Time delay for the gravitational lens system B0218+357

A. D. Biggs 2 I. W. A. Browne 2 P. Helbig 2 L. V. E. Koopmans 1 P. N. Wilkinson 2 R. A. Perley 0 0 National Radio Astronomy Observatory , PO Box 0, Socorro, NM 87801, USA 1 University of Groningen, Kapteyn Astronomical Institute , Postbus 800, 9700 AV Groningen, the Netherlands 2 University of Manchester, Nuffield Radio Astronomy Laboratories , Jodrell Bank, Macclesfield, Cheshire SK11 9DL A B S T R A C T Measurement of the time delay between multiple images of a gravitational lens system is potentially an accurate method of determining the Hubble constant over cosmological distances. One of the most promising candidates for an application of this technique is the system B0218 357, which was found in the Jodrell Bank/VLA Astrometric Survey (JVAS). This system consists of two images of a compact radio source, separated by 335 milliarcsec, and an Einstein ring which can provide a strong constraint on the mass distribution in the lens. We present here the results of a three-month VLA monitoring campaign at two frequencies. The data are of high quality, and both images show clear variations in total flux density, percentage polarization and polarization position angle at both frequencies. The time delay between the variations in the two images has been calculated using a chi-squared minimization to be 10:5 6 0:4 d at 95 per cent confidence, with the error being derived from Monte Carlo simulations of the light curves. Although mass modelling of the system is at a preliminary stage, taking the lensing galaxy to be a singular isothermal ellipsoid and using the new value for the time delay, we obtain a value for the Hubble constant of 69 1139 km s 1 Mpc 1, again at 95 per cent confidence. I N T R O D U C T I O N Long before the first gravitational lens was discovered, it had been shown (Refsdal 1964) that measurement of a time delay between the images of a lens could be used to calculate the Hubble constant, H0, independently of any other distance determination to the lens or lensed object. This technique has so far been applied predominantly to the double quasar B0957 561 (Walsh, Carswell & Weymann 1979) where a long-running controversy as to the length of the time delay has only recently been resolved (Kundc et al. 1997; Haarsma et al. 1999). In the first of these two papers, an H0 of 64 6 13 km s 1 Mpc 1 was derived, based on an optically determined time delay of 417 6 3 d (at 95 per cent confidence). However, the deflecting mass is complicated (comprising a galaxy and a galaxy cluster), and modelling it satisfactorily has proved difficult and constitutes the biggest source of error on the value of H0 derived from this system at this time. Systems containing an Einstein ring are ideal candidates for determining H0, as the presence of the ring can firmly constrain the mass distribution in the lens (Kochanek 1990). A good example of this is B0218 357 (Patnaik et al. 1993), first identified as a gravitational lens through observations carried out as part of the Jodrell Bank/VLA Astrometric Survey (JVAS) (Patnaik et al. 1992). This lens system has a simple morphology (see Fig. 1), which consists of two compact images (A and B) of a strongly variable flat-spectrum radio core and a steep-spectrum Einstein ring, the diameter of which is the same as the separation of the compact components, 335 milliarcsec (mas). This is the smallest separation yet found in a galactic-mass gravitational lens system and, as a consequence, the time delay between the variations in components A and B is small. The ring is believed to be an image of part of the extended structure of the kpc-scale radio jet, and will therefore vary on much longer time-scales than the variations seen in the images of the compact cores. The deflecting mass comprises a single isolated galaxy which, in contrast to B0957 561, can be modelled relatively simply. The galaxy is also almost certainly a spiral, because radio absorption observations have shown that the column density of absorbing material is very high (Carilli, Rupen & Yanny 1993; Wiklind & Combes 1995) and because a large differential Faraday rotation measure exists between A and B at radio wavelengths (Patnaik et al. 1993). The redshifts of the lensed object and lensing galaxy are well determined at 0.96 (Lawrence 1996) and 0.6847 (Browne et al. 1993) respectively. As these are relatively low for a lens system, the assumed Figure 1. VLA 15-GHz radio map of B0218 357. As well as the two compact components (A to the right) and the Einstein ring, also clearly visible is a (non-lensed) radio jet to the south. cosmology introduces less uncertainty in the value of H0 than with other systems. Previous work (Corbett et al. 1996) derived a time delay of 12 d (B lagging A) with a 1j error of 63 d from VLA observations of the percentage polarized flux at 15 GHz. In this paper we present new results of a three-month monitoring campaign conducted with the VLA at 8.4 and 15 GHz. O B S E R VAT I O N S A N D D ATA R E D U C T I O N B0218 357 was observed with the VLA in A configuration between the months of 1996 October and 1997 January. Observations were taken at two frequencies, 15 and 8.4 GHz, each with a bandwidth of 50 MHz. Each band is further split into two intermediate frequencies, or IFs, separated slightly in frequency. With resolutions of 120 mas at 15 GHz and 200 mas at 8.4 GHz, the variable components A and B are easily resolved and can be monitored for variations in total flux density, percentage linear polarization and polarization position angle. In all, data were obtained at 47 epochs, with an average spacing between observations of ,2 d. The observing strategy was kept as consistent as possible over the period of the monitoring. Each epoch contained two observations of 3C 84, one before and one after B0218 357, for amplitude and phase calibration purposes. The 3C 84 data are also used to correct for instrumental polarization on the assumption that 3C 84 is unpolarized. 3C 119 was observed as a control source to check for variations in the flux density of 3C 84 (each epoch is calibrated assuming the same flux for 3C 84) and to calibrate the polarization position angle of B0218 357. 3C 119 is a steep-spectrum source known to contain a very weak core (Ren-dong et al. 1991), and so any variations in its total flux density should be very small. An innovation compared to the previous monitoring campaign was that antenna pointing offset observations were made of each source to ensure that gain variations associated with pointing errors were minimized. B0218 357 was observed for ,20 min at 15 GHz and ,3 min at 8.4 GHz, resulting in expected rms noise levels of 0.19 and 0.12 mJy respectively for one IF. Calibration was performed using the NRAO Astronomical Image Processing Software package aips, and each IF was calibrated separately. As the primary amplitude and phase calibrator, 3C 84, is slightly resolved at the observed frequencies, the first step in the ca (...truncated)