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Andrew Fletcher

Publications and source records attributed to Andrew Fletcher.

At least 19 recordsLinked to original sources

Large-scale multidisciplinary design optimization of the NASA lift-plus-cruise concept using a novel aircraft design framework

The conceptual design of eVTOL aircraft is a high-dimensional optimization problem that involves large numbers of continuous design parameters. Therefore, eVTOL design method would benefit from numerical optimization algorithms capable of systematically searching these high-dimensional parameters spaces, using comprehensive and multidisciplinary models of the aircraft. By leveraging recent progress in sensitivity analysis methods, a computational framework called the Comprehensive Aircraft high-Dimensional DEsign Environment (CADDEE) has been developed for large-scale multidisciplinary design optimization (MDO) of electric air taxis. CADDEE uses a geometry-centric approach that propagates geometry changes in a differentiable manner to meshes for physics-based models of arbitrary fidelity level. The paper demonstrates the capabilities of this new aircraft design tool, by presenting large-scale MDO results for NASA's Lift+Cruise eVTOL concept. MDO with over 100 design variables, 17 constraints, and low-fidelity predictive models for key disciplines is demonstrated with an optimization time of less than one hour with a desktop computer. The results show a reduction in gross weight of 11.4% and suggest that CADDEE can be valuable in the conceptual design and optimization of eVTOL aircraft.

cs.CE

An In-depth Investigation of Faraday Depth Spectrum Using Synthetic Observations of Turbulent MHD Simulations

In this paper we present a detailed analysis of the Faraday depth (FD) spectrum and its clean components obtained through the application of the commonly used technique of Faraday rotation measure synthesis to analyze spectro-polarimetric data. In order to directly compare the Faraday depth spectrum with physical properties of a magneto-ionic medium, we generated synthetic broad-bandwidth spectro-polarimetric observations from magnetohydrodynamic (MHD) simulations of a transonic, isothermal, compressible turbulent medium. We find that correlated magnetic field structures give rise to a combination of spiky, localized peaks at certain FD values, and broad structures in the FD spectrum. Although the majority of these spiky FD structures appear narrow, giving an impression of a Faraday thin medium, we show that they arise from strong synchrotron emissivity at that FD. Strong emissivity at a FD can arise because of both strong spatially-local polarized synchrotron emissivity at a FD or accumulation of weaker emissions along the distance through a medium that have Faraday depths within half the width of the rotation measure spread function. Such a complex Faraday depth spectrum is a natural consequence of MHD turbulence when the lines of sight pass through a few turbulent cells. This therefore complicates the convention of attributing narrow FD peaks to presence of a Faraday rotating medium along the line of sight. Our work shows that it is difficult to extract the FD along a line of sight from the Faraday depth spectrum using standard methods for a turbulent medium in which synchrotron emission and Faraday rotation occur simultaneously.

astro-ph.GA

Statistical properties of Faraday rotation measure from large-scale magnetic fields in intervening disc galaxies

To constrain the large-scale magnetic field strengths in cosmologically distant galax- ies, we derive the probability distribution function of Faraday rotation measure (RM) when random lines of sight pass through a sample of disc galaxies, with axisymmetric large-scale magnetic fields. We find that the width of the RM distribution of the galaxy sample is directly related to the mean large-scale field strength of the galaxy population, provided the dispersion within the sample is lower than the mean value. In the absence of additional constraints on parameters describing the magneto-ionic medium of the intervening galaxies, and in the situation where RMs produced in the intervening galaxies have already been statistically isolated from other RM contributions along the lines of sight, our simple model of the magneto-ionic medium in disc galaxies suggests that the mean large-scale magnetic field of the population can be measured to within ~ 50% accuracy.

astro-ph.GA

IMAGINE: A comprehensive view of the interstellar medium, Galactic magnetic fields and cosmic rays

In this white paper we introduce the IMAGINE Consortium and its scientific background, goals and structure. Our purpose is to coordinate and facilitate the efforts of a diverse group of researchers in the broad areas of the interstellar medium, Galactic magnetic fields and cosmic rays, and our goal is to develop more comprehensive insights into the structures and roles of interstellar magnetic fields and their interactions with cosmic rays. To achieve a higher level of self-consistency, depth and rigour can only be achieved by the coordinated efforts of experts in diverse areas of astrophysics involved in observational, theoretical and numerical work. We present our view of the present status of this topic, identify its key unsolved problems and suggest a strategy that will underpin our work. The backbone of the consortium is the Interstellar MAGnetic field INference Engine, a publicly available Bayesian platform that employs robust statistical methods to explore the multi-dimensional likelihood space using any number of modular inputs. It provides an interpretation and modelling framework that has the power and flexibility to include a variety of observational, theoretical and numerical lines of evidence into a self-consistent and comprehensive picture of the thermal and non-thermal interstellar media. An important innovation is that a consistent understanding of the phenomena that are directly or indirectly influenced by the Galactic magnetic field, such as the deflection of ultra-high energy cosmic rays or extragalactic backgrounds, is made an integral part of the modelling. The IMAGINE Consortium, which is informal by nature and open to new participants, hereby presents a methodological framework for the modelling and understanding of Galactic magnetic fields that is available to all communities whose research relies on a state-of-the-art solution to this problem. (Abridged.)

astro-ph.GA

Topological data analysis and diagnostics of compressible MHD turbulence

The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with observations. One of the main challenges in this area is to identify robust \it{quantitative} measures to compare structures found in simulations with those inferred from astrophysical observations. A similar challenge is to compare quantitatively results from different simulations. Topological data analysis offers a range of techniques, including the Betti numbers and persistence diagrams, that can be used to facilitate such a comparison. After describing these tools, we first apply them to synthetic random fields and demonstrate that, when the data are standardized in a straightforward manner, some topological measures are insensitive to either large-scale trends or the resolution of the data. Focusing upon one particular astrophysical example, we apply topological data analysis to HI observations of the turbulent interstellar medium (ISM) in the Milky Way and to recent MHD simulations of the random, strongly compressible ISM. We stress that these topological techniques are generic and could be applied to any complex, multi-dimensional random field.

physics.data-an

Statistical properties of Faraday rotation measure in external galaxies -- I: intervening disc galaxies

Deriving the Faraday rotation measure (RM) of quasar absorption line systems, which are tracers of high-redshift galaxies intervening background quasars, is a powerful tool for probing magnetic fields in distant galaxies. Statistically comparing the RM distributions of two quasar samples, with and without absorption line systems, allows one to infer magnetic field properties of the intervening galaxy population. Here, we have derived the analytical form of the probability distribution function (PDF) of RM produced by a single galaxy with an axisymmetric large-scale magnetic field. We then further determine the PDF of RM for one random sight line traversing each galaxy in a population with a large-scale magnetic field prescription. We find that the resulting PDF of RM is dominated by a Lorentzian with a width that is directly related to the mean axisymmetric large-scale field strength $\langle B_0 \rangle$ of the galaxy population if the dispersion of $B_0$ within the population is smaller than $\langle B_0 \rangle$. Provided that RMs produced by the intervening galaxies have been successfully isolated from other RM contributions along the line of sight, our simple model suggests that $\langle B_0 \rangle$ in galaxies probed by quasar absorption line systems can be measured within $\approx50$ per cent accuracy without additional constraints on the magneto-ionic medium properties of the galaxies. Finally, we discuss quasar sample selection criteria that are crucial to reliably interpret observations, and argue that within the limitations of the current database of absorption line systems, high-metallicity damped Lyman-$\alpha$ absorbers are best suited to study galactic dynamo action in distant disc galaxies.

astro-ph.GA

Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams

The interstellar medium (ISM) is a magnetised system in which transonic or supersonic turbulence is driven by supernova explosions. This leads to the production of intermittent, filamentary structures in the ISM gas density, whilst the associated dynamo action also produces intermittent magnetic fields. The traditional theory of random functions, restricted to second-order statistical moments (or power spectra), does not adequately describe such systems. We apply topological data analysis (TDA), sensitive to all statistical moments and independent of the assumption of Gaussian statistics, to the gas density fluctuations in a magnetohydrodynamic (MHD) simulation of the multi-phase ISM. This simulation admits dynamo action, so produces physically realistic magnetic fields. The topology of the gas distribution, with and without magnetic fields, is quantified in terms of Betti numbers and persistence diagrams. Like the more standard correlation analysis, TDA shows that the ISM gas density is sensitive to the presence of magnetic fields. However, TDA gives us important additional information that cannot be obtained from correlation functions. In particular, the Betti numbers per correlation cell are shown to be physically informative. Magnetic fields make the ISM more homogeneous, reducing the abundance of both isolated gas clouds and cavities, with a stronger effect on the cavities. Remarkably, the modification of the gas distribution by magnetic fields is captured by the Betti numbers even in regions more than 300 pc from the midplane, where the magnetic field is weaker and correlation analysis fails to detect any signatures of magnetic effects.

astro-ph.GA

Statistical Topology and the Random Interstellar Medium

Current astrophysical models of the interstellar medium assume that small scale variation and noise can be modelled as Gaussian random fields or simple transformations thereof, such as lognormal. We use topological methods to investigate this assumption for three regions of the southern sky. We consider Gaussian random fields on two-dimensional lattices and investigate the expected distribution of topological structures quantified through Betti numbers. We demonstrate that there are circumstances where differences in topology can identify differences in distributions when conventional marginal or correlation analyses may not. We propose a non-parametric method for comparing two fields based on the counts of topological features and the geometry of the associated persistence diagrams. When we apply the methods to the astrophysical data, we find strong evidence against a Gaussian random field model for each of the three regions of the interstellar medium that we consider. Further, we show that there are topological differences at a local scale between these different regions.

stat.AP

Supernova-regulated ISM -- V. Space- and time-correlations

We apply correlation analysis to random fields in numerical simulations of the supernova-driven interstellar medium (ISM) with the magnetic field produced by dynamo action. We solve the thermo-magnetohydrodynamic (MHD) equations in a shearing, Cartesian box representing a local region of the ISM, subject to thermal and kinetic energy injection by supernova explosions, and parameterized optically-thin radiative cooling. We consider the cold, warm\, and hot phases of the ISM separately; the analysis mostly considers the warm gas, which occupies the bulk of the domain. Various physical variables have different correlation lengths in the warm phase: $40 pc$, $50 pc$, and $60 pc$ for random magnetic field, density, and velocity, respectively, in the midplane. The correlation time of the random velocity is comparable to the eddy turnover time, about $10^7 yr$, although it may be shorter in regions with higher star formation rate. The random magnetic field is anisotropic, with the standard deviations of its components $b_x/b_y/b_z$ having approximate ratios $0.5/0.6/0.6$ in the midplane. The anisotropy is attributed to the global velocity shear from galactic differential rotation, and locally inhomogeneous outflow to the galactic halo. The correlation length of Faraday depth along the $z$-axis, $120 pc$, is greater than for electron density, $60 - 90 pc$, and vertical magnetic field, $60 pc$. Such comparisons may be sensitive to the orientation of the line of sight. Uncertainties of the structure functions of synchrotron intensity rapidly increase with the scale. This feature is hidden in power spectrum analysis, which can undermine the usefulness of power spectra for detailed studies of interstellar turbulence.

astro-ph.GA

The distribution of mean and fluctuating magnetic fields in the multi-phase ISM

We explore the effects of the multi-phase structure of the interstellar medium (ISM) on galactic magnetic fields. Basing our analysis on compressible magnetohydrodynamic (MHD) simulations of supernova-driven turbulence in the ISM, we investigate the properties of both the mean and fluctuating components of the magnetic field. We find that the mean magnetic field preferentially resides in the warm phase and is generally absent from the hot phase. The fluctuating magnetic field does not show such pronounced sensitivity to the multi-phase structure.

astro-ph.GA

The Parker Instability in Disk Galaxies

We examine the evolution of the Parker instability in galactic disks using 3D numerical simulations. We consider a local Cartesian box section of a galactic disk, where gas, magnetic fields and cosmic rays are all initially in a magnetohydrostatic equilibrium. This is done for different choices of initial cosmic ray density and magnetic field. The growth rates and characteristic scales obtained from the models, as well as their dependences on the density of cosmic rays and magnetic fields, are in broad agreement with previous (linearized, ideal) analytical work. However, this non-ideal instability develops a multi-modal 3D structure, which cannot be quantitatively predicted from the earlier linearized studies. This 3D signature of the instability will be of importance in interpreting observations. As a preliminary step towards such interpretations, we calculate synthetic polarized intensity and Faraday rotation measure maps, and the associated structure functions of the latter, from our simulations; these suggest that the correlation scales inferred from rotation measure maps are a possible probe for the cosmic ray content of a given galaxy. Our calculations highlight the importance of cosmic rays in these measures, making them an essential ingredient of realistic models of the interstellar medium.

astro-ph.GA

Probability distribution functions of gas in M31 and M51

We present probability distribution functions (PDFs) of the surface densities of ionized and neutral gas in the nearby spiral galaxies M31 and M51, as well as of dust emission and extinction Av in M31. The PDFs are close to lognormal and those for HI and Av in M31 are nearly identical. However, the PDFs for H2 are wider than the HI PDFs and the M51 PDFs have larger dispersions than those for M31. We use a simple model to determine how the PDFs are changed by variations in the line-of-sight (LOS) pathlength L through the gas, telescope resolution and the volume filling factor of the gas, f_v. In each of these cases the dispersion sigma of the lognormal PDF depends on the variable with a negative power law. We also derive PDFs of mean LOS volume densities of gas components in M31 and M51. Combining these with the volume density PDFs for different components of the ISM in the Milky Way (MW), we find that sigma decreases with increasing length L with an exponent of -0.76 +/- 0.06, which is steeper than expected. We show that the difference is due to variations in f_v. As f_v is similar in M31, M51 and the MW, the density structure in the gas in these galaxies must be similar. Finally, we demonstrate that an increase in f_v with increasing distance to the Galactic plane explains the decrease in sigma with latitude of the PDFs of emission measure and FUV emission observed for the MW.

astro-ph.GA

Galactic magnetic fields and hierarchical galaxy formation

A framework is introduced for coupling the evolution of galactic magnetic fields sustained by the mean-field dynamo with the formation and evolution of galaxies in cold dark matter cosmology. Estimates of the steady-state strength of the large-scale and turbulent magnetic fields from mean-field and fluctuation dynamo models are used together with galaxy properties predicted by semi-analytic models of galaxy formation for a population of spiral galaxies. We find that the field strength is mostly controlled by the evolving gas content of the galaxies. Thus, because of the differences in the implementation of the star formation law, feedback from supernovae and ram-pressure stripping, each of the galaxy formation models considered predicts a distribution of field strengths with unique features. The most prominent of them is the difference in typical magnetic fields strengths obtained for the satellite and central galaxy populations as well as the typical strength of the large-scale magnetic field in galaxies of different mass.

astro-ph.GA

Structure, dynamical impact and origin of magnetic fields in nearby galaxies in the SKA era

Magnetic fields are an important ingredient of the interstellar medium (ISM). Besides their importance for star formation, they govern the transport of cosmic rays, relevant to the launch and regulation of galactic outflows and winds, which in turn are pivotal in shaping the structure of halo magnetic fields. Mapping the small-scale structure of interstellar magnetic fields in many nearby galaxies is crucial to understand the interaction between gas and magnetic fields, in particular how gas flows are affected. Elucidation of the magnetic role in, e.g., triggering star formation, forming and stabilising spiral arms, driving outflows, gas heating by reconnection and magnetising the intergalactic medium has the potential to revolutionise our physical picture of the ISM and galaxy evolution in general. Radio polarisation observations in the very nearest galaxies at high frequencies (>= 3 GHz) and with high spatial resolution (<= 5") hold the key here. The galaxy survey with SKA1 that we propose will also be a major step to understand the galactic dynamo, which is important for models of galaxy evolution and for astrophysical magnetohydrodynamics in general. Field amplification by turbulent gas motions, which is crucial for efficient dynamo action, has been investigated so far only in simulations, while compelling evidence of turbulent fields from observations is still lacking.

astro-ph.GA

Magnetic Field Tomography in Nearby Galaxies with the Square Kilometre Array

Magnetic fields play an important role in shaping the structure and evolution of the interstellar medium (ISM) of galaxies, but the details of this relationship remain unclear. With SKA1, the 3D structure of galactic magnetic fields and its connection to star formation will be revealed. A highly sensitive probe of the internal structure of the magnetoionized ISM is the partial depolarization of synchrotron radiation from inside the volume. Different configurations of magnetic field and ionized gas within the resolution element of the telescope lead to frequency-dependent changes in the observed degree of polarization. The results of spectro-polarimetric observations are tied to physical structure in the ISM through comparison with detailed modeling, supplemented with the use of new analysis techniques that are being actively developed and studied within the community such as Rotation Measure Synthesis. The SKA will enable this field to come into its own and begin the study of the detailed structure of the magnetized ISM in a sample of nearby galaxies, thanks to its extraordinary wideband capabilities coupled with the combination of excellent surface brightness sensitivity and angular resolution.

astro-ph.GA

Magnetic Fields in a Sample of Nearby Spiral Galaxies

Both observations and modelling of magnetic fields in the diffuse interstellar gas of spiral galaxies are well developed but the theory has been confronted with observations for only a handful of individual galaxies. There is now sufficient data to consider statistical properties of galactic magnetic fields. We have collected data from the literature on the magnetic fields and interstellar media (ISM) of 20 spiral galaxies, and tested for various physically motivated correlations between magnetic field and ISM parameters. Clear correlations emerge between the total magnetic field strength and molecular gas density as well as the star formation rate. The magnetic pitch angle exhibits correlations with the total gas density, the star formation rate and the strength of the axisymmetric component of the mean magnetic field. The total and mean magnetic field strengths exhibit noticeable degree of correlation, suggesting a universal behaviour of the degree of order in galactic magnetic fields. We also compare the predictions of galactic dynamo theory to observed magnetic field parameters and identify directions in which theory and observations might be usefully developed.

astro-ph.GA

3D morphology of a random field from its 2D cross-section

We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the filamentarity F of the structures seen in the cross-section (F=0 for a circle and F=1 for a line). The probability distribution of F has a robust form with a sharp maximum and truncation that are sensitive to the ellipsoids' aspect ratios. We show that the aspect ratios of triaxial ellipsoids with randomly distributed dimensions can still be recovered from the probability distribution of F. This method is applicable to many shape recognition and classification problems, here illustrated with neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with the mean axis ratio 1:2:20.

physics.flu-dyn

Constraining regular and turbulent magnetic field strengths in M51 via Faraday depolarization

We employ an analytical model that incorporates both wavelength-dependent and wavelength-independent depolarization to describe radio polarimetric observations of polarization at $λλλ\, 3.5, 6.2, 20.5$ cm in M51 (NGC 5194). The aim is to constrain both the regular and turbulent magnetic field strengths in the disk and halo, modeled as a two- or three-layer magneto-ionic medium, via differential Faraday rotation and internal Faraday dispersion, along with wavelength-independent depolarization arising from turbulent magnetic fields. A reduced chi-squared analysis is used for the statistical comparison of predicted to observed polarization maps to determine the best-fit magnetic field configuration at each of four radial rings spanning $2.4 - 7.2$ kpc in $1.2$ kpc increments. We find that a two-layer modeling approach provides a better fit to the observations than a three-layer model, where the near and far sides of the halo are taken to be identical, although the resulting best-fit magnetic field strengths are comparable. This implies that all of the signal from the far halo is depolarized at these wavelengths. We find a total magnetic field in the disk of approximately $18~μ$G and a total magnetic field strength in the halo of $\sim 4-6~μ$G. Both turbulent and regular magnetic field strengths in the disk exceed those in the halo by a factor of a few. About half of the turbulent magnetic field in the disk is anisotropic, but in the halo all turbulence is only isotropic.

astro-ph.GA