Testing and improving the luminosity relations for Gamma-Ray Bursts

Gamma Ray Bursts (GRBs) have several luminosity relations where a measurable property of a burst light curve or spectrum is correlated with the burst luminosity. These luminosity relations are calibrated for the fraction of bursts with spectroscopic redshifts and hence the known luminosities. GRBs have thus become known as a type of standard candle ; where standard candle is meant in the usual sense that their luminosities can be derived from measurable properties of the bursts. GRBs can therefore be used for the same cosmology applications as Type Ia supernovae, including the construction of the Hubble Diagram and measuring massive star formation rate. The greatest disadvantage of using GRBs as standard candles is that their accuracy is lower than desired. With the recent advent of GRBs as a new standard candle, every effort must be made to test and improve the distance measures. Here, several methods are employed to do just that. First, generalized forms of two tests are performed on all of the luminosity relations. All the luminosity relations pass the second of these tests, and all but two pass the first. Even with this failure, the redundancy in using multiple luminosity relations allows all the luminosity relations to retain value. Next, the Firmani relation is shown to have poorer accuracy than first advertised. In addition, it is shown to be exactly derivable from two other luminosity relations. For these reasons, the Firmani relation is useless for cosmology. The Amati relation is then revisited and shown to be an artifact of a combination of selection effects. Therefore, the Amati relation is also not good for cosmology. Fourthly, the systematic errors involved in measuring a popular luminosity indicator (Epeak) are measured. The result is that an irreducible systematic error of 28% exists. After that, a preliminary investigation into the usefulness of breaking GRBs into individual pulses is conducted. The results of an ideal set of data do not provide for confident results due to large error bars. Finally, the work concludes with a discussion about the impact of the work and the future of GRB luminosity relations

Does The Addition of a Duration Improve the L_iso - E_peak Relation For Gamma-Ray Bursts?

Firmani et al. proposed a new Gamma Ray Burst (GRB) luminosity relation that showed a significant improvement over the L_iso-E_peak relation. The new proposed relation simply modifies the E_peak value by multiplying it by a power of T_0.45, where T_0.45 is a particular measure of the GRB duration. We begin by reproducing the results of Firmani for his 19 bursts. We then test the Firmani relation for the same 19 bursts except that we use independently measured values for L_iso, T_0.45, and E_peak, and we find that the relation deteriorates substantially. We further test the relation by using 60 GRBs with measured spectroscopic redshifts, and find a relation that has a comparable scatter as the original L_iso-E_peak relation. That is, a much larger sample of bursts does not reproduce the small scatter as reported by Firmani et al. Finally, we investigate whether the Firmani relation is improved by the use of any of 32 measures of duration in place of T_0.45. The quality of each alternative duration measure is evaluated with the root mean square of the scatter between the observed and fitted logarithmic Liso values. Although we find some durations yield slightly better results than T_0.45, the differences between the duration measures are minimal. We find that the addition of a duration does not add any significant improvement to the L_iso-E_peak relation. We also present a simple and direct derivation of the Firmani relation from both the L_iso-E_peak and Amati relations. In all we conclude that the Firmani relation neither has an independent existence nor does it provide any significant improvement on previously known relations that are simpler.Comment: ApJ in press, 17 pages, 3 figures, 3 table

Receso unilateral de contrato en tiempos de buena fe contractual

Pacta sunt servanda: los contratos se celebran para cumplirse. Esta es una máxima en derecho contractual que refiere a la fuerza vinculante del contrato. Dicho principio aparece consagrado en nuestro ordenamiento jurídico en el Art. 1291 inciso primero del Código Civil Uruguayo (en adelante CCU): “los contratos legalmente celebrados forman una regla a la cual deben someterse las partes como a la ley misma”. Conceder a uno de los contratantes la posibilidad de que lo rescinda unilateralmente en cualquier momento, parece a priori una suerte de contraprincipio contractual. Uno de los objetivos de este trabajo será analizar las hipótesis en que dicha facultad es lícita y los casos en que su pacto deviene nulo o abusivo por incumplir normas o principios generales. El receso unilateral ofrece contornos diferenciados según se trate de contratos de duración sujetos a plazo o, si por el contrario, el plazo es indeterminado, donde en principio existe un derecho de receso unilateral ad nutum. En la investigación a desarrollar se procurará demostrar que el derecho potestativo, aún en los contratos con plazo indeterminado, no es irrestricto. “La validez y el cumplimiento de los contratos no pueden dejarse al arbitrio de uno de los contrayentes” , reza el artículo 1253 del CCU. Esto significa que, prima facie , nadie puede desvincularse por su sola voluntad de un contrato. Esta norma nos brinda una primera pauta sobre las dificultades que tendrá el contratante para rescindir unilateralmente un contrato donde se haya estipulado un plazo. Se partirá de la premisa de que es nula toda cláusula que habilite a uno de los contrayentes a rescindir el contrato por su sola voluntad durante el plazo original, aunque la doctrina no es unánime al respecto pese a los claros términos normativos. Surge la interrogante si la autonomía de la voluntad puede primar frente a principios de tanto peso como los consagrados en los Arts. 1253 y 1291 del CCU. También entra en juego el concepto de “justa causa” para determinar si resulta admisible el receso en forma previa al vencimiento de un contrato. En los contratos de duración indeterminada, en cambio, rigen los principios de libertad y de temporalidad del vínculo obligacional, por lo cual su ejercicio es legítimo. No obstante, según las particularidades de la relación contractual, podrá ser necesario un preaviso que tenga por finalidad evitar las consecuencias de un receso abusivo. Hay quienes priorizan el principio de libertad y por tanto defienden fervorosamente que la carencia de plazo habilita a rescindir el contrato en cualquier circunstancia sin ningún tipo de responsabilidad. A lo sumo admiten una reparación en forma excepcional cuando se verifica un ejercicio de esta facultad con absoluta y manifiesta mala fe. En el presente estudio se postulará que derecho potestativo no puede ser sinónimo de derecho arbitrario o discrecional. La variedad de situaciones fácticas obliga a hilar fino y a distinguir los múltiples supuestos. Algunas de las interrogantes que se nos plantean son las siguientes: ¿Es siempre nula la cláusula que habilite el receso unilateral de un contrato sujeto a plazo? ¿En qué hipótesis podría ser válida? ¿Cuál es el concepto de justa causa para rescindir un contrato con plazo vigente? ¿Qué se entiende por ejercicio abusivo del derecho de receso? ¿En qué casos se requiere del preaviso cuando se trata de rescindir un contrato con plazo indeterminado? ¿Qué naturaleza tiene y cuál es la consecuencia de la falta de preaviso? y finalmente, ¿Qué papel juega el deber de mitigar el daño? El tema elegido será ahondado en el marco de la buena fe contractual como principio orientador a los efectos de examinar la casuística. Se indagará de qué manera repercuten los principios generales de derecho, pues sobre este punto existen posiciones contrapuestas. Precisamente el título se vincula a la cuestión de determinar cuánto pesan en los hechos para nuestros jueces los principios generales, especialmente el de buena fe. ¿Realmente son tiempos de buena fe contractual? Agotado ese panorama general, se estudiarán casos específicos, a saber: las facultades de la Administración para rescindir contratos administrativos ¿En qué casos es válido el receso? ¿Existe un poder exorbitante de ius variandi que habilite a rescindir el contrato en forma unilateral? Participamos de la tesis que rechaza los poderes exorbitantes de la Administración como justificación para rescindir el contrato administrativo sin justa causa. También nos despierta particular interés la revocación del contrato de construcción por parte del comitente una vez iniciada la construcción de la obra. Mediante un análisis pormenorizado del Artículo 1847 del Código Civil se estudiará la indemnización que le corresponde a la contratista frente al receso de su co-contratante. Finalmente, el contrato “vedette” en esta materia es el de distribución. Resulta habitual que no esté sujeto a plazo, lo que lleva implícita la potestad de un receso. Sin embargo, ciertos vínculos comerciales de larga data obligan al intérprete a analizar la extinción del contrato desde una óptica más justa o si se quiere, más razonable o realista. Considerar que, por ejemplo, se puede rescindir un contrato de distribución que transcurrió durante más de tres décadas en forma intempestiva, sería privilegiar un principio en desmedro de otros. Frente a un ejercicio abusivo del derecho de receso, nace la obligación de reparar el daño derivado de esa conducta antijurídica. En este sentido, se entenderá el abuso de derecho como referencia o límite al ejercicio del desistimiento unilateral. Haciendo un paralelismo con el terreno audiovisual, buscamos proyectar una especie de documental. Allí se narran hechos seguidos de interpretaciones de los mismos. Salvando las distancias por tratarse de una obra escrita, lo que se pretende es introducir los desarrollos teóricos con un enfoque crítico, y seguidamente comentar cada tema abordando una o más sentencias para ilustrar al lector acerca de la casuística y la realidad en nuestros tribunales

The Total Errors In Measuring Epeak for Gamma-Ray Bursts

While Epeak has been extensively used in the past, for example with luminosity indicators, it has not been thoroughly examined for possible sources of scatter. In the literature, the reported error bars for Epeak are the simple Poisson statistical errors. Additional uncertainties arise due to the choices made by analysts in determining Epeak (e.g., the start and stop times of integration), imperfect knowledge of the response of the detector, different energy ranges for various detectors, and differences in models used to fit the spectra. We examine the size of these individual sources of scatter by comparing many independent pairs of published Epeak values for the same bursts. Indeed, the observed scatter in multiple reports of the same burst (often with the same data) is greatly larger than the published statistical error bars. We measure that the one-sigma uncertainty associated with the analyst's choices is 28%, i.e., 0.12 in Log10(Epeak), with the resultant errors always being present. The errors associated with the detector response are negligibly small. The variations caused by commonly-used alternative definitions of Epeak (such as present in all papers and in all compiled burst lists) is typically 23%-46%, although this varies substantially with the application. The implications of this are: (1) Even the very best measured Epeak values will have systematic uncertainties of 28%. (2) Thus, GRBs have a limitation in accuracy for a single event, with this being reducible by averaging many bursts. (3) The typical one-sigma total uncertainty for collections of bursts is 55%. (4) We also find that the width of the distribution for Epeak in the burst frame must be near zero, implying that some mechanism must exist to thermostat GRBs. (5) Our community can only improve on this situation by using collections of bursts which all have identical definitions for the Epeak calculation.Comment: 25 pages, 2 figures, ApJ accepte

A significant problem with using the Amati relation for cosmological purposes

We consider the distribution of many samples of gamma-ray bursts when plotted in a diagram with their bolometric fluence (Sbolo) versus the observed photon energy of peak spectral flux (E peak, obs). In this diagram, all bursts that obey the Amati relation (a luminosity relation where the total burst energy has a power-law relation to E peak, obs) must lie above some limiting line, although observational scatter is expected to be substantial. We confirm that early bursts with spectroscopic redshifts are consistent with this Amati limit. But we find that the bursts from BATSE, Swift, Suzaku, and Konus are all greatly in violation of the Amati limit, and this is true whether or not the bursts have measured spectroscopic redshifts. That is, the Amati relation has definitely failed. In the S bolo-E peak, obs diagram, wefind that every satellite has a greatly different distribution. This requires that selection effects are dominating these distributions, which we quantitatively identify. For detector selections, the trigger threshold and the threshold for the burst to obtain a measured E peak, obs combine to make a diagonal cutoff with the position of this cutoff varying greatly detector to detector. For selection effects due to the intrinsic properties of the burst population, the distribution of E peak, obs makes bursts with low and high values rare, while the fluence distribution makes bright bursts relatively uncommon. For a detector with a high threshold, the combination of these selection effects serves to allow only bursts within a region along the Amati limit line to be measured, and these bursts will then appear to follow an Amati relation. Therefore, the Amati relation is an artifact of selection effects within the burst population and the detector. As such, the Amati relation should not be used for cosmological tasks. This failure of the Amati relation is in no way prejudicial against the other luminosity relations. © 2012. The American Astronomical Society. All rights reserved

Gamma-ray Burst Luminosity Relations: Two-dimensional versus Three-dimensional Correlations

The large scatters of luminosity relations of gamma-ray bursts (GRBs) have been one of the most important reasons that prevent the extensive applications of GRBs in cosmology. In this paper, we extend the two-dimensional (2D) luminosity relations with $\tau_{\mathrm{lag}}$, $V$, $E_{\mathrm{peak}}$, and $\tau_{\mathrm{RT}}$ as the luminosity indicators to three dimensions (3D) using the same set of luminosity indicators to explore the possibility of decreasing the intrinsic scatters. We find that, for the 3D luminosity relations between the luminosity and an energy scale ($E_{\mathrm{peak}}$) and a time scale ($\tau_{\mathrm{lag}}$ or $\tau_{\mathrm{RT}}$), their intrinsic scatters are considerably smaller than those of corresponding 2D luminosity relations. Enlightened by the result and the definition of the luminosity (energy released in units of time), we discussed possible reasons behind, which may give us helpful suggestions on seeking more precise luminosity relations for GRBs in the future.Comment: 7 pages, 3 tables, 1 figur

Toward tight gamma-ray burst luminosity relations

The large scatters of luminosity relations of gamma-ray bursts (GRBs) have been one of the most important reasons that prevent the extensive applications of GRBs in cosmology. Many efforts have been made to seek tight luminosity relations. With the latest sample of 116 GRBs with measured redshift and spectral parameters, we investigate 6 two-dimensional (2D) correlations and 14 derived three-dimensional (3D) correlations of GRBs to explore the possibility of decreasing the intrinsic scatters of the luminosity relations of GRBs. We find the 3D correlation of $E_{\mathrm{peak}}$--$\tau_{\mathrm{RT}}$--$L$ to be evidently tighter (at the $2 \sigma$ confidence level) than its corresponding 2D correlations, i.e., the $E_{\mathrm{peak}}$--$L$ and $\tau_{\mathrm{RT}}$--$L$ correlations. In addition, the coefficients before the logarithms of $E_{\mathrm{peak}}$ and $\tau_{\mathrm{RT}}$ in the $E_{\mathrm{peak}}$--$\tau_{\mathrm{RT}}$--$L$ correlation are almost exact opposites of each other. Inputting this situation as a prior reduces the relation to $L \propto (E_{\mathrm{peak}}^{'} / \tau_{\mathrm{RT}}^{'})^{0.842 \pm 0.064}$, where $E_{\mathrm{peak}}^{'}$ and $\tau_{\mathrm{RT}}^{'}$ denote the peak energy and minimum rise time in the GRB rest frame. We discuss how our findings can be interpreted/understood in the framework of the definition of the luminosity (energy released in units of time). Our argument about the connection between the luminosity relations of GRBs and the definition of the luminosity provides a clear direction for exploring tighter luminosity relations of GRBs in the future.Comment: 9 pages, 1 figure, 1 table, added discussion and clarification, added references, minor language edit, published in The Astrophysical Journa