Polarization of prompt and afterglow emission of Gamma-Ray Bursts
PPolarization of prompt and afterglow emission ofGamma-Ray Bursts
Stefano Covino and Diego G¨otz INAF / Brera Astronomical Observatory, Via Bianchi 46, 23907, Merate (LC), Italy AIM–CEA/DRF/Irfu/Service d’Astrophysique, Orme des Merisiers, 91191 Gif-sur-Yvette, France
Abstract
Gamma-ray bursts and their afterglows arethought to be produced by an ultra-relativisticjet. One of the most important open questions isthe outflow composition: the energy may be car-ried out from the central source either as kineticenergy (of baryons and/or pairs), or in electro-magnetic form (Poynting flux). While the totalobservable flux may be indistinguishable in bothcases, its polarization properties are expected todiffer markedly. The prompt emission and af-terglow polarization are also a powerful diagnos-tic of the jet geometry. Again, with subtle andhardly detectable differences in the output flux,we have distinct polarization predictions. In thisreview we briefly describe the theoretical scenar-ios that have been developed following the obser-vations, and the now large observational datasetsthat for the prompt and the afterglow phases areavailable. Possible implications of polarimetricmeasurements for quantum gravity theory test-ing are discussed, and future perspectives for thefield briefly mentioned.
Keywords.
Polarization - Gamma-ray burst:general
Polarimetric measurements can provide usefulcomplementary information about the physi-cal processes at work in Gamma-Ray Bursts(GRBs). Indeed several different possible sce-narios have been invoked to interpret the largeamount of observational data now available forthe GRBs. Most of the theoretical efforts havebeen applied to the so-called “standard model” (Rees & Meszaros 1992; Meszaros & Rees 1993;Piran 2004) that, although a fully satisfactorypicture is still missing, offers the best (while notunique) interpretative scenario for the polarimet-ric observations.In this review we have separated the GRBphenomenology in the two traditional phases:prompt and afterglow, mainly due to the differ-ent observational techniques. Further subdivi-sions (plateau phase, steep decay, etc.) are men-tioned when required. In Sections 2.1 and 3.1we summarize the current status of theoreticalmodeling of polarization in prompt and after-glow observations, in Sections 2.2 and 3.2 wepresent the current status of the observations,and in Section 4 we provide some insights intothe implication of these measurements for fun-damental physics. Some general conclusions arefinally drawn in Section 5.
The expected level of polarization of the prompt γ -ray emission in GRBs has been estimated byseveral authors for different models, or variationswithin them. In most cases, the observed γ -rayemission is due to the synchrotron radiationfrom relativistic electrons. To have a high ra-diative efficiency and to allow for the short timescale variability in the GRB light curves, theseelectrons have to be in the fast cooling regime.Their time-averaged distribution is a brokenpower law, n ( γ ) ∝ γ − p (cid:48) with p (cid:48) = p + 1 aboveΓ m and p (cid:48) = 2 below, where Γ m is the minimum1 a r X i v : . [ a s t r o - ph . H E ] J un orentz factor of the injected distribution ofelectrons, and p (cid:39) − . syn = ( p (cid:48) + 1) / ( p (cid:48) + 7 / syn = ( p + 2) / ( p + 10 / (cid:39)
75% above ν m and Π syn = 9 / (cid:39)
70% below, where ν m , thepeak of the spectrum in νF ν , is the synchrotronfrequency of electrons at Γ m . High polarizationlevels can also be reached if inverse Comptonscatterings are the dominant radiative process.Actually different scenarios in terms of radia-tion processes and observer’s viewing angle canbe envisaged to explain the presence of polar-ized emission during the prompt phase of GRBemission. They can be roughly divided in twofamilies: intrinsic models and geometric models,for which peculiar observing conditions are re-quired.1. Synchrotron emission from shock-accelerated electrons in a relativisticjet with an ordered magnetic field containedin the plane perpendicular to the jet expan-sion . This scenario is compatible with themagnetic field being carried by the outflowfrom the central source, as the poloidalcomponent decreases much faster with ra-dius than the toroidal one. The polarizationlevel at the peak of a given pulse can be ashigh as Π / Π syn ∼ .
8, i.e. Π ∼ / Π max ∼ .
6, i.e.Π ∼
45% in this case (Granot 2003; Granot& K¨onigl 2003; Nakar et al. 2003). Themain requirement for this model to apply isto have a uniform magnetic field in space,i.e. with a coherence spatial scale Rθ B with θ B (cid:38) / Γ. In this scenario the polarizationlevel and angle can vary during the burstonly if the magnetic field is not uniform intime, while the opposite needs to be true(i.e. a magnetic field constant in time) toexplain a high level of the time-integratedpolarization (Nakar et al. 2003). But amagnetic field anchored in the centralengine and carried by the outflow to largedistance (see e.g. Spruit et al. 2001) isnot the only possibility. A magnetic fieldgenerated at the shock could also work in principle, and even favour variability, butthis requires a process capable of locallyincreasing the field coherence scale (thefield is most probably initially generatedon small, skin-depth, scales). The existenceof such a process is not yet settled in ourpresent knowledge of the micro-physics inmildly relativistic shocks. Note that thecondition θ B (cid:38) / Γ is really necessaryonly in the pulses with the highest levelof polarization. If θ B is smaller, so that anumber N ∼ (Γ θ B ) − of mutually incoher-ent patches are present in the visible region,the level of polarization will decrease, butthe variability (both of the polarizationlevel and angle) will increase (Granot2003). Indeed if the radiating electronsare accelerated in internal shocks (Rees& Meszaros 1994; Kobayashi et al. 1997;Daigne & Mochkovitch 1998), the Lorentzfactor associated with the individual shellsis necessarily varying in the outflow, whichcan be an additional source of variabilityfor the polarization. If θ B and 1 / Γ areclose, the number of coherent patches in thevisible region could vary from one pulse toanother. This scenario could hence producetime variable polarization, as long as thecoherence scale θ B of the field is larger than1 / Γ in most of the emitting regions. Apotential difficulty remains: an additionalrandom component of the magnetic fieldis probably necessary to allow for particleacceleration in shocks. This componentwould reduce the coherence of the fieldand hence the level of polarization bysome factor, which is however difficult toestimate, as the intensity of this additionalcomponent is not well constrained (Granot2003; Nakar et al. 2003);2.
Synchrotron emission from a purely elec-tromagnetic outflow . In this scenario theGRB is powered by the rotational energyof a magnetar-like progenitor (e.g. Metzgeret al. 2011). It is first converted intomagnetic energy by the dynamo action ofthe unipolar inductor, propagated in theform of Poynting-flux-dominated flow, andthen dissipated at large distances from the2ource. The estimated level of polarizationin this case is comparable with the previousscenario (up to ∼ Synchrotron emission from shock-accelerated electrons in a relativistic jet witha random field generated at the shock andcontained in the plane perpendicular to thejet velocity . A high level of polarization canbe obtained even with a random magneticfield of the jet is observed from just outsideits edge (Ghisellini & Lazzati 1999; Wax-man 2003). The polarization at the peakof a given pulse can reach Π / Π syn (cid:39) . (cid:39)
60% resulting in a time-integratedvalue of the order of Π / Π syn (cid:39) . − . (cid:39) −
45% (Granot 2003; Granot &K¨onigl 2003; Nakar et al. 2003). Howeverthese high values are obtained if the jet isseen with θ obs (cid:39) θ j + 1 / Γ, where θ j is theopening angle of the jet and θ obs the anglebetween the line-of-sight and the jet axis.Such viewing conditions are rare, except if θ j ∼ / Γ. Variability of the polarizationlevel is expected if the Lorentz factor isvarying in the outflow, as for instance inthe internal shock model. Observations aremade at θ obs = θ j + k/ Γ with k being largerfor emitting regions with a larger Lorentz factor. The maximum level of polarizationis obtained for k ∼ k for k ≥
0. On average,the highest polarization should thereforenot be found in the brightest pulses. Thisis however difficult to test, as the intrinsicluminosity of each pulse is not necessarilythe same. In addition, as the emissionfrom several pulses can be superposed, themeasured polarization level, which is flux-weighted, could be reduced by a sizeablefactor (Granot & K¨onigl 2003). Finally, theobserved polarization can also be reduced ifthe jet edges are not sharp enough (Nakaret al. 2003). As shown by Granot & K¨onigl(2003), similar conditions as for scenario(3) would be required for a scenario wherethe field is ordered but parallel to the jet,leading to the same conclusions.4.
Synchrotron emission from shock-accelerated electrons in a relativisticjet with an ordered magnetic field parallelto the jet velocity . This case has beenstudied by Granot & K¨onigl (2003) andgives very similar results to model (3). Theviewing conditions have to be the same andit suffers from the same difficulties as listedabove.5.
Inverse Compton emission from relativisticelectrons in a jet propagating within a pho-ton field (”Compton drag” model) . InverseCompton scattering of external light bythe electrons in highly relativistic narrowlycollimated jets as the origin of GRBs hasbeen suggested for the first time by Shaviv& Dar (1995). The level of polarizationin this scenario can be even higher thanfor the synchrotron radiation and reach60 − θ j (cid:46) θ obs (cid:39) θ j + 1 / Γ. These viewingconditions are very similar to those ofmodel (3). This scenario predicts a lowerlevel of polarization for the afterglow phase(see later, Dado et al. 2004). Again, the3olarization is reduced if the edges of thejet are not sharp enough. Variability of theLorentz factor will again result in a varyingpolarization, with the same difficultiesregarding the final level of polarization asin model (3). However, variations of theLorentz factor could possibly be less largein this scenario as part of the variabilityof the light curve can be related to theinhomogeneity of the ambient photon field.6. Independently from the emission process(synchrotron or inverse Compton), frag-mented fireballs (shotguns, cannonballs,sub-jets) can produce highly polarized emis-sion, with a variable polarization amplitude.The fragments are responsible for the singlepulses and have different intrinsic proper-ties (such as Lorentz factors), opening an-gles, orientations with respect to the ob-servers and magnetic domains. (e.g. Lazzati& Begelman 2009). In this case the mostpolarized pulses are those which have aboutone tenth of the flux of the main pulse, i.e.an anti-correlation between the polarizationlevel an the GRB pulse flux is expected.
The measurement of polarization during theprompt phase of GRBs has always been challeng-ing. This is mainly due to the fact that no widefield gamma-ray polarimeter with a large effec-tive area has yet been flown, and that many ofthe measurements attempted to date have beenperformed with instruments which have somepolarimetric capabilities, but do not have anexplicit polarimetric oriented design. In addi-tion at odds to the afterglow emission, the GRBprompt emission is very limited in time, mostlyless than ∼
100 s, and hence in spite of the highaverage flux of GRBs, the total number of col-lected photons is often too limited to derive sta-tistically stringent limits for polarization.
The first attempt to measure linear polariza-tion in the prompt emission of GRBs was re-ported by Coburn & Boggs (2003). They used the Reuven Ramaty High Energy Solar Spectro-scopic Imager (RHESSI) observations of GRB021206. RHESSI has an array of nine large-volume (300 cm ) coaxial germanium (Ge) detec-tors with high spectral resolution, and has beendesigned to study solar flares in the 3 keV–17MeV energy range. In the soft gamma-ray en-ergy range (0.15–2.0 MeV) the dominant photoninteraction in RHESSI is Compton scattering.Polarization at high energies can be measured,thanks to the polarization dependency of the dif-ferential cross section for Compton scattering dσd Ω = r (cid:18) E (cid:48) E (cid:19) (cid:18) E (cid:48) E + E E (cid:48) − θ cos φ (cid:19) (1)where r is the classical electron radius, E theenergy of the incident photon, E (cid:48) the energy ofthe scattered photon, θ the scattering angle, and φ the azimuthal angle relative to the polariza-tion direction. Linearly polarized photons scat-ter preferentially perpendicularly to the incidentpolarization vector. Hence by examining the an-gles of scattering of the photons among the Gedetectors, one can in principle derive the degreeand angle of linear polarization of the incidentphotons.Coburn & Boggs (2003) reported a high levelof linear polarization of Π=80 ±
20% (close to andbeyond the theoretical value, see Section 2 . > σ ) for GRB021206. In the RHESSI detector a small fractionof the incident photons undergoes a Comptonscattering in a given detector before being photo-electrically absorbed in a second detector (or un-dergo other scatterings). The accurate analysisof the photon scattering angles can be exploitedto measure the degree of polarization of the inci-dent photons. In addition RHESSI is a rotatinginstrument (4 s period), which presents the ad-vantage of averaging out the effects of asymme-tries in the detector and the passive materials.GRB 021206 was a quite bright GRB with a flu-ence of 1.6 × − erg cm − in the 25–100 keVenergy band, and a peak flux of 2.9 × − ergcm − s − . Scattered photons represent about10% of the total events. Coburn & Boggs (2003)interpreted the angular modulation measured inthe data as a high-level polarization signal.However subsequent re-analyses of the samedata set could not confirm this result reporting4 polarization level compatible with zero (Rut-ledge & Fox 2004; Wigger et al. 2004). These au-thors show that the number of suitable events forpolarization analysis has been over-estimated bya factor 10 (830 ±
150 versus 9840 ± >
35% and Π > At the time of its discovery by the
INTEGRAL
Burst Alert System (IBAS) (Mereghetti et al.2003), GRB 041219A (McBreen et al. 2006; G¨otzet al. 2011) was among the top 1% in termsof GRB fluence. This prompted different at-tempts to measure its polarization with the in-struments that observed it. The first attemptwas performed using the SPI spectrometer onboard
INTEGRAL . SPI (Vedrenne et al. 2003)is made by individual hexagonal Ge detector andthe measuring technique used is similar to theone used for RHESSI. Kalemci et al. (2007) re-ported a high level of polarization for this GRB(Π = 98 ± +31 − % and the polariza-tion angle to P.A. = 70 +1411 degrees. However,they could not completely exclude the presenceof a systematic effect mimicking the observed po-larization degree.GRB041219A was also observed by the Im-ager on Board the INTEGRAL Satellite (IBIS;Ubertini et al. 2003). Thanks to its two super-posed pixellated detection planes – ISGRI (Le-brun et al. 2003), made of CdTe crystals (4 × × × × N ( φ ) = S [1 + a cos 2( φ − φ )] , (2)one can derive the polarization angle, P A = φ − π/ nπ , and the polarization fractionΠ = a /a , where a is the amplitude ex-pected for a 100% polarized source derived byMonte Carlo simulations (see Forot et al. 2008).IBIS has been used to measure the polarizationfrom bright gamma-ray sources such as the Crabnebula Forot et al. (2008), and the black hole bi-nary Cyg X–1 Laurent et al. (2011b).Indeed to perform the polarization analysis,the source flux as a function of φ is derived,and the scattered photons are then divided in6 bins of 30 ◦ . To improve the signal-to-noise ra-tio in each bin, one can take advantage of the π -symmetry of the differential cross section, i.e.the first bin contains the photons with 0 ◦ < φ < ◦ and 180 ◦ < φ < ◦ , etc. The chance coin-cidences (i.e. photons interacting in both detec-tors within a time window of 3.8 µ s but not re-lated to a Compton event), have been estimatedusing the data before the GRB and subtractedfrom each detector image following the proceduredescribed in Forot et al. (2008). The derived de-tector images are then deconvolved to obtain skyimages, where the flux of the source in each binis measured by fitting the instrumental PSF to5he source peak, building a so-called polarigramof the source, see Fig. 1.The polarigrams can then be fitted with Eq. 2using a least squares technique to derive a and φ . Confidence intervals on a and φ cannot, onthe other hand, be derived from the fit, since thetwo variables are not independent. They werederived from the probability density distributionof measuring a and φ from N independent datapoints over a π period, based on Gaussian dis-tributions for the orthogonal Stokes components(see Eq. 2 in Forot et al. 2008).Using the same method polarization couldbe measured for two other GRBs (061122 and140206A, see Fig. 2) with IBIS (G¨otz et al. 2013,2014), see Tab. 2, but no time-resolved analysiscould be performed due to the limited statistics,making GRB041219A the only GRB for which atime variable polarization signal could be mea-sured to date with IBIS. High levels of linear polarization could be mea-sured also for three GRBs (100826A, 110301Aand 110721) by the Gamma-Ray Burst Polarime-ter (GAP; Yonetoku et al. 2011a) experiment onboard the IKAROS spacecraft (Yonetoku et al.2011b, 2012). GAP is designed to measure thedegree of linear polarization in the prompt emis-sion of GRBs in the energy range 70–300 keV.Also in the GAP case the detection principle isthe anisotropy of the differential Klein-Nishinacross section for Compton scattering. The GAPconsists of a dodecagon (twelve-sided polygon)plastic scintillator with a single non-position sen-sitive photomultiplier tube of 17 cm in diameterand 6 cm in thickness surrounded by 12 CsI(Tl)scintillators with 5 mm in thickness. The centralplastic scintillator serves as a Compton photonscatterer and the angular distribution of scat-tered photons coinciding in time with the plas-tic scintillator is measured by the surroundingCsI scintillators each with an angular resolutionof 30 ◦ . In fact, by examining the coincidenceswithin a time window of 5 µ s, one can measurean asymmetry in the detector number counts forthe CsI detectors. A consistent polarization measurement has been ob-tained with SPI by McGlynn et al. (2009).
As shown in Table 2 the GAP succeeded tomeasure the linear polarization for three GRBs.In particular for GRB 100826A (see Fig. 3),which had a similarly high fluence as 041219A,Yonetoku et al. (2011b) were able to measure achange in the polarization angle by dividing theGRB in two ∼
50 s long time intervals: the an-gle changed from 159 ± ◦ to 75 ± ◦ (1 σ c.l.for two parameters of interest) with a signifi-cance of 3.5 σ for the change. For this burstthe averaged background coincidence rate is 5.6counts s − CsI − , and the total coincidence γ -rays suitable for polarization analysis are 4281and 2733 for the first and second intervals re-spectively. The detector response to a polar-ized source has been calculated with GEANT4Monte Carlo simulations and the predicted mod-ulation curves have been computed for differentgeometrical and spectral input parameters. Theobserved modulation curves have then been fit-ted using a least-squares method to the modelledcurves. Attempts to review the whole subject or someselected topic have been carried out by severalauthors (Bj¨ornsson 2003; Lazzati 2004; Covinoet al. 2004; Malesani et al. 2005; Lazzati 2006,2010; Covino 2010; Kobayashi 2012). We nowdiscuss at first some of the main theoretical sce-narios that have been developed in the context ofthe “standard model”, and later follow in somedetail the observations so far carried out and howthey have been modeled in this context. We de-vote our attention to afterglow phase althoughmention of phenomena possibly more related tothe prompt emission, e.g. X-ray flares or opti-cal emission during the prompt phase itself, arepossible. On the contrary, phenomena definitelyof high interest but not directly related to theGRB emissions, e.g. polarization of supernovae(SN) associated with GRBs, are not discussedhere (see Wang & Wheeler 2008).
The concept of an afterglow, following the main,high-energy, GRB emission was probably firstexplicitly introduced in Paczynski & Rhoads6igure 1: Polarigrams of the different time intervals that have been analysed for GRB041291A (seeTable 1). For comparison purposes, the curves have been normalized to their average flux level.The crosses represent the data points (replicated once for clarity) and the continuous line the fitdone using Eq. 2. For each polarigram the probability, P , is shown that the polarigram measuredcorresponds to an un-polarized (Π < < φ )/S.. From G¨otz et al. (2013).7able 1: Polarization results for the different time intervals. From G¨otz et al. (2009)Name T start T stop Π P A
ImageU.T. U.T. % degrees SNRFirst Peak 01:46:22 01:47:40 < ±
25 38 ±
16 20.0P6 01:46:47 01:46:57 22 ±
13 121 ±
17 21.5P8 01:46:57 01:27:07 65 ±
26 88 ±
12 15.9P9 01:47:02 01:47:12 61 ±
25 105 ±
18 18.2P28 01:48:37 01:48:47 42 ±
42 106 ±
37 9.9P30 01:48:47 01:48:57 90 ±
36 54 ±
11 11.8Errors are given at 1 σ c.l. for one parameter of interest.Table 2: Summary of recent GRB polarization measurement by IBIS/SPI and GAP.GRB Π Peak energy Fluence Energy Range Redshift Instrument(68% c.l.) (keV) (erg cm − ) z ±
26% 201 +80 − × − +0 . − . IBIS, SPI06122 >
60% 188 ±
17 2.0 × − +0 . − . IBIS, SPI100826A 27 ±
11% 606 +134 − × −
20 keV–10 MeV 0.71–6.84 GAP110301A 70 ±
22% 107 ± × −
10 keV–1 MeV 0.21–1.09 GAP110721 84 +16 − % 393 +199 − × −
10 keV–1 MeV 0.45–3.12 GAP140206A >
48% 98 ±
17 2.0 × − ± redshift based on empirical prompt emission correlations, not on afterglow observations.(1993). As for all phenomena involving parti-cle acceleration, polarimetry (Tinbergen 1996) isnaturally considered a powerful diagnostic tool.The first attempt to derive predictions to becompared with observations came probably byLoeb & Perna (1998). The original idea is in-deed still of some interest, and it is based on theobservation that a cosmological GRB should ap-pear on the sky as a narrow expanding emissionring (e.g., Waxman 1997). After about a day,the ring radius, ∼ × cm (t/day) / , shouldbe comparable to the Einstein radius of a solarmass lens at cosmological distance. Microlens-ing by an intervening star can therefore signif-icantly affect both the light curve and the po-larization signal (Ioka & Nakamura 2001). Thepredictions are clearly dependent on the specificafterglow model and outflow energy structure,and on the mechanisms producing the polarizedflux. The idea of observing microlensing eventsfor GRBs was originally introduced well beforethe detection of the first afterglow (Gould 1992;Mao 1993), and the probability for a stellar mi-crolensing of a source at a cosmological redshift is estimated to be ∼ . ∗ b (Press & Gunn 1973;Gould 1995), where Ω ∗ is the mean density ofstellar-mass objects in the universe, in units ofthe critical density, and b is the impact param-eters in units of the Einstein radius. Adoptingtypical parameters as in Loeb & Perna (1998) theprobability turns out to be close to unity and thelensing duration is about one day, driven by theemitting area expansion rate.The afterglow polarization in Loeb & Perna(1998) is generated locally at the afterglow emis-sion region, which is modeled as a finite set ofdiscrete patches, each having a coherent and in-dependent magnetic field. The synchrotron ra-diation emitted by each patch, if the electron en-ergy distribution follows a power-law with index p , is polarized at a level (Rybicki & Lightman1979): Π = p + 1 p + 7 / , (3)which for p ∼ ∼ .
7. Clearly,a microlensing phenomenon able to magnify partof the emitting region might allow us to study indetail its magnetic and energy structure. The8igure 3: Left:∆ χ map of confidence contours in the Π, φ p ) plane for GRB 100826A, obtainedby the combined fit of the Interval-1 and -2 data. Here φ p is the phase angle for Interval-1. Thewhite dot is the best-fit result, and we calculate ∆ χ values relative to this point. A color scale baralong the right side of the contour shows the levels of the ∆ χ values. The null hypothesis (zeropolarization degree) can be ruled out with 99.4% (2.9 σ ) confidence level. Right: Number of coinci-dence γ -ray photons (polarization signals) against the scattering angle of GRB 100826A measuredby the GAP in 70–300 keV band. Black filled and open squares are the angular distributions ofCompton scattered γ -rays of Interval-1 and -2, respectively. The gray solid lines are the best-fitmodels calculated with our GEANT4 Monte Carlo simulations. From (Yonetoku et al. 2011b).total polarization observable from the whole af-terglow emission depends on the sum of the po-larized flux from each patch, which can haverandom orientation. In this case the total av-erage polarized flux, < P > ∝ /N , and tends tozero for a large number of independent patches.Given the statistical nature of the sum involvedin the derivation of the total polarization, onecan expect random variations of both the totalpolarized flux and position angle in time, duringthe afterglow evolution. However, in case a lenscan magnify a part of the emitting region thisis going to dominate the sum and substantiallymodify the expected observable polarization andoffer a powerful diagnostic tool for the magneticfield and energy structure of the afterglow out-flow.The scenario with polarization generated by alarge number of independent magnetic domainswas further developed by Gruzinov & Waxman(1999). The authors observed that the magneticfields must be generated in the blast wave be-cause to match the afterglow observations mag- netic fields much larger than those typically ex-istent in shock-compressed interstellar medium[ISM, B ∼ Γ B ISM ∼ − (Γ / ) G, where Γis the shock Lorentz factor] are required. How-ever, the resulting polarization for an unresolvedsource depends also on the coherence length ofthe generated field. If their length grows atabout the speed of light, and it is therefore com-parable to the thickness of the blast wave, amaximum polarization at about 10% is expected.The emitting region will be covered by a hun-dred mutually incoherent patches. The degreeand direction of polarization should depend ontime. The polarization coherence time is ∼ (cid:15)t with a polarization degree Π ∼ (cid:15) / %, where t is the observing time and (cid:15) ( <
1) is rate ofgrowth of the coherence length in units of thespeed of light. Polarization at a much lower levelwould imply that the magnetic fields generatedat the shock are highly tangled and confined tothe shock front.How magnetic fields can be generated in ul-tra relativistic shocks is still far from being fully9nderstood (Bykov et al. 2012). Beyond shock-compression of the ISM magnetic field, it is pos-sible that a magnetic field already existent in anyGRB progenitor is carried by the outflow plasmaor by a precursor wind. Because of the flux freez-ing, the field amplitude would decrease as thewind expands and even in the case of a progeni-tor with very strong magnetic field ( B ∼ G)at R ∼ cm the field amplitude would be afew orders of magnitude too low to match theobservations. Several authors (e.g., Medvedev& Loeb 1999; Inoue et al. 2011) proposed thatrelativistic two-stream instabilities can generatemagnetic fields with 10 − − − of the equipar-tition energy density ( U B / π ) in collisionlessshocks (see however Gruzinov 1999). The gen-erated fields are parallel to the shock front andfluctuate on the very short scale of the plasmaskin depth. Since the afterglow synchrotron ra-diation is beamed toward the observer within avery small opening angle, Θ ∼ Γ − (cid:28)
1, whichis considerably smaller than the beaming angleof the jet associated with the GRB, the regionof the blast wave actually accessible to a dis-tant observer is then very small. The emissionalong the line-of-sight axis to the source centersuffers from the shortest geometric time delay,and hence originates at a larger radius (lowerLorentz factor) and is dimmer than slightly off-axis emission. The source therefore appears asa narrow limb-brightened ring (Granot et al.1999). The outer cutoff of the ring is set by thesharp decline of the relativistic beaming and dueto the relativistic aberration the shock surfacefor a distance observer appears almost alignedwith the line of sight at the edge of the ring.The small scale randomly generated magneticfield at the limb of the ring does not averageout and some net polarization directed radiallyis possible. Since the source for a distant ob-server is symmetric the net polarization fromsuch a source is expected to vanish unless thesymmetry is broken, for instance due to polar-ization scintillation in the radio band or, as al-ready mentioned, by gravitational microlensing(Loeb & Perna 1998). A late-time decline inthe amplitude of intensity scintillations for ra-dio afterglows has been detected and allowed usto derive direct constraints on the physical sizeof the emitting region (Frail et al. 1997; Taylor Figure 4: Geometry of the beamed fireball. Notethat photons emitted in the comoving frame atan angle π/ θ ∼ / Γ with the line of sightin the observer frame. From Ghisellini & Lazzati(1999).et al. 1998). A rather detailed analysis of theexpected polarization due to scintillation on ra-dio observations of GRB afterglows was carriedout by Medvedev & Loeb (1999). At early timesthe source size is small compared to the charac-teristic angular scale of the scintillation and theexpected polarization is low, however it growsmonotonically with the source angular size andshould saturate to the intrinsic polarization levelemitted at the source (possibly that predicted byEq. 3) in several weeks.A different, and in principle complementary,approach was developed almost simultaneouslyby Ghisellini & Lazzati (1999) and Sari (1999).The idea is based on the assumption that we areseeing a collimated fireball, i.e. a jet, slightlyoff-axis. Even in case the locally generated mag-10etic field at the shock is completely tangled,the anisotropy introduced by the interplay be-tween the physically collimated emitting regionand the aberration due to the ultra relativisticmotion of the shock front can introduce some lin-ear polarization. The magnetic field is assumedto be completely tangled if the shock is observedface-on, but with some degree of alignment ifobserved edge-on. This might happen for themagnetic configuration discussed in Medvedev &Loeb (1999) and Gruzinov (1999) but also due tothe effect of compression along one direction ofthe shocked region as proposed by Laing (1980).Photons emitted at right angle in the shock co-moving frame can be polarized at a level, P ,depending on the degree of order of the mag-netic field in the plane perpendicular to the shockfront. Since the emitting region is supposed tomove with Γ (cid:29) θ c is the outflow open-ing angle and θ is the angle between the lineof sight and the jet axis ( θ ≤ θ c ), we can iden-tify three regimes for the polarization dependingon the time evolution of the outflow Lorentz fac-tor. At early times Γ is sufficiently high to allowthe observation of a small area of the emittingregion and the situation is perfectly symmetric,no or very small polarization should be observ-able. This is also true at late-time when thearea accessible to the observer is large enough toinclude the whole outflow cone. At intermedi-ate times, apart from the null probability case ofline of sight perfectly aligned with the jet axis,1 / Γ becomes comparable to θ c − θ , and the ob-server begins to see the physical edge of the col-limated outflow. The global symmetry is brokenand some polarization is observed. This geomet-ric model allows one to derive the polarizationtime-evolution since depending on the percent-age of the outflow border visible for the observerthe horizontal and vertical polarization compo-nent mix in a different way. Two polarizationmaxima are then expected (the first is due to thehorizontal component, and the latter to the ver-tical one) with a period of null polarization in be-tween. Between the two maxima a sharp rotationof the position angle by 90 ◦ is predicted. Thesecond maximum is always larger than the first and, according to Ghisellini & Lazzati (1999): P max (cid:39) . P (cid:18) θ o θ c (cid:19) . (4)The above relation is true within a few percentif 1 / ≤ ( θ o /θ c ) ≤ ◦ ≤ θ c ≤ ◦ .Bj¨ornsson & Lindfors (2000) explored the effectof a possible lateral expansion of the jet, whicheffectively translates into a change of the θ o /θ c ratio. The authors argued that decreasing theratio shifts the maxima toward later times anddecreases their magnitude.The specific polarization predictions dependon the detail of the deceleration of the fireballand on the values of θ c and θ (and P ). How-ever the general picture is independent of themodel parameters and a strong link between thetotal flux from the afterglow and polarizationcan be singled out. The epoch correspondingto the position angle rotation should roughly co-incide with the jet-break occurrence, i.e. whena distant observer realizes that the source is notspherical symmetric and records a deficit in emit-ting area that translates to a steeper decline ofthe light-curve. Therefore, the total and polar-ized flux time evolution should be closely linkedto each other offering a powerful observationaltest for the model and the fireball parameters.The possible effect of an ordered field in theambient medium for the observed polarizationfrom GRB afterglows was investigated by Gra-not & K¨onigl (2003). The rationale was to pos-sibly explain observations showing a constant orslowly variable polarization level during the af-terglow evolution with almost constant positionangle. We have already mentioned that for typ-ical ISM the post-shock field would be too weakto produce the observed synchrotron emission.However, it could be stronger if the shock prop-agates into a magnetized wind of a progenitorstar or into a pulsar-wind bubble (the magneticenergy fraction, (cid:15) B , would increase from about10 − to 10 − − − ). An ordered magnetic fieldwould affect the observed polarization dependingon ratio of the ordered-to-random field. The to-tal polarization from an afterglow with a locallygenerated random magnetic field, B rnd , and an11rdered component, B ord , turns out to be: P = (cid:18) ηP ord η (cid:19)(cid:34) (cid:18) P rnd ηP ord (cid:19) − (cid:18) P rnd ηP ord (cid:19) cos 2 δ (cid:35) / (5) θ = 12 arctan (cid:18) sin 2 δ cos 2 δ − ηP ord /P rnd (cid:19) (6)where η ≡ I ord /I rnd ≈ (cid:104) B (cid:105) / (cid:104) B (cid:105) is the ratioof the observed intensities in the two componentsand δ is the angle between the ordered field andthe jet axis. Assuming that P ord is close to themaximum theoretical polarization (Eq. 3) typi-cally we have P ord >> P rnd , and the low valuesof the observed polarization degrees (Tables 3, 4,5, 7, and 8) imply that η <<
1. The time evo-lution of the polarization essentially depends onthe time evolution of η , which in turn dependson the ambient medium, making possible a largevariety of different behaviors. In general, until ηP ord > P rnd , the changes in the position anglewould be moderate, whereas the variation in P could be significant.In addition, the magnetic field in the GRBejecta is potentially much more ordered than inthe shocked ambient medium behind the after-glow shock, reflecting the likely presence of a dy-namically important, predominantly transverse,large-scale field advected from the source. Thiscould generate a large polarization value duringthe very early afterglow if the emission is dom-inated by the reverse-shock (Piran 2004; Japeljet al. 2014).A potentially important diagnostic of the ex-istence of ordered magnetic fields is providedby the observation of circular polarimetry (Mat-sumiya & Ioka 2003). Circular polarization couldbe intrinsic, i.e. due to the synchrotron emissionof the afterglow or can be generated by plasmaeffects as Faraday conversion. The Faraday con-version can convert some of the linear polariza-tion from a source to circular polarization and iseffective for synchrotron sources close to the self-absorption frequency typically for the afterglowsin the radio bands. The detailed analysis carriedout by Matsumiya & Ioka (2003) showed that ifthe magnetic fields are tangled the circular polar-ization vanishes, while if the ordered componentof the magnetic field is at least comparable to the tangled one, circular polarization at about 1% inthe radio bands, and 0.01% in the optical is ex-pected. During the early reverse shock it is alsopossible to have circular polarization one orderof magnitude larger even if the ordered magneticfield component is very weak. A deeper analysisof the plasma effects on the observed polarizationwas carried out by Sagiv et al. (2004), derivingresults qualitatively analogous to Matsumiya &Ioka (2003), although based also on a more accu-rate treatment of the effects of synchrotron lossesthat give a higher degree of circular polarizationclose to the frequencies where Faraday conver-sion from linear to circular polarization is moreeffective. A detailed study of the circular to lin-ear polarization ratio in typical GRB afterglowconfigurations was also recently carried out byNava et al. (2016). Their main results show thatit is possible to assume “ad-hoc” configurationsallowing a large local circular polarization. How-ever, once transformations from the local to theobserver frame and integration across the wholevisible region are performed, the circular to lin-ear polarization ratio always vanishes in any real-istic optical thin synchrotron emission afterglowmodel.Observations in the radio band can be very ef-fective not only for accessing the early afterglowon a more relaxed time-scale, but also by meansof relatively later-time observations able to pro-vide information about the electron-proton cou-pling in the relativistic collisionless shocks sup-posed to originate the GRB afterglows (Tomaet al. 2008). The fraction of electrons that arecoupled to protons and accelerated, f , is usu-ally hidden in the fraction of the total energythat goes in accelerating the electrons duringsynchrotron emission, (cid:15) e . This has importantpossible consequences in the evaluation of theenergetic of the events that would be larger bya factor f − compared to the case with perfectcoupling, f = 1. In case the coupling is inef-fective, f <
1, there could be thermal electronsavailable and the effect of Faraday rotation onthese thermal electrons (Toma et al. 2008) maysuppress the linear polarization of the afterglowat frequencies higher than the absorption fre-quency and below a characteristic frequency thatdepends on the electron-proton coupling frac-tion. This effect would therefore be measur-12ble by means of radio polarization observationsat different frequencies. This mechanism couldhowever work only if the magnetic fields are glob-ally ordered to some extent (Sagiv et al. 2004),while if the field is random with short coherencelength the Faraday depolarization does not occur(Matsumiya & Ioka 2003).The geometric models were originally devel-oped assuming a homogeneous jet structure, i.e.at any given angle from the apex of the jet the lu-minosity emitted per unit solid angle along thejet axis and along the jet borders is the same.It is however of great interest to explore thepossibility that the jet structure is more elab-orated. Typical ideas can assume that the radi-ated power per unit solid angle is larger along thejet axis than along the wings, the so-called struc-tured jets, or even that the jet luminosity followsa Gaussian distribution, the so-called Gaussianjets, with a core with almost constant luminos-ity that decreases exponentially outside of it (seeFig. 5). Rossi et al. (2002) and Salmonson (2003)showed that the light-curves of the total fluxfrom these configurations are very similar to eachother. Things are, on the contrary, very differentas far as linear polarization is concerned, sug-gesting the possibility that polarimetry could bea powerful diagnostic of the afterglow jet struc-ture (Rossi et al. 2004). In general, for any off-axis observer, polarization is produced becausedifferent parts of the emitting jet surfaces do notcontribute equally to the observed flux. In thehomogeneous jet model this starts to occur whenthe emitting surface available to the observer in-cludes the near border of the jet. In structuredjet models the required asymmetry is intrinsic inthe assumption that the emission depends on theangular distance from the jet axis. As it is shownin Fig. 5, based on the comprehensive analysisdiscussed in Rossi et al. (2004), the predictionsfor different jet structures are markedly different.Structured jets show some (weak) polarizationfrom the beginning, but the most important dif-ference is for the 90 ◦ rotation of the position an-gle predicted for homogeneous jets. Structuredand Gaussian jets, since their emission is alwaysdominated by the central core at the same anglewith respect to the line of sight, do not show aposition angle rotation with one only maximumfor the polarization, typically close or after the jet-break time, depending on the specific jet pa-rameters and structure.In general, all the considerations discussedabout the jet structure are based on single com-ponent jets. Wu et al. (2005) also considered thepossibility of a two-component jet, with the in-ner component narrow and more energetic, andouter one wide and less energetic. The resultinglight curves and polarization evolution dependstrongly on the ratio of the intrinsic parametersof the two components, allowing a considerablefreedom in modeling the observations.The scenario depicted by the standard after-glow model can also be modified in case the ax-ial symmetry is broken for instance if the energyper solid angle of the blast-wave display angu-lar variations, the so-called “patchy-shell” model(Nakar & Oren 2004). This idea was mainly de-veloped to deal with the observations of GRBafterglows with fluctuations in their light-curvessuperposed to the general behavior predicted bythe standard afterglow model. The variationsin the degree and angle of polarization are herecorrelated to the light-curve variability.Although observationally very demanding, theearly afterglow has always attracted a consider-able attention for its relevant diagnostic power.Fan et al. (2004) analyzed the reverse shock emis-sion powered by a magnetized outflow, possiblygenerated if the progenitor is magnetized andthe field is dissipated. The reverse shock canproduce a considerably bright optical flash de-pending on the magnetization parameter, σ (theratio of the electromagnetic energy to the par-ticle energy) and the circumburst matter den-sity profile. As a general rule, relatively lowvalues for σ ∼ . − . σ is indeed predicted tobe after the magnetic dissipation close to unitybased on energy equipartition arguments. As itwas already pointed out (e.g., Granot & K¨onigl2003), the net linear polarization, Π, resultingfrom these bright optical flashes depend on theratio between the ordered and random magneticfields, b , and during the reverse shock Fan et al.(2004) computed Π (cid:39) . b b . For low σ thecorresponding toroidal magnetic field is strongerthan that generated at the shock and b >> left ) Three possible jet configurations. The figure shows the energy per unit solid angleof the jets logarithmically scaled. ( right ) Light-curves (upper panel) and polarization curves (lowerpanel) comparison between a structured jet (SJ), a homogeneous jet (HJ) and a Gaussian jet (GJ)with given parameters. From Rossi et al. (2004).an ultra-relativistic ejecta, due to beaming ef-fects, only a small portion of the of the emittingregion is visible. However, if the line of sightis even slightly off-axis the symmetric axis ofthe ordered magnetic field high polarization isstill expected since the average of regions withdifferent magnetic field directions is not effec-tive. A very detailed study of the polarizationin the early afterglow was also produced by Lanet al. (2016a). Reverse- and forward-shock con-tributions are considered, and the hydrodynam-ics of the ejecta are computed in the case of thickand thin shells. The authors assumed that forthe forward-shock the generated magnetic fieldis mainly random, while in the reverse-shock re-gion the magnetic field can be large-scale or-dered. This field is carried out from the centralengine but later magnetic dissipations during theprompt GRB phase may reduce the magnetiza-tion degree to a lower level so that the ejecta isdominated by baryons and leptons in the after-glow phase but the large-scale structure of themagnetic field remains. The polarization evo-lutions of the early afterglows are mainly de-termined by the detailed magnetic field config- urations and two field configurations were con-sidered: toroidal and aligned with the jet axis.The magnetic field configurations can be asso-ciated to different progenitors, i.e. an alignedconfiguration would point to a magnetar, whilea toroidal field is possibly indicating a black-hole.As a general conclusion, if the emission is dom-inated by the forward-shock, the polarization isexpected to be very low in particular at earlytimes. If the reverse-shock dominates, the po-larization can reach ∼ − ◦ is expected for some configurations aroundthe reverse-shock shell crossing time.Finally, a complementary way to derive infor-mation about GRB emission ejecta magnetiza-tion would be the polarimetric study of X-rayflares (Chincarini et al. 2007) as discussed in Fanet al. (2005, 2008) and Fan (2010). In general, X-ray polarimetry of the afterglow would open ex-14iting diagnostic possibilities (see also Lan et al.2016b). The different temporal behavior of theoptical and X-ray afterglows observed in manyevents suggested the possibility that X-ray emis-sion traces also a prolonged activity of the cen-tral engine while the optical afterglow is morerelated to the real forward-shock emission (Ghis-ellini et al. 2007). This would make the polariza-tion behavior of the optical and X-ray afterglowsat least partially independent and with the ca-pability to explore different emission regions ofthe GRB phenomenon. As discussed earlier, theearly optical afterglow is expected to be weaklypolarized unless a large scale ordered magneticfield is present. X-ray flares and plateau, as ar-gued by Fan et al. (2004), might be driven byPoynting-flux dominated emission, so possiblyshowing a high level of linear polarization. The first identification of a GRB afterglow wasobtained for GRB 970228 (Costa et al. 1997; vanParadijs et al. 1997), although for GRB 940217a long-lasting high-energy emission possibly tobe associated to the afterglow phase was alreadydetected (Hurley et al. 1994).The first linear polarimetric observations (seeTables 3, 4, 5, 7, and 8) were carried out in theradio band with the VLA about three weeks af-ter GRB 980329 (Taylor et al. 1998), yielding arather shallow 21% upper limit and about a weekafter the event for GRB 980703 with 8% upperlimit (Frail et al. 1998). These limits are sub-stantially lower than the theoretical synchrotronemission value (Eq. 3). However, the interpre-tation of the result is not direct since it de-pends on the location of the observing frequencycompared to the synchrotron self-absorption fre-quency. At frequencies lower than the absorptionfrequency any intrinsic polarization is expectedto be smeared out. The idea that the GRB af-terglow emission is due to synchrotron emissionwas consistent with the broad-band spectral en-ergy distribution observed for this event (Palazziet al. 1998), but the debate was still open at thattime.Much more stringent was the 2 .
3% upper limitfor linear polarization obtained by Hjorth et al. (1999) for the bright GRB 990123 in the opti-cal with the NOT . The observations were per-formed about 18 hours after the event. Such alow value was interpreted as possibly due to ajetted geometry with the GRB observed close tothe beam axis. In a spherical geometry, again un-der the hypothesis that the emission was due tosynchrotron radiation, such a low level requireshighly tangled magnetic fields confined to theshock front (Hjorth et al. 1999). Milder upperlimits for circular (see Table 6) and linear po-larization were also obtained in the radio withthe VLA (Kulkarni et al. 1999; Granot & Taylor2005).Polarimetry at a few percent level can be de-manding for rapidly fading sources as GRB af-terglows, and therefore it is not a surprise thatthe first positive detections in the optical bandcame a few months after the first unit of theVLT, with its collecting area and flexibility, be-came operational. GRB 990510 was observedtwo times by two independent teams (Covinoet al. 1999; Wijers et al. 1999) at 18-21 hoursafter the burst with the ESO-VLT, providinga small but highly significant polarization levelat P = 1 . ± .
2% (Fig. 6). A later measure-ment one day after gave a result consistent witha non-variability of the observed polarization.Polarization at this level is not common forextragalactic sources, however it is possible thatit is due to polarization induced by dust grainsinterposed along the line of sight, which may bepreferentially aligned due to the galactic mag-netic fields. The effect is well known in ourGalaxy (Serkowski et al. 1975) where it is ob-served that dust-induced polarization typicallyis in the range P max ≤ . E B − V and follows anempirically relation known as “Serkowki law”: P ( λ ) /P max = e K ln ( λ max /λ ) , (7)where K ∼ − .
15 and λ max in in the range 0.45-0.8 µm (Serkowski et al. 1975).Large variations are anyway expected, and ob-served, for specific lines of sights. On the otherhand, the effect due to dust in the Galaxy canbe in principle easily checked and removed if asufficiently large number of stars are observed inthe same field of view. Since stars are typically S ( φ ) gives the degree and positionangle of the observed polarization (di SeregoAlighieri 1997).intrinsically unpolarized (at least at this level ofaccuracy) any dust induced (as well as instru-mental) polarization can be singled out. Dust-induced polarization in other galaxies has beenstudied only in a limited number of nearby cases(e.g., Clayton et al. 2004) with results partly dif-ferent compared to the Milky Way. For the caseof GRB 9905010, a sizable effect of dust inducedpolarization in the host galaxy could be ruledout since multi-band observations of the after-glow showed it could be effectively modeled as apower-law, according to the requirements of syn-chrotron shock model (M´esz´aros & Rees 1997),with essentially no rest-frame extinction (Covinoet al. 1999).Electron scattering can also lead to some po-larization, as observed in supernovae and usuallyattributed to asymmetries in their photospheres(Wang & Wheeler 2008). However, the degreeof induced polarization is of the order of theelectron optical depth that cannot be more than ∼ − a day after the event (Wijers et al. 1999).We mention in passing that electron scattering assource of some polarized flux in GRB afterglows was also proposed by Gnedin et al. (2006) study-ing the polarization effects of radiation scatteredin conical thin plasma envelopes. With differentassumptions about the magnetic field geometryand the inclination of the cone axis with respectto the line of sight, it was possible to obtain thepolarization at a few per cent level observed inGRB afterglows as due to Thomson scatteringin the plasma of the conical jet. In this sce-nario synchrotron radiation does not contributeto the observed flux, and the observed polariza-tion position angle should be essentially constantin time.GRB 990510 was also the first GRB with anachromatic (at least in the optical band) steep-ening, a jet-break, of the afterglow light-curveclearly observed (Israel et al. 1999; Harrisonet al. 1999; Stanek et al. 1999). The observa-tions with solid polarization detections were per-formed before the jet-break. Due to the largeLorentz factor of the outflow, Γ, only a fraction ∼ / Γ of the emitting region is accessible to theobserver. Photons produced in regions at an an-gle 1 / Γ with respect to the line of sight are emit-ted, in the comoving frame, at ∼ ◦ from the ve-locity vector. A comoving observer at this anglecan then see a compressed emitting region (Ghis-ellini & Lazzati 1999) and a projected magneticfield structure with a preferred orientation. Ifthe gradual steepening of the light curve is a jet-break, we would observe only regions at a view-ing angle 1 / Γ at variance with an axis-symmetricsituation, and this asymmetry can be the causeof the observed linear polarization that thereforebecomes the “smoking gun” of synchrotron emis-sion for GRB afterglows.A few months later, for GRB 990712, fur-ther evidence for the intrinsic origin of the ob-served afterglow polarization was obtained byRol et al. (2000). Three epochs of linear polari-metric observations from about 10 to 35 hr fromthe high energy event were obtained. The polar-ization was always in the 1-3% range, but showedsome variability with the minimum at the sec-ond epoch, while the position angle remainedconstant. The evidence for variability was onlyslightly better than 3 σ , yet no color variationof the afterglow was identified during the timeperiod covered by the observations, making thepossibility that the observed variation was due16o dust in the host galaxy even less likely. Theconstancy of the position angle on such a long,compared to the afterglow evolution, monitor-ing is in disagreement with the hypothesis thatthe observed polarization could be due to a ran-dom mix of highly polarized emissions from in-dependent magnetic domains (Gruzinov & Wax-man 1999; Gruzinov 1999). While it is possi-ble to have a low polarization assuming a largenumber of magnetic domains, the position an-gle should typically vary with the polarizationduring the afterglow evolution. And basicallythe same objection holds for polarization due tomicro-lensing. The observations for GRB 990712were carried out during a phase of regular decayof the afterglow, i.e. no break was detected. Thequality of the last observation of this dataset,which is consistent with both the first or thesecond observations due to the larger error bars,does not allow us to draw any further specific testbased on the idea that the afterglow polarizationis described by a geometric model (Ghisellini &Lazzati 1999; Sari 1999) and these observationsare generally consistent with that scenario, asalso discussed in Bj¨ornsson & Lindfors (2000).Only upper limits were instead obtained forGRB 991216, observed in the optical with theVLT (Covino et al. 2004) and in the radio withthe VLA (Granot & Taylor 2005). Being themost stringent limit at 2.7%, it is possible thatfor this event the entire polarization evolutionwas characterized by lower values. It became in-deed immediately clear that the best (largest)available facilities were required to derive ef-fective polarimetry at 1% level for GRB after-glows. Nevertheless, attempts were carried outwith smaller size facilities or in the NIR, wherethe observing conditions are more difficult forpolarimetry. GRB 000301C was observed in the K band with the Calar Alto 3.5m telescope ,and only a mild upper limit at 30% was obtained(Stecklum et al. 2001). GRB 010222 was insteadobserved with the NOT about 23 hours from theGRB in the V band yielding a low significancedetection at 1 . ± .
64% (Bj¨ornsson et al. 2002).However, the low average polarization level typ-ically detected in late-time GRB afterglows of-ten resulted in upper limits with the largest fa-cilities too, in particular when the observations could not be carried out before about one dayfrom the high-energy event. GRB 011211 wasobserved about 35 hours after the GRB with theVLT and an upper limit at 3 σ of 2.7% was de-rived (Covino et al. 2002). These limits werepoorly constraining yet generally consistent withthe predictions of the geometric models (Ghis-ellini & Lazzati 1999; Sari 1999).The attempt to identify a time-evolution of thepolarization degree and position angle generateda richer dataset for several events. GRB 020405was observed with the VLA (Granot & Taylor2005), the VLT (Masetti et al. 2003; Covinoet al. 2003) and the Multiple Mirror Telescope(MMT , Bersier et al. 2003) between one andthree days from the burst. The polarization levelwas observed at about 1.2-2% for the VLT ob-servations but at the MMT a much higher polar-ization at about 10% was detected. Only mildupper limits were obtained at the radio frequen-cies. The position angle possibly showed a slowchange ( ∼ ◦ ) from the first to the last obser-vations. GRB 020405 is characterized by a largegalaxy superposed to the afterglow position, butduring the polarimetric campaign the afterglowwas much brighter than the host galaxy andtherefore able to only slightly affect the measure-ments (Covino et al. 2003). During the observa-tions the afterglow light-curve showed a regularand smooth decay (Masetti et al. 2003). The ob-servations derived with the VLT before and afterthe MMT observations are substantially consis-tent with a constant afterglow polarization, pos-sibly also with an important contribution of dustin the host galaxy. The rapid variation requiredto move from the ∼
1% to ∼
10% in a timescaleof about one hour is essentially inconsistent withbasically all the geometric models and also withthe patchy-shell idea (Ghisellini & Lazzati 1999;Sari 1999; Gruzinov & Waxman 1999). In princi-ple a micro-lensing phenomenon (Loeb & Perna1998) could be responsible for the polarization”flare”, although the rapid time scale, the almostconstant position angle and the lack of an anal-ogous brightening in the total flux curve makeeven this interpretation unlikely. The high po-larization observed by Bersier et al. (2003) onlyabout one hour after the observation carried outby Masetti et al. (2003) is therefore still of diffi- Event t − t P lin Θ ν Instrument z Ref(hour) (%) (deg) (Hz)GRB 980329 500 <
21 (2 σ ) 8 . × VLA 3.5 (Taylor et al. 1998)GRB 980703 100 < σ ) 4 . × VLA 0.97 (Frail et al. 1998)100 < σ ) 8 . × VLA (Frail et al. 1998)GRB 990123 18.25 < . σ ) 4 . × NOT 1.6 (Hjorth et al. 1999)30.0 <
23 (3 σ ) 8 . × VLA (Kulkarni et al. 1999)(Granot & Taylor 2005)GRB 990510 18.5 1 . ± . ± . × VLT 1.62 (Covino et al. 1999)20.6 1 . ± . ± . × VLT (Wijers et al. 1999)43.4 2 . +1 . − . +17 − . × VLT (Wijers et al. 1999)GRB 990712 10.56 2 . ± . . ± . . × VLT 0.43 (Rol et al. 2000)16.8 1 . ± . . ± . . × VLT (Rol et al. 2000)34.8 2 . ± . . ± . . × VLT (Rol et al. 2000)GRB 991216 35.0 < . σ ) 5 . × VLT 1.02 (Covino et al. 2004)35.8 <
11 (3 σ ) 8 . × VLA (Granot & Taylor 2005)60.0 < σ ) 5 . × VLT (Covino et al. 2004)64.3 < σ ) 8 . × VLA (Granot & Taylor 2005)GRB 000301C 43 <
30 4 . × VLT 2.03 (Stecklum et al. 2001)GRB 010222 22.65 1 . ± .
64 5 . × NOT 1.48 (Bj¨ornsson et al. 2002)GRB 011211 35 < . σ ) 4 . × VLT 2.14 (Covino et al. 2002)GRB 020405 28.6 <
11 (3 σ ) 8 . × VLA 0.69 (Granot & Taylor 2005)29.5 1 . ± .
40 172 ± . × VLT (Masetti et al. 2003)31.7 9 . ± . . ± . . × MMT (Bersier et al. 2003)52.0 1 . ± .
33 154 ± . × VLT (Covino et al. 2003)76.2 1 . ± .
43 168 ± . × VLT (Covino et al. 2003)GRB 020813 4.7-7.9 1 . − . −
162 3 . − . × Keck 1.25 (Barth et al. 2003)21.55 1 . ± .
22 154 . ± . . × VLT (Gorosabel et al. 2004)22.5 1 . ± .
25 137 . ± . . × VLT (Gorosabel et al. 2004)23.41 1 . ± .
22 150 . ± . . × VLT (Gorosabel et al. 2004)24.39 1 . ± .
23 146 . ± . . × VLT (Gorosabel et al. 2004)26.80 1 . ± .
44 155 . ± . . × VLT (Gorosabel et al. 2004)27.34 1 . ± .
53 163 . ± . . × VLT (Gorosabel et al. 2004)27.78 1 . ± .
49 142 . ± . . × VLT (Gorosabel et al. 2004)47.51 1 . ± .
34 164 . ± . . × VLT (Gorosabel et al. 2004)97.29 0 . ± .
08 13 . ± . . × VLT (Gorosabel et al. 2004)
Event t − t P lin Θ ν Instrument z Ref(hour) (%) (deg) (Hz)GRB 021004 8.88 1 . ± .
46 189 ± . × NOT 2.33 (Rol et al. 2003)9.12 2 . ± .
51 175 ± . × NOT (Rol et al. 2003)9.60 < .
60 4 . × NOT (Rol et al. 2003)10.76 < . σ ) 2 . × TNG (Lazzati et al. 2003)14.62 0 . ± .
10 126 ± . × VLT (Lazzati et al. 2003)16.08 0 . ± .
13 140 ± . × VLT (Rol et al. 2003)18.83 0 . − . −
147 3 . − . × VLT (Lazzati et al. 2003)(Wang et al. 2003)90.7 0 . ± .
20 45 ±
12 5 . × VLT (Lazzati et al. 2003)GRB 030226 25.39 < . σ ) 4 . × VLT 1.99 (Klose et al. 2004a)GRB 030328 18.5 2 . ± . ± . × VLT 1.52 (Maiorano et al. 2006)GRB 060418 0.057 < σ ) 5 . × LT 1.49 (Mundell et al. 2007)GRB 071010A 21.51 < . σ ) 4 . × VLT 0.99 (Covino et al. 2008)GRB 080310 24.21 < . σ ) 5 . × VLT 2.43 (Littlejohns et al. 2012)47.08 < . σ ) 5 . × VLT (Littlejohns et al. 2012)70.48 < . σ ) 5 . × VLT (Littlejohns et al. 2012)GRB 080928 15.2 2 . ± . ± . − . × VLT 1.69 (this paper)GRB 090102 0.045 10 . ± . . × LT 1.55 (Steele et al. 2009)GRB 091208B 0.10 10 . ± . ± . × Kanata 1.06 (Uehara et al. 2012)GRB 100906A ∼ . <
10 (60%) ∼ × MASTER 1.73 (Gorbovskoy et al. 2012)GRB 110205A 0.0675 <
16 (3 σ ) 5 . × LT 2.21 (Cucchiara et al. 2011)0.93 < . σ ) 5 . × LT (Cucchiara et al. 2011)3.53 1 . . × CAHA (Gorosabel et al. 2011)GRB 120308A 0.0292 28 ± ± . × LT (Mundell et al. 2013)0.0594 23 ± ± . × LT (Mundell et al. 2013)0.0892 17 +5 − ± . × LT (Mundell et al. 2013)0.1189 16 +7 − ±
10 5 . × LT (Mundell et al. 2013)0.1792 16 +5 − ± . × LT (Mundell et al. 2013)GRB 121011A ∼ . <
15 (60%) ∼ × MASTER (Pruzhinskaya et al. 2014)GRB 130427 36 < . σ ) 4 . × EVN 0.34 (van der Horst et al. 2014)60 < . σ ) 4 . × EVN (van der Horst et al. 2014)110 <
21 (3 σ ) 4 . × EVN (van der Horst et al. 2014)GRB 131030A 0.9 2 . ± . ±
22 4 . × Skinakas 1.3m 1.29 (King et al. 2014)GRB 140430A 0.051 <
22 (3 σ ) 5 . × LT 1.60 (Kopaˇc et al. 2015)GRB 150301B 0.023 > . × MASTER 1.52 (Gorbovskoy et al. 2016) . The linear polarization was slightlyhigher than 2% at about 5-8 hours after theGRB, and later was detected at ∼
1% level withan almost constant (or weakly changing) positionangle. In particular, no large rotation of the po-sition angle was observed before and after thejet-break time (0.4-0.9 days). GRB 020813 wasalso characterized by a very smooth light-curve(Gorosabel et al. 2004), ensuring that inhomo-geneities in the fireball or in the surrounding cir-cumstellar medium are not important and there-fore unable to significantly affect the polarizationmeasurements. In Lazzati et al. (2004a) sev-eral possibilities were discussed, including sce-narios with magnetized jets. An important re-sult was that models based on homogeneous jets,implying a 90 ◦ rotation, are ruled out by thedata. On the contrary, models described bystructured jets, predicting a polarization peakclose to the jet-break time (Rossi et al. 2002;Lazzati et al. 2004a; Rossi et al. 2004), are moreconsistent with the data. However, as suggestedby the relatively high polarization value found atearly times, models assuming a magnetized jet,i.e. a jet with a non-negligible toroidal compo-nent, are also able to satisfactorily fit the databoth for homogeneous and structured jets. Wuet al. (2005) showed that GRB 020813 polarimet-ric and photometric data could also be success-fully modeled by a two-component jet with the line of sight within the wide component to en-sure the constancy of the polarization positionangle. Attempts to model the polarization evolu-tion of GRB 080203 were also proposed by Dadoet al. (2004), in the context of their “cannonball”model. Since the intrinsic afterglow emissionfrom the fireballs, plasmoids ejected by the cen-tral engine of the GRB at very high Lorentz fac-tor (see Dado et al. 2004, and references therein)should be unpolarized, the observed polarizationis attributed to the effect of dust along the lineof sight in the GRB host galaxies. The lack ofsizable reddening in the total multicolor light-curve modeling is however difficult to reconcilewith this scenario.Multiple observations covering the afterglowevolution from about 0.3 to 3 days after the high-energy event were obtained also for GRB 021004.In this case the light-curve was characterizedby several re-brightenings making the modelingmore complex (Bj¨ornsson et al. 2004) and notallowing in particular to single out unambigu-ously the jet-break time. Polarimetry was car-ried out with the NOT (Rol et al. 2003) at about9 hours after the GRB and with the ESO-VLT afew hours later. The polarization degree was ap-proximately constant at 1 − .
5% but the positionangle changed by ∼ ◦ between the NOT andVLT observations. More polarimetric observa-tions were presented by Lazzati et al. (2003) ob-tained with the TNG in the J band ∼
10 hoursafter the GRB and with the ESO-VLT in theoptical between ∼
14 and ∼
90 hours after thehigh-energy event. The TNG observation gavea 5% upper limit while with the VLT the mea-sured polarization decreased from ∼ .
3% downto ∼ . ◦ rotation withrespect to the earliest measurements. Spectro-polarimetry, obtained with the ESO-VLT about18 hours after the GRB, showing a polarization ∼ .
8% and position angle ∼ ◦ , were pre-sented and discussed by Wang et al. (2003) andLazzati et al. (2003).The typically low observed polarization andthe relatively high redshift of the GRBs implythat any possible contribution due to dust in thehost galaxy must be carefully considered. Thepossibility that the observed linear polarization p dust ≡ q + u to background unpolarizedsources, by a Mueller matrix (Tinbergen 1996; diSerego Alighieri 1997) of the form: M = e − τ q u q q + Au p qu (1 − A ) p u qu (1 − A ) p u + Aq p
00 0 0 A (8)where A ≡ (cid:113) − p , and e − τ is the opacityof the medium to non-polarized radiation. For adeeper discussion about the range of validity ofEq. 8, see Landstreet & Angel (1972).Simulations carried out for the case ofGRB 021004 (Lazzati et al. 2003) showed thatfor low polarization levels a change of the posi-tion angle by a large amount due to the superpo-sition of a varying, in intensity and polarization,source (the afterglow) and the effect of dust inthe host galaxy is possible. However, a detailedfit based on the geometric model (Ghisellini &Lazzati 1999; Sari 1999) was difficult to achieve.The irregularities of the light-curve could pos-sibly be due to inhomogeneities in the externalmedium or in the fireball itself. In both cases thebreak of the symmetry of the system can gen-erate some polarization superposed to the gen-eral trend, making a reliable modeling depen-dent on too many free parameters consideringthe limited observational data. As a matter offact, Bj¨ornsson et al. (2004) showed that withthe addition of a few episodes of energy injec-tions the light-curve and the polarization evolu-tion can satisfactorily be modeled assuming anhomogenous jet structure. The effect of energyinjection on polarization is due to the tempo-rary increase of the fireball Lorentz factor Γ. In-creasing Γ the flux also increases, the relativis-tic aberration becomes more important and theemitting surface area decreases with a net re-sult of a smaller polarization degree compared toan unperturbed situation. Rather interestingly, adopting a blast wave energy distribution lackingof axial symmetry allows one to obtain correlatedlight-curve and polarization degree and positionangle variations, also able to satisfactorily modelthe GRB 021004 data (Nakar & Oren 2004).For two more events only a few polarimet-ric measurements could be carried out. Astringent upper limit at 1.1% was obtained forGRB 030226 about one day after the GRB (Kloseet al. 2004a). For GRB 030328 polarization at P ∼ .
4% was instead observed about 18 hoursafter the GRB (Maiorano et al. 2006), probablyintrinsic to the event due to the low local extinc-tion as inferred by multi-color photometry andspectroscopy of the afterglow.A fundamental breakthrough in the obser-vational activities of GRB afterglows occurredwith GRB 030329 (Greiner et al. 2003; Magal-haes et al. 2003; Klose et al. 2004b; Taylor et al.2004, 2005). GRB 030329 was discovered by theHETE II satellite and was one of the few casesof low redshift GRBs ( z ∼ . andmuch longer in the radio with the VLBA . Theafterglow polarization showed a strong variabil-ity in polarization degree and position angle.The polarization was typically in the 0.3-2.5%range, and spectropolarimetry or multi-band ob-servations showed that the position angle wasconstant in the optical and NIR bands. Thelight-curve of GRB 030329 was characterized bynumerous bumps and wiggles, and after about10 days a supernova component also affected theobservations. The modeling of these polarizationdata is beyond the capabilities of any scenariodiscussed so far, lacking for instance of any clearcorrelation between polarization and light-curvebehavior. Possibly, the observed emission andpolarization is therefore due to the superpositionof different phenomena that make a proper mod-eling difficult to achieve (Greiner et al. 2003). http://space.mit.edu/HETE/ https://public.nrao.edu/telescopes/vlba (LT) af-ter about three minutes, in a large band roughlycentered on the V and Rc filters (Mundell et al.2007). The observations yielded only a mild up-per limit, P < telescope (Molinari et al. 2007)shows that very likely the initial optical peak ofGRB 060418 is due to the forward-shock onset,and that reverse-shock emission for this eventwas at most comparable to the one from theforward-shock (Mundell et al. 2007; Jin & Fan http://telescope.livjm.ac.uk P < . ∼
10% level was measured about 3 minutesafter the high energy event. The analysis ofthe optical light-curve of GRB 090102 (Gendreet al. 2010) suggested that the early-time emis-sion could be interpreted as the decaying partof a reverse-shock. The simplest interpretationfor the high polarization is that a large-scale or-dered magnetic field is driving the relativisticoutflow, and this would be the first direct evi-dence of such magnetic fields in these sources. Ahigh (and declining with time) polarization dur-ing the reverse-shock phase is a common featureof magnetic models of GRBs (e.g., Zhang & Yan2011).Another large dataset was obtained with theESO-VLT for GRB 091018 (Wiersema et al.2012), comprising optical linear polarimetry,covering the evolution of the afterglow within0.13 - 2.3 days after the burst, and deep opti-cal circular polarimetry. Near-infrared linear po-larimetry was also obtained. The afterglow evo-lution was also very well sampled allowing theauthors a very reliable analysis of the polariza-tion evolution. The linear polarization degreeshows variability from 0 up to 3% both on shortand long time-scales. For the circular polariza-22able 5: Linear polarization measurements carried out for the afterglow of GRB 030329.
Event t − t P lin Θ ν Instrument z Ref(hour) (%) (deg) (Hz)GRB 030329 12.77 0 . ± .
10 86 . ± .
43 4 . × VLT 0.17 (Greiner et al. 2003)13.18 0 . ± .
09 86 . ± .
40 4 . × VLT (Greiner et al. 2003)13.61 0 . ± .
09 88 . ± .
64 4 . × VLT (Greiner et al. 2003)14.04 0 . ± .
09 91 . ± .
88 3 . − . × VLT (Greiner et al. 2003)16.61 0 . ± .
07 78 . ± .
94 4 . × VLT (Greiner et al. 2003)17.11 0 . ± .
07 76 . ± .
89 4 . × VLT (Greiner et al. 2003)17.62 0 . ± .
05 74 . ± .
11 4 . × VLT (Greiner et al. 2003)35.19 2 . ± .
20 54 . ± . . × CAHA (Klose et al. 2004b)36.49 1 . ± .
48 83 . . × IAG-USP (Magalhaes et al. 2003)36.72 1 . ± .
40 70 ±
11 4 . × CAHA (Greiner et al. 2003)(Klose et al. 2004b)37.20 1 . ± .
11 61 . ± .
38 4 . × VLT (Greiner et al. 2003)37.92 1 . ± .
12 62 . ± .
44 4 . × VLT (Greiner et al. 2003)40.08 1 . ± .
09 59 . ± .
51 3 . − . × VLT (Greiner et al. 2003)40.80 1 . ± .
08 66 . ± .
45 4 . × VLT (Greiner et al. 2003)(Klose et al. 2004b)41.28 1 . ± .
08 67 . ± .
60 4 . × VLT (Greiner et al. 2003)41.76 1 . ± .
08 70 . ± .
51 4 . × VLT (Greiner et al. 2003)64.32 0 . ± .
06 30 . ± .
04 3 . − . × VLT (Greiner et al. 2003)64.80 0 . ± .
12 12 . ± .
63 4 . × VLT (Greiner et al. 2003)65.28 0 . ± .
07 24 . ± .
94 4 . × VLT (Greiner et al. 2003)84.96 0 . ± .
09 53 . ± .
08 4 . × VLT (Greiner et al. 2003)85.44 0 . ± .
08 57 . ± .
06 4 . × VLT (Greiner et al. 2003)85.92 0 . ± .
10 62 . ± .
10 4 . × VLT (Greiner et al. 2003)135.84 1 . ± .
18 66 . ± .
38 4 . × NOT (Greiner et al. 2003)183.36 2 . ± .
28 75 . ± .
32 4 . × VLT (Greiner et al. 2003)185.04 < σ ) 8 . × VLBA (Taylor et al. 2004)230.16 1 . ± .
14 70 . ± .
31 4 . × VLT (Greiner et al. 2003)326.40 2 . ± .
57 1 . ± .
64 4 . × VLT (Greiner et al. 2003)540.00 0 . ± .
10 42 . ± .
26 4 . × VLT (Greiner et al. 2003)696.00 1 . ± .
56 99 . ± .
60 4 . × VLT (Greiner et al. 2003)900.00 1 . ± .
48 25 . ± .
41 4 . × VLT (Greiner et al. 2003)1992 < . σ ) 8 . × VLBA (Taylor et al. 2005)5208 < . σ ) 8 . × VLBA (Taylor et al. 2005)
Table 6: Circular polarization measurements carried out for several GRB afterglows.
Event t − t P circ ν Instrument z Ref(hour) (%) (Hz)GRB 990123 30.0 <
32 (3 σ ) 8 . × VLA 1.6 (Kulkarni et al. 1999)(Granot & Taylor 2005)GRB 991216 35.8 <
17 (3 σ ) 8 . × VLA 1.02 (Granot & Taylor 2005)64.3 <
15 (3 σ ) 8 . × VLA (Granot & Taylor 2005)GRB 020405 28.6 <
19 (3 σ ) 8 . × VLA 0.69 (Granot & Taylor 2005)GRB 091018 3.74 < .
15 (2 σ ) 4 . × VLT 0.97 (Wiersema et al. 2012)GRB 121024A 3.59 0 . ± .
13 4 . × VLT 2.30 (Wiersema et al. 2014)GRB 130427 36 < . σ ) 4 . × EVN 0.34 (van der Horst et al. 2014)60 < . σ ) 48 × EVN (van der Horst et al. 2014)110 <
15 (3 σ ) 48 × EVN (van der Horst et al. 2014) P circ < .
15% was derived.Linear polarization data are reported in Table 7while circular polarization data are reported inTable 6. The analyses of the light-curve allowedthe identification of an achromatic break, the so-called jet-break, and the polarimetric observa-tions well cover the earlier and later evolution ofthe afterglow. The initial part shows a smoothincrease up to P lin ∼
2% rather well described bya model assuming a homogenous jet (Rossi et al.2004). After the jet-break the polarimetric be-havior is more chaotic, possibly due to the pres-ence of low-intensity bumps in the total light-curve. Nevertheless, the position angle seems toshow a rotation by ∼ ◦ , as predicted by the ge-ometric models (Ghisellini & Lazzati 1999; Sari1999). This is the first possible identification ofthe position angle swing in a GRB afterglow po-larization curve (Fig. 7). The low level of circularpolarization detected during the first hours of af-terglow evolution is also in agreement with theexpectations for an afterglow not characterizedby a strong ordered magnetic field (Toma et al.2008).One more measurement of high polarizationat early times was carried out for GRB 091208Bwith the Kanata 1.5m telescope obtaining P ∼
10% several minutes after the events (Ueharaet al. 2012). The early-time afterglow light-curveis consistent with a standard forward-shock emis-sion. The high symmetry of the early afterglowevolution phase should be characterized by a lowpolarization level, if any, unless some other com-ponent is present, i.e. a reverse shock, or thesymmetry is broken as due to a large scale mag-netic field. If the emission is indeed due to theforward-shock the magnetic field is not likely ad-vected from the central source by the expandingoutflow and should be generated locally. Ueharaet al. (2012) suggest that if the shock sweeps in-homogeneous external medium instabilities cangrow producing strong random magnetic fieldson large scales (Sironi & Goodman 2007; Inoueet al. 2011) that could decay slow enough to sur-vive in the entire emission region. Applying thesame idea developed for the “patchy-model” byGruzinov & Waxman (1999), the length scale ofthese fluctuations must be l p ∼ × cm and http://hasc.hiroshima-u.ac.jp/telescope/kanatatel-e.html the polarization angle should change randomlywith time.The interest in the early-time GRB optical po-larization is also shown by the development ofinstruments able to measure linear polarimetryof very bright GRB optical counterparts as theMASTER Global Robotic Net . Some of thesemeasurements could possibly be more related tothe prompt emission rather than the afterglows.Yet we report them here for completeness. InGorbovskoy et al. (2010) polarization at severalpercent for GRB 091127 was reported but a re-analysis of the data showed that it was likely anartifact due to adverse atmospheric conditions(Gorbovskoy et al. 2013). Upper limits at about10% and 15% are also reported for GRB 100906Aand GRB 121011A during the first hour of after-glow evolution (Gorbovskoy et al. 2012; Pruzhin-skaya et al. 2014). Sparse data indicating a pos-sible polarization at a few per cent level dur-ing early afterglow evolution of GRB 110205Awere also reported by Cucchiara et al. (2011)and Gorosabel et al. (2011) with the LT and theCAHA.An amazing discovery, made again with theLT, was the observation of a decaying polar-ization, with an essentially constant positionangle, with a maximum polarization at about30% several minutes after the high-energy eventof GRB 120308A (Mundell et al. 2013). Theconstancy of the position angle basically rulesout plasma or magnetohydrodynamical insta-bilities that are not supposed to show coher-ent properties during the early afterglow evolu-tion. Modeling in addition the early-time light-curve with contributions both from the reverse-and forward-shock, these observations imply amagnetized baryonic jet with a large-scale uni-form field (Mundell et al. 2013; Lyutikov 2013).GRB 120308A polarimetry was also analyzed indetail by Zhang et al. (2015) using all the avail-able afterglow data. They derived that thestrength of the magnetic field in the reverse-shock region should have been an order of magni-tude stronger than in the forward-shock region.As a consequence, the outflow turned out to bemildly magnetized, at a level σ of a few per-cent. The polarimetric observations thereforedefinitely show that for at least some GRBs a http://observ.pereplet.ru Event t − t P lin Θ ν Instrument z Ref(hour) (%) (deg) (Hz)GRB 091018 3.17 < .
32 (1 σ ) 4 . × VLT 0.97 (Wiersema et al. 2012)4.33 0 . ± .
31 177 . ± . . × VLT (Wiersema et al. 2012)4.73 0 . ± .
27 37 . ± . . × VLT (Wiersema et al. 2012)5.11 0 . ± .
31 9 . ± . . × VLT (Wiersema et al. 2012)5.53 < .
32 4 . × VLT (Wiersema et al. 2012)5.91 1 . ± .
30 179 . ± . . × VLT (Wiersema et al. 2012)6.33 0 . ± .
31 3 . ± . . × VLT (Wiersema et al. 2012)6.70 0 . ± .
30 171 . ± . . × VLT (Wiersema et al. 2012)10.34 2 . ± . . ± . . × VLT (Wiersema et al. 2012)10.92 1 . ± .
32 2 . ± . . × VLT (Wiersema et al. 2012)11.30 0 . ± .
32 8 . ± . . × VLT (Wiersema et al. 2012)27.35 1 . ± .
36 69 . ± . . × VLT (Wiersema et al. 2012)27.73 3 . ± .
35 57 . ± . . × VLT (Wiersema et al. 2012)28.16 1 . ± .
35 27 . ± . . × VLT (Wiersema et al. 2012)28.54 1 . ± .
36 114 . ± . . × VLT (Wiersema et al. 2012)28.97 0 . ± .
38 101 . ± . . × VLT (Wiersema et al. 2012)29.35 1 . ± .
38 102 . ± . . × VLT (Wiersema et al. 2012)32.64 0 . ± .
34 168 . ± . . × VLT (Wiersema et al. 2012)33.40 0 . ± .
32 32 . ± . . × VLT (Wiersema et al. 2012)34.78 1 . ± .
35 88 . ± . . × VLT (Wiersema et al. 2012)57.37 1 . ± .
37 169 . ± . . × VLT (Wiersema et al. 2012) a L i n p o l a r i s a t i o n ( % ) bθ + 90°θ - 90°θ θ P o s i t i o n an g l e t/t break Figure 7: Linear polarization (top) and polarization angle (bottom) as a function of the time sinceburst in terms of the break time in the optical light-curves of GRB 091018 (green) and GRB 121014A(red). The dotted lines show the average position angle before and after the jet-break to show thepredicted 90 ◦ position angle swing. From Wiersema et al. (2014).25elevant fraction of the energy is released in theform of Poynting flux. Lan et al. (2016a) ana-lyzed the total and polarized early-time curvesfor this event deriving that both a toroidal andaligned with the jet axis configurations for themagnetic field are possible.Relatively later time observations cannot fol-low the diagnostically important early afterglowbut can carry out observations with bigger tele-scopes allowing us to test unexplored regimes.This was the case of GRB 121024A that wasintensively observed with the VLT (Wiersemaet al. 2014) starting from a few hours after theGRB and obtaining a positive and highly unex-pected detection of circular polarization, P circ =0 . ± . P lin ∼ ◦ ro-tation of the position angle. Analysis of thelight-curve allowed us to identify a jet-break be-tween the two sets of observations and this is avery clear identification of the polarization angleswing predicted to occur around the jet-breaktime of a homogeneous jet that is not spread-ing sideways (Rossi et al. 2004). During the cir-cular polarimetry measurement the linear polar-ization was about 4%, and therefore the circu-lar to linear polarimetry ratio turned out to be P circ /P lin ∼ .
15, a very high value, orders ofmagnitudes greater than the theoretical expecta-tions (Matsumiya & Ioka 2003; Sagiv et al. 2004;Toma et al. 2008). If the emission process issynchrotron the expected polarization is indeed P circ ∼ γ − , where γ e is the random Lorentz fac-tor of the accelerated electrons emitting the ob-served radiation. This relation holds under theassumption of isotropic pitch-angle distributionand ordered magnetic fields (Toma et al. 2008),and the high value of measured circular polariza-tion poses a challenge to this assumption. Fur-thermore, a detailed analysis carried out by Navaet al. (2016) suggests that under the hypothe-sis of optically thin synchrotron emission such ahigh value of circular to linear polarization ra-tio is not possible even with extremely isotropicpitch-angle distribution. A satisfactory interpre- tation of this striking result is still missing.Radio observations at 4.8 GHz with the EVN reporting upper limits at a few per cent lev-els both for linear and circular polarimetry ofGRB 13042A7 were obtained by van der Horstet al. (2014), while a low-significance polariza-tion measurement obtained with the SkinakasObservatory 1.3 m telescope , during the firsttwo hours after GRB 131003A, are reported byKing et al. (2014). The LT obtained a lowerlimit at about 22% for GRB 140430A when theprompt phase was still active, a few minutes af-ter the high-energy event (Kopaˇc et al. 2015).How to interpret the limits depends on how manycomponents were contributing to the measuredoptical photons, i.e. reverse- and forward-shockand in which proportion. The analysis of theearly-time observations for this event unfortu-nately did not allow us to derive a firm conclu-sion. Finally, the MASTER network was ableto obtain a rather interesting lower limit, atabout 8%, 1-2 minutes after GRB 150301B (Gor-bovskoy et al. 2016). An interesting aspect related to measurements oflinear polarization of GRBs and in general of cos-mological sources is the possibility to constrainLorentz invariance violations (LIV), i.e. the in-variance of the laws of physics under rotationand boosts.In general, it is possible to describe light ascomposed of two independently propagating con-stituent waves, each possessing a polarizationand a velocity. Certain forms of relativity vi-olations cause light to experience birefringence,a change in polarization as it propagates. Thechanges grow linearly with distance travelled,so birefringence over cosmological scales offers asensitive probe for relativity violations. Searchesfor this vacuum birefringence using polarizedlight emitted from sources at cosmological dis-tances yield some of the sharpest existing tests ofrelativity (Kosteleck´y & Mewes 2006). In addi-tion, polarimetry of a large number of cosmologi- http://skinakas.physics.uoc.gr/en/ Event t − t P lin Θ ν Instrument z Ref(hour) (%) (deg) (Hz)GRB 121024A 2.69 4 . ± .
20 163 . ± . . × VLT 2.30 (Wiersema et al. 2014)2.96 4 . ± .
20 160 . ± . . × VLT (Wiersema et al. 2014)4.11 3 . ± .
20 182 . ± . . × VLT (Wiersema et al. 2014)4.46 3 . ± .
19 175 . ± . . × VLT (Wiersema et al. 2014)4.84 3 . ± .
18 178 . ± . . × VLT (Wiersema et al. 2014)5.23 3 . ± .
18 180 . ± . . × VLT (Wiersema et al. 2014)5.62 3 . ± .
18 174 . ± . . × VLT (Wiersema et al. 2014)25.45 0 . ± .
09 51 . ± . . × VLT (Wiersema et al. 2014)26.62 1 . ± .
78 93 . ± . . × VLT (Wiersema et al. 2014)28.62 2 . ± .
60 83 . ± . . × VLT (Wiersema et al. 2014)29.39 0 . ± .
72 101 . ± . . × VLT (Wiersema et al. 2014) cal sources can also allow interesting tests for theexistence and physical properties of very lightaxion-like particles (Bassan et al. 2010; Menaet al. 2011).The possible unification at the Planck energyscale of the theory of General Relativity and thequantum theory in the form of the StandardModel requires to quantize gravity, which canlead to fundamental difficulties: one of these isto admit the Lorentz Invariance Violation (LIV)(e.g. Jacobson et al. 2006; Liberati & Maccione2009; Mattingly 2005)A possible experimental test for such viola-tion is to measure the helicity dependence of thepropagation velocity of photons (see e.g. Laurentet al. 2011a, and references therein). The lightdispersion relation is given in this case by ω = k ± ξk M P l ≡ ω ± (9)where E = (cid:126) ω , p = (cid:126) k , M P l is the PlanckMass, and the sign of the cubic term is deter-mined by the chirality (or circular polarization)of the photons, which leads to a rotation of thepolarization during the propagation of linearlypolarized photons. This effect is known as vac-uum birefringence.Equation 9 can be approximated as follows ω ± = | k | (cid:115) ± ξkM P l ≈ | k | (1 ± ξkM P l ) (10)where ξ gives the order of magnitude of the ef-fect. In practice some quantum-gravity theories (e.g. Myers & Pospelov 2003) predict that thepolarization plane of the electromagnetic wavesemitted by a distant source rotates by a quantity∆ θ while the latter propagates through space,and this as a function of the energy of the pho-tons, see Eq. 11, where d is the distance of thesource:∆ θ ( p ) = ω + ( k ) − ω − ( k )2 d ≈ ξ k d M P l (11)As a consequence the signal produced by a lin-early polarized source, observed in a given en-ergy band could vanish, if the distance is largeenough, since the differential rotation acting onthe polarization angle as a function of energywould in the end add opposite oriented polar-ization vectors, and hence in a net un-polarizedsignal. But this effect is very tiny, since itis inversely proportional to the Planck Mass( M P l ∼ × GeV), the observed sourceneeds to be at cosmological distances. The sim-ple fact to detect the polarization signal from adistant source, can put a limit to such a pos-sible violation. This experiment has been per-formed recently by Laurent et al. (2011a), Tomaet al. (2012), and G¨otz et al. (2013) makinguse of the prompt emission of GRBs. Indeed,since GRBs are at the same time at cosmologi-cal distances, and emitting at high energies, theirpolarization measurements are highly suited tomeasure and improve upon these limits. Laurentet al. (2011a), taking advantage of the polariza-tion measurements obtained with IBIS on GRB2741219A in different energy bands (200–250 keV,250–325 keV), and from the measure of distanceof the source (z > ξ < × − . We note that, althoughToma et al. (2012) claim to have derived a morestringent limit ( ξ < × − ), their measure doesnot rely on a real measure of the distance of theGRBs they analyse, but they use a distance esti-mate based on an empirical spectral-luminosityrelation (Yonetoku et al. 2010), whose selectioneffects, physical interpretation, and absolute cal-ibration are not yet completely understood. Byusing the distance measured from the afterglowabsorption spectrum of GRB140206A (23 Gpc)G¨otz et al. (2014) obtained ξ < M P l ∆ θ ( k )( k − k ) d ≈ × − , (12)improving the previous limit obtained by thesame authors on GRB 061122 (G¨otz et al. 2013)by a factor of three.Another powerful LIV test was carried out byFan et al. (2007) by means of the spectopolari-metric observations of the optical afterglows ofGRB 020813 and GRB 021004. Since linear po-larization is a superposition of two monochro-matic waves with opposite circular polarizations(see Eq. 10), the plane of linear polarization issubject to a rotation along the photons’ path be-cause of the difference between the two circu-lar components. For a photon of frequency ν obs emitted at redshift z and with intrinsic polariza-tion Φ we have :Φ ( n ) = Φ + 7 . × ξ l n +1 p c n +1 (2 πν obs ) n +1 F ( z, n ) , (13)where l p = (cid:112) (cid:126) G/c = (cid:126) c/E pl is the Planck’slength-scale, c the speed of light, G the gravita-tional constant, and F ( z, n ) a function that de-pends on the adopted cosmology. For the concor-dance cosmology, F ( z, n ) (cid:39) z ∼ ν n +1 , immediately showingthe importance of obtaining polarimetry of cos- The original Eq. 3 in (Fan et al. 2007) contained atypographical error here corrected. mological sources at the highest possible ener-gies.Fan et al. (2007) analyzed the case with n = 1and, by the lack of any rotation of the polar-ization plane of the spectra of GRB 020813 andGRB 021004, they could constrain | ξ | < × − at 3 σ .We mention in passing that other limitson cosmological birefringence were obtained bymeans of polarization studies of different classesof cosmological sources, e.g. radio-galaxies (diSerego Alighieri et al. 2010). In this paper we have separated the prompt andafterglow GRB phases mainly for making thepresentation easier to follow and because the ob-servational techniques and, to some extent, thetheoretical scenarios are different. Nevertheless,some of the general conclusions hold for bothphases and the available observational materialdefinitely provides one of the most relevant set ofconstraints to the large family of models and pa-rameters describing the GRB phenomenologies.The large set of observations available for theafterglows, mainly but not only in the optical(Section 3.2), allows us to derive a few impor-tant conclusions. First of all, the simple ob-servations of variable polarization implies thatthe afterglow radiation is intrinsically polarized,thus offering strong observational evidence forthe synchrotron origin of the afterglow emission,although different scenarios cannot yet be com-pletely ruled out. The observations of specificpatterns (i.e. the position angle swing) duringthe evolution of the afterglows in polarimetrythat have been predicted in advance give alsoconfidence to the general interpretative scenario,although exceptions are present. And the de-tection of circular polarimetry at a level muchhigher than expected instead poses a formidablechallenge to our present GRB afterglow emissioninterpretation. The solid observations of highpolarization during the early-afterglow stronglyimplies that at least some of the GRBs have animportant magnetic energy content. A strikingdiscovery in itself.The success of recent observational campaignsclearly show that a massive approach, trying to28ollow the afterglow evolution from the early-time, with intermediate-size robotic telescope, tothe late phases, with the biggest available fa-cilities, is required. And the parameter spacefor discoveries is still huge. Radio observationsare promising, in particular with future high-sensitivity facilities, and mm observations withALMA can help to dramatically extend the en-ergy range of the observations and the testingcapabilities of the various interpretative scenar-ios.For the prompt phase the situation is lessclear, but also offering perspective for excitingdiscoveries in the near future. A final answerto distinguish between intrinsic and geometricmodels could be obtained by accumulating moreobservations. Indeed, models (1-2, 6) – as de-fined in Section 2.1 – predict a polarized emis-sion for all bursts, whereas models (3-5) wouldpredict that only a small fraction of GRBs arehighly polarized. This shows the importance ofaccumulating polarimetric measurements for theunderstanding of intrinsic properties of GRBs,but the current instrumentation is statisticallylimited and can provide measurements just forthe brightest events.Nevertheless, although all currently availablemeasures (see Table 2), taken individually, havenot a very high significance ( (cid:38) σ ), they indicatethat GRBs are indeed good candidates for highly γ -ray polarized sources, and that they are primetargets for future polarimetry experiments. Onthe other hand, as can be seen from Table 2 thecurrently available GRB sample does not showextreme spectral characteristics, e.g. in terms ofpeak energy, but they are on the upper end ofthe GRB fluence distribution. This means that,on one hand, this sample may be well representa-tive of the whole GRB population. On the otherhand the fluence bias is clearly an instrumen-tal selection effect due to the high photon statis-tics needed to perform the polarization measure-ments in IBIS and GAP.As discussed above, prompt polarization fea-tures can be explained by synchrotron radiationin an ordered magnetic field (Granot 2003; Gra-not & K¨onigl 2003; Nakar et al. 2003), by the jetstructure (Lazzati & Begelman 2009), or , inde-pendently from the magnetic field structure orthe emission processes, by the observer’s view- ing angle with respect to the jet (Lazzati et al.2004b), even in the case of thermal radiationfrom the jet photosphere (Lundman et al. 2014).In addition the level of magnetization of the jetcan also play a role (Spruit et al. 2001; Lyutikov2006). For instance the ICMART model (Zhang& Yan 2011), which implies a magnetically dom-inated wind launched by the central engine, pre-dicts a decrease of the polarization level duringGRB individual pulses, but this hypothesis can-not be tested with the current data. Indeed, aspointed out by Toma et al. (2009), the differ-ent models are hardly distinguishable relayingonly on γ -ray data, and a result can be achievedonly on statistical grounds, i.e. having a sam-ple of several tens of measures at high energies.This will hardly be achieved before the adventof dedicated GRB polarimetry experiments, e.g.POLAR (Bao et al. 2012) or POET (McConnellet al. 2009).Recently, a few polarization measurements ofthe very early optical afterglow have been re-ported sometime while the prompt high-energyphase was still on going (see also Section 3.2).While Kopaˇc et al. (2015) and Gorbovskoy et al.(2016) do not report significant detections forGRB140430A and GRB150413A respectively, forGRB 150301B a lower limit of 8% has beenreported (Gorbovskoy et al. 2016) (the earli-est measurement in the co-moving time frameto date) and for GRB 120308A a high level,Π=28 ± γ -ray and optical emission in the prompt phaseof GRBs (e.g. Vestrand et al. 2005; Stratta et al.2009; G¨otz et al. 2011; Guidorzi et al. 2011). Acknowledgments
This work has been supported by ASI grantI/004/11/2. SC thanks Gabriele Ghisellini forinvaluable, in number and quality, discussionsand suggestions. Davide Lazzati for having29hared the beginning of this quest long time ago.Finally, a special mention for Javier GorosabelUrkia, a friend and colleague who left us tooearly. DG acknowledges the financial supportof the UnivEarthS Labex program at SorbonneParis Cit´e (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02).