arXiv subjects

Takahiro Kudoh

Publications and source records attributed to Takahiro Kudoh.

At least 19 recordsLinked to original sources

arXiv2022

The Magnetic Field versus Density relation in Star-Forming Molecular Clouds

We study the magnetic field to density ($B-ρ$) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density $ρ_{\rm T}$ between the relatively flat low density regime and a power-law regime at higher densities. We present an analytic theory for $ρ_{\rm T}$ based on the interplay of the magnetic field, turbulence, and gravity. The break density $ρ_{\rm T}$ scales with the strength of the initial Alfvén Mach number $\mathcal{M}_{\rm A0}$ for sub-Alfvénic ( $\mathcal{M}_{\rm A0}<1$) and trans-Alfvénic ($\mathcal{M}_{\rm A0} \sim 1$) clouds. We fit the variation of $ρ_{\rm T}$ for model clouds as a function of $\mathcal{M}_{\rm A0}$, set by different values of initial sonic Mach number $\mathcal{M_{\rm 0}}$ and the initial ratio of gas pressure to magnetic pressure $β_{\rm 0}$. This implies that $ρ_{\rm T}$, which denotes the transition in mass-to-flux ratio from the subcritical to supercritical regime, is set by the initial turbulent compression of the molecular cloud.

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arXiv2019

The Transition from a Lognormal to a Power-Law Column Density Distribution in Molecular Clouds: An Imprint of the Initial Magnetic Field and Turbulence

We introduce a theory for the development of a transitional column density $Σ_{\rm TP}$ between the lognormal and the power-law forms of the probability distribution function (PDF) in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of $Σ_{\rm TP}$ increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for $Σ_{\rm TP}$ based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value $Σ_{\rm TP}$ scales with $\mathcal{M}^2_{\rm 0}$, the square of the initial sonic Mach number, and $β_{0}$, the initial ratio of gas pressure to magnetic pressure. We fit the variation of $Σ_{\rm TP}$ among different model clouds as a function of $\mathcal{M}^2_{\rm 0} β_{0}$, or equivalently the square of the initial Alfvénic Mach number $\mathcal{M}^2_{\rm A0}$. This implies that the transition value $Σ_{\rm TP}$ is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of $Σ_{\rm TP}$ denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.

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arXiv2019

Fragmentation of Filamentary Cloud Permeated by Perpendicular Magnetic Field II. Dependence on the Initial Density Profile

We examine the linear stability of a filamentary cloud permeated by a perpendicular magnetic field. The initial magnetic field is assumed to be uniform and perpendicular to the cloud axis. The model cloud is assumed to have a Plummer-like density profile and to be supported against the self-gravity by turbulence. The effects of turbulence are taken into account by enhancing the effective pressure of a low density gas. We derive the effective pressure as a function of the density from the condition of the hydrostatic balance. It is shown that the model cloud is more unstable against radial collapse, when the radial density slope is shallower. When the magnetic field is mildly strong, the radial collapse is suppressed. If the displacement vanishes in the region very far from the cloud axis, the model cloud is stabilized completely by a mildly strong magnetic field. If rearrangement of the magnetic flux tubes is permitted, the model cloud is unstable even when the magnetic field is extremely strong. The stability depends on the outer boundary condition as in case of the isothermal cloud. The growth rate of the rearrangement mode is smaller when the radial density slope is shallower.

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arXiv2017

The Effect of Magnetic Fields and Ambipolar Diffusion on the Column Density Probability Distribution Function in Molecular Clouds

Simulations generally show that non-self-gravitating clouds have a lognormal column density ($Σ$) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynamic simulations including ambipolar diffusion with different initial conditions to see the effect of strong magnetic fields and nonlinear initial velocity perturbations on the evolution of the column density PDFs. Our simulations show that column density PDFs of clouds with supercritical mass-to-flux ratio, with either linear perturbations or nonlinear turbulence, quickly develop a power-law tail such that $dN/d \log Σ\propto Σ^{-α}$ with index $α\simeq 2$. Interestingly, clouds with subcritical mass-to-flux ratio also proceed directly to a power-law PDF, but with a much steeper index $α\simeq 4$. This is a result of gravitationally-driven ambipolar diffusion. However, for nonlinear perturbations with a turbulent spectrum ($v_{k}^{2} \propto k^{-4}$), the column density PDFs of subcritical clouds do retain a lognormal shape for a major part of the cloud evolution, and only develop a distinct power-law tail with index $α\simeq 2$ at greater column density when supercritical pockets are formed.

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arXiv2017

Fragmentation of Filamentary Cloud Permeated by Perpendicular Magnetic Field

We examine the linear stability of an isothermal filamentary cloud permeated by a perpendicular magnetic field. Our model cloud is assumed to be supported by gas pressure against the self-gravity in the unperturbed state. For simplicity, the density distribution is assumed to be symmetric around the axis. Also for simplicity, the initial magnetic field is assumed to be uniform and turbulence is not taken into account. The perturbation equation is formulated to be an eigenvalue problem. The growth rate is obtained as a function of the wavenumber for fragmentation along the axis and the magnetic field strength. The growth rate depends critically on the outer boundary. If the displacement vanishes in the region very far from the cloud axis (fixed boundary), cloud fragmentation is suppressed by a moderate magnetic field, which means the plasma beta is below 1.67 on the cloud axis. If the displacement is constant along the magnetic field in the region very far from the cloud, the cloud is unstable even when the magnetic field is infinitely strong. The cloud is deformed by circulation in the plane perpendicular to the magnetic field. The unstable mode is not likely to induce dynamical collapse, since it is excited even when the whole cloud is magnetically subcritical. For both the boundary conditions the magnetic field increases the wavelength of the most unstable mode. We find that the magnetic force suppresses compression perpendicular to the magnetic field especially in the region of low density.

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arXiv2017

Cosmic Magnetism in Centimeter and Meter Wavelength Radio Astronomy

Magnetic field is ubiquitous in the Universe and it plays essential roles in various astrophysical phenomena, yet its real origin and evolution are poorly known. This article reviews current understanding of magnetic fields in the interstellar medium, the Milky Way Galaxy, external galaxies, active galactic nuclei, clusters of galaxies, and the cosmic web. Particularly, the review concentrates on the achievements that have been provided by centimeter and meter wavelength radio observations. The article also introduces various methods to analyze linear polarization data, including synchrotron radiation, Faraday rotation, depolarization, and Faraday tomography.

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arXiv2017

Magnetic Ribbons: A Minimum Hypothesis Model for Filaments

We develop a magnetic ribbon model for molecular cloud filaments. These result from turbulent compression in a molecular cloud in which the background magnetic field sets a preferred direction. We use our model to calculate a synthetic observed relation between apparent width in projection versus observed column density. The relationship is relatively flat, in rough agreement with the observations, and unlike the simple expectation based on a Jeans length argument.

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arXiv2016

A Magnetic Ribbon Model for Star-Forming Filaments

We develop a magnetic ribbon model for molecular cloud filaments. These result from turbulent compression in a molecular cloud in which the background magnetic field sets a preferred direction. We argue that this is a natural model for filaments and is based on the interplay between turbulence, strong magnetic fields, and gravitationally-driven ambipolar diffusion, rather than pure gravity and thermal pressure. An analytic model for the formation of magnetic ribbons that is based on numerical simulations is used to derive a lateral width of a magnetic ribbon. This differs from the thickness along the magnetic field direction, which is essentially the Jeans scale. We use our model to calculate a synthetic observed relation between apparent width in projection versus observed column density. The relationship is relatively flat, similar to observations, and unlike the simple expectation based on a Jeans length argument.

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arXiv2016

Resolving 4-D Nature of Magnetism with Depolarization and Faraday Tomography: Japanese SKA Cosmic Magnetism Science

Magnetic fields play essential roles in various astronomical objects. Radio astronomy has revealed that magnetic fields are ubiquitous in our Universe. However, the real origin and evolution of magnetic fields is poorly proven. In order to advance our knowledge of cosmic magnetism in coming decades, the Square Kilometre Array (SKA) should have supreme sensitivity than ever before, which provides numerous observation points in the cosmic space. Furthermore, the SKA should be designed to facilitate wideband polarimetry so as to allow us to examine sightline structures of magnetic fields by means of depolarization and Faraday Tomography. The SKA will be able to drive cosmic magnetism of the interstellar medium, the Milky Way, galaxies, AGN, galaxy clusters, and potentially the cosmic web which may preserve information of the primeval Universe. The Japan SKA Consortium (SKA-JP) Magnetism Science Working Group (SWG) proposes the project "Resolving 4-D Nature of Magnetism with Depolarization and Faraday Tomography", which contains ten scientific use cases.

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arXiv2014

Induced Core Formation Time in Subcritical Magnetic Clouds by Large-Scale Trans-Alfvénic Flows

We clarify the mechanism of accelerated core formation by large-scale nonlinear flows in subcritical magnetic clouds by finding a semi-analytical formula for the core formation time and describing the physical processes that lead to them. Recent numerical simulations show that nonlinear flows induce rapid ambipolar diffusion that leads to localized supercritical regions that can collapse. Here, we employ non-ideal magnetohydrodynamic simulations including ambipolar diffusion for gravitationally stratified sheets threaded by vertical magnetic fields. One of the horizontal dimensions is eliminated, resulting in a simpler two-dimensional simulation that can clarify the basic process of accelerated core formation. A parameter study of simulations shows that the core formation time is inversely proportional to the square of the flow speed when the flow speed is greater than the Alfvén speed. We find a semi-analytical formula that explains this numerical result. The formula also predicts that the core formation time is about three times shorter than that with no turbulence, when the turbulent speed is comparable to the Alfvén speed.

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arXiv2014

Linear Growth of the Kelvin-Helmholtz Instability with an Adiabatic Cosmic-ray Gas

We investigate effects of cosmic-rays on the linear growth of the Kelvin-Helmholtz instability. Cosmic-rays are treated as an adiabatic gas and allowed to diffuse along magnetic field lines. We calculated the dispersion relation of the instability for various sets of two free parameters, the ratio of the cosmic-ray pressure to the thermal gas pressure and the diffusion coefficient. Including cosmic-ray effects, a shear layer is more destabilized and the growth rates can be enhanced in comparison with the ideal magnetohydrodynamical case. Whether the growth rate is effectively enhanced or not depends on the diffusion coefficient of cosmic-rays. We obtain the criterion for effective enhancement by comparing the growing time scale of the instability with the diffusion time scale of cosmic-rays. These results can be applied to various astrophysical phenomena where a velocity shear is present, such as outflows from star-forming galaxies, AGN jet, channel flows resulting from the nonlinear development of the magnetorotational instability, and galactic disks.

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arXiv2013

Dynamo activities driven by magneto-rotational instability and Parker instability in galactic gaseous disk

We carried out global three-dimensional magneto-hydrodynamic simulations of dynamo activities in galactic gaseous disks without assuming equatorial symmetry. Numerical results indicate the growth of azimuthal magnetic fields non-symmetric to the equatorial plane. As magneto-rotational instability (MRI) grows, the mean strength of magnetic fields is amplified until the magnetic pressure becomes as large as 10% of the gas pressure. When the local plasma $β$ ($ = p_{\rm gas}/p_{\rm mag}$) becomes less than 5 near the disk surface, magnetic flux escapes from the disk by Parker instability within one rotation period of the disk. The buoyant escape of coherent magnetic fields drives dynamo activities by generating disk magnetic fields with opposite polarity to satisfy the magnetic flux conservation. The flotation of the azimuthal magnetic flux from the disk and the subsequent amplification of disk magnetic field by MRI drive quasi-periodic reversal of azimuthal magnetic fields in timescale of 10 rotation period. Since the rotation speed decreases with radius, the interval between the reversal of azimuthal magnetic fields increases with radius. The rotation measure computed from the numerical results shows symmetry corresponding to a dipole field.

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arXiv2011

Scaling Law of Relativistic Sweet-Parker Type Magnetic Reconnection

Relativistic Sweet-Parker type magnetic reconnection is investigated by relativistic resistive magnetohydrodynamic (RRMHD) simulations. As an initial setting, we assume anti-parallel magnetic fields and a spatially uniform resistivity. A perturbation imposed on the magnetic fields triggers magnetic reconnection around a current sheet, and the plasma inflows into the reconnection region. The inflows are then heated due to ohmic dissipation in the diffusion region, and finally become relativistically hot outflows. The outflows are not accelerated to ultra-relativistic speeds (i.e., Lorentz factor ~ 1), even when the magnetic energy dominates the thermal and rest mass energies in the inflow region. Most of the magnetic energy in the inflow region is converted into the thermal energy of the outflow during the reconnection process. The energy conversion from magnetic to thermal energy in the diffusion region results in an increase in the plasma inertia. This prevents the outflows from being accelerated to ultra-relativistic speeds. We find that the reconnection rate R obeys the scaling relation R S^{-0.5}, where S is the Lundquist number. This feature is the same as that of non-relativistic reconnection. Our results are consistent with the theoretical predictions of Lyubarsky (2005) for Sweet-Parker type magnetic reconnection.

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arXiv2010

Formation of collapsing cores in subcritical magnetic clouds: three-dimensional MHD simulations with ambipolar diffusion

We employ the three-dimensional magnetohydrodynamic simulation including ambipolar diffusion to study the gravitationally-driven fragmentation of subcritical molecular clouds, in which the gravitational fragmentation is stabilized as long as magnetic flux-freezing applies. The simulations show that the cores in an initially subcritical cloud generally develop gradually over an ambipolar diffusion time, which is about a few $\times 10^7$ years in a typical molecular cloud. On the other hand, the formation of collapsing cores in subcritical clouds is accelerated by supersonic nonlinear flows. Our parameter study demonstrates that core formation occurs faster as the strength of the initial flow speed in the cloud increases. We found that the core formation time is roughly proportional to the inverse of the square root of the enhanced density created by the supersonic nonlinear flows. The density dependence is similar to that derived in quasistatically contracting magnetically supported clouds, although the core formation conditions are created by the nonlinear flows in our simulations. We have also found that the accelerated formation time is not strongly dependent on the initial strength of the magnetic field if the cloud is highly subcritical. Our simulation shows that the core formation time in our model subcritical clouds is several $\times 10^6$ years, due to the presence of large-scale supersonic flows ($\sim 3$ times sound speed). Once a collapsing core forms, the density, velocity, and magnetic field structure of the core does not strongly depend on the initial strength of the velocity fluctuation. The infall velocities of the cores are subsonic and the magnetic field lines show weak hourglass shapes.

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arXiv2010

The Primordial Origin Model of Magnetic Fields in Spiral Galaxies

We propose a primordial-origin model for the composite configurations of global magnetic fields in spiral galaxies. We show that uniform tilted magnetic field wound up into a rotating disk galaxy can evolve into composite magnetic configurations comprising bisymmetric spiral (S=BSS), axisymmetric spiral (A=ASS), plane-reversed spiral (PR), and/or ring (R) fields in the disk, and vertical (V) fields in the center. By MHD simulations we show that these composite galactic fields are indeed created from weak primordial uniform field, and that the different configurations can co-exist in the same galaxy. We show that spiral fields trigger the growth of two-armed gaseous arms. The centrally accumulated vertical fields are twisted and produce jet toward the halo. We find that the more vertical was the initial uniform field, the stronger is the formed magnetic field in the galactic disk.

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arXiv2008

How was the mushroom-shaped GW 123.4--1.5 formed in the Galactic disk?

The unusual mushroom-shaped HI cloud, GW 123.4--1.5, is hundreds of parsecs in size but does not show any correlations to HI shells or chimney structures. To investigate the origin and velocity structure of GW 123.4--1.5, we perform three-dimensional hydrodynamical simulations of the collision of a high-velocity cloud with the Galactic disk. We also perform a parameter study of the density, radius, and incident angle of the impact cloud. The numerical experiments indicate that we reproduce the mushroom-shaped structure which resembles GW 123.4--1.5 in shape, size, position-velocity across the cap of the mushroom, and the density ratio between the mushroom and surrounding gas. GW 123.4--1.5 is expected to be formed by the almost head-on collision of a HVC with velocity $\sim 100 \kms$ and mass $\sim 10^5 \Msun$ about $5 \times 10^7 \yr$ ago. A mushroom-shaped structure like GW 123.4--1.5 must be infrequent on the Galactic plane, because the head-on collision which explains the mushroom structure seems rare for observed HVCs. HVC-disk collision explains not only the origin of the mushroom-shaped structure but also the formation of a variety of structures like shells, loops, and vertical structures in our Galaxy.

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arXiv2008

Three-dimensional Simulation of Magnetized Cloud Fragmentation Induced by Nonlinear Flows and Ambipolar Diffusion

We demonstrate that the formation of collapsing cores in subcritical clouds is accelerated by nonlinear flows, by performing three-dimensional non-ideal MHD simulations. An initial random supersonic (and trans-Alfvenic) turbulent-like flow is input into a self-gravitating gas layer that is threaded by a uniform magnetic field (perpendicular to the layer) such that the initial mass-to-flux ratio is subcritical. Magnetic ambipolar diffusion occurs very rapidly initially due to the sharp gradients introduced by the turbulent flow. It subsequently occurs more slowly in the traditional near-quasistatic manner, but in regions of greater mean density than present in the initial state. The overall timescale for runaway growth of the first core(s) is several times, 10^6 yr, even though previous studies have found a timescale of several times, 10^7 yr when starting with linear perturbations and similar physical parameters. Large-scale supersonic flows exist in the cloud and provide an observationally testable distinguishing characteristic from core formation due to linear initial perturbations. However, the nonlinear flows have decayed sufficiently that the relative infall motions onto the first core are subsonic, as in the case of starting from linear initial perturbations. The ion infall motions are very similar to those of neutrals; however, they lag the neutral infall in directions perpendicular to the mean magnetic field direction and lead the neutral infall in the direction parallel to the mean magnetic field.

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arXiv2007

Three-dimensional simulations of molecular cloud fragmentation regulated by magnetic fields and ambipolar diffusion

We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion-neutral friction in regulating gravitationally-driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infall speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (\ga 0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent with previous two-dimensional simulations. We also found that a snapshot of the relation between density (rho) and the strength of the magnetic field (B) at different spatial points of the cloud coincides with the evolutionary track of an individual core. When the density becomes large, both relations tend to B \propto ρ^{0.5}.

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