1 Gamma-Ray Bursts: Central Engines, Early Afterglows, and X-Ray Flares Zigao Dai Nanjing University FAN4-HKU, 8-12 July 2013

2 Outline 1.A brief introduction to GRBs 2.Central engines (inc. magnetar models) 3.Early afterglows (plateaus, brightening) 4.X-ray flares and high-energy emission 5.Summary

1. A brief introduction to GRBs 3

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

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

6 Bimodal distribution of durations Short Hard Long Soft 2 s

7 Why extremely relativistic? Sufficient condition: High energy (≥10 51 ergs) and short rise time require extremely compact fireball and high radiative pressure. Necessary conditions: ① Nonthermal spectrum  Lorentz factor ≥ 100 (v≥0.9999c); ② GeV photons  Lorentz factor ≥ 100; ③ Peak time of afterglow  Lorentz factor ≥ 100.

8 v ≥ c

2. Central engine models 9

10 Requirements to central engines also see Dai & Lu (1998, PRL, 81, 4301) ① Observed fluence and redshift → extremely high luminosity and energy: L iso ~ erg s -1 and E iso ~ ergs. ② Variable light curves in general Δt var ~0.01 s (Δt min ~0.1 ms) → multi-explosions at typical T dur ~ tens of seconds. ③ Observed power-law spectrum and GeV photons → Lorentz factor  ≥100 → very low baryon contamination. ④ Observed jet break and extremely high E iso → jet. ⑤ Detection rate → burst rate ~ /galaxy/year. ⑥ 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, L wind due to neutrino annihilation is too low? Spin energy of the BH → Blandford-Znajek mechanism: L BZ ~3*10 50 B 15 2 (M BH /3M sun ) 2 a 2 f(a) erg s -1 for a~1, M BH ~ 3M sun and B~10 15 Gauss.

12 (2) Millisecond magnetars (collapsars or mergers) Gravitational energy of an accretion disk → thermal energy → neutrino-cooling-dominated disk: much higher L wind (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): M crust ≤10 -5 M sun → very low baryon contamination Phase-transition energy ~3*10 52 erg (Cheng & Dai 1996) Rotational energy and differentially-rotational energy ~3*10 52 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)

3. Early afterglows 14

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

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 F ollowing 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 η x =1

Implications from Rowlinson et al. (2013)  The energy injection model of pulsars provides an excellent explanation for shallow decay of SGRBs.  P 0 <10 ms and B s ~10 15 G for most of SGRBs.  For short GRB101219A, e.g., P 0 ≈0.95 ms, possibly implying gravitational radiation for rotation parameter >  If efficiency η x <1, we require a smaller spinning period, showing gravitational radiation for more SGRBs. 20

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

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

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

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

25 “Spin evolution of millisecond magnetars with hyperaccreting fallback disks: implications for early afterglows” (Dai & Liu 2012, ApJ, 759, 58) RLRL R 0 ≈R m magnetospheric radius R c : corotation radius R L : light cylinder

26 Accretion rate of a fallback disk in the collapsar model MacFadyen 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 Typical light curve in relativistic wind bubble model Reverse shock emission Forward shock emission Total emission

31

4. X-ray flares 32

33 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.

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

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

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

37 Late-internal-shock model for X-ray flares Two-shock structure: Reverse Contact Forward shock (S2) discontinuity shock (S1) unshocked shocked materials unshocked shell shell 1 Gamma_3 = Gamma_2 P_3 = P_2 Dynamic s

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

39 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. Abdo et al. (2011): Swift and Fermi observations of X-ray flares of GRB100728A

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

41 Energy source models of X-ray flares How to restart the central engine? ① Fragmentation of a stellar core (King et al. 2005) ② Fragmentation of an accretion disk (Perna, Armitage & Zhang 2005) ③ Magnetic-driven barrier of an accretion disk (Proga & Zhang 2006) ④ Magnetic activities of a newborn millisecond pulsar (for short GRB) (Dai, Wang, Wu & Zhang 2006) ⑤ Tidal ejecta of a neutron star-black hole merger (Rosswog 2007)

42 Rosswog et al. (2003) t acc ~ 0.5 s

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

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

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

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

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

48 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)

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

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

Explanation Self-organized criticality (SOC): subsystems will self-organize to a critical state at which a small perturbation can trigger an avalanche of any size within the system (Bak et al. 1997). The slopes of frequency distributions for energies and durations depends on the Euclidean dimensions S (Aschwanden 2012): S ≈ 1 for X-ray flares, and S ≈ 3 for solar flares. Wang FY & Dai (2013) suggest that magnetic reconnection from ultra-strongly magnetized millisecond pulsars proposed by Dai et al. (2006) may trigger an S ≈ 1 SOC process. 51

52 Summary Some GRBs originate from millisecond magnetars. They inject their rotational energy to blast waves, leading to shallow decay of early afterglows or brightening (due to fallback disks). In addition, energy injection to ejecta following NS-NS mergers  bright broadband emission (Gao, Ding, Wu, Zhang & Dai 2013, ApJ). Differential rotation in stellar interiors  magnetic reconnection-driven events and thus X-ray flares. This model is consistent with statistical similarities between solar flares and X-ray flares. Thank you!