Acta Polytechnica doi:10.14311/AP.2013.53.0687 Acta Polytechnica 53(Supplement):687–692, 2013 © Czech Technical University in Prague, 2013 available online at http://ojs.cvut.cz/ojs/index.php/ap INVESTIGATING THE E p, i – E iso CORRELATION Lorenzo Amatia,∗, Simone Dichiarab a Istituto Nazionale di Astrofisica – IASF Bologna, Via P. Gobetti 101, I-40129 Bologna, Italy b University of Ferrara, Department of Physics, via Saragat 1, 44100 Ferrara, Italy ∗ corresponding author: amati@iasfbo.inaf.it Abstract. The correlation between the spectral peak photon energy, Ep, and the radiated energy or luminosity (i.e., the “Amati relation” and other correlations derived from it) is one of the central and most debated topics in GRB astrophysics, with implications for physics and the geometry of prompt emission, the identification and understanding of various classes of GRBs (short/long, XRFs, sub-energetic), and GRB cosmology. Fermi is exceptionally suited to provide, also in conjunction with Swift observations, a significant step forward in this field of research. Indeed, one of the main goals of Fermi/GBM is to make accurate measurements of Ep, by exploiting its unprecedented broad energy band from ∼ 8 keV to ∼ 30 MeV; in addition, for a small fraction of GRBs, the LAT can extend the spectral measurements up to the GeV energy range, thus allowing a reliable estimate of the bolometric radiated energy/luminosity. We provide a review, an update and a discussion of the impact of Fermi observations in the investigation, understanding and testing of the Ep,i –Eiso (“Amati”) relation. Keywords: gamma-rays: observations, gamma-rays: bursts. 1. Introduction Despite the huge observational advances and theoreti- cal efforts of the last 20 years, the gamma-ray bursts (GRB) phenomenon is still far from being fully under- stood. Open issues include the fraction and peculiar characteristics (mass, rotational speed, metallicity, core collapse physics) of highly energetic type Ic SNe (“hyper-novae”) producing long GRBs, the progeni- tors of short GRBs (coalescence of NS–NS or BH–NS binary systems, magnetars, etc.); the mechanisms through which the gravitational energy of the central engine is converted into an ultra-relativistically ex- panding plasma, and the kinetic (or magnetic) energy of this “fireball” (or “firejet”) is converted into X- and gamma-rays; the explanation of the early afterglow phenomenology (steep decay, plateau, flares) and of the properties of the GeV emission; the degree of col- limation of the emission and the structure of the jet; and other topics. After several years of deep inves- tigations of the multi-wavelength properties of early and late afterglow emission, following the discoveries of BeppoSAX and Swift, the focus of the community is getting back to the physics of the prompt emission, prompted by the very high-energy measurements by Fermi and based on refined re-analysis of the BATSE, BeppoSAX, HETE-2 and Konus/WIND data. In this respect, one of the most intriguing and most investigated pieces of observational evidence is the correlation between the photon energy at which the νFν spectra of GRBs peak, Ep,i, and their radiated energy, Eiso (or other GRB intensity indicators, e.g. average luminosity or peak luminosity). Indeed, this correlation can provide useful constraints to the mod- els for prompt emission physics and geometry. It can also be used to identify and understand the different sub-classes of GRBs (short/long, sub-energetic, X-Ray Flashes) and to standardize these sources for cosmo- logical investigations. Thanks to its unprecedented capability to measure the GRB prompt emission from ∼ 8 up to ∼ 30 MeV for hundreds of GRBs and up to tens of GeV for a few GRBs per year, the Fermi satellite is making a major contribution to this field of research. In this paper, after reviewing the basic properties, implications and uses of Fermi we show how its mea- surements are confirming and extending the Ep,i –Eiso correlation in GRBs, providing further evidence of its reliability. 2. The Ep,i – Eiso correlation in GRBs 2.1. Observations GRB spectra are typically described by the empirical smoothed broken-power-law introduced by [1], with parameters α (low-energy index), β (high-energy in- dex), E0 (break energy). In terms of νFν, they show a peak at the photon energy Ep = E0 × (2 + α). This quantity is a relevant parameter in most of the models for GRB prompt emission, see, e.g., [2]. Presently, more than 250 GRBs have measured redshift, and about 40 ÷ 50 % of them have well-measured spec- tra. From the measured spectrum and the measured redshift it is then possible to compute two fundamen- tal quantities in the cosmological rest-frame of these sources: the intrinsic spectral peak energy, Ep,i, and the radiated energy in the assumption of isotropic emission, Eiso. Both Ep,i and Eiso span several orders 687 http://dx.doi.org/10.14311/AP.2013.53.0687 http://ojs.cvut.cz/ojs/index.php/ap Lorenzo Amati, Simone Dichiara Acta Polytechnica Figure 1. Location of long GRBs in the Ep,i –Eiso plane as of July 2011. Fermi GRBs are marked with red (GBM detection) and blue (GBM + LAT detec- tion) color. The continuous line and the dotted line show the best fit power–law of the Ep,i –Eiso correla- tion and its ±2σ limits, respectively, as determined by Amati et al. [6]. of magnitude and a distribution which can be de- scribed by a Gaussian plus a low–energy tail (intrinsic XRFs and sub-energetic events). In 2002, based on a small sample of BeppoSAX GRBs with known redshift, it was discovered [3] that a very significant correlation exists between Ep,i and Eiso (Fig. 1). The Ep,i –Eiso correlation for GRBs with known redshift was then confirmed, and was ex- tended in the subsequent years by measurements of all other GRB detectors with spectral capabilities [4–6]. These include the Ep,i values for Swift GRBs mea- sured by Konus/WIND, Suzaku/WAM, Fermi/GBM and Swift/BAT itself (only when Ep is inside or close to 15 ÷ 150 keV). Despite its strength, this correlation is character- ized by a significant dispersion of the data around the best-fit power-law; the distribution of the residuals can be fitted by a Gaussian with σ(log Ep,i) ∼ 0.2. This extra-Poissonian scatter of the data can be quan- tified by performing a fit with a maximum likelihood method which accounts for the sample variance and the uncertainties on both X and Y quantities [7]. This method, by expressing Ep,i in keV and Eiso in units of 1052 erg, provides an extrinsic scatter σext(log Ep,i) of 0.19 ± 0.02 and an index of 0.54 ± 0.03 [6, 8]. In recent years, definite evidence has been found that short GRBs do not follow the Ep,i –Eiso correlation, thus showing that the Ep,i –Eiso plane can be used as a tool for distinguishing between short and long events and for getting clues on their different nature [5, 9]. Finally, the only long GRB outlier to the correlation is GRB 980425, an event which is peculiar in several respects: it has a very low redshift (z = 0.0085), it is sub-energetic, and it is inconsistent with most other GRB properties. 2.2. Implications and uses The physics of the prompt emission of GRBs is still not settled, and various scenarios have been proposed: synchrotron emission in internal shocks (SSM, Inverse Compton (IC) dominated internal shocks), external shocks, photospheric emission dominated models, ki- netic energy/Poynting flux dominated fireballs, and more. The existence and properties of the Ep,i –Eiso correlation can be used to discriminate among differ- ent models and to constrain the physical parameters within each model [2]. In addition, the extension of the correlation over several orders of magnitude from the brightest events to the softest XRFs provides challeng- ing evidence for models in which the observed proper- ties of GRBs depend strongly on the jet structure and the viewing angle [4, 10]. An Ep,i –Eiso correlation with properties consistent with the observed proper- ties is also predicted by alternative scenarios like the “cannonball” model [11], the “fireshell” model [12] and the “precessing jet” model [13]. As mentioned above, the Ep,i –Eiso plane is also a useful tool for identifying sub-classes of GRBs, first of all short and long GRBs. Only very recently, redshift estimates for short GRBs became available, thanks to the observational progress. The estimates and limits on Ep,i and Eiso for short GRBs show that they are inconsistent with the Ep,i –Eiso correlation holding for long GRBs. In addition, a long weak soft emission following the short spike has been observed in some cases. Intriguingly, this component is consistent with the correlation, showing that the Ep,i –Eiso plane can be used to identify and understand not only short and long GRBs but also “hybrid” GRBs. Another issue concerns sub-energetic GRBs. Indeed, the only long GRB not following the correlation is GRB 980425, which is not only a prototype event of GRB/SN con- nection but is also the closest GRB (z = 0.0085) and a very sub-energetic event (Eiso ∼ 1048 erg). More- over, GRB 031203, which is the most similar case to GRB 980425, being very close (z = 0.105), associated to a bright type Ic SN (SN2003lw) and sub-energetic, may also be inconsistent with the correlation (however, only an upper limit to Ep,i is available for this burst). The most common explanations for the (apparent?) sub-energetic nature of GRB 980425 and GRB 031203 and their violation of the Ep,i –Eiso correlation is that they are “normal” events seen very off-axis [10]. GRB 060218, very close (z = 0.033, second only to GRB 9809425), with a prominent association with SN2006aj, and very low Eiso (6×1049 erg) is very sim- ilar to GRB 980425 and GRB 031203, but, contrary to these two events, it is consistent with the Ep,i –Eiso correlation. This provides evidence that it is a truly (and not apparent) sub-energetic GRB, pointing to the likely existence of a population of under-luminous GRB detectable only in the local universe. Finally, the Ep,i –Eiso correlation can also provide clues to a better understanding of the GRB–SN con- nection. Except for the peculiar sub-energetic GRBs 688 vol. 53 supplement/2013 Investigating the E p, i – E iso Correlation 980425 and 031203, associated with SN1998bw and SN2003dh, respectively, GRB 060218 and other GRBs with the firmest evidence of association with an SN are consistent with the Ep,i –Eiso correlation. In par- ticular, the location of these GRBs in the Ep,i –Eiso plane seems to be independent from the magnitude of the associated SN. Furthermore, GRB 060614, a long GRB with a very deep lower limit to the magnitude of an associated SN, is also consistent with the correla- tion. These pieces of evidence support the hypothesis that the GRB properties are not, or are only weakly, linked to those of the SN explosion which produced them. Recently, Swift detected an X-ray transient associated with SN 2008D at z = 0.0064, showing a light curve and duration similar to GRB 060218. The properties of this event gave rise to a debate: are we facing a very soft/weak GRB or an SN shock break- out? Based on Swift XRT and UVOT data, it can be found that the peak energy limits and energetics of this transient (also named XRF 080109) are consistent with a very low energy extension of the Ep,i –Eiso correlation. This provides evidence that the transient may really be a very soft and weak GRB, thus con- firming the existence of a population of sub-energetic GRBs. 2.3. GRB cosmology An interesting aspect of the Ep,i –Eiso correlation is that it can be used to infer limits or ranges of red- shift for long GRBs. Redshift estimates available only for a small fraction of GRBs have occurred in the last 15 years, based on optical spectroscopy. Pseudo- -redshift estimates for the large number of GRBs with- out measured redshift would provide us with funda- mental insights into the GRB luminosity function, the star formation rate evolution up to z > 6, etc. In addi- tion, in some cases the optical measurements provide more than one possible value for the redshift. The most straightforward method for using the Ep,i –Eiso correlation for pseudo-redshift estimates or for dis- entangling different possible redshifts from optical spectroscopy/photometry, is to study the track in the Ep,i –Eiso plane as a function of z, i.e., to compute, based on the measured fluence and spectral parame- ters, the values of Ep,i and Eiso for each possible value of the redshift and see for which range of redshift the GRB would be consistent with the correlation. This method often does not provide precise z estimates, but it is anyway useful for low-z GRB and in general when combined with optical measurements. An outstanding case is that of GRB 090429B, for which photometric analysis pointed to a redshift of ∼ 9.4, but also pro- vided a very small probability that the GRB was at very low redshift [14]. The consistency of this GRB with the Ep,i –Eiso correlation only for z > 1 further supported the very high redshift estimate from the photometric analysis. However, one of the most intriguing, debated and investigated issues about the Ep,i –Eiso correlation and other spectrum–energy correlations derived from it is their use for GRB cosmology. All GRBs with mea- sured redshift (∼ 250 up to now, including a few short GRBs) lie at cosmological distances (z ∼ 0.033 ÷ 9.4) (except for the peculiar GRB 980425, at z = 0.0085). This fact, combined with the huge radiated power of these events, would make them very powerful cosmo- logical probes. Nevertheless, the isotropic luminosities and radiated energies of GRBs span several orders of magnitude, thus these sources are not standard candles (unfortunately). Given that it links a quan- tity, Ep,i, which can be derived from the observables based only on the redshift, and a quantity, Eiso, whose computation requires the assumption of a cosmology, the Ep,i –Eiso correlation can, in principle, be used to “standardize” GRBs. Indeed, it can be found [8, 15] that a fraction of the extrinsic scatter of the corre- lation is due to the cosmological parameters used to compute Eiso. In particular, by assuming, e.g., a stan- dard ΛCDM flat universe, it can be found that the scatter minimizes for ΩM ∼ 0.25 ÷ 0.3, in very good agreement with the estimate coming from other cos- mological probes (SN Ia, CMB, BAO, clusters). More in general, this simple analysis provides evidence, in- dependent from SN Ia and other cosmological probes, that, if we are in a flat ΛCDM universe, as result- ing from CMB analysis, ΩM is lower than 1. By using a maximum likelihood method, the extrinsic scatter can be parametrized and quantified. For ex- ample, [8] found ΩM constrained to 0.04÷0.43 (68 %) and 0.02 ÷ 0.71 (90 %) for a flat ΛCDM universe (ΩM = 1 excluded at 99.9 % c.l.), and that significant constraints on both ΩM and ΩΛ are expected from sample enrichment. And, indeed, the analysis of an updated sample of 109 GRBs shows significant im- provements in the constraints on ΩM (0.06 ÷ 0.36 at 68 % and 0.03÷0.59 at 90 %) with respect to the sam- ple of 70 GRBs (0.06 ÷ 0.36 at 68 % and 0.03 ÷ 0.59 at 90 %), providing evidence of the reliability and per- spectives of the use of the Ep,i –Eiso correlation for estimating of cosmological parameters. 2.4. Reliability Different GRB detectors are characterized by different detection and spectroscopy sensitivity as a function of the GRB intensity and spectrum, see, e.g., [16]. This may introduce relevant selection effects/biases in the observed Ep,i –Eiso and other correlations. In the past, there were claims that a high fraction (70 ÷ 90 %) of BATSE GRBs without redshift would be inconsistent with the correlation for any redshift [17]. However, this would imply unreliable huge selection effects in the sample of GRBs with known redshift. In addi- tion, other authors [9, 18, 19] have shown that most BATSE GRBs with unknown redshift are consistent with the Ep,i –Eiso correlation. Moreover, [6] showed that the normalization of the correlation varies only marginally using GRBs measured by individual instru- ments with different sensitivities and energy bands, 689 Lorenzo Amati, Simone Dichiara Acta Polytechnica Figure 2. Location of Fermi GRBs in the Ep – fluence plane based on the analysis reported by Nava et al. [21]. In the left and right panels we show those GRBs for which the spectral parameters and the fluence were derived by fitting the data with a cut-off power-law and with the Band function, respectively. GRBs have been divided according to their durations: short (red points), intermediate (cyan points) and long (black points). The red and blue lines represent the limits above which a GRB would be inconsistent with the Ep,i –Eiso correlation at 2σ or 3σ, respectively, for any redshift. which provides further evidence that the instrumental limits do not have a significant impact. Selection effects in the process leading to the redshift estimate may also play a role. Thanks to its capability of providing quick and accurate localization of GRBs, Swift is reducing selection effects in the sample of GRB with measured redshift. Thus, Swift GRBs are expected to provide a robust test of the Ep,i –Eiso cor- relation. By considering the Ep,i of Swift GRBs mea- sured by Konus-WIND, Suzaku/WAM, Fermi/GBM and Swift/BAT (only when Ep is inside or close to 15÷150 keV and the values provided by the Swift/BAT team, it can be found that they are consistent with the Ep,i –Eiso correlation. Finally, based on time-resolved analysis of BATSE, BeppoSAX and Fermi GRBs, it was found that the Ep,i –Liso correlation holds also within a good fraction of GRBs [20], which is robust evidence for a physical origin, also providing clues to its explanation. 3. The Fermi contribution The key features of Fermi for the study of GRBs are: detection, arcmin localization and study of GRBs in the GeV energy range through the Fermi/LAT instrument, with dramatic improvement w/r CGRO/EGRET; detection, rough localization (within a few degrees) and accurate determination of the shape of the spectral continuum of the prompt emission of GRBs from 8 keV up to 30 MeV through the Fermi/GBM instrument. The investi- gated Ep,i –Eiso correlation with Fermi can thus be done under the following respects: a) location in the Ep,i –Eiso plane of GRBs with known z (most of which were detected and localized by Swift) and with Ep accurately measured by GBM (direct test); b) testing the Ep,i –Eiso correlation by analyzing the location of hundreds of GBM GRBs in the Ep–Fluence plane (as done with BATSE GRBs); c) exploiting joint analysis of GBM and LAT spectra to investigate the impact of the extension from 10 MeV up to > 1 GeV of the spectral–energetic analysis. 3.1. Fermi GRBs in the Ep,i – Eiso plane Up to now, GBM has detected several hundreds of GRBs, providing accurate Ep estimates for ∼ 90 % of them. However, only ∼ 15 % of these events were simultaneously detected by Swift, leading to a final ∼ 5 % with Ep and z estimates. GRB fluences and spectral data of Fermi GRBs are presently available from four main data sets: GCNs (preliminary results for most GRBs by the Fermi collaboration); [21] (430 GRBs); [22] (52 bright GRBs by the Fermi collabo- ration); [23] (32 GRBs with known redshift by the Fermi collaboration). Based on GCN data, [6] showed that all Fermi/GBM long GRBs with known z are fully consistent with the Ep,i –Eiso correlation, as de- termined by previous experiments (Fig. 1): further confirmation of non relevant instrumental effects. In addition, the analysis of the Fermi/GBM GRB 090510 further confirms that short GRBs do not follow the correlation. Very recently, [23] (an official Fermi team) performed a refined analysis of the updated sample of Fermi/GBM GRBs with known z, confirming that long ones are consistent with Ep,i –Eiso correlation, while short GRBs are not. The slightly higher nor- malization and dispersion of the Ep,i –Eiso correlation found by them with respect to previous analysis is possibly due to the use, for some GRBs, of the cut-off power-law model, instead of the Band model, which leads to an overestimate of Ep,i and an underestimate of Eiso). 690 vol. 53 supplement/2013 Investigating the E p, i – E iso Correlation Figure 3. Location in the Ep–fluence plane of GRBs simulated by assuming the existence of the Ep,i –Eiso correlation and the sensitivity limits of the Fermi/GBM. In the right panel we have also included in the simulations the effect of the spectral evolution Ep,i ∝ L0.5 observed for most GRBs. The red and blue lines represent the limits above which a GRB would be inconsistent with the Ep,i –Eiso correlation at 2σ or 3σ, respectively, for any redshift. 3.2. Fermi GRBs without redshift As mentioned above, besides the small sample of GRBs with measured redshift, Fermi/GBM is providing a large sample of hundreds of GRBs without redshift but with accurate measurements of the spectral peak energy Ep and fluence F. This sample can be used to test the reliability of the Ep,i –Eiso correlation. This is similar to what was done in the past with BATSE GRBs, but it takes advantage of the bet- ter accuracy in the spectral parameters allowed by the unprecedented wide energy band of this instru- ment (8 keV÷30 MeV). Given that we are considering GRBs without measured redshift, this analysis re- quires a conversion from the Ep,i –Eiso correlation in the cosmological rest-frame plane to an Ep –F cor- relation in the observer plane. By considering the Ep,i –Eiso correlation in the form Ep,i = K × Emiso and taking into account that Ep,i = Ep × (1 + z) and Eiso = F×(4πD2L)/(1+z), where DL is the luminosity distance to the source, we obtain Ep = f(z)×K×Fm, where f(z) = (4πD2L) m/(1 + z)m+1. Given that f(z) shows a maximum for z ∼ 4, we can convert the best-fit and 2σ or 3σ upper limits of the Ep,i –Eiso correlation into lines in the logarithmic Ep –S plane above which a GRB would be inconsistent with the Ep,i –Eiso correlation at the corresponding confidence level for any redshift (see Figs. 2 and 3). We applied the above method to Fermi GRBs, using the different resources described above for the spectral parameters and fluence. In all cases, we have found that most (90÷95 %) of the long GRBs are potentially consistent with the Ep,i –Eiso correlation, whereas most short ones are not. In addition, we have found that, when considering only those GRBs with well measured spectral parameters and fluence, properly modeled with the Band function instead of the cut-off power-law, and with integration times not shorter than 75 % of the total duration of the event, all long Fermi GRBs are potentially consistent with the Ep,i –Eiso correlation. As an example, we show in Fig. 2 the impact of the fitting model (Band function vs. cut-off power-law) for the sample by [21]. In addition, we performed Monte Carlo simulations aimed at evaluating the impact on the location of GRBs in the Ep –S plane of the combination of spec- tral evolution with detector sensitivity. Indeed, time resolved analysis of GRBs generally shows, that Ep is correlated with the flux: the higher the flux, the higher the spectral peak energy. This means that if we detect only the brightest part of a GRB, we will overestimate Ep and underestimate the fluence. In order to evaluate this effect, we generated thou- sands of fake GRBs by assuming the existence and the measured parameters of the Ep,i –Eiso correlation, accounting for the observed distributions of relevant parameters (Eiso, z, Eiso vs. z). We also attributed to each GRB a specific light curve and a spectral evo- lution of the type Ep,i ∝ Ln, where n is between 0.4 and 0.6, as observed in several GRBs [20]. Then by accounting for cosmological effects and Fermi/GBM instrumental sensitivity as a function of Ep,i [16, 24], we computed for each GRB the Ep and fluence that would be measured by the GBM. As can be seen in Fig. 3, when accounting for the spectral evolution, the observed small fraction of outliers in the Ep –S plane is reproduced. 3.3. Extremely energetic Fermi GRBs Thanks to its sensitivity and its huge energy band, Fermi is detecting and characterizing from ∼ 10 keV up to several GeVs the sub-class of very energetic GRBs also detected by LAT. As pointed out by [6], GRB 080916C, the most energetic GRB ever (Eiso ∼ 1055 erg in the 1 keV ÷ 10 GeV band), and the other extremely energetic GRBs 090323 and 090902B are fully consistent with the Ep,i –Eiso correlation (Fig. 1). Thus, Fermi is providing a further extension of the correlation and evidence that the physics behind the X-ray and soft gamma-ray emission of extremely ener- getic events with GeV emission is similar to the physics 691 Lorenzo Amati, Simone Dichiara Acta Polytechnica of normal events. In addition, based on the fact that GRB 080916C showed a spectrum extending up to tens of GeV without any excess or cut-off, [6] investi- gated the impact on the correlation of the extension of the energy range over which Eiso is computed from the canonical upper bound of 10 MeV up to 10 GeV, find- ing no significant change in the slope and dispersion of the correlation. It also has to be cautioned that, given that for a few events GBM plus LAT spectral fitting shows an additional power-law component with respect to the simple Band function, the extrapolation of the spectrum at energies higher than 10 MeV is not straightforward. 4. Conclusions The Ep,i –Eiso correlation in long GRBs is one of the most robust pieces of observational evidence in the GRB field. Implications and uses of the Ep,i –Eiso correlation include: prompt emission physics and ge- ometry, identification and understanding of sub-classes of GRBs (e.g., short, sub-energetic), GRB cosmology. Refined analysis of large samples of GRBs without red- shifts, combined with simulations, further support the reliability of the correlation. The Fermi observatory is providing a significant contribution to investiga- tions of the property and reliability of this correlation. First of all, GBM is significantly increasing the num- ber and the accuracy of Ep,i estimates for GRBs with known redshift. It is found that GBM long GRBs in the Ep,i –Eiso plane follow the same correlation as measured by previous/other instruments; as ex- pected short GRBs do not. Furthermore, the analysis of the spectral peak energy and the fluences of hun- dreds of GBM GRBs without redshift, joined with Monte Carlo simulations, confirm that the Ep,i –Eiso correlation is not significantly affected by instrumen- tal effects. Finally, extremely energetic Fermi long GRBs with significant GeV emission detected by LAT (e.g., 080916c, 090323) further confirm and extend the correlation. 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