Photospheric thermal radiation from GRB collapsar jets

Akira MIZUTA(KEK) AM, Nagataki, Aoi (ApJ, 732 26, 2011) AM, Nagataki, Ioka (in prep)

1.Gamma-ray burst (GRB)2.Model3.Hydrodynamics4.Thermal radiation Light curve, spectrum,5.Amati relation6.Summary

HEPROIIIBarcelona11.06.27 -07.01

Long GRB-SN connection Association long duration GRB-SN is observed.ex. GRB980425/SN1998bw, GRB030329/SN2003dh XRF060218/SN2006aj. GRB091127/SN2009nz XRF100316D/SN2010bhThe explosion energy of most SN-GRB is 10 times higher than thatof normal Sne (HyprenovaeE=1052erg)

power law : afterglow

SN componentappears

Spectrum :after a few days ~ after a month from the burst

time

Progenitor mass

Explosionenergy

λ(A)

Mazzali et al. (2006)

GRB090902B Ryde et al (2010)thermal component wasfound.

Spectrum of GRB prompt emissionBand function: Broken power-law

α~-1Band functionBand et al.(1993)

β~ -2.3

Briggs et al. (1999)

νν3

ν-0.5

Plankian How can the photospheric thermal radiation be seen ? light curve, spectrum viewing angle effect --jet like explosion

Non-thermal radiation is expected.There is no theoretical modelto explain the index for low energy band.

Method : HydrodynamicsModel

Jet : t [0:100s]Power: 5.5x1050 erg/sLorentz factor :Γ0 = 5specific internal energy : ε0/c2=80half opening angle : θ0= 10/ 5 degrees

Very low densitywind ρ r∝ -2

Progenitorsurface

Radial mass profileProgenitor: Model 16TI Woosley & Heger (2006) 14 solar mass at pre-SN stage. Radius:4x1010cmOutside progenitor:Wind like distribution ρ r∝ -2

very low density : optically thin

Computational Domain : 2D (r x θ) spherical (109cm<r<3x1013cm 　 0<θ<π/2) (c.f. jet formation ~10^7cmequatorial plane symmetry2D-relativistic hydrodynamic code(constant specific heat ratio=4/3) approximate Riemann solver,2nd order accuracy in space & time Mizuta et al. (2004,2006)

1.e12 r (cm)

1.e111.e101.e9

Log ρ

movie

internal shocks

BackflowInteraction betweenjet and progenitorenvelopes.

High pressure cocoonconfinement anda bent backflowenhance theappearanceof internal obliqueshocks.The jet includesknotty structure.

log10(ρ/cm^3)

Γ

Shock-break

AM, Kino, Nagakura('10)

progenitor

Expanding envelopes

jet

Expanding cocoon

Jet propagation ~cExpansion of cocoon,and shocked envelopes~c_s(~0.5c)

The head of the jet isRelaxed. LateralExpansion is observed.

The density andPressure of theExpanding envelopesDecrease, as time goeson.

Free expansion is possible for the jetsinjected later.

log10(ρ/cm^3)

Γ

After shock-break I　　r~10^11cm

Maximum Lorentz factorappears in the freeexpansion region~500(=Γ0*h0=533)

Hot Bubbledissipated

Cold Bulletfree expansionno dissiparion

log10(ρ/cm^3)

Γ

After shock-break II

r~10^12 cm

Recollimation shock

Method : Thermal Radiation from the jet.Step1. Remapping 2D hydor-data into 3D box using the assumptionof axisymmetry

Step2. Assuming the observer is at infinity, prepare a screen outsidethe computational box and consider photon rays perpendicular to thescreen

Step.3 calculate the optical depth along the photon rays until τ becomesunity where is the photo-sphere for Thomson scattering.

(Abramowicz et al.1991) is unit vector which is parallel to LOS n : electron number density 2 ρ/m_He Step4. Calculate the blackbody luminosity for each elementsAnd integrate them

T is the local temperature derived from p=aT4/3

(τ＝１)

1/beaming factor ~ 1/Γ (for β // n: LOS)

Mass density, Lorentzfactor, and photospherecontours.

Γ

Γ

Γ

log10(ρ)

log10(ρ)

Since the denisty is lowAnd the beaming factorIs high near the jet axis,The photospere is quiteConcave shape.

The arrival time of theRadiation from innerPhotosphre to the observerIs expected to delay inthe light curve

~c

log10(ρ)

Γ

Light curveDuration of light curve ~ jet injection.A few seconds time variabilityIn early phase caused by Internal discontinuity in the jet.

Dissipated region Free expanding region

Morsony et al..’07Lazzati et al.‘11

Spectrum Constructed by superposition of Plankian (local temp.) boosted by beaming factor δ (relativisticeffect)

Peak energy shiftsto low energy band,as the observer moves to off-axis.

Multicolor contributioncan be applied to explain this propertycf. multicolor modelapplied to accretiondisk model

Up-scattering via Inverse Compton Is necessary

GRB090926B?

Rayleigh-Jeans tail

Cold Bulletfree expansion

The length of both coldbullet and hot bubbledoes not change soMuch at the scale of1012-13cm

dissipated (hot bubble)region length/c ~bright phase in lightcurve

θ0=10degreesΓ

θ0=5degreesΓ

Cold bullet shouldbe short for largerradiative efficiency.

Stray bullet problem?

Cold Bulletfree expandion

ε0,Γ0,dE/dt constant 4 times dense model θ0=10 defrees top θ0=5 2degrees bottom

OA10

OA05

Lazzati et al. (2011)also observes same trend

θv small

Lazzati et al. ‘11 ApJ submitted

Amati Relation (Amati 2002,2006)

05

Conclusion●Light curves and spectrum of photospheric thermal radiation is derived from numerical hydrodynamic simulations of relativistic jets from collapsars.

●Isotropic luminosity is comparable to GRB prompt emission. time variability in a few seconds is observed.

●spectrum has a peak energy and spectrum power law indexis much softer than that of single temperature single Plank distribution, i.e., “multi-colored”. The index is comparable foroff-axis cases and 2.0-2.5 for on-axis case (θv~0-2 degrees).

● We observed “numerical” Amati relation relation.It is interesting to extend jet parameters and to develop theoretical models.