Hydrodynamic Simulations of the Bardeen-Petterson Effect

We present SPH simulations of accretion discs in orbit about rotating compact objects such as black holes and neutron stars, and study the structure of warped discs produced by the Bardeen-Petterson effect. We calculate the transition radius out to which the disc specific angular momentum vector is aligned with that of the black hole. We focus on the parameter regime where the warp dynamics are controlled by bending wave propagation, but also consider models in which warps are subject to diffusion rather than wave transport, and are able to consider the fully nonlinear regime. Because of hydrodynamic or pressure effects, for the parameter range investigated, the transition radius is always found to be much smaller than that obtained by Bardeen & Petterson (1975). For discs with midplane Mach numbers of about 10, the transition occurs between 10 - 16 gravitational radii, whereas for a Mach number of about 30 it occurs at around 30 gravitational radii. A thicker disc with a Mach number of 5 is found to produce no discernible warped structure. The rate of black hole - disc alignment is found to be consistent with the ideas of Ress (1978), with the alignment torque behaving as if it arises from the accreted material transferring its misaligned component of angular momentum at the larger transition radius of Bardeen & Petterson (1975). The inclusion of Einstein precession in the calculations modified both the warped disc structure and, consistent with linear analysis, produced an increased alignment rate by up to a factor of 4 because of the effect that a non Keplerian potential has on the propagation of warps.Comment: 18 pages, 14 figures. Accepted for publication in M.N.R.A.S. A version with posctcript figures included can be obtained from http://www.maths.qmw.ac.uk/~rp

Interface Ferromagnetism in a SrMnO3/LaMnO3 Superlattice

Resonant soft x-ray absorption measurements at the O K edge on a SrMnO3/LaMnO3 superlattice show a shoulder at the energy of doped holes, which corresponds to the main peak of resonant scattering from the modulation in the doped hole density. Scattering line shape at the Mn L3,2 edges has a strong variation below the ferromagnetic transition temperature. This variation has a period equal to half the superlattice superperiod and follows the development of the ferromagnetic moment, pointing to a ferromagnetic phase developing at the interfaces. It occurs at the resonant energies for Mn3+ and Mn4+ valences. A model for these observations is presented, which includes a double-exchange two-site orbital and the variation with temperature of the hopping frequency tij between the two sites.Comment: 8.1 pages, 6 figure

Effects of CP Violation from Neutral Heavy Fermions on Neutrino Oscillations, and the LSND/MiniBooNE Anomalies

Neutrinos may mix with ultralight fermions, which gives flavor oscillations, and with heavier fermions, which yields short distance flavor change. I consider the case where both effects are present. I show that in the limit where a single oscillation length is experimentally accessible, the effects of heavier fermions on neutrino oscillations can generically be accounted for by a simple formula containing four parameters, including observable CP violation. I consider the anomalous LSND and MiniBooNE results, and show that these can be fit in a model with CP violation and two additional sterile neutrinos, one in the mass range between 0.1 and 20 eV, and the other with mass between 33 eV and 40 GeV. I also show that this model can avoid conflict with constraints from existing null short baseline experimental results.Comment: 12 pages, 3 figure

Optimal approximate matrix product in terms of stable rank

We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows. Here $\tilde{r}$ is the maximum stable rank, i.e. squared ratio of Frobenius and operator norms, of the two matrices being multiplied. This is a quantitative improvement over previous work of [MZ11, KVZ14], and is also optimal for any oblivious dimensionality-reducing map. Furthermore, due to the black box reliance on the subspace embedding property in our proofs, our theorem can be applied to a much more general class of sketching matrices than what was known before, in addition to achieving better bounds. For example, one can apply our theorem to efficient subspace embeddings such as the Subsampled Randomized Hadamard Transform or sparse subspace embeddings, or even with subspace embedding constructions that may be developed in the future. Our main theorem, via connections with spectral error matrix multiplication shown in prior work, implies quantitative improvements for approximate least squares regression and low rank approximation. Our main result has also already been applied to improve dimensionality reduction guarantees for $k$-means clustering [CEMMP14], and implies new results for nonparametric regression [YPW15]. We also separately point out that the proof of the "BSS" deterministic row-sampling result of [BSS12] can be modified to show that for any matrices $A, B$ of stable rank at most $\tilde{r}$, one can achieve the spectral norm guarantee for approximate matrix multiplication of $A^T B$ by deterministically sampling $O(\tilde{r}/\varepsilon^2)$ rows that can be found in polynomial time. The original result of [BSS12] was for rank instead of stable rank. Our observation leads to a stronger version of a main theorem of [KMST10].Comment: v3: minor edits; v2: fixed one step in proof of Theorem 9 which was wrong by a constant factor (see the new Lemma 5 and its use; final theorem unaffected

Radiation counting technique allows density measurement of metals in high-pressure/ high-temperature environment

Radioactive tracers induced by neutron irradiation provide a gamma ray flux proportional to the density of a metal, allowing density measurement of these metals in extreme high-temperature and high-pressure environments. This concept is applicable to most metals, as well as other substances

Quasars in the 2MASS Second Incremental Data Release

Using the 2MASS Second Incremental Data Release, we have searched for near infrared counterparts to 13214 quasars from the Veron-Cetty & Veron(2000) catalog. We have detected counterparts within 4 arcsec for 2277 of the approximately 6320 quasars within the area covered by the 2MASS Second Incremental Data Release. Only 1.6% of these are expected to be chance coincidences. Though this sample is heterogeneous, we find that known radio-loud quasars are more likely to have large near-infrared-to-optical luminosity ratios than radio-quiet quasars are, at a statistically significant level. This is consistent with dust-reddened quasars being more common in radio-selected samples than in optically-selected samples, due to stronger selection effects against dust-reddened quasars in the latter. We also find a statistically significant dearth of optically luminous quasars with large near-infrared-to-optical luminosity ratios. This can be explained in a dust obscuration model but not in a model where synchrotron emission extends from the radio into the near-infrared and creates such large ratios. We also find that selection of quasar candidates from the B-J/J-K color-color diagram, modelled on the V-J/J-K selection method of Warren, Hewett & Foltz (2000), is likely to be more sensitive to dust-obscured quasars than selection using only infrared-infrared colors.Comment: To be published in May issue of Astronomical Journal (26 pages, 8 figures, 2 tables) Replaced Figure 6 and

Hydrodynamic Simulations of Propagating Warps and Bending Waves In Accretion Discs

We present the results of a study of propagating warp or bending waves in accretion discs. Three dimensional hydrodynamic simulations were performed using SPH, and the results of these are compared with calculations based on the linear theory of warped discs. We consider primarily the physical regime in which the dimensionless viscosity parameter `alpha' < H/r, the disc aspect ratio, so that bending waves are expected to propagate. We also present calculations in which `alpha' > H/r, where the warps are expected to behave diffusively. Small amplitude perturbations are studied in both Keplerian and slightly non Keplerian discs, and we find that the SPH results can be reasonably well fitted by those of the linear theory. The main results of these calculations are: (1) the warp in Keplerian discs when `alpha' < H/r propagates with little dispersion and damps at a rate expected from estimates of the code viscosity, (2) warps evolve diffusively when `alpha' > H/r, (3) the non Keplerian discs exhibit a substantially more dispersive behaviour of the warps. Initially imposed higher amplitude nonlinear warping disturbances were studied in Keplerian discs. The results indicate that nonlinear warps can lead to the formation of shocks, and that the evolution of the warp becomes less wave-like and more diffusive in character. This work is relevant to the study of the warped accretion discs that may occur around Kerr black holes or in misaligned binary systems. The results indicate that SPH can accurately model the hydrodynamics of warped discs, even when using rather modest numbers of particles.Comment: 14 pages, 9 figures, to appear in MNRA