Background

The detection of gravitational waves was a major milestone in experimental physics leading to many new questions. One such question arose from the detection of a gamma ray burst (GRB) around 1.7 seconds after the merger of 2 neutron stars occurred (Goldstein et al. 2017; Savchenko et al. 2017). It is thought that a highly relativistic jet is responsible for this afterglow emission (Metzger and Berger 2012; Berger 2014). Relativistic jets are streams of particles moving at very close to the speed of light. They originate from a compact object, such as a neutron star or black hole. Many compact objects have an accretion disk. This is a torus shaped disk of gas and dust that is gravitationally bound around the object. When mass from this disk falls into the compact object, this is called accretion. 3D general relativistic magnetohydrodynamic (GRMHD) simulations are used to study this process. That is, simulations which use the principles of general relativity and dynamics of an electrically charged fluid. GRMHD simulations of black hole accretion after neutron star mergers create a black hole which can produce a jet that replicates the observed afterglow emission (Kathirgamaraju et al. 2019; Alexander et al. 2018; Margutti et al. 2018). However, there are some discrepancies in the orientation of the magnetic field within the accretion disk. There are two main ways to orient the magnetic field: toroidally and poloidally. To trace out the path of a poloidal magnetic field loop, you would start on the top of the torus and walk through the center hole, back to where you started. Many GRMHD simulations use poloidal magnetic field loops, as that is always known to create a strong jet (Blandford and Znajek 1977). To trace out the path of a toroidal magnetic field loop, you would walk around the top of the torus until you were back where you started. Theory tells us that there will be a toroidal magnetic field in the torus post neutron star merger (Kiuchi et al.2014). Historically, simulations with toroidal flux loops did not create jets at all, or created very weak jets inconsistent with observational data. Recently, simulations have shown that toroidal flux loops can create a jet of expected strength due to alpha- omega dynamo processes (Liska et al. 2018). These are processes in which the toroidal magnetic field loops buoyantly rise and are twisted into poloidal magnetic field loops by the centrifugal force of the disk.

Simulations from Christie et al. (2019) are the first known ones to also exhibit polarity flips in the magnetic flux. A striped jet is a type of jet which has a varying polarity in magnetic flux along the propagation axis (Giannios and Uzdensky 2019). The areas of same polarity in a striped jet are called current sheets. When these current sheets meet each other they create natural dissipation sites which the afterglow emission could emerge from. To quantify this, Giannios and Uzdensky compare the power spectrum of the magnetic flux to the fourier transform of the normalized distribution of the time intervals between polarity flips. Both these quantities are represented by the equation P(τ)=dP/dτ=((a-1)τ_min)^-1(τ/τ_min)^(-a) where τ is the time interval between polarity flips and a is the constant power law index. Giannios and Uzdensky predict that a will be 5/3 for a system which exhibits flips in the polarity of magnetic flux. In this paper we seek to understand the power law index seen in our simulations for various physical quantities, and determine whether they match with the theoretical predictions for systems similar to our own simulations.