*2.4. What's the Angular Structure of the Outflow?*

The angular structure of the relativistic outflow in GRBs affects a number of important observables, such as prompt GRB pulse structure [84], polarization [24], afterglow lightcurve [143], and the detectability of distant GRBs [144,145]. Outflows in GRBs are collimated into narrowly beamed bipolar jets that have an angular scale Γ*θ<sup>j</sup>* ∼ 10, where *θj* in the simplest model of a uniform conical jet, also referred to as a **top-hat** jet, represents a sharp edge. The notion of narrowly collimated jets in GRBs was first proposed by Rhoads [146], and it was later verified by observations of achromatic **jet-breaks** in the afterglow lightcurve that yielded *<sup>θ</sup><sup>j</sup>* ' 0.05 <sup>−</sup> 0.4 (e.g., [147–150]). Since <sup>Γ</sup> & <sup>10</sup><sup>2</sup> during the prompt emission phase and assuming that *θ<sup>j</sup>* remains approximately the same, this yields Γ*θ<sup>j</sup>* ∼ 5 − 40. This geometric beaming futher implies that the true radiated energy of these bursts is much smaller [149] with *<sup>E</sup><sup>γ</sup>* <sup>=</sup> *<sup>f</sup>bEγ*,iso <sup>∼</sup> <sup>10</sup><sup>48</sup> <sup>−</sup> <sup>10</sup><sup>52</sup> erg, where *f<sup>b</sup>* = (1 − cos *θj*) ' *θ* 2 *j* /2 is the geometric beaming fraction with the last equality valid for *θ<sup>j</sup>* 1, *Eγ*,iso = 4*πd* 2 *L Sγ*(1 + *z*) <sup>−</sup><sup>1</sup> <sup>∼</sup> <sup>10</sup><sup>48</sup> <sup>−</sup> <sup>10</sup><sup>55</sup> erg is the isotropic-equivalent radiated energy, *S<sup>γ</sup>* [erg cm−<sup>2</sup> ] is the burst fluence, and *d<sup>L</sup>* is the luminosity distance. Since *f<sup>b</sup>* is much smaller than 4*π*, the solid angle into which radiation from a spherical source is emitted, only observers whose line-of-sight (LOS) intersects the surface of the jet or passes very close to the jet edge can detect the GRB, which implies that the true rate of GRBs is enhanced by h*f* −1 *b* i ∼ 500 [149] over the observed rate.

A top-hat jet is clearly an idealization even though it is able to explain several features of the afterglow lightcurve. Numerical simulations of jets breaking out of the progenitor star for the long-soft GRBs [151–155] and that from the dynamical ejecta for the short-hard GRBs [155–160] find that these jets naturally develop angular structures by virtue of their interaction with the confining medium. If the true energy reservoir lies in a narrow range and the scatter in *Eγ*,iso is instead caused by different viewing angles, then either the jet half-opening angle of a top-hat jet must be different in different GRBs or the jets are not uniform and must have an underlying angular profile for both the energy per unit solid angle, *e*(*θ*) = *E*iso(*θ*)/4*π*, and the (initial) bulk LF, Γ = Γ(*θ*). Such jets are commonly referred to as **structured jets** [161–164] and can be parameterized quite generally as a power law with *<sup>e</sup>*(*θ*) ∝ Θ−*<sup>a</sup>* and <sup>Γ</sup>(*θ*) <sup>−</sup> <sup>1</sup> ∝ Θ−*<sup>b</sup>* where <sup>Θ</sup> <sup>=</sup> p 1 + (*θ*/*θc*) <sup>2</sup> with *θ<sup>c</sup>* being the core angle. A constant true jet energy among a sample of GRBs implies that *a* = 2, a model referred to as a **universal structured jet** (USJ) [161,165–167], where it corresponds to equal energy per decade in *θ* and therefore reproduces jet breaks similar to those for a top-hat jet with *θj*(top-hat) ∼ *θ*obs(USJ). This angular profile was used as an alternative model to the top-hat jet to explain the *Eγ*,iso ∝ *S<sup>γ</sup>* ∝ *t* −1 *b* correlation [149] for the afterglow emission where *t<sup>b</sup>* is the jet-break time [161,167]. Other useful parameterizations of a structured jet include a **Gaussian jet** with *e*(*θ*) ∝ Γ(*θ*) − 1 ∝ exp(−*θ* <sup>2</sup>/2*θ* 2 *c* ), which is a slightly smoother (around the edges) and more realistic version of the top-hat jet.

The large distances of GRBs have precluded direct confirmation and constraints of the outflow's angular structure. The main difficulty being the rather severe drop in fluence when they are observed outside of the almost uniform core. This changed recently with the afterglow observations of GRB 170817A [12], the first-ever short-hard GRB detected coincidentally with GWs (GW 170817; [11]) from the merger of two neutron stars. Helped by its nearby distance of *D* ' 40 Mpc and an impressive broadband (from radio to X-rays) observational campaign (e.g., [168–170]), the afterglow observations led to the first direct and significant constraint on the angular structure of the relativistic jet (e.g., [170–177]). The afterglow from this source showed a peculiar shallow rise (*F<sup>ν</sup>* ∝ *t* 0.8) to the lightcurve peak

at *t*pk ' 150 days, after which point it declined steeply (*F<sup>ν</sup>* ∝ *t* <sup>−</sup>2.2). Several useful lessons were learned. First, it was shown that a top-hat jet can only explain the afterglow lightcurve near and after the lightcurve peak [177] and not the shallow rise for which a structured jet is needed. Second, both power-law- and Gaussian-structured jets can explain the afterglow of GW 170817, where for a power-law jet the angular structure profile requires *a* ∼ 4.5 and *b* & 1.2 to explain all the observations [178].

While power-law- and Gaussian-structured jets remain most popular, a few other angular profiles have received some attention. Among them is the two-component jet model [150,179–183] that features a narrow uniform core with initial bulk LF Γ<sup>0</sup> & 100 surrounded by a wider uniform jet with Γ<sup>0</sup> ∼ 10 − 30. Nothing really guarantees or demands the outflow to be axisymmetric and uniform, in which case an outflow with small variations on small (1/Γ) angular scales can be envisioned in the form of a "patchy shell" [184] or an outflow consisting for "mini-jets" [185], with the caveat that significant variations on such causally connected angular scales are rather easily washed out and hard to maintain. In case such variations do indeed persist, it could have important consequences for the time-resolved polarization and PA. For example, patches or mini-jets can have different polarization and/or PA due to mutually incoherent B-field configurations, which can lead to smaller net polarization and PA evolution.

#### **3. Gamma-Ray Polarimetry**

Despite the wealth of information that can be obtained from prompt GRB polarization, only a few measurements with modest statistical significance exist. Moreover, many of the results presented in the past were refuted by follow-up studies. A detailed overview of many of these measurements and their respective issues is provided in [186]. The two most recent measurements, by POLAR [187] and Astrosat CZT [188], furthermore appear to be incompatible with one another, indicating probable issues in at least one of these results as well. The lack of detailed measurements, and the many issues with them, result from both the difficulty in measuring *γ*-ray polarization as well as challenging data analysis at these energies. Below, we discus first the measurement principle, which causes many of the encountered issues. This is followed by a description of the different instruments that have been able to perform measurements to date.
