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Gamma-ray Bursts & Compact Stars T Lu (陆 埮) Purple Mountain Observatory Chinese Academy of Sciences Nanjing 2003年度诺贝尔物理奖获得者 俄罗斯元老物理学家 87岁的V L Ginzburg 认为暴是 最重要的10大天体物理问题之一 Contents Observational Features Toward Standard Model • Fireball • Internal - External Shock Model • Standard Condition Origin & Energy Source Recent Developments • Selected Topics Observations GRBs The Discovery of -ray Bursts Vela5b •Earliest recorded GRB in 1967 •Vela-US Military Satellite: discovered 16 -ray bursts between 1967-1970 •Published in 1973 •http://www.astro.caltech.edu/~jsb/GRB/vela5b_1.gif Observational Features Detection Rate: 1 or 2 /day Temporal Features Spectral Features Spatial Features Afterglows Temporal Features Profiles • Complicated and irregular • Multi-peaked or single-peaked Durations (T) • ~ 5 ms to ~ 5×103 s , Typically ~ 10 s Variabilities (T) • ~ 1ms , even ~0.1ms , Typically ~ 10-2 T Examples of GRBs Profiles • complicated Duration • ~ ms - 1000 s Variability • ~ 1ms even ~0.2ms Spectral Features Photon Energy Range: • ~ 10 keV to ~ 10 GeV • Typically: ~ 0.1 to 1 MeV Non-thermal: N(E)dE∝E-αdE, α≈1.8 - 2 High Energy Tail: no sharp cutoff above 1 MeV Fluence: • Typically ~ (0.1 to 10)×10-6 ergs/cm2 A Typical Spectrum Schaefer et al 1998 GRB910503 Spectra, Examples Photon energy: 10keV – 10GeV Non-thermal, power law No cutoff at high energy Photon spectra Energy Schaefer et al 1998 Spatial distribution of GRBs since 1992 Isotropic ● Angular: Dipole and Quadrupole : (for first 1005 BATSE bursts) <cosθ>=0.017±0.018 <sin2b-1/3>= - 0.003±0.009 ● Sight direction: Inhomogeneous favors: cosmological distances of GRBs statistically. Spatial Distribution --- BATSE Highly isotropic Lack of Weak GRBs Slope(strong):~ –3/2 Slope(weak): ~ – 0.6 For uniform distribution: slope= –3/2 Where are the difficulties? Durations of GRBs are very short, difficult to arrange detailed observations. They occur at random spatially and temporally, difficult to prepare in advance. Except prompt gamma-ray (and maybe weak X-ray), no counterpart on other wave band was found before 1997, difficult to be identified through other wave band with other objects of known distances. Localization is very rough with gamma-rays, within the error box, too many objects exist, difficult to find association with object of known distance. Observations Afterglows BeppoSAX: leading to the discovery of afterglows •GRB monitor 40─700 keV •WFC 2─26 keV 40o×40o errer box ~3’ WFC covered 5% sky, roughly 1 burst per month. Distances of GRBs successfully measured BeppoSAX: Leading to the discoveries of the afterglows of γ-ray bursts (1997) Measuring the red-shift of host galaxies of GRBs Discovery of Afterglow GRB 970228 Afterglow in the overlap region Afterglows of GRBs •General feathers: Mutli-wave bands, Power law decay, Host galaxies •Time scales: X-ray: days ; Optical: months ; Radio: months •Decay power law: Fν ∝ t –α αX = 1.1 to 1.6, αOptical = 1.1 to 2.1 •Host galaxies: Red-shifts: up to 3.4 even 5 these GRBs are definitely at Cosmological Distances Optical Afterglows Examples Smooth and regular Radio Afterglows Examples Early fluctuation Small space scale Late smooth Great Break-Through Lower Energy Limit Observable Time Precision of Localization Before 1997 After 1997 10 keV 10 GHz 100 s Months or Year Milli-seconds degrees Orders improved 8-9 5-6 6-7 Long Burst & Short Burst <2 s:short burst(~25%);>2 s:long burst(~75%) Toward Standard Model Stellar Events δT ~ ms Ri ≤ cδT = 300 km (Ri: scale of initial region) Even for black hole, combined with R = 2GM/c2, M ≤ 100 M⊙ -ray bursts: Stellar Objests (Compact) Initial Fireball F ~10-6 erg/cm2, D ~3 Gpc E0~1051 erg (1 Gpc = 31027 cm) T ~1 ms Ri ~cT ~3 107 cm: take Ri ~107 cm For pure radiation fireball, we have: E0=(4/3)Ri3 aT 4 Ti 6.5 MeV a=(4/c)=7.5610-15 erg/cm3K4 =5.6710-5 erg/cm2K4s is Stefan-Boltzmann constant Estimate of optical depth of fireball Estimate: nR T2 4 3 E0 T R i 3 3 Ri me c 2 4 3 E0 2 1018 2 2 3 Ri me c is the photon energy in units of mec2. Thus, the optical depth is very large. (≫1) The initial fireball should have black body spectrum, in disagreement with observations. Expanding Fireball (Original fireball, under such high pressure, should expand to ultrarelativistic speed, and become optically thin, leading to nonthermal gamma-ray radiation.) Non-thermal Ri ≤ cδT optically thick Solution optically thin Ultra-relativistic Expansion with Lorentz factor: ≫ 1 Compactness Problem Expanding with Lorentz factor γ Ri ≤ cδT Re ≤ γ2 cδT fp/γ2α fp 2 1 2 2 ˆ (emax / mec ) 1 (optically thin) >10 2 M E/ < 10-5(E / 2×1051 ergs)M⊙ Baryon Contamination Problem Expanding Fireball A sketch showing the fireball ( C. Kouveliotou, Science, 1997) Cosmological distance Steps toward the Standard Model Large energy obs Optically thick Small volume Variabilities obs Compactness Problem obs Observed spectra Non-thermal Optically thin Shock Internal shock Prompt GRB Relativistic expansion obs External shock obs Baryon Contamination problem Afterglo w Regions of External Shocks R.Sari, T.Piran, ApJ, 455(1995), L143 Shock condition: e2 / 2 2 1 2 n2 / n1 4 2 3 4 2 e3 / 3 3 1 Velocity, Lorentz factor, distance, time use observer’s frame;thermal quantities use fluids’ rest frame. p2=p3, 2= 3, e2=e3=e, 2= 3 (=nmpc 2) 1、4 cold;2、3 very hot: e1=e4=0, p2=p3=e /3 n3 / n4 4 3 3 Only assume: 4≫1 (thus 2≫1)。 3 Reverse shock 3 is Lorentz factor of region 3 relative to region 4. Equality of preasures and velocities along CD yields: e2=e3 and 3 4 / 2 2 / 4 / 2 The time for reverse shock across the shell width : n4 1 t c( 4 2 ) 3n3 4 shocked shell 2 shocked ISM Forward shock Unshocked shell CD 1 ISM r Contact Discontinuity Importance of Non-relativistic Case Generic Model Generic Model for GRB Ejecta Newtonian Phase of Afterglows Conventional Dynamic Model • Model • Wrong Limit of Conventional Model Generic Dynamic Model • Model • Sedov Limit of Generic Model Newtonian Phase of Afterglows Y.F. Huang, Z.G. Dai, T. Lu, A&A, 336(1998), L69-72. Usually only a few days or tens of days after the burst, a fireball will enter into the adiabatic & non-relativistic phase. A useful model for accounting afterglows should thus be able to describe the overall processes from ultrarelativistic and highly radiative phase to nonrelativistic and adiabatic phase. Especially, it should lead to the well known Sedov limit: β∝ R-3/2, as the expansion getting into the nonrelativistic and adiabatic phase. Conventional Dynamic Model based on: d 2 1 dm M (Blandford-McKee 1976; Chiang-Dermer 1998) m --- rest mass of swept-up medium, --- bulk Lorentz factor, M --- total mass in co-moving frame, including internal energy U It gives a non-relativistic and adiabatic limit: β ∝ R-3 which is wrong, non-consistent with Sedov limit. Generic Dynamic Model (Y.F. Huang, Z.G. Dai, T. Lu, 1999) van Paradijs, Kouveliotou, Wijers, ARA&A, 2000, has a detailed discussion d 2 1 dm M d 2 1 dm M ej m 2(1 )m It gives the overall description from ultra-relativistic and highly radiative phase to non-relativistic and adiabatic phase, especially leads to the correct Sedov limit: β∝ R-3/2, as the fireball getting into the non-relativistic and adiabatic phase. Review Article ARA&A-2000 (van Paradijs, Kouveliotou, Wijers) Generic Model: v-R Dynamical Evolution Solid: generic model Dash-dotted: ultra-relativistic Dashed: Newtonian Generic Model: v-t Dynamical Evolution Solid: generic model Dash-dotted: ultra-relativistic Dashed: Newtonian Radiation In the shocked region, electrons accelerated by the shock, state can be known there. Two important parameters are energy density in relativistic electrons and in magnetic fields which are expressed as fractions e and B of the total internal energy density. They could at present time only be determined by observations. Spectra of Afterglows R. Sari et al, ApJ, 1998, 497, L17 Define 3 characteristic parameters: a is self absorption frequency ((sa)=1) νm is synchrotron radiation frequency of typical energy electron; νc is cooling frequency, synchrotron radiation frequency of the electron cooling within the local hydrodynamic time scale. The frequencies of νm, νc, νa decrease with time as indicated in figure; the scalings above the arrows correspond to an adiabatic evolution, and the scalings below, in square brackets, to a fully radiative evolution. F R. Sari et al, ApJ, 1998, 497, L17 Fast cooling: νc < νm =2 (ν < νa) Wien’s law =+1/3 (νa < ν < νc) synchrotron low energy tail =–1/2 (νc < ν < νm) =–p/2 (νm < ν) Emitting electrons: Slow cooling: νm < νc –p N(e) e =2 (ν<νa) =+1/3 (νa < ν < νm) =–(p–1)/2 (νm < ν < νc) =–p/2 (νc < ν) Spectra of Afterglows Spectra of Afterglows Slow Cooling Synchrotron Light Curve R. Sari et al, ApJ, 1998, 497, L17 Consider spherical shock into constant density medium Extreme limits: fully radiative & fully adiabatic Ignoring self-absorption There are 3 criticle times: t0, tc, tm. Note: c and m are dependent on time t. At t0, c=m. At tc(tm), c(m) cross the observed . Scalings within square brackets are for radiative evolution, other scalings are adiabatic evolution. Flux are calculated according to synchrotron radiation. Light Curve: Power Law High Frequency Light Curve: Power Law Low Frequency Afterglows: Power Law Fading R lg (days since triggering) Spectrum of Afterglow Observed T.J.Galama et al, ApJL, 1998 GRB970508 X-ray to radio Origin Non-uniform Environment n ~ r-k GRB970616 n ~ r-2 (wind environment) (Dai, Lu, MNRAS, 1998) Support the view of massive star origin for GRBs. (Chevaliar, Li, ApJ, 2000) Example: GRB970616 Generally, we assume an inhomogeneous medium with density: n R-k. In this case, the X-ray afterglow light curve index: = (6-k)/(4-k) - [(3-k)/(8-2k)][(3-p)/2] (Dai & Lu 1998, MNRAS, 298, 87) GRB970616: ━ About 4h after the burst, RXTE detected its X-ray afterglow (2-10 keV). ━ On June 20.35 UT, ASCA detected an X-ray flux. From these data, we have = 1.86 Spectrum requires p=2.5, so we found k = 2 implying a wind environment of GRB970616. We further pointed out: “a massive star as a GRB progenitor may be able to produce such a stellar wind”. Therefore, we suggested, for the first time, that GRB970616 is a possible wind interactor, that is, its environment is a pre-burst stellar wind. Dense Environment ·Break in optical light curve of GRB990123: n~106 cm-3 (Relativistic to non-relativistic transition break) Dai-Lu, ApJL, 1999 ·Rapidly declining optical to X-ray afterglows of GRB980519 can be explained well by dense medium, and its radio afterglow can also be excellently explained. Wang-Dai-Lu, MNRAS, 2000 Meaning of Environmental Effects •Stellar Wind Effects Stellar wind provides environment for progenitor of GRB •Density Effects Dense environment might be molecular cloud Association of GRB with star forming region Both environmental effects support the view: “GRB originated from the collapse of massive star” Energy Source GRB971214: NASA news Z=3.4 (Keck II, Caltech team): 1.2 1010 light years. -ray energy in the duration of 50 s is as large as the total radiation energy of the Milky Way in 200 years. Perhaps, there may be much larger energies carried by gravitational radiations and neutrinos. Within 1 or 2 seconds, this burster is as luminous as all the Universe except the burster. Within 100 miles round the burster, the situation can be similar to that of the early universe 1 ms after the Big Bang. The energy of the -ray burst is several hundreds bigger than SN. GRB990123: 10GRB971214 Z=1.6 11.982 Gpc (H0=65 km/s, Ω0=0.2, Λ=0) Peak absolute V-band magnitude: MV ~36.5 Intrinsic luminosity: LV ~21016 L⊙ ~Type I SN Eiso = 3-4.5 1054 erg = 1.9 M⊙c2 Optical peak: 8.95 m Initial optical flash contains most of optical fluence: ~ergs/cm2, about of the γ-ray fluence. Energy Source Models Merger of NS-NS, NS-BH (Eichler et al., 1989; Paczynski, 1991) ► ~ 108 yr (Gravitational radiation timescale) Massive star collapse (Woosley, 1993; Paczynski, 1998) ►Association with Star Forming Regions ►Association with supernovae Phase Transition of NS⇨SS (Cheng-Dai, PRL, 1996; Dai-Lu, PRL, 1998) Natural ways to avoid baryon contamination: ►A strange star Mcrust 10-5 M ►A rapidly rotating Black Hole + Maximum available energy (through Blandford-Znajek mechanism) 29% MBHc2 spin energy Disk 42% Mdiskc2 binding energy Strange Star Physically Astronomically • a huge nucleon, also a strange huge atom • bound by strong interaction: confinement • tightly bound even without gravitation • one possible final stage of stellar evolution • produced through phase transition from NS • composed of nearly equal number of u, d, s quarks A Story Damping of Radial Vibration Wang-Lu, PLB, 1984 Damping and dissipation occurs only in 3rd case, the domonative process is u+d u+s. 1 • dw , v is the volume per unit mass. Pdv dt average period Calculation of Vibrational Damping Wang-Lu, PLB, 1984 To calculate Considering dw dt average 1 , Pdv , v v0 v cos(2t / ) expanding p(t) to p(t ) p0 (p / v) 0 v period (p / nd ) 0 nd (p / ns ) 0 ns and using thermodynamic relations and Weinberg-Salam-Glashow theory, we can obtain the damping of NS with strange core or of SS in sub-second time scale. Sketch of Calculation p(t ) p0 (p / v)0 v (p / nd )0 nd (p / ns )0 ns dw dt average 1 Pdv t period dn t , here ( ) dn nd ns dt s d P(t ) dt dt 0 v dt 0 0 (dn/dt denotes net rate of us ud) ( s d ) 5 1 1/ 4 2 3 3.23 10 v 15 ms ,150erg.g.cm v 0 dn / dt 2.45 1039 vT93 155 / 4 [ I ( ) I ( )] g 1s 1 where 3 ( x )2 2 I ( ) dx, ( s d ) / kT 2 x x (2 ) (1 e )(1 e ) Bulk Viscosity Wang-Lu(1984): dw dt average 1 Pdv period Radial vibration damping • Sawyer(1989): dw 1 2 v v0 dt average 2 v0 Bulk viscosity coefficient ζ 2 2 R 1 )( 6 ) 2 ( 25 ) nuc 10 cm 10 gcm -1s -1 Time scale for damping of vibrations τD D 1s( Viscosity influenced by αc Dai-Lu, Z. Phys. A, 1996 Approximation: States --- αc considered; matrix --- not • Strong interaction effects: the non-leptonic weak rate is strongly suppressed by αc At low temperatures, viscosity is strongly suppressed; at high temperatures, it is slightly enhanced. A Wrong Discovery Nature: 16 March 1989 Kristian et al. claimed their discovery of an optical pulsar with period as short as only 0.5ms at SN1987A early 1989 Keplerian Spin Limit Upper limit of rotation of neutron stars is set by Keplerian speed: 1/ 2 3 M max K 7.7 10 M sun Rmax 10km 3 / 2 s -1 Upper limit for strange stars: (B0=57MeVfm-3) 1/ 2 B 1 K 9.4 10 s B0 3 Neutron Stars, Strange Stars & Spin Limit Upper: dashed, dotted, solid---K=300, 240, 210 MeV Lower: dotted, dashed, dash-dotted---B1/4=145, 170, 200 MeV Pulsar Spin: 1.6ms, 0.5ms M-R relations are quite different for NS than for SS Importance of Viscosity Gravitational radiation reaction instabilities set spin limit for NSs far lower than Kepler limit. High viscosities can damp away the gravitational radiation reaction instabilities. Due to very high viscosities in SSs, spin rate can be much closer to Kepler limit. This gives an important way to discover SSs from NSs based on period measurement. Declaring a Discovery Wrong Published in Nature two years later by the same group of authors 1989• two years apart •1991 by the same group A Way to Soften the Problem of Energy Crisis ---Beaming & Jets Why beamed? Variability time scale in GRB light curves: as short as: 0.1ms R < c Δt GRBs are due to stellar objects However, the energy is huge in some GRBs! GRB 971214: E,iso ~ 0.1 M⊙c2 GRB 991216: E,iso ~ 0.2 M⊙c2 GRB 990123: E,iso ~ 1.9 M⊙c2 Beaming can safely relax the crisis Evolution of jetted GRB ejecta Huang-Dai-Lu, MNRAS 2000 ●Evolution of jetted GRB ejecta, a set of equations: dR c ( 2 1) ; dt 2 d cs ( 1 ) dt R cs2 ˆ (ˆ 1)( 1) ; dm 2R 2 (1 cos )nmp dR ; d 2 1 dm M ej m 2(1 )m ; 1 c2 1 ˆ ( 1) , here ˆ (4 1) /(3 ) is the adiabatic index. ●A set of "standard" parameters: E0/Ω0=1054ergs/4π; γ0=300; n=1 cm-3; ξB2=0.01; p=2.5; ξe=0.1; θ0=0.2; θobs0; DL=106 kpc (luminosity distance) A Standard Picture Meszaros 2001 X O Recent Developments Only Selected Topics Large polarization discovered in the prompt gamma-ray emission in GRB021206 Large Polarization Detected in Prompt Gamma-ray Emission in GRB021206 Coburn, Boggs, Nature, 2003, 423, 415 Degree: 80% ±20% Use RHESSI Angular distance close brom the sun, no afterglow observation Debate 14 October Debate-17 October Paper: astro-ph/0310515 From: Steven E. Boggs <[email protected]> Date: Fri, 17 Oct 2003 20:17:17 GMT (4kb) Title: Statistical Uncertainty in the Re-Analysis of Polarization in GRB021206 Authors: Steven E. Boggs, Wayne Coburn Comments: Submitted to MNRAS \\ We recently reported the first detection of an astrophysical gamma-ray polarization from GRB021206 using the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) spacecraft. Our analysis suggested gammaRay polarization at an astoundingly high level, 80+/-20%. A recent manuscript re-analyzes this event in the RHESSI data, and sets an upper limit on potential polarization of 4.1% -- clearly inconsistent with our initial analysis. This manuscript raises a number of important concerns about the analysis, which are already being addressed in a separate methods paper under preparation. We note here, however, that the limit set on the potential polarization by this re-analysis is significantly underestimated using their novel statistical methods. \\ ( http://arXiv.org/abs/astro-ph/0310515 , 4kb) Associations GRB with SN Comparison between GRBs & SNs Burst Energy (up to) Time Scale Profile Wave band GRBs SNs 1054 ergs 10 sec irregular γ-ray Afterglow 1051 ergs month smooth Optical Remnant Relic Time Scale Month 103 yr Wave band Multi-band Multi-band Understanding Fireball expansion Ultra-relativistic Non-relativistic Mechanism Stellar core collapse ??? Key process process ??? SN/GRB Associations ▲GRB980425/SN1998bw GRB 980425:Red-shift: 0.0085; Energy: E = 5×1047 ergs (Galama et al, Nature, 1998) SN 1998bw: Ic type ▲GRB980326 3 weeks after the burst it was brightened to 60 times than extrapolated from early time (Bloom et al., astro-ph/9905301) ▲GRB970228 Red-shift: 0.695; Energy: E=5×1051 ergs Late afterglow does not be consistent with fireball model; extreme reddening with time, V-I increased by ≈1.6 mag (Reichart, astro-ph/9906079) ▲GRB030329/SN2003dh Red-shift: 0.169; Energy: E = 1.3×1052 ergs SN 2003dh: Ic type (Hjorth, et al, Nature, 2003) GRB030329/SN2003dh P. Meszaros, Nature, 2003, 423, 809 GRB030329 was detected by HETE-II P A Price et al, Nature, 423, 844 Very bright event! GRB030329: 1.5 hours since burst, it reached R=12.6 mag. In comparison, GRB021004: at the same time, 16 mag; GRB990123: 17 mag. This source was also detected by RIKEN automated telescope independently. GRB030329: Light Curve of Optical Afterglow P A Price et al, Nature, 423, 844 A good broken power law Errors smaller than the plotted points Spectral Evolution of the Combined Spectra of Afterglow, SN and Host Galaxy J.Hjorth, Nature, Vol.423, 847 Comparison of the spectral evolution of SN2003dh and SN1998bw J.Hjorth, Nature, Vol.423, 847 Thank you