Magnetically-dominated relativistic jets.

Transcription

1 Magnetically-dominated relativistic jets. Serguei Komissarov University of Leeds UK N.Vlahakis, Y.Granot, A.Konigl, A.Spitkovsky, M.Barkov, J.McKinney, Y.Lyubarsky, M.Lyutikov, N.Bucciantini

2 Plan 1. Astrophysical introduction; 2. Central engine; 3. Collimation; 4. Acceleration; 5. Other issues;

3 I. Introduction 1. Jets of AGN Jet speed: Γ ~ 1-50 Collimation: 1 10 degrees Source: Super-massive BH with an accretion disk M87 jet

4 2. Jets of GRB Jet speed: Γ ~ No images available yet Collimation: few degrees Source: Stellar mass BH (NS) with an accretion disk or a magnetar

5 3. Jets of X-Ray binaries Jet speed: Γ ~ 1-3 Collimation: 1 10 degrees? Source: Stellar mass BH (NS?) with an accretion disk (a micro-agn) GRS1915

6 4. Jets and winds of pulsars Jet speed: v ~ c Wind speed: Γ ~ (theoretical) Source: NS without accretion disk Crab Nebula Likely a different origin of the jets.

7 Magnetic paradigm of relativistic jets (R.Blandford) Jets are produced by rapidly rotating BH (NS) with accretion disks. Power source - the rotational energy of BH (NS); Jets are accelerated via the Maxwell stresses; the magnetic field is provided by the accretion disks. Their collimation is also due to the Maxwell stresses (hoop stress); Energy is transported to large distances without significant losses in the form of electromagnetic and kinetic energy; Along the way, the electromagnetic energy is converted (partially?) into the kinetic energy of plasma; Dissipation occurs at shocks (kinetic energy) and/or reconnection cites (magnetic energy).

8 Equations Ideal Relativistic MHD Magnetodynamics (MD) (Force-free Degenerate Electrodynamics )

9 Resistive Relativistic MHD - Faraday equation - Maxwell equation - continuity equation - energy-momentum equation Phenomenological Ohm s law (Lichnerowicz 1967): σ- scalar electric conductivity, q 0 - proper electric charge density In the fluid frame:. Kinetic theory approach (Blackman & Field 1993). Two-fluid Relativistic MHD: (Zenitani et al, 2008)

10 II. Central engine Michel (1974): Steady-state axisymmetric MD solution for rotating magnetosphere ( limit of vanishing particle inertia). - monopole poloidal magnetic field - azimuthal component caused by the rotation - poloidal electric field caused by the rotation - Poynting flux Ω - angular velocity, ϖ - cylindrical radius, r - spherical radius. Drift speed: at infinity (radiative BC).

11 c B p Ω B t Magnetic spirals advance with the speed of light. The structure of poloidal field is unaffected by the rotation. The twist has nothing to do with the particle inertia. There is a net Poynting flux from the rotator γ γ Ω h Ψ - total magnetic flux Blandford-Znajek (1977) - similar solution for slowly rotating black holes.

12 2D GR MD simulations (Komissarov 2001,2004, McKinney 2005) H φ Kerr black hole with initially non-rotating monopole magnetic field. a=0.1 a=0.5 t=120 a=0.9 azimuthal magnetic field (colour) magnetic surfaces

13 Mass loading sets up the upper limit on the asymptotic flow speed. Cold (p=0) ideal MHD flow. Along the magnetic flux surface: - Bernoulli integral = (total energy flux)/(rest mass energy flux) = (Poynting flux)/( total particle energy flux) Asymptotically may reach provided total conversion of the Poynting flux occurs. At the base is necessary for highly relativistic outflow Thus, in the magnetosphere.

14 Mass loading argument favours BH (NS) over accretion disk slow wind heavy mass loading relativistic jet weak mass loading magnetic field suppresses plasma transport from the disk corona to the BH magnetosphere accretion disk Kerr black hole inflow outflow outflow Support from numerical simulations

15 III. Collimation Is magnetic hoop stress effective? For non-relativistic flows - Yes. (Bogovalov & Tzinganos, 1999) For relativistic flows - No. Bogovalov (2001), Komissarov (2004), Koide (2004)

16 Collimation of relativistic jets requires a nozzle, external confining medium. with nozzle Suspects: disk jet disk Thick disk (torus) Disk wind Disk magnetosphere ISM gas for AGN Once the flow has been accelerated to high Γ, the nozzle is no longer required. Jet collimation will be preserved.

17 Example. ballistic conical flow separation point Flow in a tube with diverging walls. 2D RMHD simulatons. Komissarov et al. (2009) Colour log(magnetic pressure); Lines magnetic flux surfaces.

18 Even sub-sonic (sub-fast-magnetosonic) relativistic jets can remain collimated in the absence of confining medium! nozzle Γ o v < c φ vο v free expansion

19 Generation of relativistic MHD flows in numerical simulations. Winds: Komissarov (2001,2004), Koide (2004), Bucciantini et al.(2006,2007), and others. Jets: McKinney (2006), Komissarov & Barkov (2007,2008), Bucciantini et al.(2009), McKinney & Blandford (2009), and others. Example: Collapsar jets. 2D GRMHD. Collapse of a rapidly rotating magnetic star. Evolution after BH formation. Fixed Kerr metric. Dipolar magnetic field of the collapsing star. Animation (Komissarov & Barkov, 2007) ( mass density and magnetic field lines)

20 3D GR RMHD simulations McKinney & Blandford (2009) Collimation by torus or torus wind (?) Domain size ~ 1000 r g

21 IV. Acceleration How efficient is ideal MHD acceleration? Can the Lorentz factor reach Γ max? ( Full conversion of the Poynting flux into kinetic energy.) Steady-state outflows which pass through slow, Alfven, and fast magnetosonic critical surfaces in succession. Beyond the Alfven surface (light cylinder) the azimuthal component of B dominates. The light cylinder:

22 In contrast to non-relativistic MHD flows, most of the energy conversion has to occur in the super-fast-magnetosonic zone. At the fast surface: Hence Most of the energy is still in the electromagnetic form! Magnetic acceleration in the super-fast magnetosonic regime is rather delicate because of the possible loss of causal connection across the jet.

23 Thermal acceleration conical jet A R j v~c Mass conservation: Energy conservation: Bernoulli equation: Very fast acceleration!

24 Magnetic acceleration (cold jets) A v~c R j Mass conservation: Energy conservation: The Bernoulli equation: No acceleration!

25 Jet with curved streamlines v v v δr A R Consider the flow between two close flux surfaces,. Acceleration only when decreases! Hence, a restructuring of magnetic flux distribution across the jet is required.

26 Example: Rarefaction acceleration A short burst of acceleration as the jet becomes unconfined. rarefaction wave jet confinement zone v acceleration zone conical expansion weak acceleration Aloy & Rezzola (2006), Mizuno et al.(2008), Tchekhovskoy et al.(2009), Komissarov et al.(2010)

27 Example: Collimation acceleration (The standard model ) Prolonged slow acceleration of externally confined jets. Faster collimation of inner stream lines due to the magnetic hoop stress (slow self-collimation). Vast literature. Coordinated restructuring of the flux surfaces across the whole jet required causal connectivity narrow jets! Most recently, Beskin et al. Lyubarsky (2009,2010), Komissarov et al. (2007, 2009)

28 Summary of recent numerical and analytical results: Acceleration of freely expanding (unconfined) or in conical tubes is less efficient. It generally saturates before reaching. This is due to the loss of causal connection across the jets Acceleration of jets with gradually increasing collimation is more efficient. They reach ; These jets remain causally connected. Jets confined by external pressure ballistic. Acceleration saturates with with a > 2 become For θ j ~1 this reduces to the well known (Tomimatsu, 1994) For GRB jets with Γ =100 and θ = 0.1 this would imply Remain in the Poynting-dominated regime?

29 IV. Other issues (instead of Conclusions) Instability (Kink-mode)? (e.g. Istomin & Pariev 1996, Lyubarsky 1999) More 3D simulations needed to see how destructive it can be (like McKinney & Blandford, 2009). The role of velocity gradient across the jet, non-cylindrical geometry, time-dilation effect etc? Dissipation. Shocks? Inefficient for high sigma flows (e.g. Kennel & Coroniti, 1984). Magnetic dissipation in high sigma plasma (relativistic reconnection) (e.g. Lyutikov & Blandford 2003, Giannios et al. 2009, McKinney & Uzdensky 2010, Zhang & Yan 2011) Instability may promote more efficient acceleration and magnetic dissipation? (e.g. Heinz & Begelman 2000, Drenkhahn & Spruit 2002). If initial magnetization determines the terminal Lorentz factor then what processes determine the magnetisation? Why the Lorentz factors of XRB, AGN, and GRB are so different?

30 Origin of regular magnetic field in accretion disks? Its role in the accretion dynamics? Vertical transport of angular momentum? ( e.g. Blandford & Payne 1982, Spruit & Uzdensky, 2005, Lubow et al. 1994, Livio et al., 1999) Nature of the variability and its effects on the jet acceleration? (Contopoulos 1995, Granot et al.,2010) Dynamic of inhomogeneous jets with variable magnetization and shock dissipation in such jets? Particle acceleration mechanisms? Inefficient shock acceleration at high sigma shocks (e.g. Spitkovsky & Lorenzo 2009). Other missing ingredients. e.g. Compton drag and photon breading (Stern & Poutanen)? Alternative models? Thermal acceleration of GRB jets (fireball?). There are many more questions than answers.

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32 Magnetic acceleration and causal connectivity The coordinated change in the bunching of stream lines requires efficient communication via magnetosonic waves across the jet. The condition: characteristic θ j v θ Mach streamline The acceleration slows down when Γ reaches

33 For GRB jets with their typical, this gives whereas the observations require Γ = Thus, in this model we expect the GRB jets to remain magnetically-dominated, σ >> 1. This raises doubts over the connection between the jet emission and shock dissipation, and perhaps over the magnetic model of GRB jets altogether. AGN jets and X-ray binary jets may become kinetic energy dominated. (Smaller observed angles and lower observed Lorentz factors.)

34 IV. Dissipation Internal-external shock model of GRBs. Variable central engine -> patchy jet -> collisions of shells -> internal shocks -> dissipation -> prompt gamma-ray emission. v γ rays Shells merge into a single shell -> it shocks the interstellar gas and slows down -> shock dissipation -> afterglow emission. X-rays Prompt gamma-ray emission is ~10% (up to 90%) of the total jet energy. Very high radiation efficiency of GRBs! (Zhang et al. 2007)

35 Non-magnetic model of GRBs. (i) huge variations of the Lorentz factor, δγ Γ, to have high dissipation efficiency; (ii) multiple-collisions between shells, if only a small fraction of dissipated energy is radiated, to have high radiation efficiency The pumping action: ( Kobayashi & Sari, 2001). A shock dissipates a fraction of the kinetic energy A fraction of the dissipated energy is emitted The rest is converted into the kinetic energy again (expansion after the collision) Another collision

36 Perpendicular shocks in magnetically dominated plasma. Only the kinetic energy dissipates; Kinetic energy is only a small fraction of the total energy, ; Thus, only a small fraction of the total energy dissipates. For ultra-relativistic shocks, this is v B shock One half of the kinetic energy dissipates and the other half is converted into magnetic energy. (Kennel & Coroniti,1984) (Zhang & Kobayashi, 2005) Energy remains mostly in electromagnetic form!

37 Implications for the magnetic model of GRB jets 1) The prompt gamma-ray emission cannot be explained by internal shocks in the magnetic model; 2) The afterglow emission can still be associated with the external shock. Even a highly magnetized shell can drive a strong blast wave through the ISM and transfer its energy to the snowploughed ISM gas.

38 Searching for the way out 1. How to increase the efficiency of magnetic acceleration? Tangled magnetic field (Heinz & Begelman 2000) If, where α, β are constant then the magnetic field behaves as an ultra-relativistic gas with A current-driven instability? Dissipation of tangled magnetic field ( Drenkhahn & Spruit 2002) (magnetic energy) (heat) (kinetic energy)

39 Impulsive magnetic acceleration (Lyutikov 2010, Granot et al. 2010) Expansion of a highly magnetized plasma shell into vacuum vacuum v Once detached from the wall the shell keeps spreading longitudinally with the front section reaching very high Lorentz factor. Behind, the shell leaves a rarefied slow tail.

40 magnetic field magnetic pressure The averaged over energy Lorentz factor grows as until it approaches the limit total magnetic kinetic Lorentz factor Interaction with the external gas limits this effect (Levinson 2010) Similar limitation in the case with many shells when the gaps are filled with the external gas or even the tail gas.

41 Searching for the way out 2. How to increase the efficiency of dissipation? The flow remains highly magnetized. Shock are inefficient at dissipation. Instead, a direct dissipation of magnetic energy. Magnetic reconnection. ( Lyutikov & Blandford 2003, Giannios et al. 2009, McKinney & Uzdensky 2010, Zhang & Yan 2011, etc )

42 Another way out? The magnetic pump model. Variability of the central engine -> highly magnetised pulses are separated by low magnetised gaps (most of the jet energy is magnetic) -> expansion of pulses drives strong shocks -> their energy dissipates when these shocks cross the gaps -> multiple crossings result in high dissipation and radiation efficiencies. pulse gap shocks in the gaps shock in the pulse

43 The 1D toy model Chamber Key parameters:

44 Oscillations continue until the all of the dissipated energy is radiated and the magnetic pressure is uniform. From the magnetic flux conservation and the radiation efficiency For (most of the energy is in the pulse ) This can be quite high!

45 Numerical Simulations 1D RMHD with a cooling term: - thermal energy density in the fluid frame - cooling time - temperature

46 Numerical models - 50% emission time (in light crossing times) - final magnetization of plasma

47 Rate of energy loss Low gap magnetisation; Strongly dumped oscillator. High gap magnetisation; Weakly dumped oscillator.

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49 V. Conclusions 1) The magnetic field provides a robust mechanism of powering outflows from rotating central engines. When the magnetosphere is highly magnetically-dominated (relativistic Alfven speed) the outflow is relativistic. 2) An external collimation is required close to the central engine in order to produce jets. But it is not required further out in order to preserve their collimation. 3) The magnetic acceleration has to continue well beyond the fast magnetosonic surface in order to ensure efficient conversion of the Poynting flux into the kinetic energy. In this regime it becomes rather problematic. The high-γ GRB jets are likely to remain magnetically-dominated to the very end. 4) Shock dissipation in homogeneous magnetically-dominated flows is very inefficient, and cannot explain the prompt emission of GRBs. Alternative models involving magnetic reconnection are becoming increasingly popular.

50 5. In inhomogeneous magnetically dominated flows, with weakly magnetised patches, the shock dissipation can still be very efficient, and can explained the observed high radiation efficiency of GRBs.

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52 Another angle: v~c v~c Volume of the fluid element: Its magnetic field: Its magnetic energy: Thus, the magnetic energy is conserved! No energy conversion = No acceleration

53 accretion disk Kerr black hole inflow outflow outflow