5.5 Mass modelling technique: LENSTOOL
5.5.3 Model constraints
constrained. For example, withη = 0.5, rcuthas a constant mass-to-light ratio, making it inde- pendent of the galaxy luminosity. However withη = 0.8, the mass-to-light ratio scales asL0.3, which is similar to the scaling of the fundamental plane (Jørgensen et al., 1996; Natarajan and Kneib, 1997; Halkola et al., 2006).
ages created by the core lens. In extreme cases galaxy-scale halos can also increase the number of multiple images of a source, although this is very rare.
With an updated model, other multiple image candidates can be confirmed or rejected. The confirmed systems can in turn further constrain the lens model. This process is repeated until the model converges, or no new multiply-imaged systems are identified. Note that the model is also used to predict multiple images before they are observationally confirmed.
The viability of multiple image candidates can be constrained by their colours, fluxes and redshifts (if known). However the application of these properties is not always straightforward.
For example, the colour of an image can be contaminated by a nearby galaxy, making it red- der than its counter images, or an incorrect redshift prior could bias the model by forcing the Bayesian posterior into an incorrectly refined parameter space. Spectroscopic redshifts are the best inputs, but such measurements are rare, and also usually known for only one or two of the multiples within the same system. Photometric redshifts can be adequate, provided they are ac- curate enough. If computational time is not a concern, the source redshift can be set as a free parameter, giving the model more freedom. Coupled with the other observational constraints, this may lead to a more accurate redshift estimate for the multiple image system, and an independent way to check measured redshifts.
5.5.3.2 Multiple image likelihood
The constraints from the multiple images are input to the optimisation of the lens model as part of the likelihood. The multiple images’ likelihood is the probability of the observed positions, Dorxobs, given the positions predicted by the model,x(θ). The general definition of the likeli- hood function can be applied under the assumption that the uncertainties on the measured image positions are Gaussian and uncorrelated between images. The likelihood is therefore
L= P(D|x(θ)) =
N
Y
i=1
"
exp−χ2i/2/Y
j
σij
√ 2π
#
. (5.43)
with the contribution to the overallχ2 from multiply-imaged systemigiven by χ2i =
ni
X
j=1
xjobs−xj(θ)2
σij . (5.44)
HereN is the total number of sources for which multiple images are detected,ni is the number of multiple images of thei-th source, andσij is the uncertainty of the measured position of image j of sourcei. In this method, many models have to be tested and rejected before the Bayesian sampler (see above) focuses on the region of best-fit parameters.
An important aspect of theχ2 calculation is how to match the predicted and observed images one at a time.LENSTOOLuses a simplex method algorithm (Press et al., 1986) of image transport (Schneider et al., 1992) that evades the matching problems experienced by techniques for finding the roots of the lens equation. In this method the observed image and predicted image is coupled throughout the iterative improvement of the predicted position and theχ2 is simple to calculate.
However, this method fails when a model produces opposing multiple image configurations (e.g.
a tangential instead of radial system), and that model is rejected. This situation often occurs when the model is relatively unconstrained and the rejections significantly retard the speed of the model convergence.
This issue can be circumvented by computing theχ2in the source plane rather than the image plane. This equates to finding the difference between the source position of an observed image, xS(θ), and the barycentre position of all the ni source positions,hxS(θ)i. Theχ2 in the source plane is therefore given by
χ2S
i =
ni
X
j=1
xjS(θ)−
xjS(θ)2
µ−2j σij2 , (5.45)
where µj is the magnification for image j. In this form, it is unnecessary to solve the lens equation, speeding up the computation ofχ2.
The Bayesian MCMC method implemented inLENSTOOL(see§5.5.1) incorporates both the image plane and source plane optimization to calculateχ2. To achieve the best balance between computation time and accurate refinement of the model, the best-fit region is narrowed using the source plane method, and then the image plane method is invoked to refine the models.
GRAVITATIONAL LENSING WITH THE HUBBLE FRONTIER FIELDS PROGRAM
Gravitational lensing is an exceptionally effective tool for probing the dark matter distribution within massive clusters. On the cluster scale, it is a probe of the deep universe as massive clusters act as “cosmic telescopes”, magnifying undetectable high-redshift galaxies into the observable frame.
Successful strong lensing cluster studies rely on high quality imaging in which several mul- tiple images can be located. The superior resolution and multi-colour images from the Hubble Space Telescope (HST) make it an ideal telescope for strong lensing analysis. In 2013, the Space Telescope Science Institute (STScI) started the Hubble Frontier Fields1 (HFF) program, the aim of which is to exploit the gravitational magnification by massive clusters to study the distant universe to unparalleled depth. Six massive galaxy clusters were selected for the program, each observed for 140 orbits spread over 7 passbands, covering the optical up to the near-infrared, the latter wavelength coverage being mandatory to identify high-redshift objects. All six targets have
1http://www.stsci.edu/hst/campaigns/frontier-fields/
154
mass models derived from pre-HFF data which are publicly available2. This pre-HFF mass map- ping initiative allows the high-redshift community, which includes non-lensing experts, access to lensing mass models to study the high redshift universe.
In this section we present the results obtained by strong lensing analysis of two HFF clusters as part of the CATS collaboration, carried out with theLENSTOOLsoftware. Both clusters were discovered in the MAssive Cluster Survey (MACS; Ebeling et al., 2010). The work detailed below has led to three peer-reviewed papers (Jauzac et al., 2014, 2015a,c) and a press release by the European Space Agency3. My contribution to these papers was the identification and verification of multiple image systems for the strong lensing analysis.
6.1 MACSJ0416.1-2403
MACSJ0416.1-2403 (z=0.397, hereafter MACSJ0416) was first observed by HST with WFPC2 in 2007 as part of a SNAPshot program (ObsID: GO-11103, PI: Ebeling). These observations showed MACSJ0416 to have a large Einstein radius and was hence selected as one of the “high magnification” clusters for the Cluster Lensing And Supernova survey with Hubble (CLASH;
Postman et al., 2012). The CLASH data consisted of one orbit per band over 16 passbands covering the UV to the near infrared. The first strong lensing mass model of this cluster was published by Zitrin et al. (2013). The pre-HFF mass mapping initiative led to the revision of this model by the 6 lensing teams involved in the program, some of them combining both strong and weak lensing constraints (Richard et al., 2014; Johnson et al., 2014; Coe et al., 2015).
As part of the HFF program, MACSJ0416 was observed with theAdvanced Camera for Sur- vey (ACS) between 5th of January and the 9th of February 2014 in three passbands, namely F435W, F606W, F814W with observing times of 20, 12, and 48 orbits in these bands, respec- tively. HFF observations with theWide Field Camera 3(WFC3) over the remaining four HFF passbands (observed from July to September 2014) were not yet taken at the time of this work.
Basic data reduction steps were followed using HSTCAL using the most recent HST calibration
2https://archive.stsci.edu/prepds/frontier/lensmodels/
3http://www.spacetelescope.org/news/heic1416/
files. For each passband, all orbit images were combined, resulting in a single image for each band. The pixel scale of these images is 0.0300. In the following we discuss the HFF lensing anal- ysis of MACSJ0416 (Jauzac et al., 2014, 2015a), focusing on the multiple image identification and strong lensing (SL) mass modelling.