Constraining properties of GRB magnetar central engines using the observed plateau luminosity and duration correlation

An intrinsic correlation has been identified between the luminosity and duration of plateaus in the X-ray afterglows of Gamma-Ray Bursts (GRBs; Dainotti et al. 2008), suggesting a central engine origin. The magnetar central engine model predicts an observable plateau phase, with plateau durations and luminosities being determined by the magnetic fields and spin periods of the newly formed magnetar. This paper analytically shows that the magnetar central engine model can explain, within the 1$\sigma$ uncertainties, the correlation between plateau luminosity and duration. The observed scatter in the correlation most likely originates in the spread of initial spin periods of the newly formed magnetar and provides an estimate of the maximum spin period of ~35 ms (assuming a constant mass, efficiency and beaming across the GRB sample). Additionally, by combining the observed data and simulations, we show that the magnetar emission is most likely narrowly beamed and has $\lesssim$20% efficiency in conversion of rotational energy from the magnetar into the observed plateau luminosity. The beaming angles and efficiencies obtained by this method are fully consistent with both predicted and observed values. We find that Short GRBs and Short GRBs with Extended Emission lie on the same correlation but are statistically inconsistent with being drawn from the same distribution as Long GRBs, this is consistent with them having a wider beaming angle than Long GRBs.Comment: MNRAS Accepte

Metastability of life

The physical idea of the natural origin of diseases and deaths has been presented. The fundamental microscopical reason is the destruction of any metastable state by thermal activation of a nucleus of a nonreversable change. On the basis of this idea the quantitative theory of age dependence of death probability has been constructed. The obtained simple Death Laws are very accurately fulfilled almost for all known diseases.Comment: 3 pages, 4 figure

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

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

Empirical maximum lifespan of earthworms is twice that of mice

We considered a Gompertzian model for the population dynamics of Eisenia andrei case-cohorts in artificial OECD soil under strictly controlled conditions. The earthworm culture was kept between 18 and 22°C at a constant pH of 5.0. In all, 77 lumbricids were carefully followed for almost 9 years, until the oldest died. The Eisenia median longevity is 4.25 years and the oldest specimen was 8.73 years. Eisenia cocoons were hand-sorted every 3 weeks, washed in distilled water, placed in Petri dishes, and counted. Regular removal did not reduce breeding. Each fertile cocoon contained on average two or three embryos. The failure rates (mortality and infertility percentages) are smooth power functions where the rate at time (n + 1) captured most of the phenomenology of the previous rate at time n, as expected by the considered law, but not at both the beginning and the end of this long-term laboratory study

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.

Interplay between distribution of live cells and growth dynamics of solid tumours

Experiments show that simple diffusion of nutrients and waste molecules is not sufficient to explain the typical multilayered structure of solid tumours, where an outer rim of proliferating cells surrounds a layer of quiescent but viable cells and a central necrotic region. These experiments challenge models of tumour growth based exclusively on diffusion. Here we propose a model of tumour growth that incorporates the volume dynamics and the distribution of cells within the viable cell rim. The model is suggested by in silico experiments and is validated using in vitro data. The results correlate with in vivo data as well, and the model can be used to support experimental and clinical oncology

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.

A comparison between radio loud and quiet gamma-ray bursts, and evidence for a potential correlation between intrinsic duration and redshift in the radio loud population

We extend our study of energetic radio-loud and -quiet gamma-ray bursts (GRBs), suggesting these GRBs potentially come from two separate progenitor systems. We expand the sample from our previous paper and find that our results are strengthened—radio-quiet GRBs have significantly shorter intrinsic prompt duration, and are also less energetic on average. However, the tenuous correlation between isotropic energy and intrinsic duration in the radio dark sample remains tenuous and is slightly weakened by adding more bursts. Interestingly, we find an anticorrelation between the intrinsic duration and redshift in the radio bright sample but not the radio dark sample, further supporting that these two samples may come from separate progenitors. We also find that very high energy (0.1–100 GeV) extended emission is only present in the radio-loud sample. There is no significant difference between the presence of X-ray/optical plateaus or the average jet opening angles between the two samples. We explore the interpretation of these results in the context of different progenitor models. The data are consistent with the radio-loud GRBs coming from a helium merger system and the radio-quiet GRBs coming from a collapsar system, but may also reflect other dichotomies in the inner engine such as a neutron star versus black hole core