The GRB luminosity function in the internal shock model confronted to observations

We compute the expected luminosity function of GRBs in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power Edot and contrast in Lorentz factor Kappa = Gamma_max/Gamma_min. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist) the luminosity function has two branches. At high luminosity it follows the distribution of Edot while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the log N - log P curve, the Ep distribution of bright BATSE bursts and the XRF/GRB ratio obtained by HETE2 we show that single and broken power-laws can provide equally good fits of these data. Present observations are therefore unable to favor one form of the other. However when a broken power-law is adopted they clearly indicate a low luminosity slope ~ -0.6 +- 0.2, compatible with the prediction of the internal shock model.Comment: 9 pages, 5 figure

The GRB luminosity function: predictions from the internal shock model and comparison with observations

International audienceWe compute the expected luminosity function of gamma-ray bursts (GRBs) in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power and contrast in Lorentz factor κ = Γmax/Γmin. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist), then the luminosity function has two branches. At high luminosity it follows the distribution of while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the logN-logP curve, the Ep distribution of bright Burst and Transient Source Experiment (BATSE) bursts and the X-ray flash (XRF)/GRB ratio obtained by High Energy Transient Explorer 2 (HETE2), we show that single and broken power laws can provide equally good fits of these data. Present observations are therefore unable to favour one form or the other. However, when a broken power law is adopted they clearly indicate a low-luminosity slope ~= -0.6 +/- 0.2, compatible with the prediction of the internal shock model

COVID-19 Lockdown: A Global Study Investigating the Effect of Athletes' Sport Classification and Sex on Training Practices

PURPOSE: To investigate differences in athletes' knowledge, beliefs, and training practices during COVID-19 lockdowns with reference to sport classification and sex. This work extends an initial descriptive evaluation focusing on athlete classification. METHODS: Athletes (12,526; 66% male; 142 countries) completed an online survey (May-July 2020) assessing knowledge, beliefs, and practices toward training. Sports were classified as team sports (45%), endurance (20%), power/technical (10%), combat (9%), aquatic (6%), recreational (4%), racquet (3%), precision (2%), parasports (1%), and others (1%). Further analysis by sex was performed. RESULTS: During lockdown, athletes practiced body-weight-based exercises routinely (67% females and 64% males), ranging from 50% (precision) to 78% (parasports). More sport-specific technical skills were performed in combat, parasports, and precision ( approximately 50%) than other sports ( approximately 35%). Most athletes (range: 50% [parasports] to 75% [endurance]) performed cardiorespiratory training (trivial sex differences). Compared to prelockdown, perceived training intensity was reduced by 29% to 41%, depending on sport (largest decline: approximately 38% in team sports, unaffected by sex). Some athletes (range: 7%-49%) maintained their training intensity for strength, endurance, speed, plyometric, change-of-direction, and technical training. Athletes who previously trained >/=5 sessions per week reduced their volume (range: 18%-28%) during lockdown. The proportion of athletes (81%) training >/=60 min/session reduced by 31% to 43% during lockdown. Males and females had comparable moderate levels of training knowledge (56% vs 58%) and beliefs/attitudes (54% vs 56%). CONCLUSIONS: Changes in athletes' training practices were sport-specific, with few or no sex differences. Team-based sports were generally more susceptible to changes than individual sports. Policy makers should provide athletes with specific training arrangements and educational resources to facilitate remote and/or home-based training during lockdown-type events