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

The Axisymmetric Pulsar Magnetosphere

We present, for the first time, the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, ${\bf E\cdot B}=0$, everywhere. The unique distribution of electric current along the open magnetic field lines which is required for the solution to be continuous and smooth is obtained numerically. With the geometry of the field lines thus determined we compute the dynamics of the associated MHD wind. The main result is that the relativistic outflow contained in the magnetosphere is not accelerated to the extremely relativistic energies required for the flow to generate gamma rays. We expect that our solution will be useful as the starting point for detailed studies of pulsar magnetospheres under more general conditions, namely when either the force-free and/or the ideal MHD condition ${\bf E\cdot B}=0$ are not valid in the entire magnetosphere. Based on our solution, we consider that the most likely positions of such an occurrence are the polar cap, the crossings of the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.Comment: 15 pages AAS Latex, 5 postscript 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

Collimation of astrophysical jets - the role of the accretion disk magnetic field distribution

We have applied axisymmetric MHD simulations to investigate the impact of the accretion disk magnetic flux profile on the jet collimation. Using the ZEUS-3D code modified for magnetic diffusivity, our simulations evolve from an initial hydrostatic equilibrium state in a force-free magnetic field. Considering a power law for the disk poloidal magnetic field profile Bp ~ r^{-mu} and for the disk wind density profile rho ~ r^{-mu_rho} we performed a systematic study over a wide parameter range mu and mu_rho. We find a degree of collimation (ratio of mass flow rates in axial and lateral direction) decreasing for steeper disk magnetic field profiles (increasing mu). Varying the total magnetic flux doesn't change the degree of jet collimation substantially, it only affects the time scale of outflow evolution and the terminal jet speed. As our major result we find a general relation between the collimation degree with the disk wind magnetization power law exponent. Outflows with high collimation degree resulting from a flat disk magnetic field profile tend to be unsteady, producing axially propagating knots as discussed earlier. Depending slightly on the inflow density profile this unsteady behavior sets in for mu < 0.4. We also performed simulations of jet formation with artificially enhanced decay of the toroidal magnetic field in order to investigate the idea of a purely "poloidal collimation" discussed in the literature. These outflows remain weakly collimated and propagate with lower velocity. Thanks to our large numerical grid size (7x14 AU for protostars), we may apply our results to recently observed hints of jet rotation (DG Tau) indicating a relatively flat disk magnetic field profile, mu ~ 0.5. In general, our results are applicable to both stellar and extragalactic sources of MHD jets.Comment: accepted by ApJ, high resolution version under www.mpia-hd.mpg.de/homes/fendt

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

Cannonballs in the context of Gamma Ray Bursts: Formation sites ?

We investigate possible formation sites of the cannonballs (in the gamma ray bursts context) by calculating their physical parameters, such as density, magnetic field and temperature close to the origin. Our results favor scenarios where the cannonballs form as instabilities (knots) within magnetized jets from hyperaccreting disks. These instabilities would most likely set in beyond the light cylinder where flow velocity with Lorentz factors as high as 2000 can be achieved. Our findings challenge the cannonball model of gamma ray bursts if these indeed form inside core-collapse supernovae (SNe) as suggested in the literature; unless hyperaccreting disks and the corresponding jets are common occurrences in core-collapse SNe.Comment: 10 pages, 12 figure

Global axisymmetric simulations of photoevaporation and magnetically driven protoplanetary disk winds

Photoevaporation and magnetically driven winds are two independent mechanisms to remove mass from protoplanetary disks. In addition to accretion, the effect of these two principles acting concurrently could be significant and the transition between those two has not been extensively studied and quantified in the literature yet. In order to contribute to the understanding of disk winds, we present the phenomena emerging in the framework of two-dimensional axisymmetric, non-ideal magnetohydrodynamic simulations including EUV-/ X-ray driven photoevaporation. Of particular interest are the examination of the transition region between photoevaporation and magnetically driven wind, the possibility of emerging magneto-centrifugal wind effects, as well as the morphology of the wind itself depending on the strength of the magnetic field. We use the PLUTO code in a 2.5D axisymmetric configuration with additional treatment of EUV-/ X-ray heating and dynamic ohmic diffusion based on a semi-analytical chemical model. We identify the transition between both outflow types to occur for values of the initial plasma beta $\beta \geq 10^7$, while magnetically driven winds generally outperform photoevaporation for stronger fields. In our simulations we observe irregular and asymmetric outflows for stronger magnetic fields. In the weak field regime the photoevaporation rates are slightly lowered by perturbations of the gas density in the inner regions of the disk. Overall, our results predict a wind with a lever arm smaller than 1.5, consistent with a hot magneto-thermal wind. Stronger accretion flows are present for values of $\beta < 10^7$.Comment: Published in A&A 633, A21 (2020

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

Molecular outflows in the young open cluster IC348

We present a wide-field survey of the young open cluster IC348 for molecular H2 outflows. Outflow activity is only found at its south-western limit, where a new subcluster of embedded sources is in an early phase of its formation. If the IC348 cluster had been built up by such subclusters forming at different times, this could explain the large age-spread that Herbig (1998) found for the IC348 member stars. In addition to several compact groups of H2 knots, our survey reveals a large north-south oriented outflow, and we identify the newly discovered far-infrared and mm-object IC348MMS as its source. New deep images in the 1-0 S(1) line of molecular hydrogen trace the HH211 jet and counterjet as highly-collimated chains of knots, resembling the interferometric CO and SiO jets. This jet system appears rotated counter-clockwise by about 3 degrees with respect to the prominent H2 bow shocks. Furthermore, we resolve HH211-mm as a double point-like source in the mm-continuum.Comment: 10 pages, 9 figures, accepted for publication in Ap

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