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Register a new userThe GRB luminosity function in the internal shock model confronted to observations
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H. Zitouni
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We compute the expected luminosity function of GRBs in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power Edot and contrast in Lorentz factor Kappa = Gamma_max/Gamma_min. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist) the luminosity function has two branches. At high luminosity it follows the distribution of Edot while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the log N - log P curve, the Ep distribution of bright BATSE bursts and the XRF/GRB ratio obtained by HETE2 we show that single and broken power-laws can provide equally good fits of these data. Present observations are therefore unable to favor one form of the other. However when a broken power-law is adopted they clearly indicate a low luminosity slope ~ -0.6 +- 0.2, compatible with the prediction of the internal shock model.
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While the Band function or other phenomenological functions are commonly used to fit GRB prompt emission spectra, we propose a new parametric function that is inspired by an internal shock physical model. We use this function as a proxy of the model to confront it easily to GRB observations. We built a parametric function that represents the spectral form of the synthetic bursts provided by our internal shock synchrotron model (ISSM). We simulated the response of the Fermi instruments to the synthetic bursts and fitted the obtained count spectra to validate the ISSM function. Then, we applied this function to a sample of 74 bright GRBs detected by the Fermi/GBM, and we computed the width of their spectral energy distributions around their peak energy. For comparison, we fitted also the phenomenological functions that are commonly used in the literature. Finally, we performed a time-resolved analysis of the broadband spectrum of GRB 090926A, which was jointly detected by the Fermi GBM and LAT. The ISSM function reproduces 81% of the spectra in the GBM bright GRB sample, versus 59% for the Band function, for the same number of parameters. It gives also relatively good fits to the GRB 090926A spectra. The width of the MeV spectral component that is obtained from the fits of the ISSM function is slightly larger than the width from the Band fits, but it is smaller when observed over a wider energy range. Moreover, all of the 74 analysed spectra are found to be significantly wider than the synthetic synchrotron spectra. We discuss possible solutions to reconcile the observations with the internal shock synchrotron model, such as an improved modeling of the shock micro-physics or more accurate spectral measurements at MeV energies.
As the standard gamma-ray burst (GRB) prompt-emission model, the internal shock (IS) model can reproduce the fast-rise and slow-decay features of the pulses in the GRB light curve. The time- and energy-dependent polarization can deliver important physical information on the emission region and can be used to test models. Polarization predictions for the GRB prompt phase with the magnetized IS model should be investigated carefully. The magnetic field of the magnetized IS model is very likely to be mixed and decays with radius. The synchrotron emission in the presence of such a decaying magnetic field can recover the Band-like spectrum of the GRB prompt phase. We investigate the dependence of the polarization of GRB prompt emission on both time and energy in the framework of the magnetized IS model. Due to the large range of parameters, it is hard to distinguish the magnetized IS model and the magnetic-reconnection model through polarization degree (PD) curves. The energy-dependent PD could increase toward the high-energy band for the magnetized IS model, while it decreases to zero above the megaelectronvolt band for the dissipative photosphere model. Therefore, we conclude that the energy dependence of PD can be used to distinguish these two models for the GRB prompt emission. Finally, we find that, independent of the observational energy band, the profiles of the $xi_B-PD$ curve for the time-integrated and time-resolved PDs are very similar, where $xi_B$ is the magnetic field strength ratio of the ordered component to the random component.
Several trends have been identified in the prompt gamma-ray burst (GRB) emission: e.g. hard-to-soft evolution, pulse width evolution with energy, time lags, hardness-intensity/-fluence correlations. Recently Fermi has significantly extended the spectral coverage of GRB observations and improved the characterization of this spectral evolution. We study how internal shocks can reproduce these observations. In this model the emission comes from the synchrotron radiation of shock accelerated electrons, and the spectral evolution is governed by the evolution of the physical conditions in the shocked regions. We present a comprehensive set of simulations of a single pulse and investigate the impact of the model parameters, related to the shock microphysics and to the initial conditions in the ejecta. We find a general qualitative agreement between the model and the various observations used for the comparison. All these properties or relations are governed by the evolution of the peak energy and photon indices of the spectrum. In addition, we identify the conditions for a quantitative agreement. We find that the best agreement is obtained for (i) steep electron slopes (p>~2.7), (ii) microphysics parameters varying with shock conditions so that more electrons are accelerated in stronger shocks, (iii) steep variations of the initial Lorentz factor in the ejecta. When simulating short GRBs by contracting all timescales, all other parameters being unchanged, we show that the hardness-duration correlation is reproduced, as well as the evolution with duration of the pulse properties. Finally, we investigate the signature at high energy of these different scenarios and find distinct properties - delayed onset, longer emission, and flat spectrum in some cases - suggesting that internal shocks could have a significant contribution to the prompt LAT emission. [abridged]
We present new observational determinations of the evolution of the 2-10keV X-ray luminosity function (XLF) of AGN. We utilise data from a number of surveys including both the 2Ms Chandra Deep Fields and the AEGIS-X 200ks survey, enabling accurate measurements of the evolution of the faint end of the XLF. We combine direct, hard X-ray selection and spectroscopic follow-up or photometric redshift estimates at z<1.2 with a rest-frame UV colour pre-selection approach at higher redshifts to avoid biases associated with catastrophic failure of the photometric redshifts. Only robust optical counterparts to X-ray sources are considered using a likelihood ratio matching technique. A Bayesian methodology is developed that considers redshift probability distributions, incorporates selection functions for our high redshift samples, and allows robust comparison of different evolutionary models. We find that the XLF retains the same shape at all redshifts, but undergoes strong luminosity evolution out to z~1, and an overall negative density evolution with increasing redshift, which thus dominates the evolution at earlier times. We do not find evidence that a Luminosity-Dependent Density Evolution, and the associated flattening of the faint-end slope, is required to describe the evolution of the XLF. We find significantly higher space densities of low-luminosity, high-redshift AGN than in prior studies, and a smaller shift in the peak of the number density to lower redshifts with decreasing luminosity. The total luminosity density of AGN peaks at z=1.2+/-0.1, but there is a mild decline to higher redshifts. We find >50% of black hole growth takes place at z>1, with around half in Lx<10^44 erg/s AGN.
The correlation between the peak spectra energy ($E_p$) and the equivalent isotropic energy ($E_{rm iso}$) of long gamma-ray bursts (GRBs), the so-called Amati relation, is often used to constrain the high-redshift Hubble diagram. Assuming Lambda cold dark matter ($Lambda$CDM) cosmology, Wang et al. found a $gtrsim 3sigma$ tension in the data-calibrated Amati coefficients between low- and high-redshift GRB samples. To reduce the impact of fiducial cosmology, we use the Parameterization based on cosmic Age (PAge), an almost model-independent framework to trace the cosmological expansion history. We find that the low- and high-redshift tension in Amati coefficients stays almost the same for the broad class of models covered by PAge, indicating that the cosmological assumption is not the dominant driver of the redshift evolution of GRB luminosity correlation. Next, we analyze the selection effect due to flux limits in observations. We find Amati relation evolves much more significantly across energy scales of $E_{rm iso}$. We debias the GRB data by selectively discarding samples to match low-$z$ and high-$z$ $E_{rm iso}$ distributions. After debiasing, the Amati coefficients agree well between low-$z$ and high-$z$ data groups, whereas the evidence of $E_{rm iso}$-dependence of Amati relation remains to be strong. Thus, the redshift evolution of GRB luminosity correlation can be fully interpreted as a selection bias, and does not imply cosmological evolution of GRBs.
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