Optimising Boltzmann codes for the Planck era

High precision measurements of the Cosmic Microwave Background (CMB) anisotropies, as can be expected from the Planck satellite, will require high-accuracy theoretical predictions as well. One possible source of theoretical uncertainty is the numerical error in the output of the Boltzmann codes used to calculate angular power spectra. In this work, we carry out an extensive study of the numerical accuracy of the public Boltzmann code CAMB, and identify a set of parameters which determine the error of its output. We show that at the current default settings, the cosmological parameters extracted from data of future experiments like Planck can be biased by several tenths of a standard deviation for the six parameters of the standard Lambda-CDM model, and potentially more seriously for extended models. We perform an optimisation procedure that leads the code to achieve sufficient precision while at the same time keeping the computation time within reasonable limits. Our conclusion is that the contribution of numerical errors to the theoretical uncertainty of model predictions is well under control -- the main challenges for more accurate calculations of CMB spectra will be of an astrophysical nature instead.Comment: 13 pages, 4 figure

Magnetohydrodynamic jets from different magnetic field configurations

Using axisymmetric MHD simulations we investigate how the overall jet formation is affected by a variation in the disk magnetic flux profile and/or the existence of a central stellar magnetosphere. Our simulations evolve from an initial, hydrostatic equilibrium state in a force-free magnetic field configuration. We find a unique relation between the collimation degree and the disk wind magnetization power law exponent. The collimation degree decreases for steeper disk magnetic field profiles. Highly collimated outflows resulting from a flat profile tend to be unsteady. We further consider a magnetic field superposed of a stellar dipole and a disk field in parallel or anti-parallel alignment. Both stellar and disk wind may evolve in a pair of outflows, however, a reasonably strong disk wind component is essential for jet collimation. Strong flares may lead to a sudden change in mass flux by a factor two. We hypothesize that such flares may eventually trigger jet knots.Comment: 5 pages, 4 figures; proceedings from conference: Protostellar Jets in Context, held in Rhodes, July 7-12, 200

Pico: Parameters for the Impatient Cosmologist

We present a fast, accurate, robust and flexible method of accelerating parameter estimation. This algorithm, called Pico, can compute the CMB power spectrum and matter transfer function as well as any computationally expensive likelihoods in a few milliseconds. By removing these bottlenecks from parameter estimation codes, Pico decreases their computational time by 1 or 2 orders of magnitude. Pico has several important properties. First, it is extremely fast and accurate over a large volume of parameter space. Furthermore, its accuracy can continue to be improved by using a larger training set. This method is generalizable to an arbitrary number of cosmological parameters and to any range of l-values in multipole space. Pico is approximately 3000 times faster than CAMB for flat models, and approximately 2000 times faster then the WMAP 3 year likelihood code. In this paper, we demonstrate that using Pico to compute power spectra and likelihoods produces parameter posteriors that are very similar to those using CAMB and the official WMAP3 code, but in only a fraction of the time. Pico and an interface to CosmoMC are made publicly available at http://www.astro.uiuc.edu/~bwandelt/pico/.Comment: 9 pages, 10 figures, submitted to ApJ, LaTeX with emulateap

Accretion-Powered Stellar Winds II: Numerical Solutions for Stellar Wind Torques

[Abridged] In order to explain the slow rotation observed in a large fraction of accreting pre-main-sequence stars (CTTSs), we explore the role of stellar winds in torquing down the stars. For this mechanism to be effective, the stellar winds need to have relatively high outflow rates, and thus would likely be powered by the accretion process itself. Here, we use numerical magnetohydrodynamical simulations to compute detailed 2-dimensional (axisymmetric) stellar wind solutions, in order to determine the spin down torque on the star. We explore a range of parameters relevant for CTTSs, including variations in the stellar mass, radius, spin rate, surface magnetic field strength, the mass loss rate, and wind acceleration rate. We also consider both dipole and quadrupole magnetic field geometries. Our simulations indicate that the stellar wind torque is of sufficient magnitude to be important for spinning down a ``typical'' CTTS, for a mass loss rate of $\sim 10^{-9} M_\odot$ yr$^{-1}$. The winds are wide-angle, self-collimated flows, as expected of magnetic rotator winds with moderately fast rotation. The cases with quadrupolar field produce a much weaker torque than for a dipole with the same surface field strength, demonstrating that magnetic geometry plays a fundamental role in determining the torque. Cases with varying wind acceleration rate show much smaller variations in the torque suggesting that the details of the wind driving are less important. We use our computed results to fit a semi-analytic formula for the effective Alfv\'en radius in the wind, as well as the torque. This allows for considerable predictive power, and is an improvement over existing approximations.Comment: Accepted for publication in Ap

Particle acceleration close to the supermassive black hole horizon: the case of M87

The radio galaxy M87 has recently been found to be a rapidly variable TeV emitting source. We analyze the implications of the observed TeV characteristics and show that it proves challenging to account for them within conventional acceleration and emission models. We discuss a new pulsar-type scenario for the origin of variable, very high energy (VHE) emission close to the central supermassive black hole and show that magneto-centrifugally accelerated electrons could efficiently Compton upscatter sub-mm ADAF disk photons to the TeV regime, leading to VHE characteristics close to the observed ones. This suggests, conversely, that VHE observations of highly under-luminous AGNs could provide an important diagnostic tool for probing the conditions prevalent in the inner accretion disk of these sources.Comment: 5 pages, one figure (typos corrected); based on presentation at "High Energy Phenomena in Relativistic Outflows", Dublin, Sept. 2007; accepted for publication in International Journal of Modern Physics

Ultra-Relativistic Magneto-Hydro-Dynamic Jets in the context of Gamma Ray Bursts

We present a detailed numerical study of the dynamics and evolution of ultrarelativistic magnetohydrodynamic jets in the black hole-disk system under extreme magnetization conditions. We find that Lorentz factors of up to 3000 are achieved and derived a modifiedMichel scaling (Gamma ~ sigma) which allows for a wide variation in the flow Lorentz factor. Pending contamination induced by mass-entrainment, the linear Michel scaling links modulations in the ultrarelativistic wind to variations in mass accretion in the disk for a given magnetization. The jet is asymptotically dominated by the toroidal magnetic field allowing for efficient collimation. We discuss our solutions (jets) in the context of Gamma ray bursts and describe the relevant features such as the high variability in the Lorentz factor and how high collimation angles (~ 0-5 degrees), or cylindrical jets, can be achieved. We isolate a jet instability mechanism we refer to as the "bottle-neck" instability which essentially relies on a high magnetization and a recollimation of the magnetic flux surfaces. The instability occurs at large radii where any dissipation of the magnetic energy into radiation would in principle result in an optically thin emission.Comment: 31 pages, 6 figures. Submitted to ApJ. Higher Quality figures at http://www.capca.ucalgary.ca/paper

Dynamics and Structure of Three-Dimensional Trans-Alfvenic Jets. II. The Effect of Density and Winds

Two three-dimensional magnetohydrodynamical simulations of strongly magnetized conical jets, one with a poloidal and one with a helical magnetic field, have been performed. In the poloidal simulation a significant sheath (wind) of magnetized moving material developed and partially stabilized the jet to helical twisting. The fundamental pinch mode was not similarly affected and emission knots developed in the poloidal simulation. Thus, astrophysical jets surrounded by outflowing winds could develop knotty structures along a straight jet triggered by pinching. Where helical twisting dominated the dynamics, magnetic field orientation along the line-of-sight could be organized by the toroidal flow field accompanying helical twisting. On astrophysical jets such structure could lead to a reversal of the direction of Faraday rotation in adjacent zones along a jet. Theoretical analysis showed that the different dynamical behavior of the two simulations could be entirely understood as a result of dependence on the velocity shear between jet and wind which must exceed a surface Alfven speed before the jet becomes unstable to helical and higher order modes of jet distortion.Comment: 25 pages, 15 figures, in press Astrophysical Journal (September

Rico: An Accurate Cosmological Recombination Code

We present Rico, a code designed to compute the ionization fraction of the Universe during the epoch of hydrogen and helium recombination with an unprecedented combination of speed and accuracy. This is accomplished by training the machine learning code Pico on the calculations of a multi-level cosmological recombination code which self-consistently includes several physical processes that were neglected previously. After training, Rico is used to fit the free electron fraction as a function of the cosmological parameters. While, for example at low redshifts (z<~900), much of the net change in the ionization fraction can be captured by lowering the hydrogen fudge factor in Recfast by about 3%, Rico provides a means of effectively using the accurate ionization history of the full recombination code in the standard cosmological parameter estimation framework without the need to add new or refined fudge factors or functions to a simple recombination model. Within the new approach presented here it is easy to update Rico whenever a more accurate full recombination code becomes available. Once trained, Rico computes the cosmological ionization history with negligible fitting error in ~10 milliseconds, a speed-up of at least 10^6 over the full recombination code that was used here. Also Rico is able to reproduce the ionization history of the full code to a level well below 0.1%, thereby ensuring that the theoretical power spectra of CMB fluctuations can be computed to sufficient accuracy and speed for analysis from upcoming CMB experiments like Planck. Furthermore it will enable cross-checking different recombination codes across cosmological parameter space, a comparison that will be very important in order to assure the accurate interpretation of future cosmic microwave background data.Comment: 14 pages, 11 figures, submitted to PR