FURTHER EVIDENCE FOR LARGE CENTRAL MASS-TO-LIGHT RATIOS IN EARLY-TYPE GALAXIES: THE CASE OF ELLIPTICALS AND LENTICULARS IN THE A262 CLUSTER^*

As part of the HST Snapshot Proposal 10884 (P.I.: G. A. Wegner), the galaxies NGC 679, NGC 687, NGC 708, NGC 759, and UGC 1308, were observed with the Wide Field Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope (HST) between 2007 July 14 and 2008 September 27. For each galaxy, two 300 s exposures were taken with the filter F622W. All exposures were performed with the telescope guiding in fine lock, which typically gave an rms tracking error of 0003. The centers of the galaxies were positioned on the Planetary Camera (PC) chip in order to get the best possible spatial resolution. This consists of 800 × 800 pixels of 00455 × 00455 each, yielding a field of view of about 36'' × 36''. The two pointings were shifted along the pixel diagonal by 03535. This pattern corresponds to a shift of 5.5 × 5.5 pixels on the PC chip.

In the following, our photometric analysis is limited to the PC chip since the nuclear surface-brightness profiles were matched to available radially extended ground-based photometry. Indeed, all the sample galaxies were observed in the R band of the Kron-Cousins system as a part of the EFAR project (Colless et al. 1993; Saglia et al. 1997b).

The WFPC2 images were reduced using the CalWFPC reduction pipeline in IRAF⁸ maintained by the Space Telescope Science Institute. Reduction steps include bias subtraction, dark current subtraction, and flat-fielding, as described in detail in the WFPC2 instrument and data handbooks (Baggett & McMaster 2002; McMaster & Biretta 2008). Subsequent analysis was performed using IRAF standard tasks. The bad pixels were corrected by means of a linear one-dimensional interpolation using the data quality files and the WFIXUP task. For each galaxy, the alignment of the images was checked by comparing the centroids of stars in the field of view. The images were aligned to an accuracy of a few hundredths of a pixel using IMSHIFT and knowledge of the offsets. They were then combined with IMCOMBINE. A check was performed to verify that the alignment and combination did not introduce a significant blurring of the data. To this aim, the FWHM of the Gaussian fitting to the field stars was measured in the original and combined frames. It was found that they did not change to within a few percent. In combining the images, pixels deviating by more than three times the local standard deviation (calculated from the combined effect of Poisson and readout noise) were flagged as cosmic rays and rejected. The residual cosmic rays and bad pixels were corrected by manually editing the resulting image with IMEDIT. The HST images of four of the galaxies are shown in Figure 1.

The reduced EFAR images were available to one of us (R.P.S.). To calibrate the images, the photometric zero points in Saglia et al. (1997b) were adopted and their coefficients were applied to correct the measured magnitudes for Galactic absorption and K_R correction and to correct the measured surface brightnesses for Galactic absorption, K_R correction, and cosmological dimming. The EFAR images were used to determine the zero points and calibrate the WFPC2 images.

To this aim, the isophotal profiles of the galaxies were measured by fitting the isophotes in the WFPC2 and EFAR images with ellipses using the isophotal shape algorithm described by Bender & Moellenhoff (1987). For the fitted isophotes the algorithm provides the azimuthally averaged surface brightness (μ), ellipticity (), position angle (P.A.), center coordinates (x₀, y₀) and third, fourth, and sixth cosine (a₃, a₄, and a₆) and sine (b₃, b₄, and b₆) Fourier coefficients describing the deviation of the isophotal shape from a perfect ellipse. Foreground stars, residual cosmic rays, and bad pixels were masked before fitting. Moreover, the centers of ellipses were allowed to vary. As a first step, the sky background was measured in regions free of sources at the edges of the field of view and then subtracted. Its final value in the WFPC2 images was determined through the matching of the ground-based photometry.

The surface-brightness radial profiles measured in the WFPC2 images were matched to the EFAR ones typically between 3'' and 10'' by determining the zero point and sky value that minimize the surface-brightness flux differences. The galaxies were assumed to have no R − m_F622W color gradient in the matched radial region. The resulting distribution of the differences Δm = R − m_F622W after minimization gives a standard deviation about the mean σ_Δm = 0.035 mag for NGC 679, σ_Δm = 0.017 mag for NGC 687, and σ_Δm = 0.050 mag for UGC 1308. Therefore, the scatter σ_Δm is the dominant source of error in the zero point of the WFPC2 images because the EFAR final data set has a common zero point to better than 0.01 mag (Saglia et al. 1997b).

The prominent dust lanes crossing the nucleus of NGC 708 (Figure 1) did not allow us to measure reliable isophotal parameters within a few arcseconds from the galaxy center in both the WFPC2 and EFAR images. To minimize the impact of dust on the measurement of the isophote shape, we analyzed the H-band image obtained by Gavazzi et al. (1996) retrieved from the GOLDMine Archive (Gavazzi et al. 2003). The near-infrared data were taken on 1995 February 13 at Calar Alto Observatory, Spain using the 2.2 m telescope mounted on the Max-Planck-Institut für Astronomie General-purpose Infrared Camera with a Rockwell 256 × 256 NICMOS3 HgCdTe detector array. The spatial scale was 161 pixel⁻¹, yielding a field of view of 68 × 68. The total exposure time was 192 s. A two-dimensional fit with a circular Gaussian to the field stars in the resulting image yielded an FWHM = 22. The surface-brightness radial profiles measured in the GOLDMine and EFAR images were matched between 5'' and 26'' with 〈Δm〉 = +0.006 mag and σ_Δm = 0.026 mag.

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For NGC 679, NGC 687, NGC 759, and UGC 1308, the P.A.s measured in the available HST and ground-based available images match within 2°, ellipticities match within less than 0.05, cosine and sine Fourier coefficients match within less than 1%, and the center coordinates of the fitting ellipses match within 02.

The radial profiles of the azimuthally averaged surface brightness; ellipticity; P.A.; center coordinates; and third, fourth, and sixth cosine and sine Fourier coefficients of the sample galaxies are presented in Figure 2 and Table 5. For NGC 679, NGC 687, NGC 759, and UGC 1308 they are the combination of HST and EFAR data. For NGC 708 they are measured on the GOLDMine image. For IC 171, NGC 703, and NGC 712 they are obtained from the EFAR images.

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Classed as early-type galaxies on ground-based data (Wegner et al. 1996, but see also de Vaucouleurs et al. 1991), the HST images show that four of the galaxies in this investigation—NGC 679, NGC 708, UGC 1308, and NGC 759—have absorbing material in their central regions, as shown in Figure 1. These resemble the dust features described elsewhere (e.g., Martini et al. 2003; Lauer et al. 2005) and found in two of our Coma Cluster galaxies (Corsini et al. 2008). Only NGC 687 shows no dust features in its nucleus.

NGC 679. The nucleus of the galaxy hosts a nearly face-on ring of dust. It has a radius of 45 (1.5 kpc).

NGC 708. The strong dark stripe of NGC 708 appears to be consistent with a dust disk seen nearly edge-on as it runs roughly north–south through the center of the galaxy image. It extends out to 32 (1.1 kpc) on its south side and 58 (2.0 kpc) on the north side. Individual dark blobs can be seen along the edge of the band, particularly to the west side.

NGC 759. The galaxy has a nuclear dusty disk which is close to being face-on. It has a radius of 50 (1.7 kpc) and it is characterized by tightly wound multiple spiral arms.

UGC 1308. The galaxy nucleus appears to have an inclined dust disk. The projected elliptical shape has a major axis of 32 (1.1 kpc) across in the north–south direction and a minor axis of 26 (0.9 kpc). It is asymmetric in that it is stronger on the west side and is not present on the east side.

Long-slit spectroscopic data of the sample galaxies were obtained with the 2.4 m Hiltner telescope of the MDM Observatory at Kitt Peak, AZ on 2003 November 14–23 (run 1), 2005 October 25–31 (run 2), and 2006 November 10–16 (run 3).

In runs 1 and 2 the telescope mounted on the Moderate Resolution Spectrograph with a plane reflection grating with 1200 grooves mm⁻¹ blazed at 5000 Å at the first order and a 19 × 96 slit. The "Echelle" CCD was adopted as detector. It is a thinned and backside-illuminated Site CCD with 2048 × 2048 pixels of 24 × 24 μm². The gain and readout noise are 2.7 e⁻ ADU⁻¹ and 7.9 e⁻ (rms), respectively. In run 3 the Boller & Chivens CCD Spectrograph was mounted with a plane reflection grating with 600 grooves mm⁻¹ blazed at 5875 Å in the second order. A 17 × 52 slit with an LG370 order-blocking filter was used. The "Ohio State University Loral C" CCD was the detector. The latter is a thinned and backside-illuminated Loral CCD with 1200 × 800 pixels of 15 × 15 μm². The gain and readout noise are 2.1 e⁻ ADU⁻¹ and 7.0 e⁻ (rms), respectively. No pixel binning was adopted. The wavelength range from 4670 to 6541 Å was covered with a reciprocal dispersion of 0.870 Å pixel⁻¹ in run 1, from 4675 to 6530 Å with 0.906 Å pixel⁻¹ in run 2, and from 6270 to 7175 Å with 0.755 Å pixel⁻¹ in run 3. The spatial scale was 0606 pixel⁻¹ in runs 1 and 2, and 041 pixel⁻¹ in run 3.

In runs 1 and 2 the spectra were obtained along the major, minor, and a diagonal axis for all the sample galaxies, except for UGC 1308 which was observed only along the major and minor axis. The major axis of IC 171 and NGC 679 and the minor axis of UGC 1308 were observed in both runs to perform a consistency check between the measurements of stellar kinematics and line-strength indices of the two runs. In run 3 the spectra were obtained along a diagonal axis. Only NGC 708 was also observed along the major and minor axes. For NGC 759 the spectra were also taken close to the major axis and along the minor axis. The integration time of the single galaxy spectra was 3600 s in runs 1 and 2 and 1800 s in run 3. Total integration times and slit P.A. of the galaxy spectra as well as the log of the spectroscopic observations are given in Table 2.

At the beginning of each exposure the galaxy was centered on the slit using the guiding camera which looks onto the slit. In runs 1 and 2 several spectra of giant stars with spectral type ranging from late-G to early-K were obtained for templates in measuring stellar kinematics and line-strength indices. The template stars were selected from Faber et al. (1985) and González (1993). At least one flux standard star per night was observed to calibrate the flux of the spectra before line-strength indices were measured. Spectra of the comparison arc lamp were taken before and/or after object exposures.

All the spectra were bias-subtracted, flat-field corrected, cleaned of cosmic rays, corrected for bad columns, and wavelength and flux calibrated using standard IRAF routines. Each spectrum was rebinned using the wavelength solution obtained from the corresponding arc-lamp spectrum. The difference between the measured and predicted wavelengths in the comparison arc-lamp spectra have an rms of 0.05 Å, corresponding to 3 km s⁻¹ at 5170 Å (i.e., the wavelength of the Mg i absorption triplet) in runs 1 and 2 and 2 km s⁻¹ at Hα in run 3. Systematic errors of the absolute wavelength calibration (⩽10 km s⁻¹) were estimated from the brightest night-sky emission lines in the observed spectral range (Osterbrock et al. 1996). The instrumental resolution in each run was derived as the mean of the Gaussian FWHMs measured for a number of unblended arc-lamp lines which were distributed over the whole spectral range of a wavelength-calibrated spectrum. The mean FWHM of the arc-lamp lines was 2.3 Å in run 1 and 2.4 Å in run 2 and the corresponding instrumental resolution was derived at 5170 Å is σ_inst ≃ 60 km s⁻¹. In run 3 the mean FWHM was 3.2 Å corresponding to σ_inst ≃ 60 km s⁻¹ at Hα. All the galaxy and stellar spectra were corrected for CCD misalignment. The sky contribution was determined by interpolating along the outermost 10''–30'' at the two edges of the slit, where the galaxy or stellar light was negligible, and then subtracted. A sky subtraction better than 1% was achieved. Each spectrum was flux-calibrated using the sensitivity function obtained from the flux standard star spectrum of the corresponding night. In each run the spectra obtained for the same galaxy along the same axis were coadded using the center of the stellar continuum as a reference, thus improving the signal-to-noise ratio (S/N) of the final two-dimensional spectrum. The spectra of the template stars were deredshifted to laboratory wavelengths.

The stellar kinematics of the galaxies was measured from the galaxy absorption features present in the wavelength range and centered on the Mg i line triplet (λλ5164, 5173, 5184) using the Penalized Pixel-Fitting (pPXF; Cappellari & Emsellem 2004) and Gas and Absorption Line Fitting (GANDALF; Sarzi et al. 2006) IDL⁹ codes adapted for dealing with MDM spectra.

The spectra of runs 1 and 2 were rebinned along the dispersion direction to a logarithmic scale, and along the spatial direction to obtain an S/N ⩾ 40 per resolution element. It decreases to S/N ≈ 20 per resolution element at the outermost radii. The quality of the final spectrum depends on the resulting S/N. Examples of central spectra obtained in runs 1 and 2 covering the quality classes listed in Table 2 are shown in Figure 3. The quality parameter is 1 for S/N ⩾ 100 per resolution element, 2 for 50 ⩽ S/N < 100, and 3 for 30 ⩽ S/N < 50.

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At each radius a linear combination of template stellar spectra from the empirical library by Sánchez-Blázquez et al. (2006, i.e., the MILES library) was convolved with the line-of-sight velocity distribution (LOSVD) and fitted to the observed galaxy spectrum by χ² minimization in pixel space. The LOSVD was assumed to be a Gaussian plus third- and fourth-order Gauss-Hermite polynomials ${\cal H}_3$ and ${\cal H}_4$, which describe the asymmetric and symmetric deviations of the LOSVD from a pure Gaussian profile (van der Marel & Franx 1993; Gerhard 1993). This allowed us to derive profiles of the line-of-sight velocity (v), velocity dispersion (σ), and third- (H₃) and fourth-order (H₄) Gauss-Hermite moments of the stars.

The galaxy spectra were convolved with a Gaussian function to match the MILES spectral resolution (FWHM = 2.5 Å; Beifiori et al. 2010). Bad pixels coming from imperfect subtraction of cosmic rays and sky emission lines were properly masked and excluded from the fitting procedure. Ionized-gas emission lines were simultaneously fitted and a fourth-order additive Legendre polynomial was added to correct for the different shape of the continuum in the galaxy and template spectra.

The uncertainties for the kinematic parameters were estimated by Monte Carlo simulations. The simulated spectra were obtained by convolving the template spectra with an LOSVD parameterized as a Gauss-Hermite series and adding photon, readout, and sky noise. The simulated spectra were measured as if they were real. Extensive testing was performed to provide an estimate of the biases of the pPXF method with the adopted instrumental setup and spectral sampling. No bias was found in the ranges of S/N and σ which characterize the spectra of the sample galaxies. The values of H₃ and H₄ measured for the simulated spectra differ from the intrinsic ones only within the measured errors.

The measured stellar kinematics are reported in Table 6 where velocities are relative to the galaxy centers. The folded kinematic profiles are plotted in Figure 4. The multiple observations of IC 171, NGC 679, and UGC 1308 agree within the errors.

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View extended figure (8 panels)

Figure 5 shows the comparison between the measurements of σ obtained along the major axis of the sample galaxies and values available in the literature. The mean difference in velocity dispersion with respect to the measurements by Wegner et al. (1999) is 〈Δlog σ〉 = 0.0008 ± 0.0054 and has a scatter σ_Δlog σ = 0.023. The central velocity dispersion of all the sample galaxies, except for NGC 712 and UGC 1308, was measured by Bernardi et al. (2002) and Wegner et al. (2003) too. The mean difference is 〈Δlog σ〉 = −0.012 ± 0.013 with σ_Δlog σ = 0.032. Our values thus agree with published data sets within their measured errors.

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Figure 6 shows the central values of σ obtained along the minor and diagonal axes of the sample galaxies as a variance-weighted mean of the values available within an aperture of 3''. They are plotted as a function of the corresponding values obtained along the major axis. Most of the data are consistent within 3σ errors. No systematic effects are observed for the remaining ones.

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The ionized-gas kinematics were measured from the emission lines present in the spectra of run 3, namely [N ii] λλ6548, 6583, Hα, [S ii] λλ6716, 6731. Each observed emission line was fitted by a Gaussian, while describing the stellar continuum with a low-order polynomial. The Gaussians were assumed to share the same line-of-sight velocity (v_gas) and velocity dispersion (σ_gas). A flux ratio of 1:2.96 was assumed for the [N ii] doublet, as dictated by atomic physics (e.g., Osterbrock 1989).

The best-fitting Gaussian parameters were derived using a nonlinear least-squares minimization based on the robust Levenberg–Marquardt method by Moré et al. (1980). The actual computation has been done using the MPFIT algorithm (Markwardt 2009) under the IDL environment. We averaged adjacent spectral rows to increase the S/N of the relevant emission lines. All the spectra of run 3 have S/N < 30 per resolution element in the continuum and were assigned to quality class 4 (Table 2). We checked that the error in the kinematic parameter determination derived by Monte Carlo simulations did not differ significantly from the formal errors given as output by the least-squares fitting routine. We therefore decided to assume the latter as error bars on the gas kinematics.

The measured ionized-gas kinematics are reported in Table 7 where velocities are given relative to galaxy centers and velocity dispersions are corrected for instrumental FWHM. The folded kinematic profiles are plotted in Figure 4.

The Mg, Fe, and Hβ line-strength indices were measured following Faber et al. (1985) and Worthey et al. (1994) from flux calibrated spectra obtained in runs 1 and 2. The average iron index 〈Fe〉 = (Fe₅₂₇₀ + Fe₅₃₃₅)/2 (Gorgas et al. 1990) and the combined magnesium–iron index with [MgFe] = (Mgb〈Fe〉)^1/2 (González 1993) were computed too. Spectra were rebinned in the dispersion direction as well as in the radial direction as before. The difference between our spectral resolution and that of the Lick/IDS system (FWHM = 8.6 Å; Worthey & Ottaviani 1997) was taken into account by degrading our spectra to match the Lick/IDS resolution before measuring the line-strength indices. The original Lick/IDS spectra are not flux-calibrated contrary to ours. Such a difference in the continuum shape is expected to introduce small systematic offsets of the measured values of the indices. To establish these offsets and to calibrate our measurements to the Lick/IDS system, the values of the line-strength indices measured for the templates were compared to those obtained by Worthey et al. (1994). Figure 7 shows the differences between our and Lick/IDS line-strength indices for the stars observed in runs 1 and 2. The offsets were evaluated as the mean of the differences between our and Lick/IDS line-strength values, and neglected if they were smaller than the mean error of the differences. The latter was the case for Hβ, Mg₂, and Mgb for which no offset was adopted. On the contrary, it was applied as an offset to the measured values of Fe₅₂₇₀ (ΔFe₅₂₇₀ = −0.29 Å for run 1, −0.28 Å for run 2) and Fe₅₃₃₅ (ΔFe₅₃₃₅ = −0.48 Å for run 1, −0.44 Å for run 2) to bring our data to the Lick/IDS system. No focus correction was applied because atmospheric seeing was the dominant effect during observations (see Mehlert et al. 1998 for details). Errors on indices were derived from photon statistics and CCD readout noise, and calibrated by means of Monte Carlo simulations.

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The measured values of Hβ, [MgFe], 〈Fe〉, Mgb, and Mg₂ are listed in Table 8 and plotted in Figure 4. Figure 6 shows the central values of Hβ, [MgFe], 〈Fe〉, Mgb, and Mg₂ obtained along the minor and diagonal axes of the sample galaxies as a variance-weighted mean of the values available within an aperture of 3'' and those obtained along the corresponding major axes. Most of the data are consistent within 3σ errors. No systematic effects are observed for the remaining ones.

The traditional and effective method of studying stellar-population properties uses diagrams of different pairs of line-strength indices. Here, the modeling of the line-strength indices measured in the previous section followed the method described in Saglia et al. (2010) and Pu et al. (2010). Among the measured line-strength indices, Hβ, 〈Fe〉, and Mgb were considered since Hβ is sensitive to early-type stars and thus useful as an age indicator, 〈Fe〉 gives the metal abundance, and Mgb covers the α-element abundance. The SSP models of Maraston (1998, 2005) and the models of Lick/IDS line-strength indices with the α-element overabundance of Thomas et al. (2003) were spline interpolated on a fine grid in age t (up to 15 Gyr on steps of 0.1 Gyr), metallicity [Z/H] (from −2.25 to 0.67 dex on steps of 0.02 dex) and overabundances [α/Fe] (from −0.3 to 0.5 dex on steps of 0.05 dex). At each radius r of the galaxies the best-fit values of τ, [Z/H], and [α/Fe] were determined by minimizing the χ² function

$$\begin{equation} \chi ^2(r)= \Delta ^2 {\rm H}\beta (r) + \Delta ^2 {\rm Mg}b(r) + \Delta ^2 \langle {\rm Fe} \rangle (r), \end{equation} \tag{ 1 }$$

where

$$\begin{equation} \Delta ^2 {\rm I} (r) = \left(\frac{{\rm I}(r) - {\rm I}_{\rm SSP}(\tau ,[Z/{\rm H}],[\alpha /{\rm Fe}])}{\sigma _{\rm I}(r)} \right)^2. \end{equation} \tag{ 2 }$$

Here σ_I(r) is the error on the index I(r) measured at a distance r and I_SSP(τ, [Z/H], [α/Fe]) is the value predicted by the SSP models for the given set of age, metallicity, and overabundance. As in Saglia et al. (2010) and Pu et al. (2010), the best-fit values of τ, [Z/H], and [α/Fe] are derived to the same accuracy through the χ² minimization by giving the same weight to Hβ, 〈Fe〉, and Mgb. We did not extrapolate to values outside the model grid. Therefore, the minimum χ² solutions are sometimes found at the edges of the parameter space. Once the set of best-fit values, i.e., the set (τ_min, [Z/H]_min, [α/Fe]_min) that minimizes χ²(r) was determined, we computed the values of the mass-to-light ratios of the corresponding SSP models for the Kroupa IMF (ϒ_Krou). The resulting values of ϒ_Krou, stellar-population ages, metallicities, and overabundances (inside r_eff) are given in Table 3. Errors on all quantities were derived by considering the minimal and maximal parameter variations compatible with Δχ² = χ² − χ²_min = 1. Note, however, that errors on age and metallicity are correlated to some extent (Worthey 1994).

Figure 8 compares the projected dynamical masses of the A262 galaxies with strong gravitational lenses from SLACS (Auger et al. 2009). The comparison is done exactly as in Thomas et al. (2011) and we refer the reader to this paper for further details. We find no significant differences between the A262 galaxies, Coma galaxies, and SLACS lenses, respectively. Note that the scatter in the dynamical masses is not larger than in the lensing masses. This implies that possible biases in the dynamical modeling related to spatially limited kinematic observations and/or symmetry assumptions are unlikely (as they would increase the scatter in dynamical masses of galaxies observed at random viewing angles). That the Coma and A262 galaxies must have nearly axisymmetric shapes is consistent with the lack of isophotal twists or minor-axis rotation in the photometric and kinematic observations, respectively (except for IC 171 and NGC 708; cf. Section 6.2).

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Figure 10 compares the circular velocity v_circ obtained from stellar dynamics and rotation velocity v_rot of the ionized gas. The comparison is restricted to radii r_gas where the pressure support in the gas component is small (σ_gas ⩽ 60 km s⁻¹) and therefore the gas velocity is supposed to trace v_circ (Bertola et al. 1995; Pignatelli et al. 2001; Dalcanton & Stilp 2010). The line-of-sight gas velocity v_gas is derived from the observed one after subtracting the systemic velocity and folding around the galaxy center. It was deprojected into v_rot by assuming that the gaseous component rotates in circular orbits in an infinitesimally thin disk. The orientation of the gaseous disk with respect to the line of sight is given by its inclination (i_gas) and the P.A. of its line of nodes (P.A._gas). Therefore, it is

$$\begin{equation} v_\mathrm{rot} = \frac{v_\mathrm{gas}}{\sin {i_\mathrm{gas}} \cos {\vartheta }}, \end{equation} \tag{ 8 }$$

where

$$\begin{equation} \vartheta = \arctan {\frac{\tan {\Delta \mathrm{P.A.}_\mathrm{gas}}}{\cos {i_\mathrm{gas}}}} \end{equation} \tag{ 9 }$$

and

$$\begin{equation} \Delta \mathrm{P.A.}_\mathrm{gas} = \mathrm{P.A.}_\mathrm{gas}- \mathrm{P.A.}_\mathrm{slit}. \end{equation} \tag{ 10 }$$

P.A._slit is the position angle of the slit where v_gas is measured. Likewise, the deprojected radius is

$$\begin{equation} r = r_\mathrm{gas} \cos {\vartheta } \cos {\Delta \mathrm{P.A.}_\mathrm{gas}}. \end{equation} \tag{ 11 }$$

In an axisymmetric spheroidal system, the position angle P.A._stars of the stellar isophotes is constant with radius and a rotating gaseous disk is confined to the equatorial plane. Hence, the unique stellar P.A._stars coincides with the P.A._gas of the gaseous disk. The same holds the for the inclinations. For the ionized-gas component of the A262 galaxies we only have observations along a few slits and can neither verify the assumption of an infinitesimally thin disk nor, given the case, derive its orientation (i.e., P.A._gas and i_gas) directly. Therefore, we performed two different deprojections of the gas kinematics for each galaxy.

First, we assumed that the galaxy is an axisymmetric spheroid and deprojected the gas kinematics with i_gas = i_stars and P.A._gas = P.A._stars from the dynamical model (Table 4). The corresponding values v_rot are open dots in Figure 10 (when missing, they fall outside the plot range). We used i_gas = 85° when the dynamical model has i_stars = 90° since an infinitesimally thin and exactly edge-on gas disk would not be observable at any P.A. different from the galaxy's major axis.

Second, since the isophotal P.A. of the A262 galaxies shows some scatter, we varied i_gas and P.A._gas and minimized the χ²-difference between v_rot and v_circ. The P.A._gas was changed between the minimum and maximum values measured for the P.A. of the galaxy isophotes. The best-fitting values of v_rot are shown by the filled circles in Figure 10. For each galaxy, the figure also quotes i_gas and P.A._gas for both sets of deprojection. IC 171 was treated separately, as discussed below.

As Figure 10 shows, using the same P.A. and i for both the gaseous disks and dynamical models did not yield good agreement between v_rot and v_circ. However, varying i_gas and P.A._gas allowed matching the gas kinematics with predictions of the dynamical models quite well. The corresponding inclinations i_gas differ from the i_stars values of the dynamical models by less than 10°. The inclination of an elliptical galaxy can, at best, be derived dynamically with an uncertainty of ±20° (e.g., Krajnović et al. 2005; Thomas et al. 2005b; van den Bosch & van de Ven 2009). Thus, a Δi ⩽ 10° is well within the uncertainties of the dynamical models.

The case for the P.A.s is more complicated. To ease the comparison with the orientation of the stars in the galaxies, the P.A. panels in Figure 2 show the P.A.s adopted in the two deprojection sets. The red solid line corresponds to P.A._gas = P.A._stars and gives the open circles for v_rot plotted in Figure 10. The gray solid line marks the gas orientation that minimizes the χ² between gas rotation and dynamical v_circ and leads to the filled circles for v_rot given in Figure 10. The dotted lines in Figure 2 delimit the 68% confidence region of P.A._gas.

The ionized-gas kinematics for our A262 galaxies has limited spatial coverage and radial extension because only a few slits were observed. Nevertheless, this gives a valuable consistency check. Within the above limitations and when σ_gas ⩽ 60 km s⁻¹, the gas rotation velocity is consistent with the circular velocity obtained from our axisymmetric dynamical models and supports to the total mass distributions we derived. This holds also for IC 171 and NGC 708, which are not exactly axisymmetric systems.

In the following we discuss the A262 galaxies individually, except for NGC 679 and NGC 687, which show no detectable emission line.

IC 171. The observed isophotal twist (Figure 2) suggests that IC 171 is not exactly axisymmetric, similar to NGC 708. Moreover, v_rot do not match the dynamical v_circ for any P.A. within the observed range. If IC 171 is triaxial, the gas might also be rotating around the long axis of the galaxy. To test this geometric configuration, we tried a variety of different P.A._gas tilted by about 90° with respect to the photometric major axis, fixing the inclination at i_gas = 85°. A P.A._gas = 13° brings v_rot in agreement with v_circ. If the gas rotates around the long axis of the galaxy, then the line of nodes of the gaseous disk is at P.A. = 103°. This value is consistent with the orientation of the galaxy isophotes at the corresponding deprojected radii (r ≳ 3 kpc, Figure 2).

NGC 703. The isophotes show little variation in P.A. over all the observed radii (30° ≲ P.A. ≲ 50°, Figure 2). We found P.A._stars ≈ P.A._gas and i_stars ≈ i_gas within the scatter of the data after minimizing the χ² difference between dynamical circular velocity and gas rotation velocity (Figure 10). The photometric and kinematic data are consistent with our assumptions about both the stellar and gaseous components.

NGC 708. The inner and outer isophotes (r ≲ 2.5 kpc) have different orientations (Figure 2). The dynamical model was adjusted toward the galaxy center, where the stellar kinematics were measured (Figure 4) and the largest stellar rotation is at P.A. = 130°. It vanishes at P.A. = 40°, indicating that the P.A. of the galaxy's line of nodes is close to the P.A._stars = 130° adopted for the dynamical model. The gas rotation differs as it is large along all the observed slits (Figure 4) and the derived P.A._gas is close to the P.A. measured for the outer isophotes and v_rot best matches v_circ for a nearly edge-on gas disk with P.A._gas = 34°. For i_gas = 80° the deprojected radii (r ≈ 7 kpc; Figure 10) fall into the region where the stellar system has a photometric P.A. ≈ 40° (Figure 2). The twist of the isophotes indicates that the system cannot be exactly axisymmetric. However, as P.A._gas is consistent with the stellar orientation at the corresponding radii we infer that NGC 708 is probably only mildly triaxial and that its dynamical mass is reliable.

NGC 712. The emission-line spectrum was taken close to the galaxy minor-axis, making deprojection of v_gas highly uncertain. The measured rotation velocities are low (Figure 4) and, therefore, consistent with a gaseous disk with the same i_gas = i_stars and P.A._gas = P.A._stars as adopted in the dynamical model of the galaxy.

NGC 759. The P.A. of the isophotes of NGC 759 ranges between about 10° and 50° beyond radii of 0.1 kpc (Figure 2). The gas kinematics was measured along three different axes and has a regular and symmetric rotation curve and velocity dispersion profile (Figure 4). We found P.A._stars ≈ P.A._gas and i_stars ≈ i_gas (Figure 10) confirming the orientation and intrinsic shape obtained from the stellar dynamics.

UGC 1308. The orientation of the isophotes scatters significantly within 2 kpc, but it is constant at larger radii. For the dynamical model we adopted P.A._stars = 110°, which is representative of the orientation of the major axis of the isophotes at r ≳ 2 kpc (Figure 2). A much smaller P.A._gas = 47° is needed to match v_rot measured along a diagonal axis with v_circ from stellar dynamics. However, the uncertainties in P.A._gas are large and the predictions of the dynamical model are formally consistent with the gas rotation. Also the measured photometric P.A. has large uncertainties because the galaxy is pretty round ( ≲ 0.2; Figure 2).

Figure 9 shows the χ² of Equation (7) against the dynamical mass-to-light ratios ϒ_* for the A262 galaxies. Three parameter fits including a logarithmic dark halo component ρ_halo = ρ_LOG (Equation (5); the three parameters are ϒ_*, r_c, and V_c) are displayed by solid lines and we marginalized over the halo parameters. Similarly, NFW halos are shown by the dashed lines and the dotted curves are for models in which all the mass follows the light (ρ_halo ≡ 0).

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The kinematics of NGC 679, NGC 687, and NGC 759 cannot be fit without ρ_halo > 0. The statistical significance is at least 3σ and the dark halos dominate beyond r ≈ 1.7 r_eff, 1.4 r_eff, and 1.0 r_eff, respectively (Figure 10). These radii are only slightly larger than the radius r_max of the farthest kinematic data point. For IC 171 evidence for ρ_halo > 0 is about 2σ and the dark halo outweighs the mass following the light beyond r ≈ 2.9 r_eff, which is significantly on the far side of r_max. For the remaining objects (NGC 703, NGC 708, NGC 712, and UGC 1308) a second mass-component ρ_halo does not improve the fit significantly. In fact, the best-fitting models of NGC 708, NGC 712, and UGC 1308 are obtained without any dark matter in a halo with a different mass distribution than the stars, while the best-fit halo-mass fraction inside r_eff in NGC 703 is f_halo = 0.001, its upper limit f_halo ⩽ 0.06.

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In the Coma galaxy sample of Thomas et al. (2007b) the statistical significance for dark halos is over 95% for 8 (out of 17) galaxies and the halo mass takes over the mass that follows the light roughly between r_eff and 2 r_eff. IC 171, NGC 679, NGC 687, and NGC 759 have comparable dark halos. In Coma, however, we found only one galaxy with f_halo ≈ 0 (GMP 1990; Thomas et al. 2007b), whereas the A262 sample reveals four (out of eight) galaxies of this kind.

Evidence for a dark component aside from mass that follows light is not directly connected to the spatial extent of the kinematic data (indicated by the dashed horizontal lines in Figure 10). For example, the presence of halo mass in NGC 759 is highly significant, even though r_max < r_eff. By contrast, our measurements reach r_max ≈ 1.5 r_eff in NGC 712 yet the mass distribution follows the light almost exactly. Likewise, in the Coma galaxy GMP 1990 mass follows light out to r_max ≈ 3 r_eff. The kinematic evidence for extra mass beyond the light is also not coupled to the degree of rotation or flattening. For example, UGC 1308 is round and shows almost no rotation, whereas NGC 712 is a moderately flattened, strong rotator and the Coma galaxy GMP 1990 is a highly flattened (_max ≈ 0.6) fast rotating system as well.

As already noted for the Coma galaxies, we cannot discriminate between NFW halos and logarithmic halos based on the quality of the kinematic fits. There is only one A262 galaxy where NFW halos fit worse by Δχ² ≈ 2 (NGC 703); in all other galaxies the difference is Δχ² ⩽ 1.

The two upper panels of Figure 11 plot ϒ_* and the corresponding SSP ϒ_Krou values as a function of σ_eff, i.e., the velocity dispersion averaged within r_eff. The galaxies of A262 follow trends very similar to the galaxies in the Coma Cluster. While the dynamically determined ϒ_* increases strongly with σ_eff, the SSP models result in almost constant ϒ_Krou. This implies that the ratio ϒ_*/ϒ_Krou increases with σ_eff, as shown explicitly in the bottom panel of Figure 11.

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Around σ_eff ≈ 200 km s⁻¹ the distribution of ϒ_*/ϒ_Krou has a sharp cutoff with almost no galaxy below ϒ_*/ϒ_Krou = 1 (Figure 11, bottom panel). For σ_eff ≳ 250 km s⁻¹ the lower bound of ϒ_*/ϒ_Krou increases to ϒ_*/ϒ_Krou ≳ 2 at σ_eff ≈ 300 km s⁻¹. Similar trends are also observed in the SAURON sample (Cappellari et al. 2006; cf. the triangles in the bottom panel of Figure 11), in SLACS galaxies (Treu et al. 2010; squares in Figure 11) and, recently, in the ATLAS3d survey (Cappellari et al. 2012).

Figure 12 displays the average dark halo densities 〈ρ_halo〉 inside 2 r_eff of Coma and A262 galaxies against the dynamical mass that follows the light M_* = ϒ_* × L. In contrast to the Coma galaxies not all the A262 galaxies have denser dark halos than spirals. For the three A262 galaxies closest to the spiral galaxy scaling relations (NGC 703, NGC 708, and UGC 1308) we can only determine upper limits for the amount of mass that is distributed unlike the light. In these cases, models without a halo fit the data equally well within the uncertainties, or even better than models with a halo.

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Still, the majority of cluster early types has 2–10 times denser halos than local spirals, implying a 1.3–2.2 times higher (1  +  z_DM) (assuming 〈ρ_DM〉 ∼ (1  +  z_DM)³). Thus, if spirals typically formed at z ≈ 1, then cluster ellipticals assembled at z_DM ≈ 1.6–3.4.

Averaging over all A262 galaxies we find that a fraction of 〈f_halo〉 = 0.19 of the total mass inside r_eff is in a dark halo distinct from the light. The mean over the Coma galaxies is 〈f_halo〉 = 0.23 and similar fractions come from other dynamical studies employing spherical models (e.g., Gerhard et al. 2001; Tortora et al. 2009). The A262 and Coma samples indicate an anti-correlation between ϒ_*/ϒ_Krou and 〈f_halo〉. Galaxies where the dynamical mass following the light exceeds the Kroupa value by far (ϒ_*/ϒ_Krou > 3) seem to lack matter following the halo distribution inside r_eff (〈f_halo〉 = 0.004). This is not so in galaxies near the Kroupa limit (ϒ_*/ϒ_Krou < 1.4), where the dark-halo mass fraction is at its maximum (〈f_halo〉 = 0.30). The remaining galaxies are intermediate in both their ϒ_*/ϒ_Krou and their halo-mass fractions (〈f_halo〉 = 0.22). We will return to this anti-correlation in Section 8.1.

One extreme point of view is the assumption that the stellar masses in early-type galaxies are maximal, i.e., ϒ_stars = ϒ_* (in analogy to the maximum-disk interpretation of spiral galaxy rotation curves; e.g., van Albada & Sancisi 1986). The immediate consequence is that the stellar IMF in early-type galaxies is not universal. While around σ_eff ≈ 200 km s⁻¹ there are some galaxies with ϒ_* ≈ ϒ_Krou such galaxies are lacking at higher dispersions σ_eff (Figure 11). Recent attempts to try and measure the stellar IMF directly from near-infrared observations point in the same direction (van Dokkum & Conroy 2010, 2011; Conroy & van Dokkum 2012). These spectroscopically derived IMFs (Salpeter or steeper around σ_eff ≈ 300 km s⁻¹) correspond to ϒ_*/ϒ_Krou ≈ 1.6 or larger (consistent with Figure 11) favoring the maximum stellar mass interpretation and an IMF varying from Kroupa-like at low velocity dispersions to Salpeter (or steeper) in the most massive early types.

As already noted for the Coma galaxies (Thomas et al. 2011), we do not see any correlation of ϒ_*/ϒ_Krou and the SSP ages, metallicities, and α-element overabundances of the A262 galaxies. Such correlations could be expected if the IMF is variable, since a change in the relative number of low- and high-mass stars has some influence on the chemical evolution of the galaxies (e.g., Graves & Faber 2010). However, the stellar IMF acts on the metallicities and element abundances simultaneously with other variable conditions such as the depth of the potential well and star formation timescale. Hence, the lack of significant stellar-population differences between galaxies with high ϒ_*/ϒ_Krou on the one hand and galaxies with low ϒ_*/ϒ_Krou on the other is inconclusive with respect to the IMF.

An intriguing observation is the fact that the galaxies with the highest ϒ_*/ϒ_Krou in the A262 and Coma Clusters (ϒ_*/ϒ_Krou > 3) have the lowest dark matter fractions (〈f_halo〉 ≈ 0). In contrast, galaxies with ϒ_*/ϒ_Krou < 1.4 have the highest dark matter fractions (〈f_halo〉 = 0.30). Such an anti-correlation between ϒ_*/ϒ_Krou and f_halo can easily be understood if the occasionally large ϒ_* in some galaxies results from their dark matter density following the light so closely that it becomes indistinguishable from the stellar mass (at least in the inner parts at r ≲ r_eff considered here). The more that the actual dark matter of a galaxy leaks into the mass component of our models that follow the light, the less it is expected to reside in its nominal halo component ρ_halo, resulting in the observed anti-correlation between f_halo (measuring only the dark matter in the halo) and ϒ_*/ϒ_Krou (also including the dark matter following the light). We are not aware of an immediate physical explanation why a more "massive" IMF should occur in galaxies with less dark matter.

One option to further constrain the mass decomposition of gravity-based models is to incorporate predictions from cosmological simulations that confine the maximum amount of dark matter that can be plausibly attached to a galaxy of a given stellar mass. Napolitano et al. (2010) found that the velocity dispersions of a large sample of low-redshift early-type galaxies require high central mass-to-light ratios for the stars (consistent with a Salpeter IMF on average) when using such cosmological halos without baryon contraction. Adiabatic contraction (Blumenthal et al. 1986), instead, is able to increase the amount of dark matter in the centers of ellipticals and to lower the required stellar masses toward a Kroupa IMF (see also Napolitano et al. 2011). The recent study of Cappellari et al. (2012), using the halo-contraction scenario of Gnedin et al. (2004, 2011), finds that the IMF varies systematically with mass in early-type galaxies, which points against halo contraction to be sufficient to lower the central stellar masses. Lensing studies go in the same direction (Auger et al. 2010) and numerical simulations generally indicate that the classic adiabatic scenario overpredicts the actual contraction of dark matter halos (e.g., Gnedin et al. 2004).

Therefore, while halo contraction could in principle reconcile the observed central dynamical masses with a "light" stellar IMF, the required amount of dark matter contraction seems to be rather strong. However, this constraint against a "light" IMF is not purely empirical and we here briefly discuss the halo assembly redshifts of the A262 and Coma galaxies that result in the context of a Kroupa IMF and adiabatic contraction.

An immediate consequence of a universal Kroupa IMF is that some of the mass that follows the light is actually dark matter and needs to be combined with ρ_halo, i.e.,

$$\begin{equation} \rho _\mathrm{DM,Krou} = \rho _\mathrm{halo}+ (\Upsilon _\mathrm{\ast }-\Upsilon _\mathrm{Krou}) \times \nu. \end{equation} \tag{ 14 }$$

The effect is to increase the dark matter fractions by about a factor of two; for example it is 〈f_{DM, Krou}〉 = 0.47 in the A262 sample and the same within errors in the Coma Cluster (Thomas et al. 2011). Dark matter fractions of ≈50% or more are generally found and required in the context of the assumption of a "light" IMF (e.g., Napolitano et al. 2010; Barnabè et al. 2011).

Based on ρ_{DM, Krou} we derived the dark-halo assembly redshift z_DM for the A262 galaxies following Thomas et al. (2011). The basic assumption is that the (decontracted) halo density scales with the mean density of the universe at the assembly epoch, i.e., 〈ρ_DM〉 ∼ (1  +  z_DM)³. Figure 13 compares the values of z_DM to the star formation redshifts z_* calculated from the stellar-population ages.

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The derivation of z_DM involves the adiabatic decontraction of the dark matter density ρ_{DM, Krou}. In NGC 687 and UGC 1308, the dynamical ϒ_* turns out to be lower than ϒ_Krou, such that the dark halo to be decontracted for NGC 687 would be exactly cored logarithmic. However, the adiabatic decontraction of cored logarithmic halos is not possible (cf. Thomas et al. 2011) and NGC 687 has been omitted from the analysis. The dynamical model of UGC 1308 formally leaves no space for dark matter at all and this galaxy is also not considered in further analysis.

For the A262 galaxies in Figure 13 we estimated the uncertainty in z_DM that comes from the scatter in the correlation between 〈ρ_DM〉 and (1 + z_DM)³ derived from cosmological simulations (see Figure 9 in Thomas et al. 2009b). Note that this does not include the uncertainties in ρ_halo or any uncertainties related to the contraction scenario. In the majority of Coma galaxies z_DM ≈ z_* and the assembly of these galaxies seems to have stopped before z_DM ≈ 1. In four Coma and three A262 galaxies the stars appear younger than the halo, which indicates a secondary star formation episode after the main halo assembly.

In one Coma galaxy (GMP 5568) z_DM is significantly smaller than z_*. The r_eff of GMP 5568 is, however, about three times larger than expected for its B-band luminosity, when compared to the rest of the Coma sample. The average of its dark halo density is low because of this change in the physical scale (Thomas et al. 2011). In the A262 cluster we found two galaxies with z_DM < z_* as well (IC 171 and NGC 708). Both galaxies have significant isophote twist (Section 6.2) and, in addition, IC 171 has boxy outskirts (Figure 2) while NGC 708 is a very slow rotator (Figure 4). The two galaxies may therefore be the remnants of gas-poor binary mergers. The virial theorem predicts the average density to drop by a factor of four during such a merger (assuming homology and equal-mass progenitors), whereas the stellar z_* remains constant (assuming similar stellar-population ages for the progenitors) due to the lack of gas available to form new stars. Thus, gasless major mergers move galaxies downward in Figure 13. In fact, the approximate decrease of the mean density to a quarter of its original value implies assembly redshifts of the hypothetical progenitors to be z_DM ≈ 1.7 and z_DM ≈ 1.9 for IC 171 and NGC 708, respectively. Hence, if the two galaxies have actually recently undergone a major merger, then their progenitors may well have originated from the vicinity of the one-to-one relation in Figure 13 where we find the majority of early-type galaxies with homogeneously old stellar populations.

Without trying to overinterpret the result given the assumptions going into Figure 13 (i.e., SSP models, cosmological relations between halo density and formation redshift, and halo contraction), it seems that a universal Kroupa IMF gives a consistent picture for the formation redshifts of our galaxies.

Apart from baryonic contraction, the central dark matter and stellar mass profiles could also become similar as a result of violent relaxation. This is usually invoked to explain the orbital structure of elliptical galaxies formed via collapse or merging (Lynden-Bell 1967; Nakamura 2000). Although many of its details are not fully understood (e.g., Arad & Lynden-Bell 2005), some general predictions can be made in the simplest cases of gas-rich (wet) and gas-poor (dry) major mergers, but it is apparent that their general evolution can be more complex. Hilz et al. (2012) further illustrate how violent relaxation in a galaxy can make the luminous and dark matter profiles similar.

In this paper, we have added data for some A262 early-type galaxies to those of our previously studied Coma galaxies. We derived the redshifts from when the stars and the dark matter halos formed and compared the profiles of the luminous and dark matter components. Some of this information could be interpreted as being consistent with signatures of violent relaxation. In particular, there are two pieces of evidence that are consistent with violent relaxation. The first is the division of the ellipticals into the two merger types as shown in Figure 13 and explained by models. Indeed recent analyses of the light distributions and dynamics of ellipticals support a picture requiring violent relaxation (Cox et al. 2006; Hopkins et al. 2009a, 2009b; Hoffman et al. 2010) with the conclusion that cuspy ellipticals grew from the mergers of gas-rich spirals while core ellipticals resulted from mergers of earlier gas-poor ellipticals with the orbital and mass distributions of the merger remnants providing a record of their progenitors (cf. Benson 2010 for a review). The second comes from Figures 10 and 11. If one makes the assumption that the stellar IMF is fixed, then the stellar and luminous matter distributions are close to being the same in several of the galaxies, which is what would be expected from violent relaxation in the merging that formed them.

Nevertheless, there are problems from some of the other galaxies. The dark matter follows the light closely in both the A262 galaxy NGC 712 and Coma galaxy GMP 1990. They are fast flattened rotators and show the least randomized orbital motions. Moreover, GMP 1990 is a highly flattened system and, taking the model results at face value, the assumption of a Kroupa IMF for this galaxy requires a highly flattened dark matter component ρ_{DM, *}. However, as we have not tried to fit a continuous sequence of ever more flattened halos to the kinematic data, it is not clear if a model where all the mass exactly follows the light is the only way to explain the observational data. In fact, the preference for a high ϒ_* in the models could just reflect that the actual dark halo is flatter than the (spherical) ρ_halo, though still rounder than the light distribution—on a level that the data are just better approximated by increasing the mass that follows the light rather than to make the spherical component ρ_halo more massive. The actual flattening of the galaxy's potential might be somewhere in between that of the light and ρ_halo (spherical). Lensing galaxies do not show a significant difference between the flattening of their total mass distributions and that of their light, at least not the massive ones (Koopmans et al. 2006; Barnabè et al. 2011). If this also holds for the galaxies studied here, then either the mass that follows the light is indeed stars, or, if not, then there has to be a dark matter component that is as flattened as the stellar distribution (_max ≈ 0.6).

Admittedly, we are dealing with a small sample of imperfect observations, but at present it appears that the best one can conclude is that these data do not offer strong proof for violent relaxation being a major mechanism to make the distributions of stars and dark matter sufficiently similar.

Further numerical investigations are required to test if a predominantly collisionless accretion growth of the outer parts of massive early types can lead to a similarity of the mass-density profiles of stellar and dark matter. Simulations show that accreted stars have shallower radial mass profiles than in situ formed stars (Naab et al. 2009). Since the dark matter accretion is collisionless as well, the stellar and dark matter profiles around r_eff (where accreted stars are expected to dominate) might be similar.

Finally, we note that it seems unlikely that uncertainties in the modeling process (due to limited kinematic observations and/or symmetry assumptions) can explain the particularly large mass-to-light ratios of some early-type galaxies. This is mainly because our total (i.e., luminous and dark) dynamical masses are consistent with completely independent results from strong gravitational lensing and from our gas rotation velocities being consistent with the circular velocities derived from dynamical modeling.