disks are roundand not disky. As a consequence we emphasise the fact that boxyisophotes could miss disk features (mainly if the galaxies areface-on), but not the other way round (see VCC917). Fig. 6.
Continued . Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 19
Fig. 6.
Continued
Fig. 6.
Continued . Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 21
Fig. 6.
Continued
Fig. 6.
Continued . Toloba et al.: Formation and evolution of dwarf early-type galaxies in the Virgo cluster 23
Fig. 7.