A possible gravitational lensing explanation for the excess of strong Mg ii absorbers in gamma-ray burst afterglow spectra

J. Stuart B. Wyithe 1 S. Peng Oh 0 Bartosz Pindor 1 0 Department of Physics, University of California , Santa Barbara, CA 93106 , USA 1 School of Physics, University of Melbourne , Parkville, Victoria 3010 , Australia Gamma-ray burst (GRB) afterglows offer a probe of the intergalactic medium (IGM) out to high redshift which complements observations along more abundant quasar lines of sight. Although both quasars and GRB afterglows should provide a priori random sightlines through the intervening IGM, it has been observed that strong Mg II absorbers are twice as likely to be found along sightlines towards GRBs. In this paper we study the effect of gravitational lensing by galaxies and their surrounding mass distributions on the statistics of Mg II absorption. We find that the multiband magnification bias could be very strong in the spectroscopic GRB afterglow population and that gravitational lensing is able to explain the discrepancy in density of absorbers, for plausibly steep luminosity functions. The model makes the prediction that to explain the Mg II absorber excess, approximately 20-60 per cent of the spectroscopic afterglow sample (i.e. 5-15 of 26 sources) would need to have been multiply imaged, implying that many of these GRBs were repeating bursts. We show that despite this large lensing fraction it is likely that no repeating bursts would yet have been identified by chance owing to the finite sky coverage of GRB searches, while the required multiple image fraction is currently not ruled out by direct observations of the host galaxies. A confirmation of the lensing hypothesis would allow the GRB luminosity function to be constrained down to otherwise inaccessibly faint levels, with potential consequences for GRB models. On the other hand, should multiple images be shown to be absent among the spectroscopic afterglow sample, then gravitational lensing by galaxies will be ruled out as an explanation for the observed Mg II absorber excess. 1 I N T R O D U C T I O N At moderate redshifts (0.3 z 2.2) the dispersal of metal-enriched gas through the intergalactic medium (IGM) via galactic winds is most readily traced via Mg II absorption systems in optical spectra of bright background sources. Although the detailed origin of Mg II absorbers remains uncertain, it is thought that they are associated with galaxies and galactic outflows. For example, Mg II absorbers have been shown to be associated with neutral hydrogen absorbers over a range of column densities, including damped Lyman absorbers (e.g. Rao, Turnshek & Nestor 2006). Moreover the host halo masses associated with Mg II absorbers have been estimated at z 0.5 via cross-correlation with luminous red galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 3 (Bouche et al. 2006), yielding a host mass of M 1012 M (i.e. massive galaxies). Indeed the large number of Mg II absorbers and galaxies available for cross-correlation yields a statistical accuracy of a factor of 2 in host halo mass. Obtaining an unbiased census of the density and distribution of Mg II in the IGM requires that the background sources be uncorrelated with the foreground absorbers under study. Most current knowledge regarding the census of Mg II absorption systems comes from spectra of quasars (e.g. Prochter, Prochaska & Burles 2006a). More recently, observations of gamma-ray burst (GRB) afterglows have begun to offer a new probe of the IGM out to high redshift which complements the more abundant quasar lines of sight. Indeed, since they are associated with star formation rather than supermassive black holes (which, given their long assembly times, could become extremely rare at high redshift), GRBs could potentially be seen out to much higher redshift than quasars; the current record holder is at z 8.1 (Salvaterra 2009; Tanvir et al. 2009). Interestingly, although both quasars and GRB afterglows should provide a priori random sightlines through the intervening IGM it has been observed that strong Mg II absorbers are several times as likely to be found along sightlines to GRBs as along quasar sightlines (Prochter et al. 2006b; Tejos et al. 2009; Vergani et al. 2009), indicating that one or both of these samples are biased relative to the underlying population of absorbers. A similar study did not find this discrepancy among C IV absorbers (Sudilovsky et al. 2007). The most recent collection of GRB afterglow spectra from which strong (>1 ) Mg II absorption can be studied is summarized in the work of Vergani et al. (2009) who compiled a list of 26 spectra (with a combined redshift path-length of z = 31.55) containing 22 strong Mg II absorbers among 15 of the 26 lines of sight. From that paper we take the following values for observables describing the absorber population. The fraction of lines of sight that contain one or more absorbers is FoMbgs 0.6 0.15. By contrast, the results of high-resolution spectroscopy from Prochter et al. (2006a) yielded 22 absorbers along 91 quasar lines of sight, implying that FMg,q = 0.25. Assuming the same redshift path-length distribution as the GRB sample, these values imply that the incidence of the number of strong systems in GRB afterglows relative to quasars is Robs GRB,q 2.1 0.6. Wherever required we take the redshifts of GRBs and associated absorbers, as well as the probed redshift path-lengths, from this paper. Several proposals to reconcile this discrepancy have been put forward, with a detailed discussion of possible biases presented by Porciani, Viel & Lilly (2007). For example, the incidence of Mg II systems in quasars could be lowered because of dust obscuration associated with the absorbing systems; this turns out to be too small to explain the discrepancy (Sudilovsky, Smith & Savaglio 2009). Alternatively, it has been argued that different sizes of the source could lead to different absorber incidence between GRB afterglows and quasars (Frank et al. 2007). However, from the similarity of the equivalent width distributions in GRBs and quasars, Porciani et al. (2007) show that the absorbers must be larger than the beam size, and hence it is not possible to explain the difference in this way. A third potential bias is provided through gravitational lensing of GRBs by foreground galaxies associated with the Mg II absorber. There are several lines of circumstantial evidence for this. First, imaging studies of the host galaxies of GRBs with early time afterglow spectra (Chen et al. 2009) show that additional galaxies are found within 2 arcsec of all GRB host fields where the line of sight contains a Mg II absorber, while no additional galaxies are found within 2 arcsec of GRB lines of sight that do not have any Mg II absorbers. Indeed, Chen et al. (2009) argued that the morphology of additional faint emission near the absorbing galaxy towards GRB030429 is suggestive of a lensed event. Moreover, GRB afterglows that have more than one absorber are found to be a factor of 1.7 brighter t (...truncated)