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Register a new userModels of the Cosmic Horseshoe Gravitational Lens
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Authors
Simon Dye
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We model the extremely massive and luminous lens galaxy in the Cosmic Horseshoe Einstein ring system, recently discovered in the Sloan Digital Sky Survey. We use the semi-linear method of Warren & Dye (2003), which pixelises the source surface brightness distribution, to invert the Einstein ring for sets of parameterised lens models. Here, the method is refined by exploiting Bayesian inference to optimise adaptive pixelisation of the source plane and to choose between three differently parameterised models: a singular isothermal ellipsoid, a power law model and a NFW profile. The most probable lens model is the power law with a volume mass density that scales as r^(-1.96+/-0.02) and an axis ratio of ~0.8. The mass within the Einstein ring (i.e., within a cylinder with projected distance of ~30 kpc from the centre of the lens galaxy) is (5.02+/-0.09)*10^12 M_solar, and the mass-to-light ratio is ~30. Even though the lens lies in a group of galaxies, the preferred value of the external shear is almost zero. This makes the Cosmic Horseshoe unique amongst large separation lenses, as almost all the deflection comes from a single, very massive galaxy with little boost from the environment.
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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.
The positions of images produced by the gravitational lensing of background sources provide unique insight in to galaxy-lens mass distribution. However, even quad images of extended sources are not able to fully characterize the central regions of the host galaxy. Most previous work has focused either on the radial density profile of the lenses or localized substructure clumps. Here, we concentrate on the azimuthal mass asymmetries near the image circle. The motivation for considering such mass inhomogeneities is that the transition between the central stellar dominated region and the outer dark matter dominated region, though well represented by a power law density profile, is unlikely to be featureless, and encodes information about the dynamical state and assembly history of galaxies. It also happens to roughly coincide with the Einstein radius. We ask if galaxies that have mass asymmetries beyond ellipticity can be modeled with simpler lenses, i.e., can complex mass distributions masquerade as simple elliptical+shear lenses? Our preliminary study indicates that for galaxies with elliptical stellar and dark matter distributions, but with no mass asymmetry, and an extended source filling the diamond caustic, an elliptical+shear lens model can reproduce the images well, thereby hiding the potential complexity of the actual mass distribution. For galaxies with non-zero mass asymmetry, the answer depends on the size and brightness distribution of the source, and its location within the diamond caustic. In roughly half of the cases we considered the mass asymmetries can easily evade detection.
Gravitational lenses on galaxy scales are plausibly modelled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasising that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential. We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modelled, providing a framework for a fuller investigation of dark matter substructure in galaxies and clusters. Finally we remark on the need for finite mass halo profiles when doing cosmological ray-tracing simulations, and the need for readily-calculable higher order derivatives of the lens potential when studying catastrophes in strong lenses.
It is well known that measurements of H0 from gravitational lens time delays scale as H0~1-k_E where k_E is the mean convergence at the Einstein radius R_E but that all available lens data other than the delays provide no direct constraints on k_E. The properties of the radial mass distribution constrained by lens data are R_E and the dimensionless quantity x=R_E a(R_E)/(1-k_E)$ where a(R_E) is the second derivative of the deflection profile at R_E. Lens models with too few degrees of freedom, like power law models with densities ~r^(-n), have a one-to-one correspondence between x and k_E (for a power law model, x=2(n-2) and k_E=(3-n)/2=(2-x)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of k_E and hence H0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H0 from gravitational lens time delays are more accurate than ~10%, regardless of the reported precision.
Optical photometry is presented for the quadruple gravitational lens PG1115+080. A preliminary reduction of data taken from November 1995 to June 1996 gives component ``C leading component ``B by 23.7+/-3.4 days and components ``A1 and ``A2 by 9.4 days. A range of models has been fit to the image positions, none of which gives an adequate fit. The best fitting and most physically plausible of these, taking the lensing galaxy and the associated group of galaxies to be singular isothermal spheres, gives a Hubble constant of 42 km/s/Mpc for Omega=1, with an observational uncertainty of 14%, as computed from the B-C time delay measurement. Taking the lensing galaxy to have an approximately E5 isothermal mass distribution yields H0=64 km/sec/Mpc while taking the galaxy to be a point mass gives H0=84 km/sec/Mpc. The former gives a particularly bad fit to the position of the lensing galaxy, while the latter is inconsistent with measurements of nearby galaxy rotation curves. Constraints on these and other possible models are expected to improve with planned HST observations.
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