K. Alatalo - Extensions to the Standard Model1 Extensions to the Standard Afterglow Model Katey...
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K. Alatalo - Extensions to the Standard Model 1
Extensions to the Standard Afterglow
Model Katey Alatalo
October 10th, 2005
K. Alatalo - Extensions to the Standard Model 2
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
K. Alatalo - Extensions to the Standard Model 3
Introduction
• Why do we need the extension?• What are our options?
– External density fluctuations– Energy re-injection– Off-axis viewing– Microlensing
• What else?
K. Alatalo - Extensions to the Standard Model 4
Why do we need the extension?
K. Alatalo - Extensions to the Standard Model 5
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]
K. Alatalo - Extensions to the Standard Model 6
Light Curves Gone Wild
• Some light curves are not “standard”
• 021004• 000301C• 030329
GRB000301C
GRB030329
K. Alatalo - Extensions to the Standard Model 7
The Competing Models
K. Alatalo - Extensions to the Standard Model 8
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
K. Alatalo - Extensions to the Standard Model 9
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
K. Alatalo - Extensions to the Standard Model 10
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
K. Alatalo - Extensions to the Standard Model 11
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
K. Alatalo - Extensions to the Standard Model 12
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
K. Alatalo - Extensions to the Standard Model 13
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
K. Alatalo - Extensions to the Standard Model 14
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
K. Alatalo - Extensions to the Standard Model 15
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
K. Alatalo - Extensions to the Standard Model 16
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
K. Alatalo - Extensions to the Standard Model 17
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
K. Alatalo - Extensions to the Standard Model 18
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)
K. Alatalo - Extensions to the Standard Model 19
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
K. Alatalo - Extensions to the Standard Model 20
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*
K. Alatalo - Extensions to the Standard Model 21
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
K. Alatalo - Extensions to the Standard Model 22
GRB 030329
• Light curve contained undulations beginning ~1day after the burst
• Models– 2 jets?– single broken power
law?
• note: this is also SN2003dh
GRB030329
K. Alatalo - Extensions to the Standard Model 23
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
K. Alatalo - Extensions to the Standard Model 24
The End• Special thanks to
Dr. Sarah Yost and Prof. Josh Bloom for their helpful advice on supplemental papers to read.