Takenori Nakano

Magnetorotational Instability in Protoplanetary Disks. II. Ionization State and Unstable Regions

We investigate where magnetorotational instability operates in protoplanetary disks, which can cause angular momentum transport in the disks. We investigate the spatial distribution of various charged particles and the unstable regions for a variety of models for protoplanetary disks, taking into account the recombination of ions and electrons at grain surfaces, which is an important process in most parts of the disks. We find that for all the models there is an inner region that is magnetorotationally stable due to ohmic dissipation. This must make the accretion onto the central star nonsteady. For the model of the minimum-mass solar nebula, the critical radius, inside of which the disk is stable, is about 20 AU, and the mass accretion rate just outside the critical radius is 10-7-10-6 M☉ yr-1. The stable region is smaller in a disk of lower column density. Dust grains in protoplanetary disks may grow by mutual sticking and may sediment toward the midplane of the disks. We find that the stable region shrinks as the grain size increases or the sedimentation proceeds. Therefore, in the late evolutionary stages, protoplanetary disks can be magnetorotationally unstable even in the inner regions.

Star Formation in Magnetic Clouds

This paper reexamines the widely accepted assumption that low-mass stars form mainly in magnetically subcritical cloud cores and high-mass stars form in magnetically supercritical ones. Cloud cores, as well as molecular clouds, are shown to be magnetically supercritical because although the cores are generally observed as portions of a molecular cloud having considerably higher column densities than their surroundings, magnetically subcritical condensations embedded in a cloud are not very likely to have higher column densities than their surroundings, and because it is difficult to maintain the nonthermal velocity dispersions widely observed in the cores for a significant fraction of their lifetimes if the cores are magnetically subcritical. In a magnetically supercritical condensation, which we call a core, for the pressure Ps of the surrounding medium there is a critical value Pcr above which the core cannot be in magnetohydrostatic equilibrium and collapses; Pcr depends sharply on the core mass, on the effective sound velocity in the core, which includes the effect of turbulence, and on the effective coefficient aeff for the gravity diluted by magnetic force. The cloud core begins dynamical contraction when Pcr has decreased below Ps by some mechanism. Dissipation of turbulence is the most important process in reducing Pcr. Therefore, in most cases, the timescale of star formation in each core is the dissipation time of turbulence, which is several times the free-fall time of the core. For the cores of magnetic flux Φ very close to the critical flux Φcr or with small aeff ≈ 1 - (Φ/Φcr)2, Pcr will not decrease below Ps even when turbulence has completely dissipated; this will happen only in very low mass cores because of the sharp mass dependence of Pcr. Such cores begin dynamical contraction after aeff has increased somewhat because of magnetic flux loss from their central parts by ambipolar diffusion; for this to happen, only a slight loss of magnetic flux is needed because of sharp dependence of Pcr on Φ at Φ ≈ Φcr. The timescale of star formation in this case is not much different from the dissipation time of the turbulence, though the probability that the cores have Φ ≈ Φcr must be low. It is shown to be implausible that cloud cores form from magnetically subcritical condensations via ambipolar diffusion.

Mechanism of Magnetic Flux Loss in Molecular Clouds

We investigate the detailed processes at work in the drift of magnetic fields in molecular clouds. To the frictional force, whereby the magnetic force is transmitted to neutral molecules, ions contribute more than half only at cloud densities nH 104 cm-3, and charged grains contribute more than about 90% at nH 106 cm-3. Thus, grains play a decisive role in the process of magnetic flux loss. Approximating the flux loss time tB by a power law tB ∝ B-γ, where B is the mean field strength in the cloud, we find γ ≈ 2, characteristic of ambipolar diffusion, only at nH 107 cm-3, at which ions and the smallest grains are pretty well frozen to the magnetic fields. At nH > 107 cm-3, γ decreases steeply with nH, and finally at nH ≈ ndec ≈ a few × 1011 cm-3, at which the magnetic fields effectively decouple from the gas, γ 1 is attained, reminiscent of Ohmic dissipation, although flux loss occurs about 10 times faster than by pure Ohmic dissipation. Because even ions are not very well frozen at nH > 107 cm-3, ions and grains drift slower than the magnetic fields. This insufficient freezing makes tB more and more insensitive to B as nH increases. Ohmic dissipation is dominant only at nH 1 × 1012 cm-3. While ions and electrons drift in the direction of the magnetic force at all densities, grains of opposite charges drift in opposite directions at high densities, at which grains are major contributors to the frictional force. Although magnetic flux loss occurs significantly faster than by Ohmic dissipation even at very high densities, such as nH ≈ ndec, the process going on at high densities is quite different from ambipolar diffusion, in which particles of opposite charges are supposed to drift as one unit.

Molecular cloud cores in the Orion A cloud. I: Nobeyama CS (1-0) survey

A first high-resolution survey of molecular cloud cores in the Orion A giant molecular cloud is reported. We identified 125 molecular cloud cores from an analysis of the spatial and velocity distribution of the CS (1-0) emission. The cores are generally elongated along the filamentary molecular cloud, and the axial ratio is about 0.5. The mass spectrum index of the cores is -1.6 for M≥50 M ○ .. The physical properties of the cores identified in Orion are compared with those of cores in dark clouds reported in the literature. The average radius of the cores in the Orion A cloud, 0.16 pc, is comparable to that of the cores in dark clouds

Magnetic flux loss from interstellar clouds with various grain-size distributions

The densities of charged particles and the dissipation of magnetic fields in interstellar clouds shielded from UV radiation and having densities between 1000 and 10 to the 13th/cu cm are investigated. The effect of the electric polarization of the gains on collision with ions and electrons is taken into account, and different models for the grain size distribution are used. It is found that the metal ions are not the major constitutents among the charged particles due to their ability to recombine efficiently on grain surfaces. In a cloud where the magnetic field strength is nearly equal to the critical field with which the magnetic force balances self-gravity, the magnetic flux loss time is shorter than the free-fall time only if the density is greater than the critical density, which is given for the different models. In all cases the magnetic field is strongly coupled to the gas and the magnetic flux of the cloud cannot decrease far below the critical flux. 36 refs.

Effects of Radionuclides on the Ionization State of Protoplanetary Disks and Dense Cloud Cores

We comprehensively reinvestigate the ionization rates by radionuclides with the newest data on the abundance of the nuclides for the primitive solar nebula distinguishing the ionization rates of a hydrogen molecule, , from those of a helium atom . The ionization rates by 232Th, 235U, and 238U become an order of magnitude larger than in the previous work of Umebayashi & Nakano by including all the energy released in the decay series, and these nuclides contribute about 20% of the total ionization rate by the long-lived radionuclides, 1.4 × 10–22 s–1 for a hydrogen molecule. The rest (80%) is contributed by 40K. Among the short-lived radionuclides which are extinct in the present solar system, 26Al is the dominant ionization source with the rate (7-10) × 10–19 s–1, overwhelming the long-lived nuclides. In addition, 60Fe and 36Cl are more efficient than the long-lived nuclides though at least 10 times more inefficient than 26Al. The helium abundance in the primitive solar nebula is significantly lower than in the present interstellar medium. We obtain a simple formula which transforms the ionization rates into those for the other values of the helium abundance. Ionization by radionuclides is quite inefficient when the mean dust size is greater than about 1 cm. Using these ionization rates, we investigate the ionization state for some configurations of the clouds. With an improved attenuation law of cosmic rays in geometrically thin disks, we find that the dead zones in protoplanetary disks are significantly larger than those obtained in the previous work.

Evolution of Molecular Abundances in Proto-planetary Disks with Accretion Flow

We investigate the evolution of molecular abundances in a protoplanetary disk in which matter is accreting toward the central star by solving numerically the reaction equations of molecules as an initial-value problem. We obtain the abundances of molecules, both in the gas phase and in ice mantles of grains, as functions of time and position in the disk. In the region of surface density less than 102 g cm-2 (distance from the star 10 AU for the mass accretion rate 10-8 M☉ yr-1), cosmic rays are barely attenuated even on the midplane of the disk and produce chemically active ions such as H+3 and He+. We find that through reactions with these ions considerable amounts of CO and N2, which are initially the dominant species in the disk, are transformed into CO2, CH4, NH3, and HCN. In the regions where the temperature is low enough for these products to freeze onto grains, they accumulate in ice mantles. As the matter migrates toward inner warmer regions of the disk, some of the molecules in the ice mantles evaporate. It is found that most of the molecules desorbed in this way are transformed into less volatile molecules by the gas-phase reactions, which then freeze out. Molecular abundances both in the gas phase and in ice mantles crucially depend on the temperature and thus vary significantly with the distance from the central star. Although molecular evolution proceeds in protoplanetary disks, our model also shows that significant amount of interstellar ice, especially water ice, survives and is included in ice mantles in the outer region of the disks. We also find that the timescale of molecular evolution is dependent on the ionization rate and the grain size in the disk. If the ionization rate and the grain size are the same as those in molecular clouds, the timescale of the molecular evolution, in which CO and N2 are transformed into other molecules, is about 106 yr, which is slightly smaller than the lifetime of the disk. The timescale for molecular evolution is larger (smaller) in the case of lower (higher) ionization rate or larger (smaller) grain size. We compare our results with the molecular composition of comets, which are considered to be the most primitive bodies in our solar system. The molecular abundances derived from our model naturally explain the coexistence of oxidized ice and reduced ice in the observed comets. Our model also suggests that comets formed in different regions of the disk have different molecular compositions. Finally, we give some predictions for future millimeter-wave and sub-millimeter-wave observations of protoplanetary disks.

Evolution of Molecular Abundance in Protoplanetary Disks

We investigate the evolution of molecular abundance in quiescent protoplanetary disks that are presumed to be around weak-lined T Tauri stars. In the region of surface density less than 102 g cm-2 (distance from the star 10 AU in the minimum-mass solar nebula), cosmic rays are barely attenuated even in the midplane of the disk and produce chemically active ions such as He+ and H -->+3. Through reactions with these ions, CO and N2 are finally transformed into CO2, NH3, and HCN. In the region where the temperature is low enough for these products to freeze onto grains, a considerable amount of carbon and nitrogen is locked up in the ice mantle and is depleted from the gas phase in a timescale of 3 × 106 yr. Oxidized (CO2) ice and reduced (NH3 and hydrocarbon) ice naturally coexist in this part of the disk. The molecular abundance both in the gas phase and in the ice mantle varies significantly with the distance from the central star.

Aperture Synthesis C18O J = 1-0 Observations of L1551 IRS 5: Detailed Structure of the Infalling Envelope*

We report aperture synthesis C18O J \ 1E0 observations of L1551 IRS 5 with a spatial resolution of using the Nobeyama Millimeter Array. We have detected an emission component centrally 2A.8)2A.5 condensed around IRS 5, as well as a di†use component extending in the north-south direction from the centrally condensed component. The centrally condensed component, 2380 ) 1050 AU in size, is elon- gated in the direction perpendicular to the outNow axis, indicating the existence of a Nattened circum- stellar envelope around L1551 IRS 5. The mass of the centrally condensed component is estimated to be 0.062 The position-velocity (P-V) diagrams reveal that the velocity -eld in the centrally condensed M _ . component is composed of infall and slight rotation. The infall velocity in the outer part is equal to the free-fall velocity around a central mass of D0.1 e.g., 0.5 km s~1 at r \ 700 AU, whereas the rota- M _ , tion velocity, 0.24 km s~1 at the same radius, gets prominent at inner radii with a radial dependence of r~1. We make up P-V diagrams for the model envelopes with vertical structure, in which the matter falls under the gravity and eventually settles down in Keplerian rotation inside the centrifugal radius, and compare them with the observed P-V diagrams of the centrally condensed component. The main charac- teristics of the observed P-V diagrams are reproduced by either (1) an envelope with a moderately Nat- tened density distribution, or (2) a spherical envelope with a bipolar cavity whose half-opening angle is about 50i. Detailed comparison of the observed and model P-V diagrams suggests that the C18O J \ 1E0 emission from the outer part of the centrally condensed component is well reproduced with the models with the central mass D0.15 and the mass infall rate D6 ) 10~6 yr~1. However, the M _ M _ higher velocity features of the emission near the star cannot be reproduced unless the central mass is taken to be D0.5 These facts suggest either that the gas pressure and/or magnetic force dilute the M _ . e†ect of the gravity in the outer part of the envelope, or that the velocity structure inside the centrifugal radius deviates signi-cantly from the Keplerian rotation. Subject headings: accretion, accretion disks E circumstellar matter E ISM: molecules E ISM: structure E stars: formation E stars: individual (L1551 IRS 5) E stars: preEmain-sequence

Conditions for the formation of massive stars through nonspherical accretion

Formation of massive stars through spherical accretion has been predicted to occur only in clouds which are nearly dust-free and can provide an extremely high accretion rate. It is shown that such severe restrictions are effectively removed with nonspherical accretion. By the effects of magnetic fields, rotation, and so on, the contracting envelope usually becomes rather flat. With such a configuration the thermal radiation converted from the stellar radiation by dust near its sublimation zone easily escapes from the envelope and then hardly affects the motion of dust and gas. Consequently, the gas falls nearly freely to the sublimation zone. The steady inflow occurs only when the dynamical pressure of this motion is greater than the stellar radiation pressure at this zone. With the present model the accretion onto a stellar core of 100 solar mass occurs when the accretion rate is greater than 0.0001 solar mass/yr, 50 times smaller than the rate with spherical accretion. No special restrictions on grain abundances are required, in contrast to spherical accretion. The causes for the rarity of massive stars are discussed. 59 refs.