GRB

GRBTheory and observations

Useful reviews:Waxman astro-ph/0103186Ghisellini astro-ph/0111584Piran astro-ph/0405503Meszaros astro-ph/0605208Useful linkshttp://www-astro.physics.ox.ac.uk/~garret/teaching/http://www.cv.nrao.edu/course/astr534/

http://www-astro.physics.ox.ac.uk/~garret/teaching/

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

• Nontermal Spectrum N(E) E E<E0

E E>E0

BATSE (20 keV-1 MeV)

0.1 MeV < E0< 1 MeV

-2, ~ [-1, -0.5]

Spectrum well described by a broken power lawBand approximation

The compactness problem• t ~ 1-10

msCompact sources R0 c t ~ 3 107

cm• Cosmological sources (D~3 Gpc) L~ fD2~1052

erg/s

~ p R0n T~ TL/4R0c ~1015

~ 1 MeV

1 2≥ (mec2)2 e+e-

p fraction of photons above the thereshold of pair production

Optical depth ( e+e-) >>1

T=6.25x10-

25cm2

R of our galaxy ~ 30 kpc: extragalactic objects

Implications: The fireball

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

How can the photons escape the source?

The reasons: 1. In the comoving frame below the thereshold

for pair production ’=/ ’1 ’2≤ (mec2)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

Zhang & Mészàros, IJMPA A19, 2385 (2004)

Propagation effect

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 ModelFrom IXth International

Symposium on Particles,Strings and Cosmology

Tata Institute ofFundamental Research,

Mumbai, Inda

Tsvi Piran

http://theory.tifr.res.in/pascos/Proceedings/Friday/

Piran/index.html

The Fireball modelAssumes a relativistic Outburst and works With a variety of Mechanisms.

We rely heavily on A review by Tsvi Piran.

The Fireball Model

compact source

Relativistic Particles>100or Poynting flux

~ 107 cm

Shocks

g - rays

Goodman; Paczynski; Shemi & Piran, Narayan, Paczynski & Piran; Meszaros & Rees

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 firstGRB model (Colgate 1968) Invoked SN Shocks to powerGRBs!

External Shock Predictions For GRBs

• The burst of gamma-rays 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”!)

A NO GO THEOREMExternal shocks cannot produce a variable light

curve!!! (Sari & Piran 97)

Fire

ball

Theo

rists

then

foun

d a

lot

Wro

ng w

ith th

e ex

tern

al s

hock

mod

el!

Time to Revise the Theory

• Gamma-rays and Afterglow arise from different sources

Birth of the Internal Shock Model

• 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.

D=cT

d=cdT

Internal ShocksShocks between different shells of the ejected relativistic matter

T

dT

• 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)

D=cT

d=cdT

Internal Shocks Afterglow

1) Compact Source, E>1051erg

2) Relativistic Kinetic Energy

3) Radiation due to Internal shocks = GRBs

4) Afterglow by external shocks

The Central Compact Source is Hidden

Gamma-Ray Burst: 4 Stages

Plus burst of optical emission!

InnerEngine

Relativistic Wind

The Internal-External Fireball Model

There are no direct observations of the inner engine.The -rays light curve contains the best evidence on the inner engine’s activity.

ExternalShock

Afterglow

InternalShocks

-rays

THE FIREBALL MODEL PREDICTED GRB

AFTERGLOW (late emission in lower wavelength that will

follow the GRB)Rhodes & Paczynksi, Katz,

Meszaros & Rees, Waxman, Vietri, Sari & Piran

Postdicted

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]

1013cm 1016cm

ISM

ray phaseX-ray, Opt.-IR,

RadioEfficient! [Guetta Spada & Waxman 2001]

The radiation mechanisms

The efficiency of internal shocksShells collide and merge in a single shell with

The conversion efficiency of kinetic energy into internal energy

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

If t=tv is the average interval between two pulses (interval between shells ejection)

Emission properties determined by ris

Let’s assume that a faster shell (2) impacts on a slower the leading shell (1);

Light curves from internal shocksRapid variability and complexity of GRB lightcurves result of emission from multiple shocks in a relativistic windt (interval between ejected shells) determines the pulse duration and sepration:

Numerical simulations reproduce the observed light curves

(Spada et al. 2000)

IS reproduce the observed correlation between the duration of the pulse (tp) and the subsequent interval (tp)

Spectrum of the prompt emissionPrompt emission observed has most of energy in 0.1-2 MeVGeneric 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

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

Fermi acceleration at shocks

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.

U=vu e-

Unshocked gas vd=1/4vu

Hot shocked gas vu

Fermi acceleration at shocks

Fermi acceleration at shocksNow we want to find k=-1+logP/log

Synchrotron emissionBoth 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.

a v|| v

v-

Motion of a particle in a magnetic field

Synchrotron emissionWe 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

B

me

Synchrotron emission

Synchrotron spectrumOur 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


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:

of the electron orbit, when the electron is moving directly toward the observer.


t1

1/

t2

Spectrum: Power Law + Self Absorption

Log

Log

l

-(p-1)/25/2

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.

Spectrum of the prompt emission

As observed!

Characteristic frequency of synchrotron emission is determined by m and B, Eb=hm=hm2eB/mec

ris

The strength of the magnetic field is unknown, but its

energy density B2/8 is a fraction B of the internal energy. B~1016-17 G more

than a magnetar

GRBs – 2 additional Constraints with n(e) =e

2qeB/(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 phasesm>c:All the electrons cool down to c: fast cooling.

c>m:Only electrons with e>c can cool: slow cooling.


• R(t)=

• (t)=

Time Evolution

(17Et)1/4/(4mpnc)1/4

(4ct/L)1/7L

adiabaticradiative

(17E)1/8/(1024mp

nc5t3)1/8

(4ct/L)-3/7

adiabaticradiative


Time Evolutionc=2.7x1012B

-3/2E52-1/2n1

-1td-1/2Hz

m=5.7x1014B1/2e

2E521/2td

-3/2Hz

F,max=1.1x105B1/2E52n1

1/2

D28-2mJy

c=1.3x1013B-3/2E52

-4/724/7

n1-13/14td

-2/7Hz

m=1.2x1014B1/2e

2E524/72

-4/7

n1-1/14td

-12/7Hz

F,max=4.5x103B1/2E52

8/7n15/14

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 by early afterglow observations (Sari & Piran: Rome, Oct 1998; Astro-ph/11/1/1999):

A very strongoptical flashcoinciding withthe GRBoptical

x-rays

-rays

InnerEngine

Relativistic Wind

The Internal-External Fireball Model

ExternalShock

Afterglow

InternalShocks

-rays

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 theMany Fireball free Parameters)

Sari & Piran 1999

The Parameter space allowed for Optical Flashes

The amount of energy In the optical flash Varies over many Orders of magnitude.

Prediction – dependingUpon the model, you will/will not see the flash.

Sari & Piran 1999

GRB 990123 - ThePrompt 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.

InnerEngine

Relativistic Wind

ExternalShock

Afterglow

InternalShocks

-rays

Particles in a B-field radiateRelativistic ParticlesPsynchrotron = 2q2/3c3 4

q2B2/(2m2c2)vperp2

= 2/3 r02cperp

22B2

where r0=e2/mc2

Psynch=4/3Tc22B2/(8) where T=8r0

2/3 is the Thompson Cross-Section

B

vperp

vpar

Isotropic velocities

<perp2>=22/3

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 PowerEnergy from Falling Water Drives Turbines!

Hoover Dam - Arizona/Nevada

1-2000 MegaWatts

Nuclear Energy

Breaking Bonds Within the Atom1) Fission

Diablo Canyon, CA

1,000 MWatts

Large Atom (e.g. Uranium)Captures an Electron CausingIt to Become Unstable andBreak Apart.

Some Mass is Converted to Energy E=Mc2

Nuclear EnergyII) Fusion Combining Atoms To Form A Larger Atom Can Also Release Energy!

Atomic Bomb – Can Be Fusion or Fission

Energy ConversionEnergy 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 DynamoRadiation – e.g. Photons (light), Neutrinos

MagneticDynamo

Water (Accelerated by Gravity Or Thermal Pressure) Spins Large Magnets.

The Motion Of the Magnets Drives an Electric Current-- Electricity!

Radiation

Nuclear EnergyReleased in the SunMust Make Its WayOut of the Sun ViaThe Transport of Light or Neutrinos.

Photons (Light) or NeutrinosCan Transport Energy

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





Helium Detonation on NS

Zingale et al. 2001





Fryer & Heger 1999

GRB Energy SourcesE = G M2/r

1-10 solar masses3-10 km

E=1053-1054 ergAllowing a 1-10%Efficiency!

Energy Needed: ~1052 ergOf useful energy (not leaked Out in neutrinos or Gravitational waves orLost into a black hole)!

Most GRB Models invoke Gravitational potential energyAs the energy source.

Collapse to a NS or stellarMassed BH most likely source

Gamma-Ray Burst Durations

Two Populations: Short – 0.03-3s Long – 3-1000sPossible third Population 1-10s

Burst Variability

Burst Variability on the <10-100 Millisecond level

Not only must any modelOr set of models predictA range of durations, But the bursts must also Be rapidly variable!

Durations and Variabilities

NS,BH

Variability = size scale/speed of light

Again, Neutron Stars andBlack Holes likely Candidates (either in an Accretion disk or on the NS surface).

2 10km/cs = .6 mscs = 1010cm/s

Durations and Variabilities

NS,BH

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

Harnessing the Accretion Energy

AccretionDisk

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 rotationIn the disk. This Magnetic field produces a jet.

Details Lecture 5

Disk Cools via NeutrinoEmission

Densities above 1010-1011 g cm-3

Temperatures above a few MeV

Neutrino Driven Jets

Neutrinos from accretion disk deposit their energy above the disk. This deposition can drive an explosion.

Disk Cools via NeutrinoEmission

Densities above 1010-1011 g cm-3

Temperatures above a few MeV

Neutrino Driven Jets

AbsorptionScattering

NeutrinoAnnihilation

e+,e- pair plasma

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~(4vconvective

2)1/2

• Akiyama et al. (2003): Shear-driven Dynamo – Bsat

2~(4r2W2(dlnW/dlnr)2

• Popham et al. (1999): Disk Dynamo – Bsat

2~(4vtot2)

Schematic Cross-Section of a black hole and magnetosphere

The poloidal field is shown in solid lines, typical particle velocitiesare shown with arrows. In the magnetosphere, spark gaps (SG) form

that createelectron/positronpairs.

Blandford & Znajek 1977

Electromagnetic structure of force-free magnetospherewith (a) radial and (b) para-boloidal magnetic fields.

For paraboloidal fields, the Energy appears to be Focused alonge the rotationAxis.

“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)

starIron 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/HypernovaeNomoto et al. (2003)

Failed SN?

13M~15M

EK

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

NS,BH

Mass thing…

Duration can’t be Longer than 3-3000ms

Disadvantages of the Supranova Model

NS,BH

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!

GRB

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