arXiv subjects

Farrukh Nauman

Publications and source records attributed to Farrukh Nauman.

10 recordsLinked to original sources

arXiv2019

Transport properties of Keplerian flows in extended local domains with no imposed field

We compare transport statistics of elongated incompressible shearing boxes for different Reynolds and magnetic Prandtl numbers, $Re$ and $Pm$, and aspect ratios, $L_z/L_x$. We find that at fixed aspect ratio $L_z/L_x=4$ and $Re = 10,000$, the turbulent stresses for $Pm \lesssim 1$ do not show considerable variation and follow a power law $\sim Pm^{3/2}$ for $Pm > 1$. This is qualitatively consistent with previous results based on net imposed flux and small box $L_z/L_x \sim 1$ simulations but the power law exponent is different. The saturated level of stresses, the ratio of Maxwell stress to the magnetic energy and Reynolds to Maxwell stress ratio are roughly invariant as $L_z/L_x$ is increased. For cases where the boxes are elongated in both the azimuth and vertical direction, the transport coefficient $α\in [0.1,1.0]$ that is $10-100$ times larger than the case with $L_y/L_x = 2$ and large $L_z/L_x$. Overall, our results suggest that the saturated state of turbulence is sensitive to both dissipation coefficients and aspect ratio (both $L_z/L_x$, $L_y/L_x$) motivating further work on this problem.

astro-ph.SR↗

arXiv2019

Exploring helical dynamos with machine learning

We use ensemble machine learning algorithms to study the evolution of magnetic fields in magnetohydrodynamic (MHD) turbulence that is helically forced. We perform direct numerical simulations of helically forced turbulence using mean field formalism, with electromotive force (EMF) modeled both as a linear and non-linear function of the mean magnetic field and current density. The form of the EMF is determined using regularized linear regression and random forests. We also compare various analytical models to the data using Bayesian inference with Markov Chain Monte Carlo (MCMC) sampling. Our results demonstrate that linear regression is largely successful at predicting the EMF and the use of more sophisticated algorithms (random forests, MCMC) do not lead to significant improvement in the fits. We conclude that the data we are looking at is effectively low dimensional and essentially linear. Finally, to encourage further exploration by the community, we provide all of our simulation data and analysis scripts as open source IPython notebooks.

astro-ph.SR↗

arXiv2017

The effects of large scale magnetic fields around young protostars and their disks

We study the evolution of magnetic fields in accretion flows around six different sink particles in a global star formation simulation. Using the adaptive mesh refinement capabilities of \ramses, the vicinity of the sinks is resolved with a resolution down to $2$ AU. The statistical properties of the magnetic field are tracked as a function of radius, height and time around each sink particle. All six systems are strongly magnetised with plasma beta being unity or below and we know that at least three of the sinks host an accretion disc. One of the discs is studied at a higher resolution of $0.06$ AU and we report its magnetic properties. We find that the angular momentum transport is dominated by large scale radial-azimuthal Maxwell stress. Furthermore, contrary to the weakly magnetised case studied in shearing box simulations, the large scale azimuthal field does not show smooth cycle periods but instead forms a banded structure. We conclude by speculating what this result might mean for observations and whether it will hold with highly resolved simulations including turbulence or non-ideal MHD effects.

astro-ph.SR↗

arXiv2017

Motivation and challenge to capture both large scale and local transport in next generation accretion theory

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate insight gained from simulations back into improving practical models for comparison with observations. Here we emphasize the need to incorporate the role of non-local transport more precisely. To show where large scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura-Sunyaev (1973,SS73) is necessarily a mean field theory, and one which does not include large scale transport. Observations of coronae and jets combined with the interpretation of results even from shearing box simulations of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large scale contributions and the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRi as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona, and outflow contributions. Finally, we note that any mean field theory has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

astro-ph.HE↗

arXiv2017

Sustained turbulence and magnetic energy in non-rotating shear flows

From numerical simulations, we show that non-rotating magnetohydrodynamic shear flows are unstable to finite amplitude velocity perturbations and become turbulent, leading to the growth and sustenance of magnetic energy, including large scale fields. This supports the concept that sustained magnetic energy from turbulence is independent of the driving mechanism for large enough magnetic Reynolds numbers.

physics.plasm-ph↗

arXiv2017

Shearing box simulations in the Rayleigh unstable regime

We study the stability properties of Rayleigh unstable flows both in the purely hydrodynamic and magnetohydrodynamic (MHD) regimes for two different values of the shear $q=2.1, 4.2$ ($q = - d\lnΩ/ d\ln r$) and compare it with the Keplerian case $q=1.5$. We find that the $q>2$ regime is unstable both in the hydrodynamic and in the MHD limit (with an initially weak magnetic field). In this regime, the velocity fluctuations dominate the magnetic fluctuations. In contrast, in the $q<2$ (magnetorotational instability (MRI)) regime the magnetic fluctuations dominate. This highlights two different paths to MHD turbulence implied by the two regimes, suggesting that in the $q>2$ regime the instability produces primarily velocity fluctuations that cause magnetic fluctuations, with the causality reversed for the $q<2$ MRI unstable regime. We also find that the magnetic field correlation is increasingly localized as the shear is increased in the Rayleigh unstable regime. In calculating the time evolution of spatial averages of different terms in the MHD equations, we find that the $q>2$ regime is dominated by terms which are nonlinear in the fluctuations, whereas for $q<2$, the linear terms play a more significant role.

astro-ph.SR↗

arXiv2016

Sustained Turbulence in Differentially Rotating Magnetized Fluids at Low Magnetic Prandtl Number

We show for the first time that sustained turbulence is possible at low magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the dynamical range between the energy injection scale and the dissipative scale. This has important implications for a large variety of differentially rotating systems with low magnetic Prandtl number such as protostellar disks and laboratory experiments.

astro-ph.SR↗

arXiv2014

Sensitivity of the Magnetorotational Instability to the shear parameter in stratified simulations

The magnetorotational instability (MRI) is a shear instability and thus its sensitivity to the shear parameter $q = - d\lnΩ/d\ln r $ is of interest to investigate. Motivated by astrophysical disks, most (but not all) previous MRI studies have focused on the Keplerian value of $ q=1.5$. Using simulation with 8 vertical density scale heights, we contribute to the subset of studies addressing the the effect of varying $q$ in stratified numerical simulations. We discuss why shearing boxes cannot easily be used to study $q>2$ and thus focus on $q<2$. As per previous simulations, which were either unstratified or stratified with a smaller vertical domain, we find that the $q$ dependence of stress for the stratified case is not linear, contrary to the Shakura-Sunyaev model. We find that the scaling agrees with \cite{1996MNRAS.281L..21A} who found it to be proportional to the shear to vorticity ratio $q/(2-q)$. We also find however, that the shape of the magnetic and kinetic energy spectra are relatively insensitive to $q$ and that the ratio of Maxwell stress to magnetic energy ratio also remains nearly independent of $q$. This is consistent with a theoretical argument in which the rate of amplification of the azimuthal field depends linearly on $q$ and the turbulent correlation time $τ$ depends inversely on $q$. As such, we measure the correlation time of the turbulence and find that indeed it is inversely proportional to $q$.

astro-ph.SR↗

arXiv2014

On characterizing nonlocality and anisotropy for the magnetorotational instability

The extent to which angular momentum transport in accretion discs is primarily local or non-local and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyze simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona where the disc is the MRI unstable region and corona is the magnetically dominated region. We calculate the fractional power in different quantities, including magnetic energy and Maxwell stresses and find that they are dominated by contributions from the lowest wave numbers. This is even more dramatic for the corona than the disc, suggesting that transport in the corona region is dominated by larger structures than the disc. By calculating averaged power spectra in one direction of $k$ space at a time, we also show that the MRI turbulence is strongly anisotropic on large scales when analyzed by this method, but isotropic on small scales. Although the shearing box itself is meant to represent a local section of an accretion disc, the fact that the stress and energy are dominated by the largest scales highlights that the locality is not captured within the box. This helps to quantify the intuitive importance of global simulations for addressing the question of locality of transport, for which similar analyses can be performed.

astro-ph.SR↗

arXiv2010

Quantifying the Imprecision of Accretion Theory and Implications for Multi-Epoch Observations of Protoplanetary Discs

If accretion disc emission results from turbulent dissipation, then axisymmetric accretion theory must be used as a mean field theory: turbulent flows are at most axisymmetric only when suitably averaged. Spectral predictions therefore have an intrinsic imprecision that must be quantified to interpret the variability exhibited by a source observed at different epochs. We quantify contributions to the stochastic imprecision that come from azimuthal and radial averaging and show that the imprecision is minimized for a particular choice of radial averaging, which in turn, corresponds to an optimal spectral resolution of a telescope for a spatially unresolved source. If the optimal spectral resolution is less than that of the telescope then the data can be binned to compare to the theoretical prediction of minimum imprecision. Little stochastic variability is predicted at radii much larger than that at which the dominant eddy turnover time ($\sim$ orbit time) exceeds the time interval between observations; the epochs would then be sampling the same member of the stochastic ensemble. We discuss the application of these principles to protoplanetary discs for which there is presently a paucity of multi-epoch data but for which such data acquisition projects are underway.

astro-ph.SR↗