A pulsating white dwarf in an eclipsing binary

White dwarfs are the burnt-out cores of Sun-like stars and are the fate of 97 per cent of the stars in our Galaxy. The internal structure and composition of white dwarfs are hidden by their high gravities, which causes all elements apart from the lightest ones to settle out of their atmospheres. The most direct method of probing the inner structure of stars and white dwarfs in detail is via asteroseismology. Here we present a pulsating white dwarf in an eclipsing binary system, enabling us to place extremely precise constraints on the mass and radius of the white dwarf from the lightcurve, independent of the pulsations. This 0.325-solar-mass white dwarf—one member of the SDSS J115219.99+024814.4 system—will serve as a powerful benchmark with which to constrain empirically the core composition of low-mass stellar remnants and to investigate the effects of close binary evolution on the internal structure of white dwarfs

The nil Hecke ring and singularity of Schubert varieties

We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.Comment: AMSTE

System parameters of three short-period cataclysmic variable stars

Using photometric ULTRACAM observations of three new short period cataclysmic variables, we model the primary eclipse lightcurves to extract the orbital separation, masses, and radii of their component stars. We find donor masses of 0.060 +/- 0.008 solar masses, 0.042 +/- 0.001 solar masses, and 0.042 +/- 0.004 solar masses, two being very low-mass sub-stellar donors, and one within 2 sigma of the hydrogen burning limit. All three of the new systems lie close to the modified, "optimal" model evolutionary sequence of Knigge et al. (2011). We briefly re-evaluate the long-standing discrepancy between observed donor mass and radius data, and theoretical CV evolutionary tracks. By looking at the difference in the observed period at each mass and the period predicted by the Knigge et al. (2011) evolutionary sequence, we qualitatively examine the form of excess angular momentum loss that is missing from the models below the period gap. We show indications that the excess angular momentum loss missing from CV models grows in importance relative to gravitational losses as the period decreases. Detailed CV evolutionary models are necessary to draw more quantitative conclusions in the future

Characterising eclipsing white dwarf M dwarf binaries from multi-band eclipse photometry

With the prevalence of wide-field, time-domain photometric sky surveys, the number of eclipsing white dwarf systems being discovered is increasing dramatically. An efficient method to follow these up will be key to determining any population trends and finding any particularly interesting examples. We demonstrate that multi-band eclipse photometry of binaries containing a white dwarf and an M dwarf can be used to determine the masses and temperatures of the white dwarfs to better than 5 per cent. For the M dwarfs we measure their parameters to a precision of better than 6 per cent with the uncertainty dominated by the intrinsic scatter of the M dwarf mass-radius relationship. This precision is better than what can typically be achieved with low-resolution spectroscopy. The nature of this method means that it will be applicable to LSST data in the future, enabling direct characterisation without follow-up spectroscopy. Additionally, we characterise three new post-common-envelope binaries from their eclipse photometry, finding two systems containing hot helium-core white dwarfs with low-mass companions (one near the brown dwarf transition regime) and a possible detached cataclysmic variable at the lower edge of the period gap

Spectroscopic and photometric periods of six ultracompact accreting binaries

Ultracompact accreting binary systems each consist of a stellar remnant accreting helium-enriched material from a compact donor star. Such binaries include two related sub-classes, AM CVn-type binaries and helium cataclysmic variables, in both of which the central star is a white dwarf. We present a spectroscopic and photometric study of six accreting binaries with orbital periods in the range of 40--70 min, including phase-resolved VLT spectroscopy and high-speed ULTRACAM photometry. Four of these are AM CVn systems and two are helium cataclysmic variables. For four of these binaries we are able to identify orbital periods (of which three are spectroscopic). SDSS J1505+0659 has an orbital period of 67.8 min, significantly longer than previously believed, and longer than any other known AM CVn binary. We identify a WISE infrared excess in SDSS J1505+0659 that we believe to be the first direct detection of an AM CVn donor star in a non-direct impacting binary. The mass ratio of SDSS J1505+0659 is consistent with a white dwarf donor. CRTS J1028-0819 has an orbital period of 52.1 min, the shortest period of any helium cataclysmic variable. MOA 2010-BLG-087 is co-aligned with a K-class star that dominates its spectrum. ASASSN-14ei and ASASSN-14mv both show a remarkable number of echo outbursts following superoutbursts (13 and 10 echo outbursts respectively). ASASSN-14ei shows an increased outburst rate over the years following its superoutburst, perhaps resulting from an increased accretion rate

DT/T beyond linear theory

The major contribution to the anisotropy of the temperature of the Cosmic Microwave Background (CMB) radiation is believed to come from the interaction of linear density perturbations with the radiation previous to the decoupling time. Assuming a standard thermal history for the gas after recombination, only the gravitational field produced by the linear density perturbations present on a $\Omega\neq 1$ universe can generate anisotropies at low z (these anisotropies would manifest on large angular scales). However, secondary anisotropies are inevitably produced during the nonlinear evolution of matter at late times even in a universe with a standard thermal history. Two effects associated to this nonlinear phase can give rise to new anisotropies: the time-varying gravitational potential of nonlinear structures (Rees-Sciama RS effect) and the inverse Compton scattering of the microwave photons with hot electrons in clusters of galaxies (Sunyaev-Zeldovich SZ effect). These two effects can produce distinct imprints on the CMB temperature anisotropy. We discuss the amplitude of the anisotropies expected and the relevant angular scales in different cosmological scenarios. Future sensitive experiments will be able to probe the CMB anisotropies beyong the first order primary contribution.Comment: plain tex, 16 pages, 3 figures. Proceedings of the Laredo Advance School on Astrophysics "The universe at high-z, large-scale structure and the cosmic microwave background". To be publised by Springer-Verla

Genotype-by-Sex Interaction in the Regulation of High-Density Lipoprotein: TheFramingham Heart Study

Low levels of high-density lipoprotein (HDL) are widely documented as a risk factor for cardiovascular disease (CVD). Furthermore, there is marked sexual dimorphism in both HDL levels and the prevalence of CVD. However, the extent to which genetic factors contribute to such dimorphism has been largely unexplored. We examined the evidence for genotypeby- sex effects on HDL in a longitudinal sample of 1,562 participants from 330 families in the Framingham Heart Study at three times points corresponding approximately to 1971-1974, 1980-1983, and 1988-1991. Using a variance component method, we conducted a genome scan of HDL at each time point in males and females, separately and combined, and tested for genotype-by-sex interaction at a quantitative trait locus (QTL) at each time point. Consistent findings were noted only for females on chromosome 2 near marker D2S1328, with adjusted LOD scores of 2.6, 2.2, and 2.1 across the three time points, respectively. In males suggestive linkage was detected on chromosome 16 near marker D16S3396 at the second time point and on chromosome 18 near marker D18S851 at the third time point (adjusted LOD = 2.2 and 2.4, respectively). Although the heritability of HDL is similar in males and females, sex appears to exert a substantial effect on the QTL-specific variance of HDL. When genotype-by-sex interactions exist and are not modeled, the power to detect linkage is reduced; thus our results may explain in part the paucity of significant linkage findings for HDL

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Developing the GOTO telescope control system

The Gravitational-wave Optical Transient Observer (GOTO) is a wide-field telescope project focused on detecting optical counterparts to gravitational-wave sources. The GOTO Telescope Control System (G-TeCS) is a custom robotic control system which autonomously manages the GOTO telescope hardware and nightly operations. Since the commissioning the GOTO prototype on La Palma in 2017, development of the control system has focused on the alert handling and scheduling systems. These allow GOTO to receive and process transient alerts and then schedule and carry out observations, all without the need for human involvement. GOTO is ultimately anticipated to include multiple telescope arrays on independent mounts, both on La Palma and at a southern site in Australia. When complete these mounts will be linked to form a single multi-site observatory, requiring more advanced scheduling systems to best optimise survey and follow-up observations