physics of grb jets jonathan granot kipac @ stanford “grbs: the first 3 hours”, sanrotini,...
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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