Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Time in physics wikipedia , lookup
Internal energy wikipedia , lookup
Conservation of energy wikipedia , lookup
Accretion disk wikipedia , lookup
Nuclear physics wikipedia , lookup
Effects of nuclear explosions wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
GRB Theory and observations Useful reviews: Waxman astro-ph/0103186 Ghisellini astro-ph/0111584 Piran astro-ph/0405503 Meszaros astro-ph/0605208 Useful links http://www-astro.physics.ox.ac.uk/~garret/teaching/ http://www.cv.nrao.edu/course/astr534/ Progenitor Long GRBs: Collapsar model M>30 M Modelli per un GRB Leading model for short GRBs Progenitors NS-NS merging primordial DNS Modelli per un GRB Spectrum well described by a broken power law Band approximation E •Nontermal Spectrum N(E) E<E0 E E>E0 BATSE (20 keV-1 MeV) 0.1 MeV < E0< 1 MeV -2, ~ [-1, -0.5] The compactness problem • t ~ 1-10 ms Compact sources R0 c t ~ 3 107 cm •Cosmological sources (D~3 Gpc) L ~ fD2~1052 erg/s R of our galaxy ~ 30 kpc: extragalactic objects +e2)2 ≥ (m c e e 1 2 ~ p R0n T~TL /4R0c ~1015 p fraction of photons above the thereshold of pair production Optical depth ~ 1 MeV T=6.25x10-25cm2 ( e+e-) >>1 Implications: The fireball How can the photons escape the source? Relativistic motion: A plasma of e+ e- , a Fireball, which expands and accelerate to relativistic velocities, optical depth reduced by relativistic expansion with Lorentz factor The reasons: 1. In the comoving frame below the thereshold for pair production ’ = / ’ 1 ’ 2≤ (mec2)2 1 G = 1- (v /c) 2 2. Number of photons above the threshold reduced by 2( -1) (~2 high-energy photon index); 3. Emitting region has a size of 2R0 reduced by a factor 2+2 6. < 1 for ≥100 Propagation effect Zhang & Mészàros, IJMPA A19, 2385 (2004) Finally, •dt’, comoving time of the shell where D is the Doppler factor. Fireball evolution • Fireball expands and cools pairs annihilate and photons may escape, quasi-thermal emission against observations!!! • Therefore a small barion loading (≥10-8M) is needed and the radiation energy is converted to kinetic energy. The Lorentz factor • As the fireball shell expands, the baryons will be accelerated by radiation pressure. • The fireball bulk Lorentz factor increases linearly with radius. • 0 E/M0c2, M0 total baryon mass of the fireball Fireball Model: Prediction vs. Postdiction • Prediction – (from Latin: prae- before + dicere to say): A foretelling on the basis of observation, experience or scientific reasoning. • Postdiction – (from Latin: post- after + dicere to say): To explain an observation after the fact. • If your model “predicts” all possible outcomes, it is not a prediction. This merely states that you can not constrain the answer with your current model. Fireball Model The Fireball model Assumes a relativistic Outburst and works With a variety of Mechanisms. We rely heavily on A review by Tsvi Piran. From IXth International Symposium on Particles, Strings and Cosmology Tata Institute of Fundamental Research, Mumbai, Inda Tsvi Piran http://theory.tifr.res.in/ pascos/Proceedings/Friday/ Piran/index.html The Fireball Model g - rays Relativistic Particles >100 or Poynting flux compact source ~ 107 cm Goodman; Paczynski; Narayan, Paczynski & Piran; Shemi & Piran, Meszaros & Rees Shocks Supernova Remnants (SNRs) - the Newtonian Analogue • ~ 10 solar masses are ejected at ~10,000 km/sec during a supernova explosion. • The ejecta is slowed down by the interstellar medium (ISM) emitting x-ray and radio for ~10,000 years. External Shocks External shocks are shocks between the relativistic ejecta and the ISM just like in SNRs. Can be produced by a single explosion. Recall, the first GRB model (Colgate 1968) Invoked SN Shocks to power GRBs! External Shock Predictions For GRBs • The burst of gammarays should be accompanied by a burst of optical photons (within 1 second of the explosion). • Based on these predictions, fast slewing optical telescopes were developed (e.g. ROTSE, LOTUS). GRB070228 – Optical Burst Seen! But observed much later than expected. This spelled the beginning of the end for the external shock model! (Although some claimed this as a “prediction”!) Fireball Theorists then found a lot Wrong with the external shock model! A NO GO THEOREM External shocks cannot produce a variable light curve!!! (Sari & Piran 97) Time to Revise the Theory • Gamma-rays and Afterglow arise from different sources Birth of the Internal Shock Model Internal Shocks Shocks between different shells of the ejected relativistic matter D=cT d=cdT • dT=R/cg2= d/c £ D/c=T • The observed light curve reflects the activity of the “inner engine”. Need TWO time scales. • To produce internal shocks the source must be active and highly variable over a “long” period. dT T Internal Shocks Afterglow D=cT d=cdT • Internal shocks can convert only a fraction of the kinetic energy to radiation (Sari and Piran 1997; Mochkovich et. al., 1997; Kobayashi, Piran & Sari 1997). It should be followed by additional emission. “It ain't over till it's over” (Yogi Berra) Gamma-Ray Burst: 4 Stages 1) Compact Source, E>1051erg 2) Relativistic Kinetic Energy 3) Radiation due to Internal shocks = GRBs Plus burst of optical emission! 4) Afterglow by external shocks The Central Compact Source is Hidden The Internal-External Fireball Model -rays Inner Engine Relativistic Wind Internal Shocks Afterglow External Shock There are no direct observations of the inner engine. The -rays light curve contains the best evidence on the inner engine’s activity. THE FIREBALL MODEL Postdicted PREDICTED GRB AFTERGLOW (late emission in lower wavelength that will follow the GRB) Rhodes & Paczynksi, Katz, Meszaros & Rees, Waxman, Vietri, Sari & Piran Fireball Model History • External Shock model: relativistic ejecta from very energetic explosion shocks with the interstellar medium. Synchrotron radiation in shock produces gamma-rays and optical burst. • Optical burst appeared late – theorists move to internal shocks to explain gamma-rays. How the energy is dissipated • In order to have some emission from the firebal the energy must be dissipated somehow. • Observed GRB produced by dissipation of the kinetic energy of this relativistic expanding fireball regardless the nature of the underlying source. • Possible dissipation mechanism Internal shocks: collisions between different parts of the plasma The internal/external shock scenario [Rees & Meszaros 1992, ’94] ISM 1016cm 13 10 cm ray phase Efficient! [Guetta Spada & Waxman 2001] X-ray, Opt.-IR, Radio The radiation mechanisms The efficiency of internal shocks Shells collide and merge in a single shell with æ M1G1 + M 2G2 ö G =ç ÷ è M1 /G1 + M 2 /G2 ø E in = [ M1G1 + M2G2 - ( M1 + M2 )G]c 2 The conversion efficiency of kinetic energy into internal energy æ ( M1 + M 2 )G ö h = 1- ç ÷ è M1G1 + M 2G2 ø To get high efficiency 1>> 2 and M1=M2 only a fraction e radiated max 20% can be radiated (Guetta et al. 2001) But the total afterglow energy ~ burst energy! (Freedman and Waxman 2001) Problem 1: Low efficiency of internal shocks Internal shock radius Let’s assume that a faster shell (2) impacts on a slower the leading shell (1); If t=tv is the average interval between two pulses (interval between shells ejection) d = ct v G2 >> G1 » G0 ris = cd /(v 2 - v1 ) @ 2G d = 2G ct v 2 1 2 1 G = ris @ 1013 cm(G0 /100) 2 (t v /0.1s) Emission properties determined by ris 1 1- (v /c) 2 Light curves from internal shocks Rapid variability and complexity of GRB lightcurves result of emission from multiple shocks in a relativistic wind t (interval between ejected shells) determines the pulse duration and sepration: IS reproduce the observed correlation between the duration of the pulse (tp) and the subsequent interval (tp) Numerical simulations reproduce the observed light curves (Spada et al. 2000) Spectrum of the prompt emission Prompt emission observed has most of energy in 0.1-2 MeV Generic phenomenological photon spectrum a broken power law • Internal shocks are mildly relativistic, sh~a few, particle acceleration in subrelativistic shocks. Electrons are accelerated to a power law with energy distribution dn e -p = ge dg e with p~2 and e> m Electrons accelerated in magnetic field: synchrotron emission? i.e. emission from relativistic electrons gyrating in random magnetic fields Fermi acceleration at shock • Suppose to have a shock wave propagating in a medium where energetic particles are already present. • Shock is a wave propagating with v>vsound • Density after (downstrem) and before (upstream) the shock is 2/1=+1/-1 where is the politropic index of the gas. For a gas completely ionized =5/3 and 2/1=4, v1/v2=4 Shocks Shocks Fermi acceleration at shocks U=vu Hot shocked gas vu eUnshocked gas vd=1/4vu Consider the case of a shock propagating into cold gas at speed vu. In the shock frame we see the unshocked gas ahead of us approaching at speed vu and the hot shocked gas streaming behind us at speed vd=1/4 vu. Consider now electrons initially at rest in the unshocked gas frame. They see the shock approaching at vu but they also see the hot shocked gas approaching at 3/4 vu. As they cross the shock they are accelerated to a mean speed of 3/4 vu, as viewed from the frame of the unshocked gas, and are also thermalized to a high temperature. The clever part is next: consider what would happen if, as a result of its thermal motion, an electron is carried back over the shock front. With respect to the frame it has just come from the shocked gas frame it is once again accelerated by 3/4 vu. The particle gain energy from the gas behind the shock. Let us say the fractional change in kinetic energy at each crossing is β. After n crossings, a particle with initial energy E0 will have energy E = E0βn. The particles will not continue crossing the shock indefinitely: the net momentum flux of the shocked gas downstream will carry them away in due course. So let us call the probability of remaining in the shock-crossing region after each crossing P . Then after n crossings there will be N = N0Pn of the original N0 electrons left. Fermi acceleration at shocks Fermi acceleration at shocks Now we want to find k=-1+logP/log Synchrotron emission Both prompt emission and afterglow emission are clearly non-thermal, and most natural process is synchrotron emission, i.e. emission from relativistic electrons gyrating in random magnetic fields. For an electron with comoving energy emec2 and bulk Lorentz factor the observed emission frequency is: =e2(eB/2 mec) Motion of a particle in a magnetic field • Gyro radiation is produced by electrons whose velocities are much smaller than the speed of light: v<<c. • Mildly relativistic electrons(kinetic energies comparable with rest massXc2) emit cyclotron radiation. • Ultrarelativistic electrons (kinetic energies >> rest massXc2) produce synchrotron radiation. Gyro radiation : F = e(b ´ B) Force is perpendicular to particle velocity, F · v = 0. Separating the v components along the field v|| and in a plane perpendicular to the field v- : dv|| dv- e = 0; = (v- ´ B) i.e. v|| = constant. But since the total v is constant, dt dt mc then also v- = constant. The solution of this equation is a uniform circular motion of the projected motion on the normal plan, since the acceleration in this plane is normal to v and of constant magnitude. The combination of this motion and of the uniform motion along the field is a helical motion. a v|| v v- Motion of a particle in a magnetic field In the inertial frame moving with velocity v|| , the particle orbits in a circle perpendicular to the magnetic field with the angular velocity w needed to balance the centripetal and magnetic forces : e e eB m v˙ = mw 2 R = v ´ B = wRB Þ w L = c c mc æ B ö wL 4.8 ´10-10 ´ B nL = = » 2.8 ç ÷ MHz -28 10 è Gauss ø 2p 9.1´10 ´ 3 ´10 ´ 6.28 The frequency of the emission is simply the gyration frequency. Therefore, Gyro radiation is observable only in very strong magnetic fields. An extreme astrophysical example is the magnetic field of a neutron star, B = 1012 Gauss. For example, the binary X - ray source Hercules X -1 exhibits an X - ray absorption line at photon energy E ~ 34 keV. Synchrotron emission We can use Larmor's formula to calculate the synchrotron power and synchrotron spectrum of a single electron in an inertial frame in which the electron is instantaneously at rest, but we need the Lorentz transform of special relativity to transform these results to the observer frame. Synchrotron emission During the helical motion let' s consider the point when B is parallel to the x axis. 2e 2 2e 2 2e 2 ˙ ˙ 2 2 2 P = 3 (a- ) P' = 3 (a' - ) = ( v ' ) what is a' or v ' -? 3c 3c 3c 3 v' y dy dy dt' dy' dt' dt' vy º = but y' = y then v y = = v' y = dt dt' dt dt' dt dt g dv dv dt' a' a' 1 dv' y dt' ay º y = y = = 2 y and similarly az = 2 z so dt dt' dt g dt' dt g g B 2e 2 2e 2g 2 2e 2g 4 2 2 2 a- = 2 Þ P' = 3 (a' - ) = (a ) finally, P' = P then P = (a ) g 3c 3c 3 3c 3 [Demonstration : Imagine two identical electrons of rest mass m, one at rest in the unprimed frame a' - and the other at rest in the primed frame. If one electron is slightly displaced from the other along the y - axis, they will interact as they pass each other and be accelerated in the y direction. Observers at rest in each frame see "their" electron move with some small v y << c , but the "other" electron will appear to move in the opposite y direction by a factor g more slowly because of time dilation —recall the resultv y = v' y /g above. Invoking momentum conservation, observers in each frame conclude that the "other" electron has inertial mass and hence its energy is greater by the same factor g . Thus : Pº me dE dE dt' dE dE ' dt' 1 = = = gP' =P dt dt' dt dE' dt' dt g i.e. the power is the same in all frames.] Synchrotron emission Synchrotron spectrum Our next problem is to explain how the synchrotron mechanism can yield radiation at frequencies much higher than =L/. To solve it, we first calculate the angular distribution of the radiation in the observer's frame. In the non relativistic case P goes like sin2, where is the angle between the direction of the acceleration and the direction of the photons. In the relativistic case, relativistic aberration causes the Larmor dipole pattern in the electron frame to become beamed sharply in the direction of motion as v approaches c. This beaming follows directly from the relativistic velocity equations implied by the differential form of the Lorentz transform. For an electron moving in the x direction: In the y direction perpendicular to the electron velocity, the velocity formula gives: Synchrotron spectrum Consider the synchrotron photons emitted with speed c at an angle q ' from the x' axis. Let v'x and v' y be the projections of the photon speed onto the x' and y' axes. Then : v' v' cosq '= x ; sin q '= y c c In the observer frame for the same photons we have : v v cosq = x ; sin q = y and using the above eq. for the velocities we get : c c æ v' x +v ö 1 æ c cos q '+v ö 1 cosq '+b cosq = ç ÷ =ç ÷ = 1+ b v' /c c 1+ b c cos q ' /c è ø c 1+ b cosq ' è ø x v'y sin q ' = cg (1+ bv'x /c) g (1+ b cos q ') In the frame moving with the electron, the Larmor equation implies a power pattern proportional sin q = to cos 2q, with nulls at ± p/2. In the observer's frame, these nulls appear at much smaller angles : sin q ' 1 sin q = » »q g (1+ b cos q ') g Synchrotron spectrum Relativistic beaming transforms the dipole pattern of Larmor radiation in the electron frame (dotted curve) into a narrow searchlight beam in the observer's frame. The solid curve is the observed power pattern for =5. The observed angle between the nulls of the forward beam ~2/ , and the peak power gain ~2 . For example, a 10 Gev electron has ~20000 so 2/~ 20 arcsec! The observer sees a short pulse of radiation emitted during only the tiny fraction: 2 2pg = 1 pg of the electron orbit, when the electron is moving directly toward the observer. Synchrotron spectrum t1 1/ t2 Synchrotron spectrum Synchrotron spectrum n cr g3 At n c Ln » f( ) = f ( ) but Ln = L /n c and L = 4/3s T cg 2b 2e 2 B 2 therefore : r c r 2p e2 e2 c c g3 e 2 æ nr ö f ( ) µ g and Ln » ç ÷ 2p rè c ø 1/ 3 µ g -2 / 3n 1/ 3 i.e. quite a flat spectrum. This is the spectrum of one particle in relativistic motion. Let's now consider a volume V big in comparison with the gyration radius and with the disomogeneities of the magnetic field. In this case the emissio is isotropic. Pn = ò Ng Ln dg where Ng = kg - p V Pn » Vn 1/ 3 ò g -2 / 3g - p dg if p > 1/3 the integral is dominated by the lower extreme. Pn » Vn 1/ 3g inf now, n c = - p +1/ 3 c 2pr g 3 = n G g 2 where n G = gc 2 Þ n c inf = n G g inf 2pr æn ö >ç ÷ ènG ø 1/ 2 for a n > n c inf follows that g inf Pn » Vn 1/ 3g inf - p +1/ 3 and therefore : (- p +1/ 3)/ 2 p 1 p-1 æ ö - + n 1/ 3 » Vn ç ÷ = Vv 2 2 = Vn 2 ènG ø Extrapolating the power law at low frequency the energy density would will increase until a thermodinamic equilibrium will set, I.e. energy equipartition: 3/2KT~mc2 . The electron temperature will be proportional to and ~(c/L)1/2 and therefore at each frequency there will be a temperature T~ (c/L)1/2 . Lets define the brightness temperature: Tb=Fc2/ 2, the temperature for which if F is given by the RJ formula (F~KT2) T=Tb. But we are in this situation and therefore the spectrum at low frequency is the RJ spectrum. The difference with the BB is that in the BB T=const, while in this case T~ (c/L)1/2 and therefore F~ 5/2. Log l Spectrum: Power Law + Self Absorption 5/2 -(p-1)/2 Log Spectrum of the prompt emission ì E -3 / 2 E < E b N(E) = í -1- p / 2 E > Eb îE Characteristic frequency of synchrotron emission is determined by m and B, Eb=hm=hm2eB/mec The strength of the magnetic field is unknown, but its energy density B2/8 is a fraction B of the internal energy. eB U B = 4pR cG B /8p = eB Lin = Lg ee 2 E b »1e1/B 2ee3 / 2 2 2 L1/g ,52 G t ris 2 2.5 v,-2 2 MeV B~1016-17 G more than a magnetar As observed! GRBs – 2 additional Constraints with n(e) =e2qeB/(2mec): Below some frequency, we are below the minimum electron Lorentz factor: m=e(p-2)/(p-1) mp/me Above a critical frequency, the electron loses a significant fraction of its energy to radiation: c=6mec/(TB2t) Sari, Piran, & Narayan 1998 GRBs – 2 phases m>c: All the electrons cool down to c: fast cooling. Sari, Piran, & Narayan 1998 c>m: Only electrons with e>c can cool: slow cooling. Time Evolution (4ct/L)1/7L (4ct/L)-3/7 adiabatic radiative • (t)= (17E)1/8/ (1024mp nc5t3)1/8 adiabatic radiative • R(t)= (17Et)1/4/ (4mpnc)1/4 Sari, Piran, & Narayan 1998 Time Evolution c=2.7x1012B-3/2E52-1/2n1-1td-1/2Hz m=5.7x1014B1/2e2E521/2td-3/2Hz F,max=1.1x105B1/2E52n11/2 D28-2mJy Sari, Piran, & Narayan 1998 c=1.3x1013B-3/2E52-4/724/7 n1-13/14td-2/7Hz m=1.2x1014B1/2e2E524/72-4/7 n1-1/14td-12/7Hz F,max=4.5x103B1/2E528/7n15/14 2-8/7D28-2td-3/7mJy The Early Afterglow and the Optical Flash The late afterglow observations confirmed relativistic motion. But what is the value of g during the GRB phase? 100 < 0 = E0/M0 < 105 “dirty” “clean” This could be tested -rays by early afterglow observations (Sari & Piran: Rome, Oct 1998; x-rays Astro-ph/11/1/1999): optical A very strong optical flash coinciding with the GRB The Internal-External Fireball Model -rays Inner Engine Relativistic Wind Internal Shocks Afterglow External Shock OPTICAL FLASH Optical Flash Revisited • Do internal shocks also predict prompt bursts? Predictions of the Optical Flash Depending upon the Exact details of the Explosion (width of Shock, structure of Internal shocks in Addition to all of the Many Fireball free Parameters) Sari & Piran 1999 The Parameter space allowed for Optical Flashes Sari & Piran 1999 The amount of energy In the optical flash Varies over many Orders of magnitude. Prediction – depending Upon the model, you will/will not see the flash. GRB 990123 - The Prompt Optical Flash ROTSE’s detection of a 9th magnitude prompt optical flash. Summary of GRB models Fireball Model - Summary • Thusfar, the fireball model has made very few true predictions • Current Favorite form of the Fireball model uses internal and external shocks. -rays Inner Engine Relativistic Wind Internal Shocks Afterglow External Shock Particles in a B-field radiate Relativistic Particles Psynchrotron = 2q2/3c3 4 q2B2/(2m2c2)vperp2 = 2/3 r02cperp22B2 where r0=e2/mc2 Isotropic velocities B perp2 =22/3 < > Psynch=4/3Tc22B2/(8) where T=8r02/3 is the Thompson Cross-Section vpar vperp Fireball Model - Summary • Basic Fireball model simple – Relativistic shocks with synchrotron + inverse Compton emission • Internal Shocks produce optical burst and gamma-rays, External Shocks produce afterglow • Jets alter the spectra in an observable way. Jets Make a Sharp Break in the light curve *synch emission does not include the effects of cooling. Observations place several constraints on the Engine! • Few times 1051 erg explosions (few foe) • Most of energy in gamma-rays (fireball model works if explosion relativistic) • Rapid time variability • Duration ranging from 0.01-100s • Accompanied by SN-like bursts • Occur in Star Forming Regions • Explosion Beamed (1-10 degrees) • … With the fireball model, these constraints are strengthened! • Relativistic factors above 100! • Some explosions must occur in windswept media • Some (all?) explosions are jets GRB Engines • Energy sources and conversion on earth and in astrophysics • Variability constraints – Compact object models • With observational constraints, models now fall into two categories: I) Black hole accretion disk models (compact binary merger, collapsar) II) Neutron Star Models (magnetar, supranova) Energy Sources: What Powers These Explosions? Energy Source: Gravitational Potential Energy Hydroelectric Power Energy from Falling Water Drives Turbines! 1-2000 MegaWatts Hoover Dam - Arizona/Nevada Diablo Canyon, CA Nuclear Energy Breaking Bonds Within the Atom 1) Fission 1,000 MWatts Large Atom (e.g. Uranium) Captures an Electron Causing It to Become Unstable and Break Apart. Some Mass is Converted to Energy E=Mc2 Nuclear Energy II) Fusion Combining Atoms To Form A Larger Atom Can Also Release Energy! Atomic Bomb – Can Be Fusion or Fission Energy Conversion Energy released through gravitational potential, chemical, or nuclear sources must be converted into useful energy. Useful = Electricity on Earth (to Most of Us) Explosion Energy (to the Astronomy Observer) This usually requires a mediator – something to transport the energy: Magnetic Fields – e.g. a Dynamo Radiation – e.g. Photons (light), Neutrinos Magnetic Dynamo Water (Accelerated by Gravity Or Thermal Pressure) Spins Large Magnets. The Motion Of the Magnets Drives an Electric Current -- Electricity! Radiation Photons (Light) or Neutrinos Can Transport Energy Nuclear Energy Released in the Sun Must Make Its Way Out of the Sun Via The Transport of Light or Neutrinos. Energy Sources • Chemical – rarely important in astrophysics • Nuclear Physics – Stars, Type Ia Supernovae, X-ray Bursts • Gravitational Potential Energy – All other supernovae, X-ray Binaries, Pulsars (neutron star spin arises from potential energy) and, for most theories, GRBs! Garcia-Senz et al. 1999 Energy Sources Helium Detonation on NS • Chemical – rarely important in astrophysics • Nuclear Physics – Stars, Type Ia Supernovae, X-ray Bursts • Gravitational Potential Energy – All other supernovae, X-ray Binaries, Pulsars (neutron star spin arises from potential energy) and, for most theories, GRBs! Zingale et al. 2001 Energy Sources • Chemical – rarely important in astrophysics • Nuclear Physics – Stars, Type Ia Supernovae, X-ray Bursts • Gravitational Potential Energy – All other supernovae, X-ray Binaries, Pulsars (neutron star spin arises from potential energy) and, for most theories, GRBs! Fryer & Heger 1999 Energy Sources • Chemical – rarely important in astrophysics • Nuclear Physics – Stars, Type Ia Supernovae, X-ray Bursts • Gravitational Potential Energy – All other supernovae, X-ray Binaries, Pulsars (neutron star spin arises from potential energy) and, for most theories, GRBs! Energy Sources • Chemical – rarely important in astrophysics • Nuclear Physics – Stars, Type Ia Supernovae, X-ray Bursts • Gravitational Potential Energy – All other supernovae, X-ray Binaries, Pulsars (neutron star spin arises from potential energy) and, for most theories, GRBs! Energy Sources • Chemical – rarely important in astrophysics • Nuclear Physics – Stars, Type Ia Supernovae, X-ray Bursts • Gravitational Potential Energy – All other supernovae, X-ray Binaries, Pulsars (neutron star spin arises from potential energy) and, for most theories, GRBs! GRB Energy Sources Energy Needed: ~1052 erg Of useful energy (not leaked Out in neutrinos or Gravitational waves or Lost into a black hole)! Most GRB Models invoke Gravitational potential energy As the energy source. Collapse to a NS or stellar Massed BH most likely source E = G M2/r 1-10 solar masses 3-10 km E=1053-1054 erg Allowing a 1-10% Efficiency! Gamma-Ray Burst Durations Two Populations: Short – 0.03-3s Long – 3-1000s Possible third Population 1-10s Burst Variability Not only must any model Or set of models predict A range of durations, But the bursts must also Be rapidly variable! Burst Variability on the <10-100 Millisecond level Durations and Variabilities Variability = size scale/speed of light Again, Neutron Stars and Black Holes likely Candidates (either in an Accretion disk or on the NS surface). 2 10km/cs = .6 ms cs = 1010cm/s NS, BH Durations and Variabilities Duration = Rotation Period / Disk Viscosity ( = 0.1-10-3) Period = 2 r3/2/G1/2MBH1/2 = .3 ms near BH surface Duration for small disks – 3-300ms NS, BH Harnessing the Accretion Energy Mechanism I: Neutrinos from hot disk annihilate Above the disk – Producing a Baryon-poor, High-energy jet Mechanism II: Magnetic fields are Produced by Differential rotation In the disk. This Magnetic field produces a jet. Accretion Disk Details Lecture 5 Neutrino Driven Jets Neutrinos from accretion disk deposit their energy above the disk. This deposition can drive an explosion. Disk Cools via Neutrino Emission Densities above 1010-1011 g cm-3 Temperatures above a few MeV Neutrino Driven Jets e+,e- pair plasma Neutrino Annihilation Disk Cools via Neutrino Emission Densities above 1010-1011 g cm-3 Temperatures above a few MeV Neutrino Summary • Critical Densities for most-likely accretion disks: 104-108 g/cm3 • For Collapsars type I, this corresponds to black hole masses of 10-25 Msun and delays between collapse and jet of 30-300s. Does the neutrino-driven Collapsar type I model work? • Alternatives – magnetic fields, Collapsar type II (MacFadyen & Woosley 1999) Magnetic Field Driven Jets “And then the theorist raises his magic…. I mean magnetic wand… and viola, there are jets” Shri Kulkarni Lots of Mechanisms proposed, but most boil down to a reference to the still unsolved mechanism behind the jet mechanism for Active Galactic Nuclei (Generally the Blandford-Znajek Mechanism). We are extrapolating from a non-working model – dangerous at best. Magnetic Field Mechanism – Sources of Energy • Source of Magnetic Field – Dynamo in accretion disk. • Source of Jet Energy I) Accretion Disk II) Black Hole Spin Magnetic Dynamos • Duncan & Thompson (1993): High Rossby Number Dynamo (convection driven) – Bsat~(4vconvective2)1/2 • Akiyama et al. (2003): Shear-driven Dynamo – Bsat2~(4r2W2(dlnW/dlnr)2 • Popham et al. (1999): Disk Dynamo – Bsat2~(4vtot2) Schematic Cross-Section of a black hole and magnetosphere The poloidal field is shown in solid lines, typical particle velocities are shown with arrows. In the magnetosphere, spark gaps (SG) form that create electron/ positron pairs. Blandford & Znajek 1977 Electromagnetic structure of force-free magnetosphere with (a) radial and (b) paraboloidal magnetic fields. For paraboloidal fields, the Energy appears to be Focused alonge the rotation Axis. “The overall efficiency of Electromagnetic energy Extraction from a disk Around a black hole is Difficult to calculate with Any precision” Blandford & Znajek (1977) Magnetic Jet Power • Blandford-Znajek: L~3x1052 a2 dM/dt erg/s with B~2x1015(L/1051 erg/s)1/2 (MBHa)-1 • Popham et al. 1999 (Based on BZ): L~1050a2(B/1015G)2 erg/s, B~v2 where ~1% • Katz 1997 (Parker Instability): L~1051(B/1013G)(W/104s-1)5(h/106cm) (r/1013g cm-3)-1/2(r/106cm)6 erg/s Magnetic Field Summary • Magnetically driven jets could possibly produce much more energy than neutrino annihilation (easily enough for GRBs). If it works for AGN, it must work for GRBs. • Most estimates extrapolate from an already faulty AGN jet model. No “physics” calculation or derivation has yet to be made. Black Hole Accretion Disk Models Collapsar (aka hypernova: Supernova explosion of a very massive (> 25 Msun) star Iron core collapse forming a black hole; Material from the outer shells accreting onto the black hole Accretion disk => Jets => GRB! Collapsars Observations Explained • Energetics explained • Duration and variability explained Observations Predicted • SN-like explosions along with GRB outburst • Bursts occurring in star forming regions • GRB Beaming Massive Star Models With the observations pushing toward massive stars, a number of other massive star models appeared – pushing for neutron star mechanisms! • Explosions from Magnetars • Supranova (neutron star which later collapses to a black hole) Supernovae/Hypernovae Nomoto et al. (2003) EK Failed SN? 13M~15M Supranova Model For GRBs: If a neutron star is rotating extremely rapidly, it could escape collapse (for a few months) due to centrifugal forces. Neutron star will gradually slow down, then collapse into a black hole => collapse triggers the GRB Disadvantages of the Supranova Model Mass thing… Duration can’t be Longer than 3-3000ms NS, BH Disadvantages of the Supranova Model Duration = Rotation Period / Disk Viscosity ( = 0.1-10-4) Duration can’t be Longer than 3-3000ms Current bursts with Iron lines are all Long-duration! NS, BH