K. Alatalo - Extensions to the Standard Model1 Extensions to the Standard Afterglow Model Katey...

K. Alatalo - Extensions to the Standard Model 1

Extensions to the Standard Afterglow

Model Katey Alatalo

October 10th, 2005


Papers Used

• Microlensing of Gamma-Ray Bursts by Stars and Machos– E. Baltz & L. Hui

• Microlensing and the Surface Brightness Profile of the Afterglow Image of Gamma-Ray Burst 000301C– B.S. Gaudi, J. Granot, & A. Loeb

• Modeling Fluctuations in Gamma-Ray Burst Afterglow Light Curves– E. Nakar & T. Piran

• Variability in GRB afterglows ad GRB 021004– E. Nakar, T. Piran, & J. Granot

• Gravitational Microlensing by the Galactic Halo– B. Paczyński


Introduction

• Why do we need the extension?• What are our options?

– External density fluctuations– Energy re-injection– Off-axis viewing– Microlensing

• What else?


Why do we need the extension?


A “Regular” Afterglow Light Curve

• Light curve decays in the standard way

• t is satisfied.• Steepening/

changes in the decay occurs due to a break frequency (or a jet break) passing through the observed band (c or m)

050502A [Yost et al., 2005]


Light Curves Gone Wild

• Some light curves are not “standard”

• 021004• 000301C• 030329

GRB000301C

GRB030329


The Competing Models


The Standard (no extensions yet)

• Dependences of important parameters of the shock

1 1 12 4 4

2 22 4 4

2 2

2p

0

2 20

1 1

1 2 1 1

[ ( )] [ ( )]

( ) 4 ( ) d

1 d

4

p p p

p p p

shock

R

R

p p pB e m c

p p pB e c

E A R t M R t c

M R m n r r r

R rt

c

E M nF

E M n t


Varying Density

• n changes over radius (thus, time)

• F becomes:

• Plug in equation for mass (m<<c):

• Assume m changes very slowly with time

• Solution for c<:

• *note: this includes ISM and Wind models.

14

24

1

2 1

p

p

pm c

pc

M nF

M n t

343 p

d ln 1 d ln( )

d ln 4 d ln

1 ;

1 3

m

m

F p n

t t

p Mn

n m rn

14

00 0

pm

t nF F

t n

24

0 130 0

2 ; 1

1

pc

c

t n pF F

nt nn


Varying Density: effects

• Nakar & Piran show what would happen to a light curve if the shock crashed into an overdense ISM region with a Gaussian distribution in R.

• The numerical simulations of changing energies and densities only stands for slowly varying profiles


Varying Energy

• (ISM Case) • (Wind Case)3( 1)

1 3(2 ) 1

4 3p

0

d3

p pm c

p pc

R

E RF

E R t

nm c R rt r

E E

1 32

1 1.5(2 ) 1

2

p

0

d

pp

m c

p pc

R

w

E RF

E R t

R rt A m c r

E E

•E changes with time while n stays constant.

•These equations must be solved numerically


Varying Energy: two possibilities

Refreshed Shocks• Produced by massive

and slow shells ejected late in GRB

• When the progenitor spews out slower more massive shells, it gives the shock more energy

• This energy “refreshes” the forward shock and produces a reverse shock

progenitor

progenitor

shock

shock (stronger)

massive shell ejected

reverse shock


Varying Energy: two possibilities

Initial Energy Inhomogeneities• The “Patchy Shell” scenario: only

material within an angle of -1 can “talk” to each other, meaning inhomogeneities are only smoothed to -1 scale.

• Numerical simulations [Kumar & Granot, 2002] show that the jet conserves its initial inhomogeneities for a very long time.

• When -1~n, the fluctuations begin to appear– The number of fluctuations we can see

is Nfl~(n)-1

– The amplitude of the fluctuations is

piece of jet we can see

whole jet


Off-axis Viewing

• Observer is not looking directly into the jet symmetry axis

• At a certain time, -1 will have spread to obs

• When this happens, a single bump appears in the light curve


Microlensing: what it is

• A gravitational object (star) passes through the jet

• The source object (in this case, the jet) becomes brighter as the gravitational object passes

http://cfa-www.harvard.edu/~sgaudi/Movies/centroid_s0.gif

Microlensing Simulation


Gravitational Lensing

• Einstein was the first to think about it

• where R0 is the radius of stuff that gets lensed (the extension of gravity’s ability to bend light)

20 2

4 ; d ds

s

D DGMDR D

c D


Mirolensing and GRBs

• GRBs are significantly “limb-brightened” (recall B. Metzger’s talk)

• Angular size of jet ~ as, which is the same as the Einstein radius of a solar mass lens

jet

1 12 2

2 28

os ol

ls

41.6 μas

10 cmE

GM M D

c D M

D DD

D


Microlensing and GRBs (cont…)

• The magnitude and fluctuation in the light curve due to a microlensing event depend strongly on the surface brightness profile (SBP)


Microlensing and GRBs (cont…)

• Model (a.k.a. make an equation fit) the flux

• This equation is then used to fit the GRB light curve and determine if it was lensed.

1 2

1

0,( ) ( )

s s s

b b

t tF t t F

t t


GRB 021004

• Discovered only ~500s after the GRB

• 3 bumps:– ~4000s– 7×104s– 3×105s

• Models:– density variations– “patchy shell” model– refreshed shocks

– passage of m plus a reverse shock*


GRB 000301C

• Bump appeared in light curve ~2 days after the GRB

• 2 proposed models:– standard GRB model

• > c

• ISM density profile• reasonable fit

– Microlensing• much better fit• s not constrained

GRB000301C


GRB 030329

• Light curve contained undulations beginning ~1day after the burst

• Models– 2 jets?– single broken power

law?

• note: this is also SN2003dh

GRB030329


What next?

• Recently, a new “kink” to the standard afterglow model has been reported: underluminosity at early times

• 050801: ROTSE reported a very shallow initial decay

• Nothing in the standard model can predict this

050801 Courtesy of GRBlog


The End• Special thanks to

Dr. Sarah Yost and Prof. Josh Bloom for their helpful advice on supplemental papers to read.

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