Numerical Simulations of Relativistic Outflows in …lyutikov/workshop16/talks/... · Numerical Simulations of Relativistic Outflows in GRBs ... model fit to GRB 990510 ... Calculate

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