Toyoharu Umebayashi

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.

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.

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.

Molecular evolution in planet-forming circumstellar disks

We have investigated the evolution of molecular abundance in circumstellar disks around young low-mass stars, which are considered to be the formation sites of planetary systems. Adopting the standard accretion disk model, we investigated molecular evolution mainly in the accretion phase. In the region of surface density less than 102 g cm-2 (distance from the star 10 AU), cosmic rays are barely attenuated, even in the midplane of the disk, and produce chemically active ions such as He+ and H3+. We found that a considerable amount of CO and N2, the initial dominant components of the disk, is transformed into CO2, CH4, NH3 and HCN through reactions with these ions. Where the temperature is low enough for these products to freeze onto grains, they are selectively ‘locked up’ and accumulate in the ice mantle. As the matter accretes towards inner warmer regions, the ice mantle evaporates. The desorbed molecules, such as CH4, are transformed into larger and less volatile molecules by reactions in the gas phase. The molecular abundance, both in the gas phase and in the ice mantle, depends crucially on the temperature and thus varies significantly with the distance from the central star. If the ionization rate and the grain size in the disk 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, ca. 106 years, slightly less than the life time of the disk. The timescale of molecular evolution is less for higher ionization rates and greater for lower ionization rates or larger grain size. We have compared our results with the molecular composition in comets, the most primitive bodies in our solar system. The molecular abundance derived from our model reproduces the coexistence of oxidized ice and reduced ice, as observed in comets. Our model also suggests that comets formed in different regions of the disk will have different molecular compositions.

The Role of Dust in the Dissipation of Magnetic Fields in Molecular Clouds

Dust grains play important roles in magnetic field dissipation through recombination of ions and electrons at grain surfaces and interaction of charged grains with magnetic fields. We show that not much dust is lost from the central part of the cloud even if much magnetic flux is lost.

Evolution of the Molecular Abundance in Protoplanetary Disks: Depletion of CO Molecules

We investigate the evolution of the molecular abundance in protoplanetary disks paying attention to the abundance of CO molecules in the gas phase. We take into account the adsorption of molecules onto grains as well as the reactions in the gas phase. We follow the molecular evolution for some model disks solving numerically the reaction equations. There is a critical distance from the star, R crit, at which the temperature is equal to the critical temperature ≈ 20 K for the adsorption of CO molecules. At R > R crit, CO molecules are depleted rather rapidly from the gas phase mainly due to the adsorption. For the minimum-mass solar nebula extended to the region of radius R ≈ 800 AU, for example, molecules in the gas phase at R > R crit ≈ 200 AU are depleted by a few orders of magnitude in 105 to 106 yr, while at R < R crit the depletion of CO is not significant in these time scales. This is consistent with the recent observations of the gaseous disks around some T Tauri stars.

Role of Grains in the Drift of Plasma and Magnetic Field in Dense Interstellar Clouds

The magnetic flux through an interstellar cloud or through a part of the cloud must decrease considerably by the drift of plasma and magnetic field in order that stars form in the cloud. Because most grains are negatively charged in dense clouds (Elmegreen 1979; Umebayashi and Nakano 1980), they retard magnetic flux leakage in addition to ions (Elmegreen 1979). We investigate this effect for different situations and obtain the following results (for details, see Nakano and Umebayashi 1980): 1. For nearly spherical clouds of mass ≳ 10 3 M ⊙ sustained by magnetic force the friction of grains is efficient at n H ⊙ ≳ 10 5 cm −3 , and the magnetic flux leakage time t B is greater than a few million years at any density. Grains drift as fast as ions and electrons. 2. For spherical clouds of smaller mass and disk-shaped clouds, t B becomes much smaller and the drift of grains is much slower than ions and electrons at n H ≳ 10 6 cm −3 . 3. Thus magnetic flux leakage occurs mainly in the condensations described in 2, and the abundance of heavy elements in stars deviates little from that of the parent clouds because of small grain drift.