Contents
7.1 Why do we need a new strategy ? . . . 83 7.2 The method: ISMCS . . . 84
7.1 Why do we need a new strategy ?
To derive H0from lensed quasars and their time delay(s), accurate positional constraints for the sources and lens are mandatory. High resolution images are thus more than welcome. The CASTLES project (Cfa-Arizona Space Telescope LEns Survey1) aimed at characterising the geometry of every known multiply imaged quasar. That is why they acquired HST/NICMOS2-2 (NIC2) images of a large number of gravitationally lensed quasars. This data set is available to anyone in the HST archives. Our aim is to apply the MCS deconvolution algorithm to these images to improve their quality in getting rid of the instrumental profile, the ultimate goal being to obtain constraints as accurate as possible.
Unfortunately, as the field of view of NIC2 is not large, i.e. 19.′′2× 19.′′2, we usually have no PSF star at our disposal on the frame, neither have we separate frames of stars acquired in the same conditions as the lensed systems. Moreover, there could be a mismatch of SED, i.e. Spectral Energy Distribution, between the PSF stars and the lensed quasar itself, which could modify the shape of the point sources especially through broad band filter. We thus have to use the information in the lensed images themselves.
1http://www.cfa.harvard.edu/castles
2Let us remind that NICMOS stands for Near Infrared Camera and Multi-Object Spectrometer.
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Let us recall that the original version for deriving the PSF from blended point sources (Magain et al., 2007) assumes that a part of the image contains only point sources and no diffuse component, which is not the case here. Indeed, we know there may be some diffuse structures under or not far from the point sources such as arcs or rings and the lensing galaxy. The difficulty resides in separating these contributions from the point sources themselves. That is why we need a new method: the iterative strategy combined with the MCS deconvolution algorithm, also called ISMCS and detailed in the next section.
The first object we investigate and which we test the method on is the famous Cloverleaf gravitational lens, H1413+117, a quadruply imaged quasar (see next chapter).
The iterative strategy gives astrometric and photometric measurements and reveals the primary lensing galaxy as well as a partial Einstein ring. The reliability of the method is checked on a synthetic image similar to H1413+117. In Part IV, ISMCS is applied to WFI J2033-4723, an object studied in detail by the COSMOGRAIL collaboration to obtain H0, and to two samples of gravitational mirages. The first one is composed of seven lensed quasars currently monitored by COSMOGRAIL but with no previously measured time delays and the second one is composed of eleven lensed quasars with already measured time delays.
7.2 The method: ISMCS
The originality of the present method is that the same images are used to determine the PSF and to perform the deconvolution, i.e. to detect the diffuse background and to obtain the astrometry and photometry of the object. It works only if there are several point sources in the field: this makes it possible to distinguish the structures belonging to the PSF, and thus appearing in the vicinity of each point source, from the diffuse structures assumed not to be identical around each source.
This new method is based on an iterative strategy. We start with a first approx-imation of the PSF, in the case of HST images this PSF is constructed by the Tiny Tim software (Krist & Hook, 2004; see Fig. 7.1 for an example of a Tiny Tim PSF), with a sampling step two times smaller than the original one (i.e. oversampling by a factor of 2). That instrumental profile is deconvolved by the final Gaussian PSF R(~x) in order to obtain the deconvolution kernel that we call S0(~x). This is a reasonable first approximation, although not accurate enough to obtain trustworthy deconvolved frames. Indeed, when using that deconvolution kernel to deconvolve the acquired signal which we call D0(~x), the result shows significant structures around each point source, clearly demonstrating that the Tiny Tim PSF departs from the actual one. An example is shown on Fig. 7.2: it is the simultaneous deconvolution of four frames of the Clover-leaf gravitational lens3 through the F160W filter. The ring-like structures due to the insufficient accuracy of the Tiny Tim PSF are obvious.
For all these reasons we proceed as follows:
1. First, for each individual image, we determine an improved PSFS1(~x) following
3See Sect. 8 for details on this object.
7.2 The method: ISMCS 85
Figure 7.1: PSF constructed by the Tiny Tim software for two filters available on NIC2.
They are considerably different. However, we can easily notice that they both have complex structures including spikes. Left: a PSF for the F160W filter, which will be defined in the next chapter. Right: a PSF for the F180M filter, also defined in the next chapter.
the method described in Sect. 5.3.4 (PSFsimult, Magain et al., 2007). This is done by adding a numerical component to the approximate PSF S0(~x) (here, the deconvolved Tiny Tim PSF) so that the observed imageD0(~x) is reproduced better. But, since this method assumes that the image consists of point sources only, and since our object is supposed to contain diffuse structures, a part of them will be wrongly included in the improved PSF S1(~x). If the structures of the diffuse component were identical around each point source, they would be entirely included in the new instrumental profile. On the other hand, assuming that the quasar is quadruply lensed, and if the background was completely different around each of the point sources, only around 25% of it would be included in the PSF. In practice, a variable fraction of it contaminates the PSF. As long as that fraction is below 100%, our iterative procedure will allow improvements of the results.
2. We then use the once-improved PSFsS1(~x) to perform a simultaneous deconvo-lution of all the frames. Let us insist on the fact that each image has its own instrumental profile: S1(~x) varies slightly from frame to frame. The simultaneous deconvolution allows to obtain a first approximation of the diffuse component, H1(~x), which, by construction, is the same in each image. However, since a part of the smooth structures was included in the PSFs S1(~x), H1(~x) is only the re-maining part of the actual background.
3. Third, we subtract H1(~x), reconvolved and resampled to the initial resolution, from the original images. This gives us a new version of the observed images, D1(~x), with point sources less contaminated by the diffuse structures. The first iteration is over.
4. To begin the second iteration, we determine a new set of PSFsS2(~x) on the images D1(~x). As they contain a lower amount of background thanD0(~x), the new PSFs are indeed less contaminated by diffuse structures.
Figure 7.2: Frame of the Cloverleaf resulting from a simultaneous deconvolution of four HST/NIC2 frames using Tiny Tim PSFs. Left: deconvolved image. Right: residual map (difference between the model and the original frame in units of sigma) of the deconvolu-tion. The remnant structures around each point source is obvious and is due to the use of inappropriate PSFs.
5. The simultaneous deconvolution of the original imagesD0(~x) with the new PSFs S2(~x) allows to get an improved version,H2(~x), of the diffuse background.
6. We subtractH2(~x) from the original imagesD0(~x). This closes the second itera-tion.
7. This iterative process is continued until no significant improvement is observed.
Usually around 3 to 5 iterations are necessary, depending on the structures under the sources.
Sometimes this process needs to be adapted. For example when the diffuse back-ground is not faint enough compared to the intensities of the sources, it is better to start with a simultaneous deconvolution of the data with deconvolved the Tiny Tim PSFs than to try and improve these PSFs on the strongly contaminated point sources. Before subtracting the background obtained thanks to the Tiny Tim PSFs from the original images, it is necessary to clean it from the artifact structures created to compensate the inaccuracies in the Tiny Tim PSFs. This demands some intuition to decide what is part of the real background and what is not. At this stage it is always better to remove too many structures than too few because it is always possible to recover them in the following iterations.
This iterative strategy, ISMCS, is tested on a real example in the next chapter and then illustrated on a few cases in Part IV.
Not to be absolutely certain is, I think, one of the essential things in rationality.
Bertrand Russell (1872 - 1970)