The GRB literature has been convolved with my brain

Geometric Structure of Blast Wave Outflow: Why we care

Explain Features of Afterglow Light Curves / Spectra Outside the Standard Spherical Model

Keys to Central Engine Dynamics: Collimation & Energetics

Constrain “True” GRB Rates

Improve Afterglow Models Constrain Microphysical Parameters

All Fluid Properties Uniform with Solid Angle Spherically Symmetric Hydro Always Valid (B/M or T/S)

Simplest Model: Isotropic Expansion (No Jet)

Problems with Isotropic ExpansionGRBs Are Not Supernovae

Supernovae are explosions; GRBs are irregular winds.

Supernovae are relative standard candles;

Isotropic GRB models show a wide Eiso distribution

Observational Evidence to the Contrary

Central Engine Models Favor Collimation

Its hard to maintain “clean” isotropic expansion.

BH accretion disk / Magnetar angular momentum has a preferred direction.

Special Relativity is Tricky, Secretive, and Deceitful

GRB and afterglow observers are causally-disconnected from the majority of the emission for the majority of the time.

Ultra-relativistic motion “freezes” angular profile at acceleration region.

Frail et al. (2001)

ALSO…

Just as “Simple”: Jets Are Common As

Well

Balloons, Jets, or Pancakes? How to Identify Collimated Outflow

Idea (1): Resolve Angular Emission Structure

Problems

GRB / Early Afterglow Not Resolveable

Only in Causal Contact with Small Fraction of Outflow

1 1

1beam

1beam

jetFor obs jet

beam jet

Can’t Distinguish Emission of Uniform Sphere from Uniform Jet Viewed Head-ON!

22

4jet

Idea (2): Orphan Afterglow Surveys (Rhoads 1997)

If Isotropic Expansion NRADIO = NOPTICAL = NX-RAY = NGRB

(every direction sees a GRB and each kind of afterglow)

If Collimated Expansion NRADIO > NOPTICAL > NX-RAY > NGRB

(only ~ % of GRBs are observable)

USE DISTRIBUTION OF OBSERVED AFTERGLOWS TO CONSTRAIN COLLIMATION

Problems

Orphan transients difficult to detect

Lots of biases to remove (e.g., afterglow samples are flux-limited)

In some cases various afterglows missing anyways (e.g., “Dark” bursts)

A significant fraction of GRBs may ‘fail’ due to baryon contamination but still produce afterglows (Huang, Dai, Lu 2002)

Depends on Jet Models

Idea (3): “Wait Until Structure Becomes Visible”

As the WHY was UNOBVIOUS to me, lets first take

a “Refresher” on Relativistic Emission….

In Afterglow Calculations Thus Far We Haven’t

Cared About The Causality Cone WHY?

3 2,max ,max4 3 / 4SHOCK ismF R n P D

FOR FAST COOLING

(SARI, PIRAN, and NARAYAN 1998)

(Even though microscopic quantities are correct relativistically there is no mention of an integration over some restricted solid angle)

Emission From a Homogeneous Blob: The Non-Relativistic Limit

V<< c

fi ttRj

j

to fromEmission Isotropic I

]cm / s / [erg Emissivity sHomogeneou Isotropic,

000

30

0

R0

D

RR

00

D

HOW MUCH TOTAL ENERGY PER DETECTOR AREA IS MEASURED?

,

,

2

00 0

0

f obs

obsobs

i obs obs

t

obs obs f i

t

RFl I d d dt j R t t

D

0 obs 0 0 obs 0 obsBecause the Motion is Nonrelativistic I I d d dt dtobs

And Aliens At Different Viewing Angles Would Concur

In the Blob Frame

Emission From a Homogeneous Sphere: The Ultra-Relativistic Limit

1beam

DHOW MUCH TOTAL ENERGY PER DETECTOR AREA IS

MEASURED?

, ,0

0

, ,0

,

,

2 320

0 0

0

1f obs f

obsobs

i obs obs i

f obs

obsobs

i obs obs

t t

obsTOT obs obs

t t

t

obs obs

t

tE I d d dt I d d

I d d dt

0 obs

32

obs 0 0 obs obs 00

Motion is Ultra-Relativistic I I ν ν Γ d d dt dt 2Γobs

1 R0

obs

SAME

Before A Spherical Solution is Fully Accurate Because Different Solid Angles Are Not In Causal Contact with one

Another

Observation Signature of a Jet

Will Depend on Model of Jet we Assume

1st Beaming Model: TOP HAT

Our Strategy is to

Early Support For Jets

Problem with jetting – smoothness of jet

break by panitescu and meszaros 1998

Argument against extreme beaming =>

lack of orphan afterglows

AFTERGLOW POLARIZATION: Constraining the Jet Structure?