Combined Solar System and rotation curve constraints on MOND

The Modified Newtonian Dynamics (MOND) paradigm generically predicts that the external gravitational field in which a system is embedded can produce effects on its internal dynamics. In this communication, we first show that this External Field Effect can significantly improve some galactic rotation curves fits by decreasing the predicted velocities of the external part of the rotation curves. In modified gravity versions of MOND, this External Field Effect also appears in the Solar System and leads to a very good way to constrain the transition function of the theory. A combined analysis of the galactic rotation curves and Solar System constraints (provided by the Cassini spacecraft) rules out several classes of popular MOND transition functions, but leaves others viable. Moreover, we show that LISA Pathfinder will not be able to improve the current constraints on these still viable transition functions.Comment: 13 pages, 7 figures, accepted for publication in MNRA

Basins of attraction in forced systems with time-varying dissipation

We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final value. First, we consider situations where one is interested in the basins of attraction for damping coefficients varying linearly between two given values over many different time intervals: we outline a method to reduce the computation time required to estimate numerically the relative areas of the basins and discuss its range of applicability. Second, we observe that sometimes very slight changes in the time interval may produce abrupt large variations in the relative areas of the basins of attraction of the surviving attractors: we show how comparing the contracted phase space at a time after the final value of dissipation has been reached with the basins of attraction corresponding to that value of constant dissipation can explain the presence of such variations. Both procedures are illustrated by application to a pendulum with periodically oscillating support.Comment: 16 pages, 13 figures, 7 table

Power computation for the triboelectric nanogenerator

We consider, from a mathematical perspective, the power generated by a contact-mode triboelectric nanogenerator, an energy harvesting device that has been well studied recently. We encapsulate the behaviour of the device in a differential equation, which although linear and of first order, has periodic coefficients, leading to some interesting mathematical problems. In studying these, we derive approximate forms for the mean power generated and the current waveforms, and describe a procedure for computing the Fourier coefficients for the current, enabling us to show how the power is distributed over the harmonics. Comparisons with accurate numerics validate our analysis

Modified Baryonic Dynamics: two-component cosmological simulations with light sterile neutrinos

In this article we continue to test cosmological models centred on Modified Newtonian Dynamics (MOND) with light sterile neutrinos, which could in principle be a way to solve the fine-tuning problems of the standard model on galaxy scales while preserving successful predictions on larger scales. Due to previous failures of the simple MOND cosmological model, here we test a speculative model where the modified gravitational field is produced only by the baryons and the sterile neutrinos produce a purely Newtonian field (hence Modified Baryonic Dynamics). We use two component cosmological simulations to separate the baryonic N-body particles from the sterile neutrino ones. The premise is to attenuate the over-production of massive galaxy cluster halos which were prevalent in the original MOND plus light sterile neutrinos scenario. Theoretical issues with such a formulation notwithstanding, the Modified Baryonic Dynamics model fails to produce the correct amplitude for the galaxy cluster mass function for any reasonable value of the primordial power spectrum normalisation.Comment: 11 pages, 2 figures. Submitted to JCA

The Galactic potential and the asymmetric distribution of hypervelocity stars

In recent years several hypervelocity stars (HVSs) have been observed in the halo of our Galaxy. Such HVSs have possibly been ejected from the Galactic center and then propagated in the Galactic potential up to their current position. The recent survey for candidate HVSs show an asymmetry in the kinematics of candidate HVSs (position and velocity vectors), where more outgoing stars than ingoing stars (i.e. positive Galactocentric velocities vs. negative ones) are observed. We show that such kinematic asymmetry, which is likely due to the finite lifetime of the stars and Galactic potential structure, could be used in a novel method to probe and constrain the Galactic potential, identify the stellar type of the stars in the survey and estimate the number of HVSs. Kinematics-independent identification of the stellar types of the stars in such surveys (e.g. spectroscopic identification) could further improve these results. We find that the observed asymmetry between ingoing and outgoing stars favors specific Galactic potential models. It also implies a lower limit of ~54+-8 main sequence HVSs in the survey sample (>=648+-96 in the Galaxy), assuming that all of the main sequence stars in the survey originate from the Galactic center. The other stars in the survey are likely to be hot blue horizontal branch stars born in the halo rather than stars ejected from the Galactic center.Comment: 7 pages, 3 figures. Added an appendix. Accepted to Ap

Analysis of cool DO-type white dwarfs from the Sloan Digital Sky Survey Data Release 10

We report on the identification of 22 new cool DO-type white dwarfs (WD) detected in Data Release 10 (DR10) of the Sloan Digital Sky Survey (SDSS). Among them, we found one more member of the so-called hot-wind DO WDs, which show ultrahigh excitation absorption lines. Our non-LTE model atmosphere analyses of these objects and two not previously analyzed hot-wind DO WDs, revealed effective temperatures and gravities in the ranges Teff=45-80kK and log g= 7.50-8.75. In eight of the spectra we found traces of C (0.001-0.01, by mass). Two of these are the coolest DO WDs ever discovered that still show a considerable amount of C in their atmospheres. This is in strong contradiction with diffusion calculations, and probably, similar to what is proposed for DB WDs, a weak mass-loss is present in DO WDs. One object is the most massive DO WD discovered so far with a mass of 1.07 M_sun if it is an ONe-WD or 1.09 M_sun if it is a CO-WD. We furthermore present the mass distribution of all known hot non-DA (pre-) WDs and derive the hot DA to non-DA ratio for the SDSS DR7 spectroscopic sample. The mass distribution of DO WDs beyond the wind limit strongly deviates from the mass distribution of the objects before the wind limit. We address this phenomenon by applying different evolutionary input channels. We argue that the DO WD channel may be fed by about 13% by post-extreme-horizontal branch stars and that PG1159 stars and O(He) stars may contribute in a similar extent to the non-DA WD channel.Comment: 13 pages, accepted for publication in A&

Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure