Prospects of Prompt Gamma-Ray Burst Polarimetry with POLAR-2

TL;DR

GRB prompt emission mechanisms remain debated between synchrotron and Comptonized models. The paper introduces POLAR-2/HPD and a forward-folded, unbinned spectro-polarimetric framework to extract physical parameters from synthetic prompt emissions. They demonstrate that for bright bursts with fluence $\mathcal{F} \sim 10^{-5}$ erg cm$^{-2}$, the time-integrated polarization can be measured to approximately $2.5 F_{-5}^{-1/2}$ per cent and the polarization evolution can constrain jet dynamics and magnetic-field geometry. These results indicate POLAR-2's potential to discriminate between emission mechanisms, constrain magnetic-field configurations, and inform outflow structure and magnetization, with significant implications for GRB physics and jet composition.

Abstract

The dominant radiation mechanism that powers the prompt $γ$-ray emission in gamma-ray bursts (GRBs) remains poorly understood. High quality, time- and energy-resolved linear polarization measurements of prompt $γ$-ray photons can distinguish between synchrotron and inverse-Compton processes and provide crucial constraints on the outflow properties. This will be achieved by POLAR-2 that is proposed as a dedicated GRB polarimeter and successor to POLAR. The High-energy Polarimetry Detector (HPD) is one of the three instruments of POLAR-2 that features significantly improved sensitivity in the $(40-1000)$\,keV energy range and a detection area four times larger than that of POLAR. Here we demonstrate the capabilities of the HPD to constrain key physical model parameters by creating and fitting to synthetic sources using a time-resolved spectro-polarimetric theoretical model of prompt GRB emission. The time-resolved spectral and polarization fits are performed using a novel technique featuring maximum likelihood over an unbinned (in time and energy) list of detected events. The constrained model parameters directly relate to the underlying source physics that would reveal an accelerating, coasting or decelerating emission region. For a pulse fluence of $\mathcal{F}=10^{-5}\mathcal{F}_{-5}\,{\rm erg\,cm^{-2}}$ we can constrain the time-integrated polarization degree to an absolute accuracy ($1\,σ$) of about $2.5\mathcal{F}_{-5}^{\,-1/2}$ per cent, as long as source photons dominate over the background. In bright GRBs, such unprecedented accuracy at these energies will allow to distinguish between different models for the prompt GRB emission mechanism and constrain the magnetic field geometry, jet angular structure and outflow composition.

Figures (13)

• Figure 1: Coordinate Systems: (Top) We use a fixed J2000 coordinate system that has unit vectors $(\hat{x}_J,\hat{y}_J,\hat{z}_J)$. A given GRB (or source) in the direction of the radial unit vector $\hat{z}_s$ is localized in this system with polar angle $\theta_{J,s} = \pi/2 - \delta$, where $\delta$ is the source declination in radians, and azimuthal angle $\varphi_{J,s} =\,$ RA, were RA is the source right ascension in radians. Two mutually orthogonal unit vectors $(\hat{x}_s,\,\hat{y}_s)$ in the direction of the polar ($\hat{\theta}_{J,s}$) and azimuthal ($\hat{\varphi}_{J,s}$) unit vectors, respectively, form the plane of the sky normal to $\hat{z}_s$ (red shaded region), where both vectors are tangent to the J2000 unit sphere at the location where $\hat{z}_s$ intersects it. The direction of $\hat{x}_s$ is chosen to be along the north-south great circle where $\hat{x}_s$ points from north to south. The plane of the sky also contains the polarization unit vector $\hat{\Pi}$. We report the polarization angle (PA) as $\theta_\Pi = \arccos(\hat{\Pi}\cdot\hat{x}_s)$ where it is measured in the clockwise direction from the vector $\hat{x}_s$ when looking along $\hat{z}_s$ towards the GRB. Another important coordinate system (in blue) is attached to POLAR-2, where the detector (or its zenith) points in the direction of the radial unit vector $\hat{z}_d$, which is localized in the J2000 system with coordinates $(\theta_{J,d},\varphi_{J,d})$. The two orthogonal sides of the square detector plane are along the unit vectors $\hat{x}_d$ and $\hat{y}_d$. (Bottom-Left) An off-instrument-axis source is localized in the detector plane with coordinates ($\theta_{d,s}$, $\varphi_{d,s}$) where the azimuthal angle is measured up to the dashed gray line which is the projection of $\hat{z}_s$ in the detector plane. The unit vectors $\hat{z}_d$ and $\hat{z}_s$ form a plane (gray shaded region) that intersects with the plane of the sky (red shaded region) and their intersection defines another vector $\hat{x}_0$ common to both planes. The azimuthal angle $\theta_0$ is measured in the plane of the sky from $\hat{x}_0$ up to the unit vector $\hat{x}_s$. (Bottom-Right) When the source is on-instrument-axis ($\theta_{d,s}=0$, to within the measurement accuracies of $\hat{z}_s$ and $\hat{z}_d$) then $\varphi_{d,s}$ is ill-defined and therefore it is fixed to $\varphi_{d,s}=0$ (i.e. $\hat{x}_0=\hat{x}_d$ in addition to $\hat{z}_s=\hat{z}_d$) and $\theta_0$ is then measured from one major axis of the detector. In this case, the detector plane coincides with the plane of the sky that contains the polarization vector.
• Figure 2: (Left) Effective area of the HPD detector of POLAR-2, shown as a function of the incident photon energy for an on-instrument-axis source with $(\theta_{d,s},\varphi_{d,s})=(0,0)$. The blue curve corresponds to the effective area for all events with energy depositions in the detectors, while the green curve shows the effective area specifically for Compton-scattering events. (Right) Instrument response showing the distribution of the measured (the true deposited energy cannot exceed the true energy) deposited energy as a function of the incident photon (true) energy (after DeAngelis+23).
• Figure 3: (Left) Polarimeter response showing the modulation curve or Compton scattering angle distribution for an on-instrument-axis (i.e. at the detector zenith with $\theta_{d,s}=0$) source and for $E=200$ keV photons. Blue line shows the unpolarized case and green, yellow, and red lines show the response for a 100% polarized source with PA $\theta_{d,\Pi} = \{0^\circ, 60^\circ, 90^\circ\}$. (Right) Polarimeter response showing the modulation curve for an on-instrument-axis source with $\Pi=1$, $\theta_{d,\Pi} = 90^{\circ}$, and photon energy $50\,\rm{keV}\leq E \leq 1000\,\rm{keV}$.
• Figure 4: Flow chart showcasing the adopted methodology for synthetic source creation and model fitting to the synthetic source. See §\ref{['sec:modeling']} for details.
• Figure 5: (a) Incident photon spectrum $\Phi_{E,s}(E,t)$ two-dimensional surface in the energy and time plane for the following set of model parameters: $t_0=1\,$s, $\nu_0=250\,$keV, $b_1=-0.25$, $b_2=-1.25$, $a=1$, $d=-1$, $m=0$, $\Delta R/R_0=1$, $\xi_j=10^2$, $q=0$, $\mathcal{F}=10^{-5}\,{\rm erg\,cm}^{-2}$. (b) Photon spectrum at different normalized times, $\hat{t} = t/t_0$. (c) Lightcurves at different normalized energies, $x_0 = \nu/\nu_0$. (d) Distribution of detected photons in deposited energy and arrival time, obtained by sampling a single realization of the detected photon spectrum. $N_{\rm ph}$ shows the number of sample photons. (e) Distribution of Compton detected photons in scattering azimuth and arrival time, obtained by sampling a single realization of the detected modulation curve.