Gamma-ray burst spctral volution in th intrnal shock modl in collaboration with: Žljka Marija Bošnjak Univrsity of Rijka, Croatia Frédéric Daign (Institut d Astrophysiqu d Paris) IAU$Symposium$324$0$Ljubljana,$Sptmbr$2016$
Prompt high nrgy mission in th framwork of intrnal shocks Γ Γ 1 > Γ 2 Γ γ Γ 1 Γ 2 m m Modling: 1. dynamics of intrnal shocks 2. radiativ procsss in th shockd mdium 3. obsrvd spctra and tim profils
Dynamics of th intrnal shocks Physical conditions in th shockd mdium: Lorntz factor Γ, comoving dnsity ρ*, comoving spcific nrgy dnsity ε* Lorntz factor of th shockd rgion Elctron Lorntz factor Lorntz factor in th outflow Magntic fild Dissipatd nrgy is distributd btwn protons, lctrons (fraction ε) and magntic fild (fraction εb)
Dynamics of th intrnal shocks Physical conditions in th shockd mdium: Lorntz factor Γ, comoving dnsity ρ*, comoving spcific nrgy dnsity ε* Rlativistic lctron dnsity: n'( Γ, t' = 0) Γ p Γ Γ m Lorntz factor of th shockd rgion Elctron Lorntz factor ζ < 1 of all lctrons is acclratd Magntic fild Dissipatd nrgy is distributd btwn protons, lctrons (fraction ε) and magntic fild (fraction εb)
Radiativ procsss Assumption: instantanous shock acclration Adiabatic cooling timscal: Radiativ timscal: t`x = R / Γ* c (comoving fram) t`rad t`rad << t`x high radiativ fficincy Elctron and photon distributions volv strongly with tim! Th prsnt vrsion of th cod follows th tim volution of th lctron dnsity and th photon dnsity including th following procsss: adiabatic cooling (sphrical xpansion) synchrotron invrs Compton synchrotron slf-absorption γγ annihilation Not includd: * mission from scondary lptons * IC in optically thick rgim (Comptonisation) ELECTRONS: n' ( Γ' t', t') = Γ' &- dγ' dγ' * # $ + syn+ ic + ad ( n'( Γ', t' )! %, dt' dt' ) " PHOTONS: n' t' ν = n'( Γ', t') Psyn ic ( Γ' ) dγ' cn' ν n'( Γ', t') σ abs ( Γ', ν) dγ' cn' ν + ν' > ( m c 2 ) 2 2 h ν n' ν' ( t') σ γγ ( ν, ν') dν'
Radiativ procsss Radiation: th tim volution of lctrons and photons in th comoving fram is solvd (tim-dpndnt radiativ cod) Slop -p Elctron distribution
Radiativ procsss Radiation: th tim volution of lctrons and photons in th comoving fram is solvd (tim-dpndnt radiativ cod) Comptonization paramtr Y = Lic / Lsyn IC dominant: low frquncy synchrotron pak Thomson rgim Synchrotron dominant: high frquncy synchrotron pak Klin-Nishina rgim Pak du to synchrotron radiation Pak du to IC γγ annihilation Slf-absorption Emittd photon spctrum This calculation is don at all tims along th propagation of ach shock wav All th contributions ar addd togthr to produc a synthtic gamma-ray burst (spctrum+lightcurv)
Obsrvd spctra and tim profils Th obsrvd spctra and th light curvs ar computd from th comoving mission by intgration ovr qual-arrival tim surfacs. rlativistic ffcts (Dopplr factor) gomtry (curvatur of th mitting surfac) cosmological ffct (rdshifts) photons /cm / s 2 tim [s] 50-300 kv Instantanous obsrvd spctrum: t = 0.8 s synchrotron invrs Compton total BATSE Frmi LAT
Obsrvd spctra and tim profils rlativistic ffcts (Dopplr factor) gomtry (curvatur of th mitting surfac) cosmological ffct (rdshifts) photons /cm 2 / s Th obsrvd spctra and th light curvs ar computd from th comoving mission by intgration ovr qual-arrival tim surfacs. 50-300 kv tim [s] Instantanous obsrvd spctrum: synchrotron invrs Compton total t = 2.8 0.8 s 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 BATSE Frmi LAT
Dominant radiativ procss in sub-mv rang? SYNCHROTRON CASE (B) low magntic fild 53-1 de/dt = 5 x 10 rg s, ε = 0.003, ε = 1/3, ζ = 0.003, p = 2.5, z=1 B GBM 8-260 kv BATSE Frmi/ LAT LAT 100 MV - 1 GV LAT > 1 GV Obsrvd lightcurv synchrotron invrs Compton total Obsrvd spctrum
Tmporal profils: > 100 MV bands Modl: in LAT (>100 MV) nrgy bands both componnts prsnt, synchrotron + IC LAT 100 MV - 1 GV synchrotron invrs Compton LAT > 1 GV Γmin tx [s] tsyn [s] wak shock ε* low modrat Γm larg tsyn R small tx R/Γ*c small tsyn tx larg fficincy of IC
Tmporal profils: > 100 MV bands Modl: in LAT (>100 MV) nrgy bands both componnts prsnt, synchrotron + IC LAT 100 MV - 1 GV synchrotron invrs Compton LAT > 1 GV max Γmin tx [s] tsyn [s] shock bcoms strongr Γm incrass tsyn dcrass R, tx incras tsyn tx low fficincy of IC dominant synchrotron componnt
Tmporal profils: > 100 MV bands Modl: in LAT (>100 MV) nrgy bands both componnts prsnt, synchrotron + IC LAT 100 MV - 1 GV synchrotron invrs Compton LAT 1 GV - 20 GV Γmin tx [s] tsyn [s] tail of th puls: B dcrass tsyn incrass tsyn tx incrasd fficincy of IC IC componnt dominant in GV
-3/2-2/3 Spctral proprtis 4-paramtrs Band spctrum Ep, α, β and normalization Band t al. 1993 α β α = -1.02 ± 0.27 pak nrgy Ep Briggs t al. 1999 β = -2.35 ± 0.27 Kanko t al. 2006
Spctral proprtis -2/3 νc -3/2 νm Sari, Piran & Narayan 1998 Synchrotron spctrum: fast cooling (γc < γm) photon flux -(p+2)/2 Rlativistic lctrons: dnsity γm -p νm νc frquncy Lorntz factor -2/3 Synchrotron spctrum: slow cooling (γc > γm) γm: minimum Lorntz factor at injction γc: radiativ timscal = dynamical timscal photon flux -(p+1)/2 -(p+2)/2 frquncy
Spctral proprtis 2 Normalizd E N(E) Band function α = - 1.5 β = - 2.25-1 Daign, Bosnjak & Dubus 2011 Drishv 2001 Invrs Compton scattrings in Klin-Nishina rgim hav an impact on th synchrotron slop
Spctral proprtis Thomson rgim: th lctron cooling rat du to IC scattrings rmains proportional to γ 2 as for th synchrotron powr KN rgim: th lctron cooling rat du to IC dpnds on γ Exact calculation with synchrotron + IC only (no adiabatic cooling, synchrotron slf-absorption, γγ annihilation)
High nrgy mission: light curvs Bosnjak & Daign 2014 Sharp initial Lorntz factor: Constant jctd mass flux: de/dt Γ
High nrgy mission: light curvs Bosnjak & Daign 2014 Sharp initial Lorntz factor: Constant jctd mass flux: de/dt Γ
Summary W dvlopd modling tools to comput th GRB prompt mission from intrnal shocks in a tim-dpndnt way in diffrnt spctral bands, including th high-nrgy gamma rays Th xploration of th paramtr spac shows that w can xpct two classs of broad-band spctra, which corrspond to diffrnt physical conditions in th shockd rgion: th synchrotron cas (whr th dominant procss in Frmi-GBM rang is synchrotron radiation) and th invrs Compton cas (whr th synchrotron componnt paks at low nrgy and th dominant procss in th GBM rang is invrs Compton) Frmi GRB obsrvations favor th synchrotron cas, with invrs Compton scattrings occurring in Klin-Nishina rgim. This scnario qualitativly rproducs th obsrvd spctral volution (HIC, HFC). W constrain th paramtrs of th modl (p, εb, ζ) in ordr to hav a quantitativ agrmnt Furthr dvlopmnts: currntly incorporating a mor ralistic scnario for th physical conditions in th shockd plasma and making prdictions for th CTA obsrvatory Bošnjak, Ž. IAU Symposium 324 - Ljubljana, Sptmbr 2016