arXiv subjects

Tomoyuki Hanawa

Publications and source records attributed to Tomoyuki Hanawa.

50 records · Page 3Linked to original sources

arXiv2008

Critical Accretion Rate for Triggered Star Formation

We have reexamined the similarity solution for a self-gravitating isothermal gas sphere and examined implication to star formation in a turbulent cloud. When parameters are adequately chosen, the similarity solution expresses an accreting isothermal gas sphere bounded by a spherical shock wave. The mass and radius of the sphere increases in proportion to the time, while the central density decreases in proportion to the inverse square of time. The similarity solution is specified by the accretion rate and the infall velocity. The accretion rate has an upper limit for a given infall velocity. When the accretion rate is below the upper limit, there exist a pair of similarity solutions for a given set of the accretion rate and infall velocity. One of them is confirmed to be unstable against a spherical perturbation. This means that the gas sphere collapses to initiate star formation only when the accretion rate is larger than the upper limit. We have also examined stability of the similarity solution against non-spherical perturbation. Non-spherical perturbations are found to be damped.

astro-ph↗

arXiv2008

Three Dimensional Magnetohydrodynamical Simulations of Core Collapse Supernova

We show three-dimensional magnetohydrodynamical simulations of core collapse supernova in which the progenitor has magnetic fields inclined to the rotation axis. The simulations employed a simple empirical equation of state in which the pressure of degenerate gas is approximated by piecewise polytropes for simplicity. Neither energy loss due to neutrino is taken into account for simplicity. The simulations start from the stage of dynamical collapse of an iron core. The dynamical collapse halts at $ t $ = 189 ms by the pressure of high density gas and a proto-neutron star (PNS) forms. The evolution of PNS was followed about 40 milli-seconds in typical models. When the initial rotation is mildly fast and the initial magnetic fields are mildly strong, bipolar jets are launched from an upper atmosphere ($ r \sim 60 {\rm km} $) of the PNS. The jets are accelerated to $ \sim 3 \times 10 ^4 $ km s$^{-1}$, which is comparable to the escape velocity at the foot point. The jets are parallel to the initial rotation axis. Before the launch of the jets, magnetic fields are twisted by rotation of the PNS. The twisted magnetic fields form torus-shape multi-layers in which the azimuthal component changes alternately. The formation of magnetic multi-layers is due to the initial condition in which the magnetic fields are inclined with respect to the rotation axis. The energy of the jet depends only weakly on the initial magnetic field assumed. When the initial magnetic fields are weaker, the time lag is longer between the PNS formation and jet ejection. It is also shown that the time lag is related to the Alfvén transit time. Although the nearly spherical prompt shock propagates outward in our simulations, it is ...

astro-ph↗

arXiv2006

Evolution of Rotating Molecular Cloud Core with Oblique Magnetic Field

We studied the collapse of rotating molecular cloud cores with inclined magnetic fields, based on three-dimensional numerical simulations.The numerical simulations start from a rotating Bonnor-Ebert isothermal cloud in a uniform magnetic field. The magnetic field is initially taken to be inclined from the rotation axis. As the cloud collapses, the magnetic field and rotation axis change their directions. When the rotation is slow and the magnetic field is relatively strong, the direction of the rotation axis changes to align with the magnetic field, as shown earlier by Matsumoto & Tomisaka. When the magnetic field is weak and the rotation is relatively fast, the magnetic field inclines to become perpendicular to the rotation axis. In other words, the evolution of the magnetic field and rotation axis depends on the relative strength of the rotation and magnetic field. Magnetic braking acts to align the rotation axis and magnetic field, while the rotation causes the magnetic field to incline through dynamo action. The latter effect dominates the former when the ratio of the angular velocity to the magnetic field is larger than a critical value Ω_0/ B_0 > 0.39 G^1/2 c_s^-1, where B_0, Ω_0, G, and c_s^-1 denote the initial magnetic field, initial angular velocity, gravitational constant, and sound speed, respectively. When the rotation is relatively strong, the collapsing cloud forms a disk perpendicular to the rotation axis and the magnetic field becomes nearly parallel to the disk surface in the high density region. A spiral structure appears due to the rotation and the wound-up magnetic field in the disk.

astro-ph↗

arXiv2005

Collapse and Fragmentation of Rotating Magnetized Clouds. I. Magnetic Flux - Spin Relation

We discuss evolution of the magnetic flux density and angular velocity in a molecular cloud core, on the basis of three-dimensional numerical simulations, in which a rotating magnetized cloud fragments and collapses to form a very dense optically thick core of > 5 times 10 ^10 cm^-3 . As the density increases towards the formation of the optically thick core, the magnetic flux density and angular velocity converge towards a single relationship between the two quantities. If the core is magnetically dominated its magnetic flux density approaches 1.5 (n/5 times 10^10 cm^-3)^1/2 mG, while if the core is rotationally dominated the angular velocity approaches 2.57 times 10^-3, (n/5 times 10^10 cm^-3)^1/2 yr^-1, where n is the density of the gas. We also find that the ratio of the angular velocity to the magnetic flux density remains nearly constant until the density exceeds 5 times 10^10 cm^-3. Fragmentation of the very dense core and emergence of outflows from fragments are shown in the subsequent paper.

astro-ph↗

arXiv2005

Collapse and Fragmentation of Rotating Magnetized Clouds. II. Binary Formation and Fragmentation of First Cores

Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional MHD nested-grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the center of the cloud. When the isothermal gas is stable for fragmentation in a contracting disk, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentations are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disk is supported by centrifugal force, the disk fragments through a ring configuration (ring fragmentation). This is realized in a fast rotating adiabatic core as Omega >0.2 tau_ff^-1, where Omega and tau_ff represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disk is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2 - 4 fragments (bar fragmentation). Even if a disk is thin, the disk dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows are ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.

astro-ph↗

arXiv2003

Fragmentation of a Molecular Cloud Core versus Fragmentation of the Massive Protoplanetary Disk in the Main Accretion Phase

The fragmentation of molecular cloud cores a factor of 1.1 denser than the critical Bonnor-Ebert sphere is examined though three-dimensional numerical simulations. A nested grid is employed to resolve fine structure down to 1 AU while following the entire structure of the molecular cloud core of radius 0.14 pc. A total of 225 models are shown to survey the effects of initial rotation speed, rotation law, and amplitude of bar mode perturbation. The simulations show that the cloud fragments whenever the cloud rotates sufficiently slowly to allow collapse but fast enough to form a disk before first-core formation. The latter condition is equivalent to $Ω_0 t_{\rm ff} \gtrsim 0.05$, where $Ω_0$ and $t_{\rm ff}$ denote the initial central angular velocity and the freefall time measured from the central density, respectively. Fragmentation is classified into six types: disk-bar, ring-bar, satellite, bar, ring, and dumbbell types according to the morphology of collapse and fragmentation. When the outward decrease in initial angular velocity is more steep, the cloud deforms from spherical at an early stage. The cloud deforms into a ring only when the bar mode m = 2 perturbation is very minor. The ring fragments into two or three fragments via ring-bar type fragmentation and into at least three fragments via ring type fragmentation. When the bar mode is significant, the cloud fragments into two fragments via either bar or dumbbell type fragmentation. These fragments eventually merge due to their low angular momenta, after which several new fragments form around the merged fragment via satellite type fragmentation.

astro-ph↗

arXiv2002

A Fast Algorithm for Solving the Poisson Equation on a Nested Grid

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our numerical method is suitable for computing the gravity of a centrally condensed object. It consists of two parts: the difference scheme for the Poisson equation on the nested grid and the multi-grid iteration algorithm. It has three advantages: accuracy, fast convergence, and scalability. First it computes the gravitational potential of a close binary accurately up to the quadraple moment, even when the binary is resolved only in the fine grids. Second residual decreases by a factor of 300 or more by each iteration. We confirmed experimentally that the iteration converges always to the exact solution of the difference equation. Third the computation load of the iteration is proportional to the total number of the cells in the nested grid. Thus our method gives a good solution at the minimum expense when the nested grid is large. The difference scheme is applicable also to the adaptive mesh refinement in which cells of different sizes are used to cover a domain of computation.

astro-ph↗

arXiv2000

Stability of Toomre-Hayashi Disk

We investigate stability of Toomre-Hayashi model for a self-gravitating, rotating gas disk. The rotation velocity, $ v_ϕ$, and sound speed, $ c _{\rm s} $, are spatially constant in the model. We show that the model is unstable against an axisymmetric perturbation irrespectively of the values of $ v_ϕ$ and $ c_{\rm s} $. When the ratio, $ v_ϕ/ c_{\rm s} $, is large, the model disk is geometrically thin and unstable against an axisymmetric perturbation having a short radial wavelength, i.e., unstable against fragmentation. When $ v_ϕ/ c_{\rm s} $ is smaller than 1.20, it is unstable against total collapse. Toomre-Hayashi model of $ 1.7 \la v_ϕ/ c_{\rm s} \la 3 $ was thought to be stable against axisymmetric perturbations in earlier studies in which only radial motion was taken into account. Thus, the instability of Toomre-Hayashi model having a medium $ v_ϕ/ c_{\rm s} $ is due to not change in the surface density but that in the disk height. We also find that the singular isothermal perturbation is stable against non-spherical peturbations.

astro-ph↗

arXiv2000

Growth of a Vortex Mode during Gravitational Collapse Resulting in Type II Supernova

We investigate stability of a gravitationally collapsing iron core against non-spherical perturbation. The gravitationally collapsing iron core is approximated by a similarity solution for dynamically collapsing polytropic gas sphere. We find that the similarity solution is unstable against non-spherical perturbations. The perturbation grows in proportion to $ (t - t_0) ^{-σ} $ while the the central density increases in proportion to $ (t - t_0) ^{-2} $. The growth rate is $ σ= 1/3 + \ell (γ- 4/3) $, where $ γ$ and $ \ell $ denote the polytropic index and the parameter $ \ell $ of the spherical harmonics, $ Y_{\ell} ^m (θ, ϕ) $, respectively. The growing perturbation is dominated by vortex motion. Thus it excites global convection during the collapse and may contribute to material mixing in a type II supernova.

astro-ph↗

arXiv1999

Stability of Dynamically Collapsing Gas Sphere

We discuss stability of dynamically collapsing gas spheres. We use a similarity solution for a dynamically collapsing sphere as the unperturbed state. In the similarity solution the gas pressure is approximated by a polytrope of $ P = K ρ^γ$. We examine three types of perturbations: bar ($ \ell = 2$) mode, spin-up mode, and Ori-Piran mode. When $ γ< 1.097 $, it is unstable against bar-mode. It is unstable against spin-up mode for any $ γ$. When $ γ< 0.961 $, the similarity solution is unstable against Ori-Piran mode. The unstable mode grows in proportion to $ | t - t_0 | ^{-σ} $ while the central density increases in proportion to $ ρ_c \propto (t - t_0) ^{-2} $ in the similarity solution. The growth rate, $ σ$ is obtained numerically as a function of $ γ$ for bar mode and Ori-Piran mode. The growth rate of the bar mode is larger for a smaller $ γ$. The spin-up mode has the growth rate of $ σ= 1/3 $ for any $ γ$.

astro-ph↗

arXiv1998

Jets from Time-Dependent Accretion Flows onto a Black Hole

We investigate time-dependent inviscid hydrodynamical accretion flows onto a black hole using numerical simulations. We consider the accretion that consists of hot tenuous gas with low specific angular momentum and cold dense gas with high specific angular momentum. The former accretes continuously and the latter highly intermittently as blobs. The high specific angular momentum gas blobs bounce at the centrifugal barrier and create shock waves. The low specific angular momentum gas is heated at the shock fronts and escapes along the rotation axis. The outgoing gas evolves into pressure-driven jets. Jet acceleration lasts until the shock waves fade out. The total amount of the mass ejection is about 1-11 % of the mass of the blobs. The jet mass increases when the gas blobs are more massive or have larger specific angular momentum. We get narrower well-collimated jets when the hot continuous flow has a lower temperature. In the numerical simulations we used a finite difference code based on the total variation diminishing scheme. It is extended to include the blackbody radiation and to apply the multi time step scheme for time marching.

astro-ph↗

arXiv1994

High Velocity Oblique Cloud Collision and Star and Star Cluster Formation through Gravitational Instability of the Shock-Compressed Slab with Rotation and Velocity Shear

We study the gravitational instability of an isothermal gaseous slab formed by cloud-cloud collision and compression at the cloud interface. The compressed gaseous slab rotates and has velocity shear except when the collision is not exactly head-on. The effects of the rotation and velocity shear on the gravitational instability have been evaluated for the first time. We obtained the growth rate of perturbations as a function of the wavelength for various gaseous slab models. We also obtained the changes in the density and velocity due to the perturbations. Two types of unstable modes are found; one is due to the self-gravity of the gaseous slab and the other is due to the velocity shear. The former instability leads to the formation of star and star clusters. Velocity shear decreases the growth rate of the former instability while it increases that of the latter instability. Rotation also decreases the growth of the former instability. As the slab grows in mass, the growth rate of the self-gravitational instability increases and eventually becomes greater than the growing timescale of the slab. Then a gravitationally bound condensation is formed and its mass is larger when the slab has stronger velocity shear and rotation.

astro-ph↗

arXiv1994

Fragmentation of a Magnetized Filamentary Molecular Cloud Rotating around its Axis

The dynamical instability of a self-gravitating magnetized filamentary cloud was investigated while taking account of rotation around its axis. The filamentary cloud of our model is supported against self-gravity in part by both a magnetic field and rotation. The density distribution in equilibrium was assumed to be a function of the radial distance from the axis, $ ρ_0 (r) \, = \, ρ_{\rm c} \, ( 1 \, + \, r ^2 / 8 H ^2 ) ^{-2} $, where $ ρ_{\rm c} $ and $ H $ are model parameters specifying the density on the axis and the length scale, respectively; the magnetic filed was assumed to have both longitudinal ($z$-) and azimuthal ($φ$-) components with a strength of $ B _0 (r) \, \propto \, \sqrt{ ρ_0 (r) } $. The rotation velocity was assumed to be $ v _{0φ} \, = \, Ω_{\rm c} \, r \, (1 \, + \, r ^2 / 8 H ^2 ) ^{-1/2} $. We obtained the growth rate and eigenfunction numerically for (1) axisymmetric $ ( m \, = \, 0 ) $ perturbations imposed on a rotating cloud with a longitudinal magnetic field, (2) non-axisymmetric $ ( m \, = \, 1 ) $ perturbations imposed on a rotating cloud with a longitudinal magnetic filed, and (3) axisymmetric perturbations imposed on a rotating cloud with a helical magnetic field. The fastest growing perturbation is an axisymmetric one for all of the model clouds studied. Its wavelength is $ λ_{\rm max} \, \le \, 11.14 \, H $ for a non-rotating cloud without a magnetic field, and is shorter

astro-ph↗

arXiv1993

Sequential Star Formation in Taurus Molecular Cloud 1

We discuss the fragmentation of a filamentary cloud on the basis of a 1-dimensional hydrodynamical simulation of a self-gravitating gas cloud. The simulation shows that dense cores are produced with a semi-regular interval in space and time from one edge to the other. At the initial stage the gas near one of the edges is attracted inwards by gravity and the accumulation of the gas makes a dense core near the edge. When the dense core grows in mass up to a certain amount, it gathers gas from the other direction. Accordingly the dense core becomes isolated from the main cloud and the parent filamentary cloud has a new edge. This cycle repeats and the fragmentation process propagates towards the other edge. The propagation speed is a few tens of percent larger than the sound speed. According to the theory, the age difference for the northwest-most and southeast-most cores in TMC-1 is estimated to be 0.68~pc/0.6~km~s$^{-1}$ = $ 10 ^6 $~y. The estimated age difference is consistent with that obtained from the chemical chronology.

astro-ph↗