Physics

Dissipation causes distortions in wave propagations. A new formula for restoring such distorted waveform based on a generalized Kac's method of solving a generalized telegrapher equation, a wave equation with dissipation, is conjectured. From the signal received over time at a point in space and given the time at which it was sent, and without the knowledge of it at other points, the signal that would have been received at the point in the absence of dissipation is then restored. The details of such a mathematical contruction of the waveform restorer are given. §

In this paper, we develop a new method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov method is applied to SPH instead of artificial dissipation terms. In the interaction between particles, we solve a non-linear Riemann problem with magnetic pressure for compressive waves and apply the method of characteristics for Alfvén waves. An extensive series of MHD test calculations is performed. In all test calculations, we compare the results of our SPH code with those of a finite-volume method with an approximate Riemann solver, and confirm excellent agreement.

We report the results of our three-dimensional radiation hydrodynamics simulation of collapsing unmagnetized molecular cloud cores. We investigate the formation and evolution of the circumstellar disk and the clumps formed by disk fragmentation. Our simulation shows that disk fragmentation occurs in the early phase of circumstellar disk evolution and many clumps form. The clump can be represented by a polytrope sphere of index n ∼ 3 and n 4 at central temperature T c 100 K and T c 100 K, respectively. We demonstrate, numerically and theoretically, that the maximum mass of the clump, beyond which it inevitably collapses, is ∼ 0.03 M ⊙ . The entropy of the clump increases during its evolution, implying that evolution is chiefly determined by mass accretion from the disk rather than by radiative cooling. Although most of the clumps rapidly migrate inward and finally fall onto the protostar, a few clumps remain in the disk. The central density and temperature of the surviving clump rapidly increase and the clump undergoes a second collapse within 1000 -2000 years after its formation. In our simulation, three second cores of masses 0.2 M ⊙ , 0.15 M ⊙ , and 0.06 M ⊙ formed. These are protostars or brown dwarfs rather than protoplanets. For the clumps to survive as planetary-mass objects, the rapid mass accretion should be prevented by some mechanisms.

The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure and asymptotic wave modes shows that all types of the MHD shocks, including the intermediate shocks, are evolutionary and perturbed solutions are uniquely defined. We also adopt our formalism to the MHD shocks in the system with resistivity without viscosity, which is often used in numerical simulation, and show that all types of shocks that are found in the system satisfy the evolutionary condition and perturbed solutions are uniquely defined. These results suggest that the intermediate shocks may appear in reality.

The protostellar outflow is star's first cry at the moment of birth. The outflows have indispensable role in the formation of single stars, because they carry off the excess angular momentum from the centre of the shrinking gas cloud, and permits further collapse to form a star. On the other hand, a significant fraction of stars is supposed to be born as binaries with circumbinary disk that are frequently observed. Here, we investigate the evolution of a magnetized rotating cloud using three-dimensional resistive MHD nested-grid code, and show that the outflow is driven by the circumbinary disk and has an important role even in the binary formation. After the adiabatic core formation in the collapsing cloud core, the magnetic flux is significantly removed from the centre of the cloud by the Ohmic dissipation. Since this removal makes the magnetic braking ineffective, the adiabatic core continuously acquires the angular momentum to induce fragmentation and subsequent binary formation. The magnetic field accumulates in the circumbinary disk where the removal and accretion of magnetic field are balanced, and finally drives circumbinary outflow. This result explains the spectacular morphology of some specific young stellar objects such as L1551 IRS5. We can infer that most of the bipolar molecular outflows observed by low density tracers (i.e., CO) would correspond to circumbinary or circum-multiple outflows found in this report, since most of the young stellar objects are supposed to be binaries or multiples.

We performed N-body simulations of a dust layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of non-axisymmetric wake-like structures, the creation of aggregates, and the collisional growth of the aggregates. Finally, a few large aggregates and many small aggregates are formed. The mass of the largest aggregate is larger than the mass predicted by the linear perturbation theory. We examined the dependence of system parameters on the planetesimal formation. We found that the mass of the largest aggregates increase as the size of the computational domain increases. However the ratio of the aggregate mass to the total mass M aggr /M total is almost constant 0.8 − 0.9. The mass of the largest aggregate increases with the optical depth and the Hill radius of particles.

We investigate the effects of viscosity on disk-planet interaction and discuss how type I migration of planets is modified. We have performed a linear calculation using shearing-sheet approximation and obtained the detailed, high resolution density structure around the planet embedded in a viscous disk with a wide range of viscous coefficients. We use a time-dependent formalism that is useful in investigating the effects of various physical processes on disk-planet interaction. We find that the density structure in the vicinity of the planet is modified and the main contribution to the torque comes from this region, in contrast to inviscid case. Although it is not possible to derive total torque acting on the planet within the shearing-sheet approximation, the one-sided torque can be very different from the inviscid case, depending on the Reynolds number. This effect has been neglected so far but our results indicate that the interaction between a viscous disk and a planet can be qualitatively different from an inviscid case and the details of the density structure in the vicinity of the planet is critically important.

The early evolution of the magnetic field and angular momentum of newly formed protostars are studied using three-dimensional resistive MHD nested grid simulations. Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field, we calculate the cloud evolution from the molecular cloud core (n c ≃ 10 4 cm −3 , r = 4.6 × 10 5 AU, where n c and r are central density and radius, respectively) to the stellar core (n c ≃ 10 22 cm −3 , r ∼ 1R ⊙ ). The magnetic field strengths at the center of clouds with the same initial angular momentum but different magnetic field strengths converge to a certain value as the clouds collapse for n c 10 12 cm −3 . For 10 12 n c 10 16 cm −3 , Ohmic dissipation largely removes the magnetic field from a collapsing cloud core, and the magnetic field lines, which are strongly twisted for n c 10 12 cm −3 , are de-collimated. The magnetic field lines are twisted and amplified again for n c 10 16 cm −3 , because the magnetic field is recoupled with warm gas. Finally, protostars at their formation epoch (n c ≃ 10 21 cm −3 ) have magnetic fields of ∼0.1-1 kG, which is comparable to observations. The magnetic field strength of a protostar depends slightly on the angular momentum of the host cloud. A protostar formed from a slowly rotating cloud core has a stronger magnetic field. The evolution of the angular momentum is closely related to the evolution of the magnetic field. The angular momentum in a collapsing cloud is removed by magnetic effects such as magnetic braking, outflow and jets. The formed protostars have rotation periods of 0.1-2 days at their formation epoch, which is slightly shorter than observations. This indicates that a further removal mechanism for the angular momentum, such as interactions between the protostar and the disk, wind, or jets, is important in the further evolution of protostars.

The formation and evolution of a circumstellar disk in magnetized cloud cores is investigated from prestellar core stage until ∼ 10 4 yr after protostar formation. In the circumstellar disk, fragmentation first occurs due to gravitational instability in a magnetically inactive region, and substellar-mass objects appear. The substellar-mass objects lose their orbital angular momenta by gravitational interaction with the massive circumstellar disk and finally fall onto the protostar. After this fall, the circumstellar disk increases its mass by mass accretion and again induces fragmentation. The formation and falling of substellar-mass objects are repeated in the circumstellar disk until the end of the main accretion phase. In this process, the mass of fragments remain small, because the circumstellar disk loses its mass by fragmentation and subsequent falling of fragments before it becomes very massive. In addition, when fragments orbit near the protostar, they disturb the inner disk region and promote mass accretion onto the protostar. The orbital motion of substellar-mass objects clearly synchronizes with the time variation of the accretion luminosity of the protostar. Moreover, as the objects fall, the protostar shows a strong brightening for a short duration. The intermittent protostellar outflows are also driven by the circumstellar disk whose magnetic field lines are highly tangled owing to the orbital motion of fragments. The time-variable protostellar luminosity and intermittent outflows may be a clue for detecting planetary-mass objects in the circumstellar disk.

Fragmentation and binary formation processes are studied using threedimensional resistive MHD nested grid simulations. Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field, we calculate the cloud evolution from the molecular cloud core (n = 10 4 cm −3 ) to the stellar core (n ≃ 10 22 cm −3 ), where n denotes the central density. We calculated 147 models with different initial magnetic, rotational, and thermal energies, and the amplitudes of the non-axisymmetric perturbation. In a collapsing cloud, fragmentation is mainly controlled by the initial ratio of the rotational to the magnetic energy, regardless of the initial thermal energy and amplitude of the non-axisymmetric perturbation. When the clouds have large rotational energies in relation to magnetic energies, fragmentation occurs in the low-density evolution phase (10 12 cm −3 n 10 15 cm −3 ) with separations of 3-300 AU. Fragments that appeared in this phase are expected to evolve into wide binary systems. On the other hand, fragmentation does not occur in the low-density evolution phase, when initial clouds have large magnetic energies in relation to the rotational energies. In these clouds, fragmentation only occurs in the high-density evolution phase (n 10 17 cm −3 ) after the clouds experience significant reduction of the magnetic field owing to Ohmic dissipation in the period of 10 12 cm −3 n 10 15 cm −3 . Fragments appearing in this phase have separations of 0.3 AU, and are expected to evolve into close binary systems. As a result, we found two typical fragmentation epochs, which cause different stellar separations. Although these typical separations are disturbed in the subsequent gas accretion phase, we might be able to observe two peaks of binary separations in extremely young stellar groups.

We investigate thermal and dynamical evolution of a primordial gas cloud with an updated deuterium chemistry. We consider a fragment of a postshock-cooled sheet that is expected to form by collapse of a massive cloud ( greater, similar108 M middle dot in circle) and by blast waves due to supernova explosions. At first we investigate molecule formation in a primordial shock. We show that almost all deuterium can be converted to HD within the age of the universe at the collapsed redshift in the case of a cloud that has a virial temperature of approximately 106 K and collapses at z>1. When the postshock sheet fragments owing to gravitational instability, the fractional H2 and HD abundances become approximately 10-2 and approximately 10-5, respectively, which are 103-104 times higher than the result of molecule formation in the expanding universe after recombination. To study the subsequent evolution of a fragment, we performed one-dimensional simulations of a spherical/cylindrical cloud, of which initial conditions (e.g., fractional abundances of chemical composition, temperature) are derived from the result of the shock. It is found that, in case of a cylindrical collapse, the cooling by HD molecules keeps the temperature of the cloud less than 100 K and the cloud evolves almost isothermally. When the cloud becomes optically thick to the HD line emission ( approximately 1010 cm-3) and the gravitational fragmentation of the cylindrical cloud becomes effective, the Jeans mass becomes comparable to 0.1 M middle dot in circle. This series of processes enables the formation of primordial low-mass stars, and possibly brown dwarfs, in primordial gas clouds.

The propagation of a shock wave into an interstellar medium is investigated by two-dimensional numerical hydrodynamic calculation with cooling, heating and thermal conduction. We present results of the high-resolution two-dimensional calculations to follow the fragmentation due to the thermal instability in a shock-compressed layer. We find that geometrically thin cooling layer behind the shock front fragments into small cloudlets. The cloudlets have supersonic velocity dispersion in the warm neutral medium in which the fragments are embedded as cold condensations. The fragments tend to coalesce and become larger clouds.

The fragmentation process of primordial-gas cores during prestellar collapse is studied using three-dimensional nested-grid hydrodynamics. Starting from the initial central number density of n c ∼ 10 3 cm −3 , we follow the evolution of rotating spherical cores up to the stellar density n c ≃ 10 22 cm −3 . An initial condition of the cores is specified by three parameters: the ratios of the rotation and thermal energies to the gravitational energy (β 0 , and α 0 , respectively), and the amplitude of the bar-mode density perturbation (A φ ). Cores with rotation β 0 > 10 −6 are found to fragment during the collapse. The fragmentation condition hardly depends on either the initial thermal energy α 0 or amplitude of bar-mode perturbation A φ . Since the critical rotation parameter for fragmentation is lower than that expected in the first star formation, binaries or multiples are also common for the first stars.

We develop an unconditionally stable numerical method for solving the coupling between two fluids (frictional forces/heatings, ionization, and recombination), and investigate the dynamical condensation process of thermally unstable gas that is provided by the shock waves in a weakly ionized and magnetized interstellar medium by using two-dimensional two-fluid magnetohydrodynamical simulations. If we neglect the effect of magnetic field, it is known that condensation driven by thermal instability can generate high density clouds whose physical condition corresponds to molecular clouds (precursor of molecular clouds). In this paper, we study the effect of magnetic field on the evolution of supersonic converging HI flows and focus on the case in which the orientation of magnetic field to converging flows is orthogonal. We show that the magnetic pressure gradient parallel to the flows prevents the formation of high density and high column density clouds, but instead generates fragmented, filamentary HI clouds. With this restricted geometry, magnetic field drastically diminishes the opportunity of fast molecular cloud formation directly from the warm neutral medium, in contrast to the case without magnetic field.