The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

Cosmic-ray streaming perpendicular to the mean magnetic field

The distribution function of cosmic rays streaming perpendicular to the mean magnetic field in a turbulent medium is re-examined. Urch's (1977) discovery that, in quasilinear theory, the flux is due to particles at 90° pitch angle is discussed and shown to be consistent with previous formulations of the theory. We point out that this flux of particles at 90° cannot be arbitrarily set equal to zero, and hence we dismiss the alternative theory which proceeds from this premise. A further, basic inconsistency in Urch's new transport equation is demonstrated, and the connection between quasilinear theory and compound diffusion is discussed.     

On a perturbation theory using Lie transforms

Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations.     

Peculiar velocities of galaxies and clusters

We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both non-linear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with exponential wings. The model is easily extended to study how the statistic depends on the type of particle used to trace the velocity field (dark matter particles, dark matter haloes, galaxies), and on the density of the environment in which the test particles are located. Comparisons with simulations suggest that our model is accurate. We also show that the evolution of the peculiar velocities depends on the local, rather than the global, density. Since clusters populate denser regions on average, using cluster velocities with the linear theory scaling may lead to an overestimate of the global value of Ω₀. Conversely, using linear theory with the global value of Ω₀ to scale cluster velocities from the initial to the present time results in an underestimate of their true velocities. In general, however, the directions of motions of haloes are rather well described by linear theory. Our results help to simplify models of redshift-space distortions considerably.     

Cosmological evolution and hierarchical galaxy formation

We calculate the rate at which dark matter haloes merge to form higher mass systems. Two complementary derivations using Press–Schechter theory are given, both of which result in the same equation for the formation rate. First, a derivation using the properties of the Brownian random walks within the framework of Press–Schechter theory is presented. We then use Bayes' theorem to obtain the same result from the standard Press–Schechter mass function. The rate obtained is shown to be in good agreement with results from Monte Carlo and N -body simulations. We illustrate the usefulness of this formula by calculating the expected cosmological evolution in the rate of star formation that is due to short-lived, merger-induced starbursts. The calculated evolution is well-matched to the observed evolution in ultraviolet luminosity density, in contrast to the lower rates of evolution that are derived from semi-analytic models that do not include a dominant contribution from starbursts. Hence we suggest that the bulk of the observed ultraviolet starlight at z >1 arises from merger-induced starbursts. Finally, we show that a simple merging-halo model can also account for the bulk of the observed evolution in the comoving quasar space density.     

Corona-like atmospheric escape from KBOs: I. Gas dynamics

We show that for low temperatures (T∼30 K) and small, but non-negligible, gravitational fields the hydrodynamic escape of gas can be treated by Parker's theory of coronal expansion [Parker, E.N., 1963. Interplanetary Dynamical Processes. Interscience Publishers, New York]. We apply this theory to gas escape from Kuiper belt objects. We derive limits on the density and radius of the bodies for which this theory is applicable, and show how the flow depends on the mean molecular weight and internal degrees of freedom of the gas molecules. We use these results to explain the CH₄ dichotomy seen on KBOs [Schaller, E.L., Brown, M.E., 2007. Astrophys. J., 659, L61-L64].     

非局部对流理论及其在太阳模型中的应用(英文)

在Li&Yang (2 0 0 1 )所给出的局部对流理论的基础上 ,我们进一步采用梯度型方案给出了非局部对流理论 ,并将它用于太阳模型中。这一理论考虑了恒星对流区内的非局部效应 ,它得到了一个与原来用混合长理论或局部理论给出的结果有所区别的对流区 ,扩散效应很明显。但是 ,目前我们的理论还不能处理时间相关的对流以及对流超射等问题。这些问题将在后续工作中加以考虑。当把这一理论应用于太阳模型中时 ,我们发现它对标准太阳模型的改正非常微小。我们讨论了这一现象 ,并对其加以解释     

Quantitative analysis of clumps in the tidal tails of star clusters

Tidal tails of star clusters are not homogeneous but show well-defined clumps in observations as well as in numerical simulations. Recently, an epicyclic theory for the formation of these clumps was presented. A quantitative analysis was still missing. We present a quantitative derivation of the angular momentum and energy distribution of escaping stars from a star cluster in the tidal field of the Milky Way and derive the connection to the position and width of the clumps. For the numerical realization we use star-by-star N -body simulations. We find a very good agreement of theory and models. We show that the radial offset of the tidal arms scales with the tidal radius, which is a function of cluster mass and the rotation curve at the cluster orbit. The mean radial offset is 2.77 times the tidal radius in the outer disc. Near the Galactic Centre the circumstances are more complicated, but to lowest order the theory still applies. We have also measured the Jacobi energy distribution of bound stars and showed that there is a large fraction of stars (about 35 per cent) above the critical Jacobi energy at all times, which can potentially leave the cluster. This is a hint that the mass loss is dominated by a self-regulating process of increasing Jacobi energy due to the weakening of the potential well of the star cluster, which is induced by the mass loss itself.     

What can we hope to know about the symmetry properties of stellar magnetic fields?

We summarize evidence that neither dynamo theory nor the observational data give strong support to the idea that stellar magnetic fields must have dipolar rather than quadrupolar symmetry with respect to the stellar equator. We demonstrate that even the most basic model for magnetic stellar activity, i.e. the Parker migratory dynamo, provides many possibilities for the excitation of large-scale stellar magnetic fields of non-dipolar symmetry. We demonstrate the spontaneous transition of the dynamo-excited magnetic field from one symmetry type to another. We explore observational tests to distinguish between the two types of magnetic field symmetry, and thus detect the presence of quadrupolar magnetic symmetry in stars. Complete absence of quadrupolar symmetry would present a distinct challenge for contemporary stellar dynamo theory. We revisit some observations which, depending on further clarification, may already be revealing some properties of the quadrupolar component of the magnetic fields generated by stellar dynamos.     

Scalar fields as dark matter in spiral galaxies: comparison with experiments

We present an exact solution for a static and axially symmetric spacetime, which is obtained from a scalar-tensor theory that comes from unification theories. As an attempt to model the dark matter (DM) in spiral galaxies we find that an exponential scalar potential is enough to explain the rotation curves in such galaxies. We also present the fitting to the rotation curve of six spiral galaxies and we find an excellent agreement between observational data and the results of our model.     

On the origin of galactic magnetic fields

We discuss the properties of the large-scale galactic magnetic fields which can help to discriminate between theories of their origin. We argue that the mean-field dynamo theory in its simplest form is unique in that it can explain most of the known features from a single conceptual viewpoint. This revised version was published online in September 2006 with corrections to the Cover Date.     

Radiative Transfer Reconsidered as a Quantum Kinetic Theory Problem

We revisit the radiative transfer theory from first principles approach, inspired from quantum kinetic theory. The radiation field is described within the second quantization formalism. A master equation for the radiation density operator is derived and transformed into a balance relation in the phase space, which involves nonlocal terms owing to radiation coherence. In a perturbative framework, we focus on the lowest order term in ?-expansion and show that the radiation coherence results in an alteration of the photon group velocity. An application to the formation of hydrogen lines in stellar atmospheres is performed as an illustration.     

Mass selection bias in galaxy cluster peculiar velocities from the kinetic Sunyaev–Zel'dovich effect

Upcoming surveys for galaxy clusters using the Sunyaev–Zel'dovich effect are potentially sensitive enough to create a peculiar velocity catalogue. The statistics of these peculiar velocities are sensitive to cosmological parameters. We develop a method to explore parameter space using N -body simulations in order to quantify dark matter halo velocity statistics which will be useful for cluster peculiar velocity observations. We show that mass selection bias from a kinetic Sunyaev–Zel'dovich velocity catalogue forecasts rms peculiar velocities with a much more complicated  Ω_m  dependency than suggested by linear perturbation theory. In addition, we show that both two-point functions for velocities disagree with linear theory predictions out to  ∼40  h ⁻¹ Mpc  separations. A pedagogical appendix is included developing linear theory notation with respect to the two-point peculiar velocities functions.     

Third-order Uranus-Neptune theory

In this paper of the third order Uranus-Neptune planetary theory which is the third part of this work for the third order theory, we compute the Poisson brackets in the Lie series which is used to transform canonical variables. We apply Hori-Lie technique in this work and neglect all powers higher than the second in Poincaré variables H, K, P, Q. We restrict this work to the principal part of the disturbing function.     

Testing Bekenstein's relativistic Modified Newtonian Dynamics with lensing data

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specifically tensor–vector–scalar (TeVeS) theory, a theory which is consistent with fundamental relativistic principles and the phenomenology of Modified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we analytically derive the deflection angle for the point lens and the Hernquist galaxy profile, and study their patterns in convergence, shear and amplification. Applying our analytical lensing models, we fit galaxy-quasar lenses in the CfA-Arizona Space Telescope Lens Survey (CASTLES) sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all the cases, we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy μ function provides more efficient lensing than the standard MOND μ function. But for a handful of lenses, a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function μ and modification scale a ₀ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND μ function. We also show that the simplest TeVeS 'minimal-matter' cosmology, a baryonic universe with a cosmological constant, can fit the distance–redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity.     

Modified energy–momentum conservation laws and vacuum Cherenkov radiation

We present a general parametrization for the leading order terms in a momentum power expansion of a non-universal Lorentz-violating, but rotational invariant, kinematics and its implications for two-body decay thresholds. The considered framework includes not only modified dispersion relations for particles, but also modified energy–momentum conservation laws, something which goes beyond effective field theory. As a particular and relevant example, bounds on the departures from special relativistic kinematics from the non-observation of vacuum Cherenkov radiation are discussed and compared with those obtained within the effective field theory scenario.     

The resistances of the photosphere and of a flaring coronal loop

Solar Physics - We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called “dynamo models”, which invoke an analogy between the...     

Scalable Dynamics of High Energy Relativistic Electrons: Theory, Numerical Simulations and Experimental Results

Similarity theory, which is necessary in order to apply the results of laboratory astrophysics experiments to relativistic astrophysical plasmas, is presented. The analytical predictions of the similarity theory are compared with PIC numerical simulations and the most recent experimental data on monoenergetic electron acceleration in diluted plasmas and high harmonic generation at overdense plasma boundaries. We demonstrate that similarity theory is a reliable tool for explaining a surprisingly wide variety of laboratory plasma phenomena the predictions of which can be scaled up to astrophysical dimensions.