Separating inner and outer contributions in gravitational lenses using the perturbative method

This paper presents a reconstruction of the gravitational lens SL2S02176-0513 using the singular perturbative method presented in Alard 2007, MNRAS Letters, 382, 58 and Alard, C., 2008, MNRAS, 388, 375. The ability of the perturbative method to separate the inner and outer contributions of the potential in gravitational lenses is tested using SL2S02176-0513. In this lens, the gravitational field of the central galaxy is dominated by a nearby group of galaxies located at a distance of a few critical radius. The perturbative functionals are re-constructed using local polynomials. The polynomial interpolation is smoothed using Fourier series, and numerically fitted to HST data using a non-linear minimization procedure. The potential inside and outside the critical circle is derived from the reconstruction of the perturbative fields. The inner and outer potential contours are very different.The inner contours are consistent with the central galaxy, while the outer contours are fully consistent with the perturbation introduced by the group of galaxies. The ability of the perturbative method to separate the inner and outer contribution is confirmed, and indicates that in the perturbative approach the field of the central deflector can be separated from outer perturbations. The separation of the inner and outer contribution is especially important for the study of the shape of dark matter halo's as well as for the statistical analysis of the effect of dark matter substructures

The baryonic self similarity of dark matter

The cosmological simulations indicates that the dark matter haloes have specific self similar properties. However the halo similarity is affected by the baryonic feedback, the momentum injected by the supernovae re-shape the dark matter core and transform it to a flat density core, with a scale length imposed by the baryonic feedback. Additionally the baryon feedback impose also an equilibrium condition, which when coupled with the imposed baryonic scale length induce a new type of similarity. The new self similar solution implies that the acceleration generated by dark matter is scale free, which in turns implies that the baryonic acceleration at a reference radius is also scale free. Constant dark matter and baryonic accelerations at a reference radius have effectively been observed for a large class of different galaxies, which is in support of this approach. The new self similar properties implies that the total acceleration at larger distances is scale free, the transition between the dark matter and baryons dominated regime occurs at a constant acceleration, and the maximum of the velocity curve which defines the amplitude of the velocity curve at larger distances is proportional to $M^{\frac{1}{4}}$. These results demonstrates that in this self similar model, cold dark matter is consistent with the basics of MOND phenomenology for the galaxies. In agreement with the observation the coincidence between the self similar model and MOND is expected to break at the scale of clusters of galaxies. Some numerical experiments shows that the behavior of the density near the origin is closely approximated by a Einasto profile.Comment: Last versio

Reconstructing the cosmic Horseshoe gravitational lens using the singular perturbative approach

The cosmic horseshoe gravitational lens is analyzed using the perturbative approach. The two first order perturbative fields are expanded in Fourier series. The source is reconstructed using a fine adaptive grid. The expansion of the fields at order 2 produces a higher value of the chi-square. Expanding at order 3 provides a very significant improvement, while order 4 does not bring a significant improvement over order 3. The presence of the order 3 terms is not a consequence of limiting the perturbative expansion to the first order. The amplitude and signs of the third order terms are recovered by including the contribution of the other group members. This analysis demonstrates that the fine details of the potential of the lens could be recovered independently of any assumptions by using the perturbative approach.Comment: 22 pages 11 figure

Unbiased reconstruction of the mass function using microlensing survey data

The large number of microlensing events discovered towards the Galactic Bulge bears the promise to reconstruct the stellar mass function. The more interesting issue concerning the mass function is certainly to probe its low mass end. However due to the source confusion, even if the distribution and the kinematics of the lenses are known, the estimation of the mass function is extremely biased at low masses. The blending due to the source confusion biases the duration of the event, which in turn dramatically biases the estimation of the mass of the lens. To overcome this problem we propose to use differential photometry of the microlensing events obtained using the image subtraction method. Differential photometry is free of any bias due to blending, however the drawback of differential photometry is that the baseline flux is unknown. In this paper we will show that even without knowing the baseline flux, purely differential photometry allow to estimate the mass function without any biases. The basis of the method is that taking the scalar product of the microlensing light curves with a given function and taking its sum over all the microlensing events is equivalent to project the mass function on another function. This method demonstrates that there is a direct correspondancy between the space of the observations and the space of the mass function. Concerning the function to use in order to project the observations, we show that the principal components of the light curves are an optimal set. To illustrate the method we simulate sets consistent with the microlensing experiments. By using 1000 of these simulations, we show that for instance the exponent of the mass function can be reconstructed without any biases.Comment: 8 pages, 4 Figure, submitted to MNRA

Gravitational arcs as a perturbation of the perfect ring

The image of a point situated at the center of a circularly symmetric potential is a perfect circle. The perturbative effect of non-symmetrical potential terms is to displace and break the perfect circle. These 2 effects, displacement and breaking are directly related to the Taylor expansion of the perturbation at first order on the circle. The numerical accuracy of this perturbative approach is tested in the case of an elliptical potential with a core radius. The contour of the images and the caustics lines are well re-produced by the perturbative approach. These results suggests that the modeling of arcs, and in particular of tangential arcs may be simplified by using a general perturbative representation on the circle. An interesting feature of the perturbative approach, is that the equation of the caustic line depends only on the values on the circle of the lens displacement field along the $\theta$ direction.Comment: 9 pages, 2 figure