The Environments of the Most Energetic Gamma-Ray Bursts

We analyze the properties of a sample of long gamma-ray bursts (LGRBs) detected by the Fermi satellite that have a spectroscopic redshift and good follow-up coverage at both X-ray and optical/nIR wavelengths. The evolution of LGRB afterglows depends on the density profile of the external medium, enabling us to separate wind or ISM-like environments based on the observations. We do this by identifying the environment that provides the best agreement between estimates of $p$, the index of the underlying power-law distribution of electron energies, as determined by the behavior of the afterglow in different spectral/temporal regimes. At 11 rest-frame hours after trigger, we find a roughly even split between ISM-like and wind-like environments. We further find a 2$\sigma$ separation in the prompt emission energy distributions of wind-like and ISM-like bursts. We investigate the underlying physical parameters of the shock, and calculate the (degenerate) product of density and magnetic field energy ($\epsilon_B$). We show that $\epsilon_B$ must be $\ll 10^{-2}$ to avoid implied densities comparable to the intergalactic medium. Finally, we find that the most precisely constrained observations disagree on $p$ by more than would be expected based on observational errors alone. This suggests additional sources of error that are not incorporated in the standard afterglow theory. For the first time, we provide a measurement of this intrinsic error which can be represented as an error in the estimate of $p$ of magnitude $0.25 \pm 0.04$. When this error is included in the fits, the number of LGRBs with an identified environment drops substantially, but the equal division between the two types remains.Comment: 31 pages (+14 appendix), 9 figures, 6 tables. Accepted for publication in Ap

Fallback accretion on to a newborn magnetar : long GRBs with giant X-ray flares

Flares in the X-ray afterglow of gamma-ray bursts (GRBs) share more characteristics with the prompt emission than the afterglow, such as pulse profile and contained fluence. As a result, they are believed to originate from late-time activity of the central engine and can be used to constrain the overall energy budget. In this paper, we collect a sample of 19 long GRBs observed by Swift-XRT that contain giant flares in their X-ray afterglows. We fit this sample with a version of the magnetar propeller model, modified to include fallback accretion. This model has already successfully reproduced extended emission in short GRBs. Our best fits provide a reasonable morphological match to the light curves. However, 16 out of 19 of the fits require efficiencies for the propeller mechanism that approach 100%. The high efficiency parameters are a direct result of the high energy contained in the flares and the extreme duration of the dipole component, which forces either slow spin periods or low magnetic fields. We find that even with the inclusion of significant fallback accretion, in all but a few cases it is energetically challenging to produce prompt emission, afterglow and giant flares within the constraints of the rotational energy budget of a magnetar

A multi-messenger model for neutron star - black hole mergers

We present a semi-analytic model for predicting kilonova light curves from the mergers of neutron stars with black holes (NSBH). The model is integrated into the MOSFiT platform, and can generate light curves from input binary properties and nuclear equation-of-state considerations, or incorporate measurements from gravitational wave (GW) detectors to perform multi-messenger parameter estimation. The rapid framework enables the generation of NSBH kilonova distributions from binary populations, light curve predictions from GW data, and statistically meaningful comparisons with an equivalent BNS model in MOSFiT. We investigate a sample of kilonova candidates associated with cosmological short gamma-ray bursts, and demonstrate that they are broadly consistent with being driven by NSBH systems, though most have limited data. We also perform fits to the very well sampled GW170817, and show that the inability of an NSBH merger to produce lanthanide-poor ejecta results in a significant underestimate of the early (< 2 days) optical emission. Our model indicates that NSBH-driven kilonovae may peak up to a week after merger at optical wavelengths for some observer angles. This demonstrates the need for early coverage of emergent kilonovae in cases where the GW signal is either ambiguous or absent; they likely cannot be distinguished from BNS mergers by the light curves alone from ~2 days after the merger. We also discuss the detectability of our model kilonovae with the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST).Comment: 14 pages, 6 figures, 2 tables. Accepted for publication in MNRAS. This is the author's final submitted version. The model code is available through MOSFiT at https://github.com/guillochon/MOSFi

The Heumann-Hotzel model for aging revisited

Since its proposition in 1995, the Heumann-Hotzel model has remained as an obscure model of biological aging. The main arguments used against it were its apparent inability to describe populations with many age intervals and its failure to prevent a population extinction when only deleterious mutations are present. We find that with a simple and minor change in the model these difficulties can be surmounted. Our numerical simulations show a plethora of interesting features: the catastrophic senescence, the Gompertz law and that postponing the reproduction increases the survival probability, as has already been experimentally confirmed for the Drosophila fly.Comment: 11 pages, 5 figures, to be published in Phys. Rev.

Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B

Exact Solution of an Evolutionary Model without Ageing

We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated indicating that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups as many protozoa and coelenterates is discussed.Comment: LaTeX file, 15 pages, 2 ps figures, to appear in Phys. Rev.

The diversity of kilonova emission in short gamma-ray bursts

The historic first joint detection of both gravitational-wave and electromagnetic emission from a binary neutron star merger cemented the association between short gamma-ray bursts (SGRBs) and compact object mergers, as well as providing a well-sampled multi-wavelength light curve of a radioactive kilonova (KN) for the first time. Here, we compare the optical and near-infrared light curves of this KN, AT 2017gfo, to the counterparts of a sample of nearby (z < 0.5) SGRBs to characterize their diversity in terms of their brightness distribution. Although at similar epochs AT 2017gfo appears fainter than every SGRB-associated KN claimed so far, we find three bursts (GRBs 050509B, 061201, and 080905A) where, if the reported redshifts are correct, deep upper limits rule out the presence of a KN similar to AT 2017gfo by several magnitudes. Combined with the properties of previously claimed KNe in SGRBs this suggests considerable diversity in the properties of KN drawn from compact object mergers, despite the similar physical conditions that are expected in many NS–NS mergers. We find that observer angle alone is not able to explain this diversity, which is likely a product of the merger type (NS–NS versus NS–BH) and the detailed properties of the binary (mass ratio, spins etc.). Ultimately disentangling these properties should be possible through observations of SGRBs and gravitational-wave sources, providing direct measurements of heavy element enrichment throughout the universe

“It’s hard to tell”. The challenges of scoring patients on standardised outcome measures by multidisciplinary teams: a case study of Neurorehabilitation

Background Interest is increasing in the application of standardised outcome measures in clinical practice. Measures designed for use in research may not be sufficiently precise to be used in monitoring individual patients. However, little is known about how clinicians and in particular, multidisciplinary teams, score patients using these measures. This paper explores the challenges faced by multidisciplinary teams in allocating scores on standardised outcome measures in clinical practice. Methods Qualitative case study of an inpatient neurorehabilitation team who routinely collected standardised outcome measures on their patients. Data were collected using non participant observation, fieldnotes and tape recordings of 16 multidisciplinary team meetings during which the measures were recited and scored. Eleven clinicians from a range of different professions were also interviewed. Data were analysed used grounded theory techniques. Results We identified a number of instances where scoring the patient was 'problematic'. In 'problematic' scoring, the scores were uncertain and subject to revision and adjustment. They sometimes required negotiation to agree on a shared understanding of concepts to be measured and the guidelines for scoring. Several factors gave rise to this problematic scoring. Team members' knowledge about patients' problems changed over time so that initial scores had to be revised or dismissed, creating an impression of deterioration when none had occurred. Patients had complex problems which could not easily be distinguished from each other and patients themselves varied in their ability to perform tasks over time and across different settings. Team members from different professions worked with patients in different ways and had different perspectives on patients' problems. This was particularly an issue in the scoring of concepts such as anxiety, depression, orientation, social integration and cognitive problems. Conclusion From a psychometric perspective these problems would raise questions about the validity, reliability and responsiveness of the scores. However, from a clinical perspective, such characteristics are an inherent part of clinical judgement and reasoning. It is important to highlight the challenges faced by multidisciplinary teams in scoring patients on standardised outcome measures but it would be unwarranted to conclude that such challenges imply that these measures should not be used in clinical practice for decision making about individual patients. However, our findings do raise some concerns about the use of such measures for performance management