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Register a new userA time - luminosity correlation for Gamma Ray Bursts in the X - rays
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Added by
Vincenzo F. Cardone
Publication date
2008
fields
Physics
and research's language is
English
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Gamma ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram to very high redshift. However, the large scatter in their intrinsic properties prevents directly using them as distance indicator so that the hunt is open for a relation involving an observable property to standardize GRBs in the same way as the Phillips law makes it possible to use Type Ia Supernovae (SNeIa) as standardizable candles. We use here the data on the X - ray decay curve and spectral index of a sample of GRBs observed with the Swift satellite. These data are used as input to a Bayesian statistical analysis looking for a correlation between the X - ray luminosity L_X(T_a) and the time constant T_a of the afterglow curve. We find a linear relation between log{[L_X(T_a)]} and log{[T_a/(1+z)]} with an intrinsic scatter sigma_{int} = 0.33 comparable to previously reported relations. Remarkably, both the slope and the intrinsic scatter are almost independent on the matter density Omega_M and the constant equation of state w of the dark energy component thus suggesting that the circularity problem is alleviated for the $L_X - T_a$ relation.
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There exists an inevitable scatter in intrinsic luminosity of Gamma Ray Bursts(GRBs). If there is relativistic beaming in the source, viewing angle variation necessarily introduces variation in the intrinsic luminosity function(ILF). Scatter in the ILF can cause a selection bias where distant sources that are detected have a larger median luminosity than those detected close by. Median luminosity, as we know, divides any given population into equal halves. When the functional form of a distribution is unknown, it can be a more robust diagnostic than any that use trial functional forms. In this work we employ a statistical test based on median luminosity and apply it to test a class of models for GRBs. We assume that the GRB jet has a finite opening angle and that the orientation of the GRB jet is random relative to the observer. We parameterize the jet with constant Lorentz factor $Gamma$ and opening angle $theta_0$. We calculate $L_{median}$ as a function of redshift with an average of 17 grbs in each redshift bin($dz=0.01$) empirically, theoretically and use Fermi GBM data, noting that SWIFT data is problematic as it is biased, specially at high redshifts. We find that $L_{median}$ is close to $L_{max}$ for sufficiently extended GRB jet and does not fit the data. We find an acceptable fit with the data when $Gamma$ is between $100$ and $200$, $theta_0leq 0.1$, provided that the jet material along the line of sight to the on axis observer is optically thick, such that the shielded maximum luminosity is well below the bare $L_{max}$. If we associate an on-axis observer with a classically projected monotonically decreasing afterglow, we find that their ILF is similar to those of off-jet observer which we associate with flat phase afterglows.
The origin of extended emissions following prompt emissions of short gamma-ray bursts (SGRBs) is in mystery. The long-term activity of the extended emission is responsible for promising electromagnetic counterparts to gravitational waves and, so that it may be a key to uncovering the progenitor of SGRBs. We investigate the early X-ray light curves of 26 SGRBs with known redshifts observed with the X-Ray Telescope aboard the {it Neil Gehrels Swift Observatory} ({it Swift}). We find that the exponential temporal decay model is able to describe the extended emissions comprehensively with a rest-frame e-folding time of 20 -- 200 seconds. We also estimate the isotropic equivalent energies of the extended emission with the exponential decay model and of the prompt emission, compared with those of the prompt emission. Then, it is revealed that the extended emission is 0 -- 3 orders of magnitude less powerful than the prompt emission. We find a strong correlation between the expected maximum luminosity and e-folding time which can be described by a power-law with an index of $-3.3$ and whose chance probability of $8.2times10^{-6}$ if there is no observation bias of {it Swift}. The exponential temporal decay may be interpreted to come from the spin-down time scale of the rotation energy of a highly magnetized neutron star, and/or fallback accretion onto a disk surrounding a black hole with an exponentially decaying magnetic flux by magnetic reconnection.
Gamma-Ray Bursts (GRBs) are fascinating events due to their panchromatic nature. Their afterglow emission is observed from sub-TeV energies to radio wavelengths. We investigate GRBs that present an optical plateau, leveraging on the resemblance with the X-ray plateau shown in many GRB light curves (LCs). We comprehensively analyze all published GRBs with known redshifts and optical plateau observed mostly by the Neil Gehrels Swift Observatory (Swift). We fit 267 optical LCs and show the existence of the plateau in 102 cases, which is the largest compilation so far of optical plateaus. For 56 Swift GRBs with optical and X-ray plateaus, we compare the rest-frame end time at both wavelengths (T*_opt , T*_X), and conclude that the plateau is achromatic between T*_opt and T*_X. We also confirm the existence of the two-dimensional relations between T*_opt and the optical luminosity at the end of the plateau emission, which resembles the same luminosity-time correlation in X-rays (Dainotti et al. 2013). The existence of this optical correlation has been demonstrated for the largest sample of optical plateaus in the literature to date. The squared scatter in this optical correlation is smallest for the subset of the Gold GRBs with a decrease in the scatter equivalent to 52.4% when compared to the scatter of the entire GRB sample.
We present a possible Cepheid-like luminosity estimator for the long gamma-ray bursts based on the variability of their light curves. To construct the luminosity estimator, we use CGRO/BATSE data for 13 bursts, Wind/KONUS data for 5 bursts, Ulysses/GRB data for 1 burst, and NEAR/XGRS data for 1 burst. Spectroscopic redshifts, peak fluxes, and high resolution light curves are available for 11 of these bursts; partial information is available for the remaining 9 bursts. We find that the isotropic-equivalent luminosities L of these bursts positively correlate with a rigorously-constructed measure V of the variability of their light curves. We fit a model to these data that accommodates both intrinsic scatter (statistical variance) and extrinsic scatter (sample variance). If one excludes GRB 980425 from the fit on the grounds that its association with SN 1998bw at a redshift of z = 0.0085 is not secure, the luminosity estimator spans approx. 2.5 orders of magnitude in L, and the slope of the correlation between L and V is positive with a probability of 1 - 1.4 x 10^-4 (3.8 sigma). Although GRB 980425 is excluded from this fit, its L and V values are consistent with the fitted model, which suggests that GRB 980425 may well be associated with SN 1998bw, and that GRB 980425 and the cosmological bursts may share a common physical origin. If one includes GRB 980425 in the fit, the luminosity estimator spans approx. 6.3 orders of magnitude in L, and the slope of the correlation is positive with a probability of 1 - 9.3 x 10^-7 (4.9 sigma). Independently of whether or not GRB 980425 should be included in the fit, its light curve is unique in that it is much less variable than the other approx. 17 light curves in our sample for which the signal-to-noise is reasonably good.
We explore several models which might be proposed to explain recent possible detections of high-energy (TeV) gamma rays in association with low-energy gamma-ray bursts (GRBs). Likely values (and/or upper limits) for the source energies in low- and high-energy gamma rays and hadrons are deduced for the burst sources associated with possible TeV gamma-ray detections by the Project GRAND array. Possible spectra for energetic gammas are deduced for three models: 1) inverse-Compton scattering of ambient photons from relativistic electrons; 2) proton-synchrotron emission; and 3) inelastic scattering of relativistic protons from ambient photons creating high-energy neutral pions, which decay into high-energy photons. These models rely on some basic assumptions about the GRB properties, e.g. that: the low- and high-energy gamma rays are produced at the same location; the time variability of the high-energy component can be estimated from the FWHM of the highest peak in the low-energy gamma ray light curve; and the variability-luminosity relation of Fenimore & Ramirez-Ruiz (2000) gives a reliable estimate of the redshifts of these bursts. We also explore the impact of each of these assumptions upon our models. We conclude that the energetic requirements are difficult to satisfy for any of these models unless, perhaps, either the photon beaming angle is much narrower for the high-energy component than for the low-energy GRB or the bursts occur at very low redshifts (z<0.01). Nevertheless, we find that the energetic requirements are most easily satisfied if TeV gamma rays are produced predominantly by inverse-Compton scattering with a magnetic field strength well below equipartition or by proton-synchrotron emission with a magnetic field strength near equipartition.
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