Wind circumburst density profile: a linear E_p-E_gamma correlation

0.35 MB·English

by  L. Nava

IL NUOVOCIMENTO Vol. ?, N. ? ?
Wind circumburst density profile: a linear E -E correlation
p γ
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0 L.Nava( ),G.Ghisellini( ),G.Ghirlanda( ),F.Tavecchio( )andC.Firmani( )
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( ) Osservatorio Astronomico di Brera, Via Bianchi 46, I-23807 Merate Italy
n 2
a ( ) Instituto de Astronom´ıa, U.N.A.M., A.P. 70-264, 04510, M´exico, D.F., M´exico
J

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v Summary.— Ghirlandaet al. (2004) derivedthecollimation-corrected energy Eγ
forasampleof 15burstsundertheassumption ofahomogeneouscircumburstden-
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sityprofile. They found acorrelation (theso-called Ghirlandacorrelation) between
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4 Eγ and the rest frame peak energy of the νFν prompt spectrum (Ep). Nava et al.
1 (2006) showed that, assuming a circumburst density distribuited with a r−2 wind
0 profile, the Ghirlanda correlation remains tight and becomes linear. This implies
7 that: i) it remains linear also in the comoving frame, no matter the distribution
0 of bulk Lorentz factors, ii) it entails that different bursts have the same number of
/ relevantphotons. Wehaveupdatedthesefindingsincludingrecentlydetectedbursts
h
(21 in total), stressing thetwo important implications.
p
- PACS 98.70.Rz – Gamma-Ray bursts.
o
r
t
s
a
:
v
i
X 1. – The E -E correlation in the case of a homogeneous density profile
p γ
r
a Under the assumption that GRBs are collimated sources it is possible to estimate
the semiaperture angle of the jet θ . The main observational evidence in support of
j
this scenario is the presence of a break in the afterglow lightcurves. In order to derive
θ we need to know the jet break time t , the circumburst density n and the kinetic
j b
energyleft-overafter the promptphase. The relationlinking these quantities is different
according to the circumburst density profile ([7],[2]). Ghirlanda et al. (2004) assumed
a homogeneous density profile (n = const) and derived the jets opening angles (from
the measurements of the steepening in the optical lightcurves for a sample of 15 GRBs
([3]). They found that E = E (1−cosθ ) correlate with the peak energy E and
γ γ,iso j p
thiscorrelationistighterthanthecorrelationbetweentheisotropicenergyE andE
γ,iso p
(Amati correlation,[1]). The updated versionofthe Ghirlandacorrelationis reportedin
Fig. 1.
2. – The E -E correlation in the case of a wind density profile
p γ
The assumption of a homogeneous circumburst medium contrasts with the present
modeloflongGRBsprogenitors,whicharethoughttobeverymassivestars. Infact,the
(cid:13)c Societa`ItalianadiFisica 1
2 L.NAVAETC.
Fig. 1. – The updated Ghirlanda correlation between the rest frame peak energy and the
collimation-corrected energy in the homogeneous case (left) and in the wind case (right). The
data are listed in Tab. 1 and Tab. 2 of [6]. In addition there are three new bursts (circled
points): GRB 050820a, GRB 051022 and GRB 060124.
intense stellar wind, typical of very massive stars, should produce a circumburst density
profile which scales as n ∝ r−2. Nava et al. (2006) derived the jet opening angle θ
j,w
(andthereforethecollimation-correctedenergyE )forasampleof18burstsunderthe
γ,w
assumpion of a wind density profile. They demonstrated that the collimation-corrected
energyE stillcorrelateswithE andthisnewlyfoundcorrelationhasaslightlysmaller
γ,w p
scatter (see Fig. 1) than that of the same correlation found under the homogeneous
mediumassumption. ThemostimportantpropertyoftheE −E relationinthewind
p γ,w
case is its linearity: E ∝E .
p γ,w
The finding ofa linear E -E correlationrevealsanintriguingproperty: since both
p γ,w
E and E , being “energies”, transform in the same way (i.e. ∝Γ−1) from the source
p γ,w
rest frame to the comoving frame, the slope of the correlation is ”invariant”. Moreover,
the linear E −E correlation implies that the E /E ratio, which represents the
p γ,w γ,w p
number of relevant photons, is constant from burst to burst and its value is ∼ 1057.
Finally,thetighterandsteeperE −E correlationfoundinthe windcasecanbeused
p γ,w
to constrain the cosmological parameters (see [5]), similarly to what has done with the
E −E correlation in the homogeneous case ([4]).
p γ
REFERENCES
[1] Amati, L., Frontera, F., Tavani, M., et al., A&A,390 (2002) 81.
[2] Chevalier, R.A. & Li, Z.Y., ApJ, 536 (2000) 195.
[3] Ghirlanda, G., Ghisellini, G. & Lazzati, D.,ApJ, 616 (2004) 331.
[4] Ghirlanda, G., Ghisellini, G., Lazzati, D. & Firmani, C., ApJ, 613 (2004) L13.
[5] Ghirlanda, G., Ghisellini, G., Firmani, C., Nava, L., Tavecchio, F. & Lazzati, D.,
ApJ, 452 (2004) 839.
WINDCIRCUMBURSTDENSITYPROFILE:ALINEAREP-Eγ CORRELATION 3
[6] Nava, L., Ghisellini, G., Ghirlanda, G., et al., A&A,450 (2006) 471.
[7] Sari, R.,ApJ, 519 (1999) L17.