Electron and Proton Heating in Transrelativistic Magnetic Reconnection

<jats:title>Abstract</jats:title> <jats:p>Hot collisionless accretion flows, such as the one in Sgr A* at our Galactic center, provide a unique setting for the investigation of magnetic reconnection. Here protons are nonrelativistic, while electrons can be ultrarelativistic. By means of 2D particle-in-cell simulations, we investigate electron and proton heating in the outflows of transrelativistic reconnection (i.e., <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.1</mml:mn> <mml:mo>–</mml:mo> <mml:mn>1</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaa9380ieqn1.gif" xlink:type="simple"/> </jats:inline-formula>, where the magnetization <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaa9380ieqn2.gif" xlink:type="simple"/> </jats:inline-formula> is the ratio of magnetic energy density to enthalpy density). For both electrons and protons, we find that heating at high <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaa9380ieqn3.gif" xlink:type="simple"/> </jats:inline-formula> (here <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaa9380ieqn4.gif" xlink:type="simple"/> </jats:inline-formula> is the ratio of proton thermal pressure to magnetic pressure) is dominated by adiabatic compression (“adiabatic heating”), while at low <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaa9380ieqn5.gif" xlink:type="simple"/> </jats:inline-formula> it is accompanied by a genuine increase in entropy (“irreversible heating”). For our fiducial <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> ...