3. LENSING

As mentioned above, the main uncertainties in the determination of mass profiles from X ray studies result from the assumption of a spherical halo in hydrostatic equilibrium as well as from the difficulty to remove the background and point-like sources. Any technique has its own limitations, and it is therefore important to test various methods to gain confidence in the obtained results. Strong lensing is a gravitational effect and is therefore a natural path to probe mass in galaxies. This requires first accurate and high signal-to-noise imaging of the system, and usually assumes an a priori form for the underlying lens (e.g., isothermal sphere with r^-2). Such a technique has recently been mastered by Rusin & Kochanek [11] who used a sample of 22 lenses and the constraints provided by the fundamental plane to probe the mass profiles of early-type galaxies. As this study applies to the global sample of galaxies, it additionally assumes homology and a similar history. Optimising for the logarithmic density slope , Rusin & Kochanek [11] find that their sample of galaxies is better represented by nearly isothermal profiles, with an evolution of M / L_B with redshift given by d log(M / L_B) / dz = -0.5 ± 0.19, consistent with, e.g., the previous constraint obtained by van Dokkum et al. [12] of -0.8 < d log(M / L_B) / dz < -0.4. A Salpeter IMF would then requires a mean star formation redshift at z > 1.5.

A similar analysis but more detailed analysis was performed by Treu et al. [13] and Koopmans et al. [10] who made a joint stellar dynamical and strong lensing analysis of 15 early-type galaxies with redshift 0.06 < z < 0.33 (Sloan Lens ACS Survey, SLACS). Velocity dispersions σ were obtained from the SDSS project, and ACS/HST data were used to derive the lensing parameters. After deriving the mass within the Einstein radius, the Jeans Equations were solved assuming isotropy and a density profile of the form r^-, to compare the expected dispersion with the measured SDSS values. They finally solved for the combined probability to estimate , and found slopes still consistent with isothermal spheres ( = 2) within R_e / 2 , with no significant evolution with redshift (Fig. 3).

Figure 3. Logarithmic density slope of field galaxies plotted against redshift. The grey box indicates the rms spread of 0.19. Extracted from Koopmans et al. [10] (see paper for details).

Weak lensing studies were also used by e.g., Hoekstra et al. [14], to constrain the Virial mass M_vir of galaxies. The measured signal probe then the average properties for a sample of relatively isolated galaxies, still allowing to examine the behaviour of mass in 7 bins of luminosity. Their results are consistent with a scaling of M_vir L^1.5, and a lower stellar mass fraction in earlier-type galaxies.