Prospects for Detection of Synchrotron Emission from Secondary Electrons and Positrons in Starless Cores: Application to G0.216+0.016

We investigate the diffusion of cosmic rays into molecular cloud complexes. Using the cosmic-ray diffusion formalism of Protheroe, et al. (2008), we examine how cosmic rays diffuse into clouds exhibiting different density structures, including a smoothed step-function, as well as Gaussian and inverse-$r$ density distributions, which are well known to trace the structure of star-forming regions. These density distributions were modelled as an approximation to the Galactic centre cloud G0.216+0.016, a recently-discovered massive dust clump that exhibits limited signs of massive star formation and thus may be the best region in the Galaxy to observe synchrotron emission from secondary electrons and positrons. Examination of the resulting synchrotron emission, produced by the interaction of cosmic ray protons interacting with ambient molecular matter producing secondary electrons and positrons reveals that, due to projection effects, limb-brightened morphology results in all cases. However, we find that the Gaussian and inverse-$r$ density distributions show much broader flux density distributions than step-function distributions. Significantly, some of the compact (compared to the $2.2''$ resolution, 5.3 GHz JVLA observations) sources show non-thermal emission, which may potentially be explained by the density structure and the lack of diffusion of cosmic rays into the cloud. We find that we can match the 5.3 and 20 GHz flux densities of the non-thermal source JVLA~1 and 6 from Rodr\'{\i}guez & Zapata (2014) with a local cosmic ray flux density, a diffusion coefficient suppression factor of $\chi=0.1-0.01$ for a coefficient of $3\times10^{27}$ cm$^2$ s$^{-1}$, and a magnetic field strength of 470 $\mu$G.Comment: 4 pages, 2 figures, accepted for publication in the Astrophysical Journal Letter

Pulsar state switching, timing noise and free precession

Recent radio pulsar observations have shown that a number of pulsars display interesting long term periodicities in their spin-down rates. At least some of these pulsars also undergo sharp changes in pulse profile. This has been convincingly attributed to the stars abruptly switching between two different magnetospheric states. The sharpness of these transitions has been taken as evidence against free precession as the mechanism behind the long term variations. We argue that such a conclusion is premature. By performing a simple best-fit analysis to the data, we show that the relationship between the observed spin and modulation periods is of approximately the correct form to be accounted for by the free precession of a population of neutron stars with strained crusts, the level of strain being similar in all of the stars, and consistent with the star retaining a memory of a former faster rotation rate. We also provide an argument as to why abrupt magnetospheric changes can occur in precessing stars, and how such changes would serve to magnify the effect of precession in the timing data, making the observation of the precession more likely in those stars where such switching occurs. We describe how future observations could further test the precession hypothesis advanced here.Comment: Additional reference inserted; to appear in MNRA

Parameter choices and ranges for continuous gravitational wave searches for steadily spinning neutron stars

We consider the issue of selecting parameters and their associated ranges for carrying out searches for continuous gravitational waves from steadily rotating neutron stars. We consider three different cases (i) the "classic" case of a star spinning about a principal axis; (ii) a biaxial star, not spinning about a principal axis; (iii) a triaxial star spinning steady, but not about a principal axis (as described in Jones, MNRAS vol 402, 2503 (2010)). The first of these emits only at one frequency; the other two at a pair of harmonically related frequencies. We show that in all three cases, when written in terms of the original "source parameters", there exist a number of discrete degeneracies, with different parameter values giving rise to the same gravitational wave signal. We show how these can be removed by suitably restricting the source parameter ranges. In the case of the model as written down by Jones, there is also a continuous degeneracy. We show how to remove this through a suitable rewriting in terms of "waveform parameters", chosen so as to make the specialisations to the other stellar models particularly simple. We briefly consider the (non-trivial) relation between the assignment of prior probabilities on one set of parameters verses the other. The results of this paper will be of use when designing strategies for carrying out searches for such multi-harmonic gravitational wave signals, and when performing parameter estimation in the event of a detection.Comment: Updated to match version accepted by MNRAS: One new equation (equation 82)); typo (sign-error) corrected in equation (88); one more paragraph inserted into Summary and Discussion sectio

Three evolutionary paths for magnetar oscillations

Quasi-periodic oscillations have been seen in the light curves following several magnetar giant flares. These oscillations are of great interest as they probably provide our first ever view of the normal modes of oscillation of neutron stars. The state-of-the-art lies in the study of the oscillations of elastic-magnetic stellar models, mainly with a view to relating the observed frequencies to the structure and composition of the star itself. We advance this programme by considering several new physical mechanisms that are likely to be important for magnetar oscillations. These relate to the superfluid/superconducting nature of the stellar interior, and the damping of the modes, both through internal dissipation mechanisms and the launching of waves into the magnetosphere. We make simple order-of-magnitude estimates to show that both the frequencies and the damping time of magnetar oscillations can evolve in time, identifying three distinct `pathways' that can be followed, depending upon the initial magnitude of the mode excitation. These results are interesting as they show that the information buried in magnetar QPOs may be even richer than previously thought, and motivate more careful examination of magnetar light curves, to search for signatures of the different types of evolution that we have identified.Comment: To appear in MNRAS. This version reflects changes made in response to referee's comments, mainly extra discussion in Section 2.

Ultra-violet Finiteness in Noncommutative Supersymmetric Theories

We consider the ultra-violet divergence structure of general noncommutative supersymmetric $U(N_c)$ gauge theories, and seek theories which are all-orders finite.Comment: 11 pages, Tex, one figure. Uses harvmac (big) and eps

Fayet-Iliopoulos D-terms and anomaly mediated supersymmetry breaking

We show that in a minimal extension of the MSSM by means of an extra U(1) gauge group, the negative mass-squared problem characteristic of the Anomaly Mediated Supersymmetry Breaking scenario is naturally solved by means of Fayet-Iliopoulos D-terms. We derive a set of sum rules for the sparticle masses which are consequences of the resulting framework.Comment: 11 pages, including 1 figure. Plain TeX. Uses Harvmac and epsf. Final version to appear in Phys. Lett. B; some minor improvement

The Exact Tachyon Beta-Function for the Wess-Zumino-Witten Model

We derive an exact expression for the tachyon $\beta$-function for the Wess-Zumino-Witten model. We check our result up to three loops by calculating the three-loop tachyon $\beta$-function for a general non-linear $\sigma$-model with torsion, and then specialising to the case of the WZW model.Comment: 13pp, uses harvmac (with figures appended as a a standard PostScript file), LTH 31

Quasi-infra-red fixed points and renormalisation group invariant trajectories for non-holomorphic soft supersymmetry breaking

In the MSSM the quasi-infra-red fixed point for the top-quark Yukawa coupling gives rise to specific predictions for the soft-breaking parameters. We discuss the extent to which these predictions are modified by the introduction of additional ``non-holomorphic'' soft-breaking terms. We also show that in a specific class of theories there exists an RG-invariant trajectory for the ``non-holomorphic'' terms, which can be understood using a holomorphic spurion term.Comment: 24 pages, TeX, two figures. Uses Harvmac (big) and epsf. Minor errors corrected, and the RG trajectory explained in terms of a holomorphic spurion ter

The Gaugino \beta-Function

We present an elegant exact formula for the gaugino $\beta$-function in a softly-broken supersymmetric gauge theory, of the form $\beta_M = {\cal O}(\beta_g/g)$, where $\beta_g$ is the gauge $\beta$ function and ${\cal O}$ is a simple differential operator acting on the gauge coupling $g$ and the Yukawa coupling.Comment: 11 pages, tex, no figures. Uses harvmac. Minor error in derivation of Eq. (14) correcte