Formation of chondrules in radiative shock waves I. First results, spherical dust particles, stationary shocks

The formation of chondrules in the protoplanetary nebulae causes many questions concerning the formation process, the source of energy for melting the rims, and the composition of the origin material. The aim of this work is to explore the heating of the chondrule in a single precursor as is typical for radiation hydrodynamical shock waves. We take into account the gas-particle friction for the duration of the shock transition and calculate the heat conduction into the chondrules. These processes are located in the protoplanetary nebulae at a region around 2.5 AU, which is considered to be the most likely place of chondrule formation. The present models are a first step towards computing radiative shock waves occurring in a particle-rich environment. We calculated the shock waves using one-dimensional, time-independent equations of radiation hydrodynamics involving realistic gas and dust opacities and gas-particle friction. The evolution of spherical chondrules was followed by solving the heat conduction equation on an adaptive grid. The results for the shock-heating event are consistent with the cosmochemical constraints of chondrule properties. The calculations yield a relative narrow range for density or temperature to meet the requested heating rates of $R > 10^4\,K\, h^{-1}$ as extracted from cosmochemical constraints. Molecular gas, opacities with dust, and a protoplanetary nebula with accretion are necessary requirements for a fast heating process. The thermal structure in the far post-shock region is not fully consistent with experimental constraints on chondrule formation since the models do not include additional molecular cooling processes.Comment: 8 pages,5 figure

Acceleration of cosmic rays in supernova-remnants

It is commonly accepted that supernova-explosions are the dominant source of cosmic rays up to an energy of 10 to the 14th power eV/nucleon. Moreover, these high energy particles provide a major contribution to the energy density of the interstellar medium (ISM) and should therefore be included in calculations of interstellar dynamic phenomena. For the following the first order Fermi mechanism in shock waves are considered to be the main acceleration mechanism. The influence of this process is twofold; first, if the process is efficient (and in fact this is the cas) it will modify the dynamics and evolution of a supernova-remnant (SNR), and secondly, the existence of a significant high energy component changes the overall picture of the ISM. The complexity of the underlying physics prevented detailed investigations of the full non-linear selfconsistent problem. For example, in the context of the energy balance of the ISM it has not been investigated how much energy of a SN-explosion can be transfered to cosmic rays in a time-dependent selfconsistent model. Nevertheless, a lot of progress was made on many aspects of the acceleration mechanism

A cosmic ray driven instability

The interaction between energetic charged particles and thermal plasma which forms the basis of diffusive shock acceleration leads also to interesting dynamical phenomena. For a compressional mode propagating in a system with homogeneous energetic particle pressure it is well known that friction with the energetic particles leads to damping. The linear theory of this effect has been analyzed in detail by Ptuskin. Not so obvious is that a non-uniform energetic particle pressure can addition amplify compressional disturbances. If the pressure gradient is sufficiently steep this growth can dominate the frictional damping and lead to an instability. It is important to not that this effect results from the collective nature of the interaction between the energetic particles and the gas and is not connected with the Parker instability, nor with the resonant amplification of Alfven waves

Time-dependent galactic winds I. Structure and evolution of galactic outflows accompanied by cosmic ray acceleration

Cosmic rays are transported out of the galaxy by diffusion and advection due to streaming along magnetic field lines and resonant scattering off self-excited MHD waves. Thus momentum is transferred to the plasma via the frozen-in waves as a mediator assisting the thermal pressure in driving a galactic wind. The bulk of the Galactic CRs are accelerated by shock waves generated in SNRs, a significant fraction of which occur in OB associations on a timescale of several $10^7$ years. We examine the effect of changing boundary conditions at the base of the galactic wind due to sequential SN explosions on the outflow. Thus pressure waves will steepen into shock waves leading to in situ post-acceleration of GCRs. We performed simulations of galactic winds in flux tube geometry appropriate for disk galaxies, describing the CR diffusive-advective transport in a hydrodynamical fashion along with the energy exchange with self-generated MHD waves. Our time-dependent CR hydrodynamic simulations confirm the existence of time asymptotic outflow solutions (for constant boundary conditions). It is also found that high-energy particles escaping from the Galaxy and having a power-law distribution in energy ($\propto E^{-2.7}$) similar to the Milky Way with an upper energy cut-off at $\sim 10^{15}$ eV are subjected to efficient and rapid post-SNR acceleration in the lower galactic halo up to energies of $10^{17} - 10^{18}$ eV by multiple shock waves propagating through the halo. The particles can gain energy within less than $3\,$kpc from the galactic plane corresponding to flow times less than $5\cdot 10^6\,$years. The mechanism described here offers a natural solution to explain the power-law distribution of CRs between the "knee" and the "ankle". The mechanism described here offers a natural and elegant solution to explain the power-law distribution of CRs between the "knee" and the "ankle".Comment: 15 pages, 7 figure

Detection of the evolutionary stages of variables in M3

The large number of variables in M3 provides a unique opportunity to study an extensive sample of variables with the same apparent distance modulus. Recent, high accuracy CCD time series of the variables show that according to their mean magnitudes and light curve shapes, the variables belong to four separate groups. Comparing the properties of these groups (magnitudes and periods) with horizontal branch evolutionary models, we conclude that these samples can be unambiguously identified with different stages of the horizontal branch stellar evolution. Stars close to the zero age horizontal branch (ZAHB) show Oosterhoff I type properties, while the brightest stars have Oosterhoff II type statistics regarding their mean periods and RRab/RRc number ratios. This finding strengthens the earlier suggestion of Lee et al. (1990) connecting the Oosterhoff dichotomy to evolutionary effects, however, it is unexpected to find large samples of both of the Oosterhoff type within a single cluster, which is, moreover, the prototype of the Oosterhoff I class globular clusters. The very slight difference between the Fourier parameters of the stars (at a given period) in the three fainter samples spanning over about 0.15 mag range in M_V points to the limitations of any empirical methods which aim to determine accurate absolute magnitudes of RR Lyrae stars solely from the Fourier parameters of the light curves.Comment: 4 pages, 4 figures. Submitted to Astrophys. J. Letter

Collapse of Rotating Magnetized Molecular Cloud Cores and Mass Outflows

Collapse of the rotating magnetized molecular cloud core is studied with the axisymmetric magnetohydrodynamical (MHD) simulations. Due to the change of the equation of state of the interstellar gas, the molecular cloud cores experience several different phases as collapse proce eds. In the isothermal run-away collapse ($n \lesssim 10^{10}{\rm H_2 cm}^{-3}$), a pseudo-disk is formed and it continues to contract till the opaque core is fo rmed at the center. In this disk, a number of MHD fast and slow shock pairs appear running parallelly to the disk. After the equation of state becomes hard, an adiabatic core is formed, which is separated from the isothermal contracting pseudo-disk by the accretion shock front facing radially outwards. By the effect of the magnetic tension, the angular momentum is transferred from the disk mid-plane to the surface. The gas with excess angular momentum near the surface is finally ejected, which explains the molecular bipolar outflow. Two types of outflows are observed. When the poloidal magnetic field is strong (magnetic energy is comparable to the thermal one), a U-shaped outflow is formed in which fast moving gas is confined to the wall whose shape looks like a capit al letter U. The other is the turbulent outflow in which magnetic field lines and velocity fi elds are randomly oriented. In this case, turbulent gas moves out almost perpendicularly from the disk. The continuous mass accretion leads to the quasistatic contraction of the first core. A second collapse due to dissociation of H$_2$ in the first core follows. Finally another quasistatic core is again formed by atomic hydrogen (the second core). It is found that another outflow is ejected around the second atomic core, which seems to correspond to the optical jets or the fast neutral winds.Comment: submitted to Ap

Evolution of Rotating Molecular Cloud Core with Oblique Magnetic Field

We studied the collapse of rotating molecular cloud cores with inclined magnetic fields, based on three-dimensional numerical simulations.The numerical simulations start from a rotating Bonnor-Ebert isothermal cloud in a uniform magnetic field. The magnetic field is initially taken to be inclined from the rotation axis. As the cloud collapses, the magnetic field and rotation axis change their directions. When the rotation is slow and the magnetic field is relatively strong, the direction of the rotation axis changes to align with the magnetic field, as shown earlier by Matsumoto & Tomisaka. When the magnetic field is weak and the rotation is relatively fast, the magnetic field inclines to become perpendicular to the rotation axis. In other words, the evolution of the magnetic field and rotation axis depends on the relative strength of the rotation and magnetic field. Magnetic braking acts to align the rotation axis and magnetic field, while the rotation causes the magnetic field to incline through dynamo action. The latter effect dominates the former when the ratio of the angular velocity to the magnetic field is larger than a critical value \Omega_0/ B_0 > 0.39 G^1/2 c_s^-1, where B_0, \Omega_0, G, and c_s^-1 denote the initial magnetic field, initial angular velocity, gravitational constant, and sound speed, respectively. When the rotation is relatively strong, the collapsing cloud forms a disk perpendicular to the rotation axis and the magnetic field becomes nearly parallel to the disk surface in the high density region. A spiral structure appears due to the rotation and the wound-up magnetic field in the disk.Comment: 45 pages, 17 figures, Submitted to ApJ, For high resolution figures see http://www2.scphys.kyoto-u.ac.jp/~machidam/ms060201.pd