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

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

When Do Stalled Stars Resume Spinning Down? Advancing Gyrochronology with Ruprecht 147

Recent measurements of rotation periods () in the benchmark open clusters Praesepe (670 Myr), NGC 6811 (1 Gyr), and NGC 752 (1.4 Gyr) demonstrate that, after converging onto a tight sequence of slowly rotating stars in mass-period space, stars temporarily stop spinning down. These data also show that the duration of this epoch of stalled spin-down increases toward lower masses. To determine when stalled stars resume spinning down, we use data from the K2 mission and the Palomar Transient Factory to measure for 58 dwarf members of the 2.7 Gyr old cluster Ruprecht 147, 39 of which satisfy our criteria designed to remove short-period or near-equal-mass binaries. Combined with the Kepler data for the approximately coeval cluster NGC 6819 (30 stars with M ∗ > 0.85, our new measurements more than double the number of ≈2.5 Gyr benchmark rotators and extend this sample down to ≈0.55. The slowly rotating sequence for this joint sample appears relatively flat (22 ± 2 days) compared to sequences for younger clusters. This sequence also intersects the Kepler intermediate-period gap, demonstrating that this gap was not created by a lull in star formation. We calculate the time at which stars resume spinning down and find that 0.55 stars remain stalled for at least 1.3 Gyr. To accurately age-date low-mass stars in the field, gyrochronology formulae must be modified to account for this stalling timescale. Empirically tuning a core-envelope coupling model with open cluster data can account for most of the apparent stalling effect. However, alternative explanations, e.g., a temporary reduction in the magnetic braking torque, cannot yet be ruled out

Measurement of isolated photon production in pp and PbPb collisions at sqrt(sNN) = 2.76 TeV

Isolated photon production is measured in proton-proton and lead-lead collisions at nucleon-nucleon centre-of-mass energies of 2.76 TeV in the pseudorapidity range |eta|<1.44 and transverse energies ET between 20 and 80 GeV with the CMS detector at the LHC. The measured ET spectra are found to be in good agreement with next-to-leading-order perturbative QCD predictions. The ratio of PbPb to pp isolated photon ET-differential yields, scaled by the number of incoherent nucleon-nucleon collisions, is consistent with unity for all PbPb reaction centralities.Comment: Submitted to Physics Letters

TOI 540 b: A Planet Smaller than Earth Orbiting a Nearby Rapidly Rotating Low-mass Star

We present the discovery of TOI 540 b, a hot planet slightly smaller than Earth orbiting the low-mass star 2MASS J05051443-4756154. The planet has an orbital period of P = 1.239149 days (±170 ms) and a radius of r = 0.903 ± 0.052R⊕, and is likely terrestrial based on the observed mass-radius distribution of small exoplanets at similar insolations. The star is 14.008 pc away and we estimate its mass and radius to be M = 0.159 ± 0.014 M⊙ and R = 0.1895 ± 0.0079R⊙, respectively. The star is distinctive in its very short rotational period of Prot = 17.4264 ± 0.0094 hr and correspondingly small Rossby number of 0.007 as well as its high X-ray-to-bolometric luminosity ratio of LX/LboI = 0.0028 based on a serendipitous XMM-Newton detection during a slew operation. This is consistent with the X-ray emission being observed at a maximum value of as predicted for the most rapidly rotating M dwarfs. TOI 540 b may be an alluring target to study atmospheric erosion due to the strong stellar X-ray emission. It is also among the most accessible targets for transmission and emission spectroscopy and eclipse photometry with the James Webb Space Telescope, and may permit Doppler tomography with high-resolution spectroscopy during transit. This discovery is based on precise photometric data from the Transiting Exoplanet Survey Satellite and ground-based follow-up observations by the MEarth team

The Discovery of a Planetary Companion Interior to Hot Jupiter WASP-132 b

Hot Jupiters are generally observed to lack close planetary companions, a trend that has been interpreted as evidence for high-eccentricity migration. We present the discovery and validation of WASP-132 c (TOI-822.02), a 1.85 ± 0.10 R ⊕ planet on a 1.01 day orbit interior to the hot Jupiter WASP-132 b. Transiting Exoplanet Survey Satellite and ground-based follow-up observations, in conjunction with vetting and validation analysis, enable us to rule out common astrophysical false positives and validate the observed transit signal produced by WASP-132 c as a planet. Running the validation tools vespa and TRICERATOPS on this signal yields false-positive probabilities of 9.02 × 10-5 and 0.0107, respectively. Analysis of archival CORALIE radial velocity data leads to a 3σ upper limit of 28.23 ms-1 on the amplitude of any 1.01 day signal, corresponding to a 3σ upper mass limit of 37.35 M ⊕. Dynamical simulations reveal that the system is stable within the 3σ uncertainties on the planetary and orbital parameters for timescales of ∼100 Myr. The existence of a planetary companion near the hot Jupiter WASP-132 b makes the giant planet's formation and evolution via high-eccentricity migration highly unlikely. Being one of just a handful of nearby planetary companions to hot Jupiters, WASP-132 c carries with it significant implications for the formation of the system and hot Jupiters as a population

TIC 278956474: Two Close Binaries in One Young Quadruple System Identified by TESS

We have identified a quadruple system with two close eclipsing binaries in Transiting Exoplanet Survey Satellite (TESS) data. The object is unresolved in Gaia and appears as a single source at parallax 1.08 ± 0.01 mas. Both binaries have observable primary and secondary eclipses and were monitored throughout TESS Cycle 1 (sectors 1-13), falling within the TESS Continuous Viewing Zone. In one eclipsing binary (P = 5.488 days), the smaller star is completely occluded by the larger star during the secondary eclipse; in the other (P = 5.674 days) both eclipses are grazing. Using these data, spectroscopy, speckle photometry, spectral energy distribution analysis, and evolutionary stellar tracks, we have constrained the masses and radii of the four stars in the two eclipsing binaries. The Li i equivalent width indicates an age of 10-50 Myr and, with an outer period of 858+7-5 days, our analysis indicates this is one of the most compact young 2 + 2 quadruple systems known

Two Intermediate-mass Transiting Brown Dwarfs from the TESS Mission

We report the discovery of two intermediate-mass transiting brown dwarfs (BDs), TOI-569b and TOI-1406b, from NASA's Transiting Exoplanet Survey Satellite mission. TOI-569b has an orbital period of P=.55604±0.00016 days, a mass of Mb = 64.1±1.9 MJ, and a radius of Rb = 0.75±0.02 RJ. Its host star, TOI-569, has a mass of Må = 1.21±0.05 M, a radius of Rå = 1.47±0.03 R, [Fe H 0.29 0.09] = + dex, and an effective temperature of Teff = 5768±10K. TOI-1406b has an orbital period of P=10.57415±0.00063 days, a mass of Mb = 46.0± 2.7 MJ, and a radius of Rb = 0.86±0.03 RJ. The host star for this BD has a mass of Må = 1.18±0.09 M, a radius of Rå = 1.35±0.03 R, [Fe/H] =-0.08± 0.09 dex, and an effective temperature of Teff = 6290±100 K. Both BDs are in circular orbits around their host stars and are older than 3 Gyr based on stellar isochrone models of the stars. TOI-569 is one of two slightly evolved stars known to host a transiting BD (the other being KOI-415). TOI-1406b is one of three known transiting BDs to occupy the mass range of 40-50 MJ and one of two to have a circular orbit at a period near 10 days (with the first being KOI-205b). Both BDs have reliable ages from stellar isochrones, in addition to their well-constrained masses and radii, making them particularly valuable as tests for substellar isochrones in the BD mass-radius diagram