GRBs and Magnetic FieldsGRBs and Magnetic Fields

Shiho Kobayashi （小林史歩）Liverpool John Moores University

• Early afterglow: – RS and FS modeling– (Synchrotron and IC)– Early polarimetric measurements– Ejecta structure: Optical/X-ray polarimetry

How to constraint How to constraint the magnetization (and structure) of GRB ejectathe magnetization (and structure) of GRB ejecta

• Origin of Magnetic fields – prompt ~10^6G, afterglow ~ 1G

• How to accelerate and collimate jets?– gamma>100, E=10^52 ergs

• How to produce prompt gamma-rays– internal shocks/efficiency issue

• Lack of optical flash in most events – magnetic pressure?, SSC?

(Medvedev&Loeb1999; Nishikawa et al. 2008; Gruzinov 2001; Milosavljevic et al. 2006…)

(Usov 1992; Meszaros&Rees1997;Lyutikov &Blandford 2002; Drenkhahn& Spruit 2002..)

(Kumar1999; Beloborodov2000; SK&Sari2000;Zhang et a. 2006; Nousek et al. 2006)

(Akerlof et al. 2000; Roming et al. 2006..)

the synchrotron shock model is successful, but there are some open questions …

Magnetized jet model might solve these.

The Standard model

relativistic outflow (ejecta from central engine) Blastwave

(FS ambient medium)€

R ≈1015−17cm

Emission from Ejecta:Prompt gamma-raysOptical Flashes

Radio Flares?X-ray Flares?

Emission from BlastwaveAfterglows (X/Opt/Radio)

Insensitive to the properties of the original ejecta

Energy transfer

Forward ShockReverse Shock

５

ejecta

Method 1: RS and FS modeling

At the deceleration time (onset of afterglow)

The deceleration happens when a significant fraction of the ejecta energy is given to the forward shock region.

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Γ,e,ΔShocked −ejecta

≈ Γ,e,ΔFS−Ambient

€

Mejecta = ΓMFS−Ambient

• RS region: energy per particle smaller by

• cooling frequencies comparable

• the number of electrons is proportional to mass

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Γ

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ν syn ∝ γ e,random2

ν m, f (tdec ) ≈ Γ 2ν m,r(tdec )

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ν c ∝Γγ c2B, γ c ∝1/ΓB2t, B2 ∝ e

ν c, f (tdec ) ≈ ν c,r(tdec )

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Fmax ∝NeΓB

Fmax, f ≈ Γ−1Fmax,r(tdec )

SK&Zhang2003

If RS region has higher magnetization or

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νm,r

ν m, f

≈ Γ−2RB1/ 2,

ν c,r

ν c, f

≈ RB−3 / 2,

Fmax,r

Fmax, f

≈ ΓRB1/ 2

RB = εB ,r /εB , f

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εBmagnetic energy density expressed as a fraction of the equipartion vale

Zhang,SK&Meszaros 2003

Using these relations and theoretical decay indexes of FS and RS emission, we can model early afterglow

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ǙDZÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

Gomboc, SK, Guidorzi, Melandri, Mangano et al. 2008

GRB 061126

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t−1.65

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t−0.81

Optical Light curve

RS and FS modeling

RS region: higher magnetization, but still a baryonic jet

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RB = εB ,r /εB , f = 20 − 30

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εB , f =10−4 −10−2 Panaitescu&Kumar2002

GRB 990123, GRB 021211Zhang et al. 2003; Kumar&Panaitescu2003Fan et al. 2005

Gomboc et al. 2008

Method 2: Sync and SSC emission

Wu’s talk yesterday

Synchrotron self-inverse Compton radiation from RS

the relative strength: Syn, 1st IC and 2nd IC componentsdepends on the Compton parameter

GLAST could give constraints on the magnetization of ejecta€

y = εe /εB ,r( )1/ 3

Kobayashi et al. 2007

Method 3: Polarization measurements

Magnetized jets : threaded with a globally ordered mag. fields which originated a the central engine, and advected outwards with the expanding flow.

Polarization measurements of the ejecta emission are very interesting!

Prompt gamma-rays: Coburn&Boggs2003: controversial

Reverse shock emission -- optical flash: Mundell et al. 2007 -- radio flares: Granot&Taylor2005

X-ray flares?: in the near future?

Radio FlaresReverse shock ejecta cools adiavatically and radiatesat lower and lower freqs at later times. The emission peaks in the radio after about 1day

VLA dataLinear polarization

GRB 990123: P<23% at 1.25daysGRB 991216: P<11% at 1.49days P< 9% at 2.68daysGRB 020405: P<11% at 1-2days

Granot&Taylor2005

Early polarization measurements: opticalEarly polarization measurements: optical

• Polarimeter on our 2m robotic telescope

Liverpool telescope

GRB 060418

• Afterglow polarization measurement– 200 sec after the start of prompt gamma-ray– At the onset of afterglow (12mag)– Polarization: 8% upper limit

Mundell et al. 2007

Molinari et al. 2006

IR(REM), XRT

Optical(LT)

IR: smooth rise fading away with a unbroken power-law

the lack of color change: steep riseit is not due to the passage of the typical frequencyof the forward shock emission

Onset of the afterglow should be below optical at that time

~50% photons come from RS

If RS region has global mag fields, we expectstrong polarization.

ruling out the presense of a large-scle mag. fieldsin the emitting region.

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Fν ∝ t 2.7

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Fν ∝ t−1.2

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νm, f

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νm, f

Ruling out the presence of a large-scale mag. fields in the emitting region.

Ruling out the presence of a large-scale mag. fields in the ejecta.

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{

Poynting-flux dominated jets:high magnetic pressure might suppress RS.

No shock. No RS emission. No Polarization(the peak might contain only FS emission)

Our results still allow Poynting-flux dominated jets

Reconnections?L

t

• If we detect high polarization in early early afterglow…

– a large-scale mag. fields in the ejecta?– How fireball jet structure affects the conclusion?

Large Polarization

Waxman 2003

a) Magnetic field is ordered.b) Random Magnetic field+ Specific viewing angle The line-of-sight to GRB runs along the edge of a jet cone.

Random Magnetic fields generated by instabilities

The mag fields parallel and perpendicular to the shock normal could have significantly different averagedstrengths (Medvedev&Loeb1999)

Some degree of alignment if observed edge-on

If the slab is observed edge-on, the radiation is polarized!

Ghisellini & Lazzati 1999; Gruzinov1999;Sari1999;Granot2003;Nakar2004;Fan et al.2008…

If the emitting slab moves witha relativistic velocity,

we have to take into account the relativistic aberration of photons.

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comoving ′ θ = π /2⇒ lab θ =1/Γ

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Γ

It the line-of-sight to GRB runs along the edge of the jet cone, we might observe large polarization.

but it is rather rare to see a GRB from the preferable angle by chance.

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θ ≈1/Γ ≈10−3 −10−2

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θ jet_opening ≈10−1

Structured GRB Ejecta

• Initial angular distribution of Lorentz factor is not determined from late afterglow obs.

• Deceleration radius is a function of viewing angle.• Deceleration = the onset of afterglow

• At the onset of Afterglow, the line-of-sight runs along the edge of the emitting jet cone, polarized emission is expected!€

ε ∝θ−k, Γ ∝θ−g

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8g − k > 0

Jet decelerates around the center first.

Meszaros et al. 1999; Zhang&Meszaros2002;Rossi et al. 2002)

Granot&Kumar2003

L

t

a large-scale mag field in ejecta

optical

t

X-ray

Structured jets with random mag fields

t

optical

t

x-ray

Summary

• RS/FS modeling for a few early optical afterglows– magnetization in RS region is higher – still baryonic ejecta– no optical flashes detected in most cases

• ejecta magnetization changes from burst to burst???

• Optical Flash/Radio Flares– no presence of global magnetic fields in “the emission region”– still Poynting-flux dominated possible

• Need more polarization measurements (opt/X-ray/Gamma)– events with a clear optical flash peak

• Opt/X-ray Polarization measurements might constrain the structure of ejecta