Chung-Ming Ko

Theoretical Aspects of Gravitational Lensing in TeVeS

Since Bekensteins creation of his tensor-vector-scalar theory (TeVeS), the modified Newtonian dynamics (MOND) paradigm has been redeemed from the embarrassment of lacking a relativistic version. One primary success of TeVeS is that it provides an enhancement of gravitational lensing, which could not be achieved by other MOND theories. Following Bekensteins work, we investigate the phenomena of gravitational lensing including deflection angles, lens equations, and time delay. We find that the deflection angle maintains its value, while the distance of closest approach varies in the MOND regime. We also use the deflection angle law to derive magnifications and investigate microlensing light curves. We find that the difference in the magnification of the two images in the point-mass model is not a constant, as in general relativity (GR). Besides, microlensing light curves could deviate significantly from GR in the deep MOND regime. Furthermore, the scalar field, which is introduced to enhance the deflection angle in TeVeS, contributes a negative effect on the potential time delay. Unfortunately, this phenomenon is unmeasurable in lensing systems, where we can only observe the time delay between two images for a given source. However, this measurable time delay offers another constraint on the mass ratio of the dark matter and MOND scenarios, which in general differs from that given by the deflection angle. In other words, for a lensing system, if two masses, mgN and mgM, are mutual alternatives for the deflection angles in their own paradigm, regarding the time delay they are in general in an exclusive relation.

Nonlinear Parker Instability with the Effect of Cosmic-Ray Diffusion

We present the results of linear analysis and two-dimensional local magnetohydrodynamic (MHD) simulations of the Parker instability, including the effects of cosmic rays (CRs), in magnetized gas disks (galactic disks). As an unperturbed state for both the linear analysis and the MHD simulations, we adopted an equilibrium model of a magnetized, two-temperature, layered disk with constant gravitational acceleration parallel to the normal of the disk. The disk comprises a thermal gas, CRs, and a magnetic field perpendicular to the gravitational acceleration. CR diffusion along the magnetic field is considered; cross-field-line diffusion is supposed to be small and is ignored. We investigate two cases in our simulations. In the mechanical perturbation case, we add a velocity perturbation parallel to the magnetic field lines, while in the explosive perturbation case, we add CR energy into the sphere in which the CRs are injected. Linear analysis shows that the growth rate of the Parker instability becomes smaller if the coupling between the CRs and the gas is stronger (i.e., if the CR diffusion coefficient is smaller). Our MHD simulations of the mechanical perturbation confirm this result. We show that the falling matter is impeded by the CR pressure gradient; this causes a decrease in the growth rate. In the explosive perturbation case, the growth of the magnetic loop is faster when the coupling is stronger in the early stage. However, in the later stage the behavior of the growth rate becomes similar to the mechanical perturbation case.

Diffusive-Compression Acceleration and Turbulent Diffusion of Cosmic Rays in Quasi-periodic and Turbulent Flows

Multiple scale perturbation methods are used to study the transport and acceleration of energetic charged particles in quasi-periodic, fluid velocity structures in one, two, or three space dimensions, with spatial period lu, where lu is much less than the diffusion scale length ld = κ0/|u0| and κ0 and u0 are characteristic values of the energetic particle diffusion coefficients and fluid speed, respectively. The particle diffusion tensor K is also allowed to vary periodically on the scale lu. In the case in which the perturbation parameter = lu/ld ≡ u0lu/κ0 is small (0 < 1), the long space and time behavior of the energetic particle distribution function f at lowest order is shown to satisfy a modified Fokker-Planck equation. This equation arises from compatibility conditions imposed on the perturbation equations in order to obtain a consistent perturbation expansion that is free of secular terms. The analysis shows that the particles are accelerated stochastically on the large scale as a result of the divergence ∇ δu of the background fluid velocity perturbation δu. The net acceleration of the particles due to the velocity variations can be described in part by a second-order Fermi-like momentum space diffusion term in the long-scale transport equation obtained by averaging over the short-scale variations. The momentum space diffusion coefficient DT describing the effect depends on the two-point correlation of the fluid velocity divergence ∇ δu at different points in the flow. There is also a further energization term in the long-scale transport equation, corresponding to the work done by the scattering center fluid against the differential cosmic-ray pressure gradient that is modified as a result of the short-scale variations. The convective particle streaming is also modified as a result of the short-scale variations. The analysis shows that the effective spatial diffusion tensor for low-energy particles can be significantly modified as a result of turbulent diffusion, whereas higher energy particles with much larger diffusion tensor elements are not significantly affected by turbulent diffusion. Averaging over a random ensemble of short-scale, quasi-periodic velocity structures generalizes the turbulent transport coefficients obtained by previous authors.

Cosmic-ray-modified stellar winds. III. A numerical iterative approach

A numerical iterative method is used to determine the modification of a stellar wind flow with a termination shock by the galactic cosmic rays. A two-fluid model consisting of cosmic rays and thermal stellar wind gas is used in which the cosmic rays are coupled to the background flow via scattering with magnetohydrodynamic waves or irregularities. A polytropic model is used to describe the thermal stellar wind gas, and the cosmic-rays are modeled as a hot, low-density gas with negligible mass flux. The positive galactic cosmic-ray pressure gradient serves to brake the outflowing stellar wind gas, and the cosmic rays modify the location of the critical point of the wind, the location of the shock, the wind fluid velocity profile, and the thermal gas entropy constants on both sides of the shock. The transfer of energy to the cosmic rays results in an outward radial flux of cosmic-ray energy. 21 references.

Multi-wavelength Emission from the Fermi Bubbles. I. Stochastic Acceleration from Background Plasma

We analyze processes of electron acceleration in the Fermi bubbles in order to define parameters and restrictions of the models, which are suggested for the origin of these giant radio and gamma-ray structures. In the case of the leptonic origin of the nonthermal radiation from the bubbles, these electrons should be produced somehow in situ because of the relatively short lifetime of high-energy electrons, which lose their energy by synchrotron and inverse-Compton processes. It has been suggested that electrons in bubbles may be accelerated by shocks produced by tidal disruption of stars accreting onto the central black hole or a process of re-acceleration of electrons ejected by supernova remnants. These processes will be investigated in subsequent papers. In this paper, we focus on in situ stochastic (Fermi) acceleration by a hydromagnetic/supersonic turbulence, in which electrons can be directly accelerated from the background plasma. We showed that the acceleration from the background plasma is able to explain the observed fluxes of radio and gamma-ray emission from the bubbles, but the range of permitted parameters of the model is strongly restricted.

MULTI-WAVELENGTH EMISSION FROM THE FERMI BUBBLE. III. STOCHASTIC (FERMI) RE-ACCELERATION OF RELATIVISTIC ELECTRONS EMITTED BY SNRs

We analyse the model of stochastic re-acceleration of electrons, which are emitted by supernova remnants (SNRs) in the Galactic Disk and propagate then into the Galactic halo, in order to explain the origin on nonthermal (radio and gamma-ray) emission from the Fermi Bubbles (FB). We assume that the energy for re-acceleration in the halo is supplied by shocks generated by processes of star accretion onto the central black hole. Numerical simulations show that regions with strong turbulence (places for electron re-acceleration) are located high up in the Galactic Halo about several kpc above the disk. The energy of SNR electrons that reach these regions does not exceed several GeV because of synchrotron and inverse Compton energy losses. At appropriate parameters of re-acceleration these electrons can be re-accelerated up to the energy 10E12 eV which explains in this model the origin of the observed radio and gamma-ray emission from the FB. However although the model gamma-ray spectrum is consistent with the Fermi results, the model radio spectrum is steeper than the observed by WMAP and Planck. If adiabatic losses due to plasma outflow from the Galactic central regions are taken into account, then the re-acceleration model nicely reproduces the Planck datapoints.

Nuclear interaction gamma-ray lines from the Galactic center region

Aims. The accretion of stars onto the central supermassive black hole at the center of the Milky Way is predicted to generate large fluxes of subrelativistic ions in the Galactic center region. We analyze the intensity, shape, and spatial distribution of de-excitation gamma-ray lines produced by nuclear interactions of these energetic particles with the ambient medium. Methods. We first estimated the amount and mean kinetic energy of particles released from the central black hole during star disruption. We then calculated the energy and spatial distributions of these particles in the Galactic center region from a kinetic equation. These particle distributions were then used to derive the characteristics of the main nuclear interaction gamma-ray lines. Results. Because the time period of star capture by the supermassive black hole is expected to be shorter than the lifetime of the ejected fast particles against Coulomb losses, the gamma-ray emission is predicted to be stationary. We find that the nuclear deexcitation lines should be emitted from a region with a maximum 5 ◦ angular radius. The total gamma-ray line flux below 8 MeV is calculated to be ∼10 −4 photons cm −2 s −1 . The most promising lines for detection are those at 4.44 and ∼6.2 MeV, with a predicted flux in each line of ∼10 −5 photons cm −2 s −1 . Unfortunately, it is unlikely that this emission can be detected with the INTEGRAL observatory. But the predicted line intensities appear to be within reach of future gamma-ray space instruments. A future detection of de-excitation gamma-ray lines from the Galactic center region would provide unique information on the high-energy processes induced by the central supermassive black hole and the physical conditions of the emitting region.

Parker-Jeans Instability of Gaseous Disks Including the Effect of Cosmic Rays

We use linear analysis to examine the effect of cosmic rays (CRs) on the Parker-Jeans instability of magnetized self-gravitating gaseous disks. We adopt a slab equilibrium model in which the gravity (including self-gravity) is perpendicular to the midplane and the magnetic field lies along the slab. CRs are described as a fluid, and diffusion is considered only along magnetic field lines. The linearized equations are solved numerically. The system is susceptible to Parker-Jeans instability. In general, the system is less unstable when the CR diffusion coefficient is smaller (i.e., the coupling between the CRs and plasma is stronger). The system is also less unstable if the CR pressure is larger. This is reminiscent of the fact that Jeans instability and Parker instability are less unstable when the gas pressure is larger (or temperature is higher). Moreover, for a large CR diffusion coefficient (or a small CR pressure), perturbations parallel to the magnetic field are more unstable than those perpendicular to it. The other governing factor on the growth rate of the perturbations in different directions is the thickness of the disk or the strength of the external pressure on the disk. In fact, this is the determining factor in some parameter regimes.

Mass of galaxy lenses in modified gravity: any need for dark mass?

Mu-Chen Chiu, 2 Chung-Ming Ko, 3, 4 Yong Tian, and HongSheng Zhao Institute of Astronomy, National Central University, Jhongli, Taiwan 320, R.O.C. Scottish University Physics Alliance, Institute for Astronomy, the Royal Observatory , University of Edinburgh, Blackford Hill, Edinburgh,EH9 3HJ ,UK Department of Physics, National Central University, Jhongli, Taiwan 320, R.O.C. Center for Complex Systems, National Central University, Jhongli, Taiwan 320, R.O.C. Scottish University Physics Alliance, University of St. Andrews, KY16 9SS,UK (Dated: August 19, 2010)

LINEAR ANALYSIS OF PARKER-JEANS INSTABILITY WITH COSMIC-RAY

We present the results of the linear analysis for the Parker-Jeans instability in the magnetized gas disks including the effect of cosmic-ray diffusion along the magnetic field lines. We adopted an uni-formly rotating two temperature layered disk with a horizontal magnetic fields and solved the perturbed equations numerically. Fragmentation of gases takes place and filamentary structures are formed by the growth of the instability. Nagai et al. (1998) showed that the direction of filaments being formed by the Parker-Jeans instability depends on the strength of pressure outside the unperturbed gas disk. We found that at some range of external pressures the direction of filaments is also governed by the value of the diffusion coefficient of CR along the magnetic field lines k.