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Gamma-Ray Bursts: Central Engines,

Early Afterglows, and X-Ray Flares

Zigao DaiNanjing University

FAN4-HKU, 8-12 July 2013

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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

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

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Spectral features: broken power laws

with Ep of a few tens to hundreds of keV Temporal features: diverse and

spiky light curves.

Light Curves and Spectra

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Bimodal distribution of durations

ShortHard

LongSoft

2 s

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Why extremely relativistic?

• Sufficient condition: High energy (≥1051ergs) 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.

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v ≥ 0.9999c

2. Central engine models

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Requirements to central enginesalso see Dai & Lu (1998, PRL, 81, 4301)

① Observed fluence and redshift → extremely high luminosity and energy: Liso~1047-1054 erg s-1 and Eiso~1049-1055 ergs.

② Variable light curves in general Δtvar~0.01 s (Δtmin~0.1 ms) → multi-explosions at typical Tdur~ 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 Eiso → jet.

⑤ Detection rate → burst rate ~10-5-10-6/galaxy/year.

⑥ X-ray flares and shallow decay of afterglows in ~ one half of Swift-detected GRBs → long-lasting activity.

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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.

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(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)

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(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)

3. Early afterglows

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Early X-ray afterglows detected by Swift

Cusumano et al. (2005)

t -5.5ν-1.60.22

GRB050319

t -0.54ν-0.690.06

t -1.14ν-0.800.08

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

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Injected energy = E/2

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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.

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

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.

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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.

Acceleration of a ‘cold’ ultrarelativistic wind from Crab pulsar

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Termination shock (TS)

External shock (ES)

Contact discontinuity

Ambient gas (zone 1)

A relativistic eA relativistic e--ee++ wind wind (zone 4)

Shocked wind (zone 3)

Shocked ambient gas (zone 2)

Relativistic wind bubble (RWB)

Black hole

Dai (2004, ApJ)

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Dai (2004)

Reverse shock emission

Forward shock emission

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Early afterglows: significant brighteningLiang et al. (2007)

Apparently inconsistent with the conventional pulsar energy injection model proposed by Dai & Lu (1998).

L(t)t-q

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“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

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Accretion rate of a fallback disk in the collapsar modelMacFadyen et al. (2001)

Piro & Ott (2011); Dai & Liu (2012):

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Stellar gravitational mass as a function of time

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Spin period as a function of time

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Spin-down luminosity as a function of time

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Typical light curve in relativistic wind bubble model

Reverse shock emission

Forward shock emission

Total emission

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4. X-ray flares

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X-ray flaresBurrows 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.

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

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

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CentralEngine

Relativistic Wind

The Internal-External-Shock ModelHow to produce X-ray flares?

ExternalShock

Afterglow

InternalShocks

GRB

Late InternalShocks

XRFs

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Late-internal-shock model for X-ray flares

• Two-shock structure:

Reverse Contact Forward shock (S2) discontinuity shock (S1)unshocked shocked materials unshocked

shell 4 3 2 shell 1

Gamma_3 = Gamma_2

P_3 = P_2Dynamics

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

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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

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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

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Energy source models of X-ray flaresHow 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)

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Rosswog et al. (2003)

tacc ~ 0.5 s

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Ozel 2006, Nature, 441, 1115

Rule out soft equations of state

Obs. I.

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Demorest et al. (2010, Nature, 467, 1081): using Shapiro delay

Van Kerkwijk et al. (2010): PSR B1957+20, MPSR = 2.40±0.12M⊙

Obs. II.

Obs. III.

Support stiff nuclear equations of state

B1957+20

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Morrison et al. 2004, ApJ, 610, 941

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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.

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Left: differential energy distribution of solar flaresRight: cumulative energy distribution of X-ray flaresThe slopes: (-1.65±0.02, -1.06±0.15)

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

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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.

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SummarySome 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!