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Miguel A. Aloy

Universidad de Valencia Departamento de Astronomía y Astrofísica. General Relativistic hydrodynamic simulations of post -neutron star mergers as progenitors of sh ort GRBs. Miguel A. Aloy. In collaboration with: T.-H Janka and E. M üller (find out more @ astro-ph/0408291 ).

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Miguel A. Aloy

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  1. Universidad de Valencia Departamento de Astronomía y Astrofísica General Relativistic hydrodynamic simulations of post-neutron star mergers as progenitors of short GRBs Miguel A. Aloy In collaboration with: T.-H Janka and E. Müller (find out more @ astro-ph/0408291) UCLA Workshop III: Relativistic Astrophysics Los Angeles, 3 – 5 - 2005

  2. GRBs, phenomenology: • First detected in 60s by the military satellites Vela (but 1st publication in Klebesadel et al.1973) • Point explosion in a r-n medium @ rate: ~ 1/day • Energy: E ~ 1-103 FOE (isotropic, mainly in gamma-rays) • Causality ⇒ energy liberated in R~100 km on timescales of < secs.

  3. GRBs, phenomenology: • First detected in 60s by the military satellites Vela (but 1st publication in Klebesadel et al.1973) • Point explosion in a r-n medium @ rate: ~ 1/day • Energy: E ~ 1-103 FOE (isotropic, mainly in gamma-rays) • Causality ⇒ energy liberated in R~100 km on timescales of < secs. • Distribution: Isotropic, but inhomogeneous Log N – Log P distribution of772bursts in the energy and50 – 300 keV 3rd BATSE GRB catalogue (Meegan et al. 1996) Homogeneity (Euclidean space): N ~ R3 Dependence of the flux with R: P ~ R-2 N ~ P-3/2

  4. GRBs, phenomenology: • Non-thermal spectrum⇒optically thin emission region. • Variability of the light curves down to ~ 0.001 s. • Distance: z = 0.085 ... 5.0⇒ cosmological location! • Mejecta ~ 10-4 Msun, = ( 1 - v2/c2 )-1/2 ~ 100 • Two classes: • Short: T90< 2 s, harder • Long: T90> 2 s, softer • Afterglows: • X-rays, optical, radio • Durations ~ days after GRB Duration of 427 bursts thatdo not displaysignificant gaps 3rd BATSE GRB catalogue (Meegan et al. 1996)

  5. GRBs, theory: Fireballs • Releasing ~ 1030 erg cm-3s-1 implies the formation of an e+e_,g fireball (Cavallo & Rees 1978). • Compactness problem: Since most of the energy detected is >0.5 MeV, the optical depth against gg ⇒e+e_is huge and photons cannot escape! gg= 1013 fp F-7(D / 3Gpc)2 (t / 10ms)-2 • Relativistic expansion reduces the effective threshold energy for pair production (Fenimore et al. 1993): ~100(g/10 GeV)1/2(t/MeV)1/2 gg = 1013 / 4+2 fp F-7(D / 3Gpc)2 (t / 10ms)-2 • Theoretically, a relativistic outflow results if an initial energy E0 is imparted to a mass M0«E0/c2 (Relativistic Sedov solution; Blandford-McKee). • Starting from rl the expansion of the gas converts its Eint into Ekin until ~max~  ~ E0/M0c2 which happens at rs rl, beyond which the flow coasts with  ~  ~ constant.

  6. GRBs, theory: Internal vs External shocks • Some caveats of the fireball model: • Efficiency: Conversion of MOST of its Eint into Ekin ⇒almost no g-luminosity, low energetic efficiency. • Spectrum: Quasy-thermal spectra (observed: power-law). • Timescales: Tg-escape ~ Tthin ~ milliseconds ⇒cannot account for long events. • Solution: • the energy is initially produced in another form and is only converted in gamma-rays at large distances from the source. • How: tenuous, collisionless, relativistic shocks that reconvert Ekin of the baryons into nonthermal particle andgenergy by, e.g., Fermi process: • chaotic E,B fields • pmin ~ bulk , emin ~ (mp/me)bulk • Diffusive shock acceleration ⇒N(e) ∝e-a, a~2-3 • ⇒ Gamma radiation: Synchrotron + Inverse Compton

  7. GRBs, theory: Internal vs External shocks • Standar paradigm: fireball shocks are either external (Rees & Mészáros 1992) or internal (Rees & Mészáros 1994). • External shocks: Reff ~ 1015 – 1016 cm • Interaction with the medium • May explain some spectral properties of long, smooth bursts and afterglows. • Internal shocks: Reff ~ 1013 cm • Irregularities in the flow • may explain the shortest time scale variability (~10-3 s).

  8. SN-GRB association (L-GRBs!): SN1998bw/GRB980425 SN2003dh/GRB030329 SN2003lw/GRB031203 • GRBs: Progenitors • Difficult to identify because of lack of observational accuracy • More than 200 competing models • Most promising: catastrophic collapse events • Death of massive stars/SN ⇒ Sources of long GRBs • Collapsars (Woosley) • Hypernovae (Pacynski) 2) Mergers of compact binaries ⇒ Sources of short GRBs & strong GWs (Pacynski, Goodman, Eichler et al., Mochkovitch et al., Katz & Canel, etc.) This association was originally proposed in the 1st paper on GRBs (Klebesadel et al. 1973)!

  9. GRBs, progenitors: long bursts Collapsars (Woosley 1993) • Collapse of a massive (WR) rotating star that does not form a successful SN to a BH (MBH ~ 3Msol ) surrounded by a thick accretion disk. The hydrogen envelope is lost by stellar winds, interaction with a companion, etc. • The viscous accretion onto the BH ⇒strong heating⇒ thermal n̃annihilating preferentially around the axis ⇒ fomation of a relativistic jet (>10). Aloy et al (2000) Newtonian-HD GRHD MacFadyen & Woosley (1999)

  10. Progenitors of short GRBs: setting the stage • Merger of a system of compact binaries (SCBs): • After the merger of a SCB a central BH(MBH ~ 2-3Msol)girded by a thick accretion torus(Mtorus~ 0.05 – 0.3Msol). • Once the thick disk is formed, up to ~1051 ergs can be released above the poles of the BH in a region that contains <10-5 Msun of baryonic matter due to n annihilations preferentially near axis⇒acceleration to ultrarelativistic speeds. • If the observed duration Tobs is related to the lifetime of the system Ta this kind of events can only belong to the class of short GRBs because Tdisk~ 0.05 – 0.5 s. • Local rate of NS-NS events: ~ 800 Gpc-3 y-1 (Kalogera et al. 2004) • Local rate of short GRBs: ~ 0.8 Gpc-3 y-1 (Guetta & Piran 2004) Taking these values for granted, they agree if: a) Opening angles of short GRBs ~ 0.5o – 1.5o b) Not every merger yields a short GRB.

  11. Progenitors of short GRBs: our goals To check the viability of the scenario of merging SCBs for producing ultrarelativistic outflows (winds, jets, radial outflows, canon balls?). Sssssssssssssssssssssssss s Mechanism of collimation (if any) of the outflowing plasma.Sssssssssssssssssssssssss s Typical opening angles and consequences on the observed rate of events.Sssssssssssssssssssssssss s Expected durations of the GRB events generated in this framework and their relation to the time during which the source of energy is active (Ta).

  12. Progenitors of short GRBs: our method Progenitors modelled as non-selfgravitating relativistic perfect fluids: Tmn = (r + re + p) umun + p gmn The gravitational field is provided by central Schwarzschild BH: ds2 = -(1-2M/r) dt2 + (1-2M/r)-1dr2 + r2dq2 + r2 sin2q df2 EoS: Boltzman gas of nucleons + e+e- + radiation (Witti, Janka & Takahashi 1994). No degeneracy is assumed. P = Pgas + Prad + Pe+e- The GRHD equations are solved using the HRSC code GENESIS (Aloy et al. 1999; num. foundations in Font´s & Rezzolas’s talk) with: - likely initial model (BH + thick accretion disk) -BC: rmin BH; rmax outflow; q = 0o, 90oreflection - Release energy in a baryon clean environment

  13. GENESIS: basics It is a 1D, 2D & 3D parallelized, finite volume code, that implements a methods of lines (e.g., LeVeque 1992) to evolve the SRHD, GRHD or RMHD equations. Key elements: • Coordinates: Cartesian, Cylindrical, Spherical • Metric: Minkowski, Schwarzschild (exterior). • Riemann solver: HLLE, Marquina FF (Donat et al. 1998), Exact (Pons et al. 2000) • 2nd or 3rd order TVD Runge—Kutta scheme for time integration (Shu & Osher 1988) • piecewise linear (MinMod)/ PPM reconstruction • Vectorized Newton—Raphson iteration for recovery of the primitive variables (r, p, v) • EoS: modular implementation • Multi-species (tracer approach). • OpenMP-parallel

  14. GENESIS: extensions (I) Non-thermal radiation modules: Mimica et al. (2004) • non-thermal electrons: Ntracer species corresponding to Nlogarithmic Lorentz factor intervals from minto max • in each energy bin the energy distribution is assumed to be a power law, pi • Temporal evolution: analytic solution of the kinetic equation as a piecewise power-law (generalization of Kardaschev solution) • Radiation mechanism: Synchrotron • Two alternative parameterized shock acceleration models: ae, z • Radiation back-reaction on the dynamics • Magnetic field energy: in a fraction of equipartition with the internal energy of the fluid, aB (but the code is ready for RMHD input)

  15. GENESIS: extensions (II) RMHD: Leisman et al. (2005) • 1D, 2D Cartesian and Cylindrical • HLLE type Riemann solver • 2nd or 3rd order TVD Runge—Kutta scheme for time integration (Shu & Osher 1988) • piecewise linear (MinMod)/ PPM reconstruction • 2D Newton—Raphson iteration for recovery of the primitives (mnewt; Numerical Recipes) • contraint transport or flux central difference scheme to keep ∇B = 0 + O(machine precision) • EoS: ideal gas

  16. Ruffert & Janka (2001), A&A, 380, 544 Initial model Two approaches: Type-A: Put a toroidal-like distribution of matter and angular momentum around a Schwarzschild BH (guided by the Newtonian simulations of, e.g., Ruffert & Janka 2001, Lee et al. 2004, Setiawan et al. 2004) and let it relax to an equilibrium configuration. Mtorus ~ 0.34 Msun MBH ~ 3 Msun Menv ~ 10- 2 Msun Relaxed initial model Aloy, Janka & Müller (2004), astro-ph/0408291

  17. Ruffert & Janka (2001), A&A, 380, 544 Initial model Two approaches: Type-B: Follow Font & Daigne (2003) prescription to build up equilibrium tori around a BH. Outside use Michel (1972) spherical accretion solution. Mtorus ~ 0.34 Msun MBH ~ 2.44 Msun Menv ~ 10- 7 Msun Type-A Type-B Aloy, Janka & Müller (2005), astro-ph/0408291

  18. Modelling the energy release Guided by previous results of Janka, Ruffert et al. showing that both in NS-NS mergers (Ruffert & Janka 1999) and in BH-NS mergers (Janka et al. 1999), can be released up to 1051ergs above the poles of the black hole in a region that contains less than 10-5 Msun of baryonic matter. The dependence in z-distance is: q(z) = q0 / z5; z = r sin;0~[30o, 75o] Deposition region (baryon clean environment) z BH Accretion torus Janka et al. (1999), ApJ, 527, L39 Aloy, Janka & Müller (2005), A&A, in press

  19. Computed Models - Energy deposition region: Uniform or burst like. Within a cone of 30o to 75o around the rotation axis that extends from Rmin= 1.02 - 2.05 Rs (innermost boundary) to infinity - Grids: r (log spaced) x  (uniform) Type A: 460 x 200 zones. Rmax = 3 x 109 cm Type B: 500 x 200 zones. Rmax = 2 x 1010 cm (+resolution checks up to 2000x200 zones) Type-A Type-B

  20. Results - Pthr ~ 1048-49 erg/(s·sr): * in the initial model matter falls in through the axis of rotation (vin~0.6c- 0.97c) * might be a reason why every SBC merger DOES NOT yield a GRB * our threshold is probably higher than in real mergers (type-A) or maybe irrelevant in type-B models.

  21. Collimation:  initially the disk provides the collimation via cocoon/disk interaction, i.e., the opening angle of the beam is set by the torus inclination. - pure hydrodynamic collimation (no need for B- fields). *For low dE/dt  initial opening angle set after ~ 1-3 ms (j ~ 3-5), but modified later by the high density halo. * For high dE/dt initial opening angle set after a torus scale-height light- crossing time (~ 0.5-1 ms) with j ~ 3-5.

  22. Collimation mechanism (in low density merger environments): CD CD axis Rarefied layer Shocked layer Rarefied layer  Shocked layer P=const. q0 z r equator thick accretion torus Levinson & Eichler (2000) A radial, baryon-rich (heavy) wind collimates asymptotically a conical, baryon-poor (light) jet (BPJ). Accretion disk = slim anulus. Interaction reduced to a thin shocked layer around the BPJ. Aloy, Janka & Müller (2005) The accretion torus (very heavy) collimates along its scale hight an almost conical, BPJ. Accretion disk = thick torus. Interaction extended to a thick shock.-raref. layer around the BPJ. 

  23. Results (evolution up to 100 ms) 1049 erg/s 2x1050 erg/s 1051 erg/s 5x1051 erg/s Limit of the deposition region Type A Morphology: For P> Pthr ~ 1049 erg/s the outflows are either knotty, narrow, relativistic jets (P < 1051 erg/s) or conical, smooth, wide angle, ultrarelativistic winds (P > 1051 erg/s). Outflow open. half-angle: It is determined by the high density external medium (low P) or by the inclination angle of the side walls of the torus (large P). Propagation speed: between ~ 0.6c (P < 1051 erg/s) and ~0.97c (P > 1051 erg/s). Collimation: (dense) external medium (+ torus).

  24. Results (evolution up to 100 ms) 2x1050erg/s Type B Morphology: For P> Pthr ~ 1048 erg/(s·sr) the outflows are always conical, wide angle, ultrarelativistic jets. Outflow opening half-angle: ~20oto 30o. It is determined by the inclination angle of the side walls of the torus (large P/V). Propagation speed: larger than ~0.9999c. Collimation: torus (no LE00) Variability: extrinsec  hard to disantangle it from the engine intrinsic variability  Imprinted via KH- or SD- instabilities (Aloy et al. 2000, 2002; Zhang et al. 2003; Gómez & Hardee 2004)  Qualitatively similar to L-GRBs particularly at jet breakout.  Quantitative differences: r/re, G, h/he, preexisting breakout hole 75o 45o 60o 1049erg/s 1051erg/s 45o 45o 41.4o 45o 45o

  25. Post-switch-off evolution The typical time scale in which the merging of SCBs may release energy is of some fractions of a second. We have switched off the energy deposition after Ta=0.1s and followed the subsequent evolution of two models: one of type-A (P=5x1051 erg/s in 0=30o) and another of type-B (P=2x1050 erg/s in 0=45o). A condition to produce a successful GRB is: front ultrarelativistic  VrearVfront (a) Tobs rear Ta= 100ms front R ~ 1014 cm Type A Unsuccessful GRB:Condition (a) does not hold because the environment is too dense and the front shock of the fireball decelerates. Type B May produce a successful GRB:Condition (a) is Vrear<Vfrontin this case. Thus, the fireball stretches radially and, it can produce events with durations of several seconds, i.e., Ta «Tobs. T~ 300ms rear front Ta= 100ms R ~ 3x109 cm

  26. Post-switch-off evolution. Type-A (merger in high density environment) No GRB!!! P = 0 (switched off)  ~ 1000 in 100 ms. PA09 = 5x1051erg/s  ~ 2 in 350 ms.

  27. Post-switch-off evolution. Type-A (merger with high density halo) No GRB, instead: UV-flash. Assuming adiabatic evolution of the cloud: P = 0 (switched off) Because of the small Lm, only closeby events will be visible PA09 = 5x1051erg/s

  28. Pure thermal energy is released in this cone Pure thermal energy is released in this cone Post-switch-off evolution. Type-B (merger with low density halo) • For P = 2x1050 erg/s the Lorentz factor grows up to ~ 1000 in 500 ms. • Switching off the energy release leads to an almost selfsimilar growth it is possible to produce a successful GRB!. Model B01: P= 2x1050 erg/s, Edep = 2x1049 erg, E>100~6x1048 erg, E>10~1.2x1049 erg 0 = 45o, w = 24o, Mf= 7.4x1024 g

  29. > 100 Post-switch-off evolution. Type-B • The radially averaged variables display a • non-monotonic shape as a function of . •  ~  -2 • The sideways expansion in the comoving • frame is subsonic. • A part of the fireball is contracting!. •  G profile similar to that obtained in • collapsar simulations (e.g., Aloy et al 2000, • Zhang et al. 2003). •  growing? •  relaxing? • narrower • with time • 2-component jet? • ~+0.07c • ~ -0.05c • max ~ 70

  30. T = 0.5 s Opening angles and rates. Type-B qG>100 ~ 5o – 10o  f ~ 0.4 – 1.5% of the • hemisphere •  100 times more short GRBs than observed • (assuming isotropic detectability in all directions within the opening angle) • qG>10 ~ 15o – 25o  f ~ 7 – 18% of the • hemisphere • 10 times more short GRBs than observed • Taking for granted our jet opening angles implies: •  A rate of 100 y-1observed short GRBs • yields r1 ~10-6 - 10-5 galaxy-1 y-1 events: • smaller but consistent with estimated • NS+NS & NS+BH merger rates • r0~ 10-5 -10-4galaxy-1 y-1(e.g., Kalogera • 2004; Fryer et al. 1999; Guetta & Piran • 2004) •  r1 < r0 (+lack of GRB signal produced in • type-A models) suggests that not every • merger produces a GRB. • plateau sharp edges (>100) • kinetic+internal • kinetic

  31. T = 0.5 s Opening angles and Eiso. Type-B Our results: qG>100 ~ 5o – 10o  1050  Eiso  1051 erg. •  1051  Liso  1052 erg/s • qG>10 ~ 15o – 25o  1049  Eiso  1051 erg. •  1050  Liso  1052 erg/s • Observations/theory: •  Mao et al (1994): • Lisoshort~ Lisolong ~ 1051-52 erg/s •  Frail et al. (1997): • Eisolong ~ 1053 erg •  Our results are consistent with the • fluence-duration proportionality • (short vs long GRBs; e.g., Balazs et al 2003) • plateau sharp edges (>100) • kinetic+internal • kinetic

  32. Burst detection. Speculative picture: Normal s-GRB + Afterglow Internal shocks modulate LC Liso ~ 1050 -1052erg/s  > 10  < 20o X-Rays/optical? only external shock, Orphan afterglow? Liso ~ 1045 -1050erg/s 2 <  < 10 20o <  < 60o X-Rays/optical? only external shock, Orphan afterglow? Liso ~ 1045 -1050erg/s 2 <  < 10 20o <  < 60o radio?? only external shock, Orphan afterglow? Liso < 1045erg/s  < 2  > 60o radio?? only external shock, Orphan afterglow? Liso < 1045erg/s  < 2  > 60o

  33. Efficiency: 10% - 30% of Edepwithin the ultrarelativistic outflow ( ~ 5o – 10o) Post-switch-off evolution. Type-B

  34. G = 2 After 0.5 s only ~0.5% of Edepis converted to Ekin but the trend is to increase with time. Extrapolation of the results to ~ 1000 s very difficult but the trend seems to be: A large fraction of the energy will be kinetic before transparency sets in. G = 10 G = 50 G = 100 Post-switch-off evolution. Type-B Efficiency: 10% - 30% of Edepwithin the ultrarelativistic outflow ( ~ 5o – 10o)

  35. Post-switch-off evolution. Type-B Efficiency: 10% - 30% of Edepwithin the ultrarelativistic outflow ( ~ 5o – 10o) The jet opening angles are much larger than for long GRBs (note, however, that Guetta & Piran (2004) predict much smaller opening angles for short GRBs on the basis that every merger yield a GRB): Long GRBs (Frail et al. 2001): <w> ~ 3.6o, with 2.5o < w < 17o Short GRBs: Aloy et al. (2005): <w> ~ 20o, with 15o < w < 25o Rosswog & Ramirez-Ruiz (2003): <w> ~ 8o, with 1o < w < 21o

  36. Afterglow or not afterglow? A) If every merger event yiels a short GRB, Guetta & Piran (2004) conclude that their afterglows will be produced just minutes after the GRB because of the narrower angles they predict. B) If SCBs are ejected from the host galaxy into an external medium much less dense than the assumed ISM (next ~ 0.1 – 1 cm-3), an external blast wave will occur at much larger distances and on much longer timescales than in usual afterglows (e.g., Lee & Ramirez-Ruiz 2002). • Our (rough) estimates assuming uniform external medium density: Raft ~ 4·1016 cm (next ~ 1 cm-3) Raft ~ 2·1017 cm (next ~ 0.01 cm-3) • We favour B) because: • 1.- high density environments the outflow does not produce a GRB signature • 2.- our outflow opening angles are larger than assumed in A). •  The afterglow will be dimmerthan those of Long GRBs because we have an intrinsic energy 2 orders of magnitude smaller and, thus, below present day observational limits (Panaitescu, Kumar & Narayan 2001).

  37. Concluding remarks: Releasing energy over the poles at rates above our Pthrand with a functional depencence suggested by Janka et al (1999) relativistic (max ~ 1000), collimated conical/jet-like, outflows are produced. Collimation: via interaction with the external medium and/or the accretion torus. Aplication of the analytic Levinson & Eichler’s collimation mechanism yields wrong results. Typical opening angles: >100~ 5o – 10o (>10 ~ 20o – 30o).  An observed rate of 100 y-1short GRBs needs of 10-5 galaxy-1 y-1 s-GRB events, which is consistent withestimated NS+NS & NS+BH merger rates. While mergers in low-density environments successful GRBs can be produced, in high-density media the observational signature may be a thermal UV-flash (T~5x104 K) with very low luminosity (L~1043 erg/s) and durations of ~1000 s.  continuous transition between UV-flashes and GRBs?? The fireball stretches radially and, it can produce events with durations of few seconds (although the central engine may survive only for a few 0.1 s). Our results are consitent with the fluence-duration proportionallity (short vs long GRBs; e.g., Balazs et al 2003): Eiso ~ 1051 erg while Edep = 1049 erg (in 0.1 s). The fireball structure is inhomogeneous both in radial and angular directions (KH-instab.) and has a contractive, ultrarelativistic core + relativistic, expanding layer

  38. Open questions: What is the dependence of the outflow on the assumed energy deposition law? What is the role of the magnetic field in the acceleration, collimation and energy conversion? 3D-effects: will the outflow survive to hydromagnetic instabilities? Which part of the radially-stretched fireball stretches is responsible for the observed emission? Are there observational signatures that allow us to unambiguously differentiate between progenitors of short and of long GRBs (in addition to GW-signal)? Some hints to find answers: Other forms of the energy release needed. Optimally, a detailed neutrino transport has to be used. 3D GRMHD simulations. Extend current models x 1000 radially.  Call for AMR and/or massively parallel simulations. Neutrinos?, afterglows?, baryonic winds from the merger?    

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