The Ep,i – Eiso correlation in the Swift era

Lorenzo Amati

(INAF/IASF BO, Bologna, Italy)

Outline

The Ep,i – Eiso correlation

Updated sample and re-analysis

The Ep,i – Eiso correlation and Swift GRBs

Main implications and uses

Systematics and selection effects

Future perspectives

The Ep,i – Eiso correlation

GRB spectra typically described by the empirical Band function with parameters = low-energy index, = high-energy index, E0=break energy

Ep = E0 x (2 + ) = peak energy of the F spectrum

. CGRO/BATSE (25-2000 keV): Ep values distibuted around 200

keV

BeppoSAX (2-700 keV) and HETE-2 (2-400 keV) measurements show that the Ep distribution is broader and extending towards low energy than inferred from BATSE

Sakamoto et al., ApJ, 2005Kippen et a., Woods Hole 2001, AIP Proc.

all GRBs with measured redshift (more than 60) are long and (except for the peculiar GRB980425) lie at cosmological distances (z = 0.033 – 6.3) from distance, fluence and spectrum, it is possible to estimate the cosmologica-rest

farme peak energy Ep,i and the radiated energy assuming isotropic emission, Eiso

Ep,i and Eiso distributions for a sample of 41 long GRBs (Amati 2006)

Ep,i = Ep x (1 + z)

log(Ep,i )= 2.52 ,

= 0.43

log(Eiso)= 1.0 ,

= 0.9

Amati et al. (2002) analyzed a sample of 12 BeppoSAX events with known redshift

we found evidence of a strong correlation between Ep,i and Eiso

, highly significant ( = 0.949, chance prob. 0.005%) despite the low number of GRBs included in the sample

Ep,i = kEiso

(0.52+/-0.06)

Amati et al. , A&A, 2002

HETE-2 data confirm the Ep,i – Eiso correlation and show that it extends to XRFs, thus spanning 5 orders of magnitude in Eiso and 3 orders of magnitude in Ep,i

Lamb et al., ApJ, 2004

90% c.l. Ep of XRF020903 from refined analysis of HETE-2 WXM + FREGATE spectrum (Sakamoto et al. 2004) fully consistent with the Ep,i – Eiso correlation

Amati, ChJAA, 2003

by adding data from BATSE and HETE-2 of 10 more GRBs the correlation was confirmed and its significance increased

From Amati (2006)

increasing the sample of GRBs with known z and firm estimate of Ep,i increases the significance of the correlation

the correlation is characterized by a substantial dispersion, as indicated by the high chi-square values of the fits with a power-law

due to the scatter of the data around the best fit power-law, different sub-samples give different values of the power-law index (~0.4 – 0.6)

what about short GRBs ? Their fluence / spectral hardness indicated likely inconsistency with Ep,I – Eiso correlation

the Ep,i and Eiso values of sub-energetic and GRB/SN prototype event GRB980425/SN1998bw (z=0.008) are inconsistent with the correlation

this may also be true for the other sub-energetic event GRB031203 / SN2003lw, but ISGRI Ep,i lower limit is debated, based on dust echo measured by XMM

evidence of a sub-class of GRBs ? particular viewing conditions ?

980425

031203

analysis of the most updated sample of long GRBs/XRFs with firm estimates of z and Ep,i (41 events including 8 Swift GRBs) gives a chance probability for the Ep,i-Eiso correlation of ~10-15 and a slope of 0.57+/-0.02

the scatter of the data around the best fit power-law can be fitted with a Gaussian with (logEp,i) ~ 0.2

Amati (2006)

Updated sample and re-analysis

the “extra-statistical scatter” of the data was quantified by performing a fit whith a method (D’Agostini 2005) which accounts for sample variance

the “intrinsic” dispersion results to be int(logEp,i) = 0.14 (-0.02,+0.03)

with this method, the power-law index and normalization turn out to be ~0.5 and ~100, respectively (the commonly assumed values !)

Amati (2006)

also unfirm estimates or upper/lower limits to Ep,i are consistent with the Ep,i – Eiso correlation

two recently localized short GRBs with known z and firm esitmate of Ep,i: GRB050709 (detection and spectrum by HETE-2) and GRB051221 (detection by Swift, spectrum from konus)

they are inconsistent with the correlation (as expected from their different distribution in the hardness/intensity plane with respect to long GRBs)

Adapted from Amati (2006)

BAT sensitivity better than BATSE for Ep < ~100 keV, slightly worse than BATSE for Ep > ~100 keV but better than BeppoSAX/GRBM and HETE-2/FREGATE -> more complete coverage of the Ep-Fluence plane

The Ep,i – Eiso correlation and Swift GRBs

Band (2003, 2006)

SAX/GRBM HETE-2/FREGATE

CGRO/BATSE Swift/BAT

fast (~1 min) and accurate localization (few arcesc) of GRBs -> prompt optical follow-up with large telescopes -> substantial increase of redshift estimates and reduction of selection effects in the sample of GRBs with known redshift

fast slew -> observation of a part (or most, for very long GRBs) of prompt emission down to 0.2 keV with unprecedented sensitivity –> following complete spectra evolution, detection and modelization of low-energy absorption/emission features -> better estimate of Ep for soft GRBs

BAT “narrow” energy band allow to estimate Ep only for ~15-20% of GRBs (but for some of them Ep from HETE-2 and/or Konus

GRB060124, Romano et al., A&A, 2006

all long Swift GRBs with known redshift and firm estimate of Ep,i (13 events up to now) are consistent with the Ep,i-Eiso correlation

most remarkable cases: XRF050416a (bridging normal GRBs with XRFs, Sakamoto et al. 2006), GRB060218 (a sub energetic GRB consistent with the correlation, Amati et al. 2006, Ghisellini et al. 2006) and GRB051221 (a short GRB inconsistent with the correlation)

short

sub-en.

XRFs

both the closest (GRB060218, z = 0.033) and farthest (GRB050904, z = 6.29) events are consistent with the correlation

upper/lower limits to Ep,i of Swift GRBs with known redshift are consistent with the correlation

a preliminary analysis of BAT time integrated spectra of Swift GRBs with unknown redshift shows that most (if not all) cases for which an Ep estimate is possible are potentially consistent

GRB prompt emission physics physics of prompt emission still not settled, various scenarios: SSM internal shocks, IC-dominated internal shocks, external shocks, photospheric emission dominated models, kinetic energy dominated fireball , poynting flux dominated fireball)

e.g., Ep,i -2 L1/2 t-1 for syncrotron emission from a power-law distribution of electrons generated in an internal shock (Zhang & Meszaros 2002, Ryde 2005)

e.g., Ep,i Tpk 2 L-1/4 or

under different assumptions and to be combined with and in scenarios in whch for comptonized thermal emission from the photosphere dominates (e.g. Rees & Meszaros 2005)

Implications and uses of the Ep,i – Eiso correlation

Zhang & Meszaros, ApJ, 2002

more in general, Ep,i M and Eiso N , with M and N varying in each scenario and for different set of parameters within each scenario -> positive correlation between Ep,i – Eiso and its slope constrain parameters ranges in each scenario

also the extension in Ep.i of the correlation puts constraints on prompt emission models, showing that the distribution of Ep,i is much broader than thought before (e.g. zhang & Meszaros 2002, Asano & Kobayashi 2004)

in general, the Ep,i, - Eiso correlation is often used as input or required output for GRB synthesis models

GRB/XRF unification models and jet structure

the validity of the Ep,i– Eiso correlation from the brightest GRBs to XRFs confirms that XRFs puts constraints on jet and GRB/XRF unification models

two main jet flavours: uniform (e.g. Lamb et al. 2005, jet variable, Eiso and Ep,i constant for vjet and 0 otherwise) and universal structured (e.g. Rossi et al. 2002, jet ~ universal, Eiso and Ep,i depend on v Eiso spans more than 5 orders of magnitude while

is clustered around ~(0.5-1) x1051 erg) -> Eiso jet-2

for uniform

jets; Eiso v-2 for strucured jets

Lamb et al. (2004): in order to explain the Ep – Eiso correlation from brightest/hardest GRBs to XRFs the universal structured jet scenarios require N(XRF)/N(GRB) much higher than observed (~1/3)

Lamb et al. (2004): by assuming N(jet) ~ jet-2 the uniform jet scenario can explain the observed extension of the Ep – Eiso correlation and predicts a rate of GRBs that could be comparable to that of SN Ic

Lamb et al., ApJ, 2005

Uniform/variable

PL-structured /universal

Zhang et al. (2004): in the uniform jet scenario the Ep – Eiso correlation from brightest/hardest GRBs to XRFs requires that most GRBs have collimation angles <1° , implying values of the fireball kinetic energy much higher and/or values of the interstellar medium density much lower than estimated from the afterglow light curves

the quasi-universal gaussian structured jet scenario (e.g. Zhang et al. 2004, Lloyd-Roning et al. 2004): more in agreement with collapsar numerical simulations and predicts N(XRF)/N(GRB) in agreement with the observed one

Fisher-shape structured jets (with both ~universal or variable opening angle) reproduce the Ep,i – Eiso correlation, predict an equal number of GRBs per logarithmic Eiso interval and a broader distribution of E

Quasi-gaussian universal, Zhang et al., ApJ, 2004

Fisher-universal, Donaghy et al., ApJ, 2005

off-axis scenarios

when the viewing angle exceeds the jet opening angle both Ep,i and Eiso decrease dramatically and we observe normal GRBs as very soft and weak events (i.e. XRFs), due to relativistic beaming and Doppler effects extension to XRFs of the Ep,i-Eiso correlation Yamazaki et al. (2004):

=[(1 - cos(v - ))]-1

Ep Eiso ) -> Ep Eiso(1+)

=1÷2.3 -> Ep(v) Eiso(v)0.5÷0.3

other scenarios based on a combination of jet structure and viewing angle include: ring shaped fireball (Eichler & Levinson 2004), multi component jets / subjets (e.g. Toma et al. 2005) cannonball model (Dar, Dado, et al.)

Yamazaki et al., ApJ, 2004

sub-energetic GRBs and the GRB/SN connection

the other GRB/SN events (e.g. GRB030329 /SN2003dh) are consistent with the Ep,i-Eiso correlation

the Ep and Eiso values of the sub-energetic and GRB/SN prototype event GRB980425/SN1998bw (z=0.008) are inconsistent with the correlation

it has been claimed that this is true also for the other sub-energetic event GRB031203 / SN2003lw, but ISGRI Ep lower limit is debated, based on dust echo measured by XMM

the most common explanations for the (apparent ?) sub-energetic nature of GRB980425 and GRB031203 and their violation of the Ep,i – Eiso correlation are based on peculiar viewing conditions (e.g. Yamazaki et al. 2003, Ramirez-Ruiz et al. 2005) BUT….

Amati, MemSAIT 2004

this evidence, together with the chromatic behavior of its afterglow, suggest that this is not a very off-axis event (as suggested for GRB80425 and GRB031203)

Swift GRB060218 : a sub-energetic GRB, with prominent association to SN2006aj, the closest (z=0.033) after GRB990425/SN1998bw, is consistent with the Ep,i-Eiso correlation !

evidence that GRBs truly sub-energetic exist !

GRB060218 is the first GRB with Eiso /Ek,SN << 1 consistent with the correlation -> evidence of a population of GRBs whose energy is just a small fluctuation of that of the SN explosion

pushed to re-consider the hypothesis that GRB980425 and GRB031203 are truly sub-energetic

e.g. Ghisellini et al. (2006): deviation of GRB980425 and GRB031203 from the Ep,i-Eiso correlation may be due to scattering material with large optical depth along the line of sight (decrease Eiso and increase Ep,i) or undetected hard to soft spectral evolution

double-peak interpretation (e.g. Dado and Dar 2004): in GRB980425 and GRB031203 we are seeing the high energy peak due to Compton up-scatter of UV photons by CR electrons accelerated by SN jets

only very recently, redshift estimates for short GRBs

estimates of both Ep,i and Eiso are available for GRB050709 (HETE-2, z=0.16) and GRB051221 (z=0.55) are inconsistent with Ep,i-Eiso correlation holding for long GRBs

low Eiso values and high lower limits to Ep,i indicate inconsistency also for the other short GRBs

spectra of short GRBs consistent with those of long GRBs in the first 1-2 s: only first ~thermal part of the emission and lack or weakness (e.g. due to very high for internal shocks or low density medium for external shock) of long part

long weak soft emission in some cases

Ep,i – Eiso correlation and short GRBs

Ghirlanda et al. (2004)

Ep,i-Eiso correlation characterized by an overall dispersion of (logEp,i) ~ 0.2 (and an extra-statistical dispersion quantified to be

int(logEp,i) = 0.14 (-0.02,+0.03)

by substituting Eiso with the collimation corrected energy E or introducing directly tb, the correlation still holds, with a lower dispersion and a steeper slope (Ghirlanda et al. 2004, Dai et al. 2004)

the intrinsic dispersion of the Ep,i-Eiso correlation

in any case, these evidences suggest that that at least part of the dispersion of the Ep,i-Eiso correlation is due to the spread in jet opening angles (if break in the optical afterglow is linked to the jet opening angle)

other possible sources of the dispersion include: dispersion in the parameters of the fireball (like e.g. , tvar) , viewing angle effects (e.g. Levinson & Eichler 2005), inhomogeneous structure of the jet (e.g. multi-subjet model by Toma et al.), the presence of signifcant amount of material along the line of sight (e.g. Longo et al. 2005)

a low dispersion correlation between Ep,i, Lpeak and varability has been recently found, also based on still small number of events (Firmani et al. 2006)

differently from the Ep,i-Eiso correlation, the Ep,i-E and Ep,i-Eiso-tb correlations can be studied for only a fraction of events (a firm estimate of tb is needed), there are possible outliers (in addition to 980425 and 031203)

Swift: in several cases lack of jet break in X-ray afterglow simultaneous to the optical break

use of the Ep,i – Eiso to construct GRB redshift estimators (es. Atteia, 2003, Pelangeon et al. ): pseudo-redshift of HETE-2 bursts published in GCN

use of the spectral-energy correlation to infer the star formation rate (SFR) evolution , e.g.Yonetoku et al., 2004 , Firmani et al. 2004)

use of the Ep,i – Eiso correlation to infer the jet angle probability distribution (e.g. Liang et al. 2004, Bosnjak et al 2004)

Ep,i – Eiso correlation is often used in GRB synthesis simulations as an input or a required output

uses of the Ep,i – Eiso correlation

Atteia, A&A, 2003

Liang et al. 2004

use of the Ep,i-E , Ep,i-Eiso-tb correlations for the estimate of cosmological parameters

Ghirlanda et al.,ApJ, 2004

cautions

a) based on a still low number of events (and the Ep,i-E requires assumptions on the density and distribution of the circum-burst environment and on the kinematic to radiated energy conversion efficiency)

b) circularity problem

c) physics underlying these correlations still not settled new correlation bewteen Ep,i, Lpeak and variability (Firmani et al. 2006) seems promising (only prompt properties) but still low number of events

Systematics and selection effects

Nakar & Piran and Band & Preece 2005: a substantial fraction (50-90%) of BATSE GRBs without known redshift are potentially inconsistent with the Ep,i-Eiso correlation for any redshift value

they suggest that the correlation is an artifact of selection effects introduced by the steps leading to z estimates: we are measuring the redshift only of those GRBs which follow the correlation

they predict that Swift will detect several GRBs with Ep,i and Eiso inconsistent with the Ep,i-Eiso correlation

BUT…

up to now, all long Swift GRBs with known z show Ep,i (values or upper/lower limits) and Eiso values consistent with the Ep,i-Eiso correlation

Ghirlanda et al. (2005), Bosnjak et al. (2005), Pizzichini et al. (2005): most BATSE GRB with unknown redshift are consistent with the Ep,i-Eiso correlation

Ghirlanda et al., ApJ, 2005

consider BATSE 25-2000 keV fluences and spectra for 350 bright GRBs

Ep,i = K x Eisom , Ep,i = Ep x (1+z), Eiso=(Sx4DL2)/(1+z)

Ep,i-Eiso correlation re-fitted by computing Eiso from 25*(1+z) to 2000*(1+z) gives K ~100, m ~0.54 , (logEp,i) ~ 0.2, Kmax,2 ~ 250

-> Smin,n = min[(1+z)2.85/(4DL2)] x (Ep/Kmax,n)

1.85 (min. for z = 3.8)

Adapted from Kaneko et al., MNRAS, 2006

2

only a small fraction (and with substantial uncertainties in Ep) is below the 2 limit !

moreover (1): estimates of Ep,i of several BATSE GRBs may be biased by the lack detection of the X-ray emission, which can contribute significantly to the time-integrated spectrum -> overestimate of Ep,i moreover (2): for dim GRBs we may observe only the brightest and hardest portion of the event -> overestimate of Ep,i

BeppoSAX GRB960720 Swift GRB060124

opposite conclusions mostly due to accounting or not for correlation dispersion and errors on Ep,i , different rest-frame energy bands used for computation of Eiso, considering the Ep,i – Eiso correlation a ‘law’ instead of accounting for its intrinsic dispersion of ~0.2 dex in log(Ep,i)

BATSE Ep,i values of several events could be overestimated because of the >25 keV energy band (as indicated by BeppoSAX, HETE-2 and Swift/XRT measurements)

Swift/BAT has a sensitivity only slightly worse than BATSE and better than SAX/GRBM and HETE-2/FREGATE) for Ep > 100 keV and better than BATSE for Ep < 100 keV : all Swift long GRBs / XRFs with known z are and Ep,i are consistent with the Ep,i-Eiso correlation

existence of a sub-class of GRBs not following the Ep,i – Eiso (like e.g. GRB980425 and possibly GRB031203) because of intrinsic properties or peculiar viewing conditions or other effects (like e.g. large optical depth material along the line of sight) is anyway possible

The only unambiguous and safe test of the Ep – Eiso correlation (and of the other spectral energy correlations) can be done by increasing the number of GRBs with firm estimates of z and Ep

In some cases, Ep estimates form different instruments are inconsistent with each other -> particular attention has to be paid to systematics in the estimate of Ep (limitd energy band, data truncation effects, detectors sensitivities as a function of energies, etc.)

the fixed 1-10000 keV energy band on which is computed Eiso could not be optimal -> energy band centerd on Ep,i or larger fixed energy band (e.g. 0.01 – 100000)

see poster by Landi et al.

Future perspectives to test the correlation, to better constrain its slope, normalization and dispersion (test of GRB/XRF prompt emission physics and geometry), to identify and understand sub-energetic GRBs and short GRBs, to calibrate spectral-energy correlation for cosmological use, need to

increase the number of z estimates, reduce selection effects and optimize coverage of the fluence-Ep plane in the sample of GRBs with known redshift

more accurate estimates of Ep,i by means of sensitive spectroscopy of GRB prompt emission from a few keV (or even below) and up to at least ~1 MeV

Swift is doing greatly the first job but cannot provide a high number of firm Ep estimates, due to BAT ‘narrow’ energy band (sensitive spectral analysis only from 15 up to ~200 keV)

Ep estimates for some Swift GRBs from HETE-2 (2-400 keV) and Konus (from 15 keV to several MeV) for simultaneously detected events

presently, Ep,i vaues are mainly provided by HETE-2 (but only up to 400 keV -> mostly CPL fits) or Konus/Wind (> 15 keV, fits with Band function); in some cases, useful spectral information also from BAT, Suzaku and INTEGRAL

some future and possible GRB experiments: AGILE and GLAST (2006, 2007) : study of GRBs form 10-20 keV up to tens or hundreds of GeV

ECLAIRs (2009) : spectral study of prompt emission in 4-300 keV and optical observation of prompt emission

Spectrum-RG/e-Rosita/Lobster (>2010 ?) : spectral study of GRB in the ~0.3-500 keV enegy band

ESTREMO/WXRT: Wide Field Monitor from a few keV to 500-700 keV need of new GRB detectors capable to extend down to a few keV (or even below) and up to at least ~1 MeV: e.g., a combination of a sensitive low energy detector (CZT, silicon microstrips or SDC diodes) and moderate area scintillator high energy detector (NaI, CsI, BGO)

THE END