1. Cosmological Constraints from the Double-
Source-Plane Lens SDSSJ
T. E. Collett, M. W. Auger
Institute of Astronomy, University of Cambridge, UK
arXiv:
Figure 1. Left. Pseudocolour HST image of the lens SDSSJ
Figure 3. Right. Galaxy subtracted image of J0946. The zs1=0.609 source only contributes to the flux within the green region; the zs2≈2.3 only contributes to the blue region.
Figure 2. Above. Schematic of a double-source-plane lens. The cosmological scaling factor is the product of the red angular diameter distances divided by the product of the blue
Motivation
The Einstein Radii of strong gravitational lenses are sensitive probes of angular diameter distances and the mass of the lensing galaxies. Since the mass is unknown, more information is needed to break the degeneracy between lens mass and cosmology. SDSSJ (Figure 1) is a strong lens at zl=0.222 with two background sources at zs1=0.609 and zs2≈2.3, discovered as part of the SLACS survey[1]. With two sources feeling the same lensing mass we are able to measure the cosmological scaling factor:
Modelling Results
The mass distribution of the primary lens is very close to that of an isothermal sphere. The powerlaw index of the projected density profile and the flattening are:
The cosmological scaling factor is:
We have detected the mass of the first source at ~8σ. The Einstein radius of the first source is, arc-seconds, implying a velocity dispersion of 97 ± 7 km/s 1
Method
To model J0946 we first postulate a mass distribution for the primary lens and first source which we then use to de-lens the background sources. We write down a merit function that penalizes poor fits to the data and overly spiky sources. We then Monte Carlo over plausible mass distributions to probe the posterior distribution of the model parameter space. The need to simultaneously focus both sources means that there is only a small range of physically plausible models that can fit the data.
Constraints on Cosmology
For a flat ΛCDM Universe our measurement implies , but the main strength of our measurement is in constraining non-Λ cosmologies. With only one system, w and ΩM are degenerate, but when combined with a CMB prior from Planck[?] we are able to constrain w to be:
at 68% confidence, assuming the equation of state is constant and a flat cosmology. This is a thirty percent improvement upon the Planck constraints alone. The constraints in the w-ΩM plane are shown in Figure 6.
Figure 4. From top left clockwise. 1) Most probable model for the image of J0946, the colour scale is non-linear. 2) Noise normalized residual 3) Most probable first source, the centroid of this source's mass is shown by the black cross. 4) Most probable second source. The black bars indicate 0.5 arc-second scales.
Figure 5. The posterior for β from our model, and the model parameters that are most degenerate with it: the logarithic slope of the projected density for the first lens (η=1 corresponds to isothermal), and the Einstein radii, θE, of the primary lens and the first source in arc-seconds.
Figure 6. Constraints on the w-ΩM plane assuming a flat wCDM cosmology. The J0946 alone constraints are shown in red. Planck 2013 are in grey, and the combined constraints are in black.
Double Source Plane lenses in the LSST and Euclid Era
The combination of LSST's extreme depth and Euclid's high resolution imaging will yield roughly one hundred thousand galaxy-scale strong lenses[2]. Between one hundred and one thousand of these will be DSPLs[1]. With 100 DSPLs with β measured at the same precision as here, inference on evolving models of the equation of state can be made with comparable precision as the other stage IV probes, but with independent systematic errors.
Figure 7. Marginalized constraints on the w0-wa plane assuming an open waCDM cosmology. Red show the forecasts for 100 DSPLs, green shows the forecast for Euclid Weak Lensing[4]. Both include a Planck prior.
Acknowledgements
TEC acknowledges funding from STFC in the form of a Ph.D. studentship.
References
[1] R. Gavazzi et al. Ap. J. 677, 1046 (2008)
[2] Pawase R. S. ArXiv: (2012)
References
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