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Gamma-Ray Bursts: Central Engines, Early Afterglows, and X-Ray Flares

This presentation discusses the central engines, early afterglows, and X-ray flares of gamma-ray bursts (GRBs), including an introduction to GRBs, the requirements of central engines, and the phenomenon of early afterglows. The talk also covers the different types of central engines, such as black hole-accretion disk systems, millisecond magnetars, and strange quark stars. Additionally, the presentation explores the shallow decay of early afterglows and the implications of the pulsar energy-injection model. Finally, it delves into the acceleration of ultrarelativistic winds and the phenomenon of early afterglow brightening.

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Gamma-Ray Bursts: Central Engines, Early Afterglows, and X-Ray Flares

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  1. Gamma-Ray Bursts: Central Engines, Early Afterglows, and X-Ray FlaresZigao DaiNanjing UniversityFAN4-HKU, 8-12 July 2013

  2. Outline • A brief introduction to GRBs • Central engines (inc. magnetar models) • Early afterglows (plateaus, brightening) • X-ray flares and high-energy emission • Summary

  3. 1. A brief introduction to GRBs

  4. GRBs are short-duration flashes of gamma-rays occurring at cosmological distances.

  5. Light Curves and Spectra Spectral features: broken power laws with Ep of a few tens to hundreds of keV Temporal features: diverse and spiky light curves.

  6. Bimodal distribution of durations Long Soft Short Hard 2 s

  7. Why extremely relativistic? • Sufficient condition: High energy (≥1051ergs) and short rise time require extremely compact fireball and high radiative pressure. • Necessary conditions: • Nonthermal spectrum  Lorentz factor ≥ 100 (v≥0.9999c); • GeV photons  Lorentz factor ≥ 100; • Peak time of afterglow  Lorentz factor ≥ 100.

  8. v ≥ 0.9999c

  9. 2. Central engine models

  10. Requirements to central enginesalso see Dai & Lu (1998, PRL, 81, 4301) • Observed fluence and redshift →extremely high luminosity and energy: Liso~1047-1054 erg s-1 and Eiso~1049-1055 ergs. • Variable light curves in general Δtvar~0.01 s (Δtmin~0.1 ms) →multi-explosions at typical Tdur~ tens of seconds. • Observed power-law spectrum and GeV photons → Lorentz factor ≥100→ very low baryon contamination. • Observed jet break and extremely high Eiso→jet. • Detection rate → burst rate ~10-5-10-6/galaxy/year. • X-ray flares and shallow decay of afterglows in ~ one half of Swift-detected GRBs→long-lasting activity.

  11. Three types of central engines (1) Black hole + accretion disk systems (collapsars or mergers, Eichler et al. 1989; Woosley 1993; Narayan et al. 2001; MacFadyen et al. 2001): Gravitational energy of the disk → thermal energy → neutrino-cooling-dominated disk, Lwind due to neutrino annihilation is too low? Spin energy of the BH → Blandford-Znajek mechanism: LBZ~3*1050B152(MBH/3Msun)2a2f(a) erg s-1 for a~1, MBH~ 3Msun and B~1015 Gauss.

  12. (2) Millisecond magnetars (collapsars or mergers) Gravitational energy of an accretion disk → thermal energy → neutrino-cooling-dominated disk: much higher Lwind (Zhang & Dai 2008, 2009, 2010, ApJ) Rotational energy (Usov 1992; Duncan & Thompson 1992; Metzger et al. 2011) Differentially-rotational energy (Kluzniak & Ruderman 1998; Dai & Lu 1998; Dai et al. 2006)

  13. (3) Strange quark stars (collapsars or mergers or X-ray binaries): Mcrust≤10-5Msun → very low baryon contamination Phase-transition energy ~3*1052 erg (Cheng & Dai 1996) Rotational energy and differentially-rotational energy ~3*1052 erg (Dai & Lu 1998) Gravitational energy of an accretion disk: feed-back effect (Hao & Dai 2013) *Millisecond magnetars → shallow decay of early afterglows (Dai & Lu 1998; Zhang & Meszaros 2001; Dai 2004)

  14. 3. Early afterglows

  15. Early X-ray afterglows detected by Swift GRB050319 t -5.5ν-1.60.22 t -1.14ν-0.800.08 t -0.54ν-0.690.06 Cusumano et al. (2005)

  16. See Liang et al. (2007) for a detailed analysis of Swift GRBs: ~ one half of the detected GRB afterglows.

  17. Injected energy = E/2

  18. Following the pulsar energy-injection model, numerical simulations by some groups (e.g., Fan & Xu 2006; Dall’Osso et al. 2011) provided fits to shallow decay of some GRB afterglows with different slopes.

  19. Rowlinson et al. (2013): SGRB magnetar sample assuming ηx=1

  20. Implications from Rowlinson et al. (2013) • The energy injection model of pulsars provides an excellent explanation for shallow decay of SGRBs. • P0<10 ms and Bs~1015 G for most of SGRBs. • For short GRB101219A, e.g., P0≈0.95 ms, possibly implying gravitational radiation for rotation parameter > 0.14. • If efficiency ηx<1, we require a smaller spinning period, showing gravitational radiation for more SGRBs.

  21. Acceleration of a ‘cold’ ultrarelativistic wind from Crab pulsar To fit pulsed high-energy emission from Crab pulsar, Aharonian et al. (2012, Nature) suggested that acceleration should take place abruptly between 20RL and 50RL, where RL is the light cylinder.

  22. Relativistic wind bubble (RWB) Ambient gas (zone 1) Shocked ambient gas (zone 2) Shocked wind (zone 3) A relativistic e-e+ wind (zone 4) External shock (ES) Black hole Termination shock (TS) Contact discontinuity Dai (2004, ApJ)

  23. Dai (2004) Reverse shock emission Forward shock emission Yu & Dai (2007)

  24. Early afterglows: significant brightening Liang et al. (2007) L(t)t-q Apparently inconsistent with the conventional pulsar energy injection model proposed by Dai & Lu (1998).

  25. “Spin evolution of millisecond magnetars with hyperaccreting fallback disks: implications for early afterglows” (Dai & Liu 2012, ApJ, 759, 58) RL R0≈Rm magnetospheric radius Rc: corotation radius RL: light cylinder

  26. Accretion rate of a fallback disk in the collapsar modelMacFadyen et al. (2001) Piro & Ott (2011); Dai & Liu (2012):

  27. Stellar gravitational mass as a function of time

  28. Spin period as a function of time

  29. Spin-down luminosity as a function of time

  30. Reverse shock emission Forward shock emission Total emission Typical light curve in relativistic wind bubble model

  31. 4. X-ray flares

  32. X-ray flares Burrows et al. 2005, Science, 309, 1833 Explanation: late internal shocks (Fan & Wei 2005; Zhang et al. 2006; Wu, Dai, Wang et al. 2005), implying a long-lasting central engine.

  33. Chincarini et al. (2007, ApJ, 671, 1903): ~ one half of the detected GRB afterglows.

  34. Short GRB050724: Barthelmy et al. 2005, Nature, 438, 994

  35. Afterglow XRFs GRB Central Engine Relativistic Wind Late Internal Shocks Internal Shocks External Shock The Internal-External-Shock Model How to produce X-ray flares?

  36. Late-internal-shock model for X-ray flares • Two-shock structure: Reverse Contact Forward shock (S2) discontinuity shock (S1) unshockedshocked materialsunshocked shell 4 3 2shell 1 Gamma_3 = Gamma_2 P_3 = P_2 Dynamics

  37. Yu YW & Dai (2008): spectrum and light curve of synchrotron radiation and synchrotron self-Compton in the late IS model.

  38. Abdo et al. (2011): Swift and Fermi observations of X-ray flares of GRB100728A Wang K & Dai (2013, ApJ) performed fitting to the spectral data by considering syn. radiation and SSC in the late IS model. See Wang XY’s talk for the external IC model.

  39. Wang K & Dai (2013): fitting to GRB100728A Syn rad. and SSC from shocked wind Syn rad. and SSC from shocked medium Cross-inverse-Compton from shocked wind and medium

  40. Energy source models of X-ray flaresHow to restart the central engine? • Fragmentation of a stellar core (King et al. 2005) • Fragmentation of an accretion disk (Perna, Armitage & Zhang 2005) • Magnetic-driven barrier of an accretion disk (Proga & Zhang 2006) • Magnetic activities of a newborn millisecond pulsar (for short GRB) (Dai, Wang, Wu & Zhang 2006) • Tidal ejecta of a neutron star-black hole merger (Rosswog 2007)

  41. tacc ~ 0.5 s Rosswog et al. (2003)

  42. Obs. I. Ozel 2006, Nature, 441, 1115 Rule out soft equations of state

  43. Obs. II. Demorest et al. (2010, Nature, 467, 1081): using Shapiro delay B1957+20 Van Kerkwijk et al. (2010): PSR B1957+20, MPSR = 2.40±0.12M⊙ Obs. III. Support stiff nuclear equations of state

  44. Morrison et al. 2004, ApJ, 610, 941

  45. Kluzniak & Ruderman (1998) Lazzati (2007) Dai, Wang, Wu & Zhang 2006, Science, 311, 1127:a differentially-rotating, strongly magnetized, millisecond pulsar after the merger.

  46. Statistics of X-ray flares • Motivation: solar flares are triggered by a magnetic reconnection process, while X-ray flares may also be driven by a similar process (e.g. Dai et al. 2006). Question: do they have statistical similarities? • Wang FY & Dai (2013, Nature Physics, published online 2 July) find statistical similarities between X-ray flares and solar flares: power-law frequency distributions for energies, durations, and waiting times. • These similarities suggest that X-ray flares may also be triggered by a magnetic reconnection process.

  47. Left: differential energy distribution of solar flares Right: cumulative energy distribution of X-ray flares The slopes: (-1.65±0.02, -1.06±0.15)

  48. Differential duration time distributions of solar flares and X-ray flares. The slopes: (-2.00±0.05, -1.10±0.15).

  49. Differential waiting time distributions of solar flares and X-ray flares. The slopes: (-2.04±0.03, -1.80±0.20).

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