Cannonball Model Research Articles

The Maximum Isotropic Equivalent Energy of Gamma-Ray Bursts

In the cannonball model of gamma-ray bursts (GRBs), a highly relativistic jet of plasmoids of ordinary stellar matter that is ejected during stellar collapse or shortly after by fallback matter, produces simultaneously a GRB and a cosmic-ray burst by scattering light and charged particles in its path. This association and the observed knee at ∼1 TeV in the energy spectrum of Galactic cosmic-ray electrons imply a maximum peak energy ∼2.25 MeV in the energy spectrum of GRBs in the 1 keV–10 MeV band. Such a peak energy and the Amati correlation in GRBs imply a maximum isotropic equivalent energy release of ∼3.8 × 1054 erg in GRBs, in the 1 keV–10 MeV band. Both predictions are in good agreement with up-to-date observations.

A Drag Coefficient Modeling Approach Using Spatial and Temporal Fourier Expansions for Orbit Determination

The estimation and modeling of drag effects on low altitude satellites and debris is a limiting problem in the prediction of their orbits over time. Independent of the stochastic variations in atmospheric density, which drive the magnitude of the drag force, there are systematic variations in the drag coefficient due to satellite specific factors and atmospheric conditions. These include satellite attitude shifts, variations in ambient atmospheric parameters such as temperature, molecular composition, and the satellite wall temperature. Thus, even with accurate empirical models for the atmospheric density, there remain systematic model uncertainties and time variations in the effective coefficient of drag that affect the satellite’s motion, which are not captured using the standard constant drag coefficient model. We report on our recent research on developing Fourier expansion based models of an arbitrary object’s coefficient of drag with the overall purpose to develop corrections to the standard model. If the attitude profile of a satellite or object is known, a Fourier series expansion of the overall coefficient of drag as a function of wind vector direction in the body-frame can be introduced. For bodies with unknown or more complex attitude profiles, we introduce a periodically varying drag coefficient tied to a satellite’s position in orbit. This model enables the estimation of higher-order temporal variations in drag that would be correlated with variations in altitude, temperature and density. An improved prediction capability over the standard cannonball model is shown and the formulation of how it can be incorporated into standard filtering techniques is presented.

Analysis of Tiangong-2 orbit determination and prediction using onboard dual-frequency GNSS data

Tiangong-2 is the first Chinese real space laboratory, launched into earth orbit with an altitude of approximately 393 km on September 15, 2016. Precise orbit determination (POD) is one of the essential conditions for conducting onboard scientific research. The precise orbit of Tiangong-2 is mainly determined by the reduced-dynamic method using space-borne global navigation satellite system (GNSS) data, which are collected by an onboard dual-frequency GNSS receiver. The in-flight performance of the receiver is first assessed in terms of tracking ability, code multipath errors and noise levels of code and carrier phase observations. Then, the effects of refined non-gravitational force models and GNSS antenna phase center variations (PCVs) on the POD are analyzed. The estimated empirical accelerations are substantially reduced by 45% in the along-track direction using a macro-model compared to that using a cannonball model for drag computation. The application of antenna PCVs correction leads to better consistency between reduced-dynamic and kinematic orbit solutions. Satellite laser ranging validation shows that the accuracy of Tiangong-2 precise orbits is 1.7 cm after using the improved reduced-dynamic method. Based on the orbit determination results, the quality of Tiangong-2 orbit predictions is assessed for periods without and with the refined non-gravitational force models. The use of the macro-model and high-quality density models for drag computation is shown to help improve orbit prediction quality.

Impact of solar radiation pressure modeling on orbital dynamics in the vicinity of binary asteroids

Missions to asteroids are now an important component of the space exploration program of major space agencies in the world, with the goal of better understanding the formation of the Solar system and learn about their dynamics to be able to react in case of a possible collision with the Earth. As binary asteroids compose approximately 16% of near Earth asteroids, they are getting more attention from researchers. One mission is currently being planned to binary asteroid system 65803 Didymos. This mission motivates research on the dynamics of a spacecraft near a binary asteroid. Since the primary bodies of these binary systems have small masses, perturbations like the Solar Radiation Pressure (SRP) or the shape of the primary bodies have a great influence on the dynamics of a spacecraft in their vicinity. Studies that already exist on the effect of the SRP on the dynamics of a spacecraft near binary asteroid systems have mostly used low-fidelity SRP acceleration models, such as the cannonball model or simple flat plate model with a purely reflecting spacecraft. This study shows how the choice of the model influences the strength of the SRP acceleration acting on the spacecraft and how it is possible to take advantage of the choice of the nominal attitude of the spacecraft to influence how the SRP affects the spacecraft dynamics when using a more complex SRP acceleration model. Various types of trajectories are studied, with different results and conclusions.

Orbit determination of CE-4′s relay satellite in Earth-Moon L2 libration point orbit

The Magpie Bridge mission is a part of the Chang’E-4 mission, it is the first Chinese spacecraft carries out Earth-Moon communication mission at Earth-Moon libration points. The Magpie Bridge operations team utilizes the Beijing Aerospace Control Center (BACC) Orbit Determination and Analysis Software (BODAS) to obtain the orbit, the measurements include range, Doppler and relay, relay-rate from China Deep Space Network (CDSN) and Very Long Baseline Interferometry (VLBI) system respectively. In order to effectively improve the accuracy of the orbit, we provided the solar radiation model with multiple characteristic surfaces. The new model is based on the structure and the real-time attitude of the satellite to solve the real-time solar pressure equivalent area. Compared with the cannon-ball model, it can calculate the solar pressure equivalent area of the satellite more accurately in orbit determination. By the analysis of the tracking measurement data, we found that the new solar radiation pressure model reduces the error of position and velocity compared to the cannon-ball model.

Preliminary Study on the Orbit Determinationof Chang'e-4 Lunar Relay Satellite Mission

The Chang' e-4 mission will explore the back of the moon by the lander,inspector and relay satellites that orbit the second Lagrange point(L2). The relay satellites have been launched and entered Halo orbit around L2 successfully. Based on the mission orbit dynamics model of the relay satellite,the perturbation source magnitude of the relay satellite in Halo orbit and the main factors affecting the orbit determination and prediction are analyzed by simulation. The results show that the Solar pressure perturbation is the main factor affecting the orbit determination and prediction. In order to reduce the influence and improve the orbit determination accuracy,a method for calculating the equivalent pressure area is proposed based on the cannon-ball model,combined with the operational characteristics in orbit and the characteristics of the structure of the relay satellite. The simulation results show that the orbit determination accuracy of velocity can be improved about one order of magnitude by using the modified cannon-ball model

Averaged solar radiation pressure modeling for high area-to-mass ratio objects in geosynchronous orbits

Space Situational Awareness, among other efforts, is aimed at providing a comprehensive and accurate knowledge of all Earth-orbiting objects. This is done by maintaining a catalog of space objects’ states (position and velocity). In the absence of observations, the orbits of these objects need to be numerically simulated. In this work, we study the high area-to-mass ratio class of objects which are sensitive to very small changes in perturbations, particularly the attitude dependent solar radiation pressure. This attitude dependency renders the orbit-attitude motion to be coupled. Traditionally, a cannonball model would be used to model these perturbations. While this is acceptable for an attitude stabilized active satellite, for non-functional space debris, the cannonball model does not seem to approximate the true dynamics accurately. Hence, a more precise, albeit computationally expensive propagation model needs to be developed, which warrants a better modeling of the perturbations in the near-Earth space. This work introduces a new model that averages the solar radiation pressure force experienced by multi-layer insulation foil in geosynchronous orbits. While speeding up the computational time by 66%, this model produces errors that are small enough to stay within the field of view of surveying telescopes over the propagation period of four days. The approach is compared with other existing models.

On The Origin of Supernova-less Long Gamma-Ray Bursts

Abstract The fraction of long duration gamma-ray bursts (GRBs) without an associated bright supernova (SN-less GRBs) at low redshifts is comparable to that of GRBs associated with bright supernovae (SN-GRBs). The prompt emission and its fast decline phase in both types of GRBs are well described by the cannonball model of GRBs, where inverse Compton scattering of ambient light is the dominant γ-ray production mechanism. However, in SN-less GRBs, the fast decay of the prompt emission appears to be overtaken by an afterglow powered by a millisecond pulsar, while, in SN-GRBs, the late-time X-ray afterglow is well described by synchrotron radiation from the decelerating jet in the interstellar medium. We use their different X-ray light curves to determine the ratio of SN-less GRBs/SN-GRBs at very high redshifts. We find that at z > 4, this ratio is the same as that at small redshifts. Such a z-independent ratio suggests that the origin of SN-less GRBs is a phase transition of neutron stars to quark stars in high-mass X-ray binaries, rather than the merger of neutron stars.

Critical test of gamma-ray burst theories

Very long and precise follow-up measurements of the X-ray afterglow of very intense gamma ray bursts (GRBs) allow a critical test of GRB theories. Here we show that the single power-law decay with time of the X-ray afterglow of GRB 130427A, the record long and most accurately measured X-ray afterglow of an intense GRB by the Swift, Chandra and XMM Newton space observatories, and of all other known intense GRBs, is that predicted by the cannonball (CB) model of GRBs from their measured spectral index, while it disagrees with that predicted by the widely accepted fireball (FB) models of GRBs.

Update on the GRB universal scaling EX,iso–Eγ,iso–Epk with 10 years of Swift data

From a comprehensive statistical analysis of $Swift$ X-ray light-curves of gamma-ray bursts (GRBs) collected from December 2004 to the end of 2010, we found a three-parameter correlation between the isotropic energy emitted in the rest frame 1-10$^4$ keV energy band during the prompt emission (E$_{\rm{\gamma,iso}}$), the rest frame peak of the prompt emission energy spectrum (E$_{\rm{pk}}$), and the X-ray energy emitted in the rest frame 0.3-30 keV observed energy band (E$_{\rm{X,iso}}$), computed excluding the contribution of the flares. In this paper, we update this correlation with the data collected until June 2014, expanding the sample size with $\sim$35% more objects, where the number of short GRBs doubled. With this larger sample we confirm the existence of a universal correlation that connects the prompt and afterglow properties of long and short GRBs. We show that this correlation does not depend on the X-ray light-curve morphology and that further analysis is necessary to firmly exclude possible biases derived by redshift measurements. In addition we discuss about the behavior of the peculiar objects as ultra-long GRBs and we propose the existence of an intermediate group between long and short GRBs. Interestingly, two GRBs with uncertain classification fall into this category. Finally, we discuss the physics underlying this correlation, in the contest of the efficiency of conversion of the prompt $\gamma$-ray emission energy into the kinetic energy of the afterglow, the photosferic model, and the cannonball model.

Improving Space Object Catalog Maintenance Through Advances in Solar Radiation Pressure Modeling

This paper investigates the weaknesses of using the cannonball model to represent the solar radiation pressure force on an object in an orbit determination process, and it presents a number of alternative models that greatly improve the orbit determination performance. These weaknesses are rooted in the fact that the cannonball model is not a good representation of the true solar radiation pressure force acting on an arbitrary object. Using an erroneous force model results in poor estimates, inaccurate trajectory propagation, unrealistic covariances, and the inability to fit long and/or dense arcs of data. The alternative models presented are derived from a Fourier series representation of the solar radiation pressure force. The simplest instantiation of this model requires only two more parameters to be estimated, however, this results in orders of magnitude improvements in tracking accuracy. This improvement is illustrated through numerical examples of a discarded upper stage in a geosynchronous transfer orbit, and more drastically for a piece of high-area-to-mass ratio debris in a near-geosynchronous orbit. Implementation of improved solar radiation pressure models in this manner will alleviate track correlation, object identification, and sensor tasking issues that plague current catalog maintenance due to the inaccurate standard dynamic model.

Modelling of Solar Radiation Pressure Effects: Parameter Analysis for the MICROSCOPE Mission

Modern scientific space missions pose high requirements on the accuracy of the prediction and the analysis of satellite motion. On the one hand, accurate orbit propagation models are needed for the design and the preparation of a mission. On the other hand, these models are needed for the mission data analysis itself, thus allowing for the identification of unexpected disturbances, couplings, and noises which may affect the scientific signals. We present a numerical approach for Solar Radiation Pressure modelling, which is one of the main contributors for nongravitational disturbances for Earth orbiting satellites. The here introduced modelling approach allows for the inclusion of detailed spacecraft geometries, optical surface properties, and the variation of these optical surface properties (material degradation) during the mission lifetime. By using the geometry definition, surface property definitions, and mission definition of the French MICROSCOPE mission we highlight the benefit of an accurate Solar Radiation Pressure modelling versus conventional methods such as the Cannonball model or a Wing-Box approach. Our analysis shows that the implementation of a detailed satellite geometry and the consideration of changing surface properties allow for the detection of systematics which are not detectable by conventional models.

LONG GAMMA-RAY BURSTS TRACE THE STAR FORMATION HISTORY

We show that if the broad-line supernova explosions of type Ic (SNeIc) produce the bulk of the observed long duration gamma ray bursts (LGRBs), which include the high luminosity GRBs, low luminosity GRBs and X-ray flashes (XRFs), and if LGRBs have the geometry assumed in the cannonball (CB) model of LGRBs, then their rate measured by Swift and their redshift distribution are consistent with the star formation rate (SFR) over the entire range of redshifts where the SFR has been measured with sufficient accuracy.

Conical fireballs, cannonballs, and jet breaks in the afterglows of gamma ray bursts

The 'jet-break' in the X-ray afterglow of gamma ray bursts (GRBs) appears to be correlated to other properties of the X-ray afterglow and the prompt gamma ray emission, but the correlations are at odds with those predicted by the conical fireball model of GRBs. The correlations are in good agreement, however, with those predicted by the Cannonball model of GRBs.

ON THE RECENTLY DISCOVERED CORRELATIONS BETWEEN GAMMA-RAY AND X-RAY PROPERTIES OF GAMMA-RAY BURSTS

Recently, several new correlations between the observed $\gamma$-ray and the X-ray properties of gamma-ray bursts (GRBs) were inferred from a comprehensive analysis of the X-ray light curves of more than 650 GRBs measured with the Swift X-ray telescope (Swift/XRT) during the years 2004-2010. Like previously well established correlations, they challenge GRB models. Here we show that in the cannonball (CB) model of GRBs, the newly discovered correlations and those that follow from them, have the same simple kinematic origin as those discovered earlier. They result from the strong dependence of the observed radiations on the bulk motion Lorentz and Doppler factors of the jet of highly relativistic plasmoids (CBs) that produces these radiations by interaction with the medium through which it propagates.

CORRELATED SPECTRAL AND TEMPORAL BEHAVIOR OF LATE-TIME AFTERGLOWS OF GAMMA-RAY BURSTS

The cannonball (CB) model of gamma ray bursts (GRBs) predicts that the asymptotic behaviour of the spectral energy density of the X-ray afterglow of GRBs is a power-law in time and in frequency where the difference between the temporal and spectral power-law indexes, $\alpha_X-\beta_X$, is restricted to the values 0, 1/2 and 1. Here we report the distributions of the values $\alpha_X$, $\beta_X$ and their difference for a sample of 315 Swift GRBs. This sample includes all Swift GRBs that were detected before August 1, 2012, whose X-ray afterglow extended well beyond 1 day and the estimated error in $\alpha_X-\beta_X$ was $\leq 0.25$. The values of $\alpha_X$ were extracted from the CB model fits to the entire light curves of their X-ray afterglow while the spectral index was extracted by the Swift team from the time integrated X-ray afterglow of these GRBs. We found that the distribution of the difference $\alpha_X-\beta_X$ for these 315 Swift GRBs has three narrow peaks around 0, 1/2 and 1 whose widths are consistent with being due to the measurement errors, in agreement with the CB model prediction.

KINEMATIC ORIGIN OF CORRELATIONS BETWEEN GAMMA-RAY BURST OBSERVABLES

Recently, several new correlations between gamma ray burst (GRB) observables have been discovered. Like previously well established correlations, they challenge GRB models. Here we show that in the cannonball (CB) model of GRBs, these newly discovered correlations have the same simple kinematic origin as those discovered earlier. They all result from the strong dependence of the observed radiations on the Lorentz and Doppler factors of the jet of highly relativistic plasmoids (CBs) that produces the observed radiations by interaction with the medium through which it propagates.

ON THE EVOLUTION OF THE SPECTRAL BREAK IN THE AFTERGLOW OF GAMMA-RAY BURSTS

The temporal evolution of the spectral break in the time resolved spectral energy density of the broad band afterglow of gamma ray bursts (GRBs) 091127 and 080319B was shown recently to be inconsistent with that expected for the cooling break in the standard fireball model of GRBs. Here we show that it is, however, in good agreement with the predicted temporal evolution of the smooth injection break/bend in the cannonball model of GRBs.

Testing gamma-ray burst models with the afterglow of GRB 090102

We present the observations of the afterglow of gamma-ray burst GRB 090102. Optical data taken by the TAROT, REM, GROND, together with publicly available data from Palomar, IAC and NOT telescopes, and X-ray data taken by the XRT instrument on board the Swift spacecraft were used. This event features an unusual light curve. In X-rays, it presents a constant decrease with no hint of temporal break from 0.005 to 6 days after the burst. In the optical, the light curve presents a flattening after 1 ks. Before this break, the optical light curve is steeper than that of the X-ray. In the optical, no further break is observed up to 10 days after the burst. We failed to explain these observations in light of the standard fireball model. Several other models, including the cannonball model were investigated. The explanation of the broad band data by any model requires some fine tuning when taking into account both optical and X-ray bands.

FLARES IN LONG AND SHORT GAMMA-RAY BURSTS

The many similarities between the prompt emission pulses in gamma ray bursts (GRBs) and X-ray flares during the fast decay and afterglow phases of GRBs suggest a common origin. In the cannonball (CB) model of GRBs, this common origin is mass accretion episodes of fall-back matter on a newly born compact object. The prompt emission pulses are produced by a bipolar jet of highly relativistic plasmoids (CBs) ejected in the early, major episodes of mass accretion. As the accretion material is consumed, one may expect the engine's activity to weaken. X-ray flares ending the prompt emission and during the afterglow phase are produced in such delayed episodes of mass accretion. The common engine, environment and radiation mechanisms (inverse Compton scattering and synchrotron radiation) produce their observed similarities. Flares in both long GRBs and short hard gamma ray bursts (SHBs) can also be produced by bipolar ejections of CBs following a phase transition in compact objects due to loss of angular momentum and/or cooling. Optical flares, however, are mostly produced in collisions of CBs with massive stellar winds/ejecta or with density bumps along their path. In this paper we show that the master formulae of the CB model of GRBs and SHBs, which reproduce very well their prompt emission pulses and their smooth afterglows, seem to reproduce also very well the lightcurves and spectral evolution of the prominent X-ray and optical flares that are well sampled.