arXiv subjects

James R. Beattie

Publications and source records attributed to James R. Beattie.

32 records · Page 2Linked to original sources

arXiv2023

Availability, outage, and capacity of spatially correlated, Australasian free-space optical networks

Network capacity and reliability for free space optical communication (FSOC) is strongly driven by ground station availability, dominated by local cloud cover causing an outage, and how availability relations between stations produce network diversity. We combine remote sensing data and novel methods to provide a generalised framework for assessing and optimising optical ground station networks. This work is guided by an example network of eight Australian and New Zealand optical communication ground stations which would span approximately $60^\circ$ in longitude and $20^\circ$ in latitude. Utilising time-dependent cloud cover data from five satellites, we present a detailed analysis determining the availability and diversity of the network, finding the Australasian region is well-suited for an optical network with a 69% average site availability and low spatial cloud cover correlations. Employing methods from computational neuroscience, we provide a Monte Carlo method for sampling the joint probability distribution of site availabilities for an arbitrarily sized and point-wise correlated network of ground stations. Furthermore, we develop a general heuristic for site selection under availability and correlation optimisations, and combine this with orbital propagation simulations to compare the data capacity between optimised networks and the example network. We show that the example network may be capable of providing tens of terabits per day to a LEO satellite, and up to 99.97% reliability to GEO satellites. We therefore use the Australasian region to demonstrate novel, generalised tools for assessing and optimising FSOC ground station networks, and additionally, the suitability of the region for hosting such a network.

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arXiv2022

Turbulent diffusion of streaming cosmic rays in compressible, partially ionised plasma

Cosmic rays (CRs) are a dynamically important component of the interstellar medium (ISM) of galaxies. The $\sim$GeV CRs that carry most CR energy and pressure are likely confined by self-generated turbulence, leading them to stream along magnetic field lines at the ion Alfvén speed. However, the consequences of self-confinement for CR propagation on galaxy scales remain highly uncertain. In this paper, we use a large ensemble of magnetohydrodynamical turbulence simulations to quantify how the basic parameters describing ISM turbulence -- the sonic Mach number, $\mathcal{M}$ (plasma compressibility), Alfvén Mach number, $\mathcal{M}_{A0}$ (strength of the large-scale field with respect to the turbulence), and ionisation fraction by mass, $χ$ -- affect the transport of streaming CRs. We show that the large-scale transport of CRs whose small-scale motion consists of streaming along field lines is well described as a combination of streaming along the mean field and superdiffusion both along (parallel to) and across (perpendicular to) it; $\mathcal{M}_{A0}$ drives the level of anisotropy between parallel and perpendicular diffusion and $χ$ modulates the magnitude of the diffusion coefficients, while in our choice of units, $\mathcal{M}$ is unimportant except in the sub-Alfvénic ($\mathcal{M}_{A0} \lesssim 0.5$) regime. Our finding that superdiffusion is ubiquitous potentially explains the apparent discrepancy between CR diffusion coefficients inferred from measurements close to individual sources compared to those measured on larger, Galactic scales. Finally, we present empirical fits for the diffusion coefficients as a function of plasma parameters that may be used as sub-grid recipes for global interstellar medium, galaxy or cosmological simulations.

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arXiv2022

The density distribution and physical origins of intermittency in supersonic, highly magnetised turbulence with diverse modes of driving

The probability density function (PDF) of the logarithmic density contrast, $s=\ln (ρ/ρ_0)$, with gas density $ρ$ and mean density $ρ_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian (intermittent) features that monotonically increase with the turbulent Mach number, $\mathcal{M}$. By studying the mass- and volume-weighted $s$-PDF for an ensemble of 36 sub-to-trans-Alfvenic mean-field, supersonic, isothermal turbulence simulations with different modes of driving, relevant to molecular gas in the cool interstellar medium, we show that a more intricate picture emerges for the non-Gaussian nature of $s$. Using four independent measures of the non-Gaussian components, we find hydrodynamical-like structure in the highly magnetised plasma for $\mathcal{M} \lesssim 4$. However, for $\mathcal{M} \gtrsim 4$, the non-Gaussian signatures disappear, leaving approximately Gaussian $s$-statistics -- exactly the opposite of hydrodynamical turbulence in the high-$\mathcal{M}$ limit. We also find that the non-Gaussian components of the PDF increase monotonically with more compressive driving modes. To understand the $\mathcal{M} \lesssim 4$ non-Gaussian features we use one-dimensional (1D) pencil beams to explore the dynamics along and across the large-scale magnetic field, $\mathbf{B}_0$. We discuss kinetic, density and magnetic field fluctuations from the pencil beams, and identify physical sources of non-Gaussian components to the PDF as single, strong shocks coupled to fast magnetosonic compressions that form along $\mathbf{B}_0$. We discuss the Gaussianisation of the $\mathcal{M} \gtrsim 4$ $s$-fields through the lens of two phenomenologies: the self-similarity of the $s$-field and homogenisation of the dynamical timescales between the over- and under-dense regions in the compressible gas.

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arXiv2022

Ion Alfvén velocity fluctuations and implications for the diffusion of streaming cosmic rays

The interstellar medium (ISM) of star-forming galaxies is magnetized and turbulent. Cosmic rays (CRs) propagate through it, and those with energies from $\sim\,\rm{GeV} - \rm{TeV}$ are likely subject to the streaming instability, whereby the wave damping processes balances excitation of resonant ionic Alfvén waves by the CRs, reaching an equilibrium in which the propagation speed of the CRs is very close to the local ion Alfvén velocity. The transport of streaming CRs is therefore sensitive to ionic Alfvén velocity fluctuations. In this paper we systematically study these fluctuations using a large ensemble of compressible MHD turbulence simulations. We show that for sub-Alfvénic turbulence, as applies for a strongly magnetized ISM, the ionic Alfvén velocity probability density function (PDF) is determined solely by the density fluctuations from shocked gas forming parallel to the magnetic field, and we develop analytical models for the ionic Alfvén velocity PDF up to second moments. For super-Alfvénic turbulence, magnetic and density fluctuations are correlated in complex ways, and these correlations as well as contributions from the magnetic fluctuations sets the ionic Alfvén velocity PDF. We discuss the implications of these findings for underlying "macroscopic" diffusion mechanisms in CRs undergoing the streaming instability, including modeling the macroscopic diffusion coefficient for the parallel transport in sub-Alfvénic plasmas. We also describe how, for highly-magnetized turbulent gas, the gas density PDF, and hence column density PDF, can be used to access information about ionic Alfvén velocity structure from observations of the magnetized ISM.

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arXiv2022

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $δ\mathbf{B}$ and large-scale, $\mathbf{B}_0$ fields, $\left< (δ\mathbf{B}\cdot\mathbf{B}_0)^{2} \right>^{1/2}_{\mathcal{V}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible MHD turbulence. Furthermore, we explore the relation between the turbulent, mean-field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetised ISM.

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arXiv2022

Fundamental scales in the kinematic phase of the turbulent dynamo

The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, $k_{\rm p}$, do magnetic fields become most concentrated? There has been some disagreement about whether $k_{\rm p}$ is controlled by the viscous scale, $k_ν$ (where turbulent kinetic energy dissipates), or the resistive scale, $k_η$ (where magnetic fields dissipate). Here we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run $104$-simulations with hydrodynamic Reynolds numbers of $10 \leq {\rm Re} \leq 3600$, and magnetic Reynolds numbers of $270 \leq {\rm Rm} \leq 4000$, to explore the dependence of $k_{\rm p}$ on $k_ν$ and $k_η$. Using physically motivated models for the kinetic and magnetic energy spectra, we measure $k_ν$, $k_η$ and $k_{\rm p}$, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_ν= (0.025^{+0.005}_{-0.006})\, k_{\rm turb}\, {\rm Re}^{3/4}$ and $k_η= (0.88^{+0.21}_{-0.23})\, k_ν\, {\rm Pm}^{1/2}$, where $k_{\rm turb}$ is the turbulence driving wavenumber and ${\rm Pm}={\rm Rm}/{\rm Re}$ is the magnetic Prandtl number. We demonstrate that the principle dependence of $k_{\rm p}$ is on $k_η$. For plasmas where ${\rm Re} \gtrsim 100$, we find that $k_{\rm p} = (1.2_{-0.2}^{+0.2})\, k_η$, with the proportionality constant related to the power-law `Kazantsev' exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where ${\rm Re} > 100$, compared to ${\rm Re} < 100$. We report a minimum critical hydrodynamic Reynolds number, ${\rm Re}_{\rm crit} = 100$ for bonafide turbulent dynamo action.

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arXiv2022

Theoretical and Observational Evidence for Coriolis Effects in Coronal Magnetic Fields Via Direct Current Driven Flaring Events

All stars produce explosive surface events such as flares and coronal mass ejections. These events are driven by the release of energy stored in coronal magnetic fields, generated by the stellar dynamo. However, it remains unclear if the energy deposition in the magnetic fields is driven by direct or alternating currents. Recently, we presented observational measurements of the flare intensity distributions for a sample of $\sim10^5$ stars across the main sequence observed by $\textit{TESS}$, all of which exhibited power-law distributions similar to those observed in the Sun, albeit with varying slopes. Here we investigate the mechanisms required to produce such a distribution of flaring events via direct current energy deposition, in which coronal magnetic fields braid, reconnect, and produce flares. We adopt a topological model for this process which produces a power-law distribution of energetic flaring events. We expand this model to include the Coriolis effect, which we demonstrate produces a shallower distribution of flare energies in stars that rotate more rapidly (corresponding to a weaker decline in occurrence rates toward increasing flare energies). We present tentative evidence for the predicted rotation-power-law index correlation in the observations. We advocate for future observations of stellar flares that would improve our measurements of the power-law exponents, and yield key insights into the underlying dynamo mechanisms that underpin the self-similar flare intensity distributions.

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arXiv2021

First extragalactic measurement of the turbulence driving parameter: ALMA observations of the star-forming region N159E in the Large Magellanic Cloud

Studying the driving modes of turbulence is important for characterizing the impact of turbulence in various astrophysical environments. The driving mode of turbulence is parameterized by $b$, which relates the width of the gas density PDF to the turbulent Mach number; $b\approx 1/3$, $1$, and $0.4$ correspond to driving that is solenoidal, compressive, and a natural mixture of the two, respectively. In this work, we use high-resolution (sub-pc) ALMA $^{12}$CO ($J$ = $2-1$), $^{13}$CO ($J$ = $2-1$), and C$^{18}$O ($J$ = $2-1$) observations of filamentary molecular clouds in the star-forming region N159E (the Papillon Nebula) in the Large Magellanic Cloud (LMC) to provide the first measurement of turbulence driving parameter in an extragalactic region. We use a non-local thermodynamic equilibrium (NLTE) analysis of the CO isotopologues to construct a gas density PDF, which we find to be largely log-normal in shape with some intermittent features indicating deviations from lognormality. We find that the width of the log-normal part of the density PDF is comparable to the supersonic turbulent Mach number, resulting in $b \approx 0.9$. This implies that the driving mode of turbulence in N159E is primarily compressive. We speculate that the compressive turbulence could have been powered by gravo-turbulent fragmentation of the molecular gas, or due to compression powered by H I flows that led to the development of the molecular filaments observed by ALMA in the region. Our analysis can be easily applied to study the nature of turbulence driving in resolved star-forming regions in the local as well as the high-redshift Universe.

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arXiv2021

A multi-shock model for the density variance of anisotropic, highly-magnetised, supersonic turbulence

Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $σ^2_{ρ/ρ_0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parameterises the star formation (SF) rate of a cloud. However, models for $σ^2_{ρ/ρ_0}$ all share a common feature -- the variance is assumed to be isotropic. This assumption does not hold when a trans/sub-Alfvénic mean magnetic field, $\vec{B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $σ_{ρ/ρ_0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $σ_{ρ/ρ_0}^2$ in the high Mach number $(\mathcal{M})$ limit as small-scale density fluctuations become suppressed by the strong $\vec{B}_0$. The model reduces to the isotropic $σ_{ρ/ρ_0}^2-\mathcal{M}$ relation in the hydrodynamical limit. To validate our model, we calculate $σ_{ρ/ρ_0}^2$ from 12~high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented over-densities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic $\vec{B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

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arXiv2020

The sonic scale revealed by the world's largest supersonic turbulence simulation

Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ l^p, where we measure p_sup = 0.49 +/- 0.01 and p_sub = 0.39 +/- 0.02, respectively. We find that l_s agrees with the relation l_s / L = phi_s Mach^(-1/p_sup), where Mach is the three-dimensional Mach number, and L is either the driving scale of turbulence or the diameter of a molecular cloud. If L is the driving scale, we measure phi_s = 0.42 (+0.12) (-0.09), primarily because of the separation between the driving scale and the start of the supersonic cascade. For a supersonic cascade extending beyond the cloud scale, we get phi_s = 0.91 (+0.25) (-0.20). In both cases, phi_s < 1, because we find that the supersonic cascade transitions smoothly to the subsonic cascade over a factor of 3 in scale, instead of a sharp transition. Our measurements provide quantitative input for turbulence-regulated models of filament structure and star formation in molecular clouds.

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arXiv2020

Magnetic field fluctuations in anisotropic, supersonic turbulence

The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, $\vec{δB}$, over a wide range of turbulent Mach numbers, $\mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfvén Mach numbers, $\mathcal{M}_{\text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compressible quasi-static fluctuation model from the magnetohydrodynamical (MHD) equations and show that velocity gradients parallel to the mean magnetic field give rise to compressible modes in sub-Alfvénic flows, which prevents the flow from becoming two-dimensional, as is the case in incompressible MHD turbulence. We then generalise an analytical model for the magnitude of the magnetic fluctuations to include $\mathcal{M}$, and find $|\vec{δB}| = δB = c_s\sqrt{πρ_0}\mathcal{M}\mathcal{M}_{\text{A}0}$, where $c_s$ is the sound speed and $ρ_0$ is the mean density of gas. This new relation fits well in the strong $B$-field regime. We go on to study the anisotropy between the perpendicular ($ B_{\perp}$) and parallel ($ B_{\parallel}$) fluctuations and the mean-normalised fluctuations, which we find follow universal scaling relations, invariant of $\mathcal{M}$. We provide a detailed analysis of the morphology for the $δB_{\perp}$ and $δB_{\parallel}$ probability density functions and find that eddies aligned with $B_0$ cause parallel fluctuations that reduce $B_{\parallel}$ in the most anisotropic simulations. We discuss broadly the implications of our fluctuation models for magnetised gases in the interstellar medium.

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arXiv2019

Filaments and striations: anisotropies in observed, supersonic, highly-magnetised turbulent clouds

Stars form in highly-magnetised, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields, and magnetosonic striations introduce anisotropies into the cloud. In this study we use the two-dimensional (2D) power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\mathcal{M}_A=0.1$--$10$) and turbulent Mach numbers ($\mathcal{M}=2$--$20$), with 20 high-resolution, three-dimensional (3D) turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to $\mathcal{M}_A<1$, and $\mathcal{M}\lesssim 4$, the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for $\mathcal{M}\gtrsim 4$ the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by $\mathcal{M}$ that determine which kind of anisotropy dominates the morphology of a cloud.

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arXiv2019

The relation between the turbulent Mach number and observed fractal dimensions of turbulent clouds

Supersonic turbulence is a key player in controlling the structure and star formation potential of molecular clouds (MCs). The three-dimensional (3D) turbulent Mach number, $\mathcal{M}$, allows us to predict the rate of star formation. However, determining Mach numbers in observations is challenging because it requires accurate measurements of the velocity dispersion. Moreover, observations are limited to two-dimensional (2D) projections of the MCs and velocity information can usually only be obtained for the line-of-sight component. Here we present a new method that allows us to estimate $\mathcal{M}$ from the 2D column density, $Σ$, by analysing the fractal dimension, $\mathcal{D}$. We do this by computing $\mathcal{D}$ for six simulations, ranging between $1$ and $100$ in $\mathcal{M}$. From this data we are able to construct an empirical relation, $\log\mathcal{M}(\mathcal{D}) = ξ_1(\text{erfc}^{-1} [(\mathcal{D}-\mathcal{D}_{\text{min}})/Ω] + ξ_2),$ where $\text{erfc}^{-1}$ is the inverse complimentary error function, $\mathcal{D}_{\text{min}} = 1.55 \pm 0.13$ is the minimum fractal dimension of $Σ$, $Ω= 0.22 \pm 0.07$, $ξ_1 = 0.9 \pm 0.1$ and $ξ_2 = 0.2 \pm 0.2$. We test the accuracy of this new relation on column density maps from $Herschel$ observations of two quiescent subregions in the Polaris Flare MC, `saxophone' and `quiet'. We measure $\mathcal{M} \sim 10$ and $\mathcal{M} \sim 2$ for the subregions, respectively, which is similar to previous estimates based on measuring the velocity dispersion from molecular line data. These results show that this new empirical relation can provide useful estimates of the cloud kinematics, solely based upon the geometry from the column density of the cloud.

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arXiv2019

The relation between the true and observed fractal dimensions of turbulent clouds

Observations of interstellar gas clouds are typically limited to two-dimensional (2D) projections of the intrinsically three-dimensional (3D) structure of the clouds. In this study, we present a novel method for relating the 2D projected fractal dimension ($\mathcal{D}_{\text{p}}$) to the 3D fractal dimension ($\mathcal{D}_{\text{3D}}$) of turbulent clouds. We do this by computing the fractal dimension of clouds over two orders of magnitude in turbulent Mach number $(\mathcal{M} = 1-100)$, corresponding to seven orders of magnitude in spatial scales within the clouds. This provides us with the data to create a new empirical relation between $\mathcal{D}_{\text{p}}$ and $\mathcal{D}_{\text{3D}}$. The proposed relation is $\mathcal{D}_{\text{3D}}(\mathcal{D}_{\text{p}}) = Ω_1 erfc ( ξ_1 erfc^{-1}[ (\mathcal{D}_{\text{p}} - \mathcal{D}_{\text{p,min}})/Ω_2 ] + ξ_2 ) + \mathcal{D}_{\text{3D,min}}$, where the minimum 3D fractal dimension, $\mathcal{D}_{\text{3D,min}} = 2.06 \pm 0.35$, the minimum projected fractal dimension, $\mathcal{D}_{\text{p,min}} = 1.55 \pm 0.13$, $Ω_1 = 0.47 \pm 0.18$, $Ω_2 = 0.22 \pm 0.07$, $ξ_1 = 0.80 \pm 0.18$ and $ξ_2 = 0.26 \pm 0.19$. The minimum 3D fractal dimension, $\mathcal{D}_{\text{3D,min}} = 2.06 \pm 0.35$, indicates that in the high $\mathcal{M}$ limit the 3D clouds are dominated by planar shocks. The relation between $\mathcal{D}_{\text{p}}$ and $\mathcal{D}_{\text{3D}}$ of molecular clouds may be a useful tool for those who are seeking to understand the 3D structures of molecular clouds, purely based upon 2D projected data and shows promise for relating the physics of the turbulent clouds to the fractal dimension.

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