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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 rho propto 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 gamma, Rusin & Kochanek [11] find that their sample of galaxies is better represented by nearly isothermal profiles, with an evolution of M / LB with redshift given by d log(M / LB) / 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 / LB) / 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 rho propto r-gamma, to compare the expected dispersion with the measured SDSS values. They finally solved for the combined probability to estimate gamma, and found slopes still consistent with isothermal spheres (gamma = 2) within Re / 2 , with no significant evolution with redshift (Fig. 3).

Figure 3

Figure 3. Logarithmic density slope gamma 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 Mvir 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 Mvirpropto L1.5, and a lower stellar mass fraction in earlier-type galaxies.

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