Image processing

To obtain the light curves of the lensed images of HE 0435-1223, we apply the revised semi-automated reduction pipeline as described in Chapter 6. As already stated, the

Figure 9.1: Partial field of view of the Euler reference frame of HE 0435-1223. The reference stars are encircled and labeled from 1 to 6. Those labeled PSF are also used to determine the PSF.

main difficulty in the image processing comes from the fact that we have to assemble data coming from different telescopes: each camera has a different size, resolution and orientation on the sky.

Euler is chosen as the reference telescope to avoid dividing the pixels of its detector into smaller ones as it has the lowest resolution. The reference frame, thus chosen amongst Euler data, was acquired on the night of the 11th of November 2005 and has a seeing of 0.^′′82. The reference stars used for the alignment and the flux calibration are encircled in the field of view of HE 0435-1223 shown on Fig. 9.1. The preliminary light curves are shown in Chapter 6 on Fig. 6.4 (p. 76). Let us note that this graph includes 172 epochs, while we only use 160 epochs. Indeed, for various reasons (not enough frames acquired during a night, cosmic rays located on the lensed system, ...), 12 epochs of observation were ruled out between the elaboration of the preliminary light curves and of the final ones.

The next step is the deconvolution with the MCS algorithm. At this stage four sources amongst the reference stars are chosen to determine a PSF for each frame.

They are labeled PSF1 to PSF4 on Fig. 9.1. Here again, the deconvolved frames have half the pixel size of the original one, i.e. 0.^′′172, and the final PSF is a Gaussian with a FWHM of 2 pixels. The intensity of each source is allowed to vary from one frame to the other while the smooth background, which includes the lens galaxy, is held constant in all the frames. The deconvolved image is shown in Fig. 9.2. The point sources are labeled as in Wisotzki et al. (2002), G being the lens galaxy. To gain in precision, the relative positions of the point sources are fixed at the values extracted from deeper images acquired with the HST (see Sect. 9.3).

Figure 9.2: Result from the simultaneous deconvolution of the ground-based frames of HE 0435-1223. G is the lens galaxy and G22 its closest neighbour.

Fig. 9.3 shows the light curves obtained for each lensed image. For clarity, each season is displayed separately in Fig. 9.4. They are extracted from the simultaneous

9.2 Monitoring 105

deconvolution of all the frames. Euler was arbitrarily chosen as the reference telescope also in terms of flux. Each point in those figures is the mean of the consecutive obser-vations made during one night, i.e. of an epoch. The total uncertainty for each point of each light curve of the quasar is estimated as explained in Sect. 6.6.2 (p. 80).

2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 A

B-0.25

C+0.15

D+0.35

2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 -9.6

-9.8 -10 -10.2 -10.4 -10.6 -10.8 -11 -11.2 -11.4 1 2 3

Figure 9.3: Light curves of the four lensed images of HE 0435-1223 from December 2003 to February 2008. The magnitude is given in arbitrary units as a function of the Heliocentric Julian Day (HJD). Each color corresponds to a lensed image: red for A, blue for B, cyan for C and magenta for D, as labeled on Fig 9.2. The ±1σ error bars are also represented. On the top part of the graph, the mean seeing of each epoch is plotted against HJD.

2800 2850 2900 2950 3000 3050 3100 3150 3200

2800 2850 2900 2950 3000 3050 3100 3150 3200

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-9.6

3500 3550 3600 3650 3700 3750 3800 3850 3900 Euler

3500 3550 3600 3650 3700 3750 3800 3850 3900 -9.6

Figure 9.4: Light curves per season of the four lensed images of HE 0435-1223 from December 2003 to February 2008. The magnitude is given in arbitrary units as a function of the Helio-centric Julian Day. Each color corresponds to a telescope: blue for Euler, green for Mercator, magenta for Maidanak and red for SMARTS. The empty circles correspond to image A, the full squares to image B, the vertical lines to image C and the empty triangles to image D. The

±1σ error bars are also represented. This figure continues on the next page.

9.3 HST/NIC2 images 107

3900 3950 4000 4050 4100 4150 4200 4250 4300

Euler

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-9.6

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Euler

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-9.6

To find the flux scale to apply to SMARTS data, we compare the flux obtained during several common nights of observation with Euler (at least 10 so that the sample is representative). As the images have been treated with different processing techniques, we apply one magnitude shift per light curve to account for any discrepancy caused, e.g., by a different astrometry or lens galaxy. The statistical noise is given in Kochanek et al. (2006). As we want the total error, we need an estimation of the systematic one.

We obtain it with the same method as explained in Sect. 6.6.2 thanks to the flux of a nearby star, also given with its statistical noise in Kochanek et al. (2006).

9.3 HST/NIC2 images

In this section, our aim is to obtain accurate relative astrometry for the four components of HE 0435-1223 and its lensing galaxy in applying ISMCS (see Chapter 7). The results will be used, in the paper, as constraints for the modeling of the lensing system. It is mandatory to obtain as much precision and constraints as possible. For this purpose, we analyse some HST images available in the archives of the Space Telescope Science Institute. They were acquired in the framework of the CASTLES project² in October 2004 (PI: C.S. Kochanek) with the camera 2 of NICMOS (NIC2). The data consist in four dithered frames calibrated by CALNICA³ and acquired through the F160W filter (H-band) in the MULTIACCUM mode, each image being a combination of 19 samples.

The total exposure time amounts to approximately 44 minutes and the mean pixel scale is 0.^′′075652 (STScI NICMOS Group, 2007).

2Let us recall that CASTLES stands for Cfa-Arizona Space Telescope LEns Survey.

3Let us recall that CALNICA is the HST image reduction pipeline.

Three iterations of ISMCS are necessary to obtain a reduced χ² of 1.66. The final pixel size is half the original one and the final PSF of the deconvolved image is chosen to be a Gaussian with a FWHM of 2 pixels. Fig. 9.5 shows, from left to right, a combination of the four initial frames, the deconvolved image and the mean residual map from the last deconvolution. A nearly complete ring, i.e. a stretched and distorted version of the quasar host galaxy, is obvious.

Figure 9.5: Left: combination of the four original HST/NIC2 F160W frames of HE 0435-1223.

The field of view is 9^′′×9^′′. Middle: deconvolved image obtained from the last iteration of ISMCS with a de Vaucouleurs profile for the lens. See text for details. Right: mean residual map in units of sigma, the color scale ranging from -4 in white to +4 in black.

The astrometry and photometry of the four components and the lens are listed in Table 9.2. The relative positions are corrected from the known distortions of the NIC2 camera, as well as from the difference of pixel scale between the x and y directions. Every measurement is accompanied by its ±1σ error bars which are calculated in measuring the dispersion of the values around the mean of the individually deconvolved frames.

Based on the work of Chantry & Magain (2007) on the Cloverleaf gravitational lens, we estimate that the total error, coming amongst others from an incomplete correction of the distortion, amounts to 2 milliarcseconds, as HE 0435-1223 is twice as extended as the Cloverleaf on NIC2. The results obtained by Morgan et al. (2005) and by Kochanek et al. (2006) are shown in Table 9.3. The first ones are based on HST/ACS images, while those from the second paper come from the same NIC2 images as the ones we use.

Concerning the point sources the agreement is good with both sets of results: within their error bars, we obtain the same values. But for the lens, our result is slightly closer to Morgan et al. (2005) than to Kochanek et al. (2006). Let us note that, in order to determine the center of the lens galaxy with the highest accuracy, we make a special run of the MCS algorithm, where the numerical background is set to zero and the lens galaxy modeled by a de Vaucouleurs profile⁴(de Vaucouleurs, 1948). The center of this analytical profile is taken as the best estimate of the lens position. This procedure allows to force the de Vaucouleurs profile to adjust to the full lens galaxy light distribution.

Letting the MCS algorithm represent the lens as the sum of an analytic profile and a numerical component would allow the center of the analytic profile to depart from the

4See Sect. 5.3.2 on p. 58 for details.

9.3 HST/NIC2 images 109

center of the total light distribution.

ID ∆RA (^′′) ∆DEC (^′′) Magnitude

A 0. 0. 17.20± 0.01

B -1.4743± 0.0004 +0.5518 ± 0.0006 17.69± 0.01 C -2.4664± 0.0003 -0.6022± 0.0013 17.69± 0.02 D -0.9378± 0.0005 -1.6160± 0.0006 17.95± 0.01 G -1.1700± 0.0030 -0.5646± 0.0004 16.20± 0.12

Table 9.2: Relative astrometry and photometry of the four components and the lensing galaxy of HE 0435-1223. These results are extracted from the simultaneous deconvolution of the HST/NIC2 images. The right ascension and declination are given in arcseconds relative to component A. The apparent magnitude is given in the Vega system. The ±1σ error bars internal to the deconvolution process are indicated.

Morgan et al. (2005) Kochanek et al. (2006) ID ∆RA (^′′) ∆DEC (^′′) ∆RA (^′′) ∆DEC (^′′)

A 0. 0. 0. 0.

B -1.4772± 0.002 +0.5532 ± 0.002 -1.476 ± 0.003 +0.553± 0.001 C -2.4687± 0.002 -0.6033± 0.002 -2.467± 0.002 -0.603± 0.004 D -0.9377± 0.002 -1.6147± 0.002 -0.939± 0.002 -1.614± 0.001 G -1.1687± 0.002 -0.5723± 0.002 -1.165± 0.002 -0.573± 0.002 Table 9.3: Relative astrometry of HE 0435-1223 from Morgan et al. (2005) on HST/ACS images and from Kochanek et al. (2006) on HST/NIC2 images. The right ascension and declination are given in arcseconds relative to component A. The ±1σ error bars are also indicated.

The shape parameters of the main lens galaxy can also be derived from this ad-justment of a de Vaucouleurs profile. They are presented in Table 9.4: the PA⁵ in degrees positive East of North, the ellipticity, the effective semi-major and semi-minor axes and the effective radius. A de Vaucouleurs profile with a small ellipticity works well, which is in complete agreement with Eigenbrod et al. (2006b) who found that a S0 profile redshifted to z=0.454 is well adapted to represent the spectrum of the lens of HE 0435-1223. Its elongation l, i.e. the semi-major to semi-minor axes ratio, amounts to 1.10± 0.09, which is in agreement with the value found by Morgan et al. (2005), i.e.

1.20^+0.23_−0.28, within the error bars. For the PA they obtained 172.6, which is very close to our result, and for the effective radius, they obtained 1.20^+0.5_−0.35 arcseconds, which is also in agreement, within their error bars, with what we obtain.

5Let us recall that PA stands for Position Angle and is the angle that folds back the direction of the major axis over the direction of the North.

ID PA (^◦) Ellipticity aef f (^′′) bef f (^′′) Ref f (^′′) G 174.8± 1.7 0.09± 0.01 1.57± 0.09 1.43± 0.08 1.50± 0.08 Table 9.4: Measured shape parameters for the lensing galaxy of HE 0435-1223. The second column gives the position angle, or PA, in degrees positive East of North. The ellipticity is given in the third column and the two next columns present respectively the effective semi-major and semi-minor axes of the elliptical isophotes, in arcseconds. The effective radius is shown in the last column. Each measurement is accompanied by its ±1σ internal error bars.