The homotopy coniveau tower

We examine the "homotopy coniveau tower" for a general cohomology theory on smooth k-schemes and give a new proof that the layers of this tower for K-theory agree with motivic cohomology. In addition, the homotopy coniveau tower agrees with Voevodsky's slice tower for $S^1$-spectra, giving a proof of a connectedness conjecture of Voevodsky. The homotopy coniveau tower construction extends to a tower of functors on the Morel-Voevodsky stable homotopy category, and we identify this $P^1$-stable homotopy coniveau tower with Voevodsky's slice filtration for $P^1$-spectra. We also show that the 0th layer for the motivic sphere spectrum is the motivic cohomology spectrum, which gives the layers for a general $P^1$-spectrum the structure of a module over motivic cohomology. This recovers and extends recent results of Voevodsky on the 0th layer of the slice filtration, and yields a spectral sequence that is reminiscent of the classical Atiyah-Hirzebruch spectral sequence.Comment: A revised and extended version of an earlier paper, which is on the K-theory serve

High Precision Radial Velocity Measurements in the Infrared: A First Assessment of the RV Stability of CRIRES

High precision radial velocity (RV) measurements in the near infrared are on high demand, especially in the context of exoplanet search campaigns shifting their interest to late type stars in order to detect planets with ever lower mass or targeting embedded pre-main-sequence objects. ESO is offering a new spectrograph at the VLT -- CRIRES -- designed for high resolution near-infrared spectroscopy with a comparably broad wavelength coverage and the possibility to use gas-cells to provide a stable RV zero-point. We investigate here the intrinsic short-term RV stability of CRIRES, both with gas-cell calibration data and on-sky measurements using the absorption lines of the Earth's atmosphere imprinted in the source spectrum as a local RV rest frame. Moreover, we also investigate for the first time the intrinsic stability of telluric lines at 4100 nm for features originating in the lower troposphere. Our analysis of nearly 5 hours of consecutive observations of MS Vel, a M2II bright giant centred at two SiO first overtone band-heads at 4100 nm, demonstrates that the intrinsic short-term stability of CRIRES is very high, showing only a slow and fully compensateable drift of up to 60 m/s after 4.5 hours. The radial velocity of the telluric lines is constant down to a level of approx. +/- 10 m/s (or 7/1000 of one pixel). Utilising the same telluriclines as a rest frame for our radial velocity measurements of the science target, we obtain a constant RV with a precision of approx. +/- 20 m/s for MS Vel as expected for a M-giant.Comment: 12 pages, 6 figures, accepted by A&

Triangle-Intersecting Families of Graphs

A family of graphs F is said to be triangle-intersecting if for any two graphs G,H in F, the intersection of G and H contains a triangle. A conjecture of Simonovits and Sos from 1976 states that the largest triangle-intersecting families of graphs on a fixed set of n vertices are those obtained by fixing a specific triangle and taking all graphs containing it, resulting in a family of size (1/8) 2^{n choose 2}. We prove this conjecture and some generalizations (for example, we prove that the same is true of odd-cycle-intersecting families, and we obtain best possible bounds on the size of the family under different, not necessarily uniform, measures). We also obtain stability results, showing that almost-largest triangle-intersecting families have approximately the same structure.Comment: 43 page

The Origin of Soft X-rays in DQ Herculis

DQ Herculis (Nova Herculis 1934) is a deeply eclipsing cataclysmic variable containing a magnetic white dwarf primary. The accretion disk is thought to block our line of sight to the white dwarf at all orbital phases due to its extreme inclination angle. Nevertheless, soft X-rays were detected from DQ Her with ROSAT PSPC. To probe the origin of these soft X-rays, we have performed Chandra ACIS observations. We confirm that DQ Her is an X-ray source. The bulk of the X-rays are from a point-like source and exhibit a shallow partial eclipse. We interpret this as due to scattering of the unseen central X-ray source, probably in an accretion disk wind. At the same time, we observe what appear to be weak extended X-ray features around DQ Her, which we interpret as an X-ray emitting knot in the nova shell.Comment: 18 pages including 4 figures, accepted for publication in Astrphyisical Journa

IX Draconis - a curious ER UMa-type dwarf nova

We report results of an extensive world-wide observing campaign devoted to a very active dwarf nova star - IX Draconis. We investigated photometric behaviour of the system to derive its basic outburst properties and understand peculiarities of IX Dra as well as other active cataclysmic variables, in particular dwarf novae of the ER Uma-type. In order to measure fundamental parameters of the system, we carried out analyses of the light curve, O-C diagram, and power spectra. During over two months of observations we detected two superoutbursts and several normal outbursts. The V magnitude of the star varied in the range 14.6 - 18.2 mag. Superoutbursts occur regularly with the supercycle length of 58.5+/-0.5 d. When analysing data over the past 20 years, we found that the supercycle length is increasing at a rate of P_dot = 1.8 * 10^{-3}. Normal outbursts appear to be irregular, with typical occurrence times in the range 3.1 - 4.1 d. We detected a double-peaked structure of superhumps during superoutburst, with the secondary maximum becoming dominant near the end of the superoutburst. The mean superhump period observed during superoutbursts equals 0.066982(36) d, which is constant over the last two decades of observations. Based on the power spectrum analysis, the evaluation of the orbital period was problematic. We found two possible values: the first one, 0.06641(3) d, which is in agreement with previous studies and our O-C analysis (0.06646(2) d), and the second one, 0.06482(3) d, which is less likely. The evolutionary status of the object depends dramatically on the choice between these two values. A spectroscopic determination of the orbital period is needed. We updated available information on ER UMa-type stars and present a new set of their basic statistics. Thereby, we provide evidence that this class of stars is not uniform.Comment: Accepted for publication in MNRAS; 15 pages, 15 figures, 6 tables; typo correcte