scaling properties of afterglow radiation - … · scaling properties of afterglow radiation a ......

Scaling Properties of Afterglow Radiation

A. MacFadyenH. van Eerten

P. DuffelJ. Zrake

(NYU)

A. MacFadyen (NYU) Fermi/Swift GRBs 2012, Munich 5/8/12

GRB photons are made far away from

engine.

Can’t observe engine directly with light.

(neutrinos, gravitational

waves?)

Electromagnetic process or neutrino annihilation to tap power of central compact object.

Hyper-accreting black hole or ms magnetar

Tess

Duffell & MacFadyen (2011)


Afterglow Jet Dynamics


Ej = 2e52θj=0.05n=1cm^-3

van Eerten & AM (2011)


0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4

0

1

2

3

4

0 2 4 6 8

0

2

4

6

8

0 2 4 6 8 10

0

2

4

6

8

10

-6.8

-6.0

-5.3

-4.5

-3.8

-3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (

10^1

8 c

m)

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4x (10^18 cm)

0

1

2

3

4

y (

10^1

8 c

m)

0 2 4 6 8x (10^18 cm)

0

2

4

6

8

0 2 4 6 8 10x (10^18 cm)

0

2

4

6

8

10

log10e

(a)

147 days

(b)

256 days

(c)

372 days

(d)

970 days

(e)

27.6 years

(f)

150.3 years

0 0.19 0.79


1018

1019

R (

cm

)

(a)

0.01

0.10

1.00

10.00

!!v_

r

(b)

100 1000 10000Time (day)

10-6

10-4

10-2

100

e (

erg

/cm

^3)

(c)

Blandford- McKee

Sedov

θ = 0,0.19,π/4Granot+(2001)Zhang&AM(2009)vanEerten+(2010)Wygoda+(2011)deColle+(2012)Vlasis+ (2012)

θj = 0.2


DeColle+ (2012)

Zhang & AM (2009)


1e-05

0.0001

0.001

0.01

0.1

1

4e+06 4.2e+06 4.4e+06 4.6e+06 4.8e+06 5e+06 5.2e+06 5.4e+06

"max.dat" using 1:(abs($4-$8)/$8)"max.dat" using 1:(abs($5-$9)/$9)

"max.dat" using 1:(abs($6-$10)/$10)

70

75

80

85

90

95

100

105

110

115

120

4e+06 4.2e+06 4.4e+06 4.6e+06 4.8e+06 5e+06 5.2e+06 5.4e+06

"max.dat" using 1:4"max.dat" using 1:8

"max.dat" using 1:11

AM (in prep, 2012)

Γ

t (s)

Fractional errors in Γ, P, ρ

120

70

θjet=0.05Eiso=1e53

n=1

Blandford-McKee

2D Moving Mesh: Γ = 110

0

20

40

60

80

100

120

0 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 4e+06 4.5e+06


t

Γ

Analytic (Blandford-McKee; green)Numerical 2D on-axis (AM; red)


50

100

150

200

250

300

350

400

450

2e+06 2.2e+06 2.4e+06 2.6e+06 2.8e+06 3e+06 3.2e+06


"max.dat" using 1:11

Γ

t

Γ = 300

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 raysperpendicular to intersecting plane

Off-Axis Light Curves

θ=0 θ=0.1 θ=0.2

θ=0.4 θ=0.8 θ=π/2

1e9 Hz

1e17 Hz

van Eerten, Zhang & AM (ApJ, 2010)

A. MacFadyen (NYU)

On Axis

A. MacFadyen (NYU)

On Edge

A. MacFadyen (NYU)

Estimated Jet Break Timefor Off-Axis Observer

θ0

θobs

Theta_likely = 2/3 Theta_0

Analytical jet models are limited when it comes to e.g.:•Trans-relativistic deceleration of jets and emergence of the counterjet

•Fluid profile of spreading jets

•Off-axis observations (including orphan afterglows & slightly off-axis)

•Shape of the jet break in the light curve

Analytical models vs. numerical jet simulations

Analytical jet models are limited when it comes to e.g.:•Trans-relativistic deceleration of jets and emergence of the counterjet

•Fluid profile of spreading jets

•Off-axis observations (including orphan afterglows & slightly off-axis)

•Shape of the jet break in the light curve

Analytical models vs. numerical jet simulations

All these issues can be addressed by numerical simulations•High-resolution relativistic hydrodynamics, adaptive mesh-refinement with RAM

•radiative transfer for synchrotron radiation

•This talk: even complex 2D simulation results are scalable

•This talk: simulation-based broadband data fitting now possible

•This talk: a tool for improved survey predictions

Generic light curves optical & low radiojet has opening angle of 0.4 rad

Examples of afterglow light curves

GRB 990510 plus best fit

These are calculated by applyingradiative transfer to the jet simulation results

From AMR RHD simulation to light curve

Simulate for energy E, density n, opening angle θ, then synchrotron radiative transfer calculation

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

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, sinceenergy over density is a combination of cm and s)

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 waveimage: Landau & Lifshitz 1952

More on scalings 2 / 2


Scaling of Jet Dynamics

Calculate jet dynamics by applying scaling

Different E and n can be obtained by scaling: greatly reduces parameter space

Scalings, the full formulae

Calculate light curves by applying scaling

All light curves can be calculated by scaling a basic set for E and n


Calculate light curves by applying scaling

Once done, no reference to simulations necessary anymore!

summarizing: what scales and what doesn’t?Scales throughout the ejecta evolution:

Dynamics: Explosion energy (through observer time) Circumburst medium density (through observer time)

Radiation: magnetic field, particle energy, particle number fraction (i.e. they all scale, this is neither new nor unexpected)

Left in parameter space:Dynamics: initial jet opening angle circumburst density structure (‘k’ )

Radiation / observer position: observer angle [ transitions between spectral regimes, use sharp / smooth spectral powerlaws ]

This implies:1. Run simulations for different jet opening angles, and for wind and ISM2. calculate light curve characteristics for different observer angles3. collect resulting overview of parameter space and link to fit code / rate predictions etc.


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 0.0016 rad, one third of jet angle 0.0048 rad

Example application: characteristic behavior

In the top row: scaling works for all observer angles

In the bottom row: schematic synchrotron, synchrotron break frequency, cooling break frequency

new insight: characteristics change quickly following jet break

time (s)time (s)frequency

The ability to quickly generate light curves and GRB afterglows to probe parameter space...

generic low energy light curvesfor different angles and frequencies

(orphan afterglows? LOFAR, SKA? etc.)

Example application: generic light curves on-line

http://cosmo.nyu.edu/afterglowlibrary

On-line website with downloadable light curves:




http://cosmo.nyu.edu/afterglowlibrary/

Supported by NASA NNX10AF62G



Summary- Both jet dynamics and broadband light curves are scalable in energy in density

as a result we now can

- iteratively fit complex 2D simulation results to data (e.g. grb990510)

- calculate arbitrary parameter value light curves ‘on demand’

which is useful for exploring parameter space (i.e. surveys) and readily generalized to similar blast wave / jet phenomena: - both long and short GRB’s - supernova blast waves (talks Assaf Horesh, Laura Chomiuk) - tidal disruption jets (talk Brian Metzger) - ....?

all light curves, spectra, fit codes etc. available on-line:

(in the [near] future also fit code and continuous parameter space light curves)




Andrew MacFadyen (NYU/ITC) ITC Lunch Feb 24, 2011

MARA

Zrake & MacFadyen (2011)

A. MacFadyen (NYU) Fermi/Swift GRBs 2012, Munich 5/8/12Zrake & AM (2012)

Turbulent amplification of Magnetic Field

! B = 10-2


Conclusions• Jet Dynamics Scale• Light Curves Scale• Γ numerical ≳ 200 (≫1/θjet)• Fit data with full dynamics• tjet ⇒ θjet + θobs ⇒ Ejet ↓• http://cosmo.nyu.edu/afterglowlibrary

• Turbulence ⇒ εB = 10-2




ms variability + non-thermal spectrum

GRB Light Curves

M = E/ Γ c2 ~ 10-6 Msun

Compactness -> Г ≥ 100 Ultra-relativistic

Ultra-clean

SN2003dh

Matheson et al.

~0.5 Msun

Ni56

Tess

Duffel & AM (2011)


GRBs from Stars• Need ejecta to escape star before engine dies.

T_engine > T_escape• T_escape ~ 2 x T_light (~3 s = 10^11 cm)• T_engine >> T_dyn for BH or NS• T_ACCRETE ~ 20-100s s for massive star• Need angular momentum (not too much)• Need to lose H envelope -> WR progenitor and

Type Ibc supernova (if Ni56)

A. MacFadyen (NYU)

Collapsar - Disk and Jet• pre-SN 15 Msun Helium star• Newtonian Hydrodynamics (PPM)• alpha viscosity• rotation• photodisintegration (NSE alpha, n, p)• neutrino cooling, thermal + URCA optically thin• Ideal nucleons, radiation, relativistic degenerate electrons,

positions• 2D axisymmetric, spherical grid• self gravity • Rin = 9 Rs Rout = 9000 Rs

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