[Paper Review] Anisotropic Energy Injection from Magnetar Central Engines in Short GRBs

Yihan Wang, Bing Zhang+1 more|arXiv (Cornell University)|Sep 26, 2023

Gamma-ray bursts and supernovaePhysics and Astronomy3 citations

TL;DR

This study uses special relativistic magnetohydrodynamic (SRMHD) simulations to show that energy injection from magnetar central engines in short gamma-ray bursts is anisotropic due to collimation within the magnetar wind nebula (MWN), reducing energy injection into ejecta by up to a factor of 10 compared to isotropic assumptions. The anisotropy is governed by the ratio $\alpha = u_{\rm A}/u_{\rm MWN}$, where high magnetization and slow expansion favor collimation, making isotropic injection unlikely in realistic short GRB conditions.

ABSTRACT

A long-lived magnetar, potentially originating from a binary neutron star system, has been proposed to explain the extended emission observed in certain short-duration gamma-ray bursts (sGRBs), and is posited as a potential central engine to power the engine-fed kilonovae. Previously, the process by which energy is injected into the surrounding ejecta/jet was widely believed to be nearly isotropic. In this study, we employ special relativity magnetohydrodynamic (SRMHD) simulations to investigate the wind injection process from a magnetar central engine. We explore the dynamics and energy distribution within the system and found that the parameter $α=u_{ m A}/u_{ m MWN}$ can be used to indicate the collimation of the magnetar wind energy injection, where $u_{ m A}$ is the local Alfven four-speed and $u_{ m MWN}$ is the four-speed of the magnetar wind nebular (MWN) formed from wind-ejecta collision. A significant portion of the injected energy from the magnetar spin-down wind will be channeled to the jet axis due to collimation within the MWN. Achieving isotropic energy injection requires a significantly small $α$ that necessitates either an ultra-relativistic expanding MWN or an extremely low magnetization MWN, both of which are challenging to attain in sGRBs. Consequently, a considerably reduced energy budget (i.e. energy per solid angle reduced by a factor of up to 10 with respect to the value under isotropic assumption) is anticipated to be injected into the ejecta for engine-fed kilonovae. Engine-fed kilonovae would appear fainter than originally anticipated.

Motivation & Objective

• To investigate the anisotropy of energy injection from magnetar central engines in short gamma-ray bursts (sGRBs), challenging the assumption of isotropic energy deposition.
• To determine the physical conditions under which magnetar wind energy injection becomes isotropic, given the dynamics of the magnetar wind nebula (MWN) formed by wind-ejecta collision.
• To assess the implications of anisotropic energy injection for engine-fed kilonovae, particularly in light of observed faintness and non-detections in some sGRB counterparts.
• To evaluate whether the low observed brightness of kilonovae in some sGRBs can be explained by reduced energy injection efficiency due to wind collimation, rather than the absence of magnetar engines.

Proposed method

• Employing special relativistic magnetohydrodynamic (SRMHD) simulations to model the dynamics of magnetar wind injection into the ejecta and the formation of the magnetar wind nebula (MWN).
• Defining the parameter $\alpha = u_{\rm A}/u_{\rm MWN}$, where $u_{\rm A}$ is the local Alfvén four-speed and $u_{\rm MWN}$ is the four-speed of the MWN, as a key indicator of wind collimation.
• Analyzing the energy distribution and flow structure within the MWN to determine how much energy is channeled along the jet axis versus isotropically.
• Varying initial conditions such as magnetization, wind speed, and ejecta profile to assess sensitivity of collimation to these parameters.
• Investigating the role of a pre-existing jet funnel in facilitating polar outflow of the magnetar wind in matter-dominated regimes.
• Comparing energy injection efficiency under anisotropic vs. isotropic assumptions to quantify the reduction in effective energy input to ejecta.

Experimental results

Research questions

• RQ1 To what extent is energy injection from a magnetar central engine in short GRBs isotropic, and what physical conditions are required for isotropy?
• RQ2 How does the magnetar wind nebula (MWN) formed by wind-ejecta collision influence the collimation of magnetar wind energy injection?
• RQ3 What is the role of the $\alpha = u_{\rm A}/u_{\rm MWN}$ parameter in determining the degree of anisotropy in energy injection?
• RQ4 How does wind collimation affect the expected luminosity of engine-fed kilonovae, and can this explain the faintness of observed kilonovae?
• RQ5 Can the observed non-detection of bright kilonovae in some sGRBs be reconciled with the presence of long-lived magnetar engines if energy injection is anisotropic?

Key findings

• The parameter $\alpha = u_{\rm A}/u_{\rm MWN}$ is a strong indicator of wind collimation, with $\alpha \gg 1$ favoring collimated energy injection along the jet axis.
• Isotropic energy injection requires either ultra-relativistic MWN expansion or extremely low magnetization in the MWN, both of which are physically challenging to achieve in realistic short GRB environments.
• A significant fraction of the magnetar wind energy is channeled along the jet axis due to collimation within the MWN, reducing energy injection into off-axis directions.
• The effective energy injection into the ejecta is reduced by a factor of up to 10 compared to the isotropic assumption, due to wind collimation, leading to fainter engine-fed kilonovae.
• The anisotropy of energy injection is insensitive to the ejecta density profile, but a pre-existing jet funnel enhances polar outflow in matter-dominated regimes.
• The results reconcile the non-detection of bright kilonovae in some sGRBs with the presence of long-lived magnetar engines, as the reduced energy injection efficiency naturally leads to lower luminosities.