Determination of the Hubble constant from the strong lensing system B0218+357

Abstract

Gravitational lensing and particularly strong lensing provide variety of subjects to study such as galaxy evolution, substructure detection in galaxies or cluster of galaxies. Also strong lensing enables us to derive the Hubble constant. The advantage of strong lensing to find this cosmological parameter is its measurement on cosmic scale.<br /> The strong lensing system B0218+357 is an isolated system and thus not significantly influenced by external shear. In addition, the redshift information of the lens and source and time delay between the images are available. These parameters make B0218+357 a promising system to determine the Hubble constant. Although radio observations provide accurate measurements of the positions of the double image, previous attempts on these data to derive the Hubble constant were not satisfactory because the lens galaxy cannot be observed in the radio. <br /> The most important observational effect in optical astronomy is the spreading of the light ray distribution of the source reaching the CCD detector due to the design of the instrument and the atmosphere, the so called PSF. The information lost in images of the CCD cameras can be recovered with ‘dithering’. In this technique, the exposures are taken with sub-pixel shifts in order to extract structures on scales smaller than a pixel. The standard method to combine such exposures, ‘Drizzle’, reverses the shifts and rotations between the exposures and corrects for the geometric distortion caused by the instrument design. Then this method averages these exposures to produce the combined image. This produces good results but is not optimal for cases in which preservation of the PSF is required. <br /> In B0218+357, with the small separation between the two images, precise subtraction of PSF is essential. Therefore, the combination process of the data should not add additional PSF to the system. In this work, an alternative method based on direct fitting with a least-squares approach is developed to combine the exposures of this system taken by the ACS/WFC detector of the HST. To have a unique solution, a smoothing constraint is also included in this method. This method has the ability of working with arbitrary rotations, shifts and dither pattern. The correction for the geometric distortion and flagging pixels affected by cosmic rays are included. To have a higher resolution, the pixels of the output result of this method has smaller size in comparison to the original exposures taken from the Hubble Space Telescope. <br /> To find the relative positions of the images with respect to the lens galaxy, the combined image of each observed visit of B0218+357 is fitted with two PSF components and a Sersic profile with additional parameters for spiral arms. With those positions and the assumption of an isothermal model for the lens potential, we are able to determine the Hubble constant to be $70pm 3 ,mathrm{km,s^{-1}, Mpc^{-1}}$ with fitting the spiral arms and $66pm 4 ,mathrm{km,s^{-1}, Mpc^{-1}}$ for the case of leaving the arms unfitted. The error bars presented here are rms scatters between the Hubble constant values derived from each visit. There might be additional systematic errors as well.<br /> In the optical data of B0218+357, one of the images (image A) suffers from extinction due to a giant molecular cloud in the line of sight which causes a systematic shift of its positions. To have more precise results, in the next step we use the positions of image A from radio observations. In this approach, the obtained value for the Hubble constant for the case not fitting the spiral arms changes to $76pm 3 ,mathrm{km,s^{-1}, Mpc^{-1}}$ and when we fit the spiral arms we derived the value of $79pm 3 ,mathrm{km,s^{-1}, Mpc^{-1}}$ for the Hubble constant. These results are consistent with previous results but rules out others.