Numerical Simulations of Relativistic Outflows in …lyutikov/workshop16/talks/... · Numerical...
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A. MacFadyen (NYU) Numerical Simulations of Relativistic Outflows in GRBs Andrew MacFadyen (NYU) H. van Eerten (MPE/Bath), P. Duffell (Berkeley), G. Ryan (NYU), Yiyang Wu (NYU), J. Zrake (Stanford) 2nd Purdue Worskshop on Relativistic Plasma Astrophysics May 11, 2016
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Transcript of Numerical Simulations of Relativistic Outflows in …lyutikov/workshop16/talks/... · Numerical...
A. MacFadyen (NYU)
Numerical Simulations of Relativistic Outflows in
GRBs
Andrew MacFadyen (NYU) H. van Eerten (MPE/Bath), P. Duffell (Berkeley),
G. Ryan (NYU), Yiyang Wu (NYU), J. Zrake (Stanford)
2nd Purdue Worskshop on Relativistic Plasma Astrophysics May 11, 2016
A. MacFadyen (NYU)
GRB051221A“Pre Swift”
Ryan+ (2014)Zhang+ (2014)
A. MacFadyen (NYU)
Need epsilon_b ~ 0.01 for synchrotron
Late GRB Afterglow
4
A. MacFadyen (NYU)
GRB051221A “Post Swift”
Ryan+ (2014)Zhang+ (2014)
“Plateau”
A. MacFadyen (NYU)
106−7
cm
1011cm
1013−15
cm
1016−18
cm
EnginePrompt + Early
Afterglow
Afterglow
Over 10 orders of mag in length scale!
Star or Cloud
A. MacFadyen (NYU)
106−7
cm
1011cm
1013−15
cm
1016−18
cm
Engine
Star or Cloud
Prompt
Afterglow
Over 10 orders of mag in length scale!
A. MacFadyen (NYU)
106−7
cm
1011cm
1013−15
cm
1016−18
cm
Engine Early Afterglow
Afterglow
Over 10 orders of mag in length scale!
Star or Cloud
A. MacFadyen (NYU)
106−7
cm
1011cm
1013−15
cm
1016−18
cm
Engine Early Afterglow
Late Afterglow
Over 10 orders of mag in length scale!
Star or Cloud
A. MacFadyen (NYU)
Afterglow Jet Dynamics
A. MacFadyen (NYU)
Ej = 2e52θj=0.05n=1cm^-3
van Eerten & AM (2011)
Granot+(01)Granot+Kumar(03,06)Zhang&AM(09)vanEerten+(10,11,12,13ab)Wygoda+(11)deColle+(12)Vlasis+ (12)
A. MacFadyen (NYU)
Synchrotron linear radiative transfer
the challenge: the jet nearly keeps up with its radiation
For a given observer / arrival time, a single intersecting plane at each emission time
- Optically thin limit: Just count all emission
- Emission & absorption, no scattering (i.e. synchrotron radiation): linear radiative transfer for all rays perpendicular to intersecting plane
A. MacFadyen (NYU)http://cosmo.nyu.edu/afterglowlibrary
Off Axis
On Axis
A. MacFadyen (NYU)
Example application: model fit to GRB 990510
• Iterative fit to radio, optical & X-ray data, based on 2D jet simulations
• Synchrotron slope p > 2, in contrast to 1.8 from Panaitescu & Kumar (2002)
• reduced χ-squared 3.235 for off-axis observer, while 5.389 on-axis
• observer angle θ is 0.016 rad, one third of jet angle 0.048 rad
From AMR RHD simulation to light curve
Simulate for energy E, density n, opening angle θ, then synchrotron radiative transfer calculation
Business as usual: rerun simulation for different E, n
A. MacFadyen (NYU)
More on scalings 1 / 2
blast wave variables:
some observations...
fluid equations can be rewritten in terms of dimensionless parameters:
dynamics invariant under transform of :
In other words, only one (numerically challenging!) simulation needed.
(A and B not explicitly required. Just compensate in r and t, since energy over density is a combination of cm and s)
A. MacFadyen (NYU)
limiting cases:
- ultrarelativistic:
- nonrelativistic:
so spherical (no ) blast waves are self-similar in these limits:
“Blandford-McKee” relativistic
“Sedov-Taylor” non-relativistic
intermediate stage in 2D more complex
Sedov-Taylor blast wave image: Landau & Lifshitz 1952
More on scalings 2 / 2
A. MacFadyen (NYU)
Scaling of Jet Dynamics
Calculate jet dynamics by applying scaling
Different E and n can be obtained by scaling: greatly reduces parameter space
Calculate light curves by applying scaling
All light curves can be calculated by scaling a basic set for E and n
A. MacFadyen (NYU)
Calculate light curves by applying scaling
Once done, no reference to simulations necessary anymore! BoxFit &ScaleFit
A. MacFadyen (NYU)
A. MacFadyen (NYU)
A. MacFadyen (NYU) Ryan et al (2015)
GRB110422A
A. MacFadyen (NYU) Ryan et al (2015)
Observer Angle
A. MacFadyen (NYU) Ryan et al (2015)
Electron slope p
A. MacFadyen (NYU)
GRB110422A
Ryan et al (2015)
A. MacFadyen (NYU)
http://cosmo.nyu.edu/afterglowlibrary/
Supported by NASA NNX10AF62G
A. MacFadyen (NYU)
106−7
cm
1011cm
1013−15
cm
1016−18
cm
Engine
Star
Early Afterglow
Afterglow
Over 10 orders of mag in length scale!
Forward Shock
Reverse Shock
ContactDiscontinuity
Ejecta
ISM
Lorentz Factor = 10
30
100
Duffell & AM (2014)
Rayleigh-Taylor Instability
Adiabatic Index = 4/3 Adiabatic Index = 1.1
Duffell & AM (2014)
Zrake & AM (2013)
A. MacFadyen (NYU)
Yiyang Wu et al (2016)
A. MacFadyen (NYU)
A. MacFadyen (NYU)
106−7
cm
1011cm
1013−15
cm
1016−18
cm
Engine
Star
Prompt
Afterglow
Over 10 orders of mag in length scale!
A. MacFadyen (NYU) 37Baryons aren’t a problem!
Relativistic Jets Can Escape Stars
Binary Black Hole Case e.g. Loeb (2016)?
Expect gamma ray variability at
~ binary frequency?
A. MacFadyen (NYU) Duffell, Quataert & AM (2015)
Baryons can help collimate a jet..
Short Burst in pre NS merger Ejecta Cloud
Left: Spherical Cloud
Right: Flat cloud
A. MacFadyen (NYU)Zhang, Woosley & MacFadyen (2003)
“Plug” 2D SRHD
A. MacFadyen (NYU) Zhang+ (2004)
3D SRHD
A. MacFadyen (NYU)
“JET” Moving Mesh Code
Relativistic MHD
Duffell & MacFadyen (2011,2013, 2014)
A. MacFadyen (NYU)
10-10
10-5
100
105
10-3 10-2 10-1 100
Den
sity
(g/c
m3 )
r / R0
Fitting FunctionMESA Output
Duffell & MacFadyen (2015)
35 →18 Msun 99% Max Rotation Low Metallicity (1e-3)
A. MacFadyen (NYU) Duffell & MacFadyen (2014)
Duffell & MacFadyen (2014)
A. MacFadyen (NYU)
1.5 s 5e9 cm 4.2 s 3e10 cm 12 s 2e11 cm
170 s 3e12 cm 8.8e4 s 1e15 cm 1.2e7 s 2e17 cm
A. MacFadyen (NYU)
Duffel & AM (2015)
A. MacFadyen (NYU)
0
20
40
60
80
100
120
10-2 100 102 104 106 108 1010
Lore
ntz
Fact
or
time (sec)
Acce
lera
tion
Coast (Top-Heavy)
Collision
Coast
BMK
γmaxγavg
Duffell & AM (2015)
A. MacFadyen (NYU)
10-6
10-5
10-4
10-3
10-2
102 103 104 105
Flux
(mJy
)
time (s)
t-1/4
t-8
t-11/8
Coast Decel
Afterglow ModelInternal Shocks
External ShocksGRB 110312A
Duffell & AM (2015)
A. MacFadyen (NYU)
αop = (p− 1)/2 = 3/4 for p = 2.5
�↵ ⌘ ↵op
� ↵X
= 3k/4� 1 ⇡ 1/2
In contrast, decelerating blast wave predicts (eg Sari et al, 1998):
Independent of p:
αop = −3 + k(p + 5)/4 νm < ν < νc
∆α = 1/4
A. MacFadyen (NYU)Zaninoni+ (2013)
A. MacFadyen (NYU)
• GRB afterglows p ~ 2.2
• OFF AXIS viewing → “Magnetars” possible
• Jets are “top heavy”
• Internal collision → steep decay
• Coasting amalgamated jet → plateau
• Decaying plateau → wind medium
• 𝚫𝞪 = 1/2
• Jets & Fireballs are RT Unstable → B field
Conclusions
