On the Charge Distribution of the Pion

Narita, Takao

doi:10.1143/ptp.43.567

Cited by 17 publications

(20 citation statements)

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“…It is well fitted as ρ(0, r) ≃ 20r −2.08 . The power law distribution ∝ r −2 is seen in a course of collapse of the isothermal rotating cloud (Norman et al 1980;Narita et al 1984) as well as the isothermal spherical collapse (Larson 1969;Penston 1969). The disk is divided into two parts: a core which shows ρ(0, r) ≃constant and an envelope which shows ρ ∝ r −2 .…”

Section: Resultsmentioning

confidence: 99%

“…From Figure 5d, it is shown that the core size, r c , which is defined as the region where σ ≃ constant, decreases with time and the column density in the core σ c is proportional to 1/r c , that is, σ c × r c ≃ constant. This is seen in a course of "run-away collapse" in rotating isothermal clouds (Norman et al 1980;Narita et al 1984). In the runaway collapse, the density in a small part of the cloud increases infinitely, even the centrifugal force prevents the cloud from global contraction.…”

Section: Resultsmentioning

confidence: 99%

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Collapse and Fragmentation of Cylindrical Magnetized Clouds: Simulation with Nested Grid Scheme

Tomisaka

1996

Publications of the Astronomical Society of Japan

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Fragmentation process in a cylindrical magnetized cloud is studied with the nested grid method. The nested grid scheme use 15 levels of grids with different spatial resolution overlaid subsequently, which enables us to trace the evolution from the molecular cloud density ∼ 100cm −3 to that of the protostellar disk ∼ 10 10 cm −3 or more. Fluctuation with small amplitude grows by the gravitational instability. It forms a disk perpendicular to the magnetic fields which runs in the direction parallel to the major axis of the cloud. Matter accrets on to the disk mainly flowing along the magnetic fields and this makes the column density increase. The radial inflow, whose velocity is slower than that perpendicular to the disk, is driven by the increase of the gravity. While the equation of state is isothermal and magnetic fields are perfectly coupled with the matter, which is realized in the density range of ρ ∼ < 10 10 cm −3 , never stops the contraction. The structure of the contracting disk reaches that of a singular solution as the density and the column density obey ρ(r) ∝ r −2 and σ(r) ∝ r −1 , respectively. The magnetic field strength on the mid-plane is proportional to ρ(r) 1/2 and further that of the center (B c ) evolves as proportional to the square root of the gas density (∝ ρ 1/2 c ). It is shown that isothermal clouds experience "run-away" collapses. The evolution after the equation of state becomes hard is also discussed.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Collapse and Fragmentation of Cylindrical Magnetized Clouds: Simulation with Nested Grid Scheme

Tomisaka

1996

Publications of the Astronomical Society of Japan

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“…This is a property of the self-similar collapse, and occurs in a rotating, magnetic disk (BM95a; Basu 1997), where efficient magnetic braking prior to collapse keeps the centrifugal support at very low levels anyway. This effect is also present in non-magnetic rotating disks (Norman et al 1980;Narita, Hayashi, & Miyama 1984;Hayashi 1987), where the centrifugal support is much greater but also cannot grow and thereby halt the collapse. After a central protostar is formed (t > 0), the collapse becomes even more dynamic in an inner region where the infall resembles free-fall onto a central point mass, e.g., the similarity solutions of Shu (1977) and Hunter (1977).…”

Section: The Centrifugal Radiusmentioning

confidence: 98%

Constraints on the Formation and Evolution of Circumstellar Disks in Rotating Magnetized Cloud Cores

Basu

1998

ApJ

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We use magnetic collapse models to place some constraints on the formation and angular momentum evolution of circumstellar disks which are embedded in magnetized cloud cores. Previous models have shown that the early evolution of a magnetized cloud core is governed by ambipolar diffusion and magnetic braking, and that the core takes the form of a nonequilibrium flattened envelope which ultimately collapses dynamically to form a protostar. In this paper, we focus on the inner centrifugally-supported disk, which is formed only after a central protostar exists, and grows by dynamical accretion from the flattened envelope. We estimate a centrifugal radius for the collapse of mass shells within a rotating, magnetized cloud core. The centrifugal radius of the inner disk is related to its mass through the two important parameters characterizing the background medium: the background rotation rate Ω b and the background magnetic field strength B ref . We also revisit the issue of how rapidly mass is deposited onto the disk (the mass accretion rate) and use several recent models to comment upon the likely outcome in magnetized cores. Our model predicts that a significant centrifugal disk (much larger than a stellar radius) will be present in the very early (Class 0) stage of protostellar evolution. Additionally, we derive an upper limit for the disk radius as it evolves due to internal torques, under the assumption that the star-disk system conserves its mass and angular momentum even while most of the mass is transferred to a central star.

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“…The dynamical evolution of supercritical cores after their formation has been studied by many researchers. Solutions exist for the collapse of nonrotating, self-gravitating spheres without thermal support (Henriksen 1994), self-gravitating spheres with thermal support (Penston 1969;Larson 1969;Shu 1977;Hunter 1977;Boss & Black 1982;Whitworth & Summers 1985;Foster & Chevalier 1993) as well as with a combined thermal and isotropic magnetic pressure support (Chiueh & Chou 1994), and self-gravitating disks with thermal support (Narita, Hayashi, & Miyama 1984;Matsumoto, Hanawa, & Nakamura 1997) and also with ordered, frozen-in magnetic fields (Nakamura, Hanawa & Nakano 1995;Li & Shu 1997, hereafter LS). In order to choose a particular solution for a given problem, one needs to know the properties of the supercritical core at the time of its formation.…”

Section: Introductionmentioning

confidence: 99%

Self‐similar Collapse of Nonrotating Magnetic Molecular Cloud Cores

Contopoulos¹,

Ciolek²,

Königl³

1998

ApJ

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We obtain self-similar solutions that describe the gravitational collapse of nonrotating, isothermal, magnetic molecular cloud cores. We use simplifying assumptions but explicitly include the induction equation, and the semianalytic solutions we derive are the first to account for the effects of ambipolar diffusion following the formation of a central point mass. Our results demonstrate that, after the protostar first forms, ambipolar diffusion causes the magnetic flux to decouple in a growing region around the center. The decoupled field lines remain approximately stationary and drive a hydromagnetic C-shock that moves outward at a fraction of the speed of sound (typically a few tenths of a kilometer per second), reaching a distance of a few thousand AU at the end of the main accretion phase for a solar-mass star. We also show that, in the absence of field diffusivity, a contracting core will not give rise to a shock if, as is likely to be the case, the inflow speed near the origin is nonzero at the time of point-mass formation. Although the evolution of realistic molecular cloud cores will not be exactly self similar, our results reproduce the main qualitative features found in detailed core-collapse simulations (Ciolek & Königl 1998).

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On the Charge Distribution of the Pion

Cited by 17 publications

References 0 publications

Collapse and Fragmentation of Cylindrical Magnetized Clouds: Simulation with Nested Grid Scheme

Collapse and Fragmentation of Cylindrical Magnetized Clouds: Simulation with Nested Grid Scheme

Constraints on the Formation and Evolution of Circumstellar Disks in Rotating Magnetized Cloud Cores

Self‐similar Collapse of Nonrotating Magnetic Molecular Cloud Cores

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