The Origin of Power-law Spectra in Relativistic Magnetic Reconnection
Hao Zhang, Lorenzo Sironi, Dimitrios Giannios, Μαρία Πετροπούλου
Abstract
Abstract Magnetic reconnection is often invoked as a source of high-energy particles, and in relativistic astrophysical systems it is regarded as a prime candidate for powering fast and bright flares. We present a novel analytical model—supported and benchmarked with large-scale three-dimensional kinetic particle-in-cell simulations in electron–positron plasmas—that elucidates the physics governing the generation of power-law energy spectra in relativistic reconnection. Particles with Lorentz factor γ ≳ 3 σ (here, σ is the magnetization) gain most of their energy in the inflow region, while meandering between the two sides of the reconnection layer. Their acceleration time is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>acc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mi>γ</mml:mi> <mml:mspace width="0.25em"/> <mml:msubsup> <mml:mrow> <mml:mi>η</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>rec</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> <mml:msubsup> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>≃</mml:mo> <mml:mn>20</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>γ</mml:mi> <mml:mspace width="0.25em"/> <mml:msubsup> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , where η rec ≃ 0.06 is the inflow speed in units of the speed of light and ω c = eB 0 / mc is the gyrofrequency in the upstream magnetic field. They leave the region of active energization after t esc , when they get captured by one of the outflowing flux ropes of reconnected plasma. We directly measure t esc in our simulations and find that t esc ∼ t acc for σ ≳ few. This leads to a universal (i.e., σ -independent) power-law spectrum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">dN</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>free</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>d</mml:mi> <mml:mi>γ</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> for the particles undergoing active acceleration, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">dN</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>d</mml:mi> <mml:mi>γ</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> for the overall particle population. Our results help to shed light on the ubiquitous presence of power-law particle and photon spectra in astrophysical nonthermal sources.