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GRB physics and cosmology with the E p,i – E iso correlation

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GRB physics and cosmology with the Ep,i – Eiso correlation

Lorenzo Amati

INAF – IASF Bologna (Italy)

Third Stueckelberg Workshop

(July 8th to 19th, 2008 - Pescara, Italy)

- Observations
- Implications for GRB physics and origin
- Tests and debates
- Cosmology
- Conclusions and future perspectives

- GRB spectra typically described by the empirical Band function with parameters a= low-energy index, b= high-energy index, E0=break energy
- Ep = E0 x (2 + a) = observed peak energy of the nFn spectrum

since 1997 GRB redshift estimates through optical spectroscopy of afterglow emission and/or host galaxies

- all GRBs with measured redshift (~100) lie at cosmological distances (z = 0.033 – 6.4) (except for the peculiar GRB980425, z=0.0085)
- the pre-Swift GRB z distribution and the Swift GRB z distribution differ

from redshift, fluence and spectrum, it is possible to estimate the cosmological-rest frame peak energy, Ep,i, and the radiated energy assuming isotropic emission, Eiso

- isotropic luminosities and radiated energy are huge; both Ep,i and Eiso and span several orders of magnitude

Ep,i = Epx (1 + z)

log(Eiso)= 1.0 , s = 0.9

log(Ep,i )= 2.52 , s = 0.43

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

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 (r = 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

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

Amati, ChJAA, 2003

- 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

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

Lamb et al., ApJ, 2004

analysis of an updated sample of longGRBs/XRFs with firm estimates of z and Ep,i (41 events) 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 s(logEp,i) ~ 0.2 (~0.17 extra-poissonian)
- confirmed by the most recent analysis (more than 70 events, Ghirlanda et al. 2008, Amati et al. 2008)
- only firm outlier the local peculiar GRB 980425 (GRB 031203 debated)

Amati et al. 2008

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

- the “intrinsic” dispersion results to be sint(logEp,i) = 0.17 (-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)

3-parameters spectrum-energy correlations

- the Ep,i-Eiso correlation becomes tighter when adding a third observable: jet opening angle (qjet -> Eg = [1cos(qjet)]*Eiso(Ghirlanda et al. 2004), break time in optical afterglow decay (Liang & Zhang 2005) or “high signal time” T0.45 (Firmani et al. 2006)
- jet angle inferred from break time in optical afterglow decay, while Ep,i-Eiso-T0.45 correlation based on prompt emission properties only

Ep,i – Eiso correlation vs. 3-param correlations

- 3-parameters spectral energy correlation less dispersed than Ep,i-Eiso correlation
- but based on lower number of events (~20 against more than 60) -> need more events to be confirmed
- addition of a third observable introduces further uncertainties
- Ep-Eg correlation requires modeling; both Ep-Eg and Ep-Eiso-tb correlations requires afterglow detection and fine sampling
- Ep-Lp-T0.45 based only on prompt emission properties and requires no modelization

Recent debate on Swift outliers to the Ep-Eg correlation (including both GRB with no break and a few GRB with achromatic break)

- different conclusions based on light curve modeling and considering early or late break

Campana et al. 2007

Ghirlanda et al. 2007

Recent evidence, based on BeppoSAX and Swift GRBs that the dispersion of the Lp-Ep-T0.45 correlation is significantly higher than thought before

Rossi et al. 2008

Ep,i – Eiso

“Amati” 02

Eiso<->Lp,iso

Ep,i – Liso

04

Ep,i – Lp,iso

“Yonetoku”04

tb,opt + jet model

tb,opt

T0.45

=

Ep,i – Eg

“Ghirlanda” 04

Ep,i – Eiso-tb

“Liang-Zhang” 05

Ep,i – Lp,iso-T0.45

“Firmani” 06

The genealogy and nomenclature of spectrum-energy correlations

Origin of the Ep.i - Eiso correlation

- Ep is a fundamental parameter in prompt emission mdels, e.g., syncrotron shock emission models (SSM)
- it may correspond to a characteristic frequency (possibly nm in fast cooling regime) or to the temperature of the Maxwellian distribution of the e-

Sari et al., ApJ, 1998

Tavani, ApJ, 1995

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 G-2 L1/2 tn-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 G Tpk G2 L-1/4 in scenarios in whch for comptonized thermal emission from the photosphere dominates (e.g. Rees & Meszaros 2005, Thomson et al. 2006)

- XRF-GRB unification models
- viewing angle effects

Uniform/variable jet

PL-structured /universal jet

Uniform/variable jet

PL-structured /universal jet

Lamb et al., ApJ, 2004 , Yonetoku et al.,ApJ, 2004

The Ep,i – Eiso correlation and sub-energetic GRB

- GRB980425 not only prototype event of GRB/SN connection but closest GRB (z = 0.0085) and sub-energetic event (Eiso ~ 1048 erg, Ek,aft ~ 1050 erg)
- GRB031203: the most similar case to GRB980425/SN1998bw: very close (z = 0.105), SN2003lw, sub-energetic

Soderberg et al., Nature, 2003

Ghirlanda et al., 2007

the most common explanations for the (apparent ?) sub-energetic nature of GRB980425 and GRB031203 and their violation of the Ep,i – Eiso correlation assume that they are NORMAL events seen very off-axis (e.g. Yamazaki et al. 2003, Ramirez-Ruiz et al. 2005)

- d=[g(1 - bcos(qv - Dq))]-1 , DEp d , DEiso d(1+a)

a=1÷2.3 -> DEiso d(2 ÷3.3)

Yamazaki et al., ApJ, 2003

Ramirez-Ruiz et al., ApJ, 2004

GRB 060218, a very close (z = 0.033, second only to GRB9809425), with a prominent association with SN2006aj, and very low Eiso (6 x 1049 erg) and Ek,aft -> very similar to GRB980425 and GRB031203

- but, contrary to GRB980425 and (possibly) GRB031203, GRB060218 is consistent with the Ep,i-Eiso correlation -> evidence that it is a truly sub-energetic GRB
- also XRF 020903 is very weak and soft (sub-energetic GRB prompt emission) and is consistent with the Ep-Eiso correlation

Amati et al., A&A, 2007

GRB060218 was a very long event (~3000 s) and without XRT mesurement (0.3-10 keV) Ep,i would have been over-estimated and found to be inconsistent with the Ep,i-Eiso correlation

- Ghisellini et al. (2006) found that a spectral evolution model based on GRB060218 can be applied to GRB980425 and GRB031203, showing that these two events may be also consistent with the Ep,i-Eiso correlation
- sub-energetic GRB consistent with the correlation; apparent outliers(s) GRB 980425 (GRB 031203) could be due to viewing angle or instrumental effect

Ep,i – Eiso correlation and short GRBs

- only very recently, redshift estimates for short GRBs
- all SHORT Swift GRBs with known redshift and lower limits to Ep.i are inconsistent with the Ep,i-Eiso correlation
- intriguingly, the soft tail of GRB050724 is consistent with the correlation

Amati, NCimB, 2006

confirmation of expectations based on the fact that short GRBs are harder and have a lower fluence

- spectra of short GRBs consistent with those of long GRBs in the first 1-2 s
- evidences that long GRBs are produced by the superposition of 2 different emissions ?
- e.g., in short GRBs only first ~thermal part of the emission and lack or weakness (e.g. due to very high G for internal shocks or low density medium for external shock) of long part
- long weak soft emission is indeed observed for some short GRBs

Ghirlanda et al. (2004)

GRB-SN connection and the Ep,i-Eiso correlation

- GRBs with firmest evidence of association with a SN are consistent with the Ep,i-Eiso correlation (except for peculiar 980425)
- GRB 060614: the long GRB with a very deep lower limit to the magnitude of an associated SN is consistent with the correlation too
- GRB 060505: stringent lower limit to SN magnitude, inconsistent with correlation, but it is likely short
- Evidence that GRB properties are independent on those of the SN ?

Amati et al. A&A, 2007

Recent Swift detection of an X-ray transient associated with SN 2008D at z = 0.0064, showing a light curve and duration similar to GRB 060218

- Peak energy limits and energetics consistent with a very-low energy extension of the Ep,i-Eiso correlation
- Evidence that this transient may be a very soft and weak GRB (XRF 080109), thus confirming the existence of a population of sub-energetic GRB ?
- XRF 080109 / SN2008D: are soft X-ray flashes due to SN shock break-out ? How they connect to “normal” GRBs ?

Modjaz et al., ApJ, 2008

Li, MNRAS, 2008

Ep,i-Eiso correlation in the fireshell model (Ruffini et al.)

- By assuming CBM profile from a real GRB and varying Etot, the correlation is obtained, with a slope of 0.45+/+0.01 (consistent with obs.)
- no correlation when assuming constant CBM profile (Guida et al. 2008)

CBM profile as GRB 050315

CBM constant (n=1cm-3)

Natural explanation of the deviation of short GRB from the correlation

- extrinsic scatter of the correlation mostly due to the inclusion of P-GRB, the computation of Ep based only on the “prompt” spectrum, cosmology

Piranomonte et al. (2008)

Ruffini et al. (2008)

Debate based on BATSE GRBs without known redshift

- 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 predicted that Swift will detect several GRBs with Ep,i and Eiso inconsistent 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
- different conclusions mostly due to the accounting or not for the dispersion of the correlation

Swift GRBs and selection effects

- Swift / 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

CGRO/BATSE

Swift/BAT

Ghirlanda et al., MNRAS, (2008)

Band, ApJ, (2003, 2006)

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
- drawback: 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 z and published estimates or limits to Ep,i are consistent with the correlation

- the parameters (index, normalization,dispersion) obatined with Swift GRBs only are fully consistent with what found before
- Swift allows reduction of selection effects in the sample of GRB with known z -> the Ep,i-Eiso correlation is passing the more reliable test: observations !

Amati 2006, Amati et al. 2008

very recent claim by Butler et al.: 50% of Swift GRB are inconsistent with the pre-Swift Ep,i-Eiso correlation

- but Swift/BAT has a narrow energy band: 15-150 keV, nealy unesuseful for Ep estimates, possible only when Ep is in (or close to the bounds of ) the passband (15-20%) and with low accuracy
- comparison of Ep derived by them from BAT spectra using Bayesian method and those MEASURED by Konus/Wind show they are unreliable
- as shown by the case of GRB 060218, missing the soft part of GRB emission leads to overestimate of Ep

GRB have huge luminosity, a redshift distribution extending far beyond SN Ia

- high energy emission -> no extinction problems
- but need to investigate their properties to find ways to standardize them (if possible)

a first step: using Ep,i – Eiso correlation for z estimates

- redshift estimates available only for a small fraction of GRB occurred in the last 10 years based on optical spectroscopy
- pseudo-redshift estimates for the large amount of GRB without measured redshift -> GRB luminosity function, star formation rate evolution up to z > 6, etc.
- use of the Ep,i – Eiso correlation for pseudo-redshift: most simple method is to study the track in the Ep,i - Eiso plane ad a function of z
- not precise z estimates and possible degeneracy for z > 1.4
- anyway useful for low –z GRB and in general when combined with optical

a step forward: standardizing GRB with 3-parameters spectrum-energy correlations

- the Ep,i-Eiso correlation becomes tighter when adding a third observable: jet opening angle (qjet -> Eg = [1-cos(qjet)]*Eiso (Ghirlanda et al. 2004) or “high signal time” T0.45 (Firmani et al. 2006)
- the logarithmic dispersion of these correlations is very low: they can be used to standardize GRB ?
- jet angle inferred from break time in optical afterglow decay, while Ep,i-Eiso-T0.45 correlation based on prompt emission properties only

Methods(e.g., Ghirlanda et al, Firmani et al., Dai et al., Zhang et al.):

Ep,i = Ep,obsx (1 + z)

Dl = Dl (z, H0, WM, WL, …)

- general purpouse: estimate c.l. contours in 2-param surface (e.g. WM-WL)
- general method: construct a chi-square statistics for a given correlation as a function of a couple cosmological parameters
- method 1 – luminosity distance: fit the correlation and construct an Hubble diagram for each couple of cosmological parameters -> derive c.l. contours based on chi-square

method 2 – minimum correlation scatter: for each couple of cosm.parameters compute Ep,i and Eiso (or Eg), fit the points with a pl and compute the chi-square -> derive c.l. contours based on chi-square surface

- method 3: bayesian method assuming that the correlation exists and is unique

Ghirlanda et al., 2004

Firmani et al. 2007

What can be obtained with 150 GRB with known z and Ep and complementarity with other probes (SN Ia, CMB)

- complementary to SN Ia: extension to much higher z even when considering the future sample of SNAP (z < 1.7), cross check of results with different probes

Ghirlanda, Ghisellini et al. 2005, 2006,2007

Drawbacks: lack of solid physical explanation

- 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 G-2 L1/2 tn-1 for syncrotron emission from a power-law distribution of electrons generated in an internal shock (Zhang & Meszaros 2002, Ryde 2005);

for Comptonized thermal emission

- geometry of the jet (if assuming collimated emission) and viewing angle effects also may play a relevant role

- differently to SN Ia, there are no low-redshift GRB (only 1 at z < 0.1) -> correlations cannot be calibrated in a “cosmology independent” way
- would need calibration with a good number of events at z < 0.01 or within a small range of redshift -> neeed to substantial increase the number of GRB with estimates of redshift and Ep
- Very recently (Kodama et al., 2008; Liang et al., 2008) calibrated GRB spectrum—energy correlation at z < 1.7 by using the cosmology independent luminosity distance – redshift relation derived for SN Ia

“Crisis” of 3-parameters spectrum-energy correlations

- Recent debate on Swift outliers to the Ep-Eg correlation (including both GRB with no break and a few GRB with chromatic break)
- Recent evidence that the dispersion of the Lp-Ep-T0.45 correlation is significantly higher than thought before and comparable to the Ep,i-Eiso corr.

Campana et al. 2007

Rossi et al. 2008

Using the simple Ep,i-Eiso correlation for cosmology

- Based on only2 observables:

a) much higher number of GRB that can be used

b) reduction of systematics

- Evidence that a fraction of the extrinsic scatter of the Ep,i-Eiso correlation is due to choice of cosmological parameters used to compute Eiso

70 GRB

Simple PL fit

Amati et al. 2008

By using a maximum likelihood method the extrinsic scatter can be parametrized and quantified (e.g., D’Agostini 2005)

- WM can be constrained to 0.04-0.40 (68%) and 0.02-0.68 (90%) for a flat LCDM universe (WM = 1 excluded at 99.9% c.l.)

Amati et al. 2008

releasing assumption of flat universe still provides evidence of low WM, with a low sensitivity to WL

- significant constraints on both WM and WL expected from sample enrichment and z extension by present and next GRB experiments (e.g., Swift, Konus_WIND, GLAST, SVOM)
- completely independent on other cosmological probes (e.g., CMB, type Ia SN, BAO; clusters…) and free of circularity problems

70 REAL

70 REAL

+ 150 SIMUL

Amati et al. 2008

possible further improvements on cosmological parameter estimates by exploiting self-calibration with GRB at similar redshift or solid phyisical model for the correlation

70 REAL

+ 150 SIMUL

70 REAL

70 REAL

70 REAL

+ 150 SIMUL

Amati et al. 2008

given their redshift distribution (0.033 - 6.3 up to now) , GRB are potentially the best-suited probes to study properties and evolution of “dark energy”

(e.g.,Chevalier & Polarski, Linder & Utherer)

70 REAL

+ 150 SIMUL (flat)

70 REAL (flat, Wm=0.27)

Amati et al. 2008

Complementarity to other probes: the case of SN Ia

- Several possible systematics may affect the estimate of cosmological parameters with SN Ia, e.g.:
- different explosion mechanism and progenitor systems ? May depend on z ?
- light curve shape correction for the luminosity normalisation may depend on z
- signatures of evolution in the colours
- correction for dust extinction
- anomalous luminosity-color relation
- contaminations of the Hubble Diagram by no-standard SNe-Ia and/or bright SNe-Ibc (e.g. HNe)

Kowalski et al. 2008

The Hubble diagram for type Ia SNe may be significantly affected by systematics -> need to carry out independent measurement of WM and WL

- GRBs allow us today to change the “experimental methodology” and provide an independent measurement of the cosmological parameters:

- GRBs are extremely bright and detectable out of cosmological distances (z=6.3 Kuwai et al. 2005, Tagliaferri et al. 2005) -> interesting objects for cosmology
- SNe-Ia are currently observed at z<1.7: GRBs appear to be (in principle) the only class of objects capable to study the evolution of the dark energy from the beginning (say from z~7-8)
- No need of correction for reddening
- Different orientation of the contours

- The Ep,i-Eiso correlation is the most firm GRB correlation followed by all normal GRB and XRF
- Swift results and recent analysis show that it is not an artifact of selection effects
- The existence, slope and extrinsic scatter of the correlation allow to test models for GRB prompt emission physics
- The study of the locations of GRB in the Ep,i-Eiso plane help in indentifying and understanding sub-classes of GRB (short, sub-energetic, GRB-SN connection)

- Given their huge luminosities and redshift distribution extending up to at least 6.3, GRB are a powerful tool for cosmology and complementary to other probes (CMB, SN Ia, BAO, clusters, etc.)
- The use of Ep,i – Eiso correlation to this purpouse is promising (already significant constraints on Wm, in agreement with “concordance cosmology), but:
- need to substantial increase of the # of GRB with known z and Ep (which will be realistically allowed by next GRB experiments: Swift+GLAST/GBM, SVOM,…)
- auspicable solid physical interpretation
- identification and understanding of possible sub-classes of GRB not following correlations

- 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 Konus (from 15 keV to several MeV) ant, to minor extent, RHESSI and SUZAKU

NARROW BAND

BROAD BAND

2008(-2011 ?): GLAST (AGILE) + Swift:

- accurate Ep (GLAST/GBM = 10-5000 keV) and z estimate (plus study of GeV emission) for simultaneously detected events
- by assuming that Swift will follow-up ALL GLAST GRB, about 80 GRB with Ep and z in 3 years
- AGILE and GLAST: second peak at E > 100 MeV ? (e.g., IC like in Blazars)

In the 2011-2015 time frame a significant step forward expected from SVOM:

- spectral study of prompt emission in 1-5000 keV -> accurate estimates of Ep and reduction of systematics (through optimal continuum shape determination and measurement of the spectral evolution down to X-rays)
- fast and accurate localization of optical counterpart and prompt dissemination to optical telescopes -> increase in number of z estimates and reduction of selection effects in the sample of GRB with known z

- optimized for detection of XRFs, short GRB, sub-energetic GRB
- substantial increase of the number of GRB with known z and Ep -> test of correlations and calibration for their cosmological use

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