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Draftversion February5,2008 PreprinttypesetusingLATEXstyleemulateapjv.6/22/04 STRONG MgII SYSTEMS IN QUASAR AND GAMMA-RAY BURST SPECTRA Cristiano Porciani 1, Matteo Viel 2,3, Simon J. Lilly 1 Draft versionFebruary 5, 2008 ABSTRACT TheincidenceofstrongMgII systemsingamma-rayburst(GRB)spectraisafewtimeshigherthan in quasar (QSO) spectra. We investigate several possible explanations for this effect, including: dust obscurationbias,clusteringoftheabsorbers,differentbeamsizesofthesources,multibandmagnifica- tion bias of GRBs, associationof the absorbers with the GRB event or the circumburst environment. We find that: i) the incidence rate of MgII systems in QSO spectra could be underestimated by a 7 factor1.3-2duetodustobscuration;ii)the equivalent-widthdistributionoftheMgII absorbersalong 0 GRBs is consistent with that observed along QSOs thus suggesting that the absorbers are more ex- 0 tended than the beam sizes of the sources; iii) on average, GRB afterglows showing more than one 2 MgII system are a factor of 1.7 brighter than the others, suggesting a lensing origin of the observed n discrepancy;iv)gravitationallensing(indifferentforms,fromgalaxylensingtomicrolensing)canbias a high the counts of MgII systems along GRBs if the luminosity functions of the prompt gamma-ray J emission and of the optical afterglows have a mean faint-end slope approaching -5/3 – -2; v) some of 5 the absorbers can be associated with the circumburst environment or produced by supernova remnants unrelated to the GRB event itself but lying in the same star-forming region. With the possible 1 exception of magnification bias, it is unlikely that one of these effects on its own can fully account v for the observed counts. However, the combined action of some of them can substantially reduce the 3 statistical significance of the discrepancy. 5 1 Subject headings: quasars: absorption lines – gamma-rays: bursts 1 0 7 1. INTRODUCTION & Rao (2005) identified over 1,300 MgII doublets with 0 Magnesium is an α-process element produced by red- W >0.3˚Aandmeasuredtheirequivalentwidthdistribu- / giant stars and dispersed in the interstellar medium by tionovertheredshiftrange0.366 z 2.269. Similarly, h ≤ ≤ supernova explosions and stellar winds. In the red- Prochter,Prochaska&Burles(2006a)foundnearly7,000 p - shiftinterval0.3< z< 2.2,theMgII doublet(2796,2804 MgII systems with W > 1 ˚A in the spectra of 50,000 o ˚A) produces ab∼sorp∼tion lines in the optical spectrum QSOs from the SDSS DR4. This corresponds to a red- tr of background sources. The strong absorption systems shift path density dN/dz ≃0.24 at z =1. These results s (with equivalent width W > 0.3 ˚A) are thus believed have been extended to lower redshift (and weaker col- a to be good tracers of metal-enrichedgas associatedwith umn densities) by Nestor, Turnshek & Rao (2006). This : v galaxies(e.g. Bergeron&Boisse1991;Steidel,Dickinson study suggests that the gas clouds associated with weak i & Persson 1994). Typically these systems have multiple MgII systems are a physically distinct population from X velocity components (Churchill and Vogt 2001). those producing strong MgII absorbers (see also Nestor ar Recenthigh-resolutionimagingstudiesofquasarfields et al. 2005). provided evidence that strong MgII absorption is pro- Gamma-ray bursts (GRBs) with bright optical after- ducedinpatchy gaseousenvelopes,up toimpact param- glowscanalsobeusedasbackgroundsources. Somewhat etersof80h−1kpc,surroundinggalaxiesofdifferentmor- surprisingly,Prochteretal. (2006b,hereafterP06)iden- phologicaltypes(Churchill,Kacprzak&Steidel2005and tified14MgII systemswithW >1˚Aalong14GRBlines references therein). The completion of large and homo- of sight (for a total redshift path of 15.5 at a mean red- geneous quasar (QSO) samples as the Sloan Digital Sky shift z¯ = 1.1). This corresponds to dN/dz = 0.90+0.83 −0.50 Survey (SDSS; York et al. 2000) and the Two-degree (symmetrical 99% Poisson 4 confidence interval), an in- fieldquasarsurvey(2Qz;Boyleetal. 2000;Croometal. cidence rate that is a few times larger than that in- 2004)allowedaccuratestatisticalstudies. Theamplitude ferred from the QSOs of the SDSS data set. A simi- of the cross-correlation function between MgII systems lar (but much less statistically significant) discrepancy, and luminous red galaxies suggests that absorbers with dN/dz = 0.62+1.13 (with an additional 30% uncer- W > 1 ˚A are hosted within dark-matter halos with −0.49 ∼ tainty due to the redshift path), has been reported by characteristic masses of 1011−12M⊙ and could be as- Stocke&Rector(1997)intheopticalspectraof21radio- sociated to galactic superwinds (Bouché et al. 2006). selected BL Lacertae objects. However, recent redshift Using the SDSS Early Data Release, Nestor, Turnshek determinations (see e.g. Sbarufatti, Treves & Falomo 1 Institute for Astronomy, ETH Zu¨rich, 8093 Zu¨rich, Switzer- 2005) showed that 1 out of the 5 strong systems found land;[email protected]; [email protected]. by Stocke & Rector (1997) is associated with the host 2 Institute of Astronomy, Madingley Road, Cambridge CB3 galaxy. This reduces the cosmological incidence rate to 0HA,UnitedKingdom 3INAF-OsservatorioAstronomicodiTrieste,ViaG.B.Tiepolo 4 Clustering of the absorbers produces super-Poisson fluctua- 11,I-34131Trieste,Italy;[email protected]. tions,thiseffectwillbediscussedin§2. 2 Strong MgII systems in QSO and GRB spectra dN/dz =0.49+1.06. −0.41 In this work, we critically review some possible explanations of the discrepancy between the counts of MgII systems along GRBs and QSOs. The paper is or- ganized as follows. In 2, we estimate the importance of § dust-obscurationbias alonglines of sighttowardsQSOs. The effect of different beam sizes between GRBs and QSOs and the solution proposed by Frank et al. (2006, where QSO beams are assumed to be larger than GRB ones by a factor of 2) are discussed in 3. The roles of § gravitational lensing and magnification bias of GRB af- terglowsarepresentedin 4. Finally,in 5,wediscussthe § § possibility that some of the MgII systems along GRBs are produced in the circumburst environment. Our results are summarized in 6. § 2. DUSTOBSCURATIONBIAS The presenceofdusty absorbersalongthe line ofsight could obscure the optical light from background QSOs and produce a selection bias in magnitude-limited sam- Fig. 1.—TheunderlyingnumberdensityofstrongMgIIsystems ples (Ostriker & Heisler 1984; Heisler & Ostriker 1988; andthefractionofdustyabsorbersthatmatchtheobservedabun- Fall&Pei1993). Iftheobscurationbiasisimportant,ra- dance of MgIIsystems (solid) and the observed fraction of ab- dioselectedQSOs(whichareunaffected bydust)should sorbers along very reddened lines of sight (dashed) in the SDSS. present a larger number of absorbers on average. Re- Thedottedlinesmarkthe0,1,2and3σPoissonfluctuationsforthe observeddensityalongGRBs. cent studies did not find strong evidence for dust reddening and extinction (Ellison et al. 2001; Akerman et al. 2005;Jorgensonetal. 2006). However,radiosamples are very small and cannot lead to definitive conclusions. eventwithcoordinatesx,y,z,t )consistsofallthepaths 0 Even though the number counts of absorbers in radio of light that reach the observer at t . Basically, it con- 0 and optically selected QSOs are in agreement, 1σ sta- tains allthe galaxiesthat the observercould detectwith tistical uncertainties are consistent with 60% of damped an ideal experiment since they are connected by null Ly-α systems being missed in optical magnitude-limited geodesics with the observer himself. We shoot 103 ran- surveys (Ellison et al. 2004). dom lines of sight for each light cone and count how Could dust obscuration bias of the QSO samples ex- many galaxies we find within a given impact parameter plainthediscrepancywiththeincidenceofMgII systems b = 80h−1 kpc (Churchill et al. 2005). We then as- in GRB spectra? A few dusty systems with color excess sociate a MgII absorber to an intervening galaxy proba- E(B V) 0.1haveindeedbeenfound(Junkkarinenet bilisticallywithacoveringfactorf =0.5(Churchilletal. − ∼ al. 2004,Ellisonetal. 2006). Ontheotherhand,statisti- 2005). We only consider galaxieswith (unextincted) ab- calstudiesgivecontrastingevidencefordustobscuration. solute magnitude M <M and chooseM to match B thr thr CharacteristicvaluesofE(B V)=0.06 0.1havebeen a given dN/dz. As a first case, we also assume that − − reportedforZnIIandCaIIsystemswithlargeW (Vladilo MgII systems contain some dust with a bimodal distri- & Peroux 2005; Wild et al. 2006). However, Murphy bution: a fraction f of them has E(B V)=0.1 (with d − & Liske (2004) found no evidence for dust-reddening of aSmallMagellanicCloud(SMC)extinctioncurve)while QSOs by foreground damped Lyman-α systems. Simi- allthe resthas E(B V)=0.01. Dust obscurationcan- − larly,York etal. (2006)couldmeasure someappreciable not be discussed separately from gravitational lensing reddeningonlyinQSOswithverystrongMgII absorbers that boosts the luminosity of background sources. For (W >1.53˚A).Moreover,radioandX-rayselectedSDSS this reason, we also compute the magnification due to quasars do not appear to be more reddened than opti- all intervening mass concentrations along a given line of callyselectedones. Inbothcasesthetypicalcolorexcess sightassuming thatthey aresingularisothermalspheres is E(B V) 0.01. (theresultingmagnificationshaveameanof1.03andan − ≃ Alltheseresultsarepuzzlingandcontradictory. Inor- r.m.s. valueof0.04butthedistributionisverypositively der to estimate the importance of dust obscuration in skewed,nearly0.8%ofthesourcesareamplifiedbymore the SDSS sample of MgII absorbers we have developed than 20%). the following simplified model. We consider a popula- Our results are summarized in Figure 1. The ab- tion of QSOs at z = 2.3 with luminosities distributed scissa shows the true number density of the underlying according to the luminosity function determined by the MgII systems (those revealed along GRB lines of sight), SDSS (Richards et al. 2006). These QSOs will be ob- while the ordinate gives f : the fraction of dusty ab- d scured by foregroundgalaxies. To model the galaxy dis- sorbers. The solid line indicates the parameter pairs for tribution,we use24mock lightconesextractedfromthe which SDSS would observe dN/dz = 0.24. Obscuration largest N-body simulation of the concordance cosmol- bias can decrease the observeddensity of absorbersby a ogy performed so far, the Millennium run (Springel et maximum factor of 3. In order to match the observed ∼ al. 2005), in which galaxies are associated with dark- density of strong MgII systems in SDSS, the number matter halos via semi-analytic modelling (Kitzbichler et density of underlying absorbers cannot be higher than al. 2006). The past light cone of an observer (i.e. an dN/dz 0.7 but, in this case, all MgII system should ≃ Porciani, Viel & Lilly 3 be very dusty. This would be in contrast with observations. York et al. (2006) found that only 14% of the MgII systems with W > 0.3 ˚A in the SDSS cata- log (and 36% of those with W > 2.4 ˚A) lie along very reddened lines of sight (∆(g i) 0.2). If this fraction − ≥ amounts to 20% for W > 1 ˚A, the only way to rec- ∼ oncile our results with the observationaldata is the case where dN/dz 0.33 (corresponding to M 21.65) thr 5 and f 0.3≃3. In this case, SDSS would m≃iss−16% of d ≃ theQSOswhichareintrinsicallybrighterthanitsmagni- tude limit (the effect of color selection is less important) andinclude1%ofthetotalnumberduetomagnification bias (plus dust obscuration). Note that the median and mean halo masses of the MgII absorbers are 3.0 1011 M⊙ and 7.5 1011 M⊙, in good agreement with B×ouché × et al. (2006). We explicitly checked that our results do not change substantially by using a Milky Way (MW) extinction curve for the dusty absorbers. In order to test if our results depend on the assumed distribution of reddening, we repeated our Monte Carlo Fig. 2.— Parameters of the reddening distribution of strong simulations assuming a two-parameter Weibull distribu- MgIIsystems. Thick and thin curves respectively mark the set tion for E(B V) (for an SMC extinction curve). The ofparametersforwhichtheobservedabundance ofabsorbersand cumulative W−eibull distribution for a variable x 0 thefractionofveryreddenedlinesofsightmatchtheSDSSvalues. is C(x) = 1 exp[ (x/λ)γ] and it is fully determ≥ined Solid,long-dashed,short-dashedanddottedlinesrefertodN/dz= 0.90,0.66,0.49,0.35 (i.e. to 0,1,2 and 3σ Poissonian fluctuations − − by the shape parameter γ > 0 and the scale parame- in the counts of GRB absorbers) respectively. The shaded area ter λ > 0. This distribution is interesting because it is bounded by the loci where the median observed color excess can attain many different shapes based on the value of λ[ln(2)]1/γ is 0.01 (lower boundary) and 0.04 (upper boundary). Models for which thin and thick curves of the same type cross γ. In particular, for γ < 1 the corresponding proba- within the shaded area are consistent with all the observational bility density function decreases monotonically and is constraints. convex; for γ = 1 it becomes the exponential distribution; for γ > 1 it vanishes at x = 0 and admits a mode at x = λ(1−1/γ)1/γ; for γ = 2 it gives the Rayleigh the variance of the counts is σ2 = N¯(1+N¯ξ¯) where ξ¯ distribution; for γ < 2.6 it is positively skewed; for is the mean two-point correlation function computed by 2.6 < γ < 3.7 it closely approximates a normal distri- averagingoverpairsofpointsbothlyingwithinanarrow bution; for γ >3.7 it is negatively skewed. We find that cylinder with radius b parallel to the line of sight. For onlymonotonicallydecreasingdistributionsforE(B−V) b = 80h−1 kpc and a redshift interval 0.3 < z < 2.2, with γ 0.3 0.5 are compatible with the data. ∼ − the galaxies hosting the absorbers have typically mean Inthiscase,therearemanysolutionsthatmatchboth correlations of some percent (slightly depending on the the density of MgII absorbers and the fraction of ab- mean galaxy luminosity). Whenever N¯> 1, superPois- sorbersalongveryreddenedQSOsobservedbySDSS(see son fluctuations are then appreciable. A∼number, X, of Figure 2). However, if we also require that the median independent lines of sight have to be combined together observed color excess is of the order of 0.01 (as found in toobtainaredshiftpathof15.5. Thisincreasesboththe theSDSSbyYorketal. 2006)wehavetoassumethatthe meancountsandthe scatterbyafactorofX sothatthe underlying incidence rate is dN/dz 0.30 (correspond- ≃ totalexcessofthescatterwithrespecttoPoissonremains ingtoM 21.7). ThisincreasesuptodN/dz 0.45 thr ≃− ≃ 1+N¯ξ¯as for single lines of sight. In consequence, the (M 21.4)ifthe2QzE(B V)value(0.04,Outram thr ≃− − scatter in the number of MgII systems is nearly Poisso- et al. 2001) is adopted. nian along QSOs and superPoissonian along GRBs. Fu- In summary, we found that estimates of dN/dz based ture data with increased statistics, might then be used on QSO spectra are likely to be underestimated by a to estimate the clustering amplitude of GRB absorbers. factor 1.3 2 if dust-obscuration bias is important. ∼ − If dN/dz ∼ 0.35 (0.45), we find that there is a 0.15% 3. STATISTICSOFABSORPTIONLINESANDBEAMSIZE (1.3%) chance to find 14 absorbers or more in a red- Franketal. (2006,herafterF06)proposedageometri- shift path of 15.5 because of random fluctuations. This cal explanation for the different incidence rate of strong shows that it is unlikely that dust obscurationbias fully MgII systems in QSO and GRB lines of sight. They ar- explains the difference in the number of MgII absorbers gued that the difference in the statistics can be readily along GRBs and QSOs. Note that in our simulations, explained if the size of the QSO beam is approximately thescatterofthenumberofabsorbersperlineofsightis 2 times larger than the GRB beam, provided the size generallylargerthan expected for a Poissondistribution of the MgII absorbers is comparable to the GRB beam because the host-galaxies of the absorbers are clustered. If, on average, there are N¯ absorbers per line of sight, and of the order of < 1016 cm2. This is in contrastwith anumberoftheoret∼icalandobservationalestimates sug- 5 Note that reducing either the maximum impact parameter b gestingthatthetypicalQSObeamisafewtimessmaller or the covering factor f would make the absorbers’ host galaxies thantheGRBbeam(seeSection4inF06andreferences fainterforagivendN/dz. therein). We show here that the solution worked out by 4 Strong MgII systems in QSO and GRB spectra F06 did not include an additional effect which changes the outcome of their model. In what follows r is the comoving radial distance and D is the angular diameter distance. For simplicity, let a us consider a population of gas clouds with comoving number density n(z), proper cross-section σ and equivalent width distribution f(W ) (normalized to unity). 0 The clouds can be detected as absorption lines in the spectrum of background continuum sources with angular beamsize Ω . If the beamsize is much smaller b than the solid angle subtended by the gas clouds, i.e. Ω σ/D2(z), the number density of absorption lines b ≪ a per unit redshift and equivalent width is d2N dr =σn(1+z)2 f(W ). (1) 0 dW dz dz 0 On the other hand, if the clouds are much smaller than the beam of the background source, i.e. Ω σ/D2(z), b ≫ a two new effects need to be accounted for. First, the observed equivalent width is proportional to the covering Fig. 3.— The cumulative probability distribution of the factor of the cloud (i.e. to the fraction of the beam area MgIIequivalentwidthsalongGRBslistedinP06(solidhistogram) coveredby a single absorber)W =σ/[Ω D2(z)]W = is compared with the fit for QSO absorbers given by Prochter et obs b a 0 al. (2006a). The two distributions are compatible at the 95.7 % [σ/σ (z)]W . Second, the mean number of absorbers b 0 confidence levelintheKolmogorov-Smirnovsense. scales proportionally to the area of the beam (note that this effect was apparently neglected by F06) so that: d2N =σ n(1+z)2 dr σb f σb W . (2) Carlo simulations). However, we found that the equiva- dW dz b dz σ σ obs lent widths listed in P06 are perfectly consistent with obs (cid:16) (cid:17) the distribution derived from SDSS QSOs (Figure 3). The last possibility is obtained when σ σ. In this b TheKolmogorov-Smirnovtestsuggeststhattheobserved ≃ case, the number of absorption lines is equivalent widths for GRB absorbers are compatible (at dN dr the 95.7 % confidence level) with being a random sam- (√σ+√σb)2n(1+z)2 , (3) pling of the probability distribution derived from SDSS dz ≃ dz QSOs. andMonte Carlosimulations must be used to derive the Therearesomeotherobservationalresultsthattheso- corresponding distribution of Wobs that depends on the lution proposed by F06 cannot explain: i) along QSOs relative positions and shape of beam and absorbers. there are no apparently unsaturated MgII absorption Let us now consider two different classes of sources lines with a doublet ratio (1:1), as would be ex- (for instance GRBs and QSOs), and denote their rela- pected if small saturated systems were being diluted tive beamsize by x = ΩG/ΩQ. At every redshift, from by a larger QSO beam; ii) an apparently unsaturated equation (2) we derive MgII absorption system with a doublet ratio (1:1) has been detected along GRB030226 (Shin et al. 2006) in d2N d2N G (W ,z)=x2 Q (W =xW ,z) . (4) thespectrumofGRB030226thussuggestingpartialcov- G Q G dWGdz dWQdz ering of the GRB beam; iii) if the strong MgII systems resemble intercloud medium of the MW their sizes are Therefore, to find four times more absorbers with likely to be in the range1-1000pc (e.g. Kobayashiet al. W > 1 ˚A along GRBs than along QSOs, the relative 2002; Rauch et al. 2002; Churchill et al. 2003; Ding et beam size must satisfy the equation4 1∞˚A ddW2NQQdz dWQ = al. 2003) which are difficult to reconcile with the sizes 1∞˚A ddW2NGGdz dWG = x x∞˚A ddW2NQQdz dWQ.RAdopting the fit proposed by F06. for the equivalent width distribution derived either by 4. STATISTICSOFABSORPTIONLINESANDLENSING R R Nestor et al. (2005) or by Prochter et al. (2006a) it is Only a few spectra of optical GRB afterglows have easytoshowthatthisequationdoesnotadmitsolutions. been taken. Is it possible that the sample is heavily bi- asedtowardslinesofsightintersectingalargenumberof Thisappliestosmallabsorbersandonlyapproximates absorbers? Gravitationallensing due to intervening ma- the case in which absorbers and beams have similar terial could in principle boost the afterglow luminosity sizes. We performed a number of Monte Carlo simu- by amplifying its beam size. This would make optical lations varying the beam and absorber sizes. For GRB spectra easier to take. afterglows we both considered disk and ring geometries Combining the data by P06 with those by Nardini et (with varying thickness) while we only considered disk- al. (2006), we find that afterglows with more than one like QSO beams. In no case could we reproduce the ob- MgII absorbers are, on average,a factor of 1.7 brighter6 servational results. If the F06 solution holds, the distribution of MgII equivalent widths along GRBs should be 6 Intermsoftheiropticalluminositymeasured12hours(inthe flatter than in QSOs (this is also evident in our Monte GRBrestframe)afterthetrigger. Porciani, Viel & Lilly 5 than the others. According to a t-Student test, there any observational constrain provided that their mass is is a 10% chance that this difference is due to random smaller than 104 M⊙ and they would behave as efficient fluctuations. If this result is strengthened by increased lenses if their physical size is smaller than their Ein- statistics (currently only four afterglows showing more stein ring, which corresponds to a lower mass limit of than one strong MgII absorber are known), it is then a few 10−6 M⊙ (Zurek, Hogan & Quinn 2006). As- × likely that some form of lensing caused by mass concen- suming that all the dark matter is in mini-clusters, we trations associated with the absorbers themselves is the expect that nearly 30% of the Swift afterglows could be cause of their increased detection probability. strongly microlensed. To explain the observed abun- The galaxies hosting the absorbers represent obvious danceofMgII absorbers,however,QSOsneednottosuf- lens candidates. However,since MgII absorbersare seen fer fromthese microlensingevents. In otherwords,QSO at large distances from galaxy cores, it is unlikely that beams have to be larger than the Einstein ring of the theycanproducelargemagnifications. OurMonteCarlo miniclusters(and,thus,oftheGRBbeams). Currentes- simulations presented in 2 show that lines of sight with timatesoftheQSOsize(<1015−16 cm)thenfavourmini § more than 2 MgII absorbers have a mean magnification cluster masseswhich are smallerthan 1 M⊙. Patchyob- of1.04andonly 2%ofthemaremagnifiedby morethan scurationoftheGRBopticalbeambydustinthecircum- afactorof1.2(seealsoMénard2005). Stronglensingisa burstenvironmentcouldmakeGRB beams smallerthan very rarephenomenon. Only a few GRBs in everythou- expected. Albeit very speculative, this scenario would sand detections are expected to be strongly lensed by certainly favour the detection of afterglows spectra with galaxy-sized halos (Porciani & Madau 2001). Millilens- an increased number of absorbers even though it is dif- ingby107M⊙ haloeshasanopticaldepthwhichisabout ficult to estimate the net effect on the observed dN/dz. 1000times smallerthan the stronglensing one (Porciani Note thatthis resultis notin contradictionwith Section & Madau 2000). 4. Iftheabsorbersizeismuchlargerthanboththebeam Afterglow spectra are generally taken within the first sizes then the equivalent width distribution function is few hours after the gamma-ray triggering event when expected to be the same for QSOs and GRBs. most of the optical emission is expected to come from An appealing possibility is that GRB afterglows are a narrow ring of radius r 4 1015(t/1hr)5/8(1 + strongly affected by magnification bias. Light sources s z )−5/8 cmwhichisexpan≃ding×atsuperluminalspeed whichareparticularlybrightinmorethanonewaveband GRB on the sky (Waxman 1997). The beam size is thus are especially likely to be lensed (Borgeest, von Linde comparable with the Einstein radius of compact so- & Refsdal 1991; Wyithe, Winn & Rusin 2003). This lar mass objects at cosmological distances r 5 “multiband magnification bias” could be very impor- E 1016(M/M⊙)1/2 and GRB afterglows can be effi≃cientl×y tant for GRBs whose optical and gamma-ray luminosi- tiesarefoundto be statisticallyindependent (Nardiniet microlensed by intervening stars and massive compact al. 2006). It is easy to show that, independently of the objects (MACHOs). When the source can be regarded lensing optical depth (and thus of the kind of lens), the as pointlike with respect to the lens, microlensing pro- fraction of lensed objects at a given redshift approaches duces a constant amplification depending on the im- unity when the mean faint-end slope of the luminosity pact parameter of the lens b (Loeb & Perna 1998). On functions in the two bands approaches -2 (Wyithe et al. timescales of days (observer frame), the magnification 2003). 7 For the faint-end of the gamma-ray luminos- then increases and reaches a maximum value when the ity function, the universal structured-jet model predicts source size crosses the lens (r = b). This rather sharp s a slope of γ = 2 (Rossi et al. 2002; Zhang & Mésza´ros brightening is a characteristic signature of microlensing − 2002) while observational estimates based on number events. For large impact parameters, when the mean counts give γ = 1.57 0.03 (Firmani et al. 2005) and magnification is < 2, and for broader source rings this − ± γ = 1.7 0.1 (Schaefer, Deng & Band 2001). The featureislesspronounced(seeFigure1inLoeb&Perna − ± luminosity function of optical afterglows is not known. 1998)andcouldthenbe noteasilydetectedobservation- Nardini et al. (2006) find that most of the observed af- ally. Forsourcesatz 2,themicrolensingopticaldepth ∼ terglows have a similar luminosity but they do not dis- isτ 0.65Ω whereΩ denotesthepresent-daydensity µl µl ≃ cuss selection effects. The fact that many afterglows are of microlenses in units of the critical density of the Uni- not detected in the optical band might suggest that the verse (Baltz & Hui 2005). Even in the most optimistic slope of the luminosity function is rather steep indeed. assumptionthat 20%ofthe darkmatter is inMACHOs, Magnificationbiascouldthenberesponsibleofthediffer- only a few percent of the GRB afterglows should be af- ent counts of MgII absorbers between GRBs and QSOs. fected by microlensing. In summary, unless the intrinsic Notethat opticallyselectedQSOshaveafaint-endslope luminosity function of GRBs (and of their afterglows) ofγ 1.6(Boyleetal. 2000;Croometal. 2004)while is extremely steep and magnification bias plays an im- ≃− (single-band) magnification bias becomes important for portantrole (see below), a lensing explanation of the in- γ 3, thereby under this scenario we do not expect creasedMgII absorptionalongGRBlinesofsightshould ≃ − beregardedasveryunlikelyinthestandardcosmological 7ThedetectionofanX-raysignalisoftenrequiredtoaccurately scenario. locate GRB afterglows for optical follow up. Three-band magni- The lensing solution works better in the presence of fication bias is even more efficient than the case discussed in the a cosmological population of small dark matter clumps. maintext. Forindependentluminositiesinthedifferentbands,the Mini clusters of dark matter (axion-like or Higgs-like) criticalmeanfaint-endslopeis-5/3(closetotheobservedvaluefor thepromptgamma-rayemission). Note,however,thatgammaand particles naturally form when a scalar field undergoes X luminosities of GRB afterglows seem to correlate rather tighly a second order phase transition below the QCD scale (e.g. Nardini et al. 2006) and this would again imply a critical (Hogan & Rees 1988). Their existence does not violate slopecloserto-2. 6 Strong MgII systems in QSO and GRB spectra QSOs to be affected by microlensing events. 43200 α t 1−α min 1 . (5) ×(cid:18) tmax (cid:19) −(cid:18)tmax(cid:19) ! 5. ASSOCIATIONOFMgIISYSTEMSTOGRBS For typical values α = β = 1.3, t = 3 days, t = 1 min max We now consider the possibility that the strong month, this gives 1058 photons per steradian that can MgII systems are associated with the GRB event. This potentially produce a second ionization of Mg atoms. solution is particularly attractive since it gives an “ad- Mostofthesephotonswillbeactuallyabsorbedbyatoms ditive” correction instead of a “multiplicative” one. In of H,C,N and O which (assuming solar abundance ra- other words, at variance with the solutions explored so tios)are more abundantthan Mg and havelower photo- far that multiply the incidence rate of MgII lines by a ionization thresholds. An optically thin shell, n < 20 constant factor, it is sufficient that a few of the 14 P06 nuclei per cm3, exposed to such a photo-ionizing flux absorbersareassociatedtotheGRBeventstofullysolve getsfullyionizedonextremelyshorttimescales. Detailed the discrepancy in dN/dz. Both the hint for a partial calculationsforhigherdensitycloudsrequireanaccurate covering of MgII systems along some GRB lines of sight treatmentofradiativetransferandarebeyondthescope andthefailedopticaldetectionofthegalaxiesresponsible of this paper. The presence of structured jets (with fast for MgII absorptions (Ellison et al. 2006) support this andslow components),alreadyinvokedto explainC IV , hypothesis. The major limitation, however, is the need Si IV and H I absorption associated with GRB 021004 for cold, metal enriched gas moving at semi-relativistic (Starling et al. 2005), is probably needed. speeds. Even assuming that the five P06 systems with In the less favoured supranova model (Vietri & Stella the largest inferred velocities are produced by interven- 1998), a supernova event preceeds the GRB with a time ing galaxies (as expected from 2), while the rest are lag ranging from weeks to a year. Radio observations § associated with GRB events, we still find that the mean suggest that the fastest ejecta of “normal” supernovae peculiar velocity of the intrinsic systems is 6 104 km Ibc (i.e. fast electrons) have typical velocities of 0.3c s−1 (with a dispersion of 3 104 km s−1). × (Berger et al. 2003) which are in agreement wi∼th the × In the fireball model, afterglow emission is produced velocities of the absorbers in P06. If the ejecta travel when the fastest ejecta from the central engine sweep at a constant velocity of 105 km s−1, they will need up and shock the circumstellar medium. This happens 10 100daystocoverad∼istanceof1016−17cm. Longer at typical distances of 1016−17 cm from the central en- ∼delay−s are needed to transport the metals produced by gine. Gas responsible of MgII absorption must thus lie the supernova at these distances. The observed narrow- further away than this. In order to produce absorption ness of MgII lines (∆v a few hundred km s−1) poses with column densities of 1015 cm−2 which fully cover some strong constraints∼on the physical size of the ab- a QSO beam one needs as little as 10−7 M⊙ of mate- sorbers. To first approximation, in an explosive event, rial with solar metallicity. Wolf-Rayet winds, binary in- ∆v/v = ∆R/R (with v velocity of the ejecta, R their teractions and a SNa explosion could have easily trans- distance from the supernova) which implies a linear size portedsuchanamountofmetalenrichedgasatthesedis- for the absorbers of 1012−13 cm. Thereby, these sys- ∼ tances. The GRB shockhasenoughenergyto accelerate tems could either be associated with narrow and dense this gas to semi-relativistic velocities only within 1018 shell-like structures or to small condensations. However, ∼ cm from the central engine. However, most likely, the itis difficult to imagine how the gascouldkeepcoldand swept up material will also be heated to temperatures to reconcile the required delays between the supernova wellabovethe ionizationthresholdofMgII .8 Therefore and the GRB phases with observations (e.g. Mésza´ros noMgII absorptionwillbepossibleuntilthegastemper- 2006). ature cools down below a few 104 K. Even though An alternative mechanism for producing the observed ∼ × the action of Rayleigh-Taylor instabilities will help re- MgII system requires that the material emitting the af- shapingthe structureofthe clouds andproduce amulti- terglow is lumpy. Mésza´ros & Rees (1998) investigated phase medium, it seems unlikely that this sequence of spectralfeaturesarisingfromultrarelativisticions inthe phenomena couldproduce the observedabsorption. Itis pre-afterglow fireball outflow. In this model, metal-rich alsodifficult toconceivehowMgII systems couldappear inhomogeneities (blobs or filaments) are typically very intheintensephotoionizationfieldoftheGRBafterglow. small(105 cm) and dense ( 1018 cm−3), although their ∼ The characteristic isotropic equivalent luminosity of the surface covering factor can be quite high. If these struc- optical afterglow in the Cousins R-band after 12 hours tures survive up to the afterglow emission they could be (intherestframe)is4.47 1030ergs−1Hz−1 (Nardiniet responsible of the observed MgII absorption since they × al. 2006). Assuming a power-law spectral energy distri- are entrained in the flow that produces the burst. Some bution with index β and a time decay with index α, the kindofmagneticmechanismshouldbe,however,invoked number of ionizing photons (with energy above the sec- to keep these blobs collimated in the afterglow phase. ond photoionizationthreshold for Mg, E >E =15.04 A promising scenario is to assume that the observed thr eV) emitted per unit solid angle from t to t = t MgII systems are associated with supernova remnants min max (both in seconds) is (SNRs) in the vicinity of the GRB. MgII absorption lines from local SNRs and superbubbles look similar dN 5.37 1055t 1.82eV β to those detected along high-z QSOs and appear to be phot = × max made of several components with small velocity disper- dΩ β(1−α) (cid:18) Ethr (cid:19) sion (Danks 2000, Bond et al. 2001, Welsh et al. 2001). Imagine that a GRB line of sight crosses the shell of a 8 Unless the relativistic shock does not penetrate the dense, youngSNRthatisexpandingatavelocityofv 3 104 metal-richcloudlet,whichisalsopossible(M.Vietripersonalcom- munication)andwouldmakeMgIIabsorptioneasier. km s−1. Also assume that the shell is sphe∼rical×and Porciani, Viel & Lilly 7 that it produces two absorption features (we postulate confidence level. This suggests that the absorbers the presence of cold pockets of gas in the shell) in the are larger than the sources and provides evidence GRB spectrum: one blueshifted and one redshifted by against the solution proposed by F06. the amount (1+z )(1 v/c). Since GRBs are nor- GRB ± mally associated with the highest-redshift absorbers in We showed that GRB afterglows with more than • their spectra, one would erroneously assign a redshift one absorber are brighter than the others by a (1+z )(1+v/c) to the GRB and say that the sec- factor of 1.7. If confirmed by increased statis- GRB ond absorber moves with a relative velocity of 2v with tics, this finding would suggest a lensing origin respect to it. How likely is it that a GRB lines of sight of the MgII discrepancy. However, in the stan- intersects a SNR? A typical star forming region like 30 dard cosmological scenario, lensing optical depths Doradus has a characteristic size of 100 pc, while a are small and difficult to reconcile with the ob- ∼ young SNR has a radius of 10 pc. The optical depth served counts of MgII absorbers. This may hint ∼ for crossing a shell along a random line of sight towards towards the existence of an exotic population of the GRB is thus of order unity if the number density of lenses. Forinstance,microlensingduetominidark SNRsis 3 10−5pc−3,whichcorrespondstonearly15 matterclumpscouldexplainthedifferencebutthis ∼ × objectswithinasinglestarformingregion. X-raystudies also requires QSO beams to be larger than GRB of30DoradushavedetectedseveralSNRcandidatesand afterglows which is in disagreement with current five superbubbles (Townsley et al. 2006 and references observational estimates. therein) thus showing that the probability for a line of sight to cross a SNR is not negligible. Note that not Duetotheirmultibandselectionandtheiremission • in all GRB spectra the expanding shell of a SNR will properties, GRB afterglows are particularly sensi- produce two absorptionlines. Sometimes features of the tive to magnification bias. Independently of the host galaxy will be present together with one line from nature of the underlying lenses, a large fraction of the SNR.Inthis casethe velocitydifference betweenthe the observed GRBs would be lensed if the average lines will be smaller. faint-end slope of their gamma and optical luminosity functions approaches -5/3 – -2. According 6. SUMMARY to current models for prompt and afterglow emis- Weaddressedpossibleexplanationsforthedifferentin- sion this is not unlikely. Present observations sug- cidence rate of strong MgII systems along GRBs which gestaslopeofγ 1.6forthepromptgamma-ray ∼− is about 4 times higherthan alongQSOs. There are a emission+whiletheluminosityfunctionsofoptical number o∼fphenomena that potentially contribute: dust- afterglows is totally unconstrained. Magnification obscuration bias, different beams sizes between GRBs biasthenprovidesaviablesolutiontotheobserved andQSOs,gravitationallensing,associationofGRB ab- discrepancy. sorbers with the circumburst environment. Our results can be summarized as follows. The production of MgII absorbers in the cir- • cumburst environment (either by cold and dense ConsideringasimplifiedmodelforMgII absorbtion cloudletsofmetal-richmaterialacceleratedtosemi- • based on a set of realistic numerical simulations relativistic speeds or, most likely, by SNRs unre- of galaxy formation and able to reproduce all the latedtothe GRBeventitselfbutlyinginthesame observationalconstraints,we showedthat the inci- star forming region) could further reduce the sta- dence rate of MgII systems in QSO spectra can be tistical significance of the observed discrepancy to underestimated by a factor 1.3-2 due to dust ob- a level compatible with statistical fluctuations due scuration bias. This is not enough to fully explain to small number statistics. thediscrepancywiththenumberofabsorbersalong GRBs. We conclude that, with the possible exceptionof mag- nificationbias,itisunlikelythatoneoftheseeffectsonits We critically discussed the solution proposed by owncanfully accountforthe observedcounts. However, • F06where QSOsareassumedto be afactoroftwo the combined action of some of them can substantially larger than GRBs. Accounting for the dependence reduce the statistical significance of the discrepancy be- of both the equivalent width and the number den- tween the incidence of strong MgII systems in QSO and sity of absorbers with the beam size, we showed GRB spectra. thatitisnotpossibletofullyexplainthedifference in the observed counts by assuming that the two classes of background sources have different char- We thank B. Carswell, M. Haehnelt, F. Miniati, M. acteristic sizes. We also found that the equivalent- Pettini, E. Pian, M. Rees and M. Vietri for useful dis- width distribution of MgII systems detected along cussions. P. 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