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Fitting Formulae (fitting + formula)
Selected AbstractsHard X-ray emission of the Earth's atmosphere: Monte Carlo simulationsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007S. Sazonov ABSTRACT We perform Monte Carlo simulations of cosmic ray-induced hard X-ray radiation from the Earth's atmosphere. We find that the shape of the spectrum emergent from the atmosphere in the energy range 25,300 keV is mainly determined by Compton scatterings and photoabsorption, and is almost insensitive to the incident cosmic ray spectrum. We provide a fitting formula for the hard X-ray surface brightness of the atmosphere as would be measured by a satellite-borne instrument, as a function of energy, solar modulation level, geomagnetic cut-off rigidity and zenith angle. A recent measurement by the INTEGRAL observatory of the atmospheric hard X-ray flux during the occultation of the cosmic X-ray background by the Earth agrees with our prediction within 10 per cent. This suggests that Earth observations could be used for in-orbit calibration of future hard X-ray telescopes. We also demonstrate that the hard X-ray spectra generated by cosmic rays in the crusts of the Moon, Mars and Mercury should be significantly different from that emitted by the Earth's atmosphere. [source] Radiative transitions of the helium atom in highly magnetized neutron star atmospheresMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008Z. Medin ABSTRACT Recent observations of thermally emitting isolated neutron stars revealed spectral features that could be interpreted as radiative transitions of He in a magnetized neutron star atmosphere. We present Hartree,Fock calculations of the polarization-dependent photoionization cross-sections of the He atom in strong magnetic fields ranging from 1012 to 1014 G. Convenient fitting formulae for the cross-sections are given along with the related oscillator strengths for various bound,bound transitions. The effects of finite nucleus mass on the radiative absorption cross-sections are examined using perturbation theory. [source] Transients from initial conditions in cosmological simulationsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2006Martín Crocce ABSTRACT We study the impact of setting initial conditions in numerical simulations using the standard procedure based on the Zel'dovich approximation (ZA). As it is well known from the perturbation theory, ZA initial conditions have incorrect second- and higher-order growth and therefore excite long-lived transients in the evolution of the statistical properties of density and velocity fields. We also study the improvement brought by using more accurate initial conditions based on second-order Lagrangian perturbation theory (2LPT). We show that 2LPT initial conditions reduce transients significantly and thus are much more appropriate for numerical simulations devoted to precision cosmology. Using controlled numerical experiments with ZA and 2LPT initial conditions, we show that simulations started at redshift zi= 49 using the ZA underestimate the power spectrum in the non-linear regime by about 2, 4 and 8 per cent at z= 0, 1, and 3, respectively, whereas the mass function of dark matter haloes is underestimated by 5 per cent at m= 1015 M, h,1 (z= 0) and 10 per cent at m= 2 × 1014 M, h,1 (z= 1). The clustering of haloes is also affected to the few per cent level at z= 0. These systematics effects are typically larger than statistical uncertainties in recent mass function and power spectrum fitting formulae extracted from numerical simulations. At large scales, the measured transients in higher-order correlations can be understood from first principle calculations based on perturbation theory. [source] Universal fitting formulae for baryon oscillation surveysMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2006Chris Blake ABSTRACT The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy redshift surveys. We express these accuracies as a function of survey parameters such as the central redshift, volume, galaxy number density and (where applicable) photometric redshift error. These fitting formulae should greatly increase the efficiency of optimizing future surveys, which requires analysis of a potentially vast number of survey configurations and cosmological models. The formulae are calibrated using a grid of Monte Carlo simulations, which are analysed by dividing out the overall shape of the power spectrum before fitting a simple decaying sinusoid to the oscillations. The fitting formulae reproduce the simulation results with a fractional scatter of 7 per cent (10 per cent) in the tangential (radial) directions over a wide range of input parameters. We also indicate how sparse-sampling strategies may enhance the effective survey area if the sampling scale is much smaller than the projected baryon oscillation scale. [source] The energy cascade from warm dark matter decaysMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY: LETTERS (ELECTRONIC), Issue 1 2008M. Valdés ABSTRACT We use a set of Monte Carlo simulations to follow the cascade produced by a primary electron of energy Ein in the intergalactic medium. We choose Ein= 3,10 keV as expected from the decay of one of the most popular warm dark matter (WDM) candidates, sterile neutrinos. Our simulation takes into account processes previously neglected such as free,free interactions with ions and recombinations, and uses the best available cross-sections for collisional ionizations and excitations with H and He and for electron,electron collisions. We precisely derive the fraction of the primary electron energy that heats the gas, ionizes atoms and produces line and continuum photons as a function of the ionization fraction. Handy fitting formulae for all the above energy depositions are provided. By keeping track of the individual photons, we can distinguish between photons in the Ly, resonance and those with energy E < 10.2 eV that do not interact further with gas. This separation is important because a Ly, background can heat or cool the gas depending on the nature of the photons, and can have effects on the 21-cm radiation emitted by neutral H, which will probably become detectable at z > 6 in the near future by the next generation radio interferometers. [source] | ||||||||||