2
Boletim da Sociedade Astronômica Brasileira, 30, no. 1, 247-248 c SAB 2018 Studies of cosmic ray acceleration in relativistic MHD jets Tania E. Medina Torrejón 1 , Elisabete de Gouveia Dal Pino 2 , Greg Kowal 3 , Yosuke Mizuno 4 , Chandra Singh 2 and Luis Kadowaki 2 1 Instituto de Física, Universidade de São Paulo. e-mail: [email protected] 2 Instituto de Astronomia Geofísica e Ciências Atmosféricas, Universidade de São Paulo. e-mail: [email protected], e-mail: [email protected], e-mail: [email protected] 3 Escola de Artes, Ciências e Humanidades, Universidade de São Paulo. e-mail: [email protected] 4 Institute of Astronomy, National Tsing-Hua University e-mail: [email protected] Abstract. Here, we explore the acceleration of high energy (HE) particles in the jet launching area, where the relativistic plasma is probably magnetically dominated. We perform a three-dimensional MHD relativistic simulation of a magnetized jet with initial helical magnetic field subject to the current-driven kink instability. We then inject thousands of test particles in the reconnected magnetic field regions of the jet and follow their trajectories as well as the evolution of their kinetic energy. Preliminary results show that the latter grows exponentially with time, as expected in Fermi acceleration. Resumo. Aqui, exploramos a aceleração de partículas de alta energia (HE) na área de lançamento de jatos, onde o plasma relativista provavelmente é dominado magneticamente. Realizamos uma simulação relativista MHD tridimensional de um jato magnetizado com o campo magnético helicoidal inicial sujeito à instabilidade da torção gerada pela corrente. Em seguida, injetamos milhares de partículas de teste nas regiões de campo magnético reconectadas do jato e seguimos suas trajetórias, bem como a evolução de sua energia cinética. Os resultados preliminares mostram que o último cresce exponencialmente com o tempo, conforme esperado na aceleração de Fermi. Keywords. acceleration of particles – magnetic reconnection – instabilities – magnetohydrodynamics (MHD) – methods: numerical 1. Introduction Very HE cosmic rays (CRs) are believed to be accelerated in the nuclear region or along the relativistic jets of compact sources like Galactic Black Hole binaries (GBHBs), active galactic nu- clei (AGNs) or gamma ray bursts (GRBs). We here investigate the acceleration of CRs by magnetic reconnection in relativistic magnetized tower jets where the acceleration can be very impor- tant. In shocks (Bell 2013), the particles confined between the upstream and downstream flows of the velocity discontinuity un- dergo a first-order Fermi acceleration. De Gouveia Dal Pino & Lazarian (2005) demonstrated that a similar mechanism would occur when particles are trapped between the two converging magnetic flux tubes moving to each other in a current sheet with the reconnection velocity V R . 3D numerical simulations of the trajectories of 10,000 particles injected with thermal ener- gies in dierent MHD domains of fast magnetic reconnection have confirmed the eciency of this acceleration mechanism and the predictions of de Gouveia Dal Pino and Lazarian (2005) model (Kowal, de Gouveia Dal Pino & Lazarian 2011, 2012, de Gouveia Dal Pino & Kowal 2015). Furthermore, these studies have been able to determine numerically the particle accelera- tion rate by magnetic reconnection as a function of the particle energy (Khiali, de Gouveia Dal Pino & del Valle 2015; del Valle, de Gouveia Dal Pino & Kowal 2016). This acceleration mecha- nism may be a dominating process in a wide range of astrophys- ical environments and currently there is extensive study in the literature applied to dierent classes of objects. This includes, relativistic jets and their sources (e.g., Giannios 2010; Sironi and Spitkovsky 2014; Uzdesnky 2011; Singh, Mizuno & de Gouveia Dal Pino 2016, de Gouveia Dal Pino et al. 2016, Kadowaki et al. 2015; Singh et al. 2015; Khiali et al. 2015a, b; Khiali & de Gouveia Dal Pino 2015) - especially in magnetically dominated regions where shocks may be absent or faint (de Gouveia Dal Pino & Kowal 2015). Astrophysical relativistic jets are associated with several kinds of astrophysics systems like AGNs, microquasars and GRBs. Very near the source the relativistic jets are probable magnetically dominated. Jets with strong helical or toroidal fields are subject to current driven kink instability, this strongly distorts may disrupt the jet and may trigger magnetic reconnec- tion (Singh, Mizuno, de Gouveia Dal Pino 2016). In this work, we will investigate the acceleration of particles by magnetic re- connection driven by current drive kink instabily in relativistic jets. 2. Methodology In order to study particle acceleration in relativistic jets, we per- formed special relativistic magnetohydrodynamics (SRMHD) simulations using the tree-dimensional (3D) general relativis- tic MHD code RAISHIN (Mizuno et al. 2006, 2012). The code setup for spatial development of CD kink instability is similar to the initial parameters used in Singh et al. (2016), that is, a jet ro- tating with an inicial angular velocity Ω 0 = 2 and initial helical magnetic field. The simulation grid is periodic along the axial z- direction. The grid is in Cartesian ( x, y, z) coordinates with box of size 6L × 6L × 6L, the grid resolution is the same in all direc- tions with ΔL = L/40. The x & y boundaries, x = y = ±3L are set us outflow boundaries. After the development of the plasma configuration in the jet simulation with density, velocity and magnetic field profiles, we injected test particles at a given snap- shot as in Figure 1 (t = 50 in code units which is given by L/c) and integrated their trajectories using the GACCEL code (Kowal et al. 2011, 2012) which solves the equation of motion d(γmu)/dt = q[(u - v) × B] for each charged particle, where γ (1 - u 2 /c 2 ) -1 is the Lorentz factor, c is the speed of light, v 247

Studies of cosmic ray acceleration in relativistic MHD jets · Very HE cosmic rays (CRs) are believed to be accelerated in the nuclear region or along the relativistic jets of compact

  • Upload
    others

  • View
    5

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Studies of cosmic ray acceleration in relativistic MHD jets · Very HE cosmic rays (CRs) are believed to be accelerated in the nuclear region or along the relativistic jets of compact

Boletim da Sociedade Astronômica Brasileira, 30, no. 1, 247-248c© SAB 2018

Studies of cosmic ray acceleration in relativistic MHD jetsTania E. Medina Torrejón1, Elisabete de Gouveia Dal Pino2, Greg Kowal3, Yosuke Mizuno4, Chandra Singh2 and LuisKadowaki2

1 Instituto de Física, Universidade de São Paulo. e-mail: [email protected] Instituto de Astronomia Geofísica e Ciências Atmosféricas, Universidade de São Paulo. e-mail: [email protected], e-mail:[email protected], e-mail: [email protected]

3 Escola de Artes, Ciências e Humanidades, Universidade de São Paulo. e-mail: [email protected] Institute of Astronomy, National Tsing-Hua University e-mail: [email protected]

Abstract. Here, we explore the acceleration of high energy (HE) particles in the jet launching area, where the relativistic plasmais probably magnetically dominated. We perform a three-dimensional MHD relativistic simulation of a magnetized jet with initialhelical magnetic field subject to the current-driven kink instability. We then inject thousands of test particles in the reconnectedmagnetic field regions of the jet and follow their trajectories as well as the evolution of their kinetic energy. Preliminary results showthat the latter grows exponentially with time, as expected in Fermi acceleration.

Resumo. Aqui, exploramos a aceleração de partículas de alta energia (HE) na área de lançamento de jatos, onde o plasma relativistaprovavelmente é dominado magneticamente. Realizamos uma simulação relativista MHD tridimensional de um jato magnetizadocom o campo magnético helicoidal inicial sujeito à instabilidade da torção gerada pela corrente. Em seguida, injetamos milhares departículas de teste nas regiões de campo magnético reconectadas do jato e seguimos suas trajetórias, bem como a evolução de suaenergia cinética. Os resultados preliminares mostram que o último cresce exponencialmente com o tempo, conforme esperado naaceleração de Fermi.

Keywords. acceleration of particles – magnetic reconnection – instabilities – magnetohydrodynamics (MHD) – methods: numerical

1. Introduction

Very HE cosmic rays (CRs) are believed to be accelerated in thenuclear region or along the relativistic jets of compact sourceslike Galactic Black Hole binaries (GBHBs), active galactic nu-clei (AGNs) or gamma ray bursts (GRBs). We here investigatethe acceleration of CRs by magnetic reconnection in relativisticmagnetized tower jets where the acceleration can be very impor-tant. In shocks (Bell 2013), the particles confined between theupstream and downstream flows of the velocity discontinuity un-dergo a first-order Fermi acceleration. De Gouveia Dal Pino &Lazarian (2005) demonstrated that a similar mechanism wouldoccur when particles are trapped between the two convergingmagnetic flux tubes moving to each other in a current sheetwith the reconnection velocity VR. 3D numerical simulations ofthe trajectories of 10,000 particles injected with thermal ener-gies in different MHD domains of fast magnetic reconnectionhave confirmed the efficiency of this acceleration mechanismand the predictions of de Gouveia Dal Pino and Lazarian (2005)model (Kowal, de Gouveia Dal Pino & Lazarian 2011, 2012, deGouveia Dal Pino & Kowal 2015). Furthermore, these studieshave been able to determine numerically the particle accelera-tion rate by magnetic reconnection as a function of the particleenergy (Khiali, de Gouveia Dal Pino & del Valle 2015; del Valle,de Gouveia Dal Pino & Kowal 2016). This acceleration mecha-nism may be a dominating process in a wide range of astrophys-ical environments and currently there is extensive study in theliterature applied to different classes of objects. This includes,relativistic jets and their sources (e.g., Giannios 2010; Sironi andSpitkovsky 2014; Uzdesnky 2011; Singh, Mizuno & de GouveiaDal Pino 2016, de Gouveia Dal Pino et al. 2016, Kadowaki etal. 2015; Singh et al. 2015; Khiali et al. 2015a, b; Khiali & deGouveia Dal Pino 2015) - especially in magnetically dominated

regions where shocks may be absent or faint (de Gouveia DalPino & Kowal 2015).

Astrophysical relativistic jets are associated with severalkinds of astrophysics systems like AGNs, microquasars andGRBs. Very near the source the relativistic jets are probablemagnetically dominated. Jets with strong helical or toroidalfields are subject to current driven kink instability, this stronglydistorts may disrupt the jet and may trigger magnetic reconnec-tion (Singh, Mizuno, de Gouveia Dal Pino 2016). In this work,we will investigate the acceleration of particles by magnetic re-connection driven by current drive kink instabily in relativisticjets.

2. Methodology

In order to study particle acceleration in relativistic jets, we per-formed special relativistic magnetohydrodynamics (SRMHD)simulations using the tree-dimensional (3D) general relativis-tic MHD code RAISHIN (Mizuno et al. 2006, 2012). The codesetup for spatial development of CD kink instability is similar tothe initial parameters used in Singh et al. (2016), that is, a jet ro-tating with an inicial angular velocity Ω0 = 2 and initial helicalmagnetic field. The simulation grid is periodic along the axial z-direction. The grid is in Cartesian (x, y, z) coordinates with boxof size 6L × 6L × 6L, the grid resolution is the same in all direc-tions with ∆L = L/40. The x & y boundaries, x = y = ±3L areset us outflow boundaries. After the development of the plasmaconfiguration in the jet simulation with density, velocity andmagnetic field profiles, we injected test particles at a given snap-shot as in Figure 1 (t = 50 in code units which is given byL/c) and integrated their trajectories using the GACCEL code(Kowal et al. 2011, 2012) which solves the equation of motiond(γmu)/dt = q[(u − v) × B] for each charged particle, whereγ ≡ (1 − u2/c2)−1 is the Lorentz factor, c is the speed of light, v

247

Page 2: Studies of cosmic ray acceleration in relativistic MHD jets · Very HE cosmic rays (CRs) are believed to be accelerated in the nuclear region or along the relativistic jets of compact

T. E. Medina Torrejón et al.: Studies of cosmic ray acceleration in relativistic MHD jets

Figure 1. Left shows a three-dimensional density isosurfaces, the solidblue lines correspond to the magnetic field lines, and the color scalesgive the values of the density. Right panels show the central xz and yzcut of the jet at t = 50 in code units, the figures shows the current-density distribution in code units.

Figure 2. Histogram of energy of test particles injected in the snapshott = 50 of Figure 1 (a) periodic injection of 1,000 test particles and (b)10,000 test particles injection with periodic re-injection only in the zdirection of the jet.

is the plasma velocity, u, m and q are the particle velocity, massand electric charge, respectively. In the current study we do notinclude particle losses, therefore test particles can gain or loseenergy only through the interactions with the moving magne-tized plasma an its fluctuations. The trajectory of the particleswas integrated for two different cases: periodic bondaries in alldirections, and periodic in the z direction only with outflow bon-daries in the x & y directions.

3. Preliminary Results

Figure 1 (right panels) shows the current density distribution intwo-dimensional cuts at the center of the simulated jet. We cansee clearly the formation of current sheets near the axis at thebottom, where the test particles are probably mostly acceleratedin our tests. We used an algorithm (developed by L. Kadowakiin our group) to identify the current sheets where there are mag-netic reconnection regions (which is based in Zhdankin et al.2013). We encounter that in t = 50 there are more regions ofreconnection than in other times. For this reason we have takenthis snapshot to inject test particles. In the left part of the Figure2, we show the particle kinetic energy evolution of 1,000 parti-cles for a periodic injection in the three-directions. This periodicre-injection continued until t = 104 hours. The re-injection ofthe particles tries to mimic the large extension of these sources,since in our simulations we only consider a small portion of realjet domains. We note that after t ∼ 2.5× 103 hours, the exponen-tial growth saturates. At this stage the particles’ Larmour radiushave become larger than the size of the accelerating zones and

the particles can no longer be accelerated by reconnection. Theyonly suffer linear drift acceleration from this time on (see Kowalet al. 2012; del Valle et al. 2016). In the right of the Figure 2we injected 10,000 test particles with a periodic re-injection in zdirection only and with an outflow scape condition in the x & ydirections. These preliminary results of test particles in magneticreconnection sites show that the particles start to be acceleratedexponentially after ∼ 100 hours of injection. From 1,000 parti-cles on, they are accelerated from 104 MeV to 1011 MeV in afew hundreds hours only, indicating that once the particles enterthe acceleration zones the process is very fast, as predicted byde Gouveia Dal Pino & Lazarian 2005, Kowal et al. 2011, 2012;de Gouveia Dal Pino et al. 2016. In these tests, we considered amagnetic field of the order of 0.01 G. For velocities of the orderof the light speed and a time interval of several hundreds hours,the dimension scale of the acceleration region is of the order ofct ∼ 1014 cm or 10−4 pc, which is compatible with the dimen-sions of the acceleration zones producing the observed gamma-ray flares in luminous AGN jets, like the blazars (Giannios et al.2009, Aharonian et al. 2007).

ReferencesAharonian, F. et al. 2007, ApJ, 664, L71Bell, A. R. 2013, arXiv, arXiv:1311.5779de Gouveia Dal Pino, E. M., & Lazarian, A. 2005, A&A, 441, 845de Gouveia Dal Pino, E. M., & Kowal, G. 2015, Magnetic Fields in DiffuseMedia, Astr. Sp. Sc. Library, 407, 373Giannios, D. 2010, MNRAS, 408, L46Giannios, D., Uzdensky, D. A., & Begelman, M. C. 2009, MNRAS, 395, L29Kadowaki, L.H.S., de Gouveia Dal Pino, E. M., & Singh, C. B. 2015, ApJ, 802,113Khiali, B., de Gouveia Dal Pino, E. M., & del Valle, M.V. 2015a, MNRAS,449, 34Khiali, B., de Gouveia Dal Pino, E. M., & Sol, H. 2015b, arXiv,arXiv:1504.07592Kowal, G., de Gouveia Dal Pino, E. M., & Lazarian, A. 2011, ApJ, 735, 102Kowal, G., de Gouveia Dal Pino, E. M., Lazarian, A. 2012, PRL 108, 241102Mizuno, Y., Lyubarsky, Y., Nishikawa, K. I., & Hardee, P. E. 2012, ApJ, 757,16Mizuno, Y., Nishikawa, K. I., Koide, S., Hardee, P., & Fishman, G. J. 2006,arXiv:astro-ph/0609004Singh, C.B., de Gouveia Dal Pino, E. M., & Kadowaki, L.H.S. 2015, ApJ, 799,L20Singh, C.B., Mizuno, Y. & de Gouveia Dal Pino, E. M. 2016, ApJ, 824, 48Sironi, L., & Spitkovsky, A. 2014, ApJ, 783, L21Uzdensky D. A. 2011, Space Sci. Rev., 160, 45del Valle, M. V., de Gouveia Dal Pino, E. M. & Kowal, G. 2016, MNRAS 463,4331Zhdankin, V., Uzdensky, D. A., Perez, J. C., & Boldyrev, S. 2013, ApJ, 771,124

248