GRB Jets & Orphan AfterglowsGRB Jets & Orphan Afterglows

Jonathan GranotJonathan Granot

Institute for Advanced Study, PrincetonInstitute for Advanced Study, Princeton

Outline of the Talk:nn GRB Jets Viewed Off-Axis:GRB Jets Viewed Off-Axis:uuThree different modelsThree different modelsuuOff-axis light curvesOff-axis light curves

nn Orphan Afterglows:Orphan Afterglows:uuBrief introductionBrief introductionuuOverview of theoretical worksOverview of theoretical worksuuExpected detection ratesExpected detection rates

nn ConclusionsConclusions

Off-Axis Light Curves:

Model 1 (dashed lines), model 2 (solid lines)

nn Model 1Model 1: a point source moving along the jet axis: a point source moving along the jet axisnn Model 2Model 2: homogeneous jet (Kumar & Panaitescu 2000): homogeneous jet (Kumar & Panaitescu 2000)

??00=5=5oo

EEjetjet=3=3••10105151 ergergn=1n=1 cmcm-3-3

z=1z=1p=2.5p=2.5εεee=0.1=0.1εεBB=0.01=0.01

Granot, Panaitescu,Kumar & Woosley

(2002)

Model 3: Hydrodynamic SimulationModel 3: Hydrodynamic Simulation((Granot, Miller,Granot, Miller, Piran Piran,, Suen Suen & Hughes 2001 & Hughes 2001))

nn Hydro-codeHydro-code: : 2D2D++AAdaptive daptive MMesh esh RRefinementefinement(Miller & Hughes)(Miller & Hughes)

nn Initial conditionsInitial conditions: a : a conecone of opening angle of opening angle ??00=0.2=0.2takentaken out oout of the f the spherical spherical self-similar Blandford-self-similar Blandford-McKee solution, with energy McKee solution, with energy EEisoiso=10=105252 ergs ergs

nn A homogeneous external medium of density A homogeneous external medium of density n=1n=1 cmcm-3-3

nn Light curves calculated numerically by integratingLight curves calculated numerically by integratingover the 4-volume of the simulation, accounting for:over the 4-volume of the simulation, accounting for:uu Relativistic transformation of the radiation fieldRelativistic transformation of the radiation fielduu The different photon arrival times for different The different photon arrival times for different ??obsobs

Hydrodynamic Simulation (model 3):

Granot et al. (2002)

??00=0.2, =0.2, EEjetjet=3=3••10105151 erg, n=1erg, n=1 cmcm-3-3, , z=1,z=1, p=2.5 p=2.5, , εεee=0.1, =0.1, εεBB=0.01=0.01

Orphan Afterglows:nn ‘orphan afterglow’ ‘orphan afterglow’ ≡≡ an afterglow detected an afterglow detected

without the detection of prompt without the detection of prompt γγ-ray emission-ray emissionnn Orphan afterglows are usually associated withOrphan afterglows are usually associated with

jets viewed off-axis (jets viewed off-axis (??obsobs > > ??00))nn The The prompt GRB prompt GRB is detectable fromis detectable from ??obsobs < < ??00

nn The afterglow is detectable out to The afterglow is detectable out to ??maxmax > > ??00

nn ??maxmax depends on the jet parameters (including depends on the jet parameters (including zz),),observed band & limiting flux for detection observed band & limiting flux for detection FFlimlim

nn For For ??0 0 << ??obsobs < < ??maxmax we expect orphan afterglows we expect orphan afterglowsnn There is There is nono orphan afterglow detection so far orphan afterglow detection so far

Overview of Theoretical Work:nn Rhoads (1997) was the first to suggest the useRhoads (1997) was the first to suggest the use

of orphan afterglows to constrain the degree ofof orphan afterglows to constrain the degree ofcollimation of collimation of GRBsGRBs

nn He pointed out that the afterglow radiation isHe pointed out that the afterglow radiation isbeamed into an increasingly larger angles asbeamed into an increasingly larger angles asthe jet deceleratesthe jet decelerates

nn Woods & Woods & Loeb Loeb (1999) calculated the ratio of X-ray &(1999) calculated the ratio of X-ray &γγ-ray -ray fluence, fluence, from the prompt GRB, for different from the prompt GRB, for different ??obsobs

nn For For ??obsobs>>??00+1/+1/γγ the fluence drops sharply the fluence drops sharply F(F(??obsobs)/F(0))/F(0)~ [~ [γγ((??obsobs--??00)])]-6-6. For . For ??obsobs>2>2??00 we reach the limit of a we reach the limit of apoint source: point source: F(F(??obsobs)/F(0))/F(0) ∝∝ ( (γγ??obsobs))-6 -6 (Granot et al. 2002)(Granot et al. 2002)

FFXX((??obsobs))//FFγγ(0) (0) –– solid lines, solid lines, FF γγ((??obsobs))//FFγγ(0) (0) –– dashed lines dashed lines

γθ0<0.1 γθ0=1

γθ0=10

γθ0=100

γθobs

Woods & Woods & LoebLoeb(1999)(1999)

nn DalalDalal, , Griest Griest & & Pruet Pruet (2002) (2002) assumed emission from aassumed emission from apoint source (at the jet center or edge) in order topoint source (at the jet center or edge) in order tocalculate calculate FFνν((??obsobs>0>0) ) givengiven FFνν((??obsobs=0=0))

nn They obtained: They obtained: ??maxmax//??0 0 ≈≈ const (for const (for ??0 0 <<<< 1) 1) ⇒⇒RRorphorph/R/RGRB GRB ≈≈ ( (??maxmax//??00))22 ≈≈ const const ⇒⇒ degeneracy degeneracy

nn Their key assumption: Their key assumption: FFνν((ttjetjet,,??obsobs=0=0) = const) = const

Light curves for:Light curves for:??00=0.07=0.07??obsobs=0.01, 0.05, 0.1, 0.2, 0.5=0.01, 0.05, 0.1, 0.2, 0.5??obsobs //??0 0 =0.14, 0.71, 1.4, 2.9, 7.1=0.14, 0.71, 1.4, 2.9, 7.1

A Pessimistic Prediction:

detdet detdet

( ) pobsjettF

obspeaktF 2

0)0,(

),( −≈ θ

θ

ν

θν

nn Granot, Panaitescu, Kumar & Woosley (2002) changed theGranot, Panaitescu, Kumar & Woosley (2002) changed theassumption assumption FFνν((ttjetjet,,??obsobs=0=0) = const) = const to to EEjetjet=const=const, as, assuggested by afterglow observations suggested by afterglow observations (Frail et al. 2001;(Frail et al. 2001;Panaitescu & Kumar 2001;Panaitescu & Kumar 2001; Piran Piran et al. 2001) et al. 2001)

nn For For EEjetjet=const=const analytic jet models analytic jet models (Rhoads 1999; Sari,(Rhoads 1999; Sari,Piran Piran & & HalpernHalpern 1999) 1999) predict that the jet dynamics, and predict that the jet dynamics, andthereby the light curves for all thereby the light curves for all ??obsobs are independent of are independent of??00 at at t >t > t tjetjet for for ??obsobs < < ??00 or or t t ≥≥ t tpeakpeak for for ??obsobs > > ??00

nn ⇒⇒ ??maxmax ≈≈ const const ⇒⇒ ΩΩorphorph ≈≈ 2 2ππ??maxmax22 ≈≈ const const

nn ⇒⇒ f fbb ≈≈ ⟨⟨??0022/2/2⟩⟩ = R= RGRBGRB/R/RGRB GRB == ((ΩΩorphorph/4/4ππ)R)RGRBGRB//RRorphorph

A More Optimistic Prediction:

detdetdetdetdetdet truetrue

1θθ =j

2θθ =j

3θθ =j

3θθ =obs

3θθ <j

Log(t)

On-axis observer

ppjet tzfFF −− ∝≈ 2

0 )( θν

Post break universal light curve

Off-axis observer

3<< θθθ 21

Log

(Fν)

obspeakjet t θθ ≈)(

pobspeak zfFF 2

0 )( −= θ

nn NakarNakar, , PiranPiran & Granot (2002) assumed & Granot (2002) assumed EEjetjet=const=const and andused the ‘universal’ post-break light curve, normalizedused the ‘universal’ post-break light curve, normalizedby by GRBsGRBs 990510 & 000926, to calculate the expected 990510 & 000926, to calculate the expectednumber of orphan afterglows in a single snapshot number of orphan afterglows in a single snapshot NNorphorph

nn For For ΩΩorphorph ≈≈ const const there isthere is a simple analytic resulta simple analytic result

The Detectability of Orphan Afterglows:

porph FFN /2

lim0 )/(∝n For a given instrument the exposure time

needed to reach a given limiting flux scales astexp(Flim)∝Flim

-2 ⇒⇒ dNdNorphorph//ddtexp∝ Flim2-2/p ~ Flim

1.1

⇒⇒ shallow surveys are better than deep surveys

(Nakar, Piran & Granot 2002)

The Expected Detection Rate:nn The number of orphans afterglow in a single snapshotThe number of orphans afterglow in a single snapshot

over the whole sky for over the whole sky for mmlimlim=23 =23 in the R-band is 3 (60)in the R-band is 3 (60)for our canonical (optimistic) parametersfor our canonical (optimistic) parameters

nn The is an uncertainty of a factor ~10 (The is an uncertainty of a factor ~10 (NNorphorph ∝∝ ??00-2-2FF00

2/p2/p))

nn TotaniTotani & Panaitescu (2002) used parameter estimates & Panaitescu (2002) used parameter estimatesfor 10 afterglows, and a homogeneous jet model, tofor 10 afterglows, and a homogeneous jet model, tocalculate off-axis light curves & orphan detection ratescalculate off-axis light curves & orphan detection rates

nn As As EEjetjet≈≈constconst for their sample, they obtain qualitatively for their sample, they obtain qualitativelysimilar results to similar results to Nakar Nakar et al., but their optical detectionet al., but their optical detectionrate is a few time larger than our most optimistic valuerate is a few time larger than our most optimistic value

nn Possible reasons for this difference are:Possible reasons for this difference are:uu Their afterglow sample is dominated by Their afterglow sample is dominated by ??00≈≈0.050.05

NNorphorph,, RRorph orph ∝∝ RRGRBGRB ∝∝ RRGRBGRB??00-2-2 ( (a factor of ~4a factor of ~4))

uu A flat peak to the light curve A flat peak to the light curve ⇒⇒ Fν stays longerabove Flim for the same for the same Fpeak ( (a factor of ~2-3a factor of ~2-3))

uu Domination by GRB 991216 with a high fluxDomination by GRB 991216 with a high fluxnormalization and small p=1.36 (normalization and small p=1.36 (a factor of ~5a factor of ~5))

Different Approach to the Same Problem:

truetrue detdet

nn Levinson, Levinson, OfekOfek, , Waxman Waxman & Gal-Yam (2002) studied& Gal-Yam (2002) studiedthe detection of orphan afterglows in the radio, whenthe detection of orphan afterglows in the radio, whenthe jet becomes non-relativistic and spherical (the jet becomes non-relativistic and spherical (t~1t~1 yryr))

nn Using the FIRST & NVSS surveys they find 25 orphanUsing the FIRST & NVSS surveys they find 25 orphancandidates candidates ⇒⇒ ⟨⟨??00

22⟩⟩<0.2 <0.2 (or (or 0.020.02 if none are orphans) if none are orphans)nn Huang, Dai & Lu (2002) suggested that failed Huang, Dai & Lu (2002) suggested that failed GRBsGRBs

((1<<1<<γγ <100 <100) form a different type of orphan afterglows) form a different type of orphan afterglowsnn We may miss on-axis jets due to lack of We may miss on-axis jets due to lack of γγ-ray coverage-ray coveragenn Off-axis jets are distinguishable from other orphans by:Off-axis jets are distinguishable from other orphans by:

uu Their initially rising light curveTheir initially rising light curveuu TypicallyTypically F Fνν∝ν∝νββ withwith ββ<0 <0 near near ttpeakpeak

uu Possibly strong linear polarization at Possibly strong linear polarization at tt≥≥ttpeakpeak(Granot et al. 2002)(Granot et al. 2002)

Other Recent Works:

Conclusions:nn For For ??obsobs > > ??00 the light curve initially rises, peaks at the light curve initially rises, peaks at ttpeakpeak

~ (~ (??obsobs//??00))22 ttjetjet and decays like and decays like ??obsobs = 0= 0nn Light curves from hydro-simulations differ in detailsLight curves from hydro-simulations differ in details

but are qualitatively similar to simpler modelsbut are qualitatively similar to simpler modelsnn For For ??obsobs > > ??00 a strong linear polarization (a strong linear polarization (≤≤40%40%) ) maymay

occur near occur near ttpeak peak and slowly decay with timeand slowly decay with timenn Such features can help distinguish between off -axisSuch features can help distinguish between off -axis

jets and other types of orphan afterglowsjets and other types of orphan afterglowsnn EEjetjet≈≈constconst ⇒⇒ ΩΩorphorph≈≈constconst ⇒⇒ RRGRBGRB=R=Rorphorph44ππ//ΩΩorphorph

nn Future orphan afterglow surveys may provideFuture orphan afterglow surveys may providevaluable data on valuable data on RRGRB GRB andand ffbb ≈≈ ⟨⟨??00

22/2/2⟩⟩

truetrue detdet

truetrue

On-Axis Light Curves (?obs= 0):

εεee=0.1, =0.1, εεBB=0.01, p=2.5,=0.01, p=2.5, ??00=0.2, z=1,=0.2, z=1, EEisoiso=10=105252 ergs, n=1 cm ergs, n=1 cm-3-3