Toru Tsuribe

Thermal and Fragmentation Properties of Star-forming Clouds in Low-Metallicity Environments

The thermal and chemical evolution of star-forming clouds is studied for different gas metallicities, Z, using the model of Omukai, updated to include deuterium chemistry and the effects of cosmic microwave background (CMB) radiation. HD-line cooling dominates the thermal balance of clouds when Z ~ 10-5 to 10-3 Z☉ and density ≈105 cm-3. Early on, CMB radiation prevents the gas temperature from falling below TCMB, although this hardly alters the cloud thermal evolution in low-metallicity gas. From the derived temperature evolution, we assess cloud/core fragmentation as a function of metallicity from linear perturbation theory, which requires that the core elongation ≡ (b - a)/a > NL ~ 1, where a (b) is the short (long) core axis length. The fragment mass is given by the thermal Jeans mass at = NL. Given these assumptions and the initial (Gaussian) distribution of , we compute the fragment mass distribution as a function of metallicity. We find that (1) for Z = 0, all fragments are very massive, 103 M☉, consistent with previous studies; (2) for Z > 10-6 Z☉ a few clumps go through an additional high-density (1010 cm-3) fragmentation phase driven by dust cooling, leading to low-mass fragments; (3) the mass fraction in low-mass fragments is initially very small, but at Z ~ 10-5 Z☉ it becomes dominant and continues to grow as Z is increased; (4) as a result of the two fragmentation modes, a bimodal mass distribution emerges in 0.01 < Z/Z☉ < 0.1; and (5) for 0.1 Z☉, the two peaks merge into a single-peaked mass function, which might be regarded as the precursor of the ordinary Salpeter-like initial mass function.

TeV γ‐rays from old supernova remnants

We study the emission from an old supernova remnant (SNR) with an age of around 10 5 yrs and that from a giant molecular cloud (GMC) encountered by the SNR. When the SNR age is around 10 5 yrs, proton acceleration is efficient enough to emit TeV γ-rays both at the shock of the SNR and that in the GMC. The maximum energy of primarily accelerated electrons is so small that TeV γ-rays and X-rays are dominated by hadronic processes, π 0 -decay and synchrotron radiation from secondary electrons, respectively. However, if the SNR is older than several 10 5 yrs, there are few high-energy particles emitting TeV γ-rays because of the energy loss effect and/or the wave damping effect occurring at low-velocity isothermal shocks. For old SNRs or SNR-GMC interacting systems capable of generating TeV γ-ray emitting particles, we calculated the ratio of TeV γ-ray (1–10 TeV) to X-ray (2–10 keV) energy flux and found that it can be more than � 10 2 . Such a source showing large flux ratio may be a possible origin of recently discovered unidentified TeV sources.

Criteria for Fragmentation of Rotating Isothermal Clouds Revisited

The collapse of rotating isothermal clouds is investigated by three-dimensional self-gravitating hydrodynamical calculations. The criterion that predicts the outcome after the collapse is presented for the initially uniform-density rigid-rotating sphere. It is shown that the central flatness, that is, the axial ratio of the isodensity contour in the central region, is a good indicator for the fate of the cloud. If the central flatness is greater than the critical value ~4π, a collapsing cloud with moderate perturbations is unstable for fragmentation, while if the central flatness is smaller than the critical value, it does not fragment at least before adiabatic core formation. The relation between the central flatness and the initial value of the ratio of the thermal (α0) and rotational energy (β0) to the gravitational energy is also presented. Warm clouds (α0 0.5) are not expected to fragment before adiabatic core formation almost independent of the initial rotation (β0) and the properties of the initial perturbation.

Dust-cooling-induced Fragmentation of Low-Metallicity Clouds

We study the dynamical collapse and fragmentation of low-metallicity cloud cores using three-dimensional hydrodynamical calculations, and we devote particular attention to whether or not the cores fragment in the dust-cooling phase. The cores become elongated in the dust-cooling phase because they are unstable to nonspherical perturbation due to the sudden temperature decrease. In the metallicity range of 10-6 to 10-5 Z☉, cores with an initial axis ratio 2 reach a critical value of the axis ratio (30) and fragment into multiple small clumps. This provides a possible mechanism to produce low-mass stars in ultra-metal-poor environments.

Criteria for Fragmentation of Rotating Isothermal Clouds. I. Semianalytic Approach

The isothermal collapse of an initially uniform-density, uniform-rotating, molecular cloud core with pressure and self-gravity is investigated using a spheroid model to determine the conditions under which a cloud is unstable to fragmentation. A semianalytic model for the collapse of rotating spheroids is developed with the method of characteristics for inwardly propagating rarefaction waves. It is shown that the criterion for fragmentation is modified from that in the literature if the property of nonhomologous collapse is taken into account. The fate of the collapsing clouds can be divided into three classes: (1) runaway collapsing clouds that approach self-similar solutions with moderate ellipsoid axial ratio (2-5) and are expected to form single adiabatic cores in the center, (2) clouds that collapse and rotationally bounce without fragmentation and are expected to develop bars and filaments, and (3) clouds that collapse into pancakes and fragment during the isothermal stage. We derive the criterion for fragmentation considering the evolution of the flatness of the central core after relaxation in the z-direction. In the small rotation limit, the evolution is determined by only one parameter, α0 (initial ratio of the thermal energy to the gravitational energy), that has the critical value, α0 = 5/π2.

GRAVITATIONAL FRAGMENTATION OF EXPANDING SHELLS. I. LINEAR ANALYSIS

We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the density profile across the thickness. It is found that the time evolution of the density profile can be divided into three evolutionary phases, deceleration-dominated, intermediate, and self-gravity-dominated phases. The density peak moves relatively from the shock front to the contact discontinuity as the shell expands. We perform a linear analysis taking into account the asymmetric density profile obtained by the semi-analytic method, and imposing the boundary conditions for the shock front and the contact discontinuity while the evolutionary effect of the shell is neglected. It is found that the growth rate is enhanced compared with the previous studies based on the thin-shell approximation. This is due to the boundary effect of the contact discontinuity and asymmetric density profile that were not taken into account in previous works.

PHYSICAL MECHANISM FOR THE INTERMEDIATE CHARACTERISTIC STELLAR MASS IN EXTREMELY METAL POOR ENVIRONMENTS

If a significant fraction of metals is in dust, star-forming cores with metallicity higher than a critical value ~10−6 to 10−5 Z☉ are able to fragment by dust cooling, thereby producing low-mass cores. Despite being above the critical metallicity, a metallicity range is found to exist around 10−5 to 10−4 Z☉ where low-mass fragmentation is prohibited. In this range, three-body H2 formation starts at low (~100 K) temperature, and thus the resulting heating causes a dramatic temperature jump, which makes the central part of the star-forming core transiently hydrostatic and thus highly spherical. With little elongation, the core does not experience fragmentation in the subsequent dust-cooling phase. The minimum fragmentation mass is set by the Jeans mass just before the H2 formation heating, and its value can be as high as ~10 M☉. For metallicity higher than ~10−4 Z☉, H2 formation is almost completed by the dust-surface reaction before the onset of the three-body reaction, and low-mass star formation becomes possible. This mechanism might explain the higher characteristic mass of metal-poor stars than in the solar neighborhood presumed from the statistics of carbon-enhanced stars.

Self-similar Viscous Accretion and Growth of the Central Core in Self-gravitating Disks

Unsteady viscous accretion in self-gravitating disks is investigated. Taking into account the growth of the central point mass, a series of self-similar solutions is derived for rotating isothermal disks. These solutions represent the inside-out evolution after central core formation. Solutions are specified by the nondimensional parameters α and Q, where α is the Shakura and Sunyaev viscous parameter and Q is the Toomre stability parameter. As a core mass increases, the rotation law changes from flat rotation to Keplerian rotation in the inner disk. In addition to the central point mass, the inner disk grows by mass accumulation due to the differing mass accretion rates in the inner and outer radii. The mass accretion rate onto the central core is found to be 3αc/QG for a variety of outer flows. We show that possibly stable solutions with Q 1 exist for a wide range of α.

GRAVITATIONAL FRAGMENTATION OF EXPANDING SHELLS. II. THREE-DIMENSIONAL SIMULATIONS

We investigate the gravitational fragmentation of expanding shells driven by H II regions using the three-dimensional Lagrangian simulation codes based on the Riemann solver, called Godunov smoothed particle hydrodynamics. The ambient gas is assumed to be uniform. In order to attain high resolution to resolve the geometrically thin dense shell, we calculate not the whole but a part of the shell. We find that perturbations begin to grow earlier than predicted by linear analysis under the thin-shell approximation. The wavenumber of the most unstable mode is larger than that in the thin-shell linear analysis. The development of the gravitational instability is accompanied by the significant deformation of the contact discontinuity. These results are consistent with a linear analysis presented by Iwasaki et al. that have taken into account the density profile across the thickness and approximate shock and contact discontinuity boundary conditions. We derive useful analytic formulae for the fragment scale and the epoch when the gravitational instability begins to grow.

The role of the inner disk in mass accretion to the star in the early phase of star formation

A physical mechanism that drives FU Orionis-type outbursts is reconsidered. We study the effect of inner part of a circumstellar disk covering a region from near the central star to the radius of approximately