Physics of GRB JetsPhysics of GRB JetsJonathan GranotJonathan Granot

KIPAC @ StanfordKIPAC @ Stanford

“GRBs: the first 3 hours”, Sanrotini, August 31, 2005

Outline of the Talk:Outline of the Talk: Observational evidence for jets in GRBs Observational evidence for jets in GRBs The jet The jet dynamicsdynamics: degree of : degree of lateral expansionlateral expansion

Semi-Analytic modelsSemi-Analytic models Simplifying the dynamical Eqs.: 2D Simplifying the dynamical Eqs.: 2D 1D 1D Full hydrodynamic simulation Full hydrodynamic simulation

The JetThe Jet Structure: Structure: how can we tell what it ishow can we tell what it is Afterglow polarizationAfterglow polarization StatisticsStatistics of the prompt & afterglow emission of the prompt & afterglow emission Afterglow light curvesAfterglow light curves

Off-axis viewing angles & X-ray flashesOff-axis viewing angles & X-ray flashes ConclusionsConclusions

Observational Evidence for Jets in GRBsObservational Evidence for Jets in GRBs The energy output in The energy output in -rays assuming isotropic -rays assuming isotropic

emission approaches (or even exceeds) emission approaches (or even exceeds) MMcc22

difficult for a stellar mass progenitordifficult for a stellar mass progenitor True energyTrue energy is much smaller for a narrow is much smaller for a narrow jet jet

Achromatic breakAchromatic break or steepening of the or steepening of the afterglow light afterglow light curves (“jet break”)curves (“jet break”)

Optical light curve ofOptical light curve ofGRB 990510GRB 990510

(Harrison et al. 1999)(Harrison et al. 1999)

Dynamics of GRB Jets:Dynamics of GRB Jets: Lateral Expansion Lateral Expansion

Simple (Semi-) Analytic Jet Models (Rhoads 97, 99; Sari, Piran & Halpern 99,…)

Typical Simplifying Assumptions: A uniform jet with sharp edges (even at A uniform jet with sharp edges (even at t > tt > tjetjet))

The shock front is a part of a sphere within The shock front is a part of a sphere within θθ < θ< θjetjet

The velocity is in the radial direction The velocity is in the radial direction (even at (even at t > tt > tjetjet))

Lateral expansion in a velocity of Lateral expansion in a velocity of ccs s c/ c/33 or or c c in in

the local rest framethe local rest frame The jet dynamics are obtained by solving simple 1D The jet dynamics are obtained by solving simple 1D

equations for conservation of energy and momentumequations for conservation of energy and momentum Most works assume a uniform external medium (ISM)Most works assume a uniform external medium (ISM)

Simplified Jet Dynamics:Simplified Jet Dynamics:(Rhoads 97, 99; Sari, Piran & Halpern 99,…)

dRdR jetjetdR + cdR + cssdt’ dt’ ( (jetjet + c + css/c/c)dR)dR

ddjetjet/dR /dR (dR (dR/dR - /dR - jetjet)/R )/R c css/c/cRR

jetjet ~~ 00 + c + css/c/c

The jet edges become visible whenThe jet edges become visible when ~ ~ 11// 00

Sideways expansion becomes large Sideways expansion becomes large ~ ~ (c(css/c) /c) / / 00

RRRRjetjet

jetjet R R / R/ R

Quick & Dirty:Quick & Dirty: E/cE/c22 ~~ extext(R)R(R)R33((jetjet))222 2 ++ jetjet ~~ ccss/c/c RR ~~ constconst

More Careful Analysis More Careful Analysis (Rhoads 99):: E/cE/c22 M M22 d(d(22)/dR = -()/dR = -(22/M)dM/dR /M)dM/dR

dM/dR = 2dM/dR = 2((jetjetR)R)22extext(R)(R),, 22/M /M 44cc22/E/E

jetjet jetjet- - 00 (c (css/c)/c)dr/dr/r ~ (cr ~ (css/cR)/cR)dr/dr/

~~ (c(css/c/c00)exp(-R/R)exp(-R/Rjetjet)),, jetjet ~~ 00(R(Rjetjet/R)exp(R/R/R)exp(R/Rjetjet))

t t dr/2cdr/2c22 ~ ~ RRjetjet/4c/4c2 2 t t-1/2-1/2

RRjetjet= [E/= [E/extext(c(css))22]]1/3 1/3 (comparable to the Sedov (comparable to the Sedov

length for the true energy, if length for the true energy, if ccss ~ c ~ c))

Most models predict a jet break but differ in the details:Most models predict a jet break but differ in the details:

The time of the jet break The time of the jet break ttjet jet (by a factor of ~20)(by a factor of ~20)

Temporal slope Temporal slope FF(( >> mm,t > t,t > tjetjet) ) t t--,, ~~ p (p (±15%±15%))

The sharpness of the jet break (~1-The sharpness of the jet break (~1- 4 decades in time)4 decades in time)

Kumar & Panaitescu (2000)Kumar & Panaitescu (2000) predicted a significantly predicted a significantly

smoother jet break for a stellar wind environment (this smoother jet break for a stellar wind environment (this

was reproduced in other works, but not observed yet) was reproduced in other works, but not observed yet)

Implications: Implications: Afterglow Light Curve

Simplifying the Dynamics: 2D 1D Integrating the hydrodynamic equations over the radial Integrating the hydrodynamic equations over the radial

direction significantly reduces the numerical difficultydirection significantly reduces the numerical difficulty This is a reasonable approximation as most of the This is a reasonable approximation as most of the

shocked fluid is within a thin layer of width shocked fluid is within a thin layer of width ~ R/10~ R/1022

(Kumar & JG 2003)

Numerical Simulations:(JG et al. 2001; Cannizzo et al. 2004; Zhang & Macfayen 2006)

The difficulties involved: The hydro-code should allow for both The hydro-code should allow for both ≫≫ 11 and and 1 1 Most of the shocked fluid lies within in a very thin Most of the shocked fluid lies within in a very thin

shell behind the shock (shell behind the shock ( ~~ R/10R/1022) ) hard to resolvehard to resolve A relativistic code in A relativistic code in at leastat least 2D2D is required is required A complementary code for calculating the radiationA complementary code for calculating the radiation

Very few attempts so farVery few attempts so far

Movie of Simulation

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Proper Density:(logarithmic color scale)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Bolometric Emissivity:(logarithmic color scale)

The Velocity Field (on top of lab frame density)

(JG, Miller, Piran, Suen & Hughes 2001)

The Jet Dynamics: very modest lateral expansion

There is slow material at the sides of the jet while most of the There is slow material at the sides of the jet while most of the emission is from its frontemission is from its front

Main Results of Hydro-Simulations: The assumptions of simple models fail: The assumptions of simple models fail:

The shock front is not sphericalThe shock front is not spherical The velocity is not radialThe velocity is not radial The shocked fluid is not homogeneousThe shocked fluid is not homogeneous

There is only very mild lateral expansion There is only very mild lateral expansion as long as the jet is relativisticas long as the jet is relativistic

Most of the emission occurs within Most of the emission occurs within θθ << θθ00

NeverthelessNevertheless, despite the differences, there is a , despite the differences, there is a sharpsharp achromatic achromatic jet breakjet break [for [for > > mm((ttjetjet))] at ] at

ttjetjet close to the value predicted by simple modelsclose to the value predicted by simple models

Comparison to (Semi-) Analytic Models: Similarities: Similarities:

An achromatic An achromatic jet breakjet break at at ttjet jet for for > > mm((ttjetjet)) The value of The value of ttjetjet is similar is similar Temporal slope, Temporal slope, FF (( > > mm, t > t, t > tjetjet) ) t t--, , is close to is close to

the analytic valuethe analytic value p p (( =1 .12p =1 .12p forfor p = 2.5 p = 2.5 and and is even closer tois even closer to p p forfor p < 2.5 p < 2.5))

Differences:Differences: The jet dynamics are very different The jet dynamics are very different For For < < mm(t(tjetjet)) (radio) (radio) changes more gradually and changes more gradually and

moderately at moderately at ttjetjet and changes more sharply only at a and changes more sharply only at a later time when later time when mm decreases belowdecreases below obsobs

Jet break is sharper than in most analytic models, Jet break is sharper than in most analytic models, and is somewhat sharper for and is somewhat sharper for θθobsobs= 0= 0 than for than for θθobs obs θθ00

Why do we see a Jet Break:

Aberration of light or ‘relativistic beaming’Source

frame Observerframe

1/

The observer sees mostly emission from within an angle of 1/1/ around the line of sight

1/

Direction to observer

Relativistic Source:

The edges of the jet become visible when drops below 1/1/jetjet , causing a jet break

For vv ~ c ~ c, jetjet ~ 1/~ 1/ so there is not

much “missing” emission from >> jetjet & the jet break is due to the decreasing dE/ddE/d + faster fall in (t)(t)

Lateral Expansion: Lateral Expansion: Evolution of Image SizeEvolution of Image Size(Taylor et al. 04,05; Oren, Nakar & Piran 04; JG, Ramirez-Ruiz & Loeb 05)(Taylor et al. 04,05; Oren, Nakar & Piran 04; JG, Ramirez-Ruiz & Loeb 05)

GRB 030329

Imag

e di

amet

er

(JG, Ramirez-Ruiz & Loeb 2005)

Model 1: vv ~ c ~ cModel 2: vv ≪≪ cc

whilewhile ≳≳ 2 2

The The StructureStructure of GRB Jets: of GRB Jets:

How can we determine the jet structure?How can we determine the jet structure?1. Afterglow polarization light curves1. Afterglow polarization light curves

the polarization is usually attributed to a jet geometrythe polarization is usually attributed to a jet geometry

Log()0 Log()

Log

( dE

/ddE

/d

)

core

-2

Structured jet††:Uniform jet†:

†Rhoads 97,99; Sari et al. 99, …

††Postnov et al. 01; Rossi et al. 02; Zhang & Meszaros 02

Log(tt)P

ttjet

(Sari 99; Ghisellini & Lazzati 99)

Log(tt)

Pttjet

(Rossi et al. 2003)

Log

( dE

/ddE

/d

)

pp = const= const

pp flips by 90 flips by 90oo at t at tjetjet

Ordered B-field*:

*Granot & Königl 03

Log(tt)P

pp = const= const

tt0

while for jetwhile for jet modelsmodels

P(tP(t t≪t≪ jj)) ≪≪ P(tP(t~t~tjj))

Linear polarization at the level of Linear polarization at the level of P P ~ ~ 1%-3%1%-3% was detected in several optical afterglowswas detected in several optical afterglows

In some cases In some cases PP varied, but usually varied, but usually pp const const Different from predictions of uniform or structured jetDifferent from predictions of uniform or structured jet

(Covino et al. 1999)(Covino et al. 1999)

(Gorosabel et al. 1999)(Gorosabel et al. 1999)

Afterglow Polarization: Afterglow Polarization: ObservationsObservations

GRB 020813GRB 020813

tj

The Afterglow polarization is affected not only by the jet The Afterglow polarization is affected not only by the jet

structure but also by factors such asstructure but also by factors such as

the the B-field structureB-field structure in the in the emitting regionemitting region

InhomogeneitiesInhomogeneities in the ambient density or in the jet in the ambient density or in the jet (JG & (JG &

Königl 2003; Nakar & Oren 2004)Königl 2003; Nakar & Oren 2004)

““refreshed shocksrefreshed shocks” - slower ejecta catching up with the ” - slower ejecta catching up with the

afterglow shock from behind afterglow shock from behind (Kumar & Piran 2000; JG, (Kumar & Piran 2000; JG,

Nakar & Piran 03; JG & Königl 03) Nakar & Piran 03; JG & Königl 03)

Therefore, Therefore, afterglow polarizationafterglow polarization is is notnot a very a very

““cleanclean” method to learn about the jet structure” method to learn about the jet structure

Afterglow Pol. & Jet Structure:Afterglow Pol. & Jet Structure: Summary Summary

Both the UJ & USJ models provide an acceptable fitBoth the UJ & USJ models provide an acceptable fit Provides many constraints Provides many constraints

but not a “clean” method but not a “clean” method

to study the jet structureto study the jet structure

Jet Structure from log N - log S distributionJet Structure from log N - log S distribution(Guetta, Piran & Waxman 04; Guetta, JG & Begelman 05; Firmiani et al. 04)(Guetta, Piran & Waxman 04; Guetta, JG & Begelman 05; Firmiani et al. 04)

(Guetta, JG & Begelman 2005)

Cumulative distribution

differential distribution

different binning

dN/ddN/d appears to favor the USJ model appears to favor the USJ model dN/ddN/ddzdz disfavors the USJ model disfavors the USJ model It is still premature to draw strong conclusions due to the inhomogeneous sample & various selection effectsIt is still premature to draw strong conclusions due to the inhomogeneous sample & various selection effects Not yet a “clean” method for extracting the jet structureNot yet a “clean” method for extracting the jet structure

Jet Structure from Jet Structure from ttjetjet ( (zz) distribution) distribution

(Perna, Sari & Frail 2003) (Nakar, JG & Guetta 2004)

Uniform “top hat” jet - extensively studied Uniform “top hat” jet - extensively studied

Afterglow Light Curves: Afterglow Light Curves: Uniform JetUniform Jet (Rhoads 97,99; Panaitescu & Meszaros 99; Sari, Piran & Halpern 99; Moderski, (Rhoads 97,99; Panaitescu & Meszaros 99; Sari, Piran & Halpern 99; Moderski,

Sikora & Bulik 00; JG et al. 01,02)Sikora & Bulik 00; JG et al. 01,02)

ee=0.1, =0.1, BB=0.01, =0.01,

p=2.5,p=2.5, θθ00=0.2, =0.2,

θθobsobs=0, z=1,=0, z=1,

EEisoiso=10=105252 ergs, ergs,

n=1 cmn=1 cm-3-3

(JG et al. 2001)

It is a “smooth edged” version of a “top hat” jetIt is a “smooth edged” version of a “top hat” jet Reproduces on-axis light curves nicelyReproduces on-axis light curves nicely

Afterglow Light Curves: Afterglow Light Curves: GaussianGaussian JetJet (Zhang & Meszaros 02; Kumar & JG 03; Zhang et al. 04)(Zhang & Meszaros 02; Kumar & JG 03; Zhang et al. 04)

(Kumar & JG 2003)

Works reasonably well but has potential problemsWorks reasonably well but has potential problems

Afterglow LCs: Afterglow LCs: Universal StructuredUniversal Structured JetJet(Lipunov, Postnov & Prohkorov 01; Rossi, Lazzati & Rees 02; Zhang & Meszaros 02)(Lipunov, Postnov & Prohkorov 01; Rossi, Lazzati & Rees 02; Zhang & Meszaros 02)

(Rossi et al. 2004)

LCs Constrain the power law indexes ‘a’ & ‘b’: LCs Constrain the power law indexes ‘a’ & ‘b’: dE/ddE/d -a-a, , 00 -b-b

1.51.5 ≲≲ aa ≲≲ 2.5 2.5,, 0 0 ≲≲ bb ≲≲ 11

Afterglow LCs: Afterglow LCs: Universal StructuredUniversal Structured JetJet

(JG & Kumar 2003)

Usual light curves + extra features: bumps, flateningUsual light curves + extra features: bumps, flatening

Afterglow LCs: Afterglow LCs: Two ComponentTwo Component JetJet (Pedersen et al. 98; Frail et al. 00; Berger et al. 03; Huang et al. 04; Peng, Konigl & (Pedersen et al. 98; Frail et al. 00; Berger et al. 03; Huang et al. 04; Peng, Konigl &

JG 05; Wu et al. 05) JG 05; Wu et al. 05)

(Peng, Konigl & JG 2005)

(Berger et al. 2003)

(Huang et al. 2004)

GRB 030329

The bump at The bump at ttdec,wdec,w for an on-axis observer is wide & smooth for an on-axis observer is wide & smoothTwo ComponentTwo Component Jet: Jet: GRB 030329GRB 030329

(Lipkin et al. 2004)

(JG 2005)

Abrupt deceleration

gradual deceleration

The The bumpbump in the light curve when in the light curve when

the narrow jet becomes visible is the narrow jet becomes visible is

smooth & widesmooth & wide

Two ComponentTwo Component Jet: Jet: XRF 030723XRF 030723

(Fynbo et al. 2004)

(JG 2005)

(Huang et al. 2005)

Afterglow Light Afterglow Light Curves:Curves: Off-AxisOff-Axis Viewing AnglesViewing Angles

Granot et al. (2002)

θθ00=0.2, E=0.2, Ejetjet=3•10=3•105151

erg, n=1erg, n=1 cmcm-3-3, , z=1,z=1, p=2.5p=2.5, , ee=0.1, =0.1,

BB=0.01=0.01

Model 2: uniform jet + sharp edges &

vv == ccss

Prompt Emission:Prompt Emission: Off-AxisOff-Axis Viewing AnglesViewing Angles

EEpeakpeak -1-1,, f f -a-a where 1+[ 1+[((obs obs --00)])]22 & a a

2 2 for 00 << obsobs ≲≲ 2 200; a a 3 3 for obsobs ≳≳ 2 200

The prompt emission from large off-axis viewing angles, 1≫ 1≫ or obsobs ≳≳ 2 200, will not be detected (“orphan afterglows”)

The prompt emission from slightly off-axis viewing angles might still be detected, but peaks at lower EEpeakpeak & has a much smaller fluence ff (X-ray flashes or X-ray rich GRBs)

Suggest a roughly uniform jet with reasonably Suggest a roughly uniform jet with reasonably sharp edges, where GRBs, XRGRBs & XRFs sharp edges, where GRBs, XRGRBs & XRFs are similar jets viewed from increasing viewing are similar jets viewed from increasing viewing angles angles (Yamazaki, Ioka & Nakamura 02,03,04)(Yamazaki, Ioka & Nakamura 02,03,04)

Light Curves of X-ray Flashes & XRGRBsLight Curves of X-ray Flashes & XRGRBs

(JG, Ramirez-Ruiz & Perna 2005)

XRF 030723 XRGRB 041006

Afterglow L.C. for Different Jet Structures:Afterglow L.C. for Different Jet Structures: Uniform conical jet Uniform conical jet

with sharp ejdges: with sharp ejdges:

Gaussian jet in both Gaussian jet in both 00

& & dE/ddE/d: might still work: might still work

Constant Constant 00 + Gaussian + Gaussian

dE/ddE/d: not flat enough: not flat enough

Core + Core + dE/ddE/d -3 -3

wings: not flat enoughwings: not flat enough

obsobs // 0/c0/c = 0,= 0, 0.5,0.5, 1,1, 1.5,1.5, 22 ,, 2.5,2.5, 3,3, 4,4, 5,5, 6 6 (JG, Ramirez-Ruiz & Perna 2005)

Conclusions: Numerical studies show Numerical studies show very little lateral expansionvery little lateral expansion

while the jet is relativistic & produce a while the jet is relativistic & produce a sharp jet breaksharp jet break

(similar to that seen in afterglow observations)(similar to that seen in afterglow observations)

There are some important differences in the resulting There are some important differences in the resulting

afterglow light curves, especially at afterglow light curves, especially at < < mm(t(tjetjet)) (radio) (radio)

The most promising way to The most promising way to constrainconstrain the the jet structurejet structure

is through the is through the afterglow light curvesafterglow light curves

XRF & XRGRB afterglow light curves favor a roughly XRF & XRGRB afterglow light curves favor a roughly

uniform jet with rather sharp edgesuniform jet with rather sharp edges

Afterglow Light Curves from Simulations