Sequential and continuum bifurcations in degenerate elliptic equations

We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurcations occur from the trivial solution. Moreover, a bifurcation occurs at each point in some unbounded interval in parameter space. We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equations

Lord of the Rings – Return of the King: Swift-XRT observations of dust scattering rings around V404 Cygni

On 2015 June 15, the black hole X-ray binary V404 Cygni went into outburst, exhibiting extreme X-ray variability which culminated in a final flare on June 26. Over the following days, the Swift-X-ray Telescope detected a series of bright rings, comprising five main components that expanded and faded with time, caused by X-rays scattered from the otherwise unobservable dust layers in the interstellar medium in the direction of the source. Simple geometrical modelling of the rings’ angular evolution reveals that they have a common temporal origin, coincident with the final, brightest flare seen by INTEGRAL's JEM X-1, which reached a 3–10 keV flux of ~25 Crab. The high quality of the data allows the dust properties and density distribution along the line of sight to the source to be estimated. Using the Rayleigh–Gans approximation for the dust scattering cross-section and a power-law distribution of grain sizes a, ∝ a-q, the average dust emission is well modelled by q = 3.90+0.09-0.08 and maximum grain size of a+ = 0.147+0.024-0.004 μm, though significant variations in q are seen between the rings. The recovered dust density distribution shows five peaks associated with the dense sheets responsible for the rings at distances ranging from 1.19 to 2.13 kpc, with thicknesses of ~40 – 80 pc and a maximum density occurring at the location of the nearest sheet. We find a dust column density of Ndust ~ (2.0–2.5) × 1011 cm-2, consistent with the optical extinction to the source. Comparison of the inner rings’ azimuthal X-ray evolution with archival Wide-field Infrared Survey Explorer (WISE) mid-IR data suggests that the second most distant ring follows the general IR emission trend, which increases in brightness towards the Galactic north side of the source

GRB060602B = Swift J1749.4-2807: an unusual transiently accreting neutron-star X-ray binary

We present an analysis of the Swift BAT and XRT data of GRB060602B, which is most likely an accreting neutron star in a binary system and not a gamma-ray burst. Our analysis shows that the BAT burst spectrum is consistent with a thermonuclear flash (type-I X-ray burst) from the surface of an accreting neutron star in a binary system. The X-ray binary nature is further confirmed by the report of a detection of a faint point source at the position of the XRT counterpart of the burst in archival XMM-Newton data approximately 6 years before the burst and in more recent XMM-Newton data obtained at the end of September 2006 (nearly 4 months after the burst). Since the source is very likely not a gamma-ray burst, we rename the source Swift J1749.4-2807, based on the Swift/BAT discovery coordinates. Using the BAT data of the type-I X-ray burst we determined that the source is at most at a distance of 6.7+-1.3 kpc. For a transiently accreting X-ray binary its soft X-ray behaviour is atypical: its 2-10 keV X-ray luminosity (as measured using the Swift/XRT data) decreased by nearly 3 orders of magnitude in about 1 day, much faster than what is usually seen for X-ray transients. If the earlier phases of the outburst also evolved this rapidly, then many similar systems might remain undiscovered because the X-rays are difficult to detect and the type-I X-ray bursts might be missed by all sky surveying instruments. This source might be part of a class of very-fast transient low-mass X-ray binary systems of which there may be a significant population in our Galaxy.Comment: Accepted for publication in MNRA

Graduate students navigating social-ecological research: insights from the Long-Term Ecological Research Network

Interdisciplinary, collaborative research capable of capturing the feedbacks between biophysical and social systems can improve the capacity for sustainable environmental decision making. Networks of researchers provide unique opportunities to foster social-ecological inquiry. Although insights into interdisciplinary research have been discussed elsewhere, they rarely address the role of networks and often come from the perspectives of more senior scientists. We have provided graduate student perspectives on interdisciplinary degree paths from within the Long-Term Ecological Research (LTER) Network. Focusing on data from a survey of graduate students in the LTER Network and four self-identified successful graduate student research experiences, we examined the importance of funding, pedagogy, research design and development, communication, networking, and culture and attitude to students pursuing social-ecological research. Through sharing insights from successful graduate student approaches to social-ecological research within the LTER Network, we hope to facilitate dialogue between students, faculty, and networks to improve training for interdisciplinary scientists

Pan-chromatic observations of the remarkable nova LMC 2012

We present the results of an intensive multiwavelength campaign on nova LMC 2012. This nova evolved very rapidly in all observed wavelengths. The time to fall two magnitudes in the V band was only 2 days. In X-rays the super soft phase began 13$\pm$5 days after discovery and ended around day 50 after discovery. During the super soft phase, the \Swift/XRT and \Chandra\ spectra were consistent with the underlying white dwarf being very hot, $\sim$ 1 MK, and luminous, $\sim$ 10$^{38}$ erg s$^{-1}$. The UV, optical, and near-IR photometry showed a periodic variation after the initial and rapid fading had ended. Timing analysis revealed a consistent 19.24$\pm$0.03 hr period in all UV, optical, and near-IR bands with amplitudes of $\sim$ 0.3 magnitudes which we associate with the orbital period of the central binary. No periods were detected in the corresponding X-ray data sets. A moderately high inclination system, $i$ = 60$\pm$10^{\arcdeg}, was inferred from the early optical emission lines. The {\it HST}/STIS UV spectra were highly unusual with only the \ion{N}{5} (1240\AA) line present and superposed on a blue continuum. The lack of emission lines and the observed UV and optical continua from four epochs can be fit with a low mass ejection event, $\sim$ 10$^{-6}$ M$_{\odot}$, from a hot and massive white dwarf near the Chandrasekhar limit. The white dwarf, in turn, significantly illuminated its subgiant companion which provided the bulk of the observed UV/optical continuum emission at the later dates. The inferred extreme white dwarf characteristics and low mass ejection event favor nova LMC 2012 being a recurrent nova of the U Sco subclass.Comment: 18 figures, 6 tables (one online only containing all the photometry

The early and late-time spectral and temporal evolution of GRB 050716

We report on a comprehensive set of observations of Gamma Ray Burst 050716, detected by the Swift satellite and subsequently followed-up rapidly in X-ray, optical and near infra-red wavebands. The prompt emission is typical of long-duration bursts, with two peaks in a time interval of T90 = 68 seconds (15 - 350 keV). The prompt emission continues at lower flux levels in the X-ray band, where several smaller flares can be seen, on top of a decaying light curve that exhibits an apparent break around 220 seconds post trigger. This temporal break is roughly coincident with a spectral break. The latter can be related to the extrapolated evolution of the break energy in the prompt gamma-ray emission, and is possibly the manifestation of the peak flux break frequency of the internal shock passing through the observing band. A possible 3 sigma change in the X-ray absorption column is also seen during this time. The late-time afterglow behaviour is relatively standard, with an electron distribution power-law index of p = 2 there is no noticable temporal break out to at least 10 days. The broad-band optical/nIR to X-ray spectrum indicates a redshift of z ~> 2 for this burst, with a host-galaxy extinction value of E(B-V) ~ 0.7 that prefers an SMC-like extinction curve.Comment: Accepted to MNRAS. 8 pages, 5 figure