The SAURON project - IV. The mass-to-light ratio, the virial mass estimator and the fundamental plane of elliptical and lenticular galaxies

TL;DR

This work uses SAURON integral-field data and advanced dynamical modelling (MGE-based Jeans and Schwarzschild orbit-superposition) for 25 early-type galaxies to measure dynamical mass-to-light ratios. It finds a tight M/L–$\sigma$ relation, with $(M/L)$ scaling as $3.80\left(\sigma_e/200\right)^{0.84}$, and demonstrates that the Fundamental Plane tilt is largely due to real M/L variations rather than structural non-homology. A direct virial estimator, calibrated by a best-fit factor $\beta \approx 5.0$, provides unbiased M/L estimates comparable to full dynamical models, supporting its use in high-redshift studies. Comparison with stellar-population M/L indicates a median dark matter fraction inside the effective radius of ~30%, and a modest IMF variation (Kroupa-like) improves agreement with dynamics, highlighting the interplay between stellar populations and dark matter in shaping central galaxy mass budgets.

Abstract

We investigate with unprecedented accuracy the correlations between the dynamical mass-to-light ratio M/L and other global observables of E and S0 galaxies. We construct two-integral Jeans and three-integral Schwarzschild dynamical models for a sample of 25 E/S0 galaxies with SAURON integral-field stellar kinematics. We find a tight correlation of the form (M/L)=(3.80+/-0.14)*(sigma/200 km/s)^(0.84+/-0.07) between the dynamical M/L (in the I-band) and the luminosity-weighted second moment (sigma) of the line-of-sight velocity-distribution within Re. The observed rms scatter in M/L for our sample is 18%, while the inferred intrinsic scatter is ~13%. The (M/L)-sigma relation can be included in the remarkable series of tight correlations between sigma and other galaxy global observables. The comparison of the observed correlations with the predictions of the Fundamental Plane (FP), and with simple virial estimates, shows that the `tilt' of the FP of early-type galaxies, is due to a real M/L variation, while structural and orbital non-homology have a negligible effect. The virial mass is a reliable estimator of the mass in the central regions of galaxies. The best-fitting virial relation has the form (M/L)_vir=(5.0+/-0.1)*Re*sigma^2/(L*G). The comparison of the dynamical M/L with the (M/L)_pop inferred from the analysis of the stellar population, indicates a median dark matter fraction in early-type galaxies of ~30% of the total mass inside one Re. (Abridged)

Figures (19)

• Figure 1: Top Panel: match between the photometric profile of NGC 3379 derived from the WFPC2/F814W (red solid line) and MDM images (diamonds). The sky-level of the WFPC2 image and the scaling factor of the MDM image are the free parameters of the fit. The flattening in the central ground-based profile is due to saturation of the image inside $R\la3\arcsec$. The fit was performed in the region between the two vertical dotted lines, where the WFPC2 and MDM profiles overlap, while excluding the innermost 3 to avoid PSF and saturation effects. Bottom Panel: fit of a de Vaucouleurs $R^{1/4}$ growth curve (green solid line) to the combined WFPC2$+$MDM observed aperture photometry (diamonds). The two vertical dotted lines define the boundaries of the region that was included in the fit, which is limited to 200 to reduce uncertainties due to the sky subtraction and contamination from nearby galaxies or foreground stars. The solid vertical line marks the location of $R_{\rm e}$.
• Figure 2: Luminosity-weighted second moment of the line-of-sight velocity distribution within an aperture of radius $R$, normalized to its value at $R_{\rm e}/2$ (see text details). This plot shows, with the thin coloured lines, all the 40 E/S0 galaxies in the SAURON sample for which $R_{\rm e}/2$ is not larger than the field-of-view. The open circles represent the biweight mean of all the curves at every given radius. The number of measurements sampled at every radius is not constant, moreover there are significant galaxy-to-galaxy variations in the profiles. The thick black line is a power-law relation $\sigma_R\propto R^{-0.066}$ which has an exponent defined by the biweight mean of the individual values for every galaxy. The dashed lines indicate the standard deviation in the individual slopes. The galaxy with the largest increase of the $\sigma_R$ profile at large radii is NGC 4550 (see Paper III).
• Figure 3: Contours of the surface brightness of NGC 3379 (in 0.5 mag arcsec$^{-2}$ steps) at three different scales. Top Panel: 35$\times$35 PC1 WFPC2 CCD. Middle Panel: the whole 160$\times$160 WFPC2 mosaic. Bottom Panel: 171$\times$171 MDM image. North is up and east is to the left. The location on the MDM field of the L-shaped WFPC2 mosaic is also shown. The galaxy at the left of the frame is NGC 3384, which was masked during the MGE fit. Superposed on the three plots are the contours of the constant-PA MGE surface brightness model, convolved with the PSF of each observation. The MGE model was fitted simultaneously to all three images.
• Figure 4: Relative variation of $M/L$ predicted from the virial equations as a function of inclination, for MGE models with different constant observed axial ratios $q'$ going from an observed flat galaxy $q'=0.3$ (green line) to an observed round object $q'=0.9$ (red line). At each observed axial ratio the density is assumed to be rounder than an extreme value of $q=0.1$. Note the small variation $\la10$% of the $M/L$ estimate at different inclinations, for $q'\la0.7$.
• Figure 5: Top Panel: black lines, from bottom to top, circular velocity $v_c$, as a function of radius $R$, of a spherical Hernquist galaxy model, with a dark halo described by a logarithmic potential, for four different values of the asymptotic halo velocity $v_0=0,0.15,0.30,0.45$. The contribution to the circular velocity of the dark halo component alone is shown with the red lines. The three vertical dashed lines indicate the position of 1, 2 and 3 half-light radii of the model. Middle Panel: Projected velocity dispersion $\sigma_p$ for the same four models shown in the top panel. The lowest curve is the Hernquist model without a dark halo ($v_0=0$). Bottom Panel: same as in the middle panel, for the luminosity-weighted aperture velocity dispersion $\sigma_{\rm R}$. This is the same quantity which is plotted in Fig. \ref{['fig:sigma_aper']} for the real galaxies.